Ratekab note for the more general case ratekanbm

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Unformatted text preview: recombina_on rate to balance the combined thermal and op_cal genera_on rates Examining the case where po>>no or no>>po Removing go from both sides of the equa_on, and assuming the case of low- level injec_on In steady state for band- band processes, δn(t)=δp(t)=Δn=Δp gopt = α r ⎡( no + po )δ n + δ n 2 ⎤ ⎣ ⎦ gopt + go (T ) = α r np = α r (no + δ n )( po + δ p ) go (T ) = ro (T ) = α r no po = α r ni2 General Case: gopt = α r ( po + no )δ n = δn τn δn = α r noδ n = τp p-type material: gopt = α r poδ n = n-type material: gopt δ n = δ p = goptτ n δn τ = α r ( no + po )δ n = δn τ NOTE: For Band-Band Recombination Where δ n(t ) = δ p(t ) = α r no po + α r ⎡( no + po )δ n + δ n 2 ⎤ ⎣ ⎦ = go (T ) + α r ⎡( no + po )δ n + δ n 2 ⎤ ⎣ ⎦ Defini_ons •  Photoluminescence: Light emission that occurs azer op_cal excita_on of carriers •  Cathodoluminescence: Light emission that occurs azer carriers have been excited by high- energy electron bombardment •  Electroluminescence: Light emission that occurs azer carriers have been introduced using an electrical current 14 Band- to- Band Recombina_on •  Consider a first- order chemical reac8on – the reac_on rate is propor_onal to the product of the concentra_on of the reactants: –  Rate=k[A][B] –  Note: for the more general case, Rate=k[A]n[B]m •  For band- to- band electron- hole recombina_on, the “reac_on rate” is propor_...
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