Recombination Rate SRH Calculator

Formula Used

The Shockley-Read-Hall recombination rate is computed as:

The auxiliary terms depend on trap energy and temperature:

Here k is the Boltzmann constant in eV/K, T is temperature, and ΔE = E_t − E_i. A positive U indicates net recombination; negative U indicates net generation.

How to Use This Calculator

1. Select the concentration unit you want to work in.
2. Enter n, p, and n_i for your material and bias point.
3. Provide τ_n and τ_p that represent trap capture effects.
4. Set ΔE to describe the trap location relative to the intrinsic level.
5. Enter temperature and press Calculate.
6. Use the download buttons to export the computed results.

Example Data Table

Example U values are approximate and depend on chosen inputs.

1) Why SRH recombination matters in real devices

Shockley–Read–Hall (SRH) recombination describes trap‑assisted carrier loss through defects in the bandgap. In silicon, SRH often dominates at low to moderate injection, shaping diode leakage, photodiode dark current, and the open‑circuit voltage of solar cells. Because SRH depends on both carrier densities and lifetimes, it connects electrical bias, illumination level, and material quality in one rate expression.

2) Interpreting the sign of the computed rate

The calculator evaluates np − n_i². If np > n_i², the result is positive and indicates net recombination (carriers decrease). If np < n_i², the rate becomes negative and represents net generation, typical of reverse bias or depleted regions where carriers are scarce.

3) Choosing realistic carrier concentrations

Use the local electron and hole concentrations at the region of interest. For doped semiconductors under equilibrium, a rough guide is n≈N_D in n‑type and p≈N_A in p‑type, while the minority carrier follows np≈n_i². Under illumination or injection, both n and p can rise significantly, often by orders of magnitude in high‑level injection.

4) Intrinsic concentration and temperature sensitivity

The intrinsic concentration n_i increases strongly with temperature, so SRH generation in depletion regions can rise noticeably at elevated T. For many materials, kT at 300 K is about 0.0259 eV, meaning even modest trap offsets can change the auxiliary terms via exponentials. Always match n_i and T to the same material model.

5) Trap energy location through ΔE

ΔE controls n₁ and p₁, which weight how efficiently the trap exchanges carriers with the bands. Midgap traps (ΔE ≈ 0) tend to maximize recombination impact because they interact comparably with electrons and holes. Traps closer to a band edge can behave more like selective centers, influencing one carrier type more strongly.

6) Lifetimes as capture strength indicators

τ_n and τ_p summarize capture cross‑sections and defect density into effective lifetimes. Smaller lifetimes mean faster capture and larger magnitude of U for the same carrier densities. In practice, lifetimes can range from nanoseconds in defect‑rich regions to milliseconds in high‑purity wafers. Use literature or measured lifetime data for credible predictions.

7) Units, scaling, and sanity checks

The SRH rate is reported as concentration per second, such as cm⁻³ s⁻¹ or m⁻³ s⁻¹. Switching units rescales the numeric value by 10⁶. If you see extreme magnitudes, check that n, p, and n_i are consistent, and that τ values are not accidentally entered in microseconds versus seconds.

8) Where to apply the results in modeling workflows

Use U as a local rate inside continuity or drift‑diffusion models, or convert it to an effective current density by integrating across a region. In solar and photodetector analysis, SRH parameters help fit dark current, quantum efficiency roll‑off, and voltage loss. In process monitoring, improving lifetime typically correlates with reduced SRH loss and better device yield.

FAQs

1) What does SRH stand for?

SRH stands for Shockley–Read–Hall recombination. It models trap‑assisted recombination or generation through defect states inside the bandgap, using carrier densities, lifetimes, temperature, and trap energy location.

2) Why can the recombination rate be negative?

A negative value indicates net generation. It happens when np is below n_i², common in depletion or reverse‑biased regions where carriers are sparse and thermal generation dominates.

3) What should I use for ΔE?

ΔE is the trap energy relative to the intrinsic level. Use 0 eV for a midgap trap. If you have a known defect level, enter its offset; the exponentials then adjust n₁ and p₁.

4) How do τn and τp relate to material quality?

Shorter lifetimes usually mean higher defect density or stronger capture cross‑sections, leading to larger SRH loss. Longer lifetimes are typical of cleaner material, better passivation, and improved device performance.

5) Can I use this for non‑silicon materials?

Yes, if you provide the correct n, p, n_i, lifetimes, ΔE, and temperature for your material. The mathematical form is general, but parameter values and intrinsic concentration models differ by semiconductor.

6) What is a good quick sanity check?

At equilibrium in a uniformly doped region, np is often close to n_i², so U should be near zero. Large deviations suggest injection, illumination, or inconsistent inputs.

7) Why do exports require a calculation first?

CSV and PDF exports use the computed results and intermediate terms. Running the calculation ensures the file contains consistent inputs, derived n₁/p₁, and the final SRH rate with the chosen unit system.