Calculator Inputs
Formula Used
This calculator uses a semiconductor carrier recombination interpretation. In the simplest excess-carrier model, recombination frequency is treated as the inverse lifetime:
frec = 1 / τ
Rsimple = Δn / τ
For advanced modeling, the page also evaluates common recombination channels:
USRH = (np − ni2) / [τp0(n + n1) + τn0(p + p1)]
Urad = B(np − ni2)
UAuger = (Cnn + Cpp)(np − ni2)
For the combined mode:
Utotal = USRH + Urad + UAuger
frec = Utotal / Δn
τeff = 1 / frec
The graph uses exponential excess-carrier decay:
Δn(t) = Δn(0)e-frec·t
Diffusion length is estimated with:
L = √(Dτeff)
How to Use This Calculator
- Choose the calculation model that matches your semiconductor analysis.
- Enter the excess carrier concentration Δn.
- For the simple model, enter lifetime τ only.
- For SRH, radiative, Auger, or combined modes, enter n, p, ni, and the needed coefficients.
- Add a diffusion coefficient if you want diffusion length output.
- Press the calculate button.
- Read the result cards, detailed table, and decay graph.
- Use the CSV or PDF buttons to save the computed outputs.
Example Data Table
| Case | Method | Δn (cm^-3) | Key Inputs | Approx. Frequency | Approx. Lifetime |
|---|---|---|---|---|---|
| Example 1 | Simple | 1.0e12 | τ = 5 µs | 2.0e5 Hz | 5.0 µs |
| Example 2 | SRH | 1.0e12 | n=1.0e15, p=1.0e10, ni=1.0e10 | Depends on SRH denominator | Trap-limited |
| Example 3 | Radiative | 1.0e12 | B = 1.0e-10, n=1.0e15, p=1.0e10 | Depends on np − ni² | Carrier-density limited |
| Example 4 | Combined | 1.0e12 | SRH + radiative + Auger | Sum of mechanisms | Effective total lifetime |
Frequently Asked Questions
1. What does recombination frequency mean here?
Here, it means how fast excess carriers disappear. The page treats it as the inverse of effective carrier lifetime for semiconductor recombination analysis.
2. Why are there several models?
Different devices lose carriers through different mechanisms. Trap-assisted loss suits SRH, photon emission suits radiative recombination, and three-carrier energy transfer suits Auger behavior.
3. When should I use the simple lifetime mode?
Use it when you already know an effective lifetime from measurement, datasheets, or prior modeling. It gives the fastest estimate and clean exponential decay.
4. What if n × p is not greater than ni²?
The advanced models then predict no positive net recombination. That condition usually means equilibrium or net generation dominates your chosen state.
5. Why does the graph look exponential?
Excess carriers often decay exponentially when an effective recombination frequency is used. The chart shows how the initial excess concentration drops with time.
6. What units should I enter?
Use carrier concentrations in cm^-3, lifetime in microseconds, diffusion coefficient in cm^2/s, radiative coefficient in cm^3/s, and Auger coefficients in cm^6/s.
7. What does diffusion length tell me?
It estimates how far carriers travel before recombining. Larger diffusion length usually indicates carriers survive longer or move more easily.
8. Can I use this for every material system?
It is best for quick educational and engineering estimates. Precise device studies still need material-specific parameters, temperature effects, and validated measurement data.