hw7_f10 - condition for equilibrium between electrons and...

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Physics 112, Spring 10: Holzapfel Problem Set 7 (6 Problems). Due Friday, October 22, 2010, 5 PM Problem 1 : Distribution Function for Double Occupancy Statistics Kittel 6.3 Problem 2 : Energy of Gas of Extreme Relativistic Particles Kittel 6.4 Problem 3 : The Relation Between Pressure and Energy Density Revisited a) Kittel 6.7 b) Calculate the pressure of a Fermi gas (in atmospheres) at zero temperature using the electron density for Copper ( n e = 8 × 10 22 cm - 3 ). Problem 4 : Gas of Atoms with Internal Degrees of Freedom Kittel 6.9 Problem 5 : Ideal Gas in Two Dimensions Kittel 6.12 Problem 6 : Chemical Equilibrium Between Electrons and Holes An electron in the conduction band interacts with a hole in the valance band. The excess energy is carried away by a phonon, a particle whose chemical potential is zero because its number is not conserved. The
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Unformatted text preview: condition for equilibrium between electrons and holes is: μ e + μ h = . Assume that the electrons and holes each form an ideal gas and that the conduction band is separated from the valance band by an energy gap E g . (a) Show that the density of electrons in the conduction band is given by: n e = 2 ± τ √ m e m h 2 π ¯ h 2 ² 3 / 2 exp ±-E g 2 τ ² , where m e and m h are the effective masses of the electrons and holes. (b) Use your result from part (a) to show that: μ e = E g 2 + 3 τ 4 ln ± m h m e ² . (c) Now consider a semiconductor that also contains a density n D of donors that each contribute one electron to the conduction band. Show that the electron density is now: n e = n D 2 + r n 2 D 4 + n 2 e . 1...
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