Solution11 - HW11 Solutions 1 Because the doping...

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HW11 Solutions 1. Because the doping concentration is much larger than the intrinsic carrier concentration, the electron concentration is equal to the doping concentration. 3 11 0 0 2 0 3 15 0 10 18 . 1 10 5 × = = × = = cm n e N N n n p cm N n kT Eg V c i d Where Eg is the bandgap of Ge, k is Boltzmann constant, and T is temperature in Kelvin. 2. a d n p n p p N N x x x x W x = = + = = 4 1 ) ( 2 . 0 2 . 0 0 0 0 0 0 The relation between doping concentrations and built-in potential is, 3 16 3 15 2 6 2 2 10 915 . 3 4 10 79 . 9 2 . 1 ) ) 10 86 . 1 ( 4 ln( 026 . 0 ) ln( × = = × = = × × = = cm N N cm N V N n N N q kT V d a d d i d a bi Where q is the charge of an electron, k is Boltzmann constant, and T is temperature in Kelvin. From Na and Nd, we can get depletion region width, m W x m W x m m N N N N q V W n p d a d a bi s μ μ μ ε 344 8 . 0 86 2 . 0 430 10 3 . 4 ) ( 2 0 0 4 2 / 1 = = = = = × = + = The formula for maximum electric field is, m V x qN E s n d 4648 0 max = = ε 3. This problem will explore the relationship between the charge density, electrical field, and voltage potential in the depletion region.
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