Advanced Hole Concentration Calculator

Calculator form

Use scientific notation where helpful, such as 1e16 or 2.4e13.

Calculation mode

Material

Temperature (K)

Band gap E_g (eV)

Intrinsic concentration at 300 K n_i,300 (cm^-3)

Hole mobility μ_p (cm²/V·s)

Acceptor concentration N_A (cm^-3)

Donor concentration N_D (cm^-3)

Electron concentration n (cm^-3)

Conductivity σ (S/cm)

Resistivity ρ (Ω·cm)

Leave as 0 when conductivity is already known.

Reset

Example data table

Method	Material	Temperature (K)	Key inputs	n_i(T)	p	n	Type
Doping	Silicon	300	Na=1.0e16, Nd=1.0e14	1.0800e+10	9.9000e+15	1.1782e+4	P-type
Doping	Germanium	325	Na=8.0e14, Nd=2.0e14	7.2243e+13	6.0858e+14	8.5759e+12	P-type
Mass action	Gallium Arsenide	300	n=1.0e7	2.1000e+6	4.4100e+5	1.0000e+7	N-type
Conductivity	Silicon	300	σ=0.72 S/cm, μp=450	1.0800e+10	9.9864e+15	1.1680e+4	P-type

Formula used

1) Intrinsic concentration versus temperature

n_i(T) = n_i,300 × (T / 300)^3/2 × exp[ -E_g / (2k) × (1/T - 1/300) ]

2) Doping balance mode

p = 0.5 × [ (N_A - N_D) + √((N_A - N_D)² + 4n_i²) ] and n = n_i² / p

3) Mass action mode

np = n_i², so p = n_i² / n

4) Conductivity mode

σ = q × p × μ_p, so p = σ / (q × μ_p)

These relations assume equilibrium, full ionization, non-degenerate behavior, and a mobility value suitable for the chosen material and operating region.

How to use this calculator

Choose a calculation mode that matches your available data.
Select a semiconductor material or switch to the custom option.
Enter temperature, band gap, intrinsic concentration at 300 K, and hole mobility.
Provide the required mode-specific inputs, such as doping levels, electron concentration, or conductivity.
Press Calculate hole concentration to display the results below the header and above the form.
Review the Plotly graph to see how hole concentration changes with temperature around your selected operating point.
Use the CSV or PDF buttons to export the current result set for reports or documentation.

FAQs

1) What is hole concentration?

Hole concentration is the number of mobile holes per cubic centimeter in a semiconductor. It helps describe p-type conduction and charge transport behavior.

2) Why does temperature matter?

Temperature changes intrinsic carrier generation. As temperature rises, intrinsic concentration usually increases, which can strongly affect minority carriers and sometimes majority carrier estimates.

3) When should I use doping balance mode?

Use doping balance mode when you know acceptor and donor concentrations. It is helpful for equilibrium estimates in doped materials with known compensation.

4) When is mass action mode useful?

Mass action mode works well when electron concentration is known. The calculator then derives holes from the equilibrium relation np = n_i².

5) Why include mobility in conductivity mode?

Conductivity alone does not uniquely define carrier concentration. Mobility connects conductivity to charge transport, allowing the calculator to estimate hole concentration from σ = q p μ_p.

6) Are the results always exact?

No. Results are model-based estimates. Heavy doping, incomplete ionization, field effects, advanced recombination, and temperature-dependent mobility can shift real device behavior.

7) What units does this page use?

Carrier concentrations use cm^-3, mobility uses cm²/V·s, conductivity uses S/cm, resistivity uses Ω·cm, temperature uses kelvin, and band gap uses electron-volts.

8) What does the graph show?

The graph shows the calculated hole concentration and intrinsic concentration across a nearby temperature range. It helps visualize sensitivity around your selected operating point.