By Clifton G. Fonstad
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Extra resources for Microelectronic Devices and Circuits 2006 Electronic Edition
1 eV, this corresponds to light in the visible and ultraviolet regions of the spectrum as well as very near-infrared radiation. In this section we will consider optical excitation of semiconductors with such light. 1 Minority Carrier Lifetime We discussed hole-electron pair generation and recombination mechanisms in Chap. 2 when we discussed detailed balance. We defined the generation rate as G and the recombination rate as R . 19) In thermal equilibrium, n = n o , p must have = p o , and d n l d t = d p / d t = 0.
It is sometimes convenient to write this in terms of ni at room temperature (300 K): In either form, we see that as temperature increases, the intrinsic carrier concentration increases exponentially and will eventually exceed the net doping concentration (donor or acceptor) and the sample will no longer appear extrinsic. Both the equilibrium hole and electron concentrations again approach ni , and the material becomes intrinsic, and, as we shall see, useless for devices. In silicon this situation does not occur until very high temperatures, but in germanium, for example, which has a much smaller energy gap A E , , this may occur at several hundred degrees centigrade.
At a given temperature, the product n,po must be independent of N, and Nd. Another way to see that the product nope must be independent of doping is to think of the process of hole-electron pair generation and recombination as a chemical reaction: Complete bond + Hole + Electron and use the law of mass action, which says that in equilibrium [Hole][Electron] [Completed bond] = K(T) where the brackets indicate concentration and K ( T ) is the mass action constant. The hole concentration is p o , and the electron concentration is n o .
Microelectronic Devices and Circuits 2006 Electronic Edition by Clifton G. Fonstad