Intrinsic Carrier Concentration Calculator

Intrinsic Carrier Concentration Calculator

Calculate the intrinsic carrier concentration in a semiconductor using the equation:
\[ n_i = \sqrt{N_c\,N_v}\,\exp\left(-\frac{E_g}{2\,k\,T}\right) \] where:
– \(N_c\) is the effective density of states in the conduction band (m\(^{-3}\)), – \(N_v\) is the effective density of states in the valence band (m\(^{-3}\)), – \(E_g\) is the bandgap energy (J), – \(T\) is the temperature (K), and – \(k\) is Boltzmann’s constant.

* Enter all values in SI units.

Step 1: Enter Parameters

Example: 2.8e25 m\(^{-3}\) (for silicon at 300 K)

Example: 1.04e25 m\(^{-3}\) (for silicon at 300 K)

Example: 1.12e-19 J (≈ 0.7 eV for silicon, note: 1 eV ≈ 1.602e-19 J)

Example: 300 K

Formula: \( n_i = \sqrt{N_c\,N_v}\,\exp\left(-\frac{E_g}{2\,k\,T}\right) \)


Practical Example:
For silicon at 300 K with \( N_c = 2.8 \times 10^{25} \) m\(^{-3}\), \( N_v = 1.04 \times 10^{25} \) m\(^{-3}\), and \( E_g = 1.12 \times 10^{-19} \) J,
the intrinsic carrier concentration is calculated as:
\[ n_i = \sqrt{(2.8 \times 10^{25})(1.04 \times 10^{25})}\,\exp\left(-\frac{1.12 \times 10^{-19}}{2 \times 1.380649 \times 10^{-23} \times 300}\right) \]
which yields a value in m\(^{-3}\) (and can be converted to cm\(^{-3}\)).