# Symposium QN04 : **Nanoscale Heat Transport**—**Fundamentals**

### Symposium Organizers

**10:30 AM - *QN04.01.01/QN05.03.01**

__Chris Dames__

^{1,2}

^{1},Lawrence Berkeley National Laboratory

^{2}

I will review several collaborative efforts at developing new non-contact methods for heating and thermometry at the nanometer scale. Examples include techniques based on SEM (e-beam as a point heater; secondary electron yield as a thermometer), TEM (thermometry using the Debye-Waller effect), and confocal microscopy (luminescence thermometry of individual nanoparticles).

**11:00 AM - QN04.01.02/QN05.03.02**

__Xiulin Ruan__

^{1}

^{1}

Conventionally, the two-temperature model has been widely used for electron-phonon coupled non-equilibrium thermal transport. However, many recent applications have shown that different phonon branches can be in strong thermal non-equilibrium. Therefore, assuming a local equilibrium lattice can lead to misleading or wrong results. Here, we present a multi-temperature model to capture the non-equilibrium among different phonon branches, and demonstrate its advantages over the conventional two-temperature model for bulk materials and across interfaces.

**11:15 AM - QN04.01.03/QN05.03.03**

__Martin Maldovan__

^{1}

^{1}

The thermal conductivity of materials is not a fixed physical property but can be manipulated by controlling the transport properties of thermal phonons. Recently, a large number of experiments have been introduced where thermal conduction is reduced by orders of magnitude via phonon mean free path reduction through diffuse surface scattering. In contrast to established work that use the diffuse surface scattering of phonons as the physical mechanism to reduce the thermal conductivities, in this talk we show that the largest reduction of thin film heat conduction is achieved via specular scattering. Our results thus create a new paradigm for heat conduction manipulation since smooth surfaces – in contrast to rough surfaces – can be more effective on suppressing thin film phonon heat conduction.

**11:30 AM - *QN04.01.04/QN05.03.04**

__Sebastian Volz__

^{1}

^{1}

Effect of structural disorder on phonon thermal conduction remains an open question with a large spectrum of physical effects, as the plane-wave description of atomic vibrations is expected to become irrelevant. In a first stage, atomic scale disorder will be investigated in various systems –silicon [1], SiGe nanowires [2], partial-crystal partial-liquid [3], 2D [4,5] - with atomic scale simulations. Secondly, thermal properties of nanoscale random materials [6,7] will be presented to raise the question of the eventual impact of localization on heat conduction.

[1] K. Sääskilahti, J. Oksanen, J. Tulkki, A. J. H. McGaughey, and S. Volz, Vibrational mean free paths and thermal conductivity of amorphous silicon from non-equilibrium molecular dynamics simulations, AIP Advances.

[2] Honggang Zhang, Haoxue Han, Shiyun Xiong, Hongyan Wang, Sebastian Volz, and Yuxiang Ni, Impeded thermal transport in composition graded SiGe nanowires, App. Phys. Lett., 111, 121907, (2017).

[3] Y. Zhou, S. Xiong, X.L. Zhang, S. Volz, M. Hu, Thermal Transport Crossover from Crystalline to Partial-crystalline Partial-liquid State, Nat. Comm., accepted.

[4] Van-Truong Tran, Jérôme Saint-Martin, Philippe Dollfus & Sebastian Volz, Optimizing the thermoelectric performance of graphene nano- ribbons without degrading the electronic properties, Sc. Rep., 7: 2313 | DOI:10.1038/s41598-017-02230-0.

[5] Van-Truong Tran, Jérôme Saint-Martin, Philippe Dollfus and Sebastian Volz, High thermoelectric performance of graphite nanofibers, Nanoscale, DOI: 10.1039/C7NR07817J

[6] J. Maire, R. Anufriev, R. Yanagisawa, A. Ramiere, S. Volz, and M. Nomura, Heat conduction tuning by wave nature of phonons, Science Advances, 3(8), e1700027 (2017).

[7] S Hu, Z Zhang, P Jiang, J Chen, S Volz, M Nomura, B Li, Randomness-Induced Phonon Localization in Graphene Heat Conduction, The journal of physical chemistry letters 9 (14), 3959-3968

**1:30 PM - *QN04.02.01**

__Ali Shakouri__

^{1},Amirkoushyar Ziabari

^{1},Sami Alajlouni

^{1}

^{1}

Self-heating and localized hotspots can limit the performance of electronic and optoelectronic devices. Contact-related artifacts and diffraction limit the accurate temperature measurements at deep submicron scale. Here we combine thermoreflectance (TR) imaging with a robust image reconstruction technique to achieve accurate temperature maps of nanoscale metal interconnects. Reconstructing accurate temperature profiles from far-field diffraction-limited images is an ill-posed inverse problem. To formulate the inverse problem, we developed a model based image processing technique based on a Bayesian framework that consists of a maximum-a-posteriori (MAP) cost function with Generalized Gaussian Markov random field priors (GGMRF). The imaging system was approximated by a Gaussian blurring kernel using the information about the pixel dimensions, numerical aperture of the lens used in the system as well as the wavelength of the light. The iterative coordinate descent (ICD) optimization is then used to minimize the corresponding cost function and extract the temperature profiles.

We performed the reconstruction both for numerically designed experiments as well as experimental thermoreflectance thermal images. Additionally, statistical analysis of the resolution limit shows that image reconstruction is a strong function of signal-to-noise ratio. We carried out detailed analysis to investigate the impact of the signal-to-noise ratio on extracting the accurate temperature of nanoscale features. Theoretical and experimental results demonstrate accurate thermal mapping of objects down to 100nm. The proposed non-contact technique provides an alternative to techniques such as scanning probe that are often slower and quite sensitive to surface roughness. Additionally, the technique can be applied to other far field imaging experiments to study the performance of nanoscale optoelectronic and plasmonic devices.

Since quasi ballistic phonons dominate submicron thermal transport in many semiconductors at room temperature, there are questions about the definition of temperature and what actually a thermometer measures. Transient hyperspectral imaging as well as resistance thermometry are used to study the apparent temperatures of various metals and nearby semiconductors and to verify our submicron TR imaging results. Indications for superdiffusive and hydrodynamic heat flow are briefly described.

**2:00 PM - QN04.02.02**

__Ruiyang Li__

^{1},Eungkyu Lee

^{1},Tengfei Luo

^{1}

^{1}

Understanding phonon transport across solid-solid interfaces can greatly impact thermal engineering in many solid-state applications. Conventionally, phonon scattering are considered impedance to thermal transport. In this study, we present systematic study of the effect of pre-interface phonon in thermal boundary conductance using non-equilibrium molecular dynamics (NEMD) simulations. We first examine the fundamental role of anharmonic phonon scattering in thermal transport across an artificial solid junction, which consists of a monoatomic lattice and a diatomic lattice. Using interatomic force parameters expanding up to the third-order, we investigate how inelastic phonon scattering processes in the diatomic lattice layer influence thermal boundary conductance. It is found that the anharmonicity inside the diatomic lattice layer promotes phonon-phonon energy conversion between optical and acoustic phonon modes, which eventually lead to enhanced thermal transport across the solid junction by populating more acoustic phonon modes with higher transmission probability through the pre-interface phonon scattering. Importantly, we find that anharmonic scattering effect in the pre-interfacial region is more important than that right at the interfaces in thermal transport. Next, we explore pre-interface phonon scattering effect in thermal transport across SiC/GaN interfaces by doping isotopes in the GaN, where the SiC/GaN interface is of technological importance in power electronics. We use ^{15}N or ^{35}Ga as isotopes in NEMD simulations. By tuning various isotope-doping characteristics (i.e., the isotope concentration, skin depth of the isotope region, and its distance from the interface), we investigate an enhancement of thermal conductance across SiC/GaN interfaces. We find that 10% of ^{15}N isotope in GaN layer can increase TBC by as much as 23% compared to the isotopically pure cases. In addition, when the isotope-doped region is located away from the SiC/GaN interface, the TBC enhancement still exist, showing pre-interface phonon scattering by isotopes is mainly responsible for the enhanced TBC. Moreover, analysis of spectral temperatures of phonon modes reveal that heat transfer rates by low frequency phonons (< 20 THz) across SiC/GaN interfaces increase after isotopes are introduced.

Our studies demonstrate that pre-interface phonon scatterings can help redistribute phonon energy, so that phonon modes with higher transmission probability can be more populated, which leads to TBC enhancements across solid-solid interfaces. Development of new theoretical models should consider this pre-interface phonon scattering effect. Practical materials design can also take advantage the results of this work to enhance interfacial thermal transport.

**2:15 PM - QN04.02.03**

*S*-Matrix Method

__Zhun-Yong Ong__

^{1}

^{1}

The phonon specularity parameter represents the probability of the phonon being specularly scattered by a surface and is crucial for understanding phonon-mediated thermal transport in low-dimensional semiconducting or insulating materials such as thin films and nanowires. However, there exists no reliable and accurate method to predict the relationship between the mode-dependent specularity parameter and the atomistic structure of a non-ideal edge or interface. [1] In addition, the dependence of the specularity parameter on wavelength, direction and polarization cannot be determined reliably with current theories.

To treat this problem, we introduce an *S*-matrix approach [2] that is grounded conceptually in conventional quantum mechanical scattering theory and developed from our earlier extension of the Atomistic Green’s Function (AGF) method, [3] allowing us to compute the scattering amplitude between an incident phonon and a reflected or transmitted phonon. The utility of our approach is illustrated through two examples. In the first example, we study the specularity dependence on edge chirality and explain how specularity is reduced for the ideal armchair edge in graphene, shedding light on the findings by Wei, Chen and Dames [4]. In the second example, we investigate grain boundary phonon scattering in graphene and provide direct evidence that the the specularity is significantly different between reflected and transmitted phonons. [5] Our *S*-matrix method resolves some of the existing difficulties in predicting the mode-dependent specularity parameter and opens the way for analyzing how edges and interfaces can be modified to control phonon scattering with atomistic precision.**References:**

1. G. Chen, *Nanoscale Energy Transport and Conversion* (Oxford University Press, Oxford, 2005).

2. Z.-Y. Ong, “Atomistic S-matrix method for numerical simulation of phonon reflection, transmission and boundary scattering,” *Phys. Rev. B* (in press).

3. Z.-Y. Ong and G. Zhang, “Efficient approach for modeling phonon transmission probability in nanoscale interfacial thermal transport,” *Phys. Rev. B* **91**, 174302 (2015); Z.-Y.Ong, “Tutorial: Concepts and numerical techniques for modeling individual phonon transmission at interfaces,” *J. Appl. Phys.* **124**, 151101 (2018).

4. Z. Wei, Y. Chen, and C. Dames, “Wave packet simulations of phonon boundary scattering at graphene edges,” *J. Appl. Phys.* **112**, 024328 (2012).

5. D. Li and A. J. H. McGaughey, “Phonon dynamics at surfaces and interfaces and its implications in energy transport in nanostructured materials — an opinion paper,” *Nanoscale Microsc. Thermophys. Eng.* **19**, 166 (2015).

**2:30 PM - *QN04.02.04**

__Kedar Hippalgaonkar__

^{2,3},Ding Ding

^{1}

^{1},Institute of Materials Research and Engineeringn

^{2},Nanyang Technological University

^{3}

With nanostructures in solid state materials reaching the size of the phonon mean free path and lower, quasiballistic and anisotropic effects play significant roles in their thermal properties. Many new experimental techniques have been developed to probe phonon physics at such lengthscales, however ascertaining spatially dependent thermal properties typically requires control of parameters in the spatial or frequency domain. Here, I will present our proposal for a one-shot optical pump-probe methodology that can potentially directly image both spatial and temporal temperature profiles. Coupled with a multi-parameter optimization of the heat diffusion equation, this technique can prove powerful in measuring anisotropic and quasiballistic heat transport directly, serving as a high-throughput tool for screening of thermal properties. Coupled with first principles DFT calculations of the gruneisen parameter and debye temperature of a large number of compounds extracted from Materialsproject.org, I will illustrate a vision of how machine learning can be used for prediction of desirable thermal properties.

**3:00 PM -**

**3:30 PM - *QN04.03.01**

__Gregory Fuchs__

^{1}

^{1}

Research into magnetic devices – emerging memory, logic, and oscillator technologies – is enabled by magnetic imaging techniques that possess simultaneous picosecond temporal resolution and 10 – 100 nm spatial resolution. Conventionally, this combination is available only at facility-based research centers using e.g., pulsed x-ray dichroism techniques. In addition, many of the most exciting magnetic material systems, including ultrathin ferromagnetic or antiferromagnets insulators buried beneath heavy metals are difficult to image with any method. To address these challenges in an accessible way, we have developed a table-top spatiotemporal magnetic microscope based on nanoscale, picosecond thermal pulses. Our method takes advantage of magneto-thermal interactions that couple heat flow to electron or spin transport, including the anomalous Nernst effect [1] and the longitudinal spin Seebeck effect [2]. Using focused light as a picosecond heating source, we demonstrate that these imaging modalities have time resolution on the order of 10 ps and sensitivities to magnetization angle of 0.1 – 0.3°/√Hz for ferromagnetic metals and insulators. In combination with phase-sensitive microwave current imaging, phase-sensitive ferromagnetic resonance imaging [3] enables direct imaging of the gigahertz-frequency magnetic driving torque vector, which is valuable for understanding spin-orbit interactions [4]. We also demonstrate magneto-thermal imaging of antiferromagnetic order in FeRh and NiO, offering a simple and accessible method to study spin-orbit torque switching of antiferromagnetic materials [5]. Finally, I will describe how time-resolved magnetic imaging can be extended to greatly exceed the optical diffraction limit, both theoretically [6] and experimentally. We demonstrate scanning a sharp gold tip illuminated by picosecond laser pulses as the basis of a nanoscale spatiotemporal magnetic microscope.

[1] J. M. Bartell, D. H. Ngai, Z. Leng, and G. D. Fuchs, *Nat. Commun*. **6**, 8460 (2015).

[2] J. M. Bartell, C. L. Jermain, S. V. Aradhya, J. T. Brangham, F. Yang, D. C. Ralph, and G. D. Fuchs, *Phys. Rev. Appl.* **7**, 044004 (2017).

[3] F. Guo, J. M. Bartell, D. H. Ngai, and G. D. Fuchs, *Phys. Rev. Appl*. **4**, 044004 (2015).

[4] F. Guo, J. M. Bartell, and G. D. Fuchs, *Phys. Rev. B* **93**, 144415 (2016).

[5] I. Gray, T. Moriyama, N. Sivadas, R. Need, B. J. Kirby, D. H. Low, G. M. Stiehl, J. T. Heron, D. C. Ralph, K. C. Nowack, T. Ono, and G. D. Fuchs, arXiv:1810.03997 (2018).

[6] J. C. Karsch, J. M. Bartell, and G. D. Fuchs, *APL Photonics* **2**, 086103 (2017).

**4:00 PM - QN04.03.02**

__Joseph Cooke__

^{1},Jennifer Lukes

^{1}

^{1}

We present calculations of phonon-magnon coupling in bulk iron and nickel using spin-lattice dynamics [1,2], an increasingly popular simulation technique in which atomic spins and positions are computed simultaneously. It has been shown recently that a position-dependent magnetic anisotropy term is required to allow for full two-way coupling of thermal energy between the spin and lattice subsystems [3,4], but the parameters in this term are not known for many materials. Here we describe a procedure to obtain these parameters from experimental data on iron and nickel. We find that simulations including our parameters yield physically meaningful thermalization of spin and lattice systems and produce coupling times on the order of 100 ps, which agrees with the order of magnitude for coupling times reported by others [3,5].**References**:

[1] P. W. Ma, C. H. Woo, and S. L. Dudarev, “Large-scale simulation of the spin-lattice dynamics in ferromagnetic iron,” Phys. Rev. B, **78**, 024434 (2008).

[2] J. Tranchida, S. J. Plimpton, P. Thibaudeau and A. P. Thompson, “Massively parallel symplectic algorithm for coupled magnetic spin dynamics and molecular dynamics”, J. Comp. Phys. **372 **p 406-425(2018)

[3] D. Beaujouan, P. Thibaudeau, and C. Barreteau, “Anisotropic magnetic molecular dynamics of cobalt nanowires,” Phys. Rev. B, **86**, 174408 (2012)

[4] D. Perera, M. Eisenbach, D. M. Bicholson, G. M. Stocks, and D. P. Landau, “Reinventing atomistic magnetic simulations with spin-orbit coupling,” Phys. Rev. B, **93**, 060402(R) (2016)

[5] A. Vaterlaus, T. Beutlet, and F. Meier, “Spin-lattice relaxation time of ferromagnetic gadolinium determined with time-resolved spin-polarized photoemissions,” Phys. Rev. Let. **67 **p 3313-2217 (1991)

**4:30 PM - *QN04.03.04**

__Xiaoqin Li__

^{1}

^{1}

In non-equilibrium phenomena, different quasiparticles such as phonons and magnons may exhibit different temperatures with the caveat that temperature is only strictly defined for an equilibrium system. Spin caloritronics, as an emerging field, investigates the interplay between the transport of spin and heat. In the representative spin Seebeck effect [1], a thermal gradient across a magnetic material generates a spin current. Many theories hypothesize that a temperature difference between the energy carriers of the spin and lattice subsystems, namely the magnons and phonons, is necessary for such thermal non-equilibrium generation of spin current. The experimental evidence for such phonon-magnon non-equilibrium has been critically lacking [2] because of the difficulty to characterize phonon and magnon temperatures independently.

We use Brillouin light scattering (BLS) to investigate thermally driven spin current in a prototypical magnetic insulator yttrium iron garnet (YIG). BLS, as an inelastic light scattering technique, is conceptually the same as Raman scattering. It is optimized to probe low-frequency excitations, e.g., acoustic phonons and magnons. These quasiparticles are the main energy and spin carriers in magnetic insulators. Three different quantities (i.e., central frequency, linewidth, and integrated intensity) associated with the BLS spectra all vary with temperature systematically and can be used as a temperature sensor for probing phonons and magnons independently [3]. We show how BLS spectra can be used to probe phonon-magnon non-equilibriums [4], measure pure spin current, and evaluate magnon chemical potential in a magnetic insulator thermally driven out of equilibrium.

