Research Projects

In intrinsic and doped semiconductors, electrical and thermal energy transport is primarily controlled by electrons and quantized lattice vibrations called phonons. Resistance to energy flow in these materials is caused by mutual collisions among phonons and electrons. The semi-classical linearized Boltzmann Transport Equation (BTE) governs the rate of energy transport, overcoming this resistance. The linearized BTE describes the path towards equilibrium for a non-equilibrium distribution of phonons or electrons through mutual collisions, leading to energy transport properties such as thermal conductivity and electronic mobility. The linearized BTE is an 8-dimensional set of partial differential equations, involving strong coupling among different electrons and phonons. Solutions of the phonon BTE in intrinsic semiconductors are commonly derived assuming the validity of the single-mode relaxation time approximation (RTA). To study electron transport in doped semiconductors, the electron BTE is typically solved by assuming that phonons remain in equilibrium during electron transport in addition to the RTA. However, simplifying approximations fail to capture the unusual thermal and electronic properties of materials like diamond, boron arsenide, boron nitride, and the exception drag effect at low temperatures observed experimentally in doped semiconductors like n-GaAs. This proposal explores the possibility of using a new symmetrized matrix formulation to solve the phonon BTE and coupled phonon-electron BTE to study the thermal and electronic transport properties of intrinsic and doped semiconductors.