Charge Carriers, Fermi Level, and Intrinsic Statistics

Manual: General · Subject: Semiconductor Science

Understand how carrier populations are determined in equilibrium.

Equilibrium Carrier Populations

Electron and hole statistics

Carrier concentrations in non-degenerate semiconductors are set by the density of states and the Fermi-Dirac distribution. In many device conditions, the Boltzmann approximation applies, giving $n \approx N_C e^{-(E_C-E_F)/kT}$ and $p \approx N_V e^{-(E_F-E_V)/kT}$ .

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Useful relation

For an intrinsic semiconductor, the Fermi level sits near midgap, and the mass-action law gives $np = n_i^2$ at equilibrium.

Interpreting the Fermi level

The Fermi level is not an energy level electrons must occupy; it is the chemical potential for electrons. Moving the Fermi level closer to the conduction band increases electron density, while moving it closer to the valence band increases hole density.

Equilibrium relationships

Quantity	Meaning	Key relation
$n$	Electron concentration	Depends on $E_C-E_F$
$p$	Hole concentration	Depends on $E_F-E_V$
$n_i$	Intrinsic concentration	$np=n_i^2$
$E_F$	Fermi level	Sets carrier balance

What happens to electron concentration when the Fermi level moves closer to the conduction band?

It decreases It increases It becomes zero It is unchanged

State the mass-action law for equilibrium in a semiconductor.

Intrinsic vs extrinsic equilibrium

Intrinsic

$n=p=n_i$
Fermi level near midgap

Extrinsic

One carrier type dominates
Fermi level shifts toward donor or acceptor levels

Solving basic equilibrium carrier problems

1

Identify whether the semiconductor is intrinsic or doped.
2

Use the appropriate carrier relation, such as $np=n_i^2$ or majority-carrier dominance.
3

Apply charge neutrality if dopants are present.
4

Check units and temperature dependence before finalizing the result.

At equilibrium in an intrinsic semiconductor, where is the Fermi level approximately located?

At the conduction band edge At the valence band edge Near the middle of the band gap Above the conduction band

What does the Fermi level physically represent?

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