The temperature coefficient of an intrinsic semiconductor is negative. This means that as the temperature increases, the conductivity of the semiconductor decreases.

Intrinsic semiconductors are pure semiconducting materials, such as silicon or germanium, that have no impurities or dopants added to them. At absolute zero temperature, the valence band of an intrinsic semiconductor is completely filled, and the conduction band is completely empty, creating a large energy gap between them. This energy gap restricts the movement of electrons, making the material behave as an insulator.

However, as the temperature increases, some of the valence electrons gain enough thermal energy to jump to the conduction band, creating electron-hole pairs. This process is known as intrinsic carrier generation. The number of electron-hole pairs increases with temperature, and this leads to an increase in carrier concentration and conductivity.

However, as the temperature continues to rise, other effects come into play. One of these effects is that the lattice vibrations, or phonons, in the semiconductor material increase with temperature. These lattice vibrations can scatter the charge carriers, impeding their movement and reducing the conductivity of the material.

The temperature coefficient of an intrinsic semiconductor is negative because the increase in carrier concentration due to intrinsic carrier generation is overshadowed by the increase in scattering caused by lattice vibrations. As a result, the overall conductivity of the material decreases with increasing temperature.

This negative temperature coefficient is in contrast to metals, which have a positive temperature coefficient. In metals, the increase in lattice vibrations with temperature leads to an increase in the number of charge carriers and therefore an increase in conductivity.

In summary, the temperature coefficient of an intrinsic semiconductor is negative because the increase in carrier concentration due to intrinsic carrier generation is counteracted by the increase in scattering caused by lattice vibrations. This makes the conductivity of the material decrease with increasing temperature.