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646s10hw11n - ox = − Q dep/C ox which depends linearly on...

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ELEG 646 ; ELEG 446 - Nanoelectronic Device Principles Spring 2010 Homework #11 - due Wednesday, 19 May 2010, in 140 Evans Hall 1. Problem 8.1 (a) only (to n-type Si), in chapter 8, p. 422 of Muller, Kamins & Chan (3rd edition) . 2. Problem 8.5 in chapter 8 of Muller & Kamins, p. 422 in 3rd edition. Start with Q s = C ox (V G V FB ψ s ), then C G = dQ s /dV G . Note: V FB is a constant with V G , but φ s is not. Recall that ψ and φ differ by a constant. Hint 1: 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. Hint 2: see Berglund, IEEE TED, v. ED13, p. 701, 1966. 3. 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
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Unformatted text preview: 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 d . Note that this result for x d can be used to yield the semiconductor contribution (Cs = ε s /x d ) to the total gate capacitance in this depletion region, by putting C S in series with C ox . 4. Problem 9.1 for nMOS and N A = 1E15 and 1E16 cm-3 only, in chapter 9, p. 477 of Muller, Kamins & Chan (3rd edition). 5. Problem 9.3, in chapter 9, p. 477 of Muller, Kamins & Chan (3rd edition). Hint: note that Q n /q is per area. 6. Problem 9.4 (a) only, in chapter 9, p. 477 of Muller, Kamins & Chan (3rd edition). Hint: Note that J = ρ charge v. Homework assignments will appear on the web at: http://www.ece.udel.edu/~kolodzey/courses/eleg646s10.html Note: On each homework and report submission, please give your name, the due date, assignment number and the course number....
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