UNIVERSITY OF CALIFORNIA, BERKELEYCollege of EngineeringDepartment of Electrical Engineering and Computer SciencesEE 130: IC Devices Spring 2003FINAL EXAMINATIONNAME: ______________ ___________________ _______________Last First SignatureSTUDENT ID#: ______________ E-MAIL: __________________________INSTRUCTIONS:1. Use the values of physical constant provided below.2. SHOW YOUR WORK. (Make your methods clear to the grader!)3. Clearly mark (underline or box) numeric answers. Specify the units on answers whenever appropriate.1 ______________ / 302 ______________ / 303 ______________ / 404 ______________ / 305 ______________ / 306 ______________ / 40Total: ___________ / 200Problem 1: Semiconductor Fundamentals [30 points]Consider the following uniformly doped n-type Si sample of length 100 µm, maintained at T = 300K:Light incident on the surface is absorbed at x = 0, resulting in Δpn0 = 108/cm3 excess holes at x = 0. (The generationrate for x > 0 is zero.)a) Describe the carrier actions (drift, diffusion, recombination-generation) in this sample. [5 pts]b) i) Write a differential equation (simplest form possible) for the excess hole concentration Δpn, for x > 0. [5 pts]ii) What is the general solution for this differential equation? [2 pts]iii) What boundary conditions must Δpn(x) satisfy? [2 pts]iv) Solve for Δpn(x) and sketch it accurately on the axes provided below. Indicate the maximum value, and thepoint at which Δpn(x) falls to 1/e of the maximum value. [3 pts]c) Draw the high-band diagram for this sample, indicating the positions of the quasi-Fermi levels for electrons andholes (FN and FP, respectively) relative to the intrinsic Fermi Level Ei. [5 pts]d) Do low-level injection conditions prevail throughout this sample? Justify your answer. [2 pts]e) Do equilibrium conditions prevail throughout this sample? Justify your answer. [2 pts]f) Estimate the resistivity of this sample. [4 pts]Problem 2: Metal-Semiconductor Contact [30 points]The following is the equilibrium (T = 300K) energy-band diagram for an ideal metal-semiconductor contact:a) Label the Schottky barrier height (φB) and built-in voltage (Vbi) on the band diagram above. Calculate the valuesof φB and Vbi. [6 pts]b) Is this a rectifying or ohmic contact? Explain why. [3 pts]c) What does qVbi represent? (Why is there a built-in voltage?) [2 pts]d) Sketch the energy-band diagram for this M-S contact with 0.3 V forward bias applied (VA = 0.3 V). Indicate qVAon your diagram. [5 pts]e) Explain how the doping concentration in the silicon can be determined from capacitance measurements. [8 pts]f) Sketch the equilibrium energy-band diagram for a metal (φM = 4.8 eV) contact of degenerately doped n-typesilicon. Why is this practically an ohmic contact? [6 pts]Problem 3: pn Junction Diode [40 points]A pn diode is formed by introducing boron into the surface region of a Si sample uniformly doped with phosphorus:a) Draw the equilibrium (T = 300K) energy-band diagram for this diode. Indicate the position of EF relative to Ei inthe quasi-neutral regions. (Numerical values are required.) Label the depletion width W and built-in potential Vbi,and calculate their values. [15 pts]b) Sketch the energy-band diagram for this diode with a large reverse bias applied. Use this diagram to explain howreverse-bias breakdown occurs. [5 pts]c) Suppose a forward bias of 0.6 V is applied to this diode: (Note that [exp(qVA/kT)] = 1010)i) Sketch the excess minority carrier profiles in the quasi-neutral regions. Indicate their values at the edges of thedepletion region. [6 pts]ii) Estimate the total amount of excess minority carrier charge (in units of C/cm2) stored in the diode. [4 pts]iii) Estimate the diode current density. [5 pts]iv) Suppose the diode is suddenly shut off at t = 0 by disconnecting it from the circuit, so that no current flows fortimes t > 0. Show how the excess minority carrier charge on the n-side changes, for t > 0. Estimate the time requiredfor the diode voltage to reach 0 V. [5 pts]Problem 5: Metal-Oxide-Semiconductor Capacitor [30 pts]a) Was this C-V characteristic measured using a high-frequency ac signal, or low-frequency ac signal? How do youknow? [3 pts]b) Is the Si substrate n-type, or p-type? Justify your answer. [3 pts]c) Is the poly-Si gate doped heavily in n-type or p-type? Justify your answer. [3 pts]d) Sketch the MOS energy-band diagram corresponding to the gate bias at point A on the C-V curve. [6 pts]e) Describe how you would obtain the following parameters from the C-V data:i) gate-oxide thickness (Tox) [3 pts]ii) substrate doping concentration (Nsub) [4 pts]iii) flatband voltage (VFB) [4 pts]iv) fixed oxide charge density (QF) [3 pts]Problem 6: MOS Field-Effect Transistor [40 points]a) In a certain CMOS technology, the electrical oxide thickness it Toxe = 3.45 nm, the body-effect factor is m = 1.2,and the absolute value of the threshold voltage of a long-channel MOSFET is |VT| = 0.4 V.i) Sketch the ID vs. VDS characteristic for an n-channel MOSFET of channel width W = 1 µm, channel length L = 1 µm, and gate bias VGS = 1.5 V. Indicate the values of VDsat and IDsat. [10 pts]ii) For what channel lengths will the effect of velocity saturation be significant (i.e. resulting in a reduction in IDsatby more than a factor of 2)? vsat = 8 x 106 cm/s. [5 pts]b) Short-Answer Questionsi) What does the factor m in the MOSFET drain current (IDS) equation account for? (Why is it needed in order to accurately predict the drain current flowing in a MOSFET?) [4 pts]ii) for a given process technology (i.e. fixed gate-oxide thickness, source/drain junction depth, and channel doping concentration), why does the magnitude of VT decrease at very short channel lengths L? [4 pts]iii) How does the leakage current of a MOSFET change with increasing temperature? Justify your answer.[4 pts]c) Indicate in the table below (by checking the appropriate box for each line) the effect of decreasing the gate oxidethickness (Toxe) on the performance parameters of an n-channel MOSFET. Provide brief justification for each ofyour answers. [12 pts]MOSFET parameterincreasesdecreasesremainsthe sameTransconductance(gm)Body effect parameter(γ)Subthreshold
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