Theoretical study of gallium-based wide bandgap channel devices using a deterministic multi-subband Boltzmann transport equation solver

Abstract

Power semiconductors are widely used in automobiles, home appliances, and industrial systems, making a great contribution to the development of human civilization, and have now become part of our lives. Many studies are currently being conducted based on wide bandgap materials that are attracting increasing attention as alternatives to silicon-based power devices. Among them, GaN and β-Ga2O3 are key materials for next-generation power semiconductors with excellent physical properties. Simulations on high-frequency and high-power devices using these wide bandgap materials have been mainly performed through momentum-based transport models such as drift-diffusion (DD) and hydrodynamic models. However, with continuous development, miniaturized power devices now require more precise simulation methods. In this dissertation, a deterministic multi-subband Boltzmann transport equation is implemented to simulate gallium-based wide bandgap devices. The traditional Gummel-type iteration loop is used to obtain a self-consistent solution of the Poisson equation (PE), Schrödinger equation (SE), and Boltzmann transport equation (BTE). GaN-based high electron mobility transistors (HEMTs) and β-Ga2O3-based modulation-doped field-effect transistors (MODFETs) are simulated and the two-dimensional PE is applied to the entire device to obtain electrostatic potential. The one-dimensional SE is used for each position in the transport direction to account for the confinement effect of electrons by the vertical field of the gate contact in a thin channel. The transport properties in a non-equilibrium state are calculated through the one-dimensional BTE. The multidimensional distribution function of the BTE was expanded by the Fourier harmonics, which allows efficient computation by replacing the angular dependence of the two-dimensional momentum space with the harmonic coefficient. In addition, H-transformation, which gives numerical stability, is applied. This sequence of processes is described in chapter 2. In chapter 3, simulations are performed on a GaN-based HEMT with high electron density and high electron mobility based on the polarization effect by the heterostructure. Through comparison with actual benchmarked devices, it was confirmed that the latest miniaturized wide bandgap-based devices can be well simulated using the MS-BTE solver. In chapter 4, optimizations for β-Ga2O3-based MODFET devices are performed. A more realistic structure is considered by implementing a coupled DD and MS-BTE model. It was confirmed that the coupled model could provide more accurate simulation results in optimization studies compared with the calibrated DD model. Continuous research on high-power and high-frequency devices is aimed at miniaturization to improve performance and efficiency in wide bandgap-based devices, as was done in silicon. The deterministic MS-BTE solver of this dissertation can be an alternative to complement the limitations of momentum-based electron transport models commonly used for power semiconductor simulations.