A Deterministic Multi-Subband Boltzmann Transport Equation Solver for GaN Based HEMTs

A high electron mobility transistor based on a GaN channel is simulated by using a deterministic Boltzmann transport equation solver. In order to verify the physical soundness of the scattering mechanisms, first, a mobility calculator has been implemented. Phonon-limited electron mobility is calculated for one-dimensional heterostructure in the low field regime. For GaN based HEMTs, the two-dimensional Poisson equation and the one-dimensional Schrodinger equation along the confinement direction are considered. The transport of electrons in the non-equilibrium state is determined by solving the Boltzmann equation expanded with the Fourier harmonics in a self-consistent manner. The polar optical phonon is considered to explain the scattering of the system and the Pauli principle is also included. The Boltzmann equation is implemented for the total energy space with H-transformation. Without assistance from the momentum-based equation, the direct bias ramping from the equilibrium solution can be performed.