Concentration of intrinsic charge carriers

In the absence of external influences (lighting, electric field, etc.), there is a nonzero concentration of free charge carriers in the semiconductor.

Notation:

1. \(k_\text{B}\) (k_B) is boltzmann_constant.

Conditions:

1. There are no external influences, such as lighting, electric field, etc.

Links:

1. University Wafer, Intrinsic carrier concentration.

charge_carriers_concentration

number_density of intrinsic charge carriers.

Symbol:

n

Latex:

\(n\)

Dimension:

1/volume

density_of_states_in_conduction_band

Effective density_of_states in the conduction band.

Symbol:

N_c

Latex:

\(N_\text{c}\)

Dimension:

1/volume

density_of_states_in_valence_band

Effective density_of_states in the valence band.

Symbol:

N_v

Latex:

\(N_\text{v}\)

Dimension:

1/volume

temperature

temperature of the semiconductor.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

band_gap

band_gap of the semiconductor.

Symbol:

E_g

Latex:

\(E_\text{g}\)

Dimension:

energy

law

n = sqrt(N_c * N_v) * exp(-E_g / (2 * k_B * T))

Latex:

\[n = \sqrt{N_\text{c} N_\text{v}} \exp{\left(- \frac{E_\text{g}}{2 k_\text{B} T} \right)}\]