[1] K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, and E. Saitoh, Nature 455, 778 (2008)

[2] M. Agrawal, V.I. Vasyuchka, A.A. Serga, A.D. Karenowska, G.A. Melkov, and B. Hillebrands, Phys. Rev. Lett. 111, 107204 (2013)

[3] K. S. Olsson, K An, X Li, Journal of Physics D: Applied Physics 51 (13), 133001

[4] K. An, K.S. Olsson, A. Weathers, S. Sullivan, X. Chen, X. Li, L.G. Marshall, X. Ma, N. Klimovich, J. Zhou, L. Shi, and X. Li, Phys. Rev. Lett. 117, 107202 (2016)

**5:00 PM - QN04.04.02**

__Yee Rui Koh__

^{1},John Gaskins

^{1},Jeffrey Braun

^{1},Patrick Hopkins

^{1}

^{1}

Picosecond acoustics have long been used to probe the response of material properties [1] and, more recently, structural excitations such as surface acoustic waves [2] [3] [4]. Optical excitation via pulsed lasers offers the ability to use picosecond acoustics to provide non-contact, non-destructive, and ultrafine temporal resolution of these phenomena. We demonstrate the generation and characterization of the two-dimensional Rayleigh surface acoustic wave (2D SAW) on a set of silicon line grating samples with varying line widths (400 nm, 800 nm, 1600 nm, and 3200 nm) fabricated via electron beam lithography. The structures were patterned with line spacing equal to the grating width, etched to a depth of 100 nm, and then conformally coated with an 80 nm aluminum film that acts as an optical transducer. The existence of this 2D SAW in patterned structures was previously studied by Li et al. [5] In this work, we use time-domain thermoreflectance (TDTR) to investigate the propagation of 2D SAWs (*v *~ 0-20 GHz) in the silicon line gratings. Prior studies [2][3] have shown that most of the acoustic oscillations die out in a few hundreds of picoseconds. Our TDTR measurements show SAW oscillations up to ~5000 ps in the 800 and 1600 nm silicon line grating samples. The time periods of the acoustic oscillations are approximately 90 ps, 300 ps, and 600 ps for the silicon line grating widths of 400 nm, 800 nm, and 1600 nm, respectively. We employed two variations of TDTR, two color (400 nm pump/800 nm probe) and two tint (spectrally split 800 nm pump/800 nm probe) in order to study the variations in excitation based on pump and probe excitation and sensing. Fast Fourier transforms (FFT) of the resultant data were used to obtain the SAW frequencies. The two tint (800 nm pump) measurements show a typical simple single SAW frequency *f*_{0}, which is caused by the periodicity of the silicon line grating. A fundamental SAW frequency *f*_{0} and a secondary SAW with a frequency 2^{0.5}*f*_{0} are excited in the two color (400 nm pump) measurements. This 2^{0.5}*f*_{0} SAW is attributed to the acoustic wave in the diagonal direction of the silicon line grating. This diagonal wave is known as a 2D SAW [5]. In addition to measurement and quantification of the 2D SAWs, we discuss the effects of the silicon grating periodicity as it relates to excitation, or lack of excitation, as a function of the TDTR system used to probe the SAW.

[1] H. T. Grahn, H. J. Maris and J. Tauc, *IEEE Jour. Quan. Electr.* **25 (12)**, 2562 (1989)

[2] G. A. Antonelli and H. J. Maris, *Jour. Appl. Phys*. **91**,3261 (2002)

[3] D. H. Hurley and K. L. Telschow, *Phys. Rev. B* **66**, 153301 (2002)

[4] J. Sadhu, J. H. Lee and S. Sinha, *Appl. Phys. Lett*. **97**, 133106 (2010)

[5] Q. Li, K. Hoogeboom-Pot, D. Nardi, M. M. Murnane, H. C. Kapteyn, M. E. Siemens, E. H. Anderson, O. Hellwig, E. Dobisz, B. Gurney, R. Yang and K. A. Nelson, *Phys. Rev. B* **85**, 195431 (2012)

**5:00 PM - QN04.04.03**

__Elisah VandenBussche__

^{1},David Flannigan

^{1}

^{1}

The demand for smaller, faster, and more efficient electronic architectures and devices has produced an urgent need to understand and mitigate the associated deleterious thermal effects. As a result, significant efforts have been devoted to the development of experimental methods that quantify nanoscale thermal transport with both high spatial and temporal resolutions, bringing about new insights into a variety of phenomena; including thermal conductivity, thermal strain, and phonon behaviors [1]. This illustrates the value of extending time-averaged metrology techniques into the combined ultrafast and nanoscale regimes, which are the native scales on which thermal-energy carriers operate. In light of this, we are exploring ultrafast electron microscopy (UEM) as a method to access this challenging parameter space. In a typical UEM experiment, a femtosecond (fs) laser pulse is used to excite (pump) the specimen *in situ*, upon which a fs-duration discrete packet of photoelectrons generated from the TEM electron source is used to probe the response [2]. By varying the relative arrival times of the pump laser pulses and the probe electron packets at the specimen, nanometer-scale ultrafast structural responses can be directly imaged, while angstrom-scale responses can be tracked in reciprocal space. In UEM, as in other ultrafast electron and X-ray experiments, the Debye-Waller (DW) effect is often invoked when explaining photoinduced scattering intensity changes and when determining transient temperatures by relating the changes to atomic thermal vibrations. While this enables direct probing of the intrinsic lattice response to thermal effects with high spatial and temporal resolutions, reliance on transient intensity changes of diffracted beams poses significant challenges. This is because factors other than mean-square atomic displacements can produce signal changes similar to those generated by thermal effects [3-5]. Therefore, in order to accurately and precisely determine nanoscale transient temperatures using ultrafast scattering methods, deleterious effects that obfuscate intensity changes arising from atomic thermal vibrations must be identified, quantified, and deconvolved.

To address this, we have systematically studied and quantified a number of potential effects that can arise during *in situ* fs photoexcitation that may impact DW-type responses and the resulting interpretations [6]. Using small-grained polycrystalline aluminum films as a well-characterized test system, we explicitly illustrate the impact of specimen tilting and translation *via* rigorous statistical analysis of Debye-Scherrer-ring intensities obtained from numerous individual specimens and measurements. Despite having more than 10^{5} individual grains within the selected areas, we find that tilting by as little as a fraction of a degree, or translating a 22.5-μm diameter illuminated region by only 20 nm, yields statistically-significant changes in the diffracted-beam intensity. This result is at first surprising, as one may have expected a uniform distribution of random zone-axis orientations under such conditions, thus circumventing any negative effects due to specimen tilting and translation. We explicitly show this is not the case, and we explore and quantify several sources of error and artifacts, such as slight texturing of the polycrystalline films due to surface-energy minimization. Possible approaches to mitigating inaccuracies in the DW-calculated temperatures are also addressed, including effective methods of data normalization and consideration of ideal specimen geometries for such studies.

[1] D. G. Cahill, *et al.* Appl. Phys. Rev. **1** (2014) 011305.

[2] D. A. Plemmons, *et al.* Chem. Mater. **27** (2015) 3178.

[3] S. Schäfer,* et al.* Chem. Phys. Lett. **515** (2011) 278.

[4] A. O. Er,* et al.* Appl. Phys. Lett. **100** (2012) 151910.

[5] R. Li,* et al.* Appl. Phys. Lett. **111** (2017) 041105.

[6] E. J. VandenBussche, *et al.* Ultramicroscopy **196** (2019) 111.

**5:00 PM - QN04.04.04**

__Daniel Du__

^{1},Daniel Cremons

^{1,2},David Flannigan

^{1}

^{1},NASA Goddard Space Flight Center

^{2}

Intense femtosecond (fs) photoexcitation of semiconducting materials can lead to the generation of high densities of charge carriers, shifting the Fermi-Dirac distribution into a highly non-equilibrium state. The relaxation pathways available to this new state are numerous, and the associated mechanisms can be intermingled and highly non-linear [1]. One particular pathway is *via* the excitation of highly-coherent, low-frequency acoustic phonons that propagate outward from the photoexcited zone [2]. For initially high carrier concentrations, this behavior is attributed either to a time-varying deformation potential or a time-varying thermoelastic effect, depending upon the band structure and the nature of photoexcitation. Importantly, these two regimes can be differentiated temporally, depending upon the carrier densities generated; at relatively high concentrations, Auger recombination begins to further augment the time-varying thermoelastic effect. Indeed, a material as simple as undoped germanium (Ge) displays several intriguing transient behaviors within the context just described. For example, the excited carrier-density lifetimes can be quite long and can significantly overlap with the electron-phonon coupling times, thus heavily interweaving the various relaxation pathways [3,4]. Further, intense fs photoexcitation can lead to the generation of hypersonic electron-hole plasma waves, the nature of which may evolve into coherent acoustic-type oscillatory behaviors [5]. This suggests such behaviors may manifest as coherent, transient lattice-strain effects, the properties of which are directly linked to the hypersonic plasma waves [6].

Here, we describe our efforts to link the photoexcited charge-carrier dynamics in single-crystal Ge to the lattice degrees of freedom using fs electron imaging in an ultrafast electron microscope [7,8]. By leveraging the extreme sensitivity of local diffraction contrast to changes in reciprocal-lattice orientation, we are able to directly image the generation and the evolution of highly-coherent acoustic phonons initially propagating at hypersonic velocities in the plane of the crystal [9]. While each phonon wavefront propagates with a constant velocity, the entire wave train displays a time-varying phase-velocity dispersion, relaxing from initial velocities greater than 35 nm/ps to the Ge longitudinal speed of sound (5 nm/ps) within one nanosecond. Analysis of the dispersion curves expected for symmetric dilatational and asymmetric flexural modes indicates the dynamics match most closely to a single, low-order symmetric mode. Interestingly, this symmetric mode appears to give rise only to increased scattering for each wavefront, indicating the reciprocal-lattice shapes (approximated here as rods) are only brought further onto the Ewald sphere rather than being equally distributed during the oscillation. Further, by using a plasma lensing technique [10], we find that the onset of the first phonon wavefronts are delayed by tens of picoseconds or more, relative to the moment of fs photoexcitation. Combined, these anomalous behaviors provide tantalizing hints of charge-carrier-dominant dynamics, rather than lattice deformations caused by coherent phonons, as producing the observed ultrafast contrast behaviors. Those possibilities are explored here.

[1] A. Othonos, J. Appl. Phys. **83** (1998) 1789.

[2] P. Ruello and V. E. Gusev, Ultrasonics **56** (2015) 21.

[3] A. Elci, *et al.*, Phys. Rev. B **16** (1977) 191.

[4] H. M. van Driel, Phys. Rev. B **19** (1979) 5928.

[5] B. Y. K. Hu, *et al.*, Phys. Rev. B **44** (1991) 11067.

[6] D. A. Reis, *et al.*, Phys. Rev. Lett. **86** (2001) 3072.

[7] D. R. Cremons, *et al.*, Nature Commun. **7** (2016) 11230.

[8] D. A. Plemmons, *et al.*, Chem. Mater. **27** (2015) 3178.

[9] D. R. Cremons,* et al.*, Phys. Rev. Mater. **1** (2017) 073801.

[10] D. A. Plemmons and D. J. Flannigan, Chem. Phys. Lett. **683** (2017) 186.

**5:00 PM - QN04.04.05**

__Ryan Duncan__

^{1},Giuseppe Romano

^{1},Marianna Sledzinska

^{2},Alexei Maznev

^{1},Jean-Philippe Peraud

^{3},Olle Hellman

^{4,5,6},Clivia Sotomayor Torres

^{2},Keith Nelson

^{1}

^{1},Catalan Institute of Nanoscience and Nanotechnology

^{2},Lawrence Berkeley National Laboratory

^{3},California Institute of Technology

^{4},Linköping University

^{5},Boston College

^{6}

In semiconductor nanostructures with feature sizes on the order of 100 nm, thermal transport is expected to be well-described by the phonon Boltzmann transport equation (BTE) with diffuse boundary scattering. However, over the past several years there have been reports of anomalously low effective thermal conductivity values in one- and two-dimensional semiconductor nanostructures. In this study, we investigate thermal transport in nanostructured holey silicon membranes using the non-contact optical transient thermal grating (TTG) technique. We compare the experimental results with two *ab-initio* BTE numerical techniques. We obtain excellent agreement between theory and experiment, indicating that semiclassical Boltzmann transport theory for phonons is adequate for describing room-temperature thermal transport in semiconductor nanostructures with feature sizes on the order of 100 nm.

**5:00 PM - QN04.04.06**

__Iorwerth Thomas__

^{1},Gyaneshwar Srivastava

^{1}

^{1}

We present a theory of anisotropic thermal interface (Kapitza) resistance for rough interfaces in nanocomposite materials. This is based on an extension [1] of a modified effective medium theory [2,3] that includes anisotropically resistive interface regions in a model of the lattice thermal conductivity of anisotropic nano insertions in anisotropically conductive hosts. The thermal conductivities of the host and nanodot insertions have been evaluated using a semi ab-initio theory [4] based on the solution of the linearised phonon Boltzmann transport equation within a generalized [5] Callaway effective relaxation time scheme [6]. Phonon boundary scattering and the Kapitza resistance at the insertion-host interface have been treated by taking into account both specular and diffuse contributions [7,8]. The theory has been applied to a transition metal dichalcogenide (TMD) nanocomposite consisting of 2H WS2 inserts in a 2H MoS2 host. In general, it is found that the effect of specular scattering due to interface roughness is more pronounced for inserts smaller than 100 nm. Analysis of the results allows us to identify key physical parameters that should prove effective in controlling (i.e. obtaining minimum) lattice thermal conductivity of TMD nanocomposites.

[1] I. O. Thomas and G. P. Srivastava, Phys. Rev. B 98, 094201 (2018).

[2] C.-W. Nan et al, J. Appl. Phys. 81, 6692 (1997).

[3] A. Minnich and G. Chen, Appl. Phys. Lett. 91, 073105 (2007).

[4] I. O. Thomas and G. P. Srivastava, J. Phys. CM 29, 505703 (2017).

[5] G. P. Srivastava, Rep. Prog. Phys. 78, 026501 (2015).

[6] J. Callaway, Phys. Rev. 113, 1046 (1959).

[7] Y. K. Koh et al, Adv. Func. Mater. 19, 610 (2009).

[8] G. Chen, Phys. Rev. B 57, 14958 (1998).

**5:00 PM - QN04.04.07**

__Vinay Chauhan__

^{1},Lingfeng He

^{2},Janne Pakarinen

^{3},David Hurley

^{2},Marat Khafizov

^{1}

^{1},Idaho National Laboratory

^{2},Belgian Nuclear Research Center (SCK-CEN)

^{3}

Thermal conductivity is a critical physical property of ceramic nuclear fuels such as uranium dioxide. While cerium dioxide is considered as a solid electrolyte in solid oxide fuel cells (SOFC), in this study it is used as surrogate material to study the properties of nuclear fuel. In nuclear fuel, these oxides are exposed to extreme environments such as high temperature and bombardment with heavy particles. The damage introduced by such conditions in the form of defects generated inside the material can be detrimental to the structural stability of the material and ability to transport heat efficiently. Also, thermal conductivity degradation impacts fuel performance negatively. As a result, thermal conductivity of ceria has been widely investigated as one of the critical properties. This study is aimed at understanding the interplay between these nanoscale defects and the thermal conductivity of ceria.

Polycrystalline ceria samples were irradiated at 600 deg C to the same dose but at different rates using protons accelerated to 2 MeV. These irradiation conditions were chosen to promote the generation of nanoscale defects and to investigate their impact on thermal conductivity of ceria. SRIM simulations were done to identify the peak and plateau damage region inside the sample. The calculations estimated the plateau damage to be ~0.14 dpa. The quantitative analysis of radiation induced dislocation loops including size and density was performed using transmission electron microscope (TEM) for which the samples were prepared using focused ion beam (FIB) system.

X-ray diffraction was used to confirm the stability of crystal structure and also revealed detectable lattice expansion caused by accumulation of nanoscale defects. In addition to this, thermal conductivity was measured using modulated thermoreflectance methods and showed a notable reduction in irradiated samples. In order to isolate the impact of different defects on thermal conductivity, measurements were done for ambient temperature range of 100 to 300 K. The changes in thermal conductivity were analyzed quantitatively using the classical thermal transport model based on Klemens-Callaway formalism that considers reduction of thermal conductivity by irradiation induced nanoscale defects.

**5:00 PM - QN04.04.08**

__Robin Daugherty__

^{1},Dragica Vasileska

^{1}

^{1}

This simulation work explores the thermal effects on electrical characteristics of CMOS devices and circuits using a multiscale dual-carrier approach. Simulating for electron and hole transport simultaneously allows for complementary logic gates to be simulated at the device level, while current and voltage continuity are maintained at the circuit level. Further, the electrical model couples with a multiscale thermal solver, which solves for electron-phonon and hole-phonon interactions at the device level and phonon-phonon thermal transport in the packaging level. This methodology allows for the study of package level thermal transport without sacrificing the nuances of device self-heating, ultimately providing a more comprehensive understanding of how these interactions affect power consumption in CMOS systems.

The electrical model is comprised of an ensemble Monte Carlo simulator coupled with a Poisson solver. This framework provides accurate electrical characteristics in quasi-static regimes by iteratively solving for the potential profile and the electric fields then simulating the effect of the electric field on charge carriers. The Monte Carlo simulator solves the Boltzmann Transport by balancing each particle’s movement in real and momentum space with the collision integral through probabilistic scattering mechanisms. This framework provides current and voltage characteristics for each device; current and voltage continuity are maintained by solving at the circuit level.

Similarly, the methodology for simulating thermal characteristics includes two scales. At the device scale, the energy balance equation determines the transfer of energy from charge carriers to phonons. High-energy electrons or holes relinquish energy to optical and acoustic phonons through scattering and optical phonons decay into acoustic phonons. At the package level, a Fourier law solver simulates the subsequent conduction of heat in the form of lattice vibrations.

This framework proved effective in previous simulations for the electro-thermal characteristics in NMOS devices. This work demonstrates the effectiveness of the dual-carrier electrical solver in simulating CMOS circuits. Future work requires the coupling the dual-carrier electrical solver with the previously proven thermal solver to provide comprehensive electro-thermal simulations of CMOS systems.

**5:00 PM - QN04.04.09**

__Fariborz Kargar__

^{1},Zahra Barani

^{1},Jacob Lewis

^{1},Ruben Salgado

^{1},Sahar Naghibi

^{1},Ece Aytan

^{1},Alexander Balandin

^{1}

^{1}

Excellent heat conduction properties of graphene and the progress in the large-scale few-layer graphene exfoliation make the prospects of graphene composite applications particularly promising [1-2]. We investigated thermal properties of the epoxy-based composites with a high loading fraction – up to f=45 vol.% – of the randomly oriented electrically conductive graphene fillers and electrically insulating boron nitride fillers [3]. It was found that both types of the composites revealed a distinctive thermal percolation threshold at the loading fraction above 20 vol.%. The graphene loading required for achieving the thermal percolation was substantially higher than the loading for the electrical percolation. Graphene fillers outperformed boron nitride fillers in the thermal conductivity enhancement. It was established that thermal transport in composites with the high filler loading is dominated by heat conduction via the network of percolating fillers. Unexpectedly, we determined that the thermal transport properties of the high loading composites were influenced strongly by the cross-plane thermal conductivity of the quasi-two-dimensional fillers. It was also found that composites with the certain types of few-layer graphene fillers reveal an efficient total electromagnetic interference shielding in the important X-band frequency range, while simultaneously providing the high thermal conductivity [4]. The efficiency of the dual functional application depends on the filler characteristics: thickness, lateral dimensions, aspect ratio and concentration. Graphene loading fractions above the electrical and thermal percolation thresholds allow for strong enhancement of both the electromagnetic interference shielding and heat conduction properties. Interestingly, graphene composites can block the electromagnetic energy even below the electrical percolation threshold, remaining electrically insulating. The dual functionality of the graphene composites can substantially improve the electromagnetic shielding and thermal management of the airborne systems while simultaneously reducing their weight and cost.

