Calculator Inputs
Example Data Table
| Scenario | Type | Model | T (K) | Doping (cm^-3) | Gold Nt (cm^-3) | Low-level lifetime | Exact lifetime |
|---|---|---|---|---|---|---|---|
| P-type baseline | P-type | Combined | 3 | 1.0000e+15 | 1.0000e+12 | 9.1038 µs | 9.1046 µs |
| N-type lighter gold | N-type | Combined | 3 | 5.0000e+14 | 5.0000e+11 | 22.4403 µs | 22.4434 µs |
| P-type higher temperature | P-type | Combined | 35 | 1.0000e+15 | 1.0000e+12 | 8.546 µs | 8.5467 µs |
| N-type stronger kill | N-type | Combined | 3 | 1.0000e+15 | 1.0000e+13 | 1.0168 µs | 1.0169 µs |
These rows are generated with the same model used by the calculator, using the default silicon and gold-center assumptions shown in the form.
Formula Used
1) Capture time constants
τn0 = 1 / (σn × vth × Nt)
τp0 = 1 / (σp × vth × Nt)
2) SRH energy terms
n1 = Nc × exp(-(Ec - Et) / (kT))
p1 = Nv × exp(-(Et - Ev) / (kT))
3) Equilibrium concentrations
For P-type silicon: p0 ≈ NA, n0 = ni² / p0
For N-type silicon: n0 ≈ ND, p0 = ni² / n0
4) Exact SRH recombination rate at entered excess
U = (np - ni²) / [τp0 × (n + n1) + τn0 × (p + p1)]
τexact = Δ / U, with n = n0 + Δ and p = p0 + Δ
5) Low-level minority lifetime estimate
τLL = [τp0 × (n0 + n1) + τn0 × (p0 + p1)] / majority_concentration
6) Combined donor and acceptor model
1 / τtotal = 1 / τacceptor + 1 / τdonor + 1 / τbackground
This is an engineering calculator. It gives a practical SRH estimate for low-level minority lifetime control by gold-related centers in silicon, not a full process-TCAD replacement.
How to Use This Calculator
- Select P-type or N-type silicon.
- Choose whether to use the gold acceptor, donor, or the combined donor-plus-acceptor model.
- Enter temperature, base doping, active gold trap density, and your expected excess carrier concentration.
- Keep the default silicon constants unless you have measured values for your material or process corner.
- Adjust the gold trap energies and capture cross sections if your lab data suggests different values.
- Press Calculate Lifetime and read the result section shown above the form.
- Compare the low-level lifetime with the exact SRH lifetime to judge whether your chosen injection level still behaves like a low-level case.
- Use the CSV and PDF buttons to export results after calculation.
FAQs
1) What does low-level injection mean here?
It means the excess carrier concentration is much smaller than the majority-carrier concentration. In that regime, minority lifetime formulas simplify. This page reports the ratio Δ to majority concentration so you can quickly judge whether that assumption still looks reasonable.
2) Why are donor and acceptor options both included?
Gold in silicon is commonly discussed with both a donor-like and an acceptor-like deep level. Some users want a single dominant-center estimate, while others prefer a parallel combined model. Including both options makes the calculator more useful for quick comparison studies.
3) Why are capture cross sections editable?
Published capture data can vary with center type, field conditions, and sample history. Editable inputs let you fit the calculator to measurement data, literature values, or internal process assumptions without changing the source code each time.
4) What is the difference between low-level and exact lifetime outputs?
The low-level result is the simplified engineering estimate. The exact output uses the entered excess-carrier concentration directly inside the SRH expression. When the two values are close, your low-level assumption is usually consistent. If they drift apart, the injection condition deserves review.
5) Can I use this for materials other than silicon?
You can change bandgap, density-of-states values, and other terms, but the default deep-level settings and framing are intended for gold-related behavior in silicon. For another material system, you should replace the trap energies and capture assumptions with appropriate data.
6) What does the background lifetime field do?
It lets you combine gold-driven recombination with an additional lifetime limit, such as another bulk mechanism. The code combines lifetime channels in parallel, which is often a practical engineering way to represent multiple independent recombination paths.
7) Why does lifetime usually shrink when gold density rises?
Higher active trap density increases recombination opportunities. Since the basic capture time constants scale inversely with trap density, stronger gold contamination or stronger deliberate lifetime killing commonly drives the minority-carrier lifetime downward.
8) Are the CSV and PDF downloads generated from the same calculation?
Yes. After you calculate, the page stores the latest result in the session. The CSV export includes the plotted data points, while the PDF provides a compact text report summarizing the chosen inputs and the main calculated lifetime values.