Physics 308: Assignment 8

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Physics 308: Assignment 8
Due in class Thursday, March 27, 2008
1. (10-32) What type of semiconductor is obtained if silicon is doped with (a) aluminum and (b) phosphorous?
(See Appendix C of the text for the electron configurations of these elements.)
2. (10-37) Compute the fractional change in the current through a pn-junction diode when the forward bias is
changed from +0.1 V to +0.2 V. Assume room temperature.
3. (10-48) Germanium can be used to measure the energy of incident particles. Consider a 660-keV gamma ray
emitted from 137 Cs. (a) Given that the band gap in germanium is 0.72 eV, how many electron-hole pairs can be
generated by
√ this incident gamma ray? (b) The number of pairs N in part (a) will have statistical fluctuations
given by ± N . What then is the energy resolution of the detector in this photon energy region?
4. (10-49) A doped n-type silicon sample with 1016 electrons per cubic centimeter in the conduction band has a
resistivity of 5 × 10−3 Ω m at 300 K. Find the mean free path of the electrons. Use 0.2me for the effective mass
of the electron. Compare your result with the mean free path of electrons in copper at 300 K.
5. (10-50) A “good” silicon diode has a current-voltage characteristic given by
I = I0 eeVb /kB T − 1
Let kB T = 0.025 eV (room temperature) and the saturation current I0 = 1 nA. (a) Show that for small reversebias voltages, the resistance is 25 MΩ. (Hint: Perform a Taylor expansion of the exponential function.) (b) Find
the dc resistance for a reverse bias of 0.5 V. (c) Calculate the ac resistance dV /dI for a 0.5-V forward bias.
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