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20085ee2_1_EE2_HW8_sol

# 20085ee2_1_EE2_HW8_sol - HW 8 solution Permittivity of free...

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HW 8 solution by Alvin (Hsing-Ting) Yu Permittivity of free space cm F m F 14 12 0 10 854 . 8 10 854 . 8 - - × = × = ε Permittivity of silicon cm F m F rs s 14 12 0 10 854 . 8 9 . 11 10 854 . 8 9 . 11 - - × × = × × = = ε ε ε rs ε : Relative permittivity of silicon = 11.9 I. p15 The general equation of minority carrier density is p p L x L x Be Ae x p ' ' ) ' ( + = Δ - (72) p162 From Taylor’s series, x e x + 1 as x<<1 and, when Wn << Lp, thus x’<<Lp, we get ] ' 1 [ ] ' 1 [ ) ' ( p p L x B L x A x p + + - = Δ (82) p170 Applying the boundary conditions ] 1 [ ] 1 [ 0 ) ( ) 0 ( p p L Wn B L Wn A Wn p B A p + + - = = Δ + = Δ By solving the above equations we get ] 1 [ 2 ) 0 ( ] 1 [ 2 ) 0 ( Wn L p B Wn L p A p p - Δ = + Δ = Substituting these values in Equation 82 we get ) ' 1 )( 0 ( ) ' ( Wn x p x p - Δ = Δ (83) p170 II.p16 n region: narrow base => Wn << Lp p172

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p region: wide base => Wp >> Ln p167 ) 1 )( ( - + = + = kT qV n po n n no p F e L n D W p D q Jn Jp J III.p17 (Please also take a look at the solution of problem V below, and example on p154) V n N N q kT V i D A bi 7 . 0 ln 2 = = + - (25) p139 Permittivity of free space cm F m F 14 12 0 10 854 . 8 10 854 . 8 - - × = × = ε Permittivity of silicon cm F m F rs s 14 12 0 10 854 . 8 9 . 11 10 854 . 8 9 . 11 - - × × = × × = = ε ε ε rs ε : Relative permittivity of silicon = 11.9 cm V V N N qN N x F bi D A A D s p 6 10 7 ) ( ) ( 2 2 1 - × = - + = ε (55) p153 cm V V
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20085ee2_1_EE2_HW8_sol - HW 8 solution Permittivity of free...

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