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646s11hw8c - ELEG 646 ELEG 446 Nanoelectronic Device...

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ELEG 646 ; ELEG 446 - Nanoelectronic Device Principles Spring 2011 Homework #8 - due Friday, 15 April 2011, in class 1. A. symmetrical abrupt Ge p-n junction has dopant concentrations of 10 15 atoms cm -3 on both sides. Calculate the avalanche breakdown voltage if the maximum field at breakdown is 2.5 x10 5 V/cm. Hint: Careful to use Ge materials data rather than Si. 2. In the problem (1) above for Ge with doping impurity concentration N I = 10 15 cm -3 , compare your breakdown voltage with the value obtained by using the following universal (but approximate) expression breakdown voltage for materials with different bandgaps: BV(volts) = 60(Eg/1.1) 3/2 (N I /10 16 ) -3/4 . Here E g is in eV, and N I is in cm -3 . Is this “universal” expression useful? 3. Problem 4.13 in chapter 4, Muller & Kamins, p. 224 in 3rd edition. Hint: In the discussion following Eq. 4.4.20, there is a discussion in the text of current (10 mA), atomic density (5E22 cm -3 ), etc. Use the data and the equations in this section to determine the tunneling probability, then work back to find the L,
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