Electrical Mobility Calculator for μ, Drift and Field
Calculate electrical mobility, drift velocity, or electric field, and optionally derive conductivity and current density.
Select the variable to solve, enter the two required transport values, and optionally add carrier concentration and charge to compute σ and J.
Electrical Mobility Calculator for μ, Drift and Field
Calculate electrical mobility, drift velocity, or electric field, and optionally derive conductivity and current density.
Use drift velocity and electric field to solve mobility.
Enter carrier concentration and charge only if you also want conductivity and current density.
About the electrical mobility calculator
Electrical mobility describes how quickly a charge carrier drifts through a material when an electric field is applied. It connects microscopic transport behavior to the measurable quantities used in semiconductor physics, electrochemistry, and conduction models. The basic definition is μ = v_d / E, where μ is mobility, v_d is drift velocity, and E is electric field strength. This calculator lets you solve any one of those three variables when the other two are known.
Mobility is usually reported in square meters per volt-second in SI units, though semiconductor texts may also use cm²/V·s. A higher mobility means carriers respond more strongly to an applied field, producing larger drift velocity for the same E. In practical terms, mobility helps explain why some materials conduct well, why others behave sluggishly, and how temperature, scattering, impurities, and lattice structure influence carrier transport.
The calculator also supports two closely related derived quantities. If you enter carrier concentration n and charge q, it computes conductivity from σ = n·q·μ. That tells you how readily the material carries current overall. It also computes current density from J = n·q·μ·E, which combines the transport response with the applied field to describe current flow per unit area. These expressions appear constantly in semiconductor device analysis and in simplified drift-current models.
Because the equations are algebraically simple, most mistakes come from units rather than mathematics. Drift velocity must be in meters per second, electric field in volts per meter, mobility in square meters per volt-second, and carrier concentration in inverse cubic meters for the output units to remain consistent. This tool keeps those relationships visible and gives you immediate feedback when you switch between solving for μ, v_d, or E.
The calculator is best suited to steady-state, average transport estimates. Real materials may show field-dependent mobility, saturation velocity, temperature sensitivity, or multiple carrier types, and advanced device simulations account for those effects explicitly. Still, these baseline equations are the standard first step in materials analysis, homework, and quick engineering checks, which makes a focused calculator like this very useful.
Electrical mobility examples
These examples show core transport calculations and the optional conductivity/current-density outputs.
| Inputs | Output | Context |
|---|---|---|
| Mode: Find mobility; v_d = 0.12 m/s, E = 40 V/m | μ = 0.003 m²/V·s | Mobility is small when carriers drift slowly under a moderate field. |
| Mode: Find drift velocity; μ = 0.0015 m²/V·s, E = 200 V/m | v_d = 0.3 m/s | Doubling the field doubles drift velocity when mobility stays constant. |
| Mode: Find mobility; v_d = 0.2 m/s, E = 50 V/m, n = 8 × 10^21 1/m³, q = 1.602 × 10^-19 C | μ = 0.004 m²/V·s; σ = 5.1264 S/m; J = 256.32 A/m² | Optional material inputs convert the transport calculation into conductivity and current-density estimates. |
How to use the electrical mobility calculator
- Choose whether you want to solve for mobility, drift velocity, or electric field.
- Enter the two transport values required by that mode using SI units.
- Optionally enter carrier concentration and charge if you also want conductivity and current density.
- Click Calculate to see the solved transport quantities and any optional derived outputs.
Electrical mobility calculator FAQ
What is electrical mobility?
Electrical mobility measures how strongly charge carriers respond to an applied electric field. A higher mobility means carriers achieve greater drift velocity for the same field strength.
Why is conductivity related to mobility?
Conductivity depends on how many carriers are available and how easily they move. The formula σ = n·q·μ captures both effects directly, combining carrier density, charge, and mobility in one term.
What does current density J represent?
Current density is the electric current flowing per unit cross-sectional area. In drift transport, J = n·q·μ·E shows that stronger fields or more mobile carriers increase the current response.
Can mobility be negative?
The sign can reflect direction conventions in some derivations, especially when discussing electron motion. In many engineering contexts, mobility is reported as a positive magnitude and direction is tracked separately through field or current sign.
When does this simple model stop being accurate?
It becomes less accurate when mobility varies strongly with electric field, temperature, carrier concentration, or material structure. High-field saturation, multiple carrier species, and nonuniform devices usually require more advanced transport models.