As a semiconductor materials expert with a background in physics and engineering, I can provide a detailed explanation of why the conductivity of a semiconductor increases with an increase in temperature.

Semiconductors are materials that have electrical conductivity between that of a conductor and an insulator. The conductivity of semiconductors is highly dependent on the temperature, and it is a fundamental property that sets them apart from metals and insulators.

At low temperatures, semiconductors behave more like insulators, with very few charge carriers available to conduct electricity. This is because the energy gap between the valence band and the conduction band is relatively large, and thermal energy is not sufficient to excite electrons from the valence band to the conduction band, where they can move freely and contribute to electrical conductivity.

However, as the temperature increases, the thermal energy provided to the semiconductor also increases. This additional thermal energy can be sufficient to excite electrons from the valence band to the conduction band. The process of electron excitation creates electron-hole pairs, where an electron is excited to the conduction band, leaving behind a hole in the valence band. Both electrons in the conduction band and holes in the valence band can move and contribute to the electrical conductivity.

The increase in temperature also increases the number of thermally generated electron-hole pairs, which in turn increases the number of charge carriers available for conduction. This leads to an increase in the conductivity of the semiconductor. This behavior is in stark contrast to metals, where an increase in temperature typically results in increased resistivity due to the increased lattice vibrations that scatter the free electrons.

In metals, the increase in temperature causes the atoms in the lattice to vibrate more vigorously. These vibrations scatter the free electrons, which hinders their movement and thus increases the resistivity of the metal. However, in semiconductors, the increase in temperature does not have the same scattering effect on the charge carriers because the charge carriers are not as free to move as they are in metals.

Another important factor to consider is the intrinsic carrier concentration, which is the number of thermally generated electron-hole pairs per unit volume. The intrinsic carrier concentration \( n_i \) is given by the formula:

\[ n_i = \sqrt{N_c N_v e^{\frac{-E_g}{2kT}}} \]

where \( N_c \) and \( N_v \) are the effective densities of states in the conduction and valence bands, \( E_g \) is the energy gap between the bands, \( k \) is the Boltzmann constant, and \( T \) is the temperature in Kelvin. As the temperature increases, the intrinsic carrier concentration increases, which directly contributes to the increase in conductivity.

In summary, the conductivity of a semiconductor increases with temperature due to the increased excitation of electrons from the valence band to the conduction band, the creation of more electron-hole pairs, and the increase in intrinsic carrier concentration. This is a fundamental property of semiconductors that makes them suitable for a wide range of applications, including transistors, diodes, and solar cells.

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The effect of increase in temperature for semiconductor and metal are different. ... On the other hand increase in temperature increases the amplitude of oscillation of kernels in the metal, thus hindering the free movement of free electrons in the metal. This results in increased resistivity or reduced conductivity.read more >>