Prelim 1 spring 08

Prelim 1 spring 08 - ECE 315 Prelim 1 Solution Spring 2008...

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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 a = φ B - qN d x 2 d 2 = 0 . 8892 - 1 . 602(10 - 19 )(10 16 )(10 - 4 ) 2 (2)1 . 035(10 - 12 ) = - 6 . 850 volts .
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