QD Inhomogeneous Broadening
Propagate quantum-dot size dispersion into Gaussian transition-energy broadening.
Description
First-order uncertainty propagation converts size dispersion into energy dispersion through a supplied sensitivity.
First-order uncertainty propagation converts size dispersion into energy dispersion through a supplied sensitivity. Gaussian FWHM is then derived from its standard deviation.1
Propagate quantum-dot size dispersion into Gaussian transition-energy broadening.
When to use QD Inhomogeneous Broadening
Use this tool to propagate quantum-dot size dispersion into Gaussian transition-energy broadening.
Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
How to use QD Inhomogeneous Broadening and understand its results
- Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
- Enter sizeStandardDeviationNanometers, energySensitivityEvPerNanometer using the field table and calculation rules, then run the tool.
- Read energySigmaEv, energyFwhmEv. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| sizeStandardDeviationNanometers | QD size standard deviation (nm) | number; minimum: 0 | Required |
| energySensitivityEvPerNanometer | Transition-energy size sensitivity (eV/nm) | number | Required |
Enter nonnegative size SD in nm and finite signed eV/nm sensitivity. Return energy SD and FWHM in eV.
sigmaE=|sigmaSize×sensitivity|; FWHM=2sqrt(2ln2)sigmaE Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| energySigmaEv | Energy standard deviation (eV) | number; minimum: 0 |
| energyFwhmEv | Gaussian inhomogeneous FWHM (eV) | number; minimum: 0 |
{
"input": {
"sizeStandardDeviationNanometers": 1,
"energySensitivityEvPerNanometer": 1
},
"output": {
"energySigmaEv": 1,
"energyFwhmEv": 2.3548200450309493
}
}Limitations and assumptions
No quantum-dot electronic model or non-Gaussian distribution fit is included.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use McWhirter Density Threshold: Calculate the McWhirter LTE minimum electron density and compare a measurement. For a complementary task, use Transient-Absorption Lifetime Fit: Fit a positive transient-absorption trace to a single exponential using log-linear regression.
References
-
QD Inhomogeneous Broadening — tool.io
Similar or alternative tools
- McWhirter Density Threshold
Calculate the McWhirter LTE minimum electron density and compare a measurement.
- Transient-Absorption Lifetime Fit
Fit a positive transient-absorption trace to a single exponential using log-linear regression.