Density of States Calculator

Model Electronic DOS (parabolic band)

This tool uses common free-carrier band approximations.

Dimension 1D (wire-like) 2D (sheet-like) 3D (bulk)

Select the confinement dimension of your system.

Effective mass m* (relative to mₑ)

Enter a positive effective mass.

Spin degeneracy gₛ

Typical value: 2 for spin-½ carriers.

Valley degeneracy gᵥ

Set to 1 unless your band structure has valleys.

Band edge Ec (eV)

DOS is zero for E ≤ Ec in this model.

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Energy input mode

Single energy

Range sweep

Custom list

Energy E (eV)

Example: 0.10 eV above a reference.

Start energy (eV)

End energy (eV)

Points

2–501 points are supported for export-friendly tables.

Energy list (eV) 0.00 0.05 0.10 0.20 0.30

Paste values from a spreadsheet or simulation output.

Compute Density of States Reset

For an electronic parabolic band, the density of states depends on the dimensionality and the energy measured from the band edge E−Ec. The calculator uses these standard forms (energy in joules):

• 1D: g(E)= (gₛ gᵥ/π)√(m*/(2ħ²)) / √(E−Ec)
• 2D: g(E)= (gₛ gᵥ m*)/(2πħ²) (constant above Ec)
• 3D: g(E)= (gₛ gᵥ/(2π²)) (2m*/ħ²)3/2 √(E−Ec)

It also reports the integrated count N(E)=∫ g(E') dE', giving states per length/area/volume up to the chosen energy.

1. Select the system dimension (1D wire, 2D sheet, or 3D bulk).
2. Enter an effective mass m* in units of the electron mass, and set degeneracy factors.
3. Choose a band edge Ec if your energy axis is offset.
4. Pick Single, Range, or List mode to define energies in eV.
5. Press Compute to see results above the form and export the table.

Sample values for a 3D system with m* = 0.26, gₛ = 2, gᵥ = 1, Ec = 0 eV (energies in eV). Your results will differ with inputs.

1) What the Density of States Represents

Density of states (DOS) is the number of quantum states available per energy interval at energy E. This calculator reports g(E) in states/(eV·m^d) and states/(eV·cm^d), where d is the selected dimension.

2) Dimensionality and the Shape of g(E)

For an ideal parabolic band, the energy dependence is distinctive. In 1D, g(E) scales as 1/√(E−Ec), so it rises steeply near the band edge. In 2D, g(E) is constant above Ec. In 3D, g(E) grows as √(E−Ec), giving a smooth increase with energy.

3) Effective Mass Controls the Scale

The effective mass m* sets the amplitude of DOS. Larger m* means heavier carriers and more available states at the same energy offset. Typical electron values include about 0.067 mₑ for GaAs and about 0.26 mₑ for silicon conduction bands.

4) Spin and Valley Degeneracy

Degeneracy multiplies the DOS linearly through gₛ×gᵥ. Spin degeneracy gₛ is often 2 for spin-1/2 carriers. Valley degeneracy gᵥ depends on band structure; bulk-like silicon models commonly use gᵥ = 6.

5) Why the Band Edge Ec Matters

Ec defines the threshold where states begin. The calculator returns zero when E ≤ Ec, matching the step behavior of these idealized expressions. For example, if Ec = 0.20 eV and you test E = 0.10 eV, the output is zero. This is useful when your energies are referenced to an arbitrary zero.

6) Units, Constants, and Conversions

Internally, energies are converted to joules using 1 eV = 1.602176634×10⁻¹⁹ J. The expressions use ħ = 1.054571817×10⁻³⁴ J·s and mₑ = 9.1093837015×10⁻³¹ kg. Results are converted back to per eV, and to per cm^d by dividing by 100^d.

7) Interpreting the Integrated States N(E)

N(E) is the integral of DOS from Ec to E, reported as states per m^d (and per cm^d). In 3D, N(E) scales as (E−Ec)^3/2, while in 2D it scales linearly with (E−Ec). For semiconductor checks, compare computed carrier densities against typical doping ranges such as 10¹⁶ to 10¹⁹ cm⁻³.

8) Practical Workflow for Research Notes

Use Single mode for quick evaluations, Range mode for smooth sweeps (2–501 points), or List mode to paste energies from simulations. After computing, export CSV for spreadsheets or PDF for sharing. Keeping Ec, m*, and degeneracy explicit helps document assumptions and reproduce results reliably in practice.

1) What does the calculator assume about the band structure?

It assumes an ideal parabolic dispersion near the band edge and uses closed-form DOS expressions. It does not include non-parabolicity, band mixing, disorder broadening, or many-body corrections.

2) Why do I get zero DOS for some energies?

These formulas apply only for energies above the chosen band edge Ec. When E ≤ Ec, the available states in this simplified model are set to zero to reflect the threshold behavior.

3) Which dimension should I choose for my material?

Choose 3D for bulk samples, 2D for quantum wells or atomically thin sheets, and 1D for nanowires. The key is whether motion is confined in two, one, or zero spatial directions.

4) What values are typical for gₛ and gᵥ?

gₛ is commonly 2 for spin-1/2 carriers. gᵥ depends on the material; some bands effectively use 1, while multi-valley systems can be 2, 4, or 6. The result scales linearly with gₛ×gᵥ.

5) How should I pick the effective mass m*?

Use an experimentally reported or literature effective mass for the specific band and direction. For quick estimates, values often fall between 0.05 and 1.0 in units of mₑ, but it can be larger in heavy bands.

6) What is the difference between g(E) and N(E)?

g(E) is a density per energy interval, showing how tightly states are packed at E. N(E) is the integrated total number of states from Ec up to E in your chosen dimensional units.

7) When should I use the CSV vs PDF export?

Use CSV when you want to plot, fit, or merge results with other data in a spreadsheet or script. Use PDF when you want a clean, fixed-format table for reports, lab notebooks, or sharing.