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 ad i NN kT V qn = , 00 0 2 dn a d qN x qV N N εε ⎛⎞ Ε=− =− ⎜⎟ + ⎝⎠ , 0 2 11 V W qNN ε =+ , (a), N a (cm -3 ) 14 51 0 × 14 0 × 14 0 × 14 0 × 14 0 × 14 0 × N d (cm -3 ) 14 10 15 10 16 10 17 10 18 10 19 0 × 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 0 × V 0 (volts) 0.754 0.814 0.874 0.933 0.993 1.05
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(b) N a = 5x10 14 /cm 3 N a = 10 19 /cm 3 5 00 0 2 2 2 ln 10 / dn ad i qN x qV N N N N N N kT Vc m NN n εε ε ⎛⎞ Ε=− =− = ⎜⎟ ++
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ece340Fall03HW9sol - ECE 340 Homework IX Fall 2003 Due...

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