Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films Including Contributions of Optical Phonons

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Arpit Mittal ◽  
Sandip Mazumder
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Monte Carlo ◽  
Heat Conduction ◽  
Phonon Scattering ◽  
Computational Domain ◽  
Optical Phonons ◽  
Phonon Modes ◽  
Silicon Thin Film ◽  
Silicon Thin Films

Abstract The Monte Carlo method has found prolific use in the solution of the Boltzmann transport equation for phonons for the prediction of nonequilibrium heat conduction in crystalline thin films. This paper contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions, in particular, optical phonons. A procedure to calculate three-phonon scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that transverse acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures (T>200 K), longitudinal acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes, especially at room temperature, where optical modes are found to carry about 25% of the energy at steady state in silicon thin films. Most importantly, it is found that inclusion of optical phonons results in better match with experimental observations for silicon thin-film thermal conductivity. The inclusion of optical phonons is found to decrease the thermal conductivity at intermediate temperatures (50–200 K) and to increase it at high temperature (>200 K), especially when the film is thin. The effect of number of stochastic samples, the dimensionality of the computational domain (two-dimensional versus three-dimensional), and the lateral (in-plane) dimension of the film on the statistical accuracy and computational efficiency is systematically studied and elucidated for all temperatures.

Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films: Role of Optical Phonons

2009 ◽  
Author(s):  
Arpit Mittal ◽  
Sandip Mazumder
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Monte Carlo ◽  
Heat Conduction ◽  
Optical Phonons ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Silicon Thin Film ◽  
Silicon Thin Films

The Monte Carlo (MC) method has found prolific use in the solution of the Boltzmann Transport Equation (BTE) for phonons for the prediction of non-equilibrium heat conduction in crystalline thin films. This paper contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions—in particular, optical phonons. A procedure to calculate scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that Transverse acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures (T > 200K), longitudinal acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes. At room temperature, optical modes are found to carry about 25% of the energy at steady state in Silicon thin films. Most importantly, inclusion of optical phonons results in better match with experimental observations for Silicon thin-film thermal conductivity.

Microscale Heat Conduction in Dielectric Thin Films

1993 ◽  
Vol 115 (1) ◽  
pp. 7-16 ◽  
Author(s):  
A. Majumdar
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Heat Flux ◽  
Heat Conduction ◽  
Radiative Transfer ◽  
Film Thickness ◽  
Heat Transport ◽  
Phonon Scattering ◽  
Fourier Law ◽  
Dielectric Thin Films

Heat conduction in dielectric thin films is a critical issue in the design of electronic devices and packages. Depending on the material properties, there exists a range of film thickness where the Fourier law, used for macroscale heat conduction, cannot be applied. This paper shows that in this microscale regime, heat transport by lattice vibrations or phonons can be analyzed as a radiative transfer problem. Based on Boltzmann transport theory, an equation of phonon radiative transfer (EPRT) is developed. In the acoustically thick limit, ξL ≫ 1, or the macroscale regime, where the film thickness is much larger than the phonon-scattering mean free path, the EPRT reduces to the Fourier law. In the acoustically thin limit, ξL ≪ 1, the EPRT yields the blackbody radiation law q = σ (T14 − T24) at temperatures below the Debye temperature, where q is the heat flux and T1 and T2 are temperatures at the film boundaries. For transient heat conduction, the EPRT suggests that a heat pulse is transported as a wave, which becomes attenuated in the film due to phonon scattering. It is also shown that the hyperbolic heat equation can be derived from the EPRT only in the acoustically thick limit. The EPRT is then used to study heat transport in diamond thin films in wide range of acoustical thicknesses spanning the thin and the thick regimes. The heat flux follows the relation q = 4σT3ΔT/(3ξL/4 + 1) as derived in the modified diffusion approximation for photon radiative transfer. The thermal conductivity, as currently predicted by kinetic theory, causes the Fourier law to overpredict the heat flux by 33 percent when ξL ≪ 1, by 133 percent when ξL = 1, and by about 10 percent when ξL increases to 10. To use the Fourier law in both ballistic and diffusive transport regimes, a simple expression for an effective thermal conductivity is developed.

