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# hw2 - EEL3306 l.N 99.“ 9° 10 Fall 2003 Homework#2 Due...

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Unformatted text preview: EEL3306 l. .N 99?.“ 9° 10. Fall 2003 Homework #2 Due: Monday Feb. 2 Under equilibrium conditions and T > OK, what is the probability of an electron state being occupied if it is located at the Fermi level? If Ef is located at 5kT below Be, determine the probability of ﬁnding electrons in states at BC — 3kT. Determine the probability of ﬁnding a hole at 4kT above Ev. Problem 3.2 from text. Problem 3.9 from text. Determine the equilibrium electron and hole concentrations inside a uniformly doped sample of silicon under the following conditions: (a) T = 300K, Na << Nd, Nd =1015 cm “3. (b) T = 300K, Na >> Nd, Na =1016 cm ‘3. (c) T = 300K, Na = 9 x1015 cm “3, Nd =1016 cm ’3. (d) T = 450K, Na = 0, Nd =1014 cm ‘3. (e) T = 500K, Na = 0, Nd =10l4 cm ‘3. For each of the conditions from #6 above (a through 6), determine the location of Bf (numerical answer required) and sketch an energy band diagram for each. NOTE: The bandgap (Eg) for Si at 450 = 1.08 eV and 1.015 eV at 500K. Use Figure 3-17 for m vs. T values. Problem 3.12 from text. Using the Hall experiment example from class, and assuming the semiconductor in question is n—type, develop and describe with words, equations and drawings why the Hall voltage (VH also called Vab in our drawing) is negative. Short answer: (a) An average hole drift velocity of 103 cm/sec results when 2 V is applied across a 1 cm long semiconductor bar. What is the hole mobility inside the bar? (b) The carrier mobility in intrinsic silicon is (choose one: higher than, lower than, the same as) that of heavily doped (> 1016 0mg) silicon. Brieﬂy explain why the mobility in intrinsic silicon is (chosen answer) that of heavily doped Si. (c) Two Si wafers, one n—type and the other p-type, are uniformly doped such that Nd (wafer 1) = Na (wafer 2) >> ni. Which wafer will exhibit the higher resistivity? Explain why. (d) A 500 ohm resistor is to be made from a bar-shaped piece of ndtype Si. The bar has a cross-sectional area of 10'2 cm2 and current-carrying length of 1 cm. Determine the doping required. (e) A lightly doped (Nd < 1014 cm'3) Si sample is heated up from room temperature to 100 degrees C. Nd >> ni at both room temperature and at 100 degrees C. Is the resistivity of the sample expected to increase or decrease? Explain. ll. 12. A bar of n-type Si 1 cm long is doped with 1015 cm"3 of donor atoms at T = 300 K and a voltage of 5 V is applied to the ends of the bar. Determine: (a) The hole drift current density. (b) The total drift current density. Draw the energy band diagram for the Si sample from problem 11 when no voltage is applied. ...
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