Estimate diffusion length with direct inputs or physical relations. Switch units, compare scenarios, and export summaries. Designed for fast, clean results.
| Case | Method | Inputs | Output |
|---|---|---|---|
| A | Direct | D = 25 cm²/s, τ = 1e-6 s | L ≈ 50 µm |
| B | Mobility | μ = 1350 cm²/V·s, T = 300 K, τ = 1e-6 s | L ≈ 59 µm |
| C | Mobility + time | μ = 450 cm²/V·s, T = 300 K, τ = 5e-7 s, x = 10 µm | L shown + t estimate shown |
Tip: Keep units consistent, especially for D and μ.
Carrier diffusion length describes how far electrons or holes typically travel by diffusion before recombination. It is a practical figure for device physics because it links microscopic transport to measurable performance in junctions, photodetectors, and solar cells.
The key metric is L = √(D·τ). Diffusion coefficient D reflects how quickly carriers spread, while lifetime τ captures recombination strength. If τ drops by 100×, L falls by 10×, even when D is unchanged.
In many semiconductors, D can vary from about 0.1 to 50 cm²/s depending on material quality and doping. Reported lifetimes can range from nanoseconds in heavily defected films to milliseconds in high purity crystals. These ranges translate to diffusion lengths from tens of nanometers up to millimeters.
When D is unknown, the calculator can estimate it using D = μ(kB T/q). At 300 K, kB T/q is about 0.0259 V, so D ≈ 0.0259·μ (in consistent SI units). This makes mobility measurements directly useful for transport estimates.
For a fixed μ, D scales linearly with temperature, so L scales with √T. However, mobility often decreases with increasing temperature due to phonon scattering. The net trend can therefore be weak, material specific, and worth evaluating over the intended operating range.
In a p–n junction under illumination, minority carriers generated within roughly one diffusion length of the depletion region have a high probability of being collected. If L is smaller than the absorber thickness, carriers recombine before reaching the junction, lowering quantum efficiency.
The optional time estimate uses ⟨x²⟩ = 2Dt in one dimension. For example, with D = 25 cm²/s (2.5×10⁻³ m²/s) and x = 10 µm, t ≈ x²/(2D) ≈ 2×10⁻⁸ s. This helps compare diffusion against fast recombination.
L can be inferred from techniques such as EBIC profiling, surface photovoltage, time resolved photoluminescence with transport models, or spectral response fitting. Use this calculator to standardize units, compare scenarios, and export results for lab notebooks and reports.
It depends on device thickness. For thin films, tens to hundreds of nanometers may be acceptable. For thicker absorbers, micrometers to millimeters are preferred to reduce recombination losses.
Diffusion is a random walk. Mean squared displacement grows linearly with time, while lifetime sets the time available before recombination. Combining them yields L = √(D·τ).
Yes. Use the appropriate diffusion coefficient or mobility and lifetime for the carrier type of interest. In many devices, minority carrier parameters are the most important.
Use it when you have mobility and temperature but lack a measured diffusion coefficient. The Einstein relation is most reliable when transport is near equilibrium and not dominated by strong degeneracy effects.
You can enter D in cm²/s or m²/s. Mobility can be entered in cm²/(V·s) or m²/(V·s). The calculator converts internally and lets you select output length units.
Small L usually comes from short lifetime, small D, or both. High defect density, surface recombination, heavy doping, and poor passivation can significantly shorten lifetime and reduce L.
It estimates how long diffusion takes to cover a chosen distance in one dimension using ⟨x²⟩ = 2Dt. It is a quick comparison tool, not a full device simulation.
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.