This work was supported, in part, by the National Science Foundation (NSF) through the Emerging Frontiers of Research Initiative (EFRI) 2-DARE award 1433395, and by the University of California – National Laboratory Collaborative Research and Training Program LFR-17-477237.

[1] A.A. Balandin, “Thermal properties of graphene and nanostructured carbon materials,” Nature Materials, 10 (8), 569–581 (2011).

[2] D. L. Nika and A. A. Balandin, “Phonons and thermal transport in graphene and graphene-based materials,” Reports on Progress in Physics, 80, 36502 (2017).

[3] F. Kargar, Z. Barani, R. Salgado, B. Debnath, J.S. Lewis, E. Aytan, R.K. Lake, A.A. Balandin, “Thermal percolation threshold and thermal properties of composites with high loading of graphene and boron nitride fillers,” ACS Applied Materials and Interfaces, (2018) DOI:10.1021/acsami.8b16616.

[4] F. Kargar, Z. Barani, M.G. Balinskiy, A.S. Magana, J.S. Lewis, A.A. Balandin, “Graphene composites with dual functionality: electromagnetic shielding and thermal management,” Advanced Electronic Materials (in print, 2018) arXiv:1808.03401.

**5:00 PM - QN04.04.10**

__Fariborz Kargar__

^{1},Elias Penilla

^{2},Chun-Yu Huang

^{1},Ece Aytan

^{1},Javier Garay

^{2},Alexander Balandin

^{1}

^{1},Advanced Materials Processing and Synthesis (AMPS) Laboratory, Department of Mechanical and Aerospace Engineering, University of California, San Diego

^{2}

Acoustic phonons make a dominant contribution to thermal transport in insulators and semiconductors, scatter electrons and holes, and participate in the non-radiative carrier recombination processes. Acoustic phonons are important in certain types of the Auger recombination processes where they are needed to satisfy the momentum conservation. A possibility of engineering the acoustic phonon spectrum provides a tuning capability for changing thermal conductivity and electron – phonon interactions [1]. Until recently, the tuning of the phonon spectrum has been associated with the nanostructured materials, where the phonon dispersion undergoes modification due to the periodic or stationary boundary conditions. In this talk, we describe a drastically different approach for changing the acoustic phonon spectrum of the materials, which does not rely on nanostructuring [1]. We change the phonon spectrum in bulk crystalline materials via introduction of a small concentration of dopant atoms that have a substantially different size and mass from those of the host atoms. We report results of Brillouin – Mandelstam spectroscopy (BMS) of transparent Al_{2}O_{3} crystals with Nd, Cr and other atoms used as substitutional dopants. The ionic radius and atomic mass of Nd atoms are distinctively different from those of the host Al atoms. Our results show that even a small concentration of Nd atoms incorporated into the Al_{2}O_{3} samples produces a profound change in the acoustic phonon spectrum. The frequency and velocity of the transverse acoustic phonons decrease by ~4 GHz and ~600 m/s, respectively, at the Nd density of only ~0.1 %. In contrast to Nd dopants, both the ionic radius and atomic mass of Cr atoms are closer to those of the host Al atoms. The BMS results show that the phonon group velocity does not significantly change when the substitutional dopants are similar in size and mass to the host atoms. Our findings confirm that even a small concentration of dopants with strongly dissimilar size and mass can result in a profound change in the bulk phonon spectrum. The difference in atomic size can result in the crystal lattice distortion, i.e. increased inter-atomic plane distance associated with the incorporation of larger atoms. The obtained results, demonstrating a possibility of fine-tuning the phonon spectrum in bulk materials, have important implications for a range of electronic and optoelectronic devices.

This work was supported, in part, by the Spins and Heat in Nanoscale Electronic Systems (SHINES), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences (BES) under Award # SC0012670. AAB acknowledges support from the Defense Advanced Research Projects Agency (DARPA) project W911NF18-1-0041 Phonon Engineered Materials for Fine-Tuning the G-R Center and Auger Recombination. JEG acknowledges support from the High Energy Laser - Joint Technology Office (HEL-JTO) administered by the Army Research Office for development of over-equilibrium doped alumina.

[1] A. A. Balandin, D.L. Nika, “Phononics in low-dimensional materials,” Materials Today, 15, 266 (2012).

[2] F. Kargar, E.H. Penilla, E. Aytan, J.S. Lewis, J.E. Garay, A.A. Balandin, “Acoustic phonon spectrum engineering in bulk crystals via incorporation of dopant atoms,” Applied Physics Letters, 112, 191902 (2018).

**5:00 PM - QN04.04.11**

__Henry Aller__

^{1},Jonathan Malen

^{1},Alan McGaughey

^{1}

^{1}

The interface between a metal and a semiconductor that have dissimilar phonon frequency spectra typically exhibits a low thermal boundary conductance, as found for many Au/semiconductor interfaces. A thin metal layer (i.e., a contact or adhesion layer) placed between the gold (i.e., the capping layer) and the semiconductor can increase the thermal boundary conductance, an effect that has been attributed to the contact serving as a vibrational bridge. The impact of a change in the electron-phonon coupling due to the presence of the contact on the thermal boundary conductance, however, is not fully understood. To assess the roles played by vibrational bridging and electron-phonon coupling, we apply a two-temperature non-equilibrium molecular dynamics simulation approach. By specifying the heat flow through a structure, we can predict the temperature profiles in the electronic and phononic subsystems and the resulting thermal boundary conductance(s). Four types of structure built from metals (M) and semiconductors (SC) are considered: M/SC, M/M/SC, M/SC/SC, and SC/SC/SC. Increasing the contact layer thickness for the M/M/SC systems results in a monotonic increase in thermal boundary conductance, matching trends from previous experimental studies. The phonon density of states in the contact layer identifies the existence of non-bulk phonon modes for small thicknesses. Increasing thickness results in contact layer phonons gradually shifting to bulk frequencies, which explains the occurrence of the plateau in thermal boundary conductance for large thicknesses. A comparison between the M/M/SC, M/SC/SC, and SC/SC/SC systems provides insight to how the electron-phonon coupling in each metal layer impacts thermal boundary conductance.

**5:00 PM - QN04.04.12**

_{3}Sn

__Scott Schiffres__

^{1},Matthias Daeumer

^{1},Arad Azizi

^{1},Sitaram Panta

^{2},Faramarz Hadian

^{2},Eric Cotts

^{2}

^{1},Binghamton University, The State University of New York

^{2}

In order to realize vertical integration for next generation electronics packaging, purely intermetallic bonding is a promising contender to replace solder. The thermal properties of these industrially important intermetallics are relatively unstudied and poorly understood. Due to their high melting temperatures intermetallic bonds provide stability through several reflows enabling vertical packaging. However, in vertical packaging the interconnects must carry a significant portion of the heat away from the chip. In an effort to better understand the thermal capability of fully intermetallic bonding Frequency Domain Frequency Domain Thermoreflectance mapping was used to determine thermal conductivity of the arc-melted Cu_{3}Sn with respect to crystallographic orientation. This will be complemented by electron backscatter diffraction mapping of the crystal orientation.

**5:00 PM - QN04.04.13**

__Hossein Honarvar__

^{1},Joshua Knobloch

^{1},Travis Frazer

^{1},Jorge Nicolas Hernandez Charpak

^{1},Begona Abad Mayor

^{1},Mahmoud Hussein

^{1},Henry Kapteyn

^{1},Margaret Murnane

^{1}

^{1}

Nanostructured and quantum materials are enabling revolutionary advances in nanoscience and nanotechnology. These engineered materials promise to go beyond what is offered by natural materials. Advances in materials growth now make it possible to synthesize 3D nanostructured materials with nanometer resolution creating nanosystems with tunable electronic, photonic, magnetic, and thermal properties for a variety of applications including nanoelectronics, thermoelectrics, photovoltaics, and sensors. However, understanding of the fundamental mechanism behind many of these applications is still incomplete, making the development of powerful theoretical and experimental tools a priority for many material research communities.

Understanding thermal transport in nanostructured systems has long been a challenge. In the last few years, experimental techniques have pushed the measurement limits on systems with characteristic dimensions and geometries down to tens of nanometers, often times finding new surprising physical behaviors [1]. However, it is still challenging to apply appropriate models that connect novel data to meaningful thermal properties and fundamental mechanisms. Most researchers rely on using effective or phenomenological diffusive models or the linearized Boltzmann transport equation that are not able to capture all of the observed nanoscale effects and nonlinear interactions [1-3]. This is because it is very difficult to perform atomistic simulations over experimentally-relevant length scales, due to prohibitive computational requirements. As a result, there is a large gap in understanding of how the nanoscale phonon physics unfolds for different size and geometries to modify the transport properties. Moreover, possible coherent effects are often not adequately included in current models.

The focus of this work is understanding thermal transport in nanostructured materials by bridging the gap between theory and experiment. In particular, previous work done in our research group uncovered a new thermal transport regime named “collectively-diffusive” by tracking the heating and cooling of periodic arrays of nanoscale heat sources on bulk crystalline silicon and sapphire substrates [1]. This regime emerges from the interaction between the nanoscale geometries and energy carriers in materials. In particular, when nanoscale heat sources are placed closer, they cool down faster than when farther apart—the opposite of heat dissipation dynamics of the macroscale. The observed increase in heat dissipation efficiency has large consequences in thermal management in microelectronic devices, and is currently not captured by models available to both researchers in academia and industry.

In this work, we present the results of steady-state molecular dynamics (MD) simulations that can model the experimentally-explored geometries, and how these results provide a global understanding of non-diffusive phonon dynamics that appear to dominate energy transport in the deep nanoscale regime. Our MD results of nanoscale heat sources indicate that we are able to successfully capture the novel collectively-diffusive thermal dynamics observed recently.

Hoogeboom-Pot et al. *PNAS* doi:10.1073/pnas.1503449112 (2015).

Hu et al. *Nature nanotechnology*, 10 (8): 701 (2015).

Ziabari et al. *Nature communications*, 9(1):255, (2018).

**5:00 PM - QN04.04.14**

__Qi Zhang__

^{1},Xue Xiong

^{2},Eugene Rasaga

^{2},Simon Phillpot

^{2},Aleksandr Chernatynskiy

^{1}

^{1},University of Florida

^{2}

Low thermal conductivity materials are important for a variety of applications, including thermal barrier coatings and thermoelectric devices. Superlattices are particularly interesting due to the possibility of lowering thermal conductivity. Numbers of explanations have been proffered for the low thermal conductivity of superlattice structures. A full explanation, however, has yet to be developed.

Here, we are presenting the thermal-transport properties of natural perovskite-structured superlattices, the Ruddlesden-Popper (RP) series of phases of the Sr-Ti-O system, formed by the interleaving of SrTiO3 perovskite layers with SrO rocksalt layers. We have computed their thermal conductivity from first principles via the Boltzmann-transport equations (BTE) approach encoded in the PhonTS software package. In short, the thermal conductivity is determined by computing the heat current using the nonequilibrium phonon density distribution function, which in turn is found as a solution of the linearized BTE for phonons. The required input for the BTE are the second and third spatial derivatives of the total energy with respect to atomic positions which we have obtained from the DFT calculations performed using the Vienna Ab initio Simulation Package (VASP) computational package. A clear minimum in the thermal conductivity as a function of a number of STO layers is observed. Results are compared with the recent experimental data.

**5:00 PM - QN04.04.15**

__Konrad Rykaczewski__

^{1},Robert Wang

^{1}

^{1}

Development of polymeric composites with high thermal conductivity is necessary for thermal management of microelectronics. Percolation of metallic filler particles and reduction of the thermal contact resistance between individual particles (e.g. via thermal or electromagnetic fusing) can significantly improve thermal conductivity of composites. However, composite materials with connected metallic particles can also conduct electricity, creating a risk of short-circuiting in chip-board and the inter-chip gaps. In this presentation we theoretically show that this problem can be resolved with the application of fusible metallic coatings to the tips of nanowires with thermally conductive, but electrically insulating cores [1]. Specifically, we use Monte Carlo simulation-validated analytical models that relate the ratio of the coated and total nanowire lengths to the fraction of fused, and thus conductive, bonds within percolating networks of these structures to show that thermally conductive, but electrically insulating composites can be achieved using these novel nanostructures. We discuss silver-like coatings, which only form conductive bonds when contacting the silver-like coating of another nanowire as well as liquid metal-like coatings, which form conductive bonds regardless of whether they contact a coated or uncoated segment of another nanowire. We show that use of the liquid metal-like coatings will yield twice as many thermally conductive bonds as silver-like coatings while maintaining a negligible risk of electrical short-circuiting.

[1] K. Rykaczewski and R. Wang, Applied Physics Letters, 112, (13), 131904, 2018.

**5:00 PM - QN04.04.16**

__Zeyu Liu__

^{1},Xufei Wu

^{1},Tengfei Luo

^{1}

^{1}

In recent years, the fundamental physics of spin-lattice (e.g., magnon-phonon) interaction has attracted significant experimental and theoretical interests given its potential paradigm-shifting impacts in areas like spin-thermoelectrics, spin-caloritronics, and spintronics. Modelling studies of the transport of magnons and phonons in magnetic crystals are very rare. In this paper, we use spin-lattice dynamics (SLD) simulations to model ferromagnetic crystalline iron, where the spin and lattice systems are coupled through the atomic position-dependent exchange function, and thus the interaction between magnons and phonons is naturally considered. We then present a method combining SLD simulations with spectral energy analysis to calculate the magnon and phonon harmonic (e.g., dispersion, specific heat, and group velocity) and anharmonic (e.g., scattering rate) properties, based on which their thermal conductivity values are calculated. This work represents an example of using SLD simulations to understand the transport properties involving coupled magnon and phonon dynamics.

**5:00 PM - QN04.04.17**

__Anant Raj__

^{1},Jacob Eapen

^{1}

^{1}

Normal modes of vibrations can be extracted from atomistic simulations by projecting the real space trajectories onto the reciprocal space. Normal modes coordinates are not unique and their primary function is to transform the coupled Hamiltonian to a set of independent harmonic oscillators. Several descriptors of normal modes exist but not all of them are appropriate for analyzing thermal transport. In most normal mode analyses (NMA), complex normal mode coordinates are employed, which combine the modal contributions of waves moving in opposite directions. The wave-vector **q **that is represented in the complex normal modes** **does not uniquely represent a wave traveling in the +**q **or –**q **direction, instead it denotes an average of both directions. Thus the popular complex normal modes have a theoretical inability to resolve a real heat current along a specific direction-dependent wave-vector **q**.

In this work, we employ a set of real asymmetric normal mode coordinates, which can distinguish lattice waves moving in opposite directions – a virtue that immediately endows the ability to discriminate a heat current in a certain direction. These normal mode coordinates have a real amplitude *A*(**q**,*p*) that is not equal to *A*(−**q**,*p*). We then derive an expression for heat current that is real, and which can be expressed as a difference between the squares of the amplitudes in +**q **and –**q **directions. Finally, we drive a correction term for phonon lifetime that arises from the correlation between modes moving along opposite directions.

**5:00 PM - QN04.04.18**

__Albert Beardo Ricol__

^{1},Juan Camacho

^{1},Lluc Sendra

^{1},Javier Bafaluy

^{1},F. Xavier Alvarez

^{1}

^{1}

Recent experiments have evidenced that effective Fourier models are unable to predict heat transfer at the nanoscale [1,2]. This has a big impact on electronic engineering that relies on this law to study the thermal behavior of their devices.

One of the last proposals to better describe thermal transport at the nanoscale has been phonon hydrodynamics. In this line, the Guyer-Krumhansl equation has been proposed as the required generalization of the Fourier law to describe heat transport at this scale [3]. This equation is combined with the Kinetic Collective Model (KCM) to obtain the included parameters from ab initio calculations [4,5]. One of the main advantages of this approach is that its simplicity allows to obtain solutions for arbitrary geometries using Finite Element Methods. Therefore, this combination offers a full predictive framework to describe thermal conductivity in semiconductors in general geometries with characteristic sizes up to the order of the hydrodynamic characteristic length.

Validation of the model has been done with experimental data for different systems such as semiconductor porous membranes with different periodic alignments, thin membranes with different constrictions or 2D materials. In parallel, the tool offers also the interpretation of the results in terms of new phenomena like vorticity and viscosity, giving an insight on the reason for the reduction of the effective thermal conductivity at reduced scales.**References:**

[1] A. Ziabari et.al., Nat. Comm. 9, 255 (2018).

[2] K. M. Hoogeboom-Pot et. al., PNAS 112 16 4851 (2015)

[3] P. Torres et al. Phys Rev. Mat. 2, 076001 (2018)

[4] Y. Guo et. al., Phys. Rev. B* *93, 035421 (2018)

[5] R.A. Guyer et. al. Phys. Rev. 2, 148 (1966)

**5:00 PM - QN04.04.19**

__Peter Sushko__

^{1},Richard Williams

^{1},Christopher Barrett

^{1},Marvin Warner

^{1}

^{1}

Ongoing efforts in low temperature experimental research, including the work on quantum materials and high energy physics experiments, underscores the need to achieve and maintain ultra-low temperatures. Of particular interest are metal/non-metal systems, in which the dominant mechanism of heat transfer switches at the interface, and nanomaterials, in which structural and chemical deviations from idealities may lead to significant deviations from the Fourier law.

We investigate how phonon component of the heat flux across nanoscale metals is affected by point defects, dislocations and model two-dimensional defects. Gaseous models for the heat source and heat sink are adopted and the computations are conducted using classical molecular dynamics approach. Analysis of the heat transfer coefficients, as derived via Green-Kubo relation, suggests that surface nanopatterning and chemical defects have larger an effect on the heat propagation than intrinsic defects.