Silicon Thin Film Thermal Conductivity in Ballistic and Diffusive Regimes Predicted by Molecular Dynamics

2005 ◽  
Author(s):  
Carlos J. Gomes ◽  
Marcela Madrid ◽  
Javier V. Goicochea ◽  
Cristina H. Amon
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Film Thickness ◽  
Interatomic Potential ◽  
Mean Free Path ◽  
Technical Conference ◽  
Silicon Thin Film ◽  
Silicon Thin Films ◽  
Out Of Plane

The thermal conductivity of silicon thin films is predicted in the directions parallel and perpendicular to the film surfaces (in-plane and out-of-plane, respectively) using equilibrium molecular dynamics, the Green-Kubo relationship and the Stillinger-Weber interatomic potential. Film thicknesses range from 2 to 220 nm and temperatures from 300 to 1000 K. In this range of temperatures, the relation between the phonon mean free path (Λ) and the film thickness (ds) spans from the ballistic regime (≫ ds) to the diffusive, bulk-like regime (≪ ds). We show that equilibrium molecular dynamics and the Green-Kubo relationship can be applied to the study of the thermal conductivity of thin films in the ballistic, transitional and diffusive regimes. When the film is thin enough, the thermal conductivity becomes orthotropic and decreases with decreasing film thickness as a consequence of the scattering of phonons with the film boundaries. The in-plane thermal conductivity follows the trend observed experimentally at 300 K. In the ballistic limit, in accordance with the kinetic theory, the predicted out-of-plane thermal conductivity varies linearly with the film thickness and is temperature-independent for temperatures near or above Debye’s temperature.   This paper was also originally published as part of the Proceedings of the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems.

Silicon Thin-Film Lattice Dynamics and Thermal Transport Properties

2012 ◽  
Author(s):  
Bruce L. Davis ◽  
Mehmet Su ◽  
Ihab El-Kady ◽  
Mahmoud I. Hussein
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Thermal Conductivity ◽  
Transport Properties ◽  
Lattice Dynamics ◽  
Dielectric Materials ◽  
Phonon Transport ◽  
Solid State Physics ◽  
Silicon Thin Film ◽  
Silicon Thin Films

Thin films composed of dielectric materials are attracting growing interest in the solid state physics and nanoscale heat transfer communities. This is primarily due to their unique thermal and electronic properties and their extensive use as components in optoelectronic, and potentially in thermoelectric, devices. In this paper, an elaborate study is presented on silicon thin films ranging from a few nanometers in thickness to very thick bulk-like thicknesses. Full lattice dynamics calculations are performed incorporating the entire film cross section and the relaxation of the free surfaces. The phonon properties emerging from these calculations are then incorporated into Holland-Callaway models to predict the thermal conductivity and other phonon transport properties. A rigorous curve fitting process to a limited set of available experimental data is carried out to obtain the scattering lifetimes. Our results demonstrate the importance of proper consideration of the full thin-film dispersion description and provide insights into the relationship between thermal conductivity, film thickness and temperature.

Assessment of Models for Extracting Thermal Conductivity From Frequency Domain Thermoreflectance Experiments

2020 ◽  
Author(s):  
Siddharth Saurav ◽  
Sandip Mazumder
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Frequency Domain ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Computational Domain ◽  
Fourier Heat Conduction

