Semiconductor Physics and Carrier Dynamics

This set covers key vocabulary and formulas related to semiconductor doping, carrier movement (drift and diffusion), conductivity, and carrier lifetime as discussed in the lecture.

p-type semiconductor

A semiconductor material doped with acceptor atoms where holes are the majority carriers and $p \gg n$.

Acceptor

An impurity atom that increases the hole concentration ($p$).

Donor

An impurity atom that increases the electron concentration ($n$).

Drift

Carrier motion generated by an electrical field across a piece of silicon, which produces drift current.

Diffusion

Carrier motion generated by a concentration gradient, where carriers move from a region of higher concentration to a region of lower concentration.

Mobility ($\mu$)

A measure of how easily a carrier moves in a particular material, defined as the drift velocity per unit field ($\mu = \frac{v}{E}$), normally expressed in $cm^2/Vs$.

Drift velocity

The average velocity with which charge carriers drift in a definite direction under the influence of an applied electric field.

Current Density ($J$)

The amount of charge crossing a plane unit area per unit time, given by the formula $J = \frac{I}{A}$.

Electron charge density ($\rho_e$)

The density of electron charge within a semiconductor, expressed as $\rho_e = -nq$.

Hole charge density ($\rho_h$)

The density of hole charge within a semiconductor, expressed as $\rho_h = +pq$.

Conductivity ($\sigma$)

A measure of a material's ability to conduct current, defined for a semiconductor as $\sigma = (n\mu_e + p\mu_p)q$, where it is the inverse of resistivity ($\sigma = \frac{1}{\rho}$).

Resistivity ($\rho$)

The reciprocal of conductivity, used in Ohm's law to determine resistance ($R = \frac{\rho L}{A}$).

Diffusion Current

An electric current produced by the directional movement of charge carriers due to their concentration gradient; it is normally absent in conductors.

Total Current Density ($J$)

The sum of the electron and hole drift currents and the electron and hole