**5:00 PM - QN04.04.21**

__Chenyang Li__

^{1},Bishwajit Debnath

^{1},Roger Lake

^{1}

^{1}

The properties of misoriented bilayer graphene have recently received renewed interest after the discovery of superconductivity at very small rotation angles. Compared to the electronic properties, the effect of misorientation on the phonon and thermal properties has received less attention. For the larger misorientation angles, the in-plane thermal conductivity depends not on the angle, but on the commensurate lattice constant, and the thermal conductivity decreases approximately linearly as the commensurate lattice constant increases [1]. This trend is qualitatively consistent with the hypothesis that the zone folding gives rise to an increase in Umklapp scattering that reduces the low-energy phonon lifetimes and thus the thermal conductivity. However, our recent calculations show that as the misorientation angle falls below 13.2^{o}, this trend reverses itself, and the thermal conductivity starts increasing back towards the value of the unrotated structure. For angles below 13.2^{o}, the thermal conductivity initially increases rapidly as the angle decreases from 13.2^{o} to 7.3^{o}, even though the commensurate lattice constant is monotonically increasing. As the angle continues to decrease down to 1.9^{o}, which is the smallest angle simulated, the thermal conductivity gradually returns to its unrotated value.

For small angles with minimal commensurate unit cells, the commensurate lattice constants monotonically increase as the angles decrease, so that it is not clear what determines the functional dependence of the thermal conductivity in the small angle regime. Is it the misorientation angle or the commensurate lattice constant? To answer this question, we investigated two very different angles, 3.9^{o} and 20.3^{o}. Both of these angles which have exactly the same commensurate lattice constant of 3.6 nm. The thermal conductivities of the two structures are identical indicating that the functional dependence of the thermal conductivity in the low angle regime continues to be on the lattice constant rather than on the misorientation angle.

As the lattice constant increases, the reciprocal lattice constant decreases, so that Umklapp scattering should become more accessible to the low-energy, small-wavevector phonons that determine the thermal conductivity. All else being equal, the increased scattering should decrease the thermal conductivity. While this picture is consistent with the trends in the large angle regime, in the small angle regime (< 13^{o}), this is the opposite of the trend that we observe. However, as the misorientation angle returns to zero degrees, the thermal conductivity must return to that of the AB aligned structure, and this is what we observe. In this talk, we will describe the thermal transport in the low angle regime, and we will present our analysis of the thermal transport that includes the average phonon velocities and density of modes, and we will also present a spectral decomposition of the lattice thermal conductivity determined from the force-velocity cross correlation function.

The investigation uses both nonequilibrium molecular dynamics (NEMD) and ab-initio density functional theory (DFT) combined with the phonon Boltzmann transport equation. For the NEMD direct calculations of the thermal conductivity, the width of the simulated bilayer graphene structures is approximately 10 nm. To ensure that the results do not depend on the sample width, multiple increasing widths are simulated until there is no longer any width dependence. The sample lengths are varied from 20 nm to 426 nm. The largest structure contains 317,600 atoms.

[1] C. Li, et al., Carbon, **138**, 451 (2018).**Acknowledgement**

This work was supported by the National Science Foundation under Award NSF EFRI-1433395. The ab initio simulations used the Extreme Science and Engineering Discovery Environment (XSEDE), supported by National Science Foundation (NSF) grant No. ACI-1548562 and allocation ID TG-DMR130081.

**5:00 PM - QN04.04.22**

__Satish Kumar__

^{1},David Brown

^{1},Wenqing Shen

^{1},Diego Vaca

^{1},Xufan Li

^{2},Kai Xiao

^{2},David Geohegan

^{2}

^{1},Oak Ridge National Laboratory

^{2}

Improving the thermal transport across interfaces is a necessary consideration for micro- and nano-electronic devices and necessitates accurate measurement of the thermal boundary conductance (TBC) and understanding of transport mechanisms. Two-dimensional transition metal dichalcogenides (TMDs) have been studied extensively for their electrical properties, including the metal-TMD electrical contact resistance, but the thermal properties of these interfaces are significantly less explored irrespective of their high importance in their electronic devices. We isolate individual islands of MoSe_{2} grown by chemical vapor deposition using photolithography and correlate the 2D variation of TBC with optical microscope images of the MoSe_{2} islands. We measure the 2D spatial variation of the TBC at metal-MoSe_{2}-SiO_{2} interfaces using a modified time-domain thermoreflectance (TDTR) technique which requires much less time than full TDTR scans. The thermoreflectance signal at a single probe delay time is compared with a correlation curve which enables us to estimate the change in the signal with respect to the TBC at metal-MoSe_{2}-SiO_{2} interface as opposed to recording the decay of the thermoreflectance signal over delay times of several nanoseconds. The results show higher TBC across Ti-MoSe_{2}-SiO_{2} interface compared to Al-MoSe_{2}-SiO_{2}. An image analysis method is developed to differentiate the TBC for different number of MoSe_{2} layers, which reveals the TBC in single-layer regions is higher than bilayer. We perform traditional TDTR measurements over a range of delay times and verify TBC is higher at Ti-MoSe_{2}-SiO_{2} interface compared to Al-MoSe_{2}-SiO_{2} highlighting the importance of the choice of metal to heat dissipation at electrical contacts in TMD devices.

**5:00 PM - QN04.04.23**

__Riley Hanus__

^{1},G. Snyder

^{1}

^{1}

Phonon transport across interfaces is an inherently complex topic of great scientific and technological importance to fields ranging from microelectronics to energy materials. Here, I will present several experimental and theoretical results which aim to establish a fundamental understanding of heat transfer across interfaces, specifically grain boundaries (GBs). First, I will demonstrate how phonon diffraction and dimensionality crossover effects arise when the nanoscale structure of interfaces and GBs is considered. An expression for the relaxation time of phonon interacting with GB strain fields (τ_{gbs}) is presented and is shown to effectively describe the temperature dependence of the lattice thermal conductivity (κ_{L}) of polycrystals at low temperatures (< 100 K). At these temperatures the total phonon relaxation time is dominated by interactions with GBs, and the temperature dependence of κ_{L} reveals important information about the nature of the phonon-GB interaction. Next, an experimental study is presented where the thermal boundary resistance is measured on individual Si-Si twist GBs at different twist angle. The thermal boundary resistance at GBs again seems to be dominated by the interfacial strain field. Finally, it is shown how the thermal boundary resistance can be controlled by modifying the GB complexion with 2D materials. Specifically, several layers of graphene can be introduced into the GBs of skutterudite materials which dramatically increases the materials thermal boundary resistance, while negligibly effecting electronic transport. This results in a significant improvement in *zT* and a 24% improvement in device efficiency which was measured experimentally.

**5:00 PM - QN04.04.25**

__Maureen Joel Lagos__

^{1},Philip Batson

^{2}

^{1},Rutgers, The State University of New Jersey

^{2}

Nanoscale phonon properties have recently received attention because new material properties can be designed by tailoring vibrational behaviour. This has triggered significant efforts towards a better nanoscale control and manipulation of thermal processes in materials. In this context, the reduction of the physical size of materials also resulted in the need of improved spectroscopic techniques and methods to characterize phonon and thermal properties of materials with higher spatial resolution. Recently, aberration-corrected electron microscopes were equipped with monochromators, thus opening the doors for phonon spectroscopy studies in nanomaterials using an electron probe of the size of a hydrogen atom. For instance, this advancement allowed us to obtain spatially-resolved maps of phonon scattering in a single nanoparticle (< 100 nm) with nanometer resolution [1]. Also, due the nature of the inelastic electron scattering by phonons, the scattering amplitude exhibit a dependence on temperature and the spatial distribution of the scattering has several types of localization. In this work, exploiting the characteristic of the phonon scattering, we present a non-invasive method to measure the local temperature of a single nanostructure using an electron probe. We determined the local temperature of nanostructures with high precision (down to 1K) and sub-nanometer spatial resolution (down to 2Å) [2].

We obtained energy-loss/energy gain spectra from nanostructures (nanoparticles and interfaces) using a Nion STEM microscope equipped with a monochromator to study the the phonon response in the infrared range using a ~ 1.5 Å probe with an energy spread of 9 meV. Our instrument allows the detection of acoustic bulk phonon excitations down to 20 meV [1]. The amplitudes of the energy-loss and energy-gain probabilities are linked by the Boltzmann factor, as established by the Principle of Detailed Balancing (PDB). We measured the nanostructure temperature by plotting the logarithm of the ratio of the scattering amplitude on the gain and loss sides of zero energy. The obtained curves are linear for several nanomaterials, supporting the use of PDB on the nanoscale. Also, this method yields measurements without reference to the nanomaterial morphology, or scattering conditions. Our experimental results obtained at room temperature indicate that the probed object indeed is close to 290 K with a precision of ~ 7-10K with ~ 99% of confidence level (3 standard deviations) and agreed very well with the accepted values for room temperature conditions. Similar results were obtained for measurements at high temperatures (up to 1000 K). We found also that temperatures obtained from bulk phonon scattering compared well with those obtained using surface phonon polariton scattering, typically present in nanoparticles [1], suggesting that temperature gradients from the inside towards the surface should be detectable. We also investigated the localization degree of our measurements and we found that highly-localized scattering, associated with the excitation of short-wavelength acoustic phonons, can be used to perform measurements with atomic resolution, because bulk scattering can vary drastically within neighboring atom columns [3]. Meanwhile, surface phonon polaritons can yield average values over a region of interest (several nanometers).

We show that the temperature of a nanoobject can be measured experimentally using phonon scattering, and we verify that PDB holds for nanomaterials at thermal equilibrium. We also think this method holds much promise for studies aimed at understanding nanoscale thermal response (heat transfer, nanoscale energy transport) in nanostructures. We acknowledge support of U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award #DE-SC0005132.

[1] M. J. Lagos, *et al*, *Nature* 543, 529 (2017).

[2] M. J. Lagos, *et al*, *NanoLetters* 18, 4556 (2018).

[3] U. Hohenester, *et al*, *Phys. Rev. B* 97, 165418 (2018).

**5:00 PM - QN04.04.26**

__James Gonzalez__

^{1},Josue Ortega

^{1},Zhi Liang

^{1}

^{1}

Using molecular dynamics (MD) simulations and theoretical calculations, we study heat transfer across liquid-gas interfaces within a planar heat pipe. To determine the thermal conductance (Kapitza conductance), *G*_{K}, at the interface, two heat transfer mechanisms, namely, conduction and evaporation/condensation are considered. In the case of interfacial heat conduction, gas molecules, particularly non-condensable gas molecules, exchange heat with liquid surfaces through gas-liquid collisions, and the theoretical expression for *G*_{K} is derived from the kinetic theory of gases. For interfacial heat transfer by evaporation or condensation, the theoretical expression for *G*_{K} is derived from the Schrage relationships. To assess the accuracies of the theoretical expressions for *G*_{K}, we compare these theoretical predictions to the *G*_{K} obtained directly from MD simulations. For all cases studied, the theoretical predictions agree with the MD simulation results very well. If the density of non-condensable gas in the heat pipe is much higher than that of the working fluid in the gas phase, we find that the interfacial heat conduction could contribute significantly to the total heat flux across the liquid-gas interfaces. The effect of *G*_{K} at liquid-gas interfaces on the overall heat transfer efficiency in a planar heat pipe is discussed.

**5:00 PM - QN04.04.28**

__Kiumars Aryana__

^{1},John Gaskins

^{1},David Olson

^{1},Patrick Hopkins

^{1}

^{1}

Chalcogenide materials such as Ge_{2}Sb_{2}Te_{5} (GST), which upon thermal excitation undergo structural transition between amorphous and crystalline phases with applied thermal load, have emerged as a potential material candidate for new memory technologies due to prospective gains in speed, device lifetime, and capacity. In these devices, thermal transport plays a pivotal role as it dictates the efficiency of the read/write process as well as overall power consumption. Here, we measure thermal properties relevant to device operation at material length scale similar to those used in actual devices, such as thermal conductivity, thermal boundary resistance (TBR), and sound speed of both amorphous and crystalline GST using time-domain thermoreflectance. Based on the acoustic echoes obtained from picosecond acoustic results we measure the sound speed of amorphous and crystalline GST to be approximately 2900 m/s. Moreover, we report the TBR with different spacer compositions (W, SiO_{2}, and SiN_{x}) in contact with GST. The SiN_{x}/GST interface shows the highest TBR compared to both W and SiO_{2} interlayers. In the case of all spacer compositions, the crystalline GST interface shows a higher interface resistance compared to its amorphous counterpart. Additionally, very thin layers of tungsten ( ≤ 4 nm) possess a higher TBR when compared to layers thicker than four nanometers, which we attribute to ballistic transport of phonons.

**5:00 PM - QN04.04.30**

__Jihui Nie__

^{1},Anirban Chandra

^{1},Zhi Liang

^{2},Pawel Keblinski

^{1}

^{1},California State University

^{2}

We use molecular dynamics to determine the mass accommodation coefficient (MAC) of water vapor molecules colliding with a rapidly moving liquid-vapor interface. This interface mimics those present in collapsing vapor bubbles and characterized by large interfacial velocities. We find that at room temperature, the MAC is generally close to unity, and even with interfaces moving at 10 km/s velocity, it has a large value of 0.8. Using a simplified atomistic fluid model, we explore the consequences of vapor molecule interfacial collision rules on pressure, temperature, and density of a vapor subjected to an incoming high-velocity liquid-vapor interface.

**5:00 PM - QN04.04.31**

__Jixiong He__

^{1},Tingyu Lu

^{1},Jun Liu

^{1}

^{1}

Recent research work has highlighted the potential to achieve high-thermal-conductivity polymers by aligning their molecular chains. Combining with other merits, such as low-cost, corrosion resistant, and lightweight, such polymers are attractive for heat transfer applications. Due to their quasi-one-dimensional structural nature, the understanding on the thermal transport in those ultra-drawn semicrystalline polymer fibers or films is still lacking. We built the ideal repeating units of semicrystalline polyethylene and studied their dependence of thermal conductivity on different crystallinity and interlamellar topology using the molecular dynamics simulations. We found that the conventional models, such as the Choy-Young’s model, the series model, and Takayanagi’s model, cannot accurately predict the thermal conductivity of the quasi-one-dimensional semicrystalline polyethylene. A modified Takayanagi’s model was proposed to explain the dependence of thermal conductivity on the bridge number at intermediate and high crystallinity. We also analyzed the heat transfer pathways and demonstrated the substantial role of interlamellar bridges in the thermal transport in the semicrystalline polyethylene. Our work could contribute to the understanding of structure-property relationship in semicrystalline polymers and shed some light to the development of plastic heat sinks and the thermal management in flexible electronics.

**5:00 PM - QN04.04.32**

__Mallory DeCoster__

^{1,2},Xin Chen

^{3},Kai Zhang

^{3},Helmut Baumgart

^{3},Patrick Hopkins

^{1}

^{1},Johns Hopkins University Applied Physics Lab

^{2},Old Dominion University

^{3}

We report on the thermal properties of lead chalcogenide-based superlattice thin films grown on planar silicon wafers by atomic layer deposition (ALD). The concept of controlling thermal energy carriers in thin film superlattices of PbTe/PbSe by varying the total thickness and period thickness is experimentally investigated in this work. We demonstrate the use of time domain thermoreflectance (TDTR) to measure the cross-plane thermal conductivity of these systems in order to understand the role of size effects and boundary scattering on the thermal conductivity of the PbTe/PbSe superlattices. The thin films of varying compositions resulted in thermal conductivities that are not strongly dependent on the period thickness, and are weakly dependent on the samples total thickness. This suggests that incoherent transport dominates in the thickness regime studied. Additionally, our results show that increased phonon boundary scattering introduced by the periodicity of the superlattice structure is effective for reducing the thermal conductivity.

**5:00 PM - QN04.04.33**

__Subash Gireesan__

^{1,2},Daniel Vakulov

^{1},Ruben Chavez

^{1},Milo Yaro Swinkels

^{3},Tom Vogelaar

^{1},Pol Torres

^{4},Ilaria Zardo

^{3},Marcel Verheijen

^{1},Sebastian Kölling

^{1},Jos Haverkort

^{1},F. Xavier Alvarez

^{4},Peter Bobbert

^{1,2},Erick Bakkers

^{1,5}

^{1},Center for Computational Energy Research

^{2},Universität Basel

^{3},Universitat Autònoma de Barcelona

^{4},Kavli Institute of Nanoscience

^{5}

Realizing ballistic transport at room temperature is challenging due to the decrease of phonon mean free paths with increasing temperature. Only a few studies have reported this non-diffusive behavior^{1,2}. Ballistic transport was observed in SiGe nanowires up to lengths of 8.3 µm at room temperature^{1}. This behavior was attributed to the localization of short-wavelength phonons due to alloy scattering, and long-wavelength phonons with a long mean free path dominating the transport. Longer wires showed diffusive transport^{1}.

Here, we report room-temperature ballistic transport in thin ultrapure GaP nanowires and an abrupt, temperature-insensitive transition to diffusive behavior on increasing the diameter. Nanowires with diameter ranging from 25-140 nm were grown using the vapor-liquid-solid technique with gold droplets as a catalyst. TEM images revealed that these wire have an atomically flat side facets, with a thin (2 nm) amorphous gallium oxide layer on top. Thermal conductivities of the individual wires were measured using a suspended device membrane^{3} with Pt meanders on top, which can be used as a heater and a thermometer.

For thick wires (diameter ≥ 50nm), the thermal conductance increases linearly with length, indicating diffusive behavior. For thin wires (diameter ≤ 25 nm), the thermal conductance is independent of length, indicating a transition to ballistic phonon transport. The ballistic transport at room temperature continues to the longest nanowires of 14 µm that we could study. The thermal conductance is surprisingly insensitive to a temperature above 50 K. This shows that boundary scattering dominates other scattering mechanisms.

The experimental results are interpreted using a model based on Landauer’s formalism for phonon transport^{4,5}. This model was used to describe heat flow in thin silicon nanowires^{5} and in holey silicon^{2}. It takes into account boundary scattering and neglects all other scattering mechanisms. Due to the presence of the thin amorphous oxide layer on the surface, the strength of the boundary scattering is determined by the k-vector perpendicular to the axis of the nanowire. The modes with a small perpendicular k-vector scatter weakly and have a frequency dependent mean free path l(ω), while the other modes scatter strongly, having a mean free path of the order of the diameter of the wire d. The model results agree well with heat transport measurements on 25 and 50 nm diameter wires, correctly predicting the magnitude of the thermal conductance and its length dependence. We explain the diffusive to ballistic transition by the localization of phonons in the 25 nm wire that reflects diffusively from the amorphous oxide layer, accompanied by a strong increase in the mean free paths of phonons that reflect mostly specularly. Our work demonstrates the possibility of increased heat extraction in nanostructures and opens new avenues for phonon-based devices.

