HW2 - Solutions

# HW2 - Solutions - UNIVERSITY OF CALIFORNIA College of...

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Page 1 of 6 UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EE 105 Prof. Salahuddin Fall 2009 Homework Assignment #2 Solution Due at the beginning of class on Friday, 9/15/09 Problem 1 [20 points]: Pglyph1197 Junction I-V The minority-carrier diffusion lengths ( L n and L p ) are related to the minority-carrier diffusion constants ( D n and D p , respectively) by the equation L = ( D τ) 0.5 , where τ is the minority-carrier lifetime. Consider a PN junction of area 100 μm 2 formed by locally introducing boron into the surface region of a silicon sample that is uniformly doped with phosphorus, as shown to the right. The minority-carrier lifetime for electrons in the P-type region is τ n = 0.01 μs, and the minority-carrier lifetime for holes in the N-type region is τ p = 1 μs. The diode is maintained at 300 K. a) Calculate the diode saturation current, I S (Use the mobility curves from Problem 3 of HW #1 to determine the minority-carrier mobilities within the quasi-neutral regions, and then use the Einstein Relation to calculate the minority-carrier diffusion constants.) b) At what applied bias voltage V D does the diode conduct 1 mA of current? What percentage of this current is carried by holes across the junction (at x = 0)? c) How would I S change if the doping concentration on the P-type side were to be increased ( e.g. to 10 19 cm -3 )? Provide a qualitative explanation for your answer (without resorting to any equations). d) The PN diode can be used as a very sensitive temperature sensor. Explain qualitatively how the diode current changes with increasing temperature (near room temperature), for a fixed forward bias voltage. You may assume that the minority-carrier mobilities and lifetimes do not change substantially with temperature. Solution 1 [20 points]: Pglyph1197 Junction I-V a) The diode saturation current is given by the equation + = + = = D p p i D p p A n n i p D p n A n i S S glyph817 D Aqn glyph817 D glyph817 D Aqn L glyph817 D L glyph817 D Aqn AJ I 1 1 1 2 2 2 τ τ τ , where A is the PN junction area in cm 2 , q is the electronic charge (1.6×10 -19 C), n i is the intrinsic carrier concentration in cm -3 , D n is the electron diffusion constant in cm 2 /s, glyph817 A is the acceptor concentration in cm -3 , L n is the electron diffusion length in cm, D p is the hole diffusion constant in cm 2 /s, glyph817 D is the donor concentration in cm -3 , L p is the hole diffusion length in cm, τ n is the electron lifetime in s, and τ p is the hole lifetime in s.

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