Electrical Mobility Calculator

About the Electrical Mobility Calculator

The electrical mobility calculator determines the transport properties of charge carriers in semiconductors and conductors. Carrier mobility (μ) is a fundamental material parameter that quantifies how quickly electrons or holes move through a material under an applied electric field, directly determining device performance in transistors, solar cells, and LEDs.

Mobility connects microscopic scattering physics to macroscopic electrical properties through the relationships: drift velocity v_d = μE, conductivity σ = nqμ, and the Einstein relation D = μkT/q. Higher mobility means carriers travel faster under the same field, enabling faster switching in transistors and higher current in power devices. Silicon has electron mobility of ~1400 cm²/V·s, while GaAs reaches ~8500 cm²/V·s, which is why GaAs excels in high-frequency applications.

This calculator computes drift velocity, conductivity, resistivity, diffusion coefficient, relaxation time, thermal velocity, and mean free path from the mobility and operating conditions. It also models the temperature dependence of mobility, which typically follows a T^(-3/2) power law for phonon-limited scattering in pure semiconductors.

When This Page Helps

Carrier mobility matters whenever you need to estimate how fast charge carriers will drift, how conductive a material will be, or how strongly temperature will affect transport. Students use it to connect the mobility equation to drift velocity and diffusion, while engineers use it to compare semiconductor materials and operating conditions.

This calculator is most useful when you want to turn a mobility value into the transport quantities that actually show up in devices and measurements.

How to Use the Inputs

1. Enter the carrier mobility in cm²/V·s (standard semiconductor unit)
2. Enter the applied electric field in V/cm
3. Select the carrier type: electrons or holes
4. Enter the operating temperature in Kelvin
5. Enter the carrier concentration in cm⁻³
6. Enter the effective mass ratio for the carrier type
7. Review drift velocity, conductivity, diffusion, and scattering parameters

Example Calculation

Tips & Best Practices

• Use presets to explore mobility values for common semiconductors
• At high fields (> 10⁴ V/cm in Si), velocity saturation limits the drift speed — this calculator uses the low-field linear model
• Hole mobility is typically 2–3× lower than electron mobility in the same material
• For heavily doped samples, use measured mobility values rather than intrinsic values
• The T^(-3/2) temperature dependence is approximate — real materials show deviations due to multiple scattering mechanisms

Mobility and Transport

Mobility connects the microscopic scattering behavior of a semiconductor to the drift velocity you observe in an electric field. It also determines conductivity, diffusion, and relaxation time through a small set of related equations.

Temperature and Doping

Carrier mobility usually falls as temperature rises because phonon scattering increases. Heavy doping can also reduce mobility by adding impurity scattering. That is why measured values often matter more than textbook values when the material is heavily processed.

Practical Use

Use this calculator when you need a quick transport estimate for device design, material comparison, or a lab report that ties mobility to a measurable electrical response.

Frequently Asked Questions

• What determines carrier mobility?

  Mobility is limited by scattering mechanisms: lattice vibrations (phonons), ionized impurities, grain boundaries, and defects. In pure semiconductors at room temperature, phonon scattering dominates.

• Why is GaAs mobility higher than silicon?

  GaAs has a lower effective electron mass (0.067 vs 1.08 m₀), which directly increases mobility since μ = qτ/m*. The lighter carriers accelerate more easily between scattering events.

• What is the Einstein relation?

  The Einstein relation D = μkT/q connects drift (mobility) and diffusion (D) transport, reflecting that both arise from the same scattering processes. It is fundamental to semiconductor device physics.

• How does doping affect mobility?

  Increasing doping adds ionized impurity scattering centers, reducing mobility. Above ~10¹⁸ cm⁻³ in silicon, mobility drops significantly from its intrinsic value.

• What is the saturated drift velocity?

  At high electric fields (> ~10⁴ V/cm in Si), drift velocity saturates at about 10⁷ cm/s due to optical phonon emission. The linear v_d = μE relationship breaks down.

• Why use cm²/V·s instead of SI units?

  Convention in semiconductor physics. To convert to SI (m²/V·s), multiply by 10⁻⁴. The cm-based system keeps common values in convenient ranges (10⁰–10⁴).