Fast tool for intrinsic and doped materials across common temperature ranges quickly. Choose input methods, validate units, then download clear summaries instantly for teams.
Illustrative values (common room-temperature semiconductor assumptions).
| Material | T (K) | Eg (eV) | Nd (cm-3) | Na (cm-3) | μn (cm²/V·s) | μp (cm²/V·s) | ni (cm-3) | n (cm-3) | p (cm-3) |
|---|---|---|---|---|---|---|---|---|---|
| Silicon-like | 300 | 1.12 | 1.0e16 | 0 | 1350 | 480 | ≈ 6.7e9 | ≈ 1.0e16 | ≈ 4.5e3 |
| Intrinsic-like | 300 | 1.12 | 0 | 0 | 1350 | 480 | ≈ 6.7e9 | ≈ 6.7e9 | ≈ 6.7e9 |
When using effective masses, the calculator estimates the conduction and valence band effective density of states:
Nc = 2 · ( 2π m*e m0 kT / h² )3/2 (converted to cm-3)
Nv = 2 · ( 2π m*h m0 kT / h² )3/2 (converted to cm-3)
ni = √(NcNv) · exp( -Eg / (2kT) )
Here k is Boltzmann’s constant in eV/K, Eg is in eV, and T is in K.
Assuming complete ionization and non-degenerate statistics:
n - p = Nd - Na , np = ni²
n = 0.5 · (Δ + √(Δ² + 4ni²)) , p = ni² / n
Where Δ = Nd − Na. For heavily doped materials, more advanced models may be required.
σ = q(nμn + pμp) , ρ = 1/σ
Carrier density controls current flow, junction behavior, and switching speed in semiconductors. Designers often compare equilibrium electrons n and holes p against process targets such as leakage limits, contact resistance, and device threshold stability. The calculator reports both carriers, highlights the majority type, and optionally estimates conductivity when mobilities are supplied.
Intrinsic carrier concentration ni sets the minimum available carriers at a given temperature. For silicon-like parameters near 300 K, typical values are around 1010 cm-3, while wider-bandgap materials exhibit much smaller ni. In the intrinsic case, the calculator yields n ≈ p ≈ ni, providing a consistent reference for doping comparisons.
Temperature raises Nc and Nv through the T3/2 dependence, and it increases ni exponentially via the term exp(−Eg/(2kT)). A modest change in bandgap can shift ni by orders of magnitude, which is why the bandgap field is treated as a critical input.
You can compute Nc and Nv from DOS-effective masses or provide them directly. At 300 K, common silicon-like values are approximately Nc ≈ 2.8×1019 cm-3 and Nv ≈ 1.0×1019 cm-3. Direct entry is useful when you already have validated literature values or temperature-dependent tables.
The calculator uses charge neutrality n − p = Nd − Na with mass-action np = ni2. When Nd ≫ Na, electrons dominate and n approaches Nd, while p falls to roughly ni2/n. The same symmetry holds for acceptor-dominated cases.
Conductivity is computed as σ = q(nμn + pμp). For many room-temperature designs, electron mobility may exceed hole mobility, meaning n can strongly influence σ even if p is nonzero. Reported resistivity ρ is in Ω·cm, with an Ω·m conversion shown for convenience.
Typical engineering inputs use T from 200–500 K and doping from 1014 to 1019 cm-3. Keep all concentrations in cm-3 and bandgap in eV. If you provide mobilities, use cm²/(V·s). Consistent units prevent silent scaling errors and keep exported reports reliable.
Results assume non-degenerate statistics and complete dopant ionization. At very high doping, low temperatures, or strong bandgap narrowing, advanced Fermi–Dirac and ionization models can be needed. Use this calculator for fast, transparent estimates, then validate against measured Hall data when precision is critical.
It is the equilibrium concentration of mobile electrons and holes in a semiconductor, usually reported in cm-3. These carriers determine conductivity, junction behavior, and recombination rates.
Doping shifts the balance. Donors raise electron density and suppress holes, while acceptors raise holes and suppress electrons. The mass-action law links both through np = ni2.
Use effective masses when you want a physics-based estimate at your temperature. Use direct Nc and Nv when you have trusted literature or measured values for a specific material.
Higher temperature increases Nc, Nv, and strongly increases ni through an exponential dependence on Eg/(kT). That can raise minority carriers significantly.
Conductivity is shown only when at least one mobility is provided. Enter μn and/or μp in cm²/(V·s) to enable σ and ρ outputs.
You can use it for quick estimates, but accuracy may drop at very high doping or low temperature. Degeneracy, incomplete ionization, and bandgap narrowing can require more advanced models.
Resistivity depends on both carrier densities and mobilities. If you know ρ, you can try plausible mobility values and solve iteratively. For best accuracy, combine ρ with Hall measurements to separate carrier type and density.
Accurate carrier estimates help design reliable electronic materials today.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.