Gt gopt r r np r n0 n p0 p nokn

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Unformatted text preview: to jump to the conduction band (phonon interactions) Generation and recombination are balanced: no(K) Ÿ༉ r g (T ) = gi = ri = α r nopo = α n 2 ri An Analogy: Molecular Speed in an Ideal Gas g(T) Ÿ༉ po(K) http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/imgkin/mxspd.gif 9 Steady Illumina_on •  Under steady illumina_on, an op_cal genera_on rate gop is added to the equilibrium genera_on rate g(T) and is balanced by the recombina_on rate r(T) –  Or: r=g(T)+gopt •  An addi_onal popula_on of electrons and holes δn=δp will be produced by illumina_on •  If the illumina_on stops, gopt=0 but recombina_on occurs at a faster rate than genera_on un_l the excess carriers are depleted no(K)+δn Ÿ༉ r gopt g(T) Ÿ༉ po(K)+δp r = α r np = α r (no + δ n )( po + δ p ) = α r [ nopo + noδ p + poδ n + δ nδ p ] = α r [ nopo + ( no + po )δ n + δ n 2 ] 10 Steady State Genera_on g = g(T ) + gopt = r = α r np = α r (n0 + δ n )( p0 + δ p ) no(K)+δn Ÿ༉ = α r [ n0 p0 + n0δ p + p0δ n + δ nδ p ] r = α r ⎡ n0 p0 + ( n0 + p0 )δ n + δ n 2 ⎤ ⎣ ⎦ = α r n0 p0 + α r ⎡( n0 + p0 )δ n + δ n 2 ⎤ ⎣ ⎦ Recall: g(T ) = α n = α r n0 p0 so 2 ri gopt g(T) Ÿ༉ po(K)+δp δn 1 ⎡( n0 + p0 )δ n + δ n 2 ⎤ α r ( n0 + p0 )δ n = τn = gop = α r ⎣ ⎦ α n ( n0 + p0 ) τn and Assume δn small compared to majority δ n = δ p = gopτ n 11 carrier concentration Steady- State Genera_on gtot (T ) = gopt + go (T ) r (T ) = gopt + go (T ) = α r np = α r (no + Δn )( po + Δp ) Prior to illumina_on, there is steady- state thermal genera_on- recombina_on 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...
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