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Unformatted text preview: 1 Department of Electrical and Computer Engineering, Cornell University ECE 407: Physics of Semiconductor and Nanostructures Spring 2009 Homework 2 Due on Feb. 03, 2009 at 5:00 PM Suggested Readings: a) Lecture notes b) Chapter 1 and Chapter 2 in Kittel (Introduction to Solid State Physics) Problem 2.1 (Pressure of a free electron gas in 3D) For a classical gas the pressure, given by: nKT P = , goes to zero when the temperature goes to zero. For a Fermi gas of free electrons this is not the case. The expression for the pressure is: N S V U P , ∂ ∂ − = where the derivative is taken keeping the TOTAL electron number and TOTAL entropy constant. One can find the pressure of a Fermi gas relatively easily at zero temperature since the entropy will remain constant and one need only worry about keeping the total electron number constant. Find the pressure of a free electron gas (in 3D). Explain physically why the pressure of an electron gas is not zero at zero temperature (as is the case in a classical gas). Problem 2.2 (Free electron gas with an anisotropic dispersion in 3D) This problem is an exercise in calculating density of states functions that will be very useful later in the course. Suppose one has a free electron gas in 3D where the electron energy-vs-wavevector relation is given by: ( ) z z y y x x m k m k m k k E 2 2 2 2 2 2 2 2 2 h h h r + + = Note that the electron has a different “mass” associated with its kinetic energy when moving in different directions. This happens in materials as a result of the interaction of the electrons with the atoms. Find the density of states function...
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- Spring '08
- Electron, Fundamental physics concepts, Reciprocal lattice, Brillouin zone, free electron gas