# Mobility, Conductivity, and Devices

## Introduction

Lecture date: Wednesday, 2014.09.03 (lecture recording)

## Charge Density and Mobility

For electrons, the mobility $\mu_n$ is defined:

$\mu_n \equiv \frac{\vec{v_d}}{\vec{E}} [=] \frac{\frac{\mathrm{m}}{\mathrm{s}}}{\frac{\mathrm{v}}{\mathrm{m}}} = \frac{\mathrm{m}^2}{\mathrm{v} \cdot \mathrm{s}} \label{eq:mobility}$

For Si at 300K, $\mu_n \approx 1360 \frac{\mathrm{cm}^2}{\mathrm{v} \cdot \mathrm{s}}$ and for holes, $\mu_p \approx 460 \frac{\mathrm{cm}^2}{\mathrm{v} \cdot \mathrm{s}}$

The flux of charge is $\frac{\text{# of charges}}{\text{area} \cdot \text{time}}$ and the drift flux is written:

$\vec{J}_{n,drift} = \vec{v}_d \cdot n_n \label{eq:driftflux}$

The drift current density is:

$\vec{q}_n = e \cdot \vec{J}_n = e \cdot \vec{v}_d \cdot n_n \label{eq:currentdensity}$

The important point here is that the current in the solid material is proportional to the free charge density.