ELEG 646; ELEG 446- Nanoelectronic Device Principles– Spring 2011Homework #12 - due Friday, 13 May 2011, in class1. Problem 8.5 in chapter 8 of Muller & Kamins, p. 422 in 3rd edition. Hints: start with Qs= −Cox(VG−VFB−ψs), then CG= −dQs/dVG. Notes: (a) The symbol φsin this problem is the same as our ψs, in the class lectures; (b) VFBis a constant with VG, but φsis not. Recall that ψand φdiffer by a constant. More hints: careful with book's notation: sometimes they use φswith the meaning as in our lectures, but sometimes they use φsto mean our ψs, 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 xd of an MOS capacitor that is valid for the depletion condition: VFB < VGS < VT. Express xdin terms of VGS, and oxide parameters such as dox, εox, etc. The suggested approach is to set up the MOS charging equation: Vox + Ψs = VGS −VFB, where Vox = −Qdep/Cox, which depends linearly on xd, and Ψs = qNAxd2/2εs. Solve the resulting quadratic equation for x
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Trigraph, Elementary algebra, Electric charge, Bipolar junction transistor