PHT.301 Physics of Semiconductor Devices

## Carrier Dynamics

There are two causes for the flow of charge in semiconductors, diffusion and drift. If charge carriers are injected into a semiconductor, they will diffuse from regions of high concentration to regions of low concentration. If an electric field is applied, electrons and holes move in response to the field. This is called drift. Both drift and diffusion occur in transistors.

Reading: Sze chapter 3 or Singh chapter 3 or Thuselt 2.5

For the exam:
• Be able to calculate the response of electrons and holes to small electric fields.
• Know that the drift velocity saturates at fields above about 1000 V/cm.
• Know when the low field formulas are not valid and what processes occur at high electric field strengths.
• Be able to explain drift and diffusion.
• Know the transport equations where the current density is described by a drift term and a diffusion term.

Drift describes the the response of mobile charge carriers (electrons and holes) to an electric field in a diffusive conductor. In a diffusive conductor, the charge carriers scatter many times as they travel through the material and the average velocity of the charge carriers is proportional to the electric field,

$$\vec{v}_{d,n}=-\mu_n\vec{E},\qquad\vec{v}_{d,p}=\mu_p\vec{E}.$$

Here $$\vec{v}_{d,n}$$ is the drift velocity of the electrons, $$\vec{v}_{d,p}$$ is the drift velocity of the holes, $$\mu_n$$ is the mobility of the electrons, $$\mu_p$$ is the mobility of the holes, and $$\vec{E}$$ is the electric field.

The drift current density $$\vec{j}_{drift}$$ is the sum of the drift currents from the electrons and the holes,

$$\vec{j}_{\text{drift}}=ne\mu_n\vec{E}+pe\mu_p\vec{E} = \sigma\vec{E},$$

where $$\sigma = ne\mu_n+pe\mu_p$$ is the conductivity and $$n$$ and $$p$$ are the carrier concentrations of the electrons and holes. The equation above is a statement of Ohm's law.

Diffusion describes the the response of mobile charge carriers to concentration gradients. Mobile charge carriers diffuse from high concentrations to low concentrations. The diffusion current is proportional to the concentration gradient,

$$\vec{j}_{\text{diff,n}}=eD_n\nabla n,\qquad \vec{j}_{\text{diff,p}}=-eD_p\nabla p.$$

Here $$D_n$$ is the diffusion constant of the electrons and $$D_p$$ is the diffusion constant of the holes.