Fundamentals of Semiconductors pp 203-241 | Cite as

# Electrical Transport

## Summary

In this chapter we have discussed the transport of charges in semiconductors under the influence of external fields. We have used the *effective mass approximation* to treat the *free carriers* as having classical charge and renormalized masses. We first considered the case of weak fields in which the field does not distort the carrier distribution but causes the entire distribution to move with a *drift velocity*. The drift velocity is determined by the length of time, known as the *scattering time*, over which the carriers can accelerate in the field before they are scattered. We also defined *mobility* as the constant of proportionality between drift velocity and electric field. We calculated the scattering rates for carriers scattered by *acoustic phonons, optical phonons, and ionized impurities*. Using these scattering rates we deduced the *temperature dependence of the carrier mobilities*. Based on this temperature dependence we introduced *modulation doping* as a way to minimize scattering by ionized impurities at low temperatures. We discussed qualitatively the behavior of carriers under high electric fields. We showed that these *hot carriers* do not obey Ohm’s law. Instead, their drift velocities at high fields saturate at a constant value known as the saturation velocity. We showed that the saturation velocity is about 107 cm/s in most semiconductors as a result of energy and momentum relaxation of carriers by scattering with optical phonons. In a few n-type semiconductors, such as GaAs, the drift velocity can *overshoot* the saturation velocity and exhibit *negative differential resistance*. This is the result of these semiconductors having secondary conduction band valleys whose energies are of the order of 0.1 eV above the lowest conduction band minimum. The existence of negative differential resistance leads to spontaneous current oscillations at microwave frequencies when thin samples are subjected to high electric fields, a phenomenon known as the *Gunn effect*. Under the combined influence of an electric and magnetic field, the transport of carriers in a semiconductor is described by an antisymmetric second rank *magneto-conductivity tensor*. One important application of this tensor is in explaining the *Hall effect*. The *Hall coefficient* provides the most direct way to determine the sign and concentration of charged carriers in a sample.

## Keywords

Drift Velocity Optical Phonon Acoustic Phonon Electrical Transport Negative Differential Resistance## Preview

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