Resistance of Semiconductors and Conductors as a Function of Temperature

In conductors i.e. metals the electrons that conduct current are called Itinerant electrons. They are essentially free to move around the metal, not bound to any particular atomic core. Resistivity can be understood as Itinerant electrons scattering off of Phonons, or thermal lattice vibrations, in a conductor. As the temperature of the metal increases, the time between Phonon scattering events decreases, leading to increased resistivity. Temperature dependence of copper’s resistivity as a function of temperature is shown in figure below.

The nonlinear region below about 50 K is where the phonons are suppressed to the point that the resistivity is dominated by impurities in the metal. It is clear from the figure that temperature coefficient of Resistivity of a Conductor is positive.

For some materials, like copper, the resistivity is essentially linear with temperature. This fact is exploited to create sensitive thermometers in which a constant current is passed through a resistor with known temperature dependence, and the voltage across the resistor is measured. For other materials, a power law better describes the temperature dependence.

In semiconductors, the resistivity generally decreases with increasing temperature. In the case of intrinsic semiconductors e.g. silicon, one might expect the resistivity to be very high: the valence band in filled and there are no conduction electrons to carry current. However, electrons can be thermally excited to the conduction band, creating electron-hole pairs which can carry current. As one might expect, the production of thermally-excited electron-hole pairs increases with increasing temperature, so the resistivity decreases with increasing temperature. Thus temperature coefficient of Resistivity of Semiconductor is negative.

The resistivity in intrinsic superconductors is still pretty high. As a result most semiconductors are doped, so that there are either more conduction electrons than there are holes (n-type), or there are more holes than there are conduction electrons (p-type). This allows for decreased resistivity and for the fine-tuning of resistivity. Thermal production of electron-hole pairs plays an important role in doped semiconductors.

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