Drift and Diffusion Current

• Drift current — an electric field $E$ pushes carriers: $J_{drift} = q(n\mu_n + p\mu_p)E$, where $\mu$ is mobility (electrons in silicon are about 3× more mobile than holes).
• Diffusion current — carriers spread from regions of high concentration to low, like ink in water: $J_{diff} = qD_n \dfrac{dn}{dx} - qD_p \dfrac{dp}{dx}$.

The two are linked by the Einstein relation: $\dfrac{D}{\mu} = \dfrac{kT}{q} \approx 25.9$ mV at 300 K — the thermal voltage $V_T$ that appears in every diode and transistor equation.