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143f2010-08-soln

# 143f2010-08-soln

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N.CHEUNG EE143 Fall 2010 Homework Assignment # 8 Solutions Problem 1 Simple resistance and capacitance calculations (a) R S = / t = 3.2x 10 -6 -cm/ 10 -4 cm = 0.032 /square (b) R = R S (L/W) = 0.032 50 = 1.6 (c) C ox = 3.9 8.854 10 -14 / 10 -4 = 3.5 10 -9 F/ cm 2 C = C ox (WL) = 3.5 10 -9 F/cm 2 0.05cm 0.001cm = 0.175 pF (d) RC = 1.6 (0.175 10 -12 ) = 0.28 psec. (e) RC = 0.28 psec/3.9 = 0.07 psec. Problem 2 Electromigration failure (a) MTF 2 / MTF 1 = exp [ -0.5eV / k) ( 1/T 2 – 1/T 1 ) For T 2 = 300K and T 1 =400K, the ratio is about 125. Note: MTF of electromigration failure degrades rapidly with elevated operating temperature. (b) I (max) = cross-sectional area x J (max) = 10 -4 cm x 10 -4 cm x 5 x 10 5 A/cm 2 = 5 mA. Comment: With future scaling of device dimensions, interconnect width has to scaled also to maintain the same pitch. Height of interconnect will also be reduced to maintain a reasonable aspect ratio from thin-film deposition and etching considerations. With a design rule of J(max) ~ 5E5A/cm 2 , I(max) will be limited to 1mA per interconnect if the cross-sectional area is reduced to 0.5 um 2 . However, circuit designers would

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143f2010-08-soln

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