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03_ex1fall_frsht

03_ex1fall_frsht - 6.012 Electronic Devices and Circuits...

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