Formula used
The standard relation connects carrier diffusion and electrical mobility. Temperature must use an absolute kelvin scale. Charge uses its positive magnitude in this calculation.
The generalized form uses mechanical mobility b. Its units are seconds per kilogram. Electrical mobility cannot replace mechanical mobility directly.
Variable meanings
| Symbol | Meaning | Common SI unit |
|---|---|---|
| D | Diffusion coefficient | m²/s |
| μ | Electrical carrier mobility | m²/(V·s) |
| b | Mechanical mobility | s/kg |
| kB | Boltzmann constant | J/K |
| T | Absolute temperature | K |
| q | Carrier charge magnitude | C |
| VT | Thermal voltage | V |
How to use this calculator
- Select the unknown quantity from the solve menu.
- Choose a carrier and optional material preset.
- Enter known values with their matching units.
- Select preferred output units and decimal precision.
- Press Calculate to view results and detailed steps.
- Copy, print, or export the completed result.
Worked example
Assume silicon electron mobility equals 1350 cm²/(V·s). Use 300 K and one elementary charge. The diffusion coefficient becomes approximately 34.9 cm²/s.
Example data table
| Material | Carrier | Mobility | Temperature | Approximate D |
|---|---|---|---|---|
| Silicon | Electron | 1350 cm²/(V·s) | 300 K | 34.9 cm²/s |
| Silicon | Hole | 480 cm²/(V·s) | 300 K | 12.4 cm²/s |
| Germanium | Electron | 3900 cm²/(V·s) | 300 K | 100.8 cm²/s |
| Gallium arsenide | Electron | 8500 cm²/(V·s) | 300 K | 219.7 cm²/s |
Values are illustrative. Real mobility changes with doping and temperature.
Assumptions and limitations
The classical relation assumes nondegenerate carriers near thermal equilibrium. Strong fields can invalidate simple mobility behavior. Degenerate semiconductors may require a correction factor.
Material presets provide approximate room-temperature reference values. Actual measurements depend on doping and crystal quality. Use verified data for critical engineering decisions.
Frequently asked questions
What is the Einstein relation?
It connects diffusion coefficient and carrier mobility. Temperature and charge determine their ratio. The relation supports many semiconductor transport calculations.
Why must temperature use kelvin?
The equation requires absolute thermodynamic temperature. Celsius and Fahrenheit include arbitrary zero points. This calculator converts them into kelvin automatically.
Does electron charge need a negative sign?
No negative sign is needed here. The relation uses the charge magnitude. Carrier type remains available for labeling results.
What is thermal voltage?
Thermal voltage equals kBT divided by charge. It is about 25.85 millivolts at 300 K. Its value rises with absolute temperature.
Can I compare electrons and holes?
Yes, select the dual-carrier calculation mode. Enter both mobility values and temperature. The calculator returns Dn and Dp together.
What is generalized Einstein–Smoluchowski mode?
It uses mechanical mobility instead of electrical mobility. The formula becomes D equals bkBT. Mechanical mobility uses seconds per kilogram.
Are material presets exact?
No, presets are convenient reference values. Mobility depends strongly on doping and temperature. Use measured values whenever accuracy is essential.
Why does D divided by μ equal voltage?
The ratio equals kBT divided by charge. That quantity is the thermal voltage. Therefore D divided by μ has volts.
When does the classical relation fail?
It may fail for degenerate carrier populations. Strong electric fields also change transport behavior. Advanced models include statistical correction factors.