646hw10sol - not consistent with quantum mechanics 2 3 From...

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ELEG 646, ELEG 446 - Nanoelectronic Device Principles – Spring 2005 Homework #10 - due noon Friday, 20 May 2005, in 140 Evans Hall solution: 1. x i = ( k T/q)/ E s = ( k T/q) sqrt[ ε s /2qN A (-2 φ pB ) ]. At T= 4K, we have: k T/q = 0.345 mV, φ pB = - 0.3 V, and N A = 1E15 cm -3 for this φ pB , assuming that all dopants are ionized (which would not be the case at 4K in practice due to carrier freeze out). This gives: x i = 0.345 mV sqrt[(12x8.85E-14 F/cm)/ (2x1.6E-19Cx1E15 cm -3 x0.6V)] = 0.257 nm. This value is much less than the wavelength of an electron (about 2 nm) so it is a classical result and is
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Unformatted text preview: not consistent with quantum mechanics. 2. 3. From data for an Al gate on p-type silicon polysilicon, we obtain Φ ms = 0.32 V. This gives: Homework assignments will appear on the web at: http://www.ece.udel.edu/~kolodzey/courses/eleg646s05.html Note: On each homework and report submission, you must please give your name, the due date, assignment number and the course number....
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