ECE340_L14_S14_Distribution

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Unformatted text preview: We can now look at specific cases: n-type, p-type, etc. 19 Solving the Differen_al Equa_on p- type Material 1) Assume low-level injection: neglect δ n 2 (t ) 2 ) p-type material so p0 n0 dδ n(t ) = −α r ⎡( n0 + p0 )δ n(t ) + δ n 2 (t ) ⎤ ⎣ ⎦ dt = −α r p0δ n(t ) The solution is: δ n(t ) = Δne−α r p0t = Δne− t /τ n where Δn = δ n(t = 0 ) 1 τn = or α r p0 1 τn = α r ( n0 + p0 ) n- type Material 1) Assume low-level injection: neglect δ p 2 (t ) 2 ) n-type material so n 0 p0 dδ p(t ) = −α r ⎡( n0 + p0 )δ p(t ) + δ p 2 (t ) ⎤ ⎣ ⎦ dt = −α r n0δ p(t ) The solution is: δ p(t ) = Δpe−α r n0t = Δne where Δp = δ p(t = 0 ) 1 τp = or α r n0 1 τp = α r ( n0 + p0 ) − t /τ p 20 Important Defini_on •  Minority Carrier Life8me or Recombina8on Life8me: the _me constant by which the excess carrier popula_on decays to the equilibrium value 21 Summary: Minority Carrier Life_me go (T ) = ro (T ) = α r no po = α r ni2 Prior to illumina_on, there is steady- state thermal genera_on- recombina_on Low- level injec_on is assumed, such that δn2 can be neglected dδ n(t ) = −α r ( po + no )δ n(t ) dt so δ n(t ) = Δne−α r ( po +no )t = Δne− t /τ 1 General Case: τ = α r ( po + no ) 1 p-type material: τ n = α r po 1 n-type material: τ p = α r no gtot (T ) = gopt + go (T ) r (T ) = gopt + go (T ) = α r np = α r (no + Δn )( po + Δp ) During steady illumina_on, thermal genera_on is augmented by op_cal genera_on With more electron- hole pairs available, the recombina_on increases above the steady- state thermal recombina_on rate to balance the combined thermal and op_cal genera_on rates The net change in carriers as a func_on of _me is the thermal genera_on rate minus the instantaneous...
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This note was uploaded on 03/06/2014 for the course ECE 340 taught by Professor Leburton during the Spring '11 term at University of Illinois, Urbana Champaign.

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