Minority Carrier Diffusion Equations
The continuity equations are "bookkeeping" equations that take into account
all of the processes that occur within a semiconductor. Drift, diffusion,
and recombination-generation are constantly occurring in a semiconductor.
Although we have studied these processes individually, they take place
at the same time. These carrier actions change the carrier concentration
in the semiconductor as a function of time and space, and because carriers
transport a charge, a current will result.
The continuity equations are too complicated to use except on a computer
as difference equations derived from an ordinary partial differential equation.
We have two equations and three unknowns, n, p, and V.
With Poisson's equation, we have the third equation we need to solve problems
using a computer.
The minority carrier diffusion equations are derived
from the continuity equations by making several assumptions. The
assumptions allow us to model a semiconductor without using a computer.
For a more visual explanation, check out the demo.
You will need the shockwave
plug-in for your browser in order for the movie to run. They should run
properly on the computers in the Vectra lab using Internet Explorer, but
they will not run on the Sun workstations. Once the page is loaded, the
movie runs on its own. For better viewing, use the "full screen"
option on your browser.