20101ee2_1_HW3 solution

20101ee2_1_HW3 solution - EE2 HW3 Solutions 1 Mobility of...

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EE2 HW3 Solutions 1. Mobility of electrons, μ n = 1200 cm 2 /V-sec = 0.12 m 2 /V-sec Given concentration of electrons, n = 10 16 cm -3 Resistivity, ρ = (qn μ n + qp μ p ) -1 For n-type Si, p << n, Therefore, ρ = (qn μ n ) -1 = (1.6 x 10 -19 x 10 16 x 1200) -1 = 0.52 -cm Effective mass, m c * = 0.26m 0 Average scattering time, sec 10 775 . 1 10 6 . 1 12 . 0 10 1 . 9 26 . 0 13 19 31 * × = × × × × = = q m n c m μ τ = 0.1775 psec 2. Hole density varies as p(x) = A exp(-x/L p ) i.e. hole density has a gradient, which obviously gives rise to diffusion Hole diffusion current density, ) / exp( )) / exp( ( ) ( , p p p p p p diff p L x L A qD dx L x A d qD dx x dp qD J = = = The current varies exponentially with distance. This is because the gradient of the hole density varies with distance, hence the diffusion flux varies too and the current is proportional to the diffusion flux. The hole density decreases with x because there is recombination with electrons. There are more electrons for larger x in a forward biased p-

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20101ee2_1_HW3 solution - EE2 HW3 Solutions 1 Mobility of...

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