Abstract The Fourier heat conduction and the hyperbolic heat conduction equations were solved numerically to simulate a frequency-domain thermoreflectance (FDTR) experimental setup. Numerical solutions enable use of realistic boundary conditions, such as convective cooling from the various surfaces of the substrate and transducer. The equations were solved in time domain and the phase lag between the temperature at the center of the transducer and the modulated pump laser signal were computed for a modulation frequency range of 200 kHz to 200 MHz. It was found that the numerical predictions fit the experimentally measured phase lag better than analytical frequency-domain solutions of the Fourier heat equation based on Hankel transforms. The effects of boundary conditions were investigated and it was found that if the substrate (computational domain) is sufficiently large, the far-field boundary conditions have no effect on the computed phase lag. The interface conductance between the transducer and the substrate was also treated as a parameter, and was found to have some effect on the predicted thermal conductivity, but only in certain regimes. The hyperbolic heat conduction equation yielded identical results as the Fourier heat conduction equation for the particular case studied. The thermal conductivity value (best fit) for the silicon substrate considered in this study was found to be 108 W/m/K, which is slightly different from previously reported values for the same experimental data.

Phonon Conduction Normal to Polysilicon Films on Diamond

2013 ◽  
Author(s):  
Jungwan Cho ◽  
Pane C. Chao ◽  
Mehdi Asheghi ◽  
Kenneth E. Goodson
Keyword(s):  
Thermal Conductivity ◽  
Transport Theory ◽  
Phonon Scattering ◽  
Phonon Transport ◽  
Silicon Films ◽  
Silicon Thin Films ◽  
Transmission Electron ◽  
Crystal Films ◽  
Polysilicon Films ◽  
Polycrystalline Silicon Films

Silicon films of thickness near and below one micrometer play a central role in many advanced technologies for computation and energy conversion. Numerous data on the thermal conductivity of silicon thin films are available in the literature, but mainly for the in-plane thermal conductivity of polycrystalline and single-crystal films. Here we use picosecond time-domain thermoreflectance (TDTR), transmission electron microscopy, and phonon transport theory to investigate heat conduction normal to polycrystalline silicon films on diamond substrates. The data agree with predictions that account for the coupled effects of phonon scattering on film boundaries and defects concentrated near grain boundaries. Using the data and the model, we estimate the polysilicon-diamond interface resistance to be 6.5–8 m2 K GW−1.

scholarly journals Reduction of Lattice Thermal Conductivity in PbTe Induced by Artificially Generated Pores

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Jae-Yeol Hwang ◽  
Eun Sung Kim ◽  
Syed Waqar Hasan ◽  
Soon-Mok Choi ◽  
Kyu Hyoung Lee ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Pore Structure ◽  
Transport Properties ◽  
Thermoelectric Materials ◽  
Thermal Transport ◽  
Lattice Thermal Conductivity ◽  
Phonon Scattering ◽  
Phonon Modes ◽  
Thermal Transport Properties

Highly dense pore structure was generated by simple sequential routes using NaCl and PVA as porogens in conventional PbTe thermoelectric materials, and the effect of pores on thermal transport properties was investigated. Compared with the pristine PbTe, the lattice thermal conductivity values of pore-generated PbTe polycrystalline bulks were significantly reduced due to the enhanced phonon scattering by mismatched phonon modes in the presence of pores (200 nm–2 μm) in the PbTe matrix. We obtained extremely low lattice thermal conductivity (~0.56 W m−1 K−1at 773 K) in pore-embedded PbTe bulk after sonication for the elimination of NaCl residue.

Soluble polycyclosilane–polysiloxane hybrid material and silicon thin film with optical properties at 193 nm and etch selectivity

2015 ◽  
Vol 3 (2) ◽  
pp. 239-242 ◽  
Author(s):  
Sung Jin Park ◽  
Hyeon Mo Cho ◽  
Myong Euy Lee ◽  
Miyoung Kim ◽  
Kwenwoo Han ◽  
...  
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Optical Properties ◽  
Hybrid Materials ◽  
Hybrid Material ◽  
Silicon Thin Film ◽  
New Class ◽  
Silicon Thin Films ◽  
193 Nm

Silicon thin films that fulfil the needs of current semiconductor lithography were prepared from a new class of polycyclosilane–polysiloxane hybrid materials.

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