19 solving the dierenal equaon p type material 1

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Unformatted text preview: onal to the product of the concentra_on of electrons and holes: Recombination Ÿ༉ EC ¢༊ EV Rn = Rp = α r np –  Rn=Rp=αrnp –  αr is the bimolecular recombina8on coefficient, also called the capture coefficient 15 Reminder: Equilibrium Condi_on The rate of recombination is proportional to the number of electrons in the conduction band times the number of holes in the valence band •  no(K) r(T) Ef g(T) •  For any semiconductor (n- type, p- type, intrinsic) in equilibrium, the thermal genera_on of electron- hole pairs (EHP) is balanced by the recombina_on rate –  Or: r(T)=g(T) Hence, the equilibrium electron and hole concentra_ons, no(T) and po(T) are maintained r (T ) = α r no (T ) po (T ) po(K) g (T ) = α r ni (T )ni (T ) r (T ) = g(T ) = α n 2 ri no (T ) po (T ) = ni2 (T ) •  The Fermi Level is used to quan_fy the electron and hole concentra_ons 16 Op_cal Genera_on Stops: gopt(t=0)=0 no(K)+δn no(K)+δn Ÿ༉ Ÿ༉ r gopt r g(T) Ÿ༉ g(T) Ÿ༉ po(K)+δp po(K)+δp Recombination: r = g(T ) + gopt Recombination: r = g(T ) + gopt Generation: g(T ) + gopt Generation: g(T ) Generation and recombination are not balanced The number of excess carriers decreases: Generation and recombination are balanced dn(t ) = g(T ) − r (t ) = α r ni2 − α r n(t ) p(t ) dt 18 A Li5le Bit of Math: g(T) r dn(t ) 2 = α r ni − α r n(t ) p(t ) dt = α r ni2 − α r [ n0 + δ n(t )][ p0 + δ p(t )] = α n − α r [ n0 + δ n(t )][ p0 + δ n(t )] 2 ri = α n − α r ⎡ n0 p0 + ( n0 + p0 )δ n(t ) + δ n (t ) ⎤ ⎣ ⎦ 2 ri 2 = −α r ⎡( n0 + p0 )δ n(t ) + δ n 2 (t ) ⎤ ⎣ ...
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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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