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 |
E_{i}, the intrinsic energy |
F_{n}, the electron quasi-Fermi energy |
F_{p}, the hole quasi-Fermi energy |
J_{n}, the electron current density |
J_{p}, the hole current density |
The ten equations are: |
Charge density equation |
(2.10.1) |
Electric field and potential equations |
(2.10.2) |
(2.10.3) |
(2.10.4) |
Carrier density equations |
(2.10.5) |
(2.10.6) |
Drift and diffusion current equations |
(2.10.7) |
(2.10.8) |
Continuity equation in steady state with SHR recombination |
(2.10.9) |
(2.10.10) |
Boulder, December 2004 |