Prelim 1 spring 08 - March 11, 2008 ECE 315 Prelim # 1...

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March 11, 2008 ECE 315 Prelim # 1 Solution Spring 2008 1. Consider a silicon p + n junction sample where the acceptor density far exceeds that of the donor density. N a = 10 19 cm - 3 N d = 10 16 cm - 3 a)(8 pts) Using the concept of overall charge neutrality, show that we can ignore the de- pletion region thickness on the p side of the diode. In the depletion region the charge on each side is equal and opposite, then: qN d x n = qN a x p -→ x p = N d N a x n = x n 1000 0 . What can be said! b)(7 pts) Compute the diode’s built in potential (I call this φ B ). The built in potential (back of exam) is given by: φ B = kT q ln N a N d n 2 i = 25 . 86(10 - 3 ) ln 10 19 10 16 [1 . 08(10 10 )] 2 = 0 . 8892 volts . c)(7 pts) At what applied voltage will the depletion region be 1 μ m thick. Neglecting the depletion on the p-side, then from back of exam: x d x n = s 2 ± s ( φ B - V A ) qN d N a N d + N a s 2 ± s ( φ B - V a ) qN d -→ V a = φ B - qN d x 2 d 2 ± . V
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Prelim 1 spring 08 - March 11, 2008 ECE 315 Prelim # 1...

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