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HW-230B-3_2010a

HW-230B-3_2010a - ECE 230B HW#3 Winter 2010 1 Consider an...

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ECE 230B, HW-#3, Winter 2010 1. Consider an n-channel MOSFET with 20 nm thick gate oxide and uniform p-type substrate doping of 10 17 cm -3 . The gate work function is that of n + Si. (a) What is the threshold voltage? Sketch the band diagram at threshold condition, ψ s = 2 ψ B . (b) What is the threshold voltage if a reverse bias of 1 V is applied to the substrate? Sketch the band diagram at threshold. (c) What is the scale length of this device and how short can the channel length be before severe short-channel effect takes place? Solution: (a) 42 . 0 ln = = i a B n N q kT ψ V 98 . 0 2 - = - - = B g fb q E V ψ V 83 . 0 97 . 0 84 . 0 98 . 0 ) 2 ( 2 2 = + + - = + + = ox B a si B fb t C qN V V ψ ε ψ V. E c E i E v Oxide p-type silicon E f E f

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(b) V E c E i E v Oxide p-type silicon E f E f E fn (c) 104 . 0 ) 2 ( 2 = = a B si dm qN W ψ ε μ m 164 . 0 3 = + = ox dm t W λ μ m 33 . 0 2 min = λ L μ m 30 . 1 44 . 1 84 . 0 98 . 0 ) 2 ( 2 2 = + + - = + + + = ox bs B a si B fb t C V qN V V ψ ε ψ
2. For an nMOSFET with t ox = 10 nm, μ eff = 500 cm 2 /V-s, v sat = 10 7 cm/s, W = 10 μ m, and L = 1 μ m, assume m = 1, (a) Use the n = 1 velocity saturation model to generate I ds vs.

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