Department of Electrical and Computer Engineering, Cornell University ECE 3150: Microelectronics Spring 2018 Exam 1 ` March 22, 2018 INSTRUCTIONS: Every problem must be done in the separate booklet Only work done on the exam booklets will be graded do not attach your own sheets to the exam booklets under any circumstances To get partial credit you must show all the relevant work Correct answers with wrong reasoning will not get points All questions do not carry equal points All questions do not have the same level of difficulty Assume room temperature if the temperature is not specified TOTAL POINTS: 0 DO NOT WRITE IN THIS SPACE 1
Problem 1 (MOS Device Physics) 35 points Consider the following standard MOS structure: x Suppose VCB 0 and V GB is such that the device is biased in the inversion region. The depletion region thickness is as indicated in the figure above. Now suppose the value of voltage V CB is increased from zero to a small positive value V CB 0. a) Find an expression for the corresponding change in the total (per unit area) depletion region charge density (units: Coulombs per unit area) in terms of VCB? Signs are important here!! (5 points) b) Find an expression for the change in the inversion layer sheet charge density (units: Coulombs per unit area) in terms of VCB? Signs are important here!! (5 points) c) Find an expression for the change QG in the sheet charge density (units: Coulombs per unit area) on the surface of the gate in terms of VCB? Signs are important here!! (5 points) For the following parts, consider the following scenario: QINT x 2
During fabrication, a zero-thickness sheet charge density of positive charge Q INT (units: Coulombs per unit area) due to fixed immobile impurity atoms got deposited right on the surface of silicon, and in between the silicon and the silicon dioxide, at x=0, as depicted in the figure above. In the following parts, you need to figure out how the device parameters change as a result. d) Find and sketch the E-field everywhere in the structure under flatband condition? (5 points) e) Find and sketch the potential everywhere in the structure under flatband condition? (5 points) f) Find the expression for the flat band voltage V FB in the presence of the charge Q INT? (5 pooints) g) Find the expression for the threshold voltage in the presence of the charge Q INT? (5 points) 3
Problem 2 (FET Circuits) 35 points Consider the following FET amplifier: Assume that for the NFET: W 1m L 0.1 m And: 2 ncox 200 A/V 1 n 0.1 V VTN 0.5 V VDD 3.0 V In the following parts assume that the load resistor R L is not connected and the output has been left open. Also, assume that VM 1.0 V and ID 0 A. a) What is the value of the voltage V BIAS and the value of the voltage V B and the value of the voltage V OUT? (5 points) b) What is the value of the resistor R? (2.5 points) c) Draw a neat and clean small signal circuit model of the circuit and find an expression for the small signal open circuit voltage gain Av vout vin? Simplify your expression for A v assuming ro1, ro2 R. (5 points) d) Find an expression for the small signal voltage ratio vm v in? Is it very large or very small? (2.5 points) e) Find an expression for the small signal short circuit transconductance gain Gm iout vin? Simplify your expression for G m assuming ro1, ro2 R. (Hint: the output in the small signal model needs to be shorted to the ground to calculate this). (5 points) 4
f) Find an expression for the small signal output resistance R out? (5 points) g) If the bias voltage V BIAS is increased from its value in part (a), which one of the two FETs, M1 and M2, will go out of saturation first, and why? (5 points) h) If the bias voltage BIAS V is decreased from its value in part (a), which one of the two FETs, M1 and M2, will go out of saturation first, and why? (5 points) 5
Problem 3 (Light and Current) 30 points Consider a P-doped semiconductor, with two metal contacts, that is illuminated with light resulting in the generation of electron-hole pairs at the uniform rate G L (units: 1/(cm 3 -s) ). The P-doping in the semiconductor is N a. The minority carrier lifetime is infinite. The electron and hole mobilities are n and p, respectively, and the diffusivities are Dn and D p, respectively. The intrinsic carrier concentration is n i. For the following questions, assume steady state. Note that half the points will be for the sketches wherever asked. So don t forget the sketches. a) What is the excess electron concentration x p' x at x L? (5 points) b) Find an expression for the excess electron concentration x for 0 x L ) and sketch it. (5 points) c) Find an expression for the excess hole concentration x 0 x L ) and sketch it. (2.5 pints) n' at x 0 and what is the excess hole concentration n' in steady state in the entire device (i.e. p' in steady state in the entire device (i.e. for d) Find and sketch the electron diffusion current everywhere in the device (i.e. for 0 x L ). (5 points) e) Sketch the hole diffusion current everywhere in the device (i.e. for 0 x L ). (2.5 points), find an expression for the electric field x f) If Dn 2Dp 0 x L ) and sketch it. (5 points) E x everywhere in the device (i.e. for g) Find an expression (with proper sign) for the current I L that flows in the external circuit. (5 points) 6
7 (Silicon) 1/cm Volts (at room temperature) 0.0258 3.9 11.7 F/m 8.85 Coulombs 1.6 J/degree 138 Constants Physical 3 12 19 23 i o ox o s o n q KT q. K