Charge Mobility

An electric field $E$ is applied across a silicon bar, causing drift current to occur.

Charge mobilities
$μ_{p}$ - Hole mobility ( $μ_{p} = 480 \frac{c m ^{2}}{V \cdot s}$ for intrinsic Si)
$μ_{n}$ - Electron mobility ( $μ_{n} = 1350 \frac{c m ^{2}}{V \cdot s}$ for intrinsic Si)

Einstein Relation
The diffusion constants and charge mobility are related by the thermal voltage.
$\frac{D _{n}}{μ _{n}} = \frac{D _{p}}{μ _{p}} = V_{T}$
$V_{T} = \frac{k T}{q}$ (~25.9mV at room temperature of $T = 300 K$ )
$k = 8.617 \times 1 0^{- 5} e V K^{- 1}$

Drift velocity
$v_{p - d r i f t} = μ_{p} E$
$v_{n - d r i f t} = - μ_{n} E$

Drift current
$I_{S, p} = A qp μ_{p} E_{d r i f t}$
$I_{S, n} = - A q n μ_{n} E_{d r i f t}$

Drift current density
$J_{S, p} = \frac{I _{S, p}}{A} = pq μ_{p} E$
$J_{S, n} = \frac{I _{S, n}}{A} = n q μ_{n} E$

Total drift current density
$J_{s} = J S, p + J_{S}, n = q (p μ_{p} + n μ_{n}) E$

Vector form of Ohm’s law
$J_{s} = E / ρ$

Resistivity
$ρ = \frac{1}{q ( p μ _{p} + n μ _{n} )}$

Resistance
$R = \frac{ρ L}{A}$

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Charge Mobility