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Unformatted text preview: EE138: Homework Assignment #4 U HOMEWORK DUE: 11/16/2009 (in lecture) HOMEWORK QUIZ: 11/18/2009 (in lecture) Problem #1: (a) Calculate the number of electrons in the conduction band for germanium at T = 300 K. Use mh* = me* and Table 8.3 in S & W. (b) Would germanium still be an intrinsic semiconductor at room temperature if the band gap was 4 eV wide? Explain! (Hint: Calculate Ne at room temperature how does this number compare to values for known semiconductors?) Problem #2: Consider a semiconductor with 1013 donors/cm3 which have an ionization energy of 10 meV. (a) What is the concentration of extrinsic conduction electrons at 300 K? (b) Assuming an energy gap of 1 eV (and m*= the mass of a free electron), what is the concentration of intrinsic conductions electrons? (c) Which contribution is larger? Problem #3: You would like to know the energy gap for germanium. Using a measurement set‐up in your lab you measure resistivity while varying temperature and obtain the following data: T (K) 385 455 556 714 0.028 0.0061 0.0013 0.000274 ohm‐m) (a) Determine the value of Eg. To confirm this bandgap, you decide to make a transmission measurement of the material. (b) At about what wavelength would you expect the onset of absorption? Problem #4: A certain semiconductor is doped with acceptor type impurities of density NA which have an impurity level at EA = Eg/5. At the temperature of interest Eg = 20kT and EF = 5kT. The effective masses of electrons and holes are me* = 0.12mo and mh* = mo, where mo is the mass of a free electron. For NA = 1023 m‐3 find the following: (a) the ionized acceptor density (b) the ratio of electron density to hole density (c) the hole density (d) the electron density (e) the temperature (f) the energy gap (Hint: In equilibrium, the semiconductor must have charge neutrality.) U U U U Problem #5: The Czochralski method is used to grow a silicon crystal. The melt contains 1017 phosphorus impurities per cubic centimeter. What will the concentration of phosphorus be in the boule during initial growth? For P in Si, kd = 0.35. Problem #6: You would like to know the mobility of a semiconductor material. You decide to use the Haynes‐Shockley experiment to make the measurement. Your measurement set‐up and the collected voltage versus time data are shown in Figure 8.13 of S &W. In your experiment, the distance between point A and C is 10 microns, there is a 1 V total difference in potential between the two points when the switch ‘S’ is closed at t1, and t2 is 2 ns. What is the mobility of the semiconductor material? Problem #7: (a) Sketch the E versus x band diagrams for p‐type Si and n‐type silicon. Label the donor level, acceptor level, bandgap, conduction band edge, valence band edge, and Fermi level. (b) Now place the p‐type and n‐type silicon in contact with one another to make a p‐n junction. Sketch the E versus x band diagrams for p‐type Si and n‐type silicon. Label the donor level, acceptor level, bandgap, conduction band edge, valence band edge, and Fermi level. Problem #8: A GaAs pn junction diode has a concentration of 1016 acceptor atoms cm‐3 on the p‐side and a concentration of 1017 donor atoms cm‐3 on the n‐side. ni = 1.2 x 106 cm‐3 and r = 13.1 (a) Calculate the built‐in potential at room temperature. (b) Calculate the depletion region width at room temperature. U U U U ...
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