# hw6 - ECE 440 Homework VI Due: Friday, October 16, 2009...

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ECE 440 Homework VI Fall 2009 Due: Friday, October 16, 2009 Please write your name and net ID on your homework. For full credit please show all work leading to your answer. Note some of the metal work functions given below may differ slightly from the textbook. This is intended to simplify the solutions. 1. MOS Band Diagrams. Consider four simple cases of the MOS capacitor, all combinations of low gate metal work function (e.g. Al qΦ M ≈ 4.05 eV), high gate metal work function (e.g. Pt M ≈ 5.15 eV), n+type silicon and p+type silicon substrate. Assume the substrate is highly doped, such that E F coincides with E C (n+) and E V (p+) respectively. The SiO 2 thickness is 2 nm. Please assume silicon electron affinity is qX S = 4.05 eV and band gap is E G = 1.1 eV. (a) Sketch the four band diagrams across all MOS structures in equilibrium (V G = 0 V). (b) Sketch the four band diagrams exactly at threshold (V G = V T ), as the surface is inverted. Is the threshold voltage V T >0 or <0 in each case? 2. MOS Capacitance vs. Voltage. Consider an MOS capacitor with Al gate (qΦ M ≈ 4.05 eV) and HfO 2 dielectric of thickness t OX = 10 nm, electron affinity qX OX = 2.8 eV, band gap E G = 5.8 eV and dielectric constant ϵ OX / ϵ 0 = 20 (relative to that of vacuum). The p-type substrate doping

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## This note was uploaded on 02/21/2010 for the course ECE 440 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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hw6 - ECE 440 Homework VI Due: Friday, October 16, 2009...

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