ee3161 spring10 Review Fermi Level

Ee3161 spring10 - Review Fermi Level(Equilibrium Ec EF Ei Ev n0 p0 = n2 = 1020/cm3 i n0 = ni e(EF −Ei/kT p0 = ni e(Ei −EF/kT n0 EF − Ei = kT

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Unformatted text preview: Review: Fermi Level (Equilibrium) Ec EF Ei Ev n0 p0 = n2 = 1020 /cm3 i n0 = ni e (EF −Ei )/kT p0 = ni e(Ei −EF )/kT n0 EF − Ei = kT ln ni p0 Ei − EF = kT ln ni n0 (cm-3) p0 (cm-3) EF - Ei (eV) 1011 1012 1013 1014 1015 0.026 ln10 = 0.06 0.026 ln102 = 0.06x2 42 EE3161 Semiconductor Devices Sang-Hyun Oh UNIVERSITY OF MINNESOTA Review: Quasi Fermi Level Sample Prob 1 Uniform illumination Minority Carrier Diffusion Eq Example hν n-type Low level injection Examples Quasi-Fermi Level ND = 1015 cm−3 , τp = 10−6 s For t ≤ 0− , GL = 0 At t ≥ 0+ , GL = 1017 EHP·cm−3 s−1 F ￿ τ) For times indt∆pn (tp , for t ≥ 0+ . = p0 + ∆p ≈ 1011 /cm3 p With photo-generation, n remains essentially unperturbed, but p has increased by many orders of magnitude. EE3161 Semiconductor Devices Sang-Hyun Oh 9 / 20 43 UNIVERSITY OF MINNESOTA Review: Quasi-Fermi Level n0=ND=1015/cm3 Ec EF Ei Ev n≅n0=1015/cm3 Ec FN FP p=1011/cm3 Ev p0= /cm3 (a) Under equilibrium n0 = ni e(EF −Ei )/kT p0 = ni e(Ei −EF )/kT FP ≡ Ei − kT ln EE3161 Semiconductor Devices Sang-Hyun Oh (b) non-equilibrium (illumination) Δn=Δp=1011/cm3 ￿ p ni ￿ Replace p0 vs. EF with p vs. FP p ≡ ni e(Ei −FP )/kT = Ei − kT ln10 = Ei − 0.06eV 44 UNIVERSITY OF MINNESOTA Quasi-Fermi Level vs. Current JP = qµp pξ − qDP ∇p ∇ p = ni e (Ei −FP )/kT p ≡ ni e(Ei −FP )/kT Ei − FP ni (Ei −FP )/kT ∇( )= e (∇Ei − ∇FP ) kT kT ξ = −∇V = −∇ ∇p = EE3161 Semiconductor Devices Sang-Hyun Oh ￿ Ei −q ￿ 1 = ∇ Ei q ￿ qp ￿ kT ￿p￿ ξ− ∇ FP kT 45 UNIVERSITY OF MINNESOTA Quasi-Fermi Level vs. Current Eliminate ∇p from JP = qµp pξ − qDP ∇p qp p JP = qµp pξ − qDP ξ + qDP ∇ FP kT kT q p = q (µp − DP ) pξ + qDP ∇ FP kT kT JP = µp p∇FP Similarly, JN = µn n∇FN If a quasi-Fermi level varies with position, current is flowing inside the semiconductor. EE3161 Semiconductor Devices 46 UNIVERSITY OF MINNESOTA Sang-Hyun Oh Exercise 2: Quasi-Fermi Level 0 Solution: x ∆pn (x) = ∆pn0 exp(−x/LP ) p = p0 + ∆pn0 e−x/LP For illuminated sample: n ≈ n0 1. Find quasi-Fermi levels in the illuminated bar. 2. Show that FP is a linear function of x where ∆pn (x) ￿ p0 EE3161 Semiconductor Devices Sang-Hyun Oh 47 UNIVERSITY OF MINNESOTA Illumination vs. Quasi-Fermi level Ec EF Ei Ev FP Ev Ec FN FP = Ei − kT ln If ∆pn (x) ￿ p0 EE3161 Semiconductor Devices Sang-Hyun Oh ∆pn0 −x/LP FP ≈ Ei − kT ln[ e ] ni ∆ p n0 = Ei − kT ln + kT (x/LP ) ni 48 ￿ p ni ￿ n ≈ n0 FN ≈ E F p0 ∆pn0 −x/LP = Ei − kT ln[ + e ] ni 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.sang-­hyunoh during the Spring '10 term at University of Minnesota Crookston.

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