Calculator Inputs
Example Data Table
| Parameter | Example Value | Unit | Notes |
|---|---|---|---|
| n | 2.0e15 | cm-3 | Electron concentration |
| p | 8.0e14 | cm-3 | Hole concentration |
| ni | 1.0e10 | cm-3 | Intrinsic concentration |
| τn0 | 1.0e-6 | s | Electron lifetime |
| τp0 | 8.0e-7 | s | Hole lifetime |
| n1 | 1.0e10 | cm-3 | Trap occupancy term |
| p1 | 1.0e10 | cm-3 | Trap occupancy term |
| B | 1.0e-14 | cm3/s | Radiative coefficient |
| Cn | 2.8e-31 | cm6/s | Electron Auger coefficient |
| Cp | 9.9e-32 | cm6/s | Hole Auger coefficient |
| Area | 0.05 | cm2 | Device active area |
| Thickness | 2.0e-4 | cm | Active region thickness |
Example outcome:
Total rate: 6.6668e+20 cm-3 s-1
Effective lifetime: 2.0999e-6 s
Current density: 2.1363e-2 A/cm2
Dominant mechanism: SRH
Formula Used
This calculator combines three common semiconductor recombination models. All concentration terms use cm-based engineering units.
Excess term:
(np - ni²)
Shockley-Read-Hall recombination:
U_SRH = (np - ni²) / [τp0(n + n1) + τn0(p + p1)]
Radiative recombination:
U_rad = B(np - ni²)
Auger recombination:
U_Auger = (Cn·n + Cp·p)(np - ni²)
Total recombination rate:
U_total = U_SRH + U_rad + U_Auger
Flux through thickness:
Flux = U_total · thickness
Recombination current density:
J_rec = q · U_total · thickness
Total current:
I_rec = q · U_total · area · thickness
Approximate effective lifetime:
τ_eff = average excess carrier concentration / |U_total|
This engineering approximation is useful for comparisons, sensitivity checks, and quick design studies.
How to Use This Calculator
- Enter electron concentration, hole concentration, and intrinsic concentration.
- Provide SRH lifetimes and trap-related terms n1 and p1.
- Enter radiative and Auger coefficients using cm-based units.
- Fill device area and active thickness for flux and current outputs.
- Press the calculate button to generate mechanism rates and totals.
- Review the result box above the form and inspect the graph.
- Download CSV for spreadsheets or PDF for reports and documentation.
FAQs
1) What does recombination rate mean here?
It is the net carrier removal rate per unit volume. Positive values mean carriers recombine overall. Negative values mean the operating point behaves like net generation instead.
2) Which mechanism usually dominates?
That depends on material quality and injection level. SRH often dominates defect-rich material, radiative matters in direct-bandgap systems, and Auger becomes important at very high carrier densities.
3) Why can my result become negative?
A negative result appears when np is smaller than ni². Under that condition, the net term shifts toward generation instead of recombination for the chosen operating point.
4) What units should I use?
Use concentrations in cm⁻³, lifetimes in seconds, B in cm³/s, Auger coefficients in cm⁶/s, area in cm², and thickness in cm. Mixed units will distort every output.
5) What are n1 and p1?
They are SRH trap occupancy terms tied to trap energy and thermal equilibrium statistics. They influence how strongly traps capture electrons and holes under different conditions.
6) Can I use this for current estimation?
Yes. The calculator estimates recombination current density and total current from the net volumetric rate, thickness, and area. It is best for engineering estimates, not full device simulation.
7) Why is the effective lifetime very small?
A tiny lifetime usually means the net recombination rate is extremely high relative to excess carriers. Strong defects, high injection, or large Auger terms can all cause this.
8) When should I trust the Auger term most?
Auger is most relevant in heavily doped or high-injection conditions. If concentrations are modest, its contribution may be negligible compared with SRH or radiative recombination.