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⚡ Intrinsic Carrier Concentration Calculator
Calculate intrinsic carrier concentration in semiconductors at different temperatures
📐 Intrinsic Carrier Concentration Formulas
n_i = √(N_c × N_v) × exp(-E_g/(2kT))
N_c = 2(2πm_n*kT/h²)^(3/2)
N_v = 2(2πm_p*kT/h²)^(3/2)
n_i = A × T^(3/2) × exp(-E_g/(2kT))
n_i = intrinsic carrier concentration, N_c = effective density of states in conduction band, N_v = effective density of states in valence band, E_g = band gap, k = Boltzmann constant, T = temperature
💡 Tips
- Intrinsic carrier concentration increases exponentially with temperature
- Larger band gap materials have lower intrinsic carrier concentration
- At room temperature (300K), Si has n_i ≈ 1.5×10¹⁰ cm⁻³
- Effective mass affects the density of states
- Fermi level is at mid-gap for intrinsic semiconductors
- Temperature dependence follows Arrhenius behavior