Semiconductor Quantum Dot Size From Emission Calculator
Invert a caller independently applicable emission effective-mass model E_em=E_bulk+A/r²-B/r-StokesLoss on its positive confinement branch. Source-qualified material coefficients and Stokes loss required; not the existing CdSe first-exciton absorption calibration, a universal size law, spectral-peak detector or fabrication recommendation.
Description
Invert a caller-qualified emission model for conditional quantum-dot radius and diameter.
An emission-based quantum-dot size estimate requires a material-specific model, not just a wavelength. This calculator inverts the supplied effective-mass relation Eem = Ebulk + A/r^2 - B/r - StokesLoss on its positive-confinement branch.
When to use this tool
Invert a caller-qualified emission model for conditional quantum-dot radius and diameter. Use it when the input measurements and conventions below match the operation you need.
- Prepare callerVerifiedSource, callerVerifiedContext, callerVerifiedAsOfDate, emissionPeakWavelengthNm, bulkBandgapEv, callerKineticCoefficientEvNm2, callerCoulombCoefficientEvNm, callerStokesLossEv, respecting the measurement basis and boundaries below.
- Compare the worked example with your intended operation before reusing its result.
How to use the tool and how it works
- Enter every field in the input table using the stated units and exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
Supply a qualified source, context and date plus wavelength in nm, bulk gap in eV, A in eV nm squared, B in eV nm and Stokes loss in eV. Wavelength, bulk gap and A must be positive; B and loss nonnegative. It computes Ephoton = 1239.841984/wavelength and delta = Ephoton plus loss minus bulk gap, requiring delta positive. The radius is 2A divided by (hypot(B, 2 sqrt(A) sqrt(delta)) plus B); diameter is twice radius. This form avoids subtracting nearly equal terms.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| callerVerifiedSource | Identify the independently checked source and edition; a nonblank label is required. | Text |
| callerVerifiedContext | State the applicable population, method, model or jurisdiction; a nonblank description is required. | Text |
| callerVerifiedAsOfDate | Gregorian date YYYY-MM-DD identifying the supplied reference context. | Text |
| emissionPeakWavelengthNm | Photoluminescence emission peak wavelength nm. Nanometers. | Finite number; greater than zero |
| bulkBandgapEv | Applicable bulk bandgap eV. Electronvolts. | Finite number; greater than zero |
| callerKineticCoefficientEvNm2 | Qualified inverse-square kinetic coefficient eV nm². | Finite number; greater than zero |
| callerCoulombCoefficientEvNm | Qualified Coulomb coefficient eV nm. Nanometers. | Finite number; zero or greater |
| callerStokesLossEv | Independently established emission Stokes loss eV. Electronvolts. | Finite number; zero or greater |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.photonEnergyEv | Photon energy ev; use the stated units and sign convention. |
| result.confinementExcessEv | Confinement excess ev; use the stated units and sign convention. |
| result.conditionalRadiusNm | Positive root of the supplied emission-model equation, in nanometers. |
| result.conditionalDiameterNm | Twice the conditional model radius, in nanometers. |
{
"input": {
"callerVerifiedSource": "illustrative-qualified-emission-model/edition",
"callerVerifiedContext": "Illustrative independently established material-specific effective-mass emission model, not CdSe absorption calibration.",
"callerVerifiedAsOfDate": "2026-01-01",
"emissionPeakWavelengthNm": 619.920992,
"bulkBandgapEv": 1,
"callerKineticCoefficientEvNm2": 2,
"callerCoulombCoefficientEvNm": 1,
"callerStokesLossEv": 0
},
"output": {
"result": {
"photonEnergyEv": 2,
"confinementExcessEv": 1,
"conditionalRadiusNm": 1,
"conditionalDiameterNm": 2
}
}
}Limitations and assumptions
- Coefficients and Stokes loss must independently apply to the material, surface and temperature. The tool does not locate a spectral peak, apply a universal CdSe absorption calibration, verify the supplied source or recommend fabrication conditions. The example's model values are illustrative.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
Use a material-specific spectral calibration or a justified emission model with independent uncertainty assessment. An absorption-peak calibration and an emission-model inversion describe different observations. Compare the scope of the nearby tools below before substituting one.
References
Similar or alternative tools
- quantum dot size distribution
A quantum-dot size distribution can be weighted by represented dot counts.
- quantum dot size from absorption
Estimate CdSe quantum-dot diameter from the first excitonic absorption peak using the Yu empirical fit; photoluminescence emission peaks are not interchangeable with this calibration.