hw3 - 3.1 j = VT ln(1019 cm3(1018 cm3 = 0.979V NA ND...

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3.1 φ j = V T ln N A N D n i 2 = 0.025 V ( 29 ln 10 19 cm - 3 ( 10 18 cm - 3 ( 10 20 cm - 6 = 0.979 V w do = 2 ε s q 1 N A + 1 N D φ j = 2 11.7 8.854 x 10 - 14 F cm - 1 ( 29 1.602 x 10 - 19 C 1 10 19 cm - 3 + 1 10 18 cm - 3 0.979V ( 29 w do = 3.73 x 10 - 6 cm = 0.0373 μ m x n = w do 1 + N D N A = 0.0373 μ m 1 + 10 18 cm - 3 10 19 cm - 3 = 0.0339 μ m | x p = w do 1 + N A N D = 0.0373 μ m 1 + 10 19 cm - 3 10 18 cm - 3 = 3.39 x 10 -3 μ m E MAX = qN A x p ε s = 1.60 x 10 - 19 C ( 29 10 19 cm - 3 ( 29 3.39 x 10 - 7 cm ( 29 11.7 8.854 x 10 - 14 F / cm = 5.24 x 10 5 V cm 3.2 p po = N A = 10 18 cm 3 | n po = n i 2 p po = 10 20 10 18 = 10 2 cm 3 n no = N D = 10 15 cm 3 | p no = n i 2 n no = 10 20 10 15 = 10 5 cm 3 φ j = V T ln N A N D n i 2 = 0.025 V ( 29 ln 10 18 cm - 3 ( 10 15 cm - 3 ( 10 20 cm - 6 = 0.748 V w do = 2 ε s q 1 N A + 1 N D φ j = 2 11.7 8.854 x 10 - 14 F cm - 1 ( 29 1.602 x 10 - 19 C 1 10 18 cm - 3 + 1 10 15 cm - 3 0.748V ( 29 w do = 98.4 x 10 - 6 cm = 0.984 μ m 3.21 i D = I S exp v D nV T - 1 or v D nV T = ln 1 + i D I S For i D I S , v D nV T 2245 ln i D I S or ln I D ( 29 = 1 nV T v D + ln I S (
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