Microelectronic Circuit Design

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CHAPTER 3 3.1 φ j = V T ln N A N D n i 2 = 0.025 V ( ) 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 ( ) 1.602 x 10 19 C 1 10 19 cm 3 + 1 10 18 cm 3 0.979V ( ) 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 ( ) 10 19 cm 3 ( ) 3.39 x 10 7 cm ( ) 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 ( ) 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 ( ) 1.602 x 10 19 C 1 10 18 cm 3 + 1 10 15 cm 3 0.748V ( ) w do = 98.4 x 10 6 cm = 0.984 μ m 3.3 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 18 cm 3 | p no = n i 2 n no = 10 20 10 18 = 10 2 cm 3 φ j = V T ln N A N D n i 2 = 0.025 V ( ) ln 10 18 cm 3 ( ) 10 18 cm 3 ( ) 10 20 cm 6 = 0.921 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 ( ) 1.602 x 10 19 C 1 10 18 cm 3 + 1 10 18 cm 3 0.921V ( ) w do = 4.881 x 10 6 cm = 0.0488 μ m 34
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