How easily electrons, or the gaps they leave behind (holes), move through a material when pushed by a voltage. Higher mobility means faster, more efficient electronics – but it is easily ruined by dirt, defects and a poor .
Going deeper
Scattering mechanisms add up: the inverse mobilities from impurities and from phonons sum, so the lower limit wins at each temperature. How the device is wired decides whether the contacts are counted as part of the material – in a two-terminal measurement they are, in a Hall bar they are not.
What mobility measures
Conductivity is the product of how many carriers there are, their charge and how freely they move: σ = n·e·μ. Mobility is the last factor, the drift velocity per unit electric field, quoted in cm2/V·s. In a simple picture it equals e·τ/m, where τ is the average time between scattering events and m the , so light carriers that scatter rarely are the most mobile.
That is one reason the numbers differ so much between materials. Electrons in MoS2 are relatively heavy, about half the free-electron mass, and couple strongly to ; graphene’s carriers behave as if nearly and couple weakly. For scale, electrons in bulk silicon reach about 1400 cm2/V·s at room temperature, but in the thin channels of modern they reach only a few hundred.
What limits it
Scattering rates from independent sources add up, so the inverse mobilities add – Matthiessen’s rule. At low temperature, charged impurities, defects, surface roughness and charge traps in the substrate dominate, and the mobility there is a good measure of how clean a sample is. At higher temperature, phonons take over: the material’s own lattice vibrations, and also remote phonons from polar such as SiO2 or HfO2, whose vibrating charges reach into an atomically thin channel.
The room-temperature value is the one that matters for devices, and phonons set a ceiling that cleaning cannot lift – calculations put it at a few hundred cm2/V·s for MoS2. hBN- graphene comes close to its own, far higher, phonon limit.
Measuring it without fooling yourself
Field-effect mobility is taken from the slope of a transistor’s transfer curve. It is quick, but depends on the gate capacitance assumed and, in a two-terminal device, on the contacts: contacts can make mobility look gate-dependent, and in some geometries can even make it appear higher than it is. is more direct. A Hall bar gives the from the Hall voltage in a magnetic field and the conductivity from a measurement between side contacts, so the contacts drop out.
A mobility means little without its context: the carrier density and temperature at which it was measured, the method, and whether it is a typical device or the best of many. A single peak value from a two-terminal curve is the least reliable number of all.
For specialists
Drift velocity per unit electric field, usually quoted in cm2/V·s. In it is limited intrinsically by phonon scattering and extrinsically by charged impurities, roughness, remote phonons and ; field-effect values extracted from two-terminal devices can be distorted by .