The Fermi level in semiconductor is one of the most important concepts in solid-state physics and electronics. It describes the energy level at which the probability of finding an electron is 50%. In simple terms, it is the “chemical potential” of electrons in a material.
Understanding the Fermi energy and its behavior in different types of materials (conductors, insulators, and semiconductors) helps us design better chips, solar cells, LEDs, and modern electronic devices.
Fermi Level Definition
The Fermi level definition:
The Fermi level is the highest occupied energy level of electrons at absolute zero temperature (0 Kelvin).
- In conductors, the Fermi level lies within the conduction band.
- In semiconductors, it lies between the conduction and valence bands.
- In insulators, the Fermi level lies far from the conduction band.
Fermi Level in Intrinsic Semiconductor
In an intrinsic semiconductor (pure material like Silicon or Germanium without doping):
- The intrinsic Fermi level lies exactly in the middle of the conduction band and the valence band.
- Electrons and holes are present in equal numbers.
This property makes intrinsic semiconductors ideal for studying the basic physics of electronic devices.
Fermi Level in Insulator vs Semiconductor
| Material Type | Band Gap Size | Position of Fermi Level | Conductivity |
|---|---|---|---|
| Conductor (Metal) | No band gap | Lies in conduction band | Very high |
| Semiconductor | Small (1 eV) | Between conduction and valence band | Moderate |
| Insulator | Large (5–9 eV) | Lies deep in the band gap | Very low |
This shows how the fermi level in insulator lies far from conduction, making current flow almost impossible under normal conditions.
Fermi Dirac Statistics & Distribution
The Fermi-Dirac statistics is used to explain how electrons are distributed across different energy states.
The Fermi-Dirac distribution function is given by: f(E)=11+e(E−EF)/kTf(E) = \frac{1}{1 + e^{(E – E_F) / kT}}f(E)=1+e(E−EF)/kT1
Where:
- f(E)f(E)f(E) = probability of an energy state being occupied
- EEE = energy level
- EFE_FEF = Fermi energy
- kkk = Boltzmann constant
- TTT = temperature
This formula helps in calculating how to calculate Fermi level for different materials.
Also Read: What is a Semiconductor?
Fermi Level in Semiconductor Formula
For an intrinsic semiconductor, the fermi level in semiconductor formula is: EF=EC+EV2+34kTln(mh∗me∗)E_F = \frac{E_C + E_V}{2} + \frac{3}{4} kT \ln\left(\frac{m^*_h}{m^*_e}\right)EF=2EC+EV+43kTln(me∗mh∗)
Where:
- ECE_CEC = conduction band edge
- EVE_VEV = valence band edge
- mh∗m^*_hmh∗ = effective mass of hole
- me∗m^*_eme∗ = effective mass of electron
This formula shows how the Fermi level shifts depending on material properties.
Fermi Level in Semiconductor Derivation (with Diagram)
Step 1: Start with electron density in conduction band n=NCe−(EC−EF)/kTn = N_C e^{-(E_C – E_F) / kT}n=NCe−(EC−EF)/kT
Step 2: Hole density in valence band p=NVe−(EF−EV)/kTp = N_V e^{-(E_F – E_V) / kT}p=NVe−(EF−EV)/kT
Step 3: For intrinsic semiconductor, n=pn = pn=p EF=EC+EV2+kT2ln(NVNC)E_F = \frac{E_C + E_V}{2} + \frac{kT}{2} \ln \left(\frac{N_V}{N_C}\right)EF=2EC+EV+2kTln(NCNV)
Diagram (textual description):
- Imagine a rectangle with two bands: Conduction Band (top) and Valence Band (bottom).
- Between them is the Band Gap.
- The Fermi Level (E_F) lies in the middle for intrinsic semiconductor, shifts up for n-type, and down for p-type.
Real-Life Uses of Fermi Level
- Semiconductor Devices: Fermi level determines how transistors, diodes, and ICs behave.
- Solar Cells: Position of Fermi level affects efficiency of light absorption.
- LEDs & Lasers: Determines color and wavelength of emitted light.
- Microchip Manufacturing: Helps in deciding doping levels for desired conductivity.
- Battery Technology: Used to calculate electron exchange in electrodes.
Conclusion
The fermi level in semiconductor is the backbone of modern electronics. From fermi dirac distribution function to fermi level in semiconductor derivation, this concept explains why materials conduct, resist, or semi-conduct electricity.
In short, without understanding fermi energy, engineers wouldn’t be able to design Semiconductor chips, processors, or even smartphones.