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Energy–momentum dispersion





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In the preceding description an important fact is ignored for the sake of simplicity: the dispersion of the energy. The reason that the energies of the states are broadened into a band is that the energy depends on the value of the wave vector, or k-vector, of the electron. The k-vector, in quantum mechanics, is the representation of the momentum of a particle.

The dispersion relationship determines the effective mass, m* , of electrons or holes in the semiconductor, according to the formula:

 

The effective mass is important as it affects many of the electrical properties of the semiconductor, such as the electron or hole mobility, which in turn influences the diffusivity of the charge carriers and the electrical conductivity of the semiconductor.

Typically the effective mass of electrons and holes are different. This affects the relative performance of p-channel and n-channel IGFETs.

The top of the valence band and the bottom of the conduction band might not occur at that same value of k. Materials with this situation, such as silicon and germanium, are known as indirect bandgap materials. Materials in which the band extrema are aligned in k, for example gallium arsenide, are called direct bandgap semiconductors. Direct gap semiconductors are particularly important in optoelectronics because they are much more efficient as light emitters than indirect gap materials.

 

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