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646s11hw12h

646s11hw12h - ELEG 646 ELEG 446 Nanoelectronic Device...

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ELEG 646 ; ELEG 446 - Nanoelectronic Device Principles Spring 2011 Homework #12 - due Friday, 13 May 2011, in class 1. Problem 8.5 in chapter 8 of Muller & Kamins, p. 422 in 3rd edition. Hints: start with Q s = −C ox (V G V FB ψ s ), then C G = −dQ s /dV G . Notes: (a) The symbol φ s in this problem is the same as our ψ s , in the class lectures; (b) V FB is a constant with V G , but φ s is not. Recall that ψ and φ differ by a constant. More hints: careful with book's notation: sometimes they use φ s with the meaning as in our lectures, but sometimes they use φ s to mean our ψ s , as in Fig. 8.8, and on page 393. See Berglund, IEEE TED, v. ED13, p. 701, 1966. 2. Derive an expression for the depletion width x d of an MOS capacitor that is valid for the depletion condition: V FB < V GS < V T . Express x d in terms of V GS , and oxide parameters such as d ox , ε ox , etc. The suggested approach is to set up the MOS charging equation: V ox + Ψ s = V GS −V FB , where V ox = −Q dep /C ox , which depends linearly on x d , and Ψ s = qN A x d 2 /2 ε s . Solve the resulting quadratic equation for x
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