Calculated result
Formula and substituted values
Calculator inputs
Select a target and enter known semiconductor values. The calculator standardises every unit internally.
Saved scenario comparison
Save calculated cases and compare their main transport values.
| Scenario | Material | Calculation | Result | D | Lifetime | Temperature |
|---|---|---|---|---|---|---|
| No scenarios saved. | ||||||
Interactive charts
Charts update after every successful calculation. They show trends around your selected operating point.
Diffusion distance versus time
Diffusion length versus lifetime
Temperature versus diffusion coefficient
One-dimensional concentration profile
Material comparison
Formula used
Diffusion length: Lₙ = √(Dₙτₙ) One-dimensional RMS distance: x = √(2Dₙt) Two-dimensional RMS distance: r = √(4Dₙt) Three-dimensional RMS distance: r = √(6Dₙt) Einstein relation: Dₙ = μₙkT/q Carrier lifetime: τₙ = Lₙ²/Dₙ Required diffusion time: t = x²/(2nDₙ)
Here, n is the selected spatial dimension. All calculations use SI units internally.
How to use
- Select the required calculation mode.
- Choose a material or use custom values.
- Enter known quantities with their units.
- Enable suitable advanced corrections.
- Press Calculate and review every result.
- Export the result when needed.
Example data
| Material | Electron mobility | Approximate D at 300 K | Example lifetime | Example diffusion length |
|---|
Reference values vary with doping, temperature, crystal quality, and fabrication.
Understanding electron diffusion
Diffusion and drift
Diffusion follows carrier concentration gradients. Drift follows an applied electric field. Both effects may occur together.
Carrier lifetime
Carrier lifetime measures average survival before recombination. Longer lifetime usually increases diffusion length. Defects can shorten lifetime greatly.
Einstein relation
The Einstein relation connects mobility and diffusion. It assumes near-equilibrium carrier transport. Strong fields may require advanced models.
Dimensional interpretation
One-dimensional motion uses one spatial axis. Two dimensions describe planar spreading. Three dimensions describe bulk spreading.
Practical applications
Diffusion length matters in solar cells. It also affects photodiodes and transistors. Engineers use it for material assessment.
Frequently asked questions
What is electron diffusion distance?
It is a statistical spreading distance. Random thermal motion drives that spreading. Individual electrons follow different paths.
Is diffusion length identical to RMS distance?
No, their contexts differ. Diffusion length uses carrier lifetime. RMS distance uses elapsed diffusion time.
Why does temperature change diffusion?
Temperature changes thermal energy and mobility. Both affect the diffusion coefficient. Material behaviour may become nonlinear.
Can I enter mobility instead?
Yes, enable the Einstein relation. The calculator derives diffusion coefficient. Temperature must remain physically valid.
What does ambipolar diffusion mean?
Electrons and holes diffuse together. Electric neutrality couples their motion. This calculator uses an equal-carrier approximation.
How is surface recombination included?
An effective lifetime correction is applied. It uses sample thickness and velocity. Complex geometries need detailed simulation.
Why are presets approximate?
Mobility depends on several conditions. Doping and defects change transport. Published values can differ substantially.
Does the calculator include electric-field drift?
No drift distance is added. Results describe diffusion-based transport only. Use a transport solver for fields.
Can results replace laboratory measurements?
No, results support preliminary analysis. Real devices include additional mechanisms. Validate important designs experimentally.