References

1. Hsiao, T. K. *et al.* Observation of room temperature ballistic thermal conduction persisting over 8.3 μm in SiGe nanowires. *Nat. Nanotechnol.* **8,** 534–538 (2013).

2. Lee, J., Lim, J. & Yang, P. Ballistic phonon transport in holey silicon. *Nano Lett.* **15,** 3273–3279 (2015).

3. Swinkels, M. Y. v *et al.* Diameter dependence of the thermal conductivity of InAs nanowires. *Nanotechnology* **26,** 385401 (2015).

4. Murphy, P. G. & Moore, J. E. Coherent phonon scattering effects on thermal transport in thin semiconductor nanowires. *Phys. Rev. B* **76,** 155313 (2007).

5. Chen, R. *et al.* Thermal conductance of thin silicon nanowires. *Phys. Rev. Lett.* **101,** 105501 (2008).

**5:00 PM - QN04.04.34**

__Andrew Kelliher__

^{1},John Tomko

^{1},Brian Lynch

^{2},Joseph Tracy

^{2},Patrick Hopkins

^{1}

^{1},North Carolina State University

^{2}

Metal nanoparticles are efficient generators of heat via the photothermal effect, in which the surface plasmon resonance is excited by incident light. Surface scattering of excited electrons contribute to the generation of hot electron-hole pairs, which then thermalize and couple with the lattice to generate phonons. Anisotropic nanostructures often exhibit additional surface plasmon modes which can be tuned by altering their geometries. Gold nanorods, studied here, exhibit plasmon resonance in the near-infrared, making them suitable for applications in medical technologies, such as drug delivery or photothermal cancer therapy. This additional plasmon resonance can be tuned further during the synthesis process to allow for selective heating and actuation of soft robotics components using shape memory polymers. Furthermore, silica overcoatings having various morphologies have been developed to improve thermal stability of these nanorods up to 873 K while reducing toxicity. When using gold nanorods for photothermal applications, the primary descriptors of thermal transport are electron-phonon coupling in the gold nanorods and at their interfaces, and the phonon-phonon thermal boundary conductance across the nanorod/matrix interface. Using complementary ultrafast pump-probe laser techniques, we explore the effect of the surface plasmon on these two thermal descriptors of gold nanorods in a polymer matrix. By using variable pump wavelengths, we are able to selectively excite the surface plasmon modes. We elucidate the effect of the plasmon excitation on electron-electron coupling and electron-phonon coupling, while showing that it has little effect on phonon-phonon thermal boundary conductance at times after the electrons have equilibrated with the phonons. Additionally, in order to assess the effects of overcoatings on thermal boundary conductance, we compare results for three types of overcoated nanorods: those with full silica shells, those with lobed silica shells, and those with silica/iron oxide composite shells.

**5:00 PM - QN04.04.35**

__Mohammad Ghashami__

^{1},Devon Jensen

^{1},Keunhan Park

^{1}

^{1}

Over recent years, thermionic energy conversion (TEC) has received keen revived attention for direct heat-to-electric power generation [1–3]. However, large electrode work functions and the accumulation of negative space charge between electrodes are major issues that have restricted the use of TEC to high-temperature heat sources exceeding 1500K. As one of the potential approaches to mitigate these issues, previous works have proposed to have a sub-micron vacuum gap between the electrodes [4–6]. However, their theoretical models are not comprehensive in accurately modeling the size effect on the electron and thermal transport processes across sub-micron gap distances.

The present work provides a comprehensive look at electron and thermal transport in a TEC system as the gap separation is scaled from tenths of a millimeter down to tens of nanometers. To this end, the energy barrier profile between the electrodes, *W(x)*, is calculated within the electrostatic framework by considering space and image charge effects. The thermionic current density and heat transfer rate are then calculated by applying the determined maximum value of the energy barrier, *W*_{max}, to the rigorous charge transport model. In addition, quantum tunneling of electrons is also considered for nanoscale gap distances. Near-field radiative heat transfer is an important thermal transport mechanism to be considered when the inter-electrode gap distance becomes comparable to or smaller than the thermal wavelength [7]. The summation of the electron (thermionic and electron tunneling) and radiative heat fluxes between the electrodes allows for an energy balance calculation to provide a more realistic anode temperature for device operation and thermionic energy conversion efficiency. Moreover, we theoretically demonstrate that the nanoscale gap distance shifts a portion of the field-induced charge acceleration regime from a negative to positive operational voltage range, resulting in the enhancement of thermionic power generation by tailoring the surface roughness of the cathode electrode. The obtained results will ultimately provide insight into the design and thermodynamic performance analysis of nano-gap TEC systems based on a fundamental understanding of nanoscale charge and thermal transport physics.

1. Schwede, J. W. et al. Photon-enhanced thermionic emission for solar concentrator systems. Nat. Mater. 9, 762–7 (2010).

2. Kato, H. et al. Heavily phosphorus-doped nano-crystalline diamond electrode for thermionic emission application. Diam. Relat. Mater. (2016). doi:10.1016/j.diamond.2015.08.002

3. Wanke, R. et al. Thermoelectronic energy conversion: Concepts and materials. MRS Bull. 42, 518–524 (2017).

4. Zeng, T. Thermionic-tunneling multilayer nanostructures for power generation. Appl. Phys. Lett. 88, 153104 (2006).

5. Lee, J.-H., Bargatin, I., Melosh, N. a. & Howe, R. T. Optimal emitter-collector gap for thermionic energy converters. Appl. Phys. Lett. 100, 173904 (2012).

6. Wang, Y. et al. Effects of nanoscale vacuum gap on photon-enhanced thermionic emission devices. J. Appl. Phys. 119, 045106 (2016).

7. Park, K. & Zhang, Z. M. Fundamentals and Applications of Near-Field Radiative Energy Transfer. Front. Heat Mass Transf. 4, 013001 (2013).

**5:00 PM - QN04.04.36**

_{3 }Films

__Shunta Harada__

^{1},Ryuta Kobayashi

^{1},Tong Shen

^{1},Ayano Nakamura

^{1},Miho Tagawa

^{1},Toru Ujihara

^{1}

^{1}

Thermal switch, which can turn on/off the heat flow, plays an important role in thermal management. Ion intercalation materials have attracted interests because of their ability to change the thermal conductivities with electrochemical reactions. In our previous study, we have reported a drastic and reversible change in the thermal conductivity of amorphous WO_{3 }film with H intercalation (0.2 W/mK ↔3.1 W/mK). This phenomenon is exactly the function of a thermal switch. In this study, we try to demonstrate another thermal conductivity change of amorphous WO_{3 }by Li intercalation and investigate the mechanism of the thermal conductivity change from a viewpoint of local cluster network model.

Amorphous WO_{3} film was prepared on ITO coated glass substrate at room temperature by RF magnetron sputtering in Ar-O_{2 }atmosphere. Li intercalation into the WO_{3 }film was performed with 1.0 M LiClO_{4} in propylene carbonate. The structure change of the film was determined by X-ray diffraction and Raman spectroscopy. The thermal conductivity of the film was measured by ac calorimetric method.

With increasing intercalated Li concentration, thethermal conductivity decreases, then remarkably increased at around *x*= 0.20, and subsequently decreases again. This tendency is similar to amorphous WO_{3}-H system. Peak positions of Raman spectra in amorphous WO_{3} almost the same as those of crystalline WO_{3} except for the existence of peak of W=O double bonds in the spectra of amorphous WO_{3}. It seems that cluster of atoms forms network. As the Li content increases, the Raman spectrum becomes more broad, indicating that the structure become disordered. Thus, heat transfer is inhibited by the disorder of the structure. On the other hand, a drastic increase in thermal conductivity may result from local structural phase change. In crystalline WO_{3} film, as the Li content increases, the crystal structure of Li* _{x}*WO

_{3 }transforms from monoclinic to tetragonal and further to cubic structure. The thermal conductivity of the cubic structure is larger than those of the other phases. Raman spectrum of amorphous WO

_{3}, at the Li content rate which thermal conductivity greatly increases, shows the peak similar to the one of cubic WO

_{3}. This indicates the local structure change from monoclinic to cubic.

In summary, the thermal conductivity decrease and drastic increase are caused by the disorder and the phase change as Li intercalation, respectively.

**5:00 PM - QN04.04.39**

__Ramteja Kondakindi__

^{1},Jui-Yung Chang

^{1},Liping Wang

^{1}

^{1}

It is predicted that when two surfaces are placed in close proximity such that the distance between them is less than the thermal wavelength, radiative heat flux could be significantly enhanced far exceeding the blackbody limit due to near-field radiation or photon tunnelling through nanometer scale vacuum gaps. Recently experimental demonstrations of super-Planckian near-field thermal radiation have been reported between plate-plate or tip-surface configurations. This study aims to develop a home-built thermal metrology for measuring near-field radiative heat transfer between a sphere and a planar surface with well controlled gap distances down to a few nanometers. A bi-material atomic force microscope (AFM) cantilever is used as a thermal sensor, whose temperatures will be measured simultaneously by two means: difference signal due to bending and sum signal with thermoreflectance obtained from a position sensitive diode (PSD). Careful calibrations for both bi-material cantilever bending and thermoreflectance will be carried out first to establish the relation between the tip temperature and the PSD difference signal from bending, or the sum signal from thermoreflectance. The temperature of AFM cantilever will be varied by the laser power, while a power meter will be used to measure the incident, reflected and scattered laser beams to determine absorbed laser power. When the planar sample maintained at room temperature is brought closer with a piezo stage at sub-nm resolution, it is expected that the AFM cantilever will be cooled due to enhanced near-field radiative heat transfer. The thermal conductance from the near-field thermal radiation at different gap distances will be calcualted from measured cantilever temperature, absorbed laser power, and sample temperature. Silica microsphere will be attached to the AFM cantilever to promote the near-field radiative heat transfer. Reference samples like quartz and silicon wafers will be measured first to compare with reported experimental results and theoretical calculations for validation. Near-field measurement results with SiC wafer, 2D materials like graphene, or nanostructured metamaterials will be reported. The outcomes of this research aim to enhance the fundamental understandings of radiative heat transfer in the near-field which could lead to advances in microelectronics, optical data storage and thermal systems including energy conversion devices.

**5:00 PM - QN04.04.40**

__Anirban Chandra__

^{1},Zhi Liang

^{2},Pawel Keblinski

^{1}

^{1},California State University, Fresno

^{2}

Using molecular dynamics(MD) simulations we study the steady state evaporation and condensation processes of molecular polar fluids in a one-dimensional heat-pipe geometry. The non-equilibrium mass flow is driven by controlling the temperatures of the source/sink. The resulting mass fluxes as a function of driving force are evaluated for systems with pure working fluids (e.g., water) and in the presence of non-condensing gases (e.g., water + air). Our results indicate that the molecular velocity distributions in the vapor phase are indeed Maxwellian distributions shifted by the velocity of the macroscopic vapor flow, as assumed in Schrage’s theoretical analysis. Furthermore, we evaluate the mass accommodation coefficient as a function of temperature using equilibrium simulations. Consequently, we determine that the Schrage equations describe the evaporation-condensation rates of molecular fluids with moderate accuracy.

### Symposium Organizers

**8:00 AM - *QN04.05.01**

__F. Xavier Alvarez__

^{1},Javier Bafaluy

^{1},Juan Camacho

^{1},Xavier Cartoixà

^{1},Pol Torres

^{1},Albert Beardo Ricol

^{1},Lluc Sendra

^{1}

^{1}

Two main characteristics make nanoscale thermal transport in semiconductors a complex phenomena full of nuances. The first is the importance of momentum conservation in the phonon-phonon collisions (Normal scattering)^{[1]}. This kind of scattering is not able to destroy momentum and consequently in their presence the phonon distribution cannot relax to its equilibrium form. The second is the large scale range that span the phonon mean free path spectrum^{[2]}. Because of this the connectivity between two regions in a sample (non-locality) depends on the kind of phonons connecting these regions. The consequence is that heat transport at the nanoscale is still an incompletely described topic.

Phonon hydrodynamics has emerged in the last years as a candidate to cover this gap. The appearance of this regime has been associated to the dominance of normal collisions. Its presence has been proven in 2D materials or at low temperatures^{[3-4]}, when N-collisions are dominant and in consequence collective effects can be observed easily. But recent works have shown that hydrodynamic effects can still have an important impact when resistive collisions are dominant^{[5-6]}. In this case its presence has to be noticed through indirect evidences. Hydrodynamics has been used, for example, to understand the lack of validity of the Mathiessen rule in silicon or the dependence of the Thermal Boundary Resistance between two materials on the size of the contact.

Kinetic Collective Model (KCM) has been developed to describe heat transport using two key concepts. On one side, the splitting in collective regime (when normal scattering is dominant) and kinetic regime (when it is not important). On the other side, the inclusion of nonlocal and memory effects that introduce hydrodynamic behavior in the description. From the combination of both concepts it can be shown that hydrodynamic phenomena can emerge in both, collective and kinetic regimes, with different particularities in each case.

The equations obtained from the model are simple enough to be solved using finite element computational tools. We will show the results from a recent developed module implemented in COMSOL. Using KCM equations in combination with ab initio calculated parameters we will describe hydrodynamic effects in 2D materials like graphene and in conventional semiconductors like silicon an use the results to interpret some of the most relevant experimental observations of the last years.

[1] Guyer & Krumhansl Phys. Rev., **148**(2), 766–778 (1966)

[2] Vermeersch et al. Phys. Rev. B, **91**(8), 085202 (2015)

[3] Ding et at. Nano Letters, **18**(1), 638–649 (2018)

[4] Cepellotti et al., Nat. Commun., **6**, 1-7 (2015)

[5] Torres et al., Phys. Rev. Mat., **2**(7) 076001 (2018)

[6] Ziabari et al., Nat. Commun. **9**(1), 255 (2018)

**8:30 AM - QN04.05.02**

__Sangyeop Lee__

^{1},Xun Li

^{1}

^{1}

Hydrodynamic phonon transport occurs when normal scattering (N-scattering) is much stronger than umklapp scattering. Due to its momentum-conserving nature, N-scattering does not directly cause thermal resistance. In particular, when a sample is extremely large and thus diffuse boundary scattering can be ignored, N-scattering alone cannot cause any thermal resistance. For a sample with finite size, however, N-scattering combined with diffuse boundary scattering affects thermal resistance. We discuss two different mechanisms of thermal resistance associated with N-scattering in finite-sized samples when phonon transport is in the strong hydrodynamic regime. The discussion is based on the Monte Carlo solution of the Peierls-Boltzmann transport equation in both real and reciprocal spaces using an *ab initio* three-phonon scattering matrix. First, when a sample has a finite width but an infinite length along the heat flow direction, the thermal resistance occurs due to the momentum transfer along the lateral direction (i.e, perpendicular to heat flow direction), called phonon viscous damping effect. The stronger N-scattering, the slower the momentum transfer, resulting in lower thermal resistance. Second, when a sample is infinitely wide but has finite length along the heat flow direction, phonons emitted from heat reservoirs change their distributions from static to displaced Bose-Einstein distributions upon N-scattering. During this transition between non-collective and collective phonon flows, N-scattering causes thermal resistance. The thermal resistance of this case depends on the shape of phonon dispersion provided that the sample length is larger than the mean free path of N-scattering. For graphitic materials, the transition between collective and non-collective phonon flows reduces heat flux by 50% from the ballistic case at room temperature.

**8:45 AM - QN04.05.03**

__Fabian Menges__

^{1}

^{1}

In an overwhelmingly large group of conducting materials thermal and electrical transport are directly related via the Wiedemann-Franz law, which states that the product of the thermal conductivity and the electrical resistivity divided by the temperature is a constant, yielding the Sommerfeld value. In stark contrast to these ordinary conductors, heat and charge flow can de-couple in strongly correlated materials yielding thermal energy dissipation and transport behavior that can be described by the theory of hydrodynamics.

In this talk, we will present recent thermal and magneto-electric transport experiments on heat and charge flow in the Weyl semimetal tungsten di-phosphide [1]. We observe a strong violation of the Wiedemann-Franz law that coincides with a transition from a conventional metallic state at high temperatures to a hydrodynamic electron fluid below 20 K. The hydrodynamic regime is characterized by a viscosity-induced dependence of electrical resistivity on the sample width and magnetic field. Based on the accompanying decoupling of momentum conserving and relaxing scattering processes we illustrate that both thermal and electrical transport are bound by the quantum indeterminacy applied to energy dissipation, independent of the underlying transport regime.

[1] Thermal and electrical signatures of a hydrodynamic electron fluid in tungsten diphosphide

J Gooth, F Menges, N Kumar, V Süβ, C Shekhar, Y Sun, U Drechsler, B Gotsmann

Nature Communications 9, 4093, 2018

**9:00 AM - *QN04.05.04**

__Irena Knezevic__

^{1}

^{1}

Theoretical understanding of phonon dynamics in nanostructures with a significant degree of surface disorder is far from complete. Here, we show how concepts from chaos theory, such as the level-spacing distribution and the geometric mean free path, can shed light on the universal features in phonon dynamics and thermal transport across structures of different dimensions and roughness. Within this context, we simulate lattice dynamics using Monte Carlo in the semiclassical limit and the finite-difference time-domain (FDTD) solution to the elastic wave equation for the elastic-solid limit.

**9:30 AM -**

**10:00 AM - QN04.05.05**

__Joseph Feser__

^{1}

^{1}

Previous work toward engineering lower thermal conductivity of nanoparticle-in-alloy semiconductor composites have indicated that optimal nanoparticle sizes should lie between the Rayleigh and geometric phonon scattering regimes (i.e the Mie regime), yet phonon scattering models that are accurate in the Mie regime have never been employed to investigate the thermal transport. Here, we exploit exact solutions from continuum mechanics that separately treat longitudinal and transverse phonon scattering from nanoparticles across a wide spectrum of wavelengths including the Rayleigh, Mie, and geometric scattering regimes. The solutions intrinsically account for material contrast effects from density and both normal and shear elastic constants. We find that consideration of Mie scattering effects drastically alters the materials selection and particle sizing process for optimal nanocomposites. In particular, a previously unreported inter-relationship between density and elastic contrast is reported: in the Mie regime, a suppression of the scattering cross section is found in cases where the sound speeds of the matrix and nanoparticle are closely matched. This suppression can extend the transition wavelength to geometric scattering by more than an order-of-magnitude, with severe effects to thermal transport. We explore how these considerations change the optimal sizing of nanoparticles for in metal/semiconductor composites, with specific application to the experimentally significant case of InGaAs composites.

