Calculate charge carrier mobility, drift velocity, conductivity, diffusion coefficient, and relaxation time in semiconductors and conductors.
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.
Carrier mobility calculations are essential for semiconductor device design, materials characterization, and solid-state physics education. This calculator helps students, researchers, and engineers quickly determine transport properties from mobility data, assess temperature effects, and compare materials for device applications ranging from MOSFETs to organic LEDs. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain.
Drift velocity: v_d = μ·E. Conductivity: σ = n·q·μ. Einstein relation: D = μ·kT/q. Relaxation time: τ = m*·μ/q. Thermal velocity: v_th = √(3kT/m*). Mean free path: λ = v_th · τ. Temperature dependence (lattice scattering): μ ∝ T^(−3/2).
Result: Drift velocity: 1.4 × 10⁵ cm/s, σ = 0.224 S/m
Silicon electron mobility of 1400 cm²/V·s at 100 V/cm gives v_d = 1400 × 100 = 140,000 cm/s. With n = 10¹⁶ cm⁻³: σ = 10¹⁶ × 10⁶ × 1.6×10⁻¹⁹ × 1400 × 10⁻⁴ ≈ 0.224 S/m.
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Mobility is limited by scattering mechanisms: lattice vibrations (phonons), ionized impurities, grain boundaries, and defects. In pure semiconductors at room temperature, phonon scattering dominates.
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.
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.
Increasing doping adds ionized impurity scattering centers, reducing mobility. Above ~10¹⁸ cm⁻³ in silicon, mobility drops significantly from its intrinsic value.
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.
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).