ee606_s09_hw9 - establishes the relationship between x and...

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Homework 9 MOSFET Transistors 1. Solve problems 17.2, 17.9, 17.11, 18.6, 18.11, 18.12, and 19.3. 2. In the class, I mentioned that the potential drop along the channel direction is linear at low fields and non-linear at high fields. In this exercise, you will derive the exact shape of the potential drop along the channel direction: (a) Divide the channel in k-segments, so that k x = L ch . Write down the expressions for current for a few segments. Sum over all the segments to show that current per unit width is given by J T = (q µ n C ox /L ch ) [ (V G -V T )VD – V D 2 /2] (1) (b) Next, instead of summing over all the segments, sum over first j segments (where x= j x) to obtain the relationship x J T = q µ n C ox [ (V G -V T )V(x) – V(x) 2 /2 ] (2) where V(x) is the quasi-Fermi level for electrons at location x (so that V=V D at x=L ch . Note that since J T is known from Eq. (1), therefore Eq. (2)
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Unformatted text preview: establishes the relationship between x and V. (c) Assume oxide thickness of 10 nm, channel length of 0.25 m, electron mobility of 300 cm 2 /V-sec. Also assume that threshold voltage is 0.5 volts and the applied gate voltage is 1.5 volts. For V D = 0.1, 0.3, ….1.5 volts, plot (it should require no more than 5-10 lines of MATLAB code). (i) V(x) vs. x (ii) Q(x) vs. x (iii) E(x) vs. x Identify the pinch off regions in these plots. Check to see that the product Q* µ n E in each segment is the same (because current must be continuous). (d) Determine the maximum frequency of oscillation for the MOSFET described in part (c) at V D =1.2 volts. Remember to use the correct formula (velocity saturation vs. square law) by comparing the approximate magnitude of the channel electric field with Fig. 6.3 of Advanced Semiconductor Fundamentals....
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