**10:15 AM - QN04.05.06**

__Yandong Sun__

^{1},Ben Xu

^{1}

^{1}

Dislocations have prominent scattering to phonons. Tuning dislocation patterns is an effective method to control the thermal conductivity in thermoelectric materials. However, clear impact of dislocation on phonon scattering is still missing, although substantial efforts have been devoted to this issue. By performing non-equilibrium molecular dynamics (NEMD) simulation, the thermal transportation of a rock salt structure PbTe crystal and a body-centered cubic (bcc) iron crystal containing quantitative dislocations have been studied. For the first time, temperature distribution in proximity to the dislocation, spectral heat flux and frequency dependent phonon mean free paths (MFPs) are explicitly obtained. The results not only show that quantitative dislocations suppress the lattice thermal conductivity but also reveal detailed phonon-dislocation scattering processes, which is due to the localization of phonon modes in sample with dislocations. Moreover, we provide a way to scale the scattering rate between the phonons and dislocations which may offer a guidance for engineering to regulate the lattice thermal conductivity by introducing or removing dislocations.

**10:30 AM - *QN04.06.01**

__Barry Zink__

^{1}

^{1}

Recent advances in thermoelectric materials through nanoscale engineering bring both tremendous promise and serious fundamental measurement challenges. For materials ranging from graphene to carbon nanotube hybrids to nanomagnetic systems or films, samples with one or more dimensions on the sub-100 nm scale are always difficult to thermally characterize. Our approach to these measurements uses micro- and nanomachined thermal isolation platforms that allow exceptional control over thermal gradients and unambiguous alignment of this gradient in the plane of a thin film or nanoscale sample. Micromachined electrical leads enable thermal conductivity, electrical conductivity, and Seebeck effect measurements all on the exact same sample. This allows particularly powerful probe of both the Wiedemann-Franz law and the thermoelectric figure-of-merit, ZT. In this talk I will first focus on our recent work on increasing ZT in sub-100 nm thin films by reducing thermal conductivity, which we have demonstrated in two very different systems. In the first, disordered films formed from carefully-selected semiconducting single-wall carbon nanotubes (CNT) show dramatic reduction in thermal conductivity when doped with organic acids.[1] This reduction is likely driven by increased phonon scattering caused by the proximity of the CNT and the dopant molecule, and raises ZT for both n- and p-type films to some of the largest values yet observed in organic systems.[2] More surprising is a strong non-monotonic temperature dependence of thermal conductivity seen in certain preparations of CNT films that drives a sharp increase in ZT over a narrow temperature range.[3] It is not yet clear if this effect is driven by changes in phonon populations or scattering, and further study could lead to a new route to reducing thermal conductivity in CNT thermoelectric systems. The second system showing a surprising reduction in thermal conductivity and increase in ZT are evaporated films of gold. Across a wide range of film thickness we see very strong violations of the Wiedemann-Franz law in gold films, with a measured Lorenz number reduced to less than half the free-electron values near room temperature.[4] Finally I will discuss magnetic metallic alloy films where careful examination of the Wiedemann-Franz law indicates a large additional thermal conductivity. Ongoing work will clarify if this is driven by primarily by phonons or magnons in these systems, and point toward new ways to manipulate spin degrees of freedom in ferromagnets with heat. Work at DU is supported by the NSF (DMR-1709646) and DOE-CINT (DE-AC04-94AL85000).

1) Avery, et al., "Tailored Semiconducting Carbon Nanotube Networks with Enhanced Thermoelectric Properties," Nature Energy v. 1, 16033 (2016)

2) MacLeod, et al., "Large n- and p-type thermoelectric power factors from doped semiconducting single-walled carbon nanotube thin films," Energy & Environmental Sciences v. 10, 2168 (2017)

3) Wesenberg, et al., "Size-dependent suppression of phonon thermal conductivity in carbon nanotube thermoelectric films," in preparation

4) Mason, et al., "Violation of Wiedemann-Franz Law through reduction of thermal conductivity in gold thin films," in preparation

**11:00 AM - QN04.06.02**

__Tianli Feng__

^{1},Yang Zhong

^{1},Jingjing Shi

^{1},Xiulin Ruan

^{1}

^{1}

As a crucial part in thermal management, interfacial thermal transport is still not well understood. In this paper, we employ the newly developed modal nonequilibrium molecular dynamics to study the Si/Ge interfacial thermal transport and clarify several long-standing issues. We find that the few atomic layers at the interface are dominated by interfacial modes, which act as a bridge that connects the bulk Si and Ge modes. Such bridging effect boosts the inelastic transport to contribute more than 50% to the total thermal conductance even at room temperature. The apparent inelastic transport can even allow effective four-phonon processes across the interface when the mass difference between the two materials is large. Surprisingly, optical phonon modes can contribute equal or more thermal conductance than the acoustic modes due to the bridging effect. From the modal temperature analysis, we find that the phonon modes are in strong thermal nonequilibrium near the interface, which impedes the thermal transport. The widely used Landauer approach that does not consider the phonon nonequilibrium can lead to inaccurate results. We have modified the Landauer approach to include the inelastic transmission and modal thermal nonequilibrium. The approach is used to analyze our modal NEMD results, and the mode-dependent phonon transmission function that includes inelastic scattering has been derived. Our results unveil the fundamental thermal transport physics across interfaces and will shed light on the future engineering in thermal management. It provides a method of calculating modal phonon transmission functions that includes inelastic scattering from molecular dynamics.

**11:15 AM - QN04.06.03**

__Alex Greaney__

^{2},Giuseppe Romano

^{1},Aria Hosseini

^{2},Jackson Harter

^{3},Todd Palmer

^{3}

^{1},University of California, Riverside

^{2},Oregon State University

^{3}

Packages that efficiently simulate the Boltzmann transport of phonons have become an established research tool for predicting thermal transport in micro and nanoscale dielectric devices. However, the widespread application of these tools, particularly in industry, is currently hindered by the numerical difficulty of modeling the thermal processes at boundaries and interfaces. Here we present a flexible framework for treating the scattering at boundaries between dissimilar materials within the Boltzmann transport equation (BTE) with the single relaxation time approximate. Our approach adds an extra collision term to the BTE that exactly satisfies detailed balance at a boundary without adding any additional thermal resistance. The correction is formulated for both sharp discontinuous boundaries, and smoothly varying graded interfaces. The form of this extra collision term also makes it possible to impose any additional thermal boundary resistance at a boundary. This approach will enable easy modeling of phonon transport in systems with complex geometry, and so will facilitate the industrial adoption of transport simulation tools. The model has been implemented within the package OpenBTE (www.opembte.org)

**11:30 AM - *QN04.06.04**

__Patrick Hopkins__

^{1}

^{1}

We report on a series of experimental measurements designed to understand the role of hot excited electrons and plasmons and resulting electron-phonon coupling on nonequilibrium electron thermal transport in metals, non-metals and metal/non-metal interfaces. We implement a pump-probe thermoreflectance using sub-picosecond laser pulses with wavelength tunability through the visible and into the IR. We use this tunable photon energy to demonstrate that electron-phonon coupling in metals (e.g., Au, Al, Pt) and non-metals (e.g., silicon and GaAs) can be strongly energy dependent, and when probing near interband transitions, scattering rates can be strongly dictated by electron number densities. We then consider the role of electron-phonon coupling at interfaces between gold and an insulating non-metal substrate with an adhesion layer between the gold and the substrate. We show that under conditions of electron-phonon nonequilibrium and ballistic electron transport, the thermal conductance due to electron-phonon coupling can lead to enhancements in the overall thermal boundary conductance across metal/non-metal interfaces. Next, we consider the heat transport processes across metal/doped semiconductor interfaces, where the energy barrier at the metal/non-metal interface is low enough to promote electron injection across this boundary. We show that electron injection across this boundary can be used as a means to control the electronic thermal transport and electron-phonon scattering rates in semiconductors within the electronic Kapitza length near the metal/doped semiconductor interface. Finally, we study the role that plasmon excitation can have on these electron interfacial properties by considering metal/doped CdO interface in which the CdO supports near-IR plasmon modes.

**1:30 PM - *QN04.07.01**

__Junichiro Shiomi__

^{1}

^{1}

To achieve the development goals related to energy, whether for sustainability or smart society, further hardware innovation is indispensable as well as software. Here, the innovation of hardware requires creation of new functional materials. Specific requirements for materials may change depending on future technological trends, but it is certain that the demands will become diverse and complex, therefore, new foundation for material development that can respond to it is urgently needed. Thermal functional materials are not an exception, where materials with larger controllability of heat transfer are strongly needed for better thermal management and harvesting. For this, advancement in phonon engineering, which is to control thermal properties by understanding and engineering the state and transport of phonons (or their interaction or correlation with other quasi-particles) is indispensable. While there has been a great progress in the last decades particularly in terms of nanostructures, the above demands require further controllability and designability. Over the last years, we and collaborators have grained the controllability by pushing the limit of phonon scattering, strain engineering, and phonon coherence. In addition, to realize better designability, we have developed frameworks to pursue materials informatics for heat transfer by combining thermal transport calculations and machine learning. In this talk, I will discuss some successful cases to design nanostructures to enhance/impede thermal transport, and to optimize the trade-off among multiple competing properties i.e. thermal conductance, electrical conductance, and Seebeck coefficient.

Finally, I will introduce an experimental realization of an optimally-designed structure taking the case of controlling the spectrum of radiative heat transfer.

**2:00 PM - QN04.07.02**

__Lucas Lindsay__

^{1},Tribhuwan Pandey

^{1},Carlos Polanco

^{1},Valentino Cooper

^{1},David Parker

^{1}

^{1}

Symmetry and dimensionality are essential factors defining lattice dynamics and thermal conductivity in materials. Here, we will present physical insights developed from predictive first principles Peierls-Boltzmann transport in 1D chains and compare them with 2D and bulk materials. In particular, we will discuss how symmetry gives rise to phonon chirality in 1D chains from which phonon-phonon scattering rules are derived. These symmetry-based selection rules limit thermal resistance, while chain coupling breaks these in weakly bonded bulk systems, giving lower κ and large κ anisotropy.

Acknowledgements: This work was supported by the U. S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.

**2:15 PM - QN04.07.03**

__Caroline Gorham__

^{1},David Laughlin

^{1}

^{1}

Thermal transport properties of the solid state are intimately tied to the structure that forms from the undercooled atomic liquid. Above approximately 50 K, the thermal conductivity of glasses ubiquitously decreases with decreasing temperatures while the thermal conductivity of crystalline materials rises sharply with decreasing temperatures; the origin of this inverse behavior has remained a matter of inquiry over the past century. This work elucidates the topological origins of the thermal transport properties of the solid state, by adopting a quaternion number to characterize the orientational order that develops by atomic clustering at temperatures below the melting temperature.

Solidification of undercooled liquids towards crystalline ground states may be viewed as a higher-dimensional realization of Bose-Einstein condensation of superfluids, that are characterized by a complex orientational order parameter, such as helium superfluids and superconductors. Just as complex ordered systems are considered to exist in restricted dimensions in two- and one-dimensions, quaternion ordered systems in four- and three-dimensions may be considered to exist in restricted dimensions. In restricted dimensions, misorientational fluctuations in the form of spontaneously generated topological defects prevent conventional long-range order at finite temperatures. Third homotopy group topological point defects in quaternion ordered systems play the role of vortices in complex ordered systems.

In restricted dimensions, one may obtain either a phase-coherent or a phase-incoherent low-temperature state by changing the non-thermal tuning parameter that characterizes the ordered system. For example, in two- and one-dimensional charged complex ordered systems (i.e., Josephson junction arrays), superinsulating ground states may be realized with infinite electrical resistance that is a mirror image of superconductivity. Similarly, solidification in four- and three-dimensions (i.e., quaternion ordered systems) can result in either crystalline and non-crystalline low-temperature states. Resulting thermal transport properties of orientationally-ordered (crystalline) and orientationally-disordered (non-crystalline) solid states are inverse to one another above approximately 50 K, in analogue to the electrical transport properties of Josephson junction arrays across the superconductor-to-superinsulator transition.

**2:30 PM -**

**3:30 PM - *QN04.08.01**

__Austin Minnich__

^{1}

^{1}

Molecular crystals that conduct heat are of interest both fundamentally and for applications. Long-standing questions regarding the thermal transport properties of these materials include how crystals with complex unit cells can still possess high uniaxial thermal conductivity despite their large scattering phase space, and what is the distribution of phonon mean free paths in actual molecular crystals that possess many defects. Here, we address these questions using advances in numerical and experimental tools. First, we use ab-initio calculations to show that high thermal conductivity along the chain axis arises from phonon focusing despite intense phonon scattering in the complex crystal. Second, we report the observation of ballistic phonons on micron length scales in semi-crystalline polyethylene using transient grating spectroscopy, allowing us to determine the mean free path distribution. These works elucidate the microscopic details of heat transport in molecular crystals.

**4:00 PM - QN04.08.02**

__Gaurav Kumar__

^{1},Francis VanGessel

^{1},Peter Chung

^{1},Daniel Elton

^{1}

^{1}

Molecular crystals form an important class of materials. They appear in vital medical and defense applications ranging from pharmaceuticals to energetics. Thermal and vibrational properties are particularly critical to know due to their influence over, for instance, tableting strength and initiation sensitivity. The accurate prediction of certain phonon properties like the thermal conductivity and energy transfer rate requires knowledge of anharmonic vibrational properties, in particular the phonon lifetimes. In this study we extend techniques previously used for atomic crystals to predict phonon lifetimes for all branches of the molecular crystal α-RDX. We use two different techniques to predict phonon lifetimes - anharmonic lattice dynamics (ALD) [1] [2] and frequency domain normal mode decomposition (NMD) [3]. We for the first time present the temperature and frequency dependence of phonon lifetimes due to normal and Umklapp processes in α-RDX, and identify phonon modes with high scattering rates which result in high energy transfer rates. Our results indicate that phonon lifetimes in α-RDX do not have a monotonic relationship with frequency. In fact, some high frequency phonons are found to exhibit longer lifetimes than low frequency phonons. This is in contrast with trends observed in atomic crystals [3] [4] [5] and predictions based on Callaway’s model [6] where higher frequency phonons generally have a smaller lifetime and therefore participate more in diffusive transport mechanisms. The longer lifetimes of optical modes enable these modes to carry a significant proportion of phonon thermal energy. In fact, in contrast to the marginal role optical phonons play in thermal transport in atomic crystals, optical phonons in the molecular crystal αRDX contribute 63-78% of the total thermal conductivity.

References

[1] A. A. Maradudin and A. E. Fein, "Scattering of Neutrons by an Anharnmnic Crystal," *Physical Review, *vol. 128, no. 6, pp. 2589-2608, Dec 1962.

[2] A. A. Maradudin, A. E. Fein and G. H. Vineyard, "On the evaluation of phonon widths and shifts," *physica status solidi (b), *vol. 2, no. 11, pp. 1479-1492, 1962.

[3] J. M. Larkin and A. J. H. McGaughey, "Predicting alloy vibrational mode properties using lattice dynamics calculations, molecular dynamics simulations, and the virtual crystal approximation," *Journal of Applied Physics, *vol. 114, no. 2, p. 3507, 2013.

[4] T. Feng and X. Ruan, "Quantum mechanical prediction of four-phonon scattering rates and reduced thermal conductivity of solids," *Phys. Rev. B, *vol. 93, no. 4, p. 5202, Jan 2016.

[5] L. Lindsay, D. A. Broido and N. Mingo, "Lattice thermal conductivity of single-walled carbon nanotubes: Beyond the relaxation time approximation and phonon-phonon scattering selection rules," *Phys. Rev. B, *vol. 80, no. 12, p. 5407, Sep 2009.

[6] J. Callaway, "Model for Lattice Thermal Conductivity at Low Temperatures," *Phys. Rev., *vol. 113, no. 4, p. 1046, Feb 1959.

**4:15 PM - QN04.08.03**

__Hao Ma__

^{1},Zhiting Tian

^{1}

^{1}

Kevlar (polyparaphenylene terephthalamide) and PBDT (poly(2,29-disulfonyl-4,49-benzidine terephthalamide))-derivatives have very similar chemical structures with aromatic rings. In this study, thermal conductivities of their single chains were calculated using molecular dynamics simulations. Chain rotation was found to be the key to reducing thermal conductivity. By introducing a new chain rotation factor (CRF), we can easily quantify the chain rotation level of single-chain polymers. We demonstrated that thermal conductivity decreases as the CRF increases. We performed further calculations on phonon properties and unveiled that the small thermal conductivity led by large chain rotation can be attributed to reduced phonon group velocities and shortened phonon mean free paths. Insights obtained in this study can be used for tuning the thermal conductivity of various polymers and facilitating their various applications including thermal energy conversion and management.

**4:30 PM - *QN04.08.04**

__Zuyuan Wang__

^{1},George Fytas

^{1,2}

^{1},IESL-FORTH

^{2}

Nanostructured materials hold promises for a wide range of applications. For example, they could be used as drug delivery carriers, novel coating ingredients, and interfacial fillers. The realization of these applications, however, relies on a good understanding of the thermomechanical properties (e.g., glass transition temperature, elasticity) of the nanomaterials, which could deviate from those of their bulk counterparts due to effects like an increased surface-area/volume ratio and spatial confinement. As a non-contact, non-destructive technique, Brillouin light scattering (BLS) spectroscopy provides unique characterizations of the thermomechanical properties of nanostructured materials via the resolution of hypersonic phonons. In this contribution, three recent applications of BLS will be presented. First, BLS is employed to study core-shell polymer based colloids. The observed nanoparticle vibrational modes provide a direct probe of the particle surface mobility, revealing the critical role of the shell architecture on the glass transition temperature and elasticity of the nanoparticles. Second, BLS is applied to “disentangle” the role of chain conformation (e.g., grafting density, degree of polymerization) on the mechanical properties of thin films of polymer tethered particle (particle-brush) materials with different grafting density and chain length. The bulk modulus, determined based on the BLS-detected sound velocities, shows a maximum in intermediate to low grafting density systems, where the hard (silica) cores are partially exposed due to the conformational fluctuations of the grafted (polystyrene) polymer chains. Third, BLS is utilized to understand the effect of confined polymer layers on the effective mechanical properties of hybrid materials composed of alternating polyvinylpyrrolidone (PVP) and hectorite nanolayers. The clear resolution of the direction-dependent quasi-longitudinal, quasi-transverse, and pure-transverse phonon modes from BLS leads to the determination of the full elastic tensor of the materials by assuming them to be transversely isotropic; materials with thinner PVP layers (i.e., stronger confinement) exhibit higher Young’s moduli in the directions parallel and perpendicular to the layers. These studies demonstrate BLS as an effectiveness tool for studying the thermomechanical properties of nanostructured materials. The results improve our understanding of the structure-property relation in the three material systems, and contribute to realizing their applications through guided engineering.

