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ece340Fall03HW9sol

# ece340Fall03HW9sol - ECE 340 Homework IX Fall 2003 Due...

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ECE 340 Homework IX Fall 2003 Due: Wednesday, October 15, 2000 (20 points total) 1. Consider the following Si p-n junctions operating at 300 K. (a) Using Eq. (5-8), calculate the contact potential V o for N a = 5x10 14 and 10 19 /cm 3 , with N d = 10 14 , 10 15 , 10 16 , 10 17 , 10 18 , 10 19 /cm 3 in each case and plot V o vs. N d . (b) Plot the maximum electric field E o vs. N d for the junctions described in (a). What levels of N d doping are required so E o can exceed 10 5 V/cm when N a = 2x10 19 /cm 3 ? (c) Plot the width of the depletion region W vs. N d for the junctions described in (a). Solutions The relevant equations used in part (a), (b), (c) are: 0 2 ln a d i N N kT V q n = , 0 0 0 2 d n a d a d qN x qV N N N N ε ε Ε = − = − + , 0 2 1 1 a d V W q N N ε = + , (a), N a (cm -3 ) 14 5 10 × 14 5 10 × 14 5 10 × 14 5 10 × 14 5 10 × 14 5 10 × N d (cm -3 ) 14 10 15 10 16 10 17 10 18 10 19 1 10 × V 0 (volts) 0.498 0.557 0.617 0.677 0.736 0.796 N a (cm -3 ) 19 10 19 10 19 10 19 10 19 10 19 10 N d (cm -3 ) 14 10 15 10 16 10 17 10 18 10 19 1 10 × V 0 (volts) 0.754 0.814 0.874 0.933 0.993 1.05

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