hw9_soln - UNIVERSITY OF CALIFORNIA AT BERKELEY College of...

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UNIVERSITY OF CALIFORNIA AT BERKELEY College of Engineering Department of Electrical Engineering and Computer Sciences Homework #9 Solutions Due Tuesday, October 30, 2007 EE 105 Fall 2007 Prof. Liu Problem 1. NMOS Capacitor — Electrostatics a) Let’s write the equation for V TH given in lecture and plug in values: V TH = V FB + 2 φ B + 1 C ox radicalbig 2 s N A 2 φ B V FB = - 1 V φ B = kT q ln parenleftbigg N A n i parenrightbigg = (60 mV) log parenleftbigg 10 17 cm - 3 10 10 cm - 3 parenrightbigg = 420 mV C ox = ǫ ox t ox = 3 . 45 × 10 - 13 F / cm 3 × 10 - 7 cm = 1 . 15 μ F / cm 2 V TH = - 15 mV This value of V TH is practically too small (since the MOSFET off state leakage would be very high). A real MOSFET with such a thin gate oxide would have a higher channel doping (which would increase φ B and V ox and therefore V TH ). b) A thinner oxide results in a higher oxide capacitance, which means the gate is more tightly coupled to the channel. This means that the voltage needed to invert the channel should be smaller, meaning the threshold voltage will

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• Fall '07
• King-Liu

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