### Symposium Organizers

**8:30 AM - *QN04.09.01**

__David Flannigan__

^{1},Daniel Cremons

^{1},Daniel Du

^{1},Alyssa McKenna

^{1},Dayne Plemmons

^{1},Yichao Zhang

^{1}

^{1}

Development of ultrafast electron and X-ray scattering methods has enabled direct routes to probing atomic-scale structural dynamics in myriad chemical and materials systems [1,2]. This in turn has led to new physical insights into molecular and crystal-lattice responses associated with chemical-bond dynamics, phase transformations, electron-lattice correlations, and nanoscale structural motion. Importantly, the detailed nature of materials responses are likely influenced by ever-present lattice discontinuities and nanoscale morphological features. Thus, direct probing of the localized structural dynamics would provide a richer, more detailed picture of the overall evolution of ultrafast energy deposition and transport. Here, I will discuss how fs electron imaging with an ultrafast electron microscope (UEM) [3] can be used to directly visualize specific coherent, low-frequency acoustic-phonon dynamics in a variety of materials, with particular emphasis placed on resolving the influence of lattice discontinuities. After a brief overview of the instrumentation and the general experimental approach, I will describe how the concepts of static, real-space imaging with conventional electron microscopes can be used to visualize local coherent lattice oscillations in crystalline materials. Once described, these concepts will aid in understanding a number of photoinduced phonon behaviors we have observed in transition metal dichalcogenides (TMDs) and thin crystals of archetypal semiconductors [4-7]. For example, in TMDs (WSe_{2}, MoS_{2}, and TaS_{2}) we have found that fs photoexcitation leads to the generation of coherent phonon wavetrains preferentially at vacuum-crystal interfaces and extended crystal step edges. This arises *via* an initial impulsive expansion along the *c*-axis van der Waals stacking direction occurring within the first few picoseconds after ultrafast excitation. This impulsive *interlayer* expansion induces the launch of coherent *intralayer* phonon wavefronts due to the picosecond development of a phase mismatch between the neighboring layers owing to varying total transit times of the speed-of-sound *c*-axis phonons between the outer layers. As with the stacking direction, the coherent intralayer modes propagate at the speed of sound (*e.g.*, 5 nm/ps) and initially along a single wavevector oriented perpendicular to the defect nucleation sites prior to the first scattering events. Similarly, in strongly-photoexcited thin crystals of undoped Ge, we directly image a variety of spatially and temporally heterogeneous effects; including the launch of highly-coherent phonon wavefronts propagating with high phase velocities (observable up to 35 nm/ps with the UEM modalities employed), the significantly-delayed (*i.e.*, 10s of picoseconds or more) generation of phonon wavetrains relative to the precise moment of fs photoexcitation, and *time-varying* phase-velocity dispersions displaying single-exponential relaxation to the Ge bulk speed of sound (5 nm/ps) within one nanosecond following fs photoexcitation. This survey of recent results will serve to illustrate the rich and detailed information obtainable with fs electron imaging, with particular emphasis placed on the low-frequency modes highlighted here.

[1] A. M. Lindenberg, *et al.*, Annu. Rev. Mater. Res. **47**, 425 (2017).

[2] D. J. Flannigan and A. M. Lindenberg, MRS Bull. **43**, 485 (2018).

[3] D. A. Plemmons, *et al*., Chem. Mater. **27**, 3178 (2015).

[4] D. R. Cremons, *et al.*, Nature Commun. **7**, 11230 (2016).

[5] A. J. McKenna, *et al.*, Nano Lett. **17**, 3952 (2017).

[6] D. R. Cremons, *et al.*, Struct. Dyn. **4**, 044019 (2017).

[7] D. R. Cremons, *et al.*, Phys. Rev. Mater. **1**, 073801 (2017).

**9:00 AM - QN04.09.02**

__Geoffrey Wehmeyer__

^{1,2},Karen Bustillo

^{3},Andrew Minor

^{3,1},Chris Dames

^{1,3}

^{1},Rice University

^{2},Lawrence Berkeley National Laboratory

^{3}

Scanning transmission electron microscopy (STEM) thermometry techniques open new possibilities for mapping temperature (T) with high spatial resolution. Existing STEM thermometry methods based on measuring thermally-induced strains must contend with small thermal expansion coefficients (<10 parts per million (ppm)/K) for some materials, as well as potentially non-local relationships between strain and temperature. In contrast, the well-known mechanism of thermal diffuse scattering (TDS) offers promise for inherently local T measurements, and Debye-Waller theory predicts that many materials should display large temperature coefficients (>1000 ppm/K) at room temperature and above. This T-dependent TDS has not been leveraged for STEM thermometry, however, because the Debye-Waller effect on the Bragg peak intensity is overwhelmed by the effects of thermal tilts and thermal drift.

Here, we demonstrate quantitative TDS measurements using STEM by measuring the diffuse background intensity (rather than the Bragg peak intensity) in energy-filtered scanning electron nanodiffraction patterns. Applying virtual apertures to these diffraction patterns during post-processing allows us to quantify the T-dependent TDS in the diffuse background between the Bragg spots; previous TEM work (with the beam in flood mode) showed that this diffuse signal is relatively insensitive to thermal tilts and drift. Using this diffuse signal, we measure a position-averaged temperature coefficient of 2400±400 ppm/K for a single-crystal gold film averaged between T=100 K and T=300 K, and compare our results with the predictions of Debye-Waller theory. The measurements display typical temperature uncertainties of 8 K and temperature sensitivities of 51 K Hz^{-1/2}. This TDS-based STEM thermometry demonstration provides a step towards the goal of non-contact nanoscale temperature mapping of thin nanostructures or microelectronics.

**9:15 AM - QN04.09.03**

__Begona Abad Mayor__

^{1},Joshua Knobloch

^{1},Travis Frazer

^{1},Jorge Nicolas Hernandez Charpak

^{1},Hiu Yan Cheng

^{2},Alex Grede

^{2},Andrew Glaid

^{2},Noel Giebink

^{2},Tom Mallouk

^{2},Pratibha Mahale

^{2},Weinan Chen

^{2},Yihuang Xiong

^{2},Ismaila Dabo

^{2},Vincent Crespi

^{2},Disha Talreja

^{2},Venkat Gopalan

^{2},John Badding

^{2},Henry Kapteyn

^{1},Margaret Murnane

^{1}

^{1},The Pennsylvania State University

^{2}

Nanoscale phononic metamaterials make it possible to engineer the thermal, magnetic, and electronic properties of materials, which is essential for nanoelectronics, thermoelectric and data storage devices, or nanoparticle-mediated thermal therapies [1]. Specifically, nanoscale metalattices are a powerful bottom-up approach to tune the propagation of high frequency phonons - highly ordered nanoscale opal templates allow for precise control over nanoscale structure in which different materials can be infiltrated. Moreover, these metamaterials can be organized into hierarchical structures on length scales from nanometers to micrometers which enable unique properties that cannot be accessed using bulk/layered materials [2,3]. In the case of nanoscale thermal transport, metalattices are a powerful approach to further advance our understanding, which is critical since macroscopic diffusive models completely break down at dimensions that are comparable to the mean free path of the heat carriers [4,5]. However, characterizing energy flow in these metalattices is extremely challenging. Most current techniques rely on visible light, which is limited in wavelength to probing heat flow away from nanostructures >100s of nanometers. We can overcome this limitation by utilizing coherent extreme ultraviolet (EUV) light generated by tabletop high harmonic generation (HHG) [6]. The short pulse duration (≈10fs) and wavelength (≈30nm) of tabletop HHG sources are an excellent match for probing the intrinsic length- and time-scales relevant to nanoscale dynamics. In this unique EUV nanometrology technique, we use an ultrafast 800nm femtosecond laser to impulsively heat periodic arrays of nickel nanolines deposited on top of a silicon metalattice. We then probe the cooling of the nanolines, and the resulting thermal transport properties of the metalattice, by monitoring the thermally-induced surface deformation using coherent EUV light. In this work, we show how the thermal transport in silicon metalattices is modified due to the metalattice structure. First, we observe a slow thermal decay of the nanolines through the metalattice, suggesting very low thermal conductivity of the metalattice. Further analysis indicates that, not only do these metalattices have lower thermal conductivity than expected from macroscopic predictions, but that the heat flow is a function of the geometry of the heat sources. In addition, these findings are supported by equilibrium Green–Kubo atomistic simulations which show that silicon metalattices are capable of significantly reducing the thermal conductivity below the prediction of continuum models. This suggests that nanostructured metalattices may be able impede heat flow even more than had been initially thought. The ability to impede the flow of phonons, while allowing electrical current to flow, can dramatically impact applications such as optimized thermoelectric materials, as well as providing routes for enhanced functionality of other nanodevices.

[1] Maldovan, M., Nature **503**, 209–217 (2013).

[2] Liu, Y. et al., Nano Lett. **18**(1), 546-552 (2018).

[3] Han, J.E. et al. Phys. Rev. Lett. **86**(4), 696-699 (2001).

[4] M. E. Siemens et al., Nat. Mater., **9**(1), 26–30 (2010).

[5] K. M. Hoogeboom-Pot et al., Proc. Natl. Acad. Sci., **112**(16), 4846–4851 (2015).

[6] A. Rundquist et al., Science **280 **(5368), 1412–1415 (1998).

**9:30 AM - *QN04.09.04**

__David Reis__

^{1}

^{1}

The ultrashort pulse duration and high brightness of x-ray free-electron lasers (XFEL) enables high-resolution measurments of lattice dynamics in the time-domain. Here I will present recent femtosecond optical pump and hard x-ray probe XFEL-based experiments and describe how we can obtain information about phonon dynamics spanning the entire Brillouin zone without the use of high-resolution monochromators or crystal analyzers [1]. Such time domain experiments are begining to yield important information on the excited-state phonon dispersion, as well as electron-phonon and phonon-phonon coupling. In particular, I will focus on two recent experiments. In the first experiment [2], we measure phonon dynamics along the Γ-X direction in photoexcited PbTe and demonstrate that the ferroelectric instability is driven by electron-phonon interactions. In the second experiment [3] we measure mode-dependent anharmonic decay channels of the coherent A1g phonon in photo-excited bisumth to pairs of high-wavevector acoustic modes. We extract coupling constants that are within an order of magnitude of first-principles-based calculation.

This work was primarily supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences through the Division of Materials Sciences and Engineering under Contract No. DE-AC02-76SF00515. Measurements were carried out at the Linac Coherent Light Source, a national user facility operated by Stanford University on behalf of the U.S. Department of Energy, Office of Basic Energy Sciences.

[1] M. Trigo, M. Fuchs, J. Chen, M. P. Jiang, M. Cammarata, S. Fahy, D. M. Fritz, K. Gaffney, S. Ghimire, A. Higginbotham, S. L. Johnson, M. E. Kozina, J. Larsson, H. Lemke, A. M. Lindenberg, G. Nd- abashimiye, F. Quirin, K. Sokolowski-Tinten, C. Uher, G. Wang, J. S. Wark, D. Zhu, and D. A. Reis. Fourier-transform inelastic x-ray scattering from time- and momentum-dependent phonon-phonon correlations. Nat. Phys, 9(12):790–794, 2013.

[2] M. P. Jiang, M. Trigo, I. Savic, S. Fahy, E. D. Murray, C. Bray, J. Clark, T. Henighan, M. Kozina, M. Chollet, J. M. Glownia, M. C. Hoffmann, D. Zhu, O. Delaire, A. F. May, B. C. Sales, A. M. Lindenberg, P. Zalden, T. Sato, R. Merlin, and D. A. Reis. The origin of incipient ferroelectricity in lead telluride. Nat. Commun, 7:12291, 07 2016.

[3] S. W. Teitelbaum, T. Henighan, Y. Huang, H. Liu, M. P. Jiang, D. Zhu, M. Chollet, T. Sato, E. D. Murray, S. Fahy, S. O’Mahony, T. P. Bailey, C. Uher, M. Trigo, and D. A. Reis. Direct measurement of anharmonic decay channels of a coherent phonon. Phys. Rev. Lett., 121:125901, 2018.

**10:00 AM -**

**10:30 AM - *QN04.10.01**

__Christian Carbogno__

^{1},Florian Knoop

^{1},Thomas Purcell

^{1},Matthias Scheffler

^{1}

^{1}

The vibrational thermal conductivity of solid materials is determined by anharmonic effects, i.e., by features of the potential-energy surface (PES) that are not captured by a harmonic second-order Taylor expansion. However, only the leading contribution to anharmonicity (the third-order term in the Taylor expansion of the PES) is accounted for in typical, perturbative first-principles calculations of thermal conductivities [1]. Higher-order terms are neglected in these models, in spite of the fact that such strong anharmonic effects are known to play a decisive role in many technologically relevant materials, e.g., perovskites [2].

In this work, we discuss the *ab initio *Green-Kubo method [3], which we have developed for the computation of thermal conductivities in strongly anharmonic materials, and present applications of this method for characteristic material-science questions. In this formalism, the full PES is explored via equilibrium *ab initio* molecular dynamics (AIMD), so to account for **all** anharmonic effects. The thermal conductivity is evaluated via the Green-Kubo equations [4] using a unique first-principles definition of the heat flux [3]. By this means, incoherent and strongly anharmonic effects are directly treated within the real-space AIMD. Coherent, almost harmonic processes are mapped into a reciprocal-space representation [5], so to overcome finite time and size effects. This robust, asymptotically exact extrapolation scheme allows to obtain accurate bulk thermal conductivities – both for strongly anharmonic materials and for very harmonic materials. This is demonstrated for various representative examples with increasing degree of complexity and anharmonicity (e.g. Si, Ga_{2}O_{3}, ZrO_{2}, and perovskites). These investigations reveal that a correct treatment of higher-order anharmonicity plays a minor role in good thermal conductors, but is essential to achieve quantitative predictions and qualitative insights in highly anharmonic systems [6]. Eventually, we critically discuss strategies to apply the developed formalism in a computationally efficient fashion in high-throughput frameworks, e.g., to search for strongly anharmonic materials with ultra-low thermal conductivities.

[1] D. A. Broido, *et al.*, *Appl. Phys. Lett.* **91**, 231922 (2007).

[2] A. Marronnier, *et al.*, *ACS Nano* **12**, 3477 (2018).

[3] C. Carbogno, R. Ramprasad, and M. Scheffler, *Phys. Rev. Lett.* **118**, 175901 (2017).

[4] R. Kubo, M. Yokota, and S. Nakajima, *J. Phys. Soc. Japan* **12**, 1203 (1957).

[5] A. McGaughey and M. Kaviany, *Phys. Rev. B* **69**, 094303 (2004).

[6] C. Carbogno, *et al.*, *Phys. Rev. B* **90**, 144109 (2014).

**11:00 AM - QN04.10.02**

_{2}and AgCrSe

_{2}

__Olivier Delaire__

^{1},Jennifer Niedziela

^{2},Dipanshu Bansal

^{1},Andrew May

^{2},Jingxuan Ding

^{1},Tyson Lanigan-Atkins

^{1},Georg Ehlers

^{2},Doug Abernathy

^{2},Ayman Said

^{3}

^{1},Oak Ridge National Laboratory

^{2},Argonne National Laboratory

^{3}

Superionic crystals exhibit ionic mobilities comparable to liquids while maintaining a periodic crystalline lattice. The atomic dynamics leading to large ionic mobility have long been debated. A central question is whether phonon quasiparticles -which conduct heat in regular solids- survive in the superionic state, where a large fraction of the system exhibits liquid-like behavior. Here we present the results of energy- and momentum-resolved scattering studies combined with first-principles calculations and show that in the superionic phase of CuCrSe_{2} and AgCrSe_{2} long-wavelength acoustic phonons capable of heat conduction remain largely intact, whereas specific phonon quasiparticles dominated by the Cu or Ag ions break down as a result of anharmonicity and disorder. The weak bonding and large anharmonicity of the Cu / Ag sublattice are present already in the normal ordered state, resulting in low thermal conductivity even in the normal phase, at temperatures below the superionic transition. Further, we find a strong repulsion between Cu / Ag neighbors, affecting the diffusion mechanism. These results show how anharmonic phonon dynamics are at the origin of low thermal conductivity and superionicity in this class of materials. Our studies of atomic dynamics and diffusion will help rationalize the emergence of ultralow thermal conductivity for thermoelectrics and facilitate the design of high-performance solid-state electrolytes for next-generation batteries.

[1] J. L. Niedziela*, D. Bansal*, A. F. May, J. Ding, T. Lanigan-Atkins, G. Ehlers, D. L. Abernathy, A. Said & O. Delaire, “Selective Breakdown of Phonon Quasiparticles across Superionic Transition in CuCrSe2”, Nature Physics (2018). https://doi.org/10.1038/s41567-018-0298-2

**11:15 AM - QN04.10.03**

__Ming Hu__

^{1}

^{1}

Materials in partial-crystalline partial-liquid (PCPL) state are now widely used as thermoelectrics [Cu_{2}Se; PRL 118, 145901 (2017), PNAS 111, 15031 (2014), Nature Mater. 11, 422 (2012)] and battery electrodes [LiSi; Nano Energy 18, 89 (2015)], due to their low thermal conductivity and high ionic conductivity, respectively. However, the well-developed computational methods for pure crystalline materials such as anharmonic lattice dynamics coupled with Boltzmann transport equation cannot be straightforwardly used to study such systems. By performing first-principles and molecular dynamics simulations, for the first time we give a robust and detailed explanation of the thermal transport mechanism in PCPL material Li_{2}S. At the temperature range in which the system can be regarded as a solid, the large hopping of Li is found to be responsible for phonon thermal conductivity’s deviation from the traditional 1/*T* relationship. At the high temperature range, the contribution of convection and liquid-phonon interaction increase significantly due to the fluidization of Li ions. Furthermore, there is an interplay between the enhanced phonon scattering and the increased force hopping between neighboring atoms as temperature arises, which results in a dip in the evolution of the virial term around 1200K. When the temperature is higher than 1200 K, the virial thermal conductivity increases with temperature due to the contribution of vibrations with extremely short mean free path (i.e., diffusons). This point is validated by the evolution of the accumulative thermal conductivity with mean free path. At 1300 K, more than 46% of the heat carried by the S sublattice is contributed by the carriers with mean free path smaller than a few angstroms, which is the typical hopping distance. Our study provides a clear physical map of the heat transport in phase change materials and describes the key mechanisms to guide the design of the future thermoelectric materials and battery electrodes.

