Intrinsic Semiconductor Conductivity Calculator

Calculator Inputs

Use cm-based mobility and density units. The calculator returns conductivity in both S/cm and S/m.

Temperature (K)

Band Gap E_g (eV)

Electron Mobility μ_n (cm²/V·s)

Hole Mobility μ_p (cm²/V·s)

Conduction Band Density N_c (cm^-3)

Valence Band Density N_v (cm^-3)

Electric Field E (V/cm)

Plot Minimum Temperature (K)

Plot Maximum Temperature (K)

Plot Points

Plotly Graph

The plot shows how conductivity and intrinsic carrier concentration vary across the selected temperature range.

Example Data Table

Material Case	Temperature (K)	Band Gap (eV)	μ_n (cm²/V·s)	μ_p (cm²/V·s)	n_i (cm^-3)	Conductivity (S/cm)
Silicon at 300 K	300	1.12	1,350	480	6.6759e+9	1.9574e-6
Germanium at 300 K	300	0.66	3,900	1,900	2.2586e+13	2.0988e-2
Gallium Arsenide at 300 K	300	1.42	8,500	400	2.1435e+6	3.0565e-9

Formula Used

Intrinsic carrier concentration

n_i = √(N_cN_v) × exp[ -E_g / (2kT) ]

Intrinsic conductivity

σ = q × n_i × (μ_n + μ_p)

Resistivity

ρ = 1 / σ

Current density

J = σ × E

Here, q is electron charge, k is Boltzmann’s constant, T is absolute temperature, E_g is band gap, N_c and N_v are effective density states, and μ_n, μ_p are carrier mobilities.

This model is useful for estimating ideal intrinsic behavior. Real materials can deviate because of impurity levels, scattering changes, temperature-dependent mobility, and non-ideal band structure effects.

How to Use This Calculator

Enter the material temperature in kelvin.
Provide the semiconductor band gap in electron volts.
Enter electron and hole mobilities in cm²/V·s.
Fill in conduction and valence band density values.
Enter electric field if you want current density.
Set the temperature range for the graph.
Press Calculate Conductivity to show results.
Use the export buttons to save CSV or PDF copies.

FAQs

1. What does intrinsic semiconductor mean?

It means the semiconductor is pure and undoped. Electrons and holes are generated thermally, and their concentrations are equal under intrinsic conditions.

2. Why does conductivity increase with temperature?

Higher temperature creates more electron-hole pairs. This usually raises intrinsic carrier concentration strongly, which increases conductivity despite mobility changes.

3. Why are N_c and N_v needed?

They describe the effective density of available states in the conduction and valence bands. They help estimate intrinsic carrier concentration more realistically.

4. What units does this calculator use?

Temperature uses kelvin. Mobilities use cm²/V·s. N_c and N_v use cm^-3. Conductivity is reported in S/cm and S/m.

5. Can I use this for doped semiconductors?

Not directly. This page is built for intrinsic behavior only. Doped materials need donor, acceptor, and charge-neutrality relations.

6. Why is the result extremely small for wide band gap materials?

A larger band gap sharply reduces thermal carrier generation. That makes intrinsic concentration and conductivity much lower at the same temperature.

7. What does current density represent here?

It shows the expected conduction current per unit area under the entered electric field. It is calculated from conductivity multiplied by field strength.

8. Is this suitable for chemistry students?

Yes. It helps connect band gap, thermal activation, carrier mobility, and electrical response in a simple, visual learning format.