Minority Carrier Lifetime Equation Calculator

Model semiconductor lifetimes from several engineering perspectives. Switch methods, inspect trends, and export calculated outputs. Designed for fast evaluation, reporting, learning, and comparison workflows.

Calculator Input

Select a lifetime model, enter engineering values, and compute the minority carrier lifetime. The result appears above this form after submission.

Calculation Mode

Excess Carrier Concentration Δn (cm⁻³)

Recombination Rate R (cm⁻³·s⁻¹)

Diffusion Length L (µm)

Diffusion Coefficient D (cm²/s)

Initial Excess Δn₀ (cm⁻³)

Final Excess Δn(t) (cm⁻³)

Elapsed Time t (µs)

Bulk Lifetime τbulk (µs)

Surface Recombination Velocity S (cm/s)

Wafer Thickness W (µm)

Plot Initial Excess Carrier (cm⁻³)

Used to draw the decay chart after lifetime is calculated.

Optional D for Estimated Diffusion Length (cm²/s)

Leave positive to estimate diffusion length from the computed lifetime.

Plotly Graph

The graph shows exponential minority carrier decay based on the calculated lifetime.

Formula Used

1) Direct recombination lifetime

τ = Δn / R

Use this when excess carrier concentration and total recombination rate are known. The result gives the average time carriers survive before recombination.

2) Diffusion length relation

τ = L² / D

Use this when carrier diffusion length and diffusion coefficient are available. Convert diffusion length into centimeters before applying the equation.

3) Exponential decay lifetime

τ = -t / ln(Δn(t) / Δn₀)

Use this for transient decay measurements. The final concentration must be smaller than the initial concentration, and time must be positive.

4) Effective lifetime with surfaces

1/τeff = 1/τbulk + 2S/W

Use this slab approximation when bulk lifetime, surface recombination velocity, and wafer thickness are known. Surface losses shorten the effective lifetime.

How to Use This Calculator

Select the engineering method that matches your semiconductor data.
Enter all required values using the units shown beside each field.
Optionally enter a diffusion coefficient for diffusion length estimation.
Set the plot starting carrier concentration for the decay graph.
Click Calculate Lifetime to generate the result.
Review the result card above the form for lifetime values.
Inspect the graph to understand carrier decay over time.
Use the CSV or PDF buttons to export the calculated output.

Example Data Table

These examples show typical calculations using the supported lifetime equations.

Mode	Input Set	Formula	Lifetime Result
Direct Recombination	Δn = 2.5×10¹³ cm⁻³, R = 5.0×10¹⁸ cm⁻³·s⁻¹	τ = Δn / R	5.0 µs
Diffusion Length	L = 150 µm, D = 25 cm²/s	τ = L² / D	9.0 µs
Exponential Decay	Δn₀ = 5.0×10¹³ cm⁻³, Δn(t) = 6.7668×10¹² cm⁻³, t = 12 µs	τ = -t / ln(Δn(t)/Δn₀)	6.0 µs
Effective Lifetime	τbulk = 25 µs, S = 120 cm/s, W = 200 µm	1/τeff = 1/τbulk + 2S/W	19.23 µs

Frequently Asked Questions

1. What does minority carrier lifetime represent?

It represents the average time an injected minority carrier exists before recombination. Longer lifetime usually supports better diffusion, collection, and device performance in many semiconductor structures.

2. When should I use the direct recombination equation?

Use it when you know the excess carrier concentration and the recombination rate directly. It is helpful in analytical studies, simulation post-processing, and simplified engineering checks.

3. Why does diffusion length require unit conversion?

Diffusion coefficient is commonly expressed in cm²/s, so diffusion length should be converted to centimeters. Consistent units are necessary to avoid large scaling errors in lifetime estimates.

4. Why must the final carrier concentration be lower?

The exponential decay formula assumes the carrier population is decreasing with time. If the final value is not lower, the logarithm term becomes invalid for decay-based lifetime extraction.

5. What does the effective lifetime model include?

It combines bulk recombination and two surface losses in a slab approximation. This is useful for wafers, passivation studies, and quick comparisons between surface conditions.

6. What does the Plotly graph show?

It shows an exponential decay curve based on the calculated lifetime. The graph helps visualize how quickly excess carriers reduce over time for the chosen starting concentration.

7. Can I estimate diffusion length from the result?

Yes. Enter an optional diffusion coefficient in the dedicated field. The calculator then estimates diffusion length using the computed lifetime and reports it with the main results.

8. Are these results suitable for final fabrication decisions?

They are useful for engineering estimates and educational analysis. Final device decisions should also consider injection level, temperature, Auger effects, SRH details, and measured material behavior.