What is the Debye length?

The Debye length λ_D is the distance over which mobile charge carriers screen an external electric field. Beyond roughly 3λ_D, the potential from a point charge falls to less than 5% of its unscreened value. Shorter Debye length = stronger screening.

What formula does this calculator use?

λ_D = √(ε₀ ε_r k_B T / (n q²)), where n represents the total charge-weighted carrier density Σnᵢzᵢ². For a 1:1 electrolyte, include both cations and anions, so the molar formula-unit density is multiplied by 2.

What is a typical Debye length in water?

For a 0.1 M NaCl solution at 25 °C, λ_D ≈ 0.96 nm. For 1 mM NaCl, λ_D ≈ 9.6 nm. Pure water (very low ion concentration) can have λ_D on the order of micrometers, though in practice surface charges limit this.

How does temperature affect λ_D?

λ_D scales as √T. Higher temperature increases thermal motion, which partially overcomes screening, so the effective screening length grows. Doubling T increases λ_D by about 41%.

What value should I use for carrier density in an electrolyte?

For a fully dissociated 1:1 electrolyte of concentration c (mol/L), this form uses total charge-weighted density n = 2 × c × 1000 × N_A. For example, 0.1 M NaCl gives approximately 1.2044 × 10²⁶ m⁻³.

Debye Length Calculator

Calculate the Debye screening length in electrolytes or plasmas from temperature, permittivity, and carrier concentration.

Parameters

Presets

Temperature T (K)

Relative permittivity ε_r (dimensionless)

Carrier number density n (m⁻³)

Carrier charge z (multiples of e)

Select a preset or enter parameters and click Calculate

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Summary

The Debye length (λ_D) is the characteristic distance over which a charge carrier's electric potential decays by a factor of 1/e due to screening by surrounding charges. This tool computes λ_D = √(ε₀ε_r k_B T / (n q²)) for a single carrier species, covering aqueous electrolytes, semiconductor junctions, and ionized plasmas. Presets for common media are included.

How it works

Select a preset (water, silicon, plasma) or enter custom parameters.
Enter the temperature T in kelvin, relative permittivity ε_r, carrier number density n in m⁻³, and carrier charge q in units of elementary charge.
The Debye length is computed as λ_D = √(ε₀ ε_r k_B T / (n q²)).
Results appear in meters with a scientific-notation breakdown and a context bar showing scale.
For aqueous 1:1 electrolytes at room temperature, λ_D ≈ 0.304 / √(I) nm, where I is the molar ionic strength.

Use cases

Estimate the double-layer thickness in an electrochemical cell or electrode interface.
Determine Debye screening length in a semiconductor depletion region.
Calculate plasma screening distance for fusion or astrophysics problems.
Explore how temperature and ionic concentration affect charge screening.
Verify hand calculations for electrostatics coursework or research.
Compare screening lengths across aqueous, organic, and semiconductor media.

Frequently Asked Questions

Last updated: 2026-06-19 · Reviewed by Nham Vu