Ee3161 spring10 hw2

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Unformatted text preview: static concept, but is the average result of the balance between competing dynamic processes (i.e. generation and recombination). For a given semiconductor material, the thermal generation rate of electron-hole pairs, Gi,th(T), depends only on temperature (intrinsic material). The rate of recombination events, Ri(n0,p0,T), however, will in general depend on both electron and hole concentration, and the temperature. In thermal equilibrium: Gi,th (T ) = Ri (n0 , p0 , T ) EE3161 Semiconductor Devices Sang-Hyun Oh 9 UNIVERSITY OF MINNESOTA Law of Mass Action: Revisited Make a Taylor expansion of Ri in two variables (n, p) at fixed temperature: Ri (n0 , p0 , T ) = ai (T ) + bi (T )n0 + ci (T )p0 + ri (T )n0 p0 +ei (T )n2 p0 + fi (T )n0 p2 + ... 0 0 Since there can be no pair-recombination in a sample in which only one carrier type is present, ai (T ) = bi (T ) = ci (T ) ≡ 0 For small carrier concentrations, the leading nonzero term is dominant: Gi,th = Ri (n0 , p0 , T ) = ri (T )n0 p0 EE3161 Semiconductor Devices Sang-Hyun Oh 10 UNIVERSITY OF MINNESOTA Law of Mass Action: Revisited Gi,th (T ) ∴ n 0 p0 = ≡ n2 (T ) i ri (T ) What happens if we “sprinkle in” more electrons, e.g. by adding n-type donors? Making n0 > ni has to result in fewer holes, p0 < ni , to prevent additional electrons to recombine with holes faster than the unchanged thermal generation rate. EE3161 Semiconductor Devices Sang-Hyun Oh 11 UNIVERSITY OF MINNESOTA Recombination The energy released in the recombination of an electron and hole can be: Emitted as light (radiative) Transferred to the lattice as heat (non-radiative) Transferred to another electron (non-radiative, Auger recombination) For detailed discussions, read Pierret 3.3.1 & 3.3.2 EE3161 Semiconductor Devices Sang-Hyun Oh 12 UNIVERSITY OF MINNESOTA Recombination Mechanisms 1. Band-to-band: An electron in the CB combines with a hole in the VB to give light. 2. R-G center: Usually an impurity near midgap traps a carrier, because they help momentum c...
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This note was uploaded on 02/24/2010 for the course EE 3161 taught by Professor Prof.sang-­hyunoh during the Spring '10 term at University of Minnesota Crookston.

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