Development of an Ab-initio Model of the Lattice Thermal Conductivity in Semiconductor Thin Films and Nanowires
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Development of an Ab-initio Model of the Lattice Thermal Conductivity in Semiconductor Thin Films and Nanowires Jie Zou and Alexander Balandin Department of Electrical Engineering University of California at Riverside Riverside, California 92521 U.S.A. ABSTRACT A model for calculating the lattice thermal conductivity in semiconductor thin films and nanowires is developed. It is based on the solution of phonon Boltzmann equation and takes into account phonon dispersion modification due to confinement effects and non-equilibrium phonon redistribution. Phonon spatial confinement at the structure boundaries leads to modification of the acoustic phonon dispersion and corresponding drop in the mode-averaged group velocity. Scattering from rough boundaries and interfaces introduces a change in the non-equilibrium phonon distribution as compared to bulk. These effects lead to a reduction in the in-plane lattice thermal conductivity in both thin films and nanowires. The predicted values for the lattice thermal conductivity and their temperature and interface roughness dependence are in good agreement with available experimental data. INTRODUCTION Quantum wire arrays as well as other nanostructured materials have recently been proposed for applications in electronic, optoelectronic and thermoelectric devices. Thermal management of electronic and optoelectronic devices based on semiconductor nanostructured materials presents significant difficulties due to increase in power dissipation per unit area and variety of size effects that complicate acoustic phonon transport at nanoscales. Development of an accurate theoretical description of heat transport in nanostructured materials is also important in the view of optimization of thermoelectric devices. In this article, we present an ab-initio model for calculating the lattice thermal conductivity in semiconductor thin films and nanowires. It is based on the solution of phonon Boltzmann equation, which takes into account (i) modification of the acoustic phonon dispersion in lowdimensional structures with the lateral feature size of 10 nm -20 nm, and (ii) change in the nonequilibrium phonon distribution due to partially diffuse boundary scattering. The characteristic dimensions of these nanostructures are approaching the thermal acoustic phonon wavelength and are less than the acoustic phonon mean free path (MFP). According to the latest experimental measurements, the effective MFP of the dominant phonons at room temperature in silicon thin films is close to 300 nm [1], which is much larger than the value of 41 nm predicted by the Debye model. Numerical simulations are carried out for free-standing silicon cylindrical nanowires (quasi one-dimensional structures) and thin films (quasi two-dimensional structures) with boundaries characterized by the different interface roughness parameter p. The value of p represents the probability that the phonon is undergoing a specular scattering event at the interface.
AA6.7.1
THEORY A. Phonon dispersion and group velocities We calculate the
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