What is cyclotron resonance?

Cyclotron resonance is the resonant absorption of electromagnetic energy by a charged particle moving in a circular orbit in a magnetic field. The particle absorbs most strongly when the radiation frequency matches its orbital frequency f = qB/(2πm).

Why do semiconductors have different resonance frequencies for electrons and holes?

In a crystal, electrons and holes move in a periodic potential that modifies their inertia. The effective mass m* captures this effect. GaAs conduction-band electrons have m* ≈ 0.067 m₀, so their cyclotron frequency is about 15 times higher than a free electron at the same field.

What magnetic field is needed for microwave-range cyclotron resonance?

For free electrons at 10 GHz, B ≈ 0.357 T. For GaAs electrons (m* = 0.067 m₀) at 10 GHz, B ≈ 0.024 T. Higher effective mass requires a stronger field to reach the same frequency.

What is the difference between cyclotron frequency and angular frequency?

The cyclotron frequency f (in Hz) is the number of orbits per second. The angular frequency ω = 2πf (in rad/s) is used in wave equations and band-structure formulas. Both are standard outputs of this calculator.

Does this formula apply to relativistic particles?

No. The formula f = qB/(2πm) assumes non-relativistic speeds. At velocities approaching c, the relativistic mass increase lowers the resonance frequency. For laboratory semiconductor and ion physics at typical fields, the non-relativistic approximation is valid.

Cyclotron Resonance Frequency Calculator

Calculate the cyclotron resonance frequency f = qB/(2πm) for electrons, holes, or ions in a magnetic field, with effective-mass presets for GaAs, Si, and Ge.

Parameters

Magnetic field B (tesla)

Particle / material

Custom effective mass (m* / m₀)

Ratio relative to free-electron mass m₀ = 9.1094 × 10⁻³¹ kg

Enter B and select a particle to calculate

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Summary

Cyclotron resonance occurs when a charged particle spiraling in a magnetic field absorbs electromagnetic radiation at its natural orbital frequency. The resonance frequency f = qB/(2πm) depends on the particle charge q, the magnetic field strength B, and the particle mass m. In semiconductors, electrons and holes have effective masses m* that differ from the free-electron mass — measuring the resonance frequency is a direct way to determine m*. This calculator covers free electrons, free holes (using free-electron mass as a baseline), and effective-mass carriers in common semiconductors.

How it works

Enter the magnetic field strength B in tesla.
Select a particle type or material preset to set the effective mass m*.
The cyclotron frequency is computed as f = qB / (2π m*), where q = 1.602 × 10⁻¹⁹ C.
Angular frequency ω = 2πf and the orbital period T = 1/f are also shown.
For a custom particle, enter its effective-mass ratio m*/m₀. For an ion with mass number A, use approximately A × 1,823.

Use cases

Determine the cyclotron resonance frequency for electrons in a GaAs heterostructure at a given field.
Cross-check experimental microwave absorption peaks against theoretical cyclotron frequency.
Find the required magnetic field to tune cyclotron resonance to a target frequency.
Compare resonance frequencies of electrons and heavy holes in silicon.
Estimate the orbital period of a proton or ion in a laboratory magnetic field.

Frequently Asked Questions

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