Semiconductor Device Simulation Using Quantum Transport Theory

The traditional semiconductor device simulation techniques are often derived from the semi-classical Boltzmann Transport Equation (BTE). In this work, the validity of the BTE is examined, and new techniques using the quantum transport theory are suggested. The Wigner distribution function is applied to simplify the Bloch Equation, which governs the density matrix at equilibrium, in order to scrutinize the validity of the classical Boltzmann distribution in equilibrium systems. Limiting conditions where quantum size effect becomes significant are derived. In cases where the classical Boltzmann distribution does not apply, the Bloch Equation needs to be solved to obtain the particle distribution. A new technique is developed by first diagonalizing the density matrix using the Wigner distribution function before solving the Bloch Equation numerically. A numerical algorithm suitable for solving the simplified Bloch Equation is also described. It is found that the method developed is both efficient and accurate compared with the conventional method which based on solution of the Schrodinger Equation. Using the same methodology, a simplified method for calculating the particle distribution for 2-D electron gas has also been developed. The quantum BTE is next derived based on the quantum Liouville Equation using the Wigner distribution function. A set of quantum hydrodynamics equations are obtained by taking the first three moment equations of the quantum BTE. By comparing these equations with the classical hydrodynamic equations, the quantum correction term due to the size effect has been identified. Furthermore, by post-processing simulation results from an energy transport device simulator, it is observed that this quantum correction term is not negligible in small geometry devices, especially near the source region in a MOSFET. To model small geometry devices accurately, it is imperative to take the quantum size effect into consideration. On the other hand, high field scattering mechanisms between carriers and lattices in a semiconductor often determine the transport properties in that semiconductor. To understand the limitations the classical models, the conventional calculation methods of the collision term are examined and critiqued. Two recently proposed high field quantum effects, namely, the collision broadening and intra-collisional field effects, are also described and discussed.