CND-15

Carrier mobility

μ = e τ / m*. Drift mobility from a mean free time.

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Electrons in solidsMobility

Governing equation

\mu=e\tau/m^*

$\tau \in \left[0.5, 200\right]$

where

\tau: Mean free time (fs)
m^*/m: Effective mass (—)
\mu: Mobility (cm²/V/s)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\mu=e\tau/m^*

$\tau \in \left[0.5, 200\right]$

$\tau = 0.5$ $\mu = 3.382$

Along the curve

②

Domain of the variable — blue

\tau_{\min} = 0.5,\quad \tau_{\max} = 200

$\tau \in \left[0.5, 200\right]$

$\tau = 0.5$ $\tau = 0.5$

Along the curve

③

Response curve — green

\mu=e\tau/m^*

$\tau \in \left[0.5, 200\right]$

$\tau = 0.5$ $\mu = 3.382$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\mu}{\mathrm{d}\tau}

$\tau \in \left[0.5, 200\right]$

$\tau = 1.755$ $\mu^{\prime} = 6.765$

Along the curve

Lecture brief

Historical brief

Drude electrons, Bloch waves, BCS pairing (1957) and Wiedemann–Franz heat are the first solids-and-metals laws. The lab is conductivity, gap and phonon heat in closed form. This sheet (CND-15 — Carrier mobility) is the form associated with Mobility. Working symbols: $\tau$ , $m^*/m$ $\rightarrow$ $\mu$ . σ = n e μ. Scattering (phonons, impurities) sets τ(T).

Purpose

Purpose: compute

\mu

from

\tau

m^*/m

in Condensed matter via

\mu=e\tau/m^*

μ = e τ / m*. Drift mobility from a mean free time. Use it when a real condensed matter question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\tau = 20.000\,\mathrm{fs}

m^*/m = 0.260\,\mathrm{—}

, the governing relation

\mu=e\tau/m^*

yields

\mu = 135.3\,\mathrm{cm^{2}/V/s}

. A carrier, a scatterer, a drift arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mean free time \tau20 fsEffective mass m^*/m0.26 —

Outputs

Mobility \mu135.3 cm²/V/s

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Narration of this film

A carrier, a scatterer, a drift arrow.

σ = n e μ. Scattering (phonons, impurities) sets τ(T).

Reading speed

Watch on YouTube