Moritz (better@not.tell) on 6/22/11 wrote:
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>I understand that heat increases tunneling and the resistance of metal,
>but why of semiconductors?
>I guess most dopant's are available for movement at below 0°C (N_A/D~=n_A/D) ,
>but isn't the rule, that more electrons get available with temperature? what about
>NTC-Thermistors ? Are there more electrons available, but the effect is off-set by collisions, leakage, ?
>

The electrical resistivity of any conducting medium depends both on the concentration of the electricity carriers and of the resistance that opposes to their movement (the reciprocal of the carrier mobility).

The mobility of the carriers in solid or liquid substances almost always decreases with the temperature. Therefore, if the concentration of carriers is constant, the resistivity increases with temperature.

Most semiconductor devices, except for NTC thermistors, are made of doped semiconductors, in order to have a certain predictable carrier concentration. In that case, in a large temperature interval, which includes the operating range of the device, the carrier concentration is almost constant (because the concentration of the thermally-generated carriers is much less than that of the carriers generated by dopant ionization), so the resistivity increases with temperature.

At very low temperatures the resistivity decreases with temperature because the carrier concentration increases due to the ionization of the dopants, while at very high temperatures the resistivity also decreases with temperature because the carrier concentration increases because the concentration of thermally-generated carriers becomes greater than the concentration of the dopants and dominates the total concentration.