In a semiconductor, there are holes and electrons being created. These charged holes and electrons are also known as carriers. The movement of these carriers in the semiconductor is due to two processes.

## Drift Current Density

One process concerns drift movement results from an electric field. The other is known as diffusion resulting from varying concentrations or gradient concentrations.

In an n-type material there are a large number of electrons. The electrons will react to an external electric field applied in one direction. This field produces a force on the negatively-charged electrons in the opposite direction. The electrons acquires a drift velocity given as

(Equation 1)

where

with units of cm^2/V-s.

The mobility is a measure how well an electron travels through a semiconductor material. The above minus sign means that the velocity is opposite direction to the applied electric field.

The electron drift creates a drift current density [latex] frac{A}{m^2}[/latex] given as

(Equation 2)

where n is the electron concentration (#/cm^3) and e is the magnitude of the electronic charge.

For a p-type material having a large number of holes, there are similar relationships. The drift velocity of holes is

(Equation 3)

where is the hold mobility. The positive sign means that the velocity is in the same direction as the applied field.

The hold drift creates a drift current density given as

(Equation 4)

The total drift current contains both electrons and hole resulting in the total drift current density, J given by

(Equation 5)

where

is the **conductivity** and where is the **resistivity **of the semiconductor.

The above relationships show that controlling the conductivity of a semiconductor can be controlled by selective doping. This approach allows us to build a variety of electronic devices currently available.

We also note that Equations 1 and 3 show that the carrier drift velocity is a linear function of the applied electric field. Increasing the electric field will increase the drift velocity of the carriers but there will be a point when carrier velocities will no longer increase. That is, the velocities reach a saturation point known as drift velocity saturation.

Also, mobility values are functions of carrier concentrations. In this case, as the carrier concentrations increase, then mobilities will decrease which affects the conductivity or resistivity of the semiconductor material.

## Diffusion Current Density

The diffusion process occurs when particles flow from regions of high concentrations to regions of low concentrations. When electrons and holes flow in a semiconductor, they go in random directions as a result of interactions with crystal atoms of the semiconductor lattice structure. Average carrier speeds are also affected by the temperature. The net result however, is that the flow of carriers move away from high-concentration region to one that has lower concentration.

Now, the diffusion current density due to the electron diffusion is given as

where e is the magnitude of the electron charge, dn/dx is the gradient of the electron concentration with respect to the distance x, is the electron diffusion coefficient.

Similarly, the diffusion current density to the hole diffusion is given as

where dp/dx is the gradient of the hole concentration, Dp is the hole diffusion coefficient.

Einstein relation shows the relationship between drift and diffusion currents. In this case, the mobilities to describe drift currents and diffusion coefficients to describe diffusion currents are not independent to each other. Einstein relation is given as

at room temperature.

We note that the total current density is the sumo of the drift and diffusion current densities. Usually, one of the two processes dominate the other.

<h2> Excess Carriers </h2>

The above discussion assumes the semiconductor crystal is in thermal equilibrium. A crystal will not be in equilibrium when a voltage is applied or a net current exists.

As valence electrons acquire enough energy to break the covalent bonds, they become free electrons and interact with photons of high0enrgy incident in the semiconductor. This interaction produces an electron and a hole pair resulting in excess electrons and excess holes. The creation of excess holes and electrons produces a non-equibrium condition of increasing concentrations of holes and electrons.

This phenomenon cannot increase indefinitely such that a free electron will recombine with a hole known as electron-hole recombination. The recombination process and excess concentration will reach a steady-state value.

The time when excess carriers exists before recombination is called the excess carrier lifetime. Solar cells and photodiodes involve excess carrier mechanisms.

Below is a collection of videos on semiconductors and will serve as a good review on semiconductor theory.

[tubepress mode="tag" tagValue='venturecaplaw, semiconductor, silicon']

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