Shockley–Queisser Limit Calculator
Introduction: how the Shockley–Queisser limit calculator works
The Shockley–Queisser limit calculator turns a semiconductor band gap, a solar-source temperature, and a cell temperature into a detailed-balance efficiency ceiling for a single-junction photovoltaic device. Instead of forcing you to work through radiative recombination integrals by hand, it packages the model into a short workflow: enter the physical conditions, let the calculator evaluate the limit, and read the efficiency estimate in a form you can compare across designs.
This kind of calculator is most useful when you need to sanity-check whether a proposed band gap is near the theoretical optimum or far from it. The notes on the page explain the fields, units, method, and model boundaries so the estimate is easier to trust. Without that context, two users can supply the same-looking numbers but mean different temperatures, and the output will look misleading even though the equations were applied consistently.
The sections below show which physical question the Shockley–Queisser model answers, how to choose the band-gap and temperature inputs, how to read the efficiency result, and which simplifying assumptions matter most before you use the number in design work.
What problem does this Shockley–Queisser calculator solve?
The Shockley–Queisser limit calculator answers a very specific solar-cell question: for a single junction, given a band gap and thermal conditions, what is the best efficiency you could hope for under detailed-balance assumptions? That matters when you are screening candidate absorber materials, comparing band-gap targets, or trying to understand why a cell with a high current may still be capped by voltage losses.
Before you start, define the design question in one sentence. Examples include: “Is this band gap close to the theoretical optimum?”, “How much efficiency do I lose if the cell runs hotter?”, “What happens if I shift the absorber to a wider gap?”, or “Does this material sit near the Shockley–Queisser sweet spot?” When the question is clear, it becomes much easier to tell whether the inputs on the page represent the physical scenario you want to test.
How to use this Shockley–Queisser calculator
- Enter Band gap energy E g (eV) with the unit shown beside the field.
- Enter Sun temperature T sun (K) with the unit shown beside the field.
- Enter Cell temperature T cell (K) with the unit shown beside the field.
- Run the calculation to refresh the results panel.
- Check the output's unit, order of magnitude, and direction before comparing scenarios.
If you are comparing materials, write down the band gap and temperature set you used so you can reproduce the same detailed-balance estimate later.
Inputs: choosing Shockley–Queisser band-gap and temperature values
The Shockley–Queisser form collects the physical variables that drive the detailed-balance limit. Many mistakes come from mixing units (eV with joules, kelvin with Celsius) or from testing values outside a realistic operating range. Use the following checklist as you enter the numbers:
- Units: confirm the unit shown next to the input and keep your data consistent.
- Ranges: if an input has a minimum or maximum, treat it as the model’s safe operating range for the detailed-balance calculation.
- Defaults: any prefilled values are placeholders; replace them with your own numbers before relying on the output.
- Consistency: if two inputs describe related quantities, make sure they don’t contradict each other.
Common inputs for Shockley–Queisser limit studies include:
- Band gap energy E g (eV): the absorber band gap you want to test against the efficiency ceiling.
- Sun temperature T sun (K): the source temperature that sets the incoming photon spectrum in the model.
- Cell temperature T cell (K): the device temperature that governs the radiative recombination side of the calculation.
If you are unsure about a value, it is better to start with a conservative estimate and then run a second scenario with a more aggressive one. That gives you a bounded range rather than a single efficiency number you might over-trust.
Formulas: how the Shockley–Queisser calculator turns inputs into efficiency
The Shockley–Queisser calculation follows a familiar pattern: it converts the band gap and temperatures into photon fluxes, balances generation against radiative loss, and then translates the current-voltage relationship into an efficiency estimate. Even though the physics is specialized, the workflow is still straightforward: normalize units, evaluate the detailed-balance expressions, and present the output in a form that is easy to compare across candidate absorber designs.
The calculator's result R can be represented as a function of the inputs x1 … xn:
A very common special case is a “total” that sums contributions from multiple components, sometimes after scaling each component by a factor:
Here, wi represents a conversion factor, weighting, or efficiency term. That is how calculators encode “this part matters more” or “some input is not perfectly efficient.” When you read the result, ask: does the output scale the way you expect if you change the band gap or temperature? If not, revisit units and assumptions.
Worked example: Shockley–Queisser limit calculation step by step
Worked examples make the band-gap and temperature inputs easier to interpret in a Shockley–Queisser context. For illustration, suppose you enter the following three values:
- Band gap energy E g (eV): 1.34
- Sun temperature T sun (K): 5778
- Cell temperature T cell (K): 300
A simple check total for the example inputs, used only as a comparison cue, is the sum of the displayed numbers:
Sanity-check total: 1.34 + 5778 + 300 = 6079.34
After you click calculate, compare the result panel with the physical story you expect. If the efficiency looks implausibly high or low, confirm that the temperatures are in kelvin and that the band gap is in eV. If the result seems reasonable, vary one input at a time to see how the Shockley–Queisser limit shifts.
Comparison table: Shockley–Queisser sensitivity to band gap energy
The table below changes only Band gap energy E g (eV) while keeping the other example values constant. The “scenario total” is shown as a simple comparison metric so you can see sensitivity at a glance.
| Scenario | Band gap energy E g (eV) | Other inputs | Comparison score | Interpretation |
|---|---|---|---|---|
| Conservative (-20%) | 1.072 | Unchanged | 6079.07 | A smaller band gap usually shifts the detailed-balance balance toward more current and less voltage. |
| Baseline | 1.34 | Unchanged | 6079.34 | This is the reference case for comparing nearby absorber choices. |
| Aggressive (+20%) | 1.608 | Unchanged | 6079.61 | A wider gap usually trims current while raising voltage until the detailed-balance optimum moves again. |
Use the calculator's actual result panel with conservative, baseline, and aggressive assumptions to see how much the outcome moves when a key input changes.
How to interpret a Shockley–Queisser efficiency result
The results panel is designed to be a clear summary of the detailed-balance limit rather than a raw dump of intermediate values. When you get a number, ask three questions: (1) does the unit match the design decision you are making? (2) is the magnitude plausible for a single-junction cell with this band gap? (3) if you tweak the band gap or temperature, does the output move in the direction the Shockley–Queisser model predicts? If you can answer “yes” to all three, you can treat the output as a useful screening estimate.
When relevant, a CSV download option gives you a portable record of the exact band gap and temperatures you tested. Saving that file helps you compare multiple absorber candidates, share assumptions with teammates, and reproduce the same detailed-balance scenario later without having to guess which numbers were used.
Limitations and assumptions in the Shockley–Queisser model
No calculator can capture every real photovoltaic detail. This tool uses the idealized Shockley–Queisser detailed-balance picture: a single junction, radiative recombination as the loss mechanism, and temperatures treated as uniform inputs. Keep these common limitations in mind:
- Input interpretation: read each input label literally; changing the meaning of a field changes the estimate.
- Unit conversions: convert source data carefully before entering values.
- Linearity: quick estimators often assume proportional relationships; real systems can be nonlinear once constraints appear.
- Rounding: the displayed Shockley–Queisser values may be rounded for readability, so small differences from hand checks are normal.
- Missing factors: optical losses, nonradiative recombination, series resistance, and device-specific edge cases are not represented here.
If you use the output for research, design screening, safety, or investment decisions, treat it as a theoretical ceiling rather than a measured performance guarantee. The best use of the calculator is to make your assumptions explicit: you can see which band gap and temperature choices drive the result, adjust them transparently, and explain the reasoning clearly.