03_ex2fall_frsht

03_ex2fall_frsht - 6.012 Electronic Devices and Circuits...

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V 6.012 Electronic Devices and Circuits Formula Sheet for Hour Exam 2, Fall 2003 Parameter Values: Periodic Table: q = 1.6 x 10 19 Coul III IV = 8.854 x 10 14 F / cm , r,Si = 11.7, = 3.9 o r,SiO 2 B C N 10 12 F / cm , SiO 2 3.5 x 10 13 F / cm Al Si P Si n i [ Si @ R . T ] 10 10 cm 3 Ga Ge As kT / q 0.025 V ; ( kT / q ) ln10 0.06 V In Sn Sb 1 m = 1 x 10 4 cm Drift/Diffusion: Electrostatics: Drift velocity : s = ± E dE ( x ) 1 x m x = ( x ) E ( x ) = ( x ) dx Conductivity : = q ( n + h p ) d dx ( x ) e ( x ) = E ( x ) dx Diffusion flux : F = D C m dx = E ( x ) m m D kT x d 2 ( x ) = ( x ) ( x ) = 1 ( x ) dxdx m Einstein relation : = dx 2 q m The Five Basic Equations: n x , t e ( 2 Electron concentration : ( ) 1 J x , t ) = g L ( x , t ) [ n ( x , t ) ( x , t ) n i ] r ( T ) t q x p p ( x , t ) + 1 J h ( x , t ) = g L ( x , t ) 2 Hole concentraton : q x [ n ( x , t ) p ( x , t ) n i ] r ( T ) t n ( x , t ) Electron current density : J ( x , t ) = q n ( x , t ) E ( x , t ) + qD e e e x p ( x , t ) Hole current density : J h ( x , t ) = q h p ( x , t ) E ( x , t ) qD h x E ( x , t ) = q [ p ( x , t ) n ( x , t ) + N d + ( x ) Poisson's equation : N ( x ) ] a x Uniform doping, full ionization, TE n - type, N d >> N a kT N D 2 n N d N N D , p o = n i n o , = ln o a n q n i p - type, N a >> N d kT N A p o N N d N A , n o = n i 2 p o , p = ln a q n i Uniform optical excitation, uniform doping dn ' n = n + n ' p = p o + p ' n ' = p ' = g l ( t ) ( p o + n + n ' ) n ' r o dt o Low level injection, n',p' << p o + n : dn ' + n ' = g l ( t )
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