Intrinsic Carrier Concentration

\[n_i=\sqrt{N_CN_V}e^{-\frac{E_g}{2kT}}\]

Variables

niintrinsic carrier concentration (1/m³)

Nceffective density of states in conduction band (1/m³)

Nveffective density of states in valence band (1/m³)

Egband gap energy (J)

kBoltzmann constant (J/K)

Tabsolute temperature (K)

Description

What is this formula?

The Intrinsic Carrier Concentration formula calculates the number of free charge carriers generated naturally inside a pure semiconductor material due to thermal energy.

When to use it

Use this formula when studying semiconductor physics, PN junctions, integrated circuits, or temperature effects in semiconductor devices.

Example

A semiconductor has:

Nc = 2.8×10^25 1/m³

Nv = 1.04×10^25 1/m³

Eg = 1.12×10^-19 J

k = 1.38×10^-23 J/K

T = 300 K

Formula:

ni = √(Nc Nv)e^(-Eg/(2kT))

Substitution:

ni = √((2.8×10^25)(1.04×10^25)) × e^(-(1.12×10^-19)/(2×1.38×10^-23×300))

Result:

ni ≈ 1.5×10^16 1/m³

The semiconductor has an intrinsic carrier concentration of approximately 1.5×10^16 carriers per cubic meter.

Applications

Semiconductor device analysis, transistor physics, diode modeling, integrated circuits, and electronic materials engineering.