314-SampleProblems-F201000007

# 314-SampleProblems-F201000007 - o o o material is found to...

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D i 13. An n-type semiconductor (N = 10 cm ) w ith an energy gap of 1.2 eV has an n = 10 17 -3 10 n p cm , : = 8,500 cm /V-sec, and : = 400 cm /V-sec at T = 300 K. Near the room -3 2 2 temperature, the mobilities are found to obey a T functional dependence, w here T is the -3/2 temperature in Kelvin. (a) Compute the conductivity at 300 K, stating all the assumptions made. (b) Compare it w ith the conductivity at 300 K of a Group III metal (assume a mobility comparable to that of the semiconductor). Comment. (c) What physical process w ould cause the mobility to decrease w ith temperature (as happens in a semiconductor)? (d) Write an expression for the temperature variation of the conductivity for this n-type semiconductor near 300 K (The only unspecified quantity in the expression should be T). (e) Write an expression for the temperature variation of the conductivity of the metal. Assume mobility still varies as T . -3/2 (f) If this semiconductor w ere intrinsic, w hat w ould be the temperature dependence of conductivity? G 14. Consider a semiconductor w ith E = 1.0 eV. The effective mass of electrons in this
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Unformatted text preview: o o o material is found to be 1.08 m and that of holes 1.5 m , w here m is the free electron rest D mass. A sample of this material is doped n-type w ith N = 10 cm and is found to have a 16-3 resistivity of 0.2 S-cm. (a) What is the electron mobility at room temperature for this sample? (b) Calculate the mean time betw een collisions for the electrons in the conduction band. c (c) The average energy of these electrons in the conduction band is [E + (3/2)kT], c w here E is the conduction band edge. If all of the (3/2)kT is kinetic energy, w hat is the average thermal speed of these electrons? (d) What is the average distance traversed by the electrons betw een collisions (mean free path)? (f) There is a strong impetus to make solid state devices ever smaller in size. Using this semiconductor, can devices be made up to the point w here the concept of mobility is no longer valid....
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