**11:30 AM - QN04.10.04**

__Djordje Dangic__

^{1,2},Olle Hellman

^{3},Eamonn Murray

^{4},Stephen Fahy

^{1},Ivana Savic

^{2}

^{1},Tyndall National Institute

^{2},California Institute of Technology

^{3},Imperial College London

^{4}

GeTe is a well-known thermoelectric material with low lattice thermal conductivity which undergoes a ferroelectric phase transition around 700 K. Using standard first principles calculations, we have shown that the lattice thermal conductivity of PbGeTe alloys could be further suppressed by driving them closer to the phase transition with varying chemical composition [1]. Here we investigate how this phase transition affects the thermal expansion and the lattice thermal conductivity of GeTe using recently developed first principles methods that account for higher-than-third order anharmonicity [2,3]. We find that GeTe exhibits negative thermal expansion near the phase transition [2]. This is caused by strong acoustic-soft optical mode coupling [2], which is also responsible for the low lattice thermal conductivity of PbGeTe alloys [1]. Surprisingly, our calculations in the framework of temperature dependent effective potentials [3] show an anomalous increase of the lattice thermal conductivity of GeTe at the phase transition. We elucidate the connection between the unexpected conductivity increase and strong anharmonicity.

[1] R. M. Murphy, E. D. Murray, S. Fahy, and I. Savic, Phys. Rev. B 95, 144302 (2017)

[2] D. Dangic, A. R. Murphy, E. D. Murray, S. Fahy, and I. Savic, Phys. Rev. B 97, 224106 (2018)

[3] O. Hellman, P. Steneteg, I. A. Abrikosov, and S. I. Simak, Phys. Rev. B 87, 104111 (2013)

**11:45 AM - QN04.10.05**

_{3}Thin Films

__Dipanjan Saha__

^{2},Alexandros Sarantopoulos

^{1},Weeliat Ong

^{2},Jonathan Malen

^{2},Francisco Rivadulla

^{1}

^{1},Carnegie Mellon University

^{2}

SrTiO_{3}, a well-studied incipient ferroelectric material, has been shown to become ferroelectric in certain conditions of strain and temperature, but the effect on its thermal conductivity is unknown. We present measurements of thermal conductivity in Nb doped SrTiO_{3} thin films from 80 K to 300 K. Thermal measurements are conducted using Frequency Domain Thermoreflectance on films deposited via Pulsed Laser Deposition on LSAT, STO, and DyScO_{3} substrates, which impose 0.95 % compressive strain, no strain, and 1.15% tensile strain, respectively.

We measure a large difference in thermal conductivity between the three substrate imposed strains, where compressive strain results in a 3-fold enhancement to thermal conductivity relative to tensile strain at room temperature. We also observe a greater than 60% reduction in thermal conductivity of the tensioned film as we reduce temperature and it becomes fully ferroelectric. Piezoresponsive Force Microscopy measurements are conducted to investigate the role of ferroelectric domain boundaries as a mechanism for the reduction in thermal conductivity in the ferroelectric phase; where ferroelectric domain boundaries serve as scattering sites for phonon transport. These results are critical to memristor and microwave applications that demand ferroelectric materials, because thermal effects play a major role in performance.

**1:30 PM - *QN04.11.01**

__Asegun Henry__

^{1}

^{1}

Over the last decade, a new method has been developed that allows for the detailed study of phonon transport in crystalline solids using first principles methods, such as density functional theory. This approach is powerful, because not only does it exhibit excellent agreement with experiments consistently, it is also capable of predicting the properties of new materials and also explaining anomalous behaviors in some materials. This approach, which is usually based on an expression derived using Fermi’s Golden Rule, however, rather implicitly relies on application of what is often termed the phonon gas model (PGM). The PGM is valid and accurate for pure crystalline solids, which do in fact make up a wide range of the materials of interest for applications. However, there is a growing body of evidence that shows that when one deviates far from an idealized perfect crystal e.g., by introducing randomly distributed defects, alloying elements, interstitials or an interface, the PGM often fails. This is because the shape/character of phonons changes when symmetry is broken and as a result, alloys, amorphous materials and interfaces remain a difficult challenge to describe with the accuracy and predictive capability of first principles.

It is in this respect that molecular dynamics (MD) can play an important role, as it in theory has the ability to fill this gap, since it can be rather ubiquitously applied to any class of solid or molecule with full inclusion of anharmonicity, provided that an accurate empirical potential exists to describe the interatomic interactions. Over the last decade several new methods have been developed that allow for direct calculation of the contributions to thermal conductivity and thermal interface conductance, but the key issue that has been challenging to overcome is still the development of accurate empirical potentials to describe the interatomic interactions. This talk will review recent progress that has been made on this issue, and will outline a potential procedure for how one can utilize first principles calculations to inform empirical potentials that are both fast and accurate (i.e., less than 5% error in forces) consistently for virtually any material where phonons are present. The key is to exploit the fact that phonons are only well defined when all of the atoms vibrate about an equilibrium site i.e., there is no diffusion of atoms or chemical reactions occurring during the MD simulation. Treating this as an implicit constraint, it is possible to use a functional form that accurately reproduces the interactions described by first principles calculations, yet is much faster than machine learned potentials. This talk will provide an overview of this approach and will show initial results for example materials – illustrating for the first time an empirical potential that exhibits less than 5% error in forces, less than 5% errors in dispersion and thermal conductivity, yet can also be used to run stable MD simulations with speed faster than commonly employed potentials such as the Tersoff potential.

**2:00 PM - QN04.11.02**

__Holden Parks__

^{1},Venkat Viswanathan

^{1},Alan McGaughey

^{1}

^{1}

Density functional theory (DFT) is an ab-initio method that has been successfully used to predict the thermal properties, such as the phonon dispersion and thermal conductivity, of a variety of insulating and semiconducting materials. DFT-based calculations are attractive because, unlike calculations based on empirical potentials, they are free from fitting parameters. A DFT calculation is made computationally tractable by describing the complicated exchange-correlation (XC) electron interactions with an effective potential, called an XC functional. There is no a priori method of choosing an XC functional, so that choosing any single XC functional introduces uncertainty in any quantity derived from that calculation.

We present a robust method for quantifying uncertainty in phonon dispersions and harmonic vibrational properties from DFT-based calculations using the BEEF-vdW XC functional. The procedure involves manually displacing atoms in an equilibrium structure and using the energies of these perturbed structures to determine harmonic force constants. Rather than generate a single energy for each perturbed lattice, BEEF-vdW generates an ensemble of energy values as a computationally efficient post-processing step by perturbing the XC functional parameters and solving for the energy of the system non-self consistently. Thus, each perturbed lattice yields an ensemble of energy values. This collection of energy ensembles are then used to determine an ensemble of force constants, which are used as input to a harmonic lattice dynamics calculation. This procedure results in an ensemble of phonon frequencies whose spread can be used to quantify the uncertainty. Ensemble dispersion relations, heat capacities, and Gruneisen parameters are presented and compared to results predicted using the PBE, RPBE, and PBEsol XC functionals.

**2:15 PM - QN04.11.03**

__Jesse Maassen__

^{1}

^{1}

Understanding and controlling heat flow on the nanoscale, and through interfaces, is important for applications related to electronics, heat management and thermoelectrics. From a theoretical perspective, the traditional heat equation and Fourier’s law are widely-believed to fail when treating thermal transport on short time- and length-scales. There exists, however, a variety of beyond-Fourier approaches that accurately and rigorously describe nanoscale heat transport, including (among others) the atomistic Green’s function (AGF) method, molecular dynamics (MD), and the Boltzmann transport equation (BTE). Each method has its advantages, from how MD naturally captures anharmonic processes to how the AGF method can provide detailed mode-resolved transmission coefficients, and thus each has proven useful to study and identify important processes and physics.

Over the past few years, we have been working to develop and apply an alternative approach to phonon transport inspired from the lessons of electron transport, referred to as the McKelvey-Shockley (McK-S) flux method. In this talk, I will briefly introduce the McK-S flux method and focus on recent findings from the application of this method to nanoscale and interfacial phonon transport. In particular, the role of ballistic, non-equilibrium, and inelastic scattering effects, which are captured with McK-S, will be discussed. Moreover, I will show how this framework easily handles first-principles phonon dispersions and scattering rates. Owing to its relatively simple form, which promotes physical insights and efficient solutions, and its ability to seamlessly span from the nanoscale to the macroscale, we believe the McK-S method helps complement the existing suite of techniques.

**2:30 PM - *QN04.11.04**

*Ab Initio*Thermal Transport—From Phonon’s Lifetime to Thermal Conductivity

__Aleksandr Chernatynskiy__

^{1}

^{1}

*Ab initio* calculations of the thermal conductivity have become routine due to the availability of the several community codes that employ Boltzmann Transport Equation for phonons. An attractive feature of this method is that it gives access not only to the overall thermal conductivity but also to the specifics of the scattering processes for every phonon in the system. Thus, an incredible level of details is emerging which permits to test analytical theories, predict and explain thermal transport properties in a variety of situations or model systems with the additional phonon scattering mechanisms. In this presentation we will review the particulars of the methodology involved, will illustrate its power on the examples of technologically important materials and discuss the applicability of this technique at the limits of high temperature and pressure. To this end, we will consider thermal transport in natural superlattices, Ruddlesden-Popper phases of the SrTiO_{3} system, phonon lifetimes of the individual phonons in GaAs, and thermal transport in MgO, one of the main constituents of the Earth’s mantle. Results of the simulations will be compared to experiment, where available.

**3:00 PM -**

**3:30 PM - *QN04.12.01**

__Masahiro Nomura__

^{1},Roman Anufriev

^{1}

^{1}

We experimentally demonstrate formation of directional fluxes of ballistic phonons in one- and two-dimensional silicon phononic nanostructures, in which periodic arrays of nano-holes or corrugations formed directionality of the thermal phonons. This effect makes guiding and even focusing of heat fluxes possible in silicon nanostructures.

First, using micro time-domain thermoreflectance experiments and Monte Carlo simulations, we studied heat conduction in silicon thin films with aligned and staggered periodic arrays of holes. We found that a significant difference in thermal conductivity appears when the characteristic size of the structures becomes smaller than 100 nm and when the temperatures was decreased [1]. This difference was attributed to directional ballistic phonon fluxes that are formed by the aligned lattice of holes.

Next, we studied heat conduction in nanowires with periodic corrugations. Our simulations and experiments show similar directional fluxes in the corrugated nanowires, though the directionality is weaker [2]. Our analysis shows that the directionality depends on the width of the narrow passages and becomes stronger as the passage narrows [1].

Thus, such periodic phononic structures can be used to guide and emit ballistic phonons in solids. To demonstrate this, we coupled the emission from a two-dimensional phononic crystal into one-dimensional nanowires, in which the ballistic path of the phonons was continued in the direction parallel to the wire. Thus, we measured corresponding nanowire length and temperature dependencies [1].

Finally, we used this concept to create thermal lens nanostructures, which can focus thermal energy in the focal point. Our theoretical and experimental results suggest that the created hotspot is smaller than 200 nm in diameter, and thus can be used in biomedicine, thermoelectrics and wherever selective heating is required [1]. The efficiency of this approach is limited only by the scale and quality of the structures. Thus, as the advancements in nanofabrication technology enable further scaling down, complete control over directionality of ballistic heat fluxes in nanostructures becomes real in the near future.

[1] R. Anufriev, A. Ramiere, J. Maire, and M. Nomura, “Heat guiding and focusing using ballistic phonon transport in phononic nanostructures,” Nat. Commun. 8, 15505 (2017).

[2] R. Anufriev, S. Gluchko, S. Volz, and M. Nomura, “Quasi-ballistic heat conduction due to Lévy phonon flights in silicon nanowires, arXiv:1809.09808.

**4:00 PM - QN04.12.02**

__Naoki Tambo__

^{1},Chun Zhou

^{2},Elizabeth Ashley

^{2},Yuxuan Liao

^{3},Kouhei Takahashi

^{1},Naito Yasuyuki

^{1},Junichiro Shiomi

^{3},Paul Nealey

^{2}

^{1},The University of Chicago

^{2},The University of Tokyo

^{3}

Recent progress in phonon engineering has revealed the effectiveness of nanotechnology on controlling the thermal transport properties of crystalline materials. However, the impact of nanostructuring on amorphous materials has not been examined thoroughly so far. This is surprising given that amorphous materials play a significant role as crystalline materials in various electronic devices. Understanding the thermal transport mechanism of amorphous materials and elucidating the impact of nanostructuring would be highly essential for thermal management of future electronic devices.

Here, we have studied the impact of ultrafine nanostructuring on the thermal transport properties of amorphous SiN* _{x }*membranes. Samples examined here are SiN

_{x}phononic crystals (PnCs) with two-dimensional array of through-holes created at various pitch sizes ranging from 38-1600 nm. Electron beam lithography was used to fabricate SiN

_{x}PnCs at pitch sizes above 60 nm. On the other hand, directed self-assembly lithography was used to fabricate ultrafine 38 nm-pitch PnCs. Room temperature thermal conductivity

*κ*of the SiN

_{x}PnCs were measured by a time-domain thermal reflectance method. We found that

*κ*of SiN

_{x}strongly depends on the minimum feature size and the surface-to-volume (S/V) ratio of the PnC structure. PnCs at typical pitch sizes of 100-1600 nm whose minimum feature size exceeds 30 nm exhibited

*κ*> 2.0 W/mK, which was comparable to that of the unpatterned membranes (

*κ*= 2.5 W/mK). On the other hand, a significant reduction in

*κ*was observed when the minimum feature size of the PnCs decreased below 30 nm. In these ultrafine PnCs, we found that the reduction in

*κ*is associated with increase in the S/V ratio. This is consistent with the feature reported in crystalline PnCs where diffuse boundary scattering of phonons is enhanced for those that exhibit higher S/V ratios. Recent studies have implied that heat transport in amorphous materials is governed by two types of vibrational modes, i.e., (i) low-frequency propagating modes called propagons with relatively long mean free path (MFP) and (ii) high-frequency diffusive mode called diffusons with extremely short MFP. The S/V ratio dependence of

*κ*observed here indicates that reduction in

*κ*of the present SiN

_{x}PnCs is related to enhanced boundary scattering of these propagating modes. Interestingly, we also found that increase in S/V ratio over 0.1 nm

^{-1}does not lead to reduction in

*κ*of SiN

_{x}below 1.1 W/mK. This implies that contribution of propagon to heat transport has been suppressed thoroughly by our ultrafine PnC structure, leaving only the diffusons to contribute to heat transport. The present study on amorphous SiN

_{x}PnCs demonstrate the effectiveness of multi-scale phonon engineering on material heat transport properties, where we control the high-frequency vibrational modes by the amorphous disorder while that of the low-frequency vibrational modes is controlled by intentional nanostructuring.

**4:15 PM - QN04.12.03**

__Shunta Harada__

^{1,2},Naoki Kosaka

^{1},Takashi Yagi

^{3},Katsushi Tanaka

^{4},Haruyuki Inui

^{5},Miho Tagawa

^{1},Toru Ujihara

^{1,3}

^{1},JST PRESTO

^{2},National Institute of Advanced Industrial Science and Technology

^{3},Kobe University

^{4},Kyoto University

^{5}

Homologous series of the Magnèli phase titanium oxides (Ti* _{n}*O

_{2n-1}) are reduced phases of rutile-type TiO

_{2}and are so-called crystallographic shear structures, in which dense planar faults are periodically introduced in the mother rutile structure with their spacing depending on the oxygen deficiency. Due to the low thermal conductivity owing to dense planar defects and tunability of their structures, the Magnèli phases received great attention to the application of thermoelectric materials. Recently, suppression and control of thermal conduction by a phononic crystal with periodic nanostructure fabricated by lithography, in which the interference of low-frequency phonons occurs, was demonstrated. Similar to the phononic crystal, it is considered that the periodic atomic scaled structure in the Magnèli phases suppresses the thermal conduction of high-frequency phonons, which would lead to the heat manipulation at room temperature. In the present study we investigated the structural perfection of an ordered arrangement of planar defects as well as the thermal conduction in the Magnèli phase titanium oxide.

The crystal of the Magnèli phase titanium oxide were prepared by the reduction annealing of rutile-type TiO

_{2}in vacuo. We observed the (132)

_{rutile}planar faults were periodically introduced with an interval of 2.9 nm in the prepared crystal. The perfection of the periodic arrangement of the planar faults are very high and the periodicity disorder was evaluated to be as small as 0.036 nm by scanning transmission electron microscopy observation in atomic scale. Furthermore, the structure perfection of the planar faults was also high, and the roughness of planar faults were evaluated to be 0.0035 nm. From the specularity parameter calculation using these evaluated values, the periodic arrangement of the planar faults is expected to behave as specular interface for phonons up to 16 THz. Time-dominant thermoreflectance (TDTR) measurements revealed that thermal conductivity is decreased by the introduction of the periodic arrangements of the planar faults. Compared to the rutile-type TiO

_{2}, the temperature dependence of the thermal conductivity for the Magnèli phase titanium oxide was small. The analysis of the temperature dependences of thermal conductivity by the Debye-Callaway model indicates that the increase of Umklapp scattering is caused by the introduction of the periodic planar faults. The Considering the structural perfection of the periodic arrangement of the planar faults, the fold of the Brillouin zone would result in the increase in the Umklapp scattering.

**4:30 PM - QN04.12.04**

__Yuxuan Liao__

^{1},Naoki Tambo

^{2},Kouhei Takahashi

^{2},Junichiro Shiomi

^{1}

^{1},Technology Innovation Division, Panasonic Corporation

^{2}

Heat in crystalline phononic crystals (c-PnCs) are carried by lattice vibrations (phonons). It is well known that thermal conductivity (*κ*) of c-PnCs can be reduced when the length scales of phononic structures are smaller than phonon mean free paths (the size effect), therefore, c-PnCs have been seen as an effective way to tune *κ* of crystalline materials [1]. Here, we theoretically show that amorphous phononic crystals (a-PnCs) can also play an important role for tuning *κ* for amorphous materials. Indeed, a large proportion of the heat carriers (atomistic vibration modes) in amorphous solids are diffusons, which are expected to have very short effective mean free paths that comparable to interatomic spacings and therefore can be hardly influenced by the size effect [2]. However, there still exist long-wave-length or low-frequency heat carriers (propagons), which propagate at the speed of sound, can have effective mean free paths exceeding tens of nanometers, and thus contribute to significant proportion of the total *κ*, despite their small density of states [3]. Therefore, it should be possible to tune *κ* by scattering propagons with phononic structures. To validate the above reasoning, we firstly prepared several a-PnCs samples for amorphous silicon, silica and silicon nitride, which are 70 nm thick 2D thin films with periodic cylindrical holes of different diameters. Then, the effective mean free paths of propagons and diffusons are obtained by combing Allen-Feldman theory and normal-mode decomposition method [3,4]. Boundary scattering effects for propagons and diffusons are evaluated by Monto Carlo Raytracing method [5]. The results show that *κ* of these a-PnCs can be as low as ~0.3 W/m K when the neck sizes between the holes reduced below 10 nm. The low *κ* suggests that a-PnCs can be used as an effect way for tuning thermal tra