How this instrument works
Electrical mobility answers a narrow, useful question: for a given electric field, how quickly do charge carriers actually move? Take the steady drift velocity a carrier reaches and divide by the field strength driving it: μ = v_drift ⁄ E. The units, square metres per volt-second, look strange until you multiply back — m²/(V·s) times V/m returns m/s, the drift speed you started with. A copper electron and a silicon electron sit at wildly different points on this scale, and that single number is most of why one conducts so much better than the other.
The formula is shaped like a ratio rather than a fixed speed because a carrier under a constant field does not keep accelerating. It collides with the crystal lattice, with impurity atoms, with other carriers, losing its extra speed each time and starting over. Within picoseconds those collisions settle the population into a steady average drift velocity that scales with the field, and mobility is simply the constant of proportionality — a property of the material and its temperature, not of any one electron's individual path.
Mobility is not a fixed property of an element the way atomic mass is — it belongs to a specific sample at a specific temperature and doping level. Warm the crystal and its atoms vibrate harder, so a carrier collides sooner and μ drops; add more dopant atoms and each ionized one becomes an extra obstacle, an effect that actually grows stronger as the sample cools and vibration-driven collisions fade out of the way. A mobility reading is therefore only ever a snapshot, the way a fluid's viscosity means little without the temperature it was measured at.
- Enter the carrier's steady-state speed in the "Drift velocity" field, in m/s (switch to ft/s from the unit menu if that's how your data was recorded).
- Enter the field strength driving that motion in the "Electric field, V ⁄ m" field — volts per metre across the sample or conductor.
- Read the result in "Electrical mobility, m² ⁄ (V·s)" — the instrument divides the first value by the second.
- Keep both entries positive; mobility here is reported as a scalar magnitude, so direction and sign are stripped out of the ratio.
- Compare the figure against known values for your material — silicon, copper, a doped compound — to sanity-check a measurement or a datasheet spec.
Worked example — a mobility reading near silicon's own
A bench measurement records a charge carrier settling into a steady drift velocity of 100 m/s inside a sample under a 1,000 V/m field — a field easily produced across a few millimetres of material with a handful of volts across a probe. The formula gives μ = 100 ⁄ 1000 = 0.1 m²/(V·s), exactly, with nothing left over to round.
That figure lands close to the commonly quoted electron mobility of lightly doped, room-temperature silicon — near 0.14 m²/(V·s), or 1,400 cm²/(V·s) in the units semiconductor datasheets prefer — which is exactly why a bench result in this neighborhood reads as plausible. A measured value far outside it usually means heavier doping, a warmer sample, or a slip somewhere in the test setup rather than a new material behavior.
Questions
What does electrical mobility actually measure?
How efficiently a charge carrier turns an electric field into steady speed. Formally μ = v_drift ⁄ E: divide the drift velocity a carrier settles into by the field driving it. A high-mobility material — copper's conduction electrons, or lightly doped silicon — reaches fast drift under a weak field; a low-mobility one needs a much stronger push for the same speed.
Why isn't drift velocity just proportional to time under acceleration?
Because carriers keep colliding with the crystal lattice, with impurities, and with each other. Every collision randomizes direction and wipes out the speed gained since the last one, so instead of accelerating without limit, a carrier settles into a steady average drift velocity within picoseconds. Mobility is the proportionality constant for that settled state, not for an idealized free particle in empty space.
How does mobility connect to Ohm's law?
Through conductivity: σ = n·q·μ, where n is carrier density and q is the elementary charge. Multiply conductivity by the field and you get current density, J = σE — the microscopic cousin of V = IR. Mobility, doping level, and geometry together are what a device engineer uses to predict a chip's resistance before it is ever fabricated.
Does mobility stay the same at every temperature?
No — a mobility figure is tied to the temperature and doping level it was measured at, not a fixed constant of the material. Warming a sample makes its lattice vibrate harder, so carriers collide sooner and μ falls; heavier doping lowers it further by adding ionized-impurity collisions, an effect most visible at low temperature. Quote μ without stating both conditions and the number is close to meaningless.
Why do the units come out as square metres per volt-second?
Because velocity in m/s divided by field in V/m leaves m/s times m/V, which is m²/(V·s). Multiply that back by a field in V/m and the metres and volts cancel, returning plain m/s — the drift speed you started with. The same unit applies whether the carrier is an electron, a hole, or an ion in solution.
If drift velocity doubles, does mobility always double too?
Only if the field driving it stays fixed. Hold the field at 1,000 V/m and raise drift velocity from 100 to 200 m/s and mobility does go from 0.1 to 0.2 m²/(V·s) in direct step. But a bigger drift velocity produced by a proportionally bigger field returns the same mobility, since the instrument reports the ratio between the two, never either number by itself.