Fermi Level, Ec, Ev, Eg Explained

Fermi Level, Ec, Ev, Eg Explained in Semiconductor Physics

Semiconductor physics is based on energy band theory. The most important concepts are:

• Ec → Conduction band energy
• Ev → Valence band energy
• Eg → Bandgap energy
• EF → Fermi level

These concepts explain how electrons move inside semiconductors like silicon, germanium, and gallium arsenide.

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1. Energy Band Diagram

In solids, discrete atomic energy levels combine to form continuous energy bands.

The two important bands are:

• Valence Band
• Conduction Band

The region between them is called the forbidden energy gap.

SVG Energy Band Diagram

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2. Valence Band (Ev)

The valence band contains bonded electrons. These electrons participate in atomic bonding and normally cannot move freely.

At absolute zero temperature, the valence band is completely filled.

Ev = Top of valence band

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3. Conduction Band (Ec)

The conduction band contains free electrons that can move through the material and conduct current.

If an electron gains enough energy, it jumps from the valence band into the conduction band.

E ≥ Ec

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4. Bandgap Energy (Eg)

The energy difference between conduction band and valence band is called the bandgap.

Eg = Ec - Ev

This energy must be supplied to free an electron.

Typical Bandgap Values

Material	Bandgap
Silicon	1.12 eV
Germanium	0.66 eV
Gallium Arsenide	1.43 eV

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5. Fermi Level (EF)

The Fermi level is one of the most important concepts in semiconductor physics.

The Fermi level is the energy level where the probability of electron occupancy is 50%.

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6. Fermi-Dirac Probability Function

The probability that an energy state contains an electron is:

f(E) = 1 / [1 + e^((E - EF)/kT)]

Where:

Symbol	Meaning
f(E)	Probability of occupancy
E	Energy level
EF	Fermi level
k	Boltzmann constant
T	Temperature

At:

E = EF

The probability becomes:

f(EF) = 1/2

Meaning:

States at the Fermi level have 50% probability of containing an electron.

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7. Electron and Hole Concentration

Electron Concentration

n = Nc e^(-(Ec - EF)/kT)

Hole Concentration

p = Nv e^(-(EF - Ev)/kT)

Where:

• n = electron concentration
• p = hole concentration
• Nc = effective density of states in conduction band
• Nv = effective density of states in valence band

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8. Intrinsic Semiconductor

In a pure semiconductor:

EF ≈ (Ec + Ev) / 2

The Fermi level lies approximately at the middle of the bandgap.

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9. n-Type Semiconductor

Donor impurities add extra electrons.

Therefore:

EF → Ec

The Fermi level shifts upward toward the conduction band.

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10. p-Type Semiconductor

Acceptor impurities create holes.

EF → Ev

The Fermi level shifts downward toward the valence band.

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