Animated Solution for Physics - Current Electricity: By increasing the temperature, the specific resistance of a conductor and a semiconductor

To understand how temperature affects different materials, we must first look at the fundamental microscopic equation for specific resistance, also known as resistivity.

The resistivity $\rho$ of any material is given by the formula:

Here, $m$ is the mass of an electron, $e$ is the elementary charge, $n$ is the number density of free charge carriers, and $\tau$ is the average relaxation time between collisions.

The battle of temperature is fought entirely between two variables in the denominator: the carrier density $n$ and the relaxation time $\tau$.

A Traffic Jam

Imagine a bustling highway. In a conductor like copper or aluminum, the number of cars (free electrons) is already at maximum capacity. Almost every atom contributes a free electron to the conduction band.

Therefore, as we increase the temperature, the charge carrier density $n$ remains practically constant.

However, the added thermal energy causes the metal ions in the lattice to vibrate violently. This creates a chaotic environment for the flowing electrons. They collide much more frequently with the vibrating ions.

Because the collisions are more frequent, the average time between them—the relaxation time $\tau$—decreases.

Looking back at our formula, since $\tau$ is in the denominator and it is decreasing, the overall resistivity $\rho$ must increase. Thus, heating a conductor makes it more resistive.

Breaking the Bonds

Now, let's shift our focus to a semiconductor like silicon. At low temperatures, a semiconductor is like an empty highway; all the electrons are locked tightly in covalent bonds.

As we increase the temperature, the thermal energy acts like a key, breaking these covalent bonds and freeing electrons. Every broken bond creates an electron-hole pair.

This causes the charge carrier density $n$ to increase exponentially with temperature.

While it is true that the increased thermal vibrations also cause the relaxation time $\tau$ to decrease in a semiconductor, this effect is completely overshadowed. The exponential explosion in $n$ dominates the equation.

Since $n$ is in the denominator and it is increasing massively, the overall resistivity $\rho$ must decrease. Heating a semiconductor makes it a better conductor.

By analyzing the microscopic mechanisms, the distinction becomes crystal clear.

For a conductor, the specific resistance increases with temperature due to increased collisions.

For a semiconductor, the specific resistance decreases with temperature due to the exponential generation of new charge carriers.

This fundamental difference is exactly why semiconductors are so uniquely powerful in modern electronics!