2.12 The diffusion equation
Table of Contents -
Glossary -
Study Aids -
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In this section:
- The continuity equation
- The diffusion equation in a quasi-neutral region
2.12.1 The continuity equation
The continuity equation describes a basic concept, namely that
a change in carrier density over time is due to a difference
between the incoming and outgoing flux of carriers plus the generation
and minus the recombination.
(dif25)
(dif26)
2.11.2 The Diffusion equation in a quasi-neutral region
In the quasi-neutral region, the current is due to diffusion
only. In addition we can use the simple recombination model for the net
recombination rate. This leads to the time dependent diffusion equations for electrons
in p-type material and for holes in n-type material:
(dif27)
(dif28)
In steady-state the partial derivatives with respect to time are
zero yielding:
(dif29)
(dif30)
The general solution to these second order differential equations are:
(pnc3)
(pnc4)
where Ln and Lp are the
diffusion lengths given by:
(pnc14)
(pnc15)
The diffusion equations can also be written as a function
of the excess carrier densities,
dn and
dp, which are
related to the total carrier densities, n
and p, and the
thermal equalibrium densities, n0 and
p0, by:
(dif32)
(dif31)
yielding:
(dif29a)
(dif30a)
2.11
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© Bart J. Van Zeghbroeck, 1996, 1997