Electrical Mobility Calculator — Carrier Drift & Conductivity
Carrier mobility μ = v_drift / E describes how quickly charge carriers (electrons or holes) move through a material in response to an electric field. Enter the drift velocity and field strength to get mobility, then add carrier density to derive conductivity and resistivity.
m/s
V/m
m⁻³
Drift velocity per unit electric field strength
- 1
Drift velocity and electric field
v_d = 0.1 m/s, E = 1,000 V/m - 2
Carrier mobility μ = v_d ÷ E
0.1 ÷ 1,000 = 0.000100Mobility is the drift velocity per unit electric field (m²/(V·s)).
How does this calculator work?
Electrical mobility μ = v_drift / E (m²/(V·s)) is the drift velocity of charge carriers per unit electric field. From μ and carrier density n, conductivity σ = n·q·μ and resistivity ρ = 1/σ. Silicon electrons: μ ≈ 0.14 m²/(V·s); copper: μ ≈ 4.4 × 10⁻³ m²/(V·s) but high n gives high σ. The 2019 SI elementary charge q = 1.602176634 × 10⁻¹⁹ C is used (exact).
Formula
How this is calculated
When an electric field E (V/m) is applied across a conductor or semiconductor, charge carriers experience a force and accelerate — but quickly reach a terminal drift velocity v_d (m/s) because of scattering from lattice vibrations, impurities and defects. The ratio μ = v_d / E is the carrier mobility, measured in m²/(V·s) or, more commonly in semiconductor datasheets, in cm²/(V·s) (1 m²/(V·s) = 10 000 cm²/(V·s)). Higher mobility means carriers respond more strongly to a given field — important for transistor speed and efficiency.
Once mobility is known, the bulk conductivity follows from σ = n · q · μ, where n is the carrier concentration in m⁻³ and q = 1.602 × 10⁻¹⁹ C is the elementary charge. Resistivity ρ = 1/σ (Ω·m) is the reciprocal. For intrinsic silicon at 300 K, electrons have μ_n ≈ 0.14 m²/(V·s) and n ≈ 1.5 × 10¹⁶ m⁻³. For copper (a metal), μ_e ≈ 4.4 × 10⁻³ m²/(V·s) but n ≈ 8.5 × 10²⁸ m⁻³, giving very high conductivity.
The calculator uses the elementary charge from the 2019 SI redefinition (exact value). The model assumes a single carrier type in a homogeneous material at a single temperature — for bi-polar transport (both electrons and holes), conductivities add: σ = (n_e·μ_e + n_h·μ_h)·q.
Frequently asked questions
Mobility measures how fast a charge carrier moves per unit electric field. High mobility means faster transistors, lower power consumption and better high-frequency performance. Silicon has moderate mobility; GaAs and GaN have higher electron mobilities, which is why they are used in high-speed RF devices.
Thermal (random) velocity is the rapid, random motion of carriers at room temperature (~10⁵–10⁶ m/s in Si). Drift velocity is the slow net motion superimposed by the electric field, typically mm/s to m/s for normal fields. Mobility describes only the drift component.
The most common technique is the Hall effect measurement: apply a magnetic field perpendicular to current flow and measure the transverse (Hall) voltage. The Hall mobility μ_H = |R_H| × σ, where R_H is the Hall coefficient. Time-of-flight and field-effect methods are also used for thin films.
Also known as
TG we-Calculate Editorial Team. (2026). Electrical Mobility Calculator — Carrier Drift & Conductivity [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/electrical-mobility-calculator
TG we-Calculate Editorial Team. "Electrical Mobility Calculator — Carrier Drift & Conductivity." TG we-Calculate. 2026. https://we-calculate.com/calculator/electrical-mobility-calculator.
TG we-Calculate Editorial Team, "Electrical Mobility Calculator — Carrier Drift & Conductivity," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/electrical-mobility-calculator
@misc{wecalculate_electrical_mobility_calculator, title = {Electrical Mobility Calculator — Carrier Drift & Conductivity}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/electrical-mobility-calculator}}, year = {2026}, note = {TG we-Calculate} }
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