In the study of solid-state physics, especially semiconductors, we often ask an important question:
Which electrons will actually take part in electrical conduction?

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To answer this, it is not enough to know only the energy bands. We also need to know how electrons are distributed among these energy levels at a given temperature. The concept that helps us to understand this distribution is called the concept of the Fermi level.

The Fermi level plays a central role in explaining the electrical behaviour of conductors, semiconductors, and insulators, and it is particularly important in semiconductor devices.

Meaning of Fermi Level

The Fermi level is defined as:

The energy level at which the probability of finding an electron is 50% at a given temperature.

In other words:

The probability that an electron occupies an energy state at the Fermi level is exactly equal to the probability that it is empty.

The Fermi level is not necessarily an actual energy level where electrons exist. Instead, it is a reference energy level used to describe electron distribution in a solid.

Fermi Level at Absolute Zero (0 K)

At absolute zero temperature:

All electrons occupy the lowest possible energy states
No thermal energy is available to excite electrons
The electron distribution is very simple

Important Rule at 0 K

All energy levels below the Fermi level are completely filled
All energy levels above the Fermi level are completely empty

Thus, at 0 K, the Fermi level represents the highest occupied energy level.

Fermi Level at Temperatures Above 0 K

When the temperature is above absolute zero, some electrons gain thermal energy. Because of this, electrons near the Fermi level can move to higher energy states. As a result, the distribution of electrons changes with temperature.

However, the definition of the Fermi level remains valid:

The probability of occupation at the Fermi level is still 50%

The position of the Fermi level may shift with temperature, especially in semiconductors.

Position of Fermi Level in Different Solids

The position of the Fermi level in the energy band structure decides the electrical nature of a material.

Fermi Level in Conductors

In conductors, the valence band and conduction band overlap, so a large number of free electrons are available. The Fermi level lies within the conduction band or in the overlapping region of the two bands. Because of this, electrons can move easily when an electric field is applied, resulting in high electrical conductivity.

Fermi Level in Semiconductors

In an intrinsic semiconductor, the valence band is completely filled and the conduction band is empty at absolute zero. There is a small energy gap between the two bands. The Fermi level lies nearly at the center of this gap. Because of this, very few electrons are available for conduction at low temperatures. As the temperature increases, electrons gain energy and move to the conduction band, so the conductivity increases.

Fermi Level in Insulators

In insulators, the forbidden energy gap is very large. The valence band is completely filled and the conduction band is empty.

The Fermi level lies:

Well inside the forbidden energy gap, closer to the middle

Because the energy gap is large, electrons cannot move to the conduction band under normal conditions, so insulators have negligible electrical conductivity.

Fermi–Dirac Distribution Function (Qualitative)

The probability that an electron occupies an energy level is given by the Fermi–Dirac distribution function:

$$f(E) = \frac{1}{1 + e^{(E – E_F)/kT}}$$

where:

E_F= Fermi energy
k = Boltzmann constant
T = absolute temperature

Important Observations

At E_F , f(E) = 0.5
Below E_F, probability > 0.5
Above E_F , probability < 0.5

Energy Band Diagrams Showing Fermi Level

Importance of Fermi Level

The concept of Fermi level is important because it:

Explains electrical conductivity of materials
Helps compare conductors, semiconductors, and insulators
Determines carrier concentration in semiconductors
Plays a key role in semiconductor devices and junctions

Important Examination Questions

Short Answer Questions

Define Fermi level.
What is the significance of Fermi level at 0 K?
Where does the Fermi level lie in an intrinsic semiconductor?

Long Answer Questions

Explain the concept of the Fermi level and its position in conductors, semiconductors, and insulators with neat diagrams.
Describe the significance of the Fermi level in determining the electrical properties of solids.
Very frequently asked question

Conceptual Questions

Why is the probability of electron occupancy 50% at the Fermi level?
Why does the position of Fermi level differ in different materials?

Concept of Fermi Level