Calculator Inputs
Use the model selector for one-dimensional wells, rectangular boxes, or spherical dots. The input area uses a responsive three-column, two-column, and one-column layout.
Example Data Table
This sample table uses your current settings while sweeping characteristic size in nanometers. It helps compare size sensitivity before exporting or documenting results.
| Characteristic Size (nm) | Confinement Shift (eV) | Transition Energy (eV) | Estimated Wavelength (nm) |
|---|---|---|---|
| 2.00 | 0.803452 | 2.543452 | 487.526 |
| 4.00 | 0.168716 | 1.908716 | 649.651 |
| 6.00 | 0.060697 | 1.800697 | 688.622 |
| 8.00 | 0.026105 | 1.766105 | 702.110 |
| 10.00 | 0.011564 | 1.751564 | 707.939 |
| 12.00 | 0.004459 | 1.744459 | 710.822 |
Formula Used
1) One-Dimensional Infinite Well
Electron: Ee = nx2h2 / (8me*m0L2)
Hole: Eh = nx2h2 / (8mh*m0L2)
Total shift: ΔE = Ee + Eh
2) Three-Dimensional Rectangular Box
Electron: Ee = h2 / (8me*m0) × [nx2/Lx2 + ny2/Ly2 + nz2/Lz2]
Hole uses the same structure with mh*.
Total shift: ΔE = Ee + Eh
3) Spherical Dot Approximation
Electron: Ee = h2 / (8me*m0R2)
Hole: Eh = h2 / (8mh*m0R2)
Coulomb term: Ec = -1.786e2 / (4π ε0 εr R)
Total shift: ΔE = Ee + Eh + Ec
4) Transition Energy and Wavelength
Estimated transition energy: Etransition = Eg,bulk + ΔE
Estimated wavelength: λ ≈ 1240 / Etransition when energy is in electronvolts and wavelength is in nanometers.
These formulas assume the effective-mass approximation and idealized confinement. They are strong engineering estimates, but real devices can differ because of finite barriers, strain, defects, and temperature.
How to Use This Calculator
- Choose the structure model that best matches your device geometry.
- Select the input length unit and enter dimensions or radius.
- Enter electron and hole effective masses relative to the free-electron mass.
- Set quantum numbers. Use the ground state with ones for the first estimate.
- Enter relative permittivity when using the spherical model.
- Add the bulk band gap if you want an estimated optical transition energy.
- Set the graph sweep range in nanometers to study size sensitivity.
- Click the calculate button. Review results, examine the chart, and export CSV or PDF when needed.
FAQs
1) What is quantum confinement energy?
Quantum confinement energy is the energy rise caused by restricting carriers inside nanoscale dimensions. As the structure shrinks, allowed energy states spread apart, usually increasing transition energy and decreasing emission wavelength.
2) How accurate is this calculator?
The calculator uses infinite-well style approximations and a Brus-style spherical model. These are useful engineering estimates, but real devices may deviate because of finite barriers, strain, nonparabolic bands, defects, and temperature.
3) What masses should I enter?
Use effective mass values relative to the free-electron mass. Many datasheets and papers list me* and mh* that way. Enter positive numbers only, because the calculator converts them internally to SI units.
4) Why do Ly and Lz seem unused in the one-dimensional model?
For the one-dimensional well, only the confinement thickness directly enters the formula. The other dimensions are not used, so you can leave them at defaults unless you switch to the box model.
5) What does the Coulomb correction mean?
The spherical model includes a Coulomb correction term between electron and hole. It usually lowers the transition energy slightly, partially offsetting the positive confinement shift produced by small radii.
6) Can I estimate wavelength directly?
Yes. The estimated optical wavelength equals 1240 divided by transition energy in electronvolts. This gives a convenient approximation for emitted or absorbed photon wavelength in nanostructure studies.
7) How can I lower the confinement energy?
Increase the size parameter while keeping masses and quantum numbers fixed. Because confinement terms scale roughly with one over size squared, energy falls quickly as dimensions become larger.
8) When should I use a more advanced model?
Use it for screening, design comparison, and educational estimates. For publication-grade predictions, validate with material-specific parameters, finite-potential models, experimental spectra, and full numerical simulations.