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Unformatted text preview: 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, s = 2 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 . ln = = i a B n N q kT V 98 . 2- =-- = B g fb q E V V 83 . 97 . 84 . 98 . ) 2 ( 2 2 = + +- = + + = ox B a si B fb t C qN V V V. E c E i E v Oxide p-type silicon E f E f (b) V E c E i E v Oxide p-type silicon E f E f E fn (c) 104 . ) 2 ( 2 = = a B si dm qN W m 164 . 3 = + = ox dm t W m 33 . 2 min = L m 30 . 1 44 . 1 84 . 98 ....
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