Chapter 2: Semiconductor Fundamentals
The drift-diffusion model of a semiconductor is frequently used to describe semiconductor devices. It contains all the features described in this chapter.
Starting with Chapter 3, we will apply the drift-diffusion model to a variety of different devices. To facilitate this analysis, we present here a simplified drift-diffusion model, which contains all the essential features. This model results in a set of ten variables and ten equations.
The assumptions of the simplified drift-diffusion model are:
Full ionization: all dopants are assumed to be ionized (shallow dopants)
Non-degenerate: the Fermi energy is assumed to be at least 3 kT below/above the conduction/valence band edge.
Steady state: All variables are independent of time.
Constant temperature: The temperature is constant throughout the device.
The ten variables are the following:
r, the charge density
n, the electron density
p, the hole density
, the electric field
f, the potential
Ei, the intrinsic energy
Fn, the electron quasi-Fermi energy
Fp, the hole quasi-Fermi energy
Jn, the electron current density
Jp, the hole current density
The ten equations are:
Charge density equation
Electric field and potential equations
Carrier density equations
Drift and diffusion current equations
Continuity equation in steady state with SHR recombination
Boulder, December 2004