454Spring08HW2_Solution

# 454Spring08HW2_Solution - –(Q ox C ox =-2.51[V 3(5 points...

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ECEN 454 Digital Integrated Circuit Design Spring 2008 Homework 2 Solution 1. (5 points) Problem 3.1 of the textbook.

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2. (5 points) Problem 3.9 of the textbook. Solution: Φ F(substrate) = (kT/q) * ln (N D,sub /n i ) = 0.026 * ln ((1*10 16 ) / (1.45 * 10 10 )) = 0.348[V] Φ F(gate) = (kT/q) * ln (N D,poly /n i ) = 0.026 * ln ((1*10 20 ) / (1.45 * 10 10 )) = 0.587[V] Φ GC = Φ F(substrate) Φ F(gate) = 0.348 – 0.587 = -0.239[V] C ox = ε ox / t ox = (3.9 * 8.85 * 10 -14 ) / (0.1 * 10 -4 ) = 3.45 * 10 -8 [F / cm 2 ] Q B0 = 2q N D,sub ε si |2 Φ F | = 2*1.6*10 -19 *10 16 *11.7*8.85*10 -14 *2*0.348 = 4.8 * 10 -8 [C / cm 2 ] V T0 = Φ GC – 2 Φ F – (Q B0 / C ox
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Unformatted text preview: ) – (Q ox / C ox ) = -2.51 [V] 3. (5 points) For the circuit given in problem 3.11 of the textbook, determine the regions of operation for the two transistors. You should explain how you reach the conclusions you’ve made. Solution: Let M2 be the bottom transistor and M1 be the upper transistor. For M2, V gs2 = 5V, and so it must be ON (saturation or linear). Furthermore, M1 must be in saturation since V gd1 = 0 < V T . At the same time V gd2 = V gs1 > V T . Thus, we can say that M2 is in the linear region. 4. (5 points) Problem 3.8 of the textbook....
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454Spring08HW2_Solution - –(Q ox C ox =-2.51[V 3(5 points...

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