ECE 230B, HW-2, Winter 2010 1. When the gate voltage greatly exceeds the threshold for strong inversion, a first-order solution of ψ s ( V g ) can be obtained from the coupled equations, Eqs. (2.195) and (2.182), by keeping only the inversion charge term. Show that ε s B ox g fb B si a kT q C V V kTN ≈ +-- 2 2 2 2 ln ( ) under these circumstances. Estimate how much s can be higher than 2 B by substituting some typical values in the logarithmic expression. 2. In the split C-V measurement in Fig. 2.37(b), show that the n + channel part of the small-signal gate capacitance is dQ dV C C C C C i g ox i ox i d = + + . Sketch the functional behavior of dQ i / dV g versus V g , and from which describe the behavior of Q i versus V g . 3. Sketch the C-V curve (high frequency) of an MOS capacitor consisting of n + poly gate on n-type Si doped to N d =10 16 cm-3 . Calculate and show the flatband voltage on the C-V.
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