2_1_Class 3 presentation - EE2 Fall 2007 Class#3 October 4...

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1 EE2 Fall 2007 Class #3 October 4, 2007
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2 Outline 1. Review of particle in a box 2. E vs k plot 3. Momentum space 4. Distribution of momentum states 5. Density of states 6. Distribution states as a function of energy 7. Electron distribution as a function of energy
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4
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6 E vs. k
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7 Momentum Space Let us consider an imaginary three dimensional space with axes p x , p y , p z as the principal axes. Momentum vector p with components p x , p y , p z will be represented as a vector originating from the origin and terminating at the point whose coordinates are p x , p y , p z . Each set of integer values for n x , n y , n z will correspond to a point in the momentum space.
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8 Momentum Space Infinite number of representative points (called phase points) in the momentum space. Points are separated by h/L x along the p x axis, h/L y along the p y axis and h/L z along the p z axis. The vector connecting the origin to the phase point n x , n y , n z represents the momentum of the state n x , n y , n z .
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