Minority Carrier Diffusion Equations

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A Brief Description

Minority carrier diffusion equations (MCDEs) are equations used to model semiconductors under special circumstances.  They are derived from the continuity equations after making a series of assumptions that therefore limit the applicability of the MCDEs.  At the same time, MCDEs can be used in a large number of situations to derive closed-form, analytical solutions that describe carrier concentrations and currents.  When semiconductors are being used (which is when they are most interesting) processes are constantly occurring within, caused by the outside influences like change in temperature, the presence or absence of light, or an applied voltage.  These may cause carrier drift, diffusion, and recombination-generation and affect the carrier concentration within the semiconductor as a function of time or space as the semiconductor attempts to bring itself back to equilibrium.  After making several assumptions, the continuity equations are simplified to the minority carrier diffusion equations (MCDEs).
Minority carrier 
 diffusion equations:
 
The MCDEs can be further simplified to obtain a less complex differential equation, with respect to either time or space.  The end result of using the MCDEs is to obtain the rate of change in minority carrier concentration with respect to time or space within a semiconductor.
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