# First Principles Modeling of Phonon Heat Conduction in Nanoscale Crystalline Structures

## Abstract

The inability to remove heat efficiently is currently one of the stumbling blocks toward further miniaturization and advancement of electronic, optoelectronic, and micro-electro-mechanical devices. In order to formulate better heat removal strategies and designs, it is first necessary to understand the fundamental mechanisms of heat transport in semiconductor thin films. Modeling techniques, based on first principles, can play the crucial role of filling gaps in our understanding by revealing information that experiments are incapable of. Heat conduction in crystalline semiconductor films occurs by lattice vibrations that result in the propagation of quanta of energy called phonons. If the mean free path of the traveling phonons is larger than the film thickness, thermodynamic equilibrium ceases to exist, and thus, the Fourier law of heat conduction is invalid. In this scenario, bulk thermal conductivity values, which are experimentally determined by inversion of the Fourier law itself, cannot be used for analysis. The Boltzmann Transport Equation (BTE) is a powerful tool to treat non-equilibrium heat transport in thin films. The BTE describes the evolution of the number density (or energy) distribution for phonons as a result of transport (or drift) and inter-phonon collisions. Drift causes the phonon energy distribution to deviate from equilibrium,more »

- Authors:

- Publication Date:

- Research Org.:
- The Ohio State University, Columbus, OH

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 984336

- Report Number(s):
- DOE/ER/46330-1

TRN: US1204486

- DOE Contract Number:
- FG02-06ER46330

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGORITHMS; APPROXIMATIONS; BOLTZMANN EQUATION; DISCRETE ORDINATE METHOD; DISTRIBUTION; ENERGY SPECTRA; LATTICE VIBRATIONS; LIFETIME; MEAN FREE PATH; MINIATURIZATION; PHONONS; POLARIZATION; SCATTERING; SHAPE; SILICON; THERMAL CONDUCTIVITY; THERMODYNAMICS; THICKNESS; THIN FILMS; UMKLAPP PROCESSES; Thermal conductivity; phonon; nanoscale; crystalline material

### Citation Formats

```
Mazumder, Sandip, and Li, Ju.
```*First Principles Modeling of Phonon Heat Conduction in Nanoscale Crystalline Structures*. United States: N. p., 2010.
Web. doi:10.2172/984336.

```
Mazumder, Sandip, & Li, Ju.
```*First Principles Modeling of Phonon Heat Conduction in Nanoscale Crystalline Structures*. United States. https://doi.org/10.2172/984336

```
Mazumder, Sandip, and Li, Ju. Wed .
"First Principles Modeling of Phonon Heat Conduction in Nanoscale Crystalline Structures". United States. https://doi.org/10.2172/984336. https://www.osti.gov/servlets/purl/984336.
```

```
@article{osti_984336,
```

title = {First Principles Modeling of Phonon Heat Conduction in Nanoscale Crystalline Structures},

author = {Mazumder, Sandip and Li, Ju},

abstractNote = {The inability to remove heat efficiently is currently one of the stumbling blocks toward further miniaturization and advancement of electronic, optoelectronic, and micro-electro-mechanical devices. In order to formulate better heat removal strategies and designs, it is first necessary to understand the fundamental mechanisms of heat transport in semiconductor thin films. Modeling techniques, based on first principles, can play the crucial role of filling gaps in our understanding by revealing information that experiments are incapable of. Heat conduction in crystalline semiconductor films occurs by lattice vibrations that result in the propagation of quanta of energy called phonons. If the mean free path of the traveling phonons is larger than the film thickness, thermodynamic equilibrium ceases to exist, and thus, the Fourier law of heat conduction is invalid. In this scenario, bulk thermal conductivity values, which are experimentally determined by inversion of the Fourier law itself, cannot be used for analysis. The Boltzmann Transport Equation (BTE) is a powerful tool to treat non-equilibrium heat transport in thin films. The BTE describes the evolution of the number density (or energy) distribution for phonons as a result of transport (or drift) and inter-phonon collisions. Drift causes the phonon energy distribution to deviate from equilibrium, while collisions tend to restore equilibrium. Prior to solution of the BTE, it is necessary to compute the lifetimes (or scattering rates) for phonons of all wave-vector and polarization. The lifetime of a phonon is the net result of its collisions with other phonons, which in turn is governed by the conservation of energy and momentum during the underlying collision processes. This research project contributed to the state-of-the-art in two ways: (1) by developing and demonstrating a calibration-free simple methodology to compute intrinsic phonon scattering (Normal and Umklapp processes) time scales with the inclusion of optical phonons, and (2) by developing a suite of numerical algorithms for solution of the BTE for phonons. The suite of numerical algorithms includes Monte Carlo techniques and deterministic techniques based on the Discrete Ordinates Method and the Ballistic-Diffusive approximation of the BTE. These methods were applied to calculation of thermal conductivity of silicon thin films, and to simulate heat conduction in multi-dimensional structures. In addition, thermal transport in silicon nanowires was investigated using two different first principles methods. One was to apply the Green-Kubo formulation to an equilibrium system. The other was to use Non-Equilibrium Molecular Dynamics (NEMD). Results of MD simulations showed that the nanowire cross-sectional shape and size significantly affects the thermal conductivity, as has been found experimentally. In summary, the project clarified the role of various phonon modes - in particular, optical phonon - in non-equilibrium transport in silicon. It laid the foundation for the solution of the BTE in complex three-dimensional structures using deterministic techniques, paving the way for the development of robust numerical tools that could be coupled to existing device simulation tools to enable coupled electro-thermal modeling of practical electronic/optoelectronic devices. Finally, it shed light on why the thermal conductivity of silicon nanowires is so sensitive to its cross-sectional shape.},

doi = {10.2172/984336},

url = {https://www.osti.gov/biblio/984336},
journal = {},

number = ,

volume = ,

place = {United States},

year = {2010},

month = {6}

}