PISCES-2ET and Its Application Subsystems - Stanford Technology ...

CHAPTER 2
DUET Carrier Transport
Model
The DUET model, a carrier transport model in semiconductors, is developed based on the moment
approach to solving Boltzmann Transport Equation (BTE). It uses six state variables to describe the
status of a semiconductor device. These six variables are: electrostatic potential, ψ, carrier
concentrations, n and p, carrier temperatures, T n and T p , and lattice temperature, T L , and they are
functions of space and time. All other device characteristics such as terminal I-V characteristics and
circuit model parameters can be calculated from the knowledge of the distribution of these basic
variables. To determine the distribution of these variables under applied bias, six independent
equations are required together with proper boundary conditions. It is well established that with the
drift-diffusion (DD) carrier transport model, Shockley semiconductor equations, i.e., Poisson’s
equation and carrier continuity equations, govern the distribution of ψ, n, and p. The carrier
concentrations can also be replaced, equivalently, by their respective quasi-Fermi levels, and ,
in classical distribution (either Boltzmann or Fermi-Dirac) functions. With the temperatures for both
carriers and lattice introduced as independent variables, three more equations are needed and they can
be derived from the energy balance principle. In this chapter, we will first introduce two (kinetic)
energy balance equations for carriers and one thermal diffusion equation for the lattice. Various macro
quantities such as carrier and energy densities will be defined using the distribution function at the
quasi-thermal equilibrium. The auxiliary expressions for transport are provided. Finally the proper
boundary conditions for solving differential equations are discussed.
φ n
φ p
PISCES-2ET – 2D Device Simulation for Si and Heterostructures 5