Quantum Dot Energy Levels Calculator

Calculator Inputs

Material Name

Size Input Type

Quantum Level Index n

Radius (nm)

Diameter (nm)

Bulk Band Gap (eV)

Electron Effective Mass Ratio

Hole Effective Mass Ratio

Dielectric Constant

Temperature (K)

Varshni Alpha (eV/K)

Varshni Beta (K)

Apply temperature correction

Include Coulomb correction

Example Data Table

Material	Radius (nm)	Bulk Band Gap (eV)	Electron Mass Ratio	Hole Mass Ratio	Dielectric Constant
CdSe	3.2	1.74	0.13	0.45	9.5
PbS	2.8	0.41	0.09	0.09	17.2
ZnS	2.0	3.68	0.28	0.59	8.1

Formula Used

This calculator applies the effective mass approximation with a Brus style transition energy model for spherical quantum dots.

Electron confinement: E_e = h²n² / (8m_e^*R²)

Hole confinement: E_h = h²n² / (8m_h^*R²)

Coulomb correction: E_c = 1.8e² / (4π ε₀ εR)

Transition energy: E = E_g(T) + E_e + E_h - E_c

Temperature correction: E_g(T) = E_g(0) - αT² / (T + β)

The model is useful for estimating size dependent optical shifts, though real nanocrystals may also require finite barrier, nonspherical, strain, and surface state corrections.

How to Use This Calculator

Enter a material name for easier result tracking.
Choose whether you want to input radius or diameter.
Provide the bulk band gap and effective mass ratios.
Enter the dielectric constant for your selected material.
Set the quantum level index to examine excited states.
Optionally enable temperature correction using Varshni parameters.
Keep Coulomb correction enabled for a more realistic transition estimate.
Press calculate to display results above the form.
Export the displayed results as CSV or print them as PDF.

FAQs

1. What does this calculator estimate?

It estimates quantum dot transition energy, wavelength, electron confinement, hole confinement, Coulomb correction, and related level dependent optical quantities from effective mass inputs.

2. Why does a smaller dot increase energy?

Confinement energy scales inversely with the square of radius. Smaller particles restrict carrier motion more strongly, raising energy spacing and usually shifting absorption toward shorter wavelengths.

3. What is the role of the dielectric constant?

It controls the electrostatic attraction between electron and hole. Larger dielectric constants weaken Coulomb attraction, reducing the magnitude of the excitonic correction term.

4. Why are effective mass ratios required?

Electron and hole confinement depend on their effective masses inside the semiconductor. Lower effective mass causes stronger confinement and larger quantization energy for the same radius.

5. Can I use diameter instead of radius?

Yes. Select the diameter option and enter the particle diameter. The calculator converts it internally to radius before applying the energy equations.

6. Why include temperature correction?

Semiconductor band gaps vary with temperature. The Varshni relation adjusts the bulk band gap before confinement terms are added, improving comparisons across measurement conditions.

7. Is this model exact for all nanocrystals?

No. It is a practical approximation. Finite barriers, ligand environments, nonspherical shapes, strain, and surface traps can shift real spectra away from the estimate.

8. What export options are included?

You can download calculated metrics as a CSV file and save a PDF using the print based export button after results appear.