20085ee2_1_homework 3_08

20085ee2_1_homework 3_08 - range of ) / , / ( a a . What is...

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EE2 Physics for Electrical Engineers Homework #3 I. The period of the one dimensional crystal is 10 Angstrom. How many quantum states do we have in the first band of the band diagram in Fig.14 (including the spin of the electron) if we use the periodic boundary condition for a one dimensional “box” of length one micron? II. If the first band in Fig14 is described by the function eV ka k E ) cos 1 ( ) ( = with a equals 10 Angstrom, Plot the energy band diagram of first band as a function of k in the range of ) / , / ( a a π . III. If we have one electron per unit cell for the crystal in Problem II, find out the Fermi energy at absolute zero. Do we have a metal in this case? Why? IV. Do the same thing as in Problem III if we have two electrons per unit cell. Do we have a metal in this case? Why? V. Plot the group velocity of the electron in the first band as a function of k in the
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Unformatted text preview: range of ) / , / ( a a . What is the maximum velocity? VI. If we apply a constant electric field to the electron with the maximum velocity, can we increase the velocity? Why? VII. Plot the effective mass of the first band as a function of k in the range of ) / , / ( a a . What is the maximum effective mass? What is the minimal positive effective mass? VIII. If we apply a constant electric field of cm V / 10 5 , what is the period of the cyclic motion of the electrons in the first band? --END-- Electrical Engineering Department The Henry Samueli School of Engineering and Applied Science University of California, Los Angeles Dee-Son Pan pan@ee.ucla.edu Phone (310)-825-1123 Fall 2008...
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This note was uploaded on 01/24/2012 for the course EE 3 taught by Professor Staff during the Spring '08 term at UCLA.

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