Name ECE Box # Problem Score Points 1 10 2 30 3 35 4 25 EE3901 A2001 Semiconductor Devices Exam 1 This is a closed book test! You are allowed one sheet (both sides) of notes. Note: Potentially useful reference charts are given on pages 2 and 3. Show all your work. Partial credit may be given. If you think you need something that you can't remember, write down what you need and what you'd do if you remembered it. Unless otherwise indicated, you may assume Si at T=300K. Look for the simple, straightforward way to solve the problem for the level of accuracy required. Don't get entangled in unnecessary algebra. As in real life, some problems may give you more information than you need. Don't assume that all information must be used! It's your job to decide what's relevant to the solution. You will have 50 minutes to complete this exam. There are 4 problems on a total of 11 pages. 1
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1. Four bonding model diagrams, labeled A D, are shown on the opposite page. For each of the five types of semiconductor situations described below, indicate the letter of the corresponding bonding diagram AND explain your choice (no more than one or two simple but convincing sentences necessary)! Note: A diagram may be used once, more than once, or not at all. i) A semiconductor doped with an acceptor impurity. Explain: [2] ii) An n-type semiconductor. Explain: [2] iii) An intrinsic semiconductor at temperature T=0K. Explain: [2] iv) A p-type semiconductor. Explain: [2] v) A semiconductor doped with a donor impurity. Explain: [2] 4
A B C D 5
2. For each of the following questions, provide the requested numerical answer (accuracy 2 significant figures) AND, for the semiconductor device terms in boldface in each question, provide a brief (one or two sentence) definition in your own words. Don t just write down a number copied from your notes sheet and expect to get credit! Example of a good definition: one that you would use in a job interview to quickly convince someone that you have some clue as to what you re talking about. Feel free to supplement your definition with any diagram(s) you might draw on an office whiteboard. a) In Si at T=300K doped with acceptors at a concentration of N A =1E+13/cm 3, determine the equilibrium concentration of mobile holes (p) and concentration of mobile electrons (n) p = n = Definitions: acceptor mobile electron 6
b) For intrinsic Si in equilibrium at T=300K, what is the probability that a state is occupied at energy E C (the lower edge of the conduction band)? Probability = Definitions: intrinsic conduction band c) What is the mobility µ p of holes in Si at T=300K doped with N A =1E+17 /cm 3? µ p = Definitions: mobility holes 7
3. An energy band diagram for a region of semiconductor material is shown in the figure on the opposite page. a) Identify and label the unlabeled energy levels on the diagram. [6] b) Do equilibrium conditions prevail? (Circle one): YES: EQUILIBRIUM NO: NONEQUILIBRIUM [1] EXPLAIN!: [5] c) Using the space in the figure, indicate which side is p-type and which side is n-type [6] d) Determine the doping density N A on the p-side and N D on the n- side (accuracy 2 significant figures): [6] N A = N A = e) Using the axes in the figure, sketch the shape of the electrostatic potential (voltage V) [5] f) Is there a nonzero electric field anywhere in the material? YES: e 0 SOMEWHERE NO: e = 0 EVERYWHERE [1] EXPLAIN!: [5] 8
Indicate here for (c): 0.56 ev 0.30 ev EF 0.56 ev EF 0.20 ev Axes for (e): V 9
4. A resistor (shown on the opposite page) is formed from a block of n-type semiconductor material which is uniformly doped with N D = 1E+15 donor/cm 3. a) Determine the resistance at T=300K (accuracy 2 significant figures). [5] R = b) If the temperature increases to T=350K, will the resistance decrease or increase? (Circle below): DECREASE INCREASE [1] EXPLAIN!: In parts (c) through (e), a voltage of 5V is applied to the resistor, and a current flows. c) Is the current diffusion current, drift current, or both? (Circle below): DIFFUSION BOTH DRIFT [1] EXPLAIN!: d) Is the current electron current, hole current, or both? (Circle below): ELECTRON BOTH HOLE [1] EXPLAIN!: e) With an applied voltage of 5V, determine the average velocity v d of a carrier (accuracy 3 significant figures). Be sure to indicate the units of your answer! [5] v d = 10
R 0.5 cm 2.0 cm 0.1cm 5V 11