Intrinsic Carrier Concentration Calculator

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Calculate the density of electrons and holes in an undoped semiconductor.

Semiconductor Parameters

Semiconductor Material

Temperature (T)

Bandgap Energy (Eg) (eV)

Calculation Results

Enter parameters to calculate

About this calculator

Quick Reference

n_iIntrinsic carrier concentration

N_c, N_vEffective density of states

E_gEnergy bandgap

kBoltzmann constant

Overview

In an intrinsic (pure) semiconductor, the concentration of mobile electrons in the conduction band equals the concentration of holes in the valence band. This concentration ($n_i$) is highly dependent on temperature and the material's bandgap energy.

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Pro Tips

Intrinsic carrier concentration increases exponentially with temperature.
Silicon at room temperature (300K) has roughly $10^{10}$ carriers per cm³.
Materials with wider bandgaps have lower intrinsic carrier concentrations.

Fun Facts

"Intrinsic carriers are the reason transistors start to leak and fail at high temperatures."
"Absolute zero temperature would mean zero intrinsic carriers."
"Doping a semiconductor (adding impurities) creates extrinsic semiconductors with much higher carrier densities."

Formula: n_i = √(N_c N_v) × exp(-E_g / 2kT)