Mobility, Conductivity, and Devices

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Lecture date: Wednesday, 2014.09.03 (lecture recording)

Charge Density and Mobility[edit]

For electrons, the mobility [math]\mu_n[/math] is defined:

[math] \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} [/math]

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

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

[math] \vec{J}_{n,drift} = \vec{v}_d \cdot n_n \label{eq:driftflux} [/math]

The drift current density is:

[math] \vec{q}_n = e \cdot \vec{J}_n = e \cdot \vec{v}_d \cdot n_n \label{eq:currentdensity} [/math]

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