# Microelectronic Circuit Design

• Notes
• 49

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CHAPTER 4 4.1 (a) V G > V TN corresponds to the inversion region (b) V G << V TN corresponds to the accumulation region (c) V G < V TN corresponds to the depletion region 4.2 (a) C ox " = ε ox T ox = 3.9 ε o T ox = 3.9 8.854 x 10 14 F / cm ( ) 50 x 10 9 m 100 cm / m ( ) = 6.91 x 10 8 F cm 2 = 69.1 nF cm 2 (b), (c) & (d): Scaling the result from part (a) yields C ox " = 69.1 nF cm 2 50 nm 20 nm = 173 nF cm 2 | C ox " = 69.1 nF cm 2 50 nm 10 nm = 346 nF cm 2 | C ox " = 69.1 nF cm 2 50 nm 20 nm = 691 nF cm 2 4.3 C d = ε s 2 ε s qN B 0.75 V ( ) = 11.7 8.854 x 10 14 F / cm ( ) 2 11.7 ( ) 8.854 x 10 14 F / cm ( ) 1.602 x 10 19 10 15 / cm 3 ( ) 0.75 V ( ) = 10.5 x 10 9 F / cm 2 4.4 (a) K n ' = μ n C ox " = μ n ε ox T ox = μ n 3.9 ε o T ox = 500 cm 2 V sec 3.9 8.854 x 10 14 F / cm ( ) 50 x 10 9 m 100 cm / m ( ) K n ' = 34.5 x 10 6 F V sec = 34.5 x 10 6 A V 2 = 34.5 μ A V 2 (b) & (c) Scaling the result from part (a) yields K n ' = 34.5 μ A V 2 50 nm 20 nm = 86.3 μ A V 2 | K n ' = 34.5 μ A V 2 50 nm 10 nm = 173 μ A V 2 | K n ' = 34.5 μ A V 2 50 nm 5 nm = 345 μ A V 2 4.5 a ( ) Q " = C ox " V GS V TN ( ) = ε ox T ox V GS V TN ( ) = 3.9 8.854 x 10 14 F / cm ( ) 25 x 10 9 m 100 cm / m ( ) 1 V ( ) = 1.38 x 10 7 C cm 2 b ( ) Q " = C ox " V GS V TN ( ) = ε ox T ox V GS V TN ( ) = 3.9 8.854 x 10 14 F / cm ( ) 10 x 10 9 m 100 cm / m ( ) 2 V ( ) = 6.91 x 10 7 C cm 2 75

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