Effect of temperature on semiconductors

We have already discussed that at absolute zero the conduction band of any semiconductor is empty and the valence band is filled with electrons.
The forbidden energy gap between the valence band and conduction band is large hence valence electron cannot reach the conduction band to become a free electron.
Therefore at absolute zero, a semiconductor behaves like an insulator.
The energy band diagram of pure silicon at absolute zero is shown in fig.

Energy band diagram

When the temperature is raised, some of the covalent bonds in a semiconductor break due to thermal energy.
The valence electrons absorb this energy and cross over to the conduction band leaving a positive charge empty space in the valence band which is known as a hole.
As the temperature is increased more valence electrons acquire sufficient energy to enter into the conduction band and become free electrons.
When a potential is applied these free electrons constitute a current.
Since the number of free electrons increased with increasing temperature, we can say that the resistance of the semiconductor is decreased.
Thus in a semiconductor with an increase in temperature, resistance decreases.

Crystal structure of silicon

Hence we can say that a semiconductor has a negative temperature coefficient of resistance, In the previous section, we studied that some of the valence electrons of silicon crystal acquire sufficient energy at room temperature and jump from the valence band into the conduction band and become free electrons.
These free electrons are also called conduction electrons. When an electron jumps from valence band to conduction band it leaves a vacancy in the valence band.
This vacancy is called a hole. For every electron raised to the conduction band, there is one hole left in the valence band.
Thus, thermal energy creates an electron-hole pair. Under the influence of an electric field, the free electrons constitute an electric current.
At the same time, another current is known as a hole current also flows in the semiconductor.
The direction of the hole current is opposite to the electron current.
This concept is illustrated in Fig.

Electron and hole current in silicon

When a voltage is applied across a piece of silicon, the thermally generated free electrons move towards the positive end.
This creates a hole in the valence band: Let us consider such a hole 'H' at the extreme end. This positive-charged hole attracts a nearby valence electron at A.
Now the valence electron at A moves towards the hole H and fills it creating a hole at A.
That is the hole has moved from H to A.
The new hole at A attracts a nearby valence electron at B.
The valence electron at B moves towards hole A and fills it.
When the valence electron moves from B to A, its hole moves from A to B.
That is the movement of the hole is opposite to its electron movement.
This movement of the hole constitutes a hole current.
The flow of a hole current can be easily explained using an energy band diagram as shown in Fig.

Silicon with a broken covalent bond

Let us assume that due to thermal energy valence electron jumps from valence band to conduction band creating a hole H in the valence band.
Now the valence electron at A moves towards H and fills the hole.
The result is that the hole disappears at H and reappears at A.
Next, the electron B moves to A and a hole is created at B.
In this way, the hole moves from A to B. That is the movement of a hole is opposite to the movement of an electron.

Recombination

When a valence electron acquires energy it jumps into a conduction band leaving a vacancy in the valence band.
When that free electron loses energy it falls back into a hole in the valence band.
This process is known as the recombination of electron-hole pairs.
When recombination takes place the hole does not move elsewhere, it disappears.
Recombination is a continuous process in a semiconductor.
Due to thermal energy new electron-hole pairs are generated and after a few nanoseconds or several microseconds, depending on the crystal structure, they recombine.
The average time between its creating and disappearing of an electron-hole pair is known as lifetime.
The lifetime depends on the crystal structure.