2_1_class slides 6 - EE 2 Fall 2007 Class 6 slides 1...

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1 EE 2 Fall 2007 Class 6 slides
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2 outline 1. Review of consequences of band theory 2. Acceleration of electrons in the band theory. 3. Holes as charge carriers 4. Insulators, conductors and semiconductors 5. Electron structure and complex atoms 6. Periodic Table 7. Covalent bond 8. Band structure of semiconductors
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4 Acceleration of electrons in the band theory According to the band theory, we saw that the velocity of an electron in a state k in the band is determined by the slope of the E vs k plot and is given by v el = (h/2 π ) -1 dE/dk What we have to address next is how to treat the acceleration of the electron under the action of an externally applied electric field. We also saw earlier that when an external force is applied, the electron goes from a state with a given k 1 to a state with another k value at a rate dk/dt equal to dk/dt = (h/2 π ) -1 times the external force
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6 Acceleration of electrons in the band theory We see that the effective mass m * depends on the curvature of the E vs k plot and is positive in the lower half of the plot and negative in the upper half of the plot. The effective mass of electrons varies with the k value or position in the band. in the states since the curvature varies. Electrons in a solid are subjected to both the externally applied force (electric field) and the internal forces due to the periodic potential variation. The net acceleration of the electron is due to the total force due to both external and internal forces. The effective mass concept enables us to treat as though the electron is free from the internal forces and responds only to the external force. Newton’s Law gives total Force = m a which relates force to acceleration. We want to express acceleration to the external force in the same form which hides the explicit use of the total force. external force = m * a where m * is called the effective mass Therefore we can write the acceleration as a = external force/ m *
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7 Acceleration of electrons in the band theory If we have a collection of electrons all with the same effective mass, then we can treat these electrons as essentially free and apply the results of our free electron model (electrons in a box) in treating the behavior of the electrons by replacing the true mass m with the effective mass m * .
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