n intrínseco aprox
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
This calculator estimates intrinsic carrier concentration (n_i) in semiconductors using the formula n_i = √(Nc·Nv)·exp(−Eg/2kT). It calculates the equilibrium density of free charge carriers (electrons and holes) by considering the bandgap energy (Eg), absolute temperature (T), and physical constants.
The formula combines the effective density of states in the conduction (Nc) and valence (Nv) bands, adjusted for temperature, with an exponential factor representing thermal excitation energy. Temperature directly influences the result: higher temperatures increase thermal excitation, raising the value of n_i.
Use this tool in semiconductor material studies, such as silicon or germanium, for electronic device design or thermal simulations. Ensure Eg values (typically in eV) and Nc/Nv parameters match the specific material being analyzed for accurate results.
Accuracy relies on input quality, especially Eg, which varies with material purity and crystal structure. At extreme temperatures (very low or high), experimental adjustments may be needed, as the formula assumes an idealized behavior.
Frequently asked questions
Why does the formula use the square root of Nc·Nv?
The square root represents the geometric mean between the conduction (Nc) and valence (Nv) band effective density of states, which depend on the material's crystal structure.
How does temperature affect the n_i value?
Temperature influences the exponential factor: higher temperatures increase thermal excitation, raising the density of free carriers.
Can I use this formula for doped semiconductors?
No. The formula assumes an intrinsic material (no doping). In doped semiconductors, carrier concentration depends on the dopant concentration, not the bandgap energy.
Which units should I use for Eg?
Bandgap energy (Eg) must be in electronvolts (eV), while temperature (T) should be in kelvins (K).