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# ps06 - 1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.012 ELECTRONIC DEVICES AND CIRCUITS Problem Set No. 6 Issued: October 10, 2003 Due: October 17, 2003 Reading Assignments: Lecture 12 (10/14/03)- Chap. 10 (10.1.1a) Lecture 13 (10/16/03)- Chap. 7 (7.2.2, 7.3.4); Chap. 8 (8.2.1); Chap. 10 (10.2.1) Lecture 14 (10/21/03)- Chap. 7 (7.4.2); Chap. 8 (8.2.2, 8.2.3); Chap. 10 (10.2.2, 10.2.3) Lecture 15 (10/23/03)- Chap. 15 (15.1, 15.2) Lecture 16 (10/28/03)- Chap. 15 (15.2.4) Problem 1 - Do Problem 9.1 in the course text using µ h = 300 cm 2 /V-s, rather than the value specified in the text. Problem 2 - Do Problem 9.8 in the course text. Problem 3 - This problem concerns the novel semiconductor-oxide-semiconductor (SOS) structure illustrated below. The two semiconductor regions are both p-type silicon with a net acceptor concentration of 10 16 cm -3 ; the oxide is a 50 nm (5 x 10 -6 cm) thick layer of silicon dioxide. The dielectric constant of silicon, e S i , is 10 -12 F/cm and of silicon dioxide, e ox , is 3.5 x 10 -13 F/cm. p-Si 10 16 cm -3 B A -w SiO 2 p-Si 10 16 cm -3 w -t ox /2 0 t ox /2 x Use the depletion approximation model when solving this problem. Assume that the depletion region widths are less than w/2. The drawing may not be to scale. (a) Sketch and label the electrostatic potential, f (x), in this structure between -w/2 and +w/2 when v AB = 0 and the structure is in thermal equilibrium. (b) A bias is applied to this device sufficient to make the electrostatic potential at x = t ox /2 equal to - f p , where f p is the thermal equilibrium electrostatic potential in the p- type regions, i.e., f (t ox /2) = - f p . We call this the onset of inversion on the right side, and name this bias the right-side threshold, V TR .

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2 (i) What is the sign of V TR ? Explain your answer. (ii) What is the width of the depletion region to the right of x = t ox /2 with this applied bias? (iii) What is the condition of the left-hand semiconductor-oxide interface, the one at x = -t ox /2 with this applied bias?
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