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AP183b2009HW2 - (b Use the concept of electrochemical...

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1 California Institute of Technology Applied Physics APh 183 Physics of Semiconductors and Semiconductor Devices Spring 2009 Homework #2 Issued: 4/7/09 Due: 4/10/09 Problems: 1. Metal-Insulator-Metal Junction and Electrochemical Potential: Consider a metal-insulator-metal junction attached to a battery, as sketched above. It has one aluminum electrode and one platinum electrode. (a) For battery voltage V B = 0, determine the magnitude and direction of the electric field in the oxide. Find also the charge density on each electrode. (b) Now find the value of V B required to make the electric field in the oxide vanish. (c) Assuming that rapid tunneling becomes possible when the electric field exceeds 5 x 10 6 V/cm, what thickness of oxide would lead to rapid tunneling? What would you expect to happen to the electric fields and charge densities in this case?
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Unformatted text preview: (b) Use the concept of electrochemical potentials to explain the difference between a metal-metal junction and a battery. For example, why can’t we measure with a voltmeter the potential difference across an Al/Pt junction, whereas we have no trouble measuring the voltage across a battery? 2. Doping Dependence of Carrier Concentrations in GaAs Consider GaAs doped with Te ( E c – E d = 0.030 eV). Assume that N c = 4.7 x 10 17 cm-3 , N v = 9.5 x 10 18 cm-3 and a bandgap of 1.42 eV. (a) Determine n i 2 at 300 K. (b) Determine np/n i 2 as a function of N d , the donor density. In particular, at what doping density does np deviate from n i 2 by as much as 10%? What happens when N d gets very large (large enough, for example, to have E F between E c and E d )? + V B - Copper Wires Al SiO 2 100 nm Pt q φ Al = 4.1ev q Pt = 5.1ev...
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