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143s2006-final

# 143s2006-final - Spring 2006 UNIVERSITY OF CALIFORNIA...

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1 Spring 2006 UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EE143 Final Exam Family Name _______________________ First name______________________SID_______________ Signature______________________________________________________________ Instructions: DO ALL WORK ON EXAM PAGES Make sure your copy of the exam paper has 11 pages (including cover page) This is a 3-hr exam (12 sheets of handwritten notes allowed) Problem 1 (40 points)________________ Problem 2 (20 points)_______________ Problem 3 (40 points) ________________ Problem 4 (40 points) ________________ Problem 5 (35 points) ________________ Problem 6 (25 points) ________________ TOTAL (200 points) __________________ Information which may be useful ε s =1.036 × 10 -12 F/cm for Si ε ox =3.45 × 10 -13 F/cm for SiO 2 q =1.6 × 10 -19 coulombs Boltzmann constant k = 8.62 × 10 -5 eV/K n i of Si= 1.45 × 10 10 cm -3 at 300K E g of Si = 1.12 eV at 300K Electron Affinity of Si =4.15 eV Electric potential φ =(E f -E i )/q n= n i exp(q φ /kT) x d = [ 2 ε s q ( φ i -V a ) ( 1 N a + 1 N d ) ] 1/2 MOS: V GB = φ MS +V ox +V Si V FB = φ MS - 1 C ox [ Q f + 0 x ox x ρ ox (x) x ox dx ] MOSFET I-V (n-channel): I DS = μ n W L C ox [ (V G - V T ) V DS - V DS 2 /2 ] (below saturation) I Dsat = μ n W L C ox [(V G -V T ) 2 /2] (above saturation) Grading: Whenever possible, use sketches to support your explanation. Show correct units and algebraic sign for numerical answers. No partial credit for numerical answers orders of magnitude off.

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