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Unformatted text preview: =0 for x<0, write down the governing equation:
d 2 ∆ pn ∆ pn Dp − =0 2 dx τp What are the boundary conditions at x=0 and ∞?
∆pn x=0 = 1010 /cm3 ∆pn x=∞ = 0 General solution of the differential equation:
∆pn (x) = Ae−x/LP + Bex/LP ∆pn (x) = ∆pn (0)e−x/LP
EE3161 Semiconductor Devices SangHyun Oh LP ≡ DP τP 36 UNIVERSITY OF MINNESOTA Pierret 3.5.1. Diffusion Length Concept
As we see in Prob. #2, excess carriers diffuse from the point of injection, which is characterized by the exponential falloff with a characteristic decay length LN or LP:
∆pn (x) = ∆pn (0)e−x/LP LP ≡ DP τp LN ≡ DN τn
37 EE3161 Semiconductor Devices SangHyun Oh UNIVERSITY OF MINNESOTA Fermi Level Meaning
The common energy at equilibrium Energy where f(E) = 1/2 The carrier concentration (equilibrium): n p EF = Ei + k T l n = Ei − k T l n ni ni Why do we need quasiFermi levels? Answer: To specify the carrier concentrations under nonequilibrium conditions, i.e. np≠ni2 EE3161 Semiconductor Devices SangHyun Oh 38 UNIVERSITY OF MINNESOTA QuasiFermi Levels
If a semiconductor material is illuminated with intense light, # of electrons and holes are not those given by thermal equilibrium. Remember that we deﬁned Fermi level in a system under equilibrium. However, important devices such as a laser and a forwardedbiased pn junction are NOT in equilibrium. In that case, how can we analyze the system?
EE3161 Semiconductor Devices SangHyun Oh 39 UNIVERSITY OF MINNESOTA QuasiFermi Levels*
In that case, describe the electron and hole distributions as being FermiDirac in form, but each having different “quasiFermi levels”. Deﬁne quasiFermi levels FN and FP to correspond to carrier concentrations even if there is not thermal equilibrium *QuasiFermi level is also sometimes known as “imrefs” (Fermi backwards). EE3161 Semiconductor Devices SangHyun Oh 40 UNIVERSITY OF MINNESOTA QuasiFermi Levels
Equilibrium and Fermi level EF:
n0 = ni e(EF −Ei )/kT p0 = ni e(Ei −EF )/kT Nonquilibrium and deﬁnition of quasiFermi levels FN and FP:
n ≡ ni e(FN −Ei )/kT FN ≡ Ei + kT ln
EE3161 Semiconductor Devices SangHyun Oh p ≡ ni e(Ei −FP )/kT
41 n ni FP ≡ Ei − kT ln p ni UNIVERSITY OF MINNESOTA...
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This note was uploaded on 02/24/2010 for the course EE 3161 taught by Professor Prof.sanghyunoh during the Spring '10 term at University of Minnesota Crookston.
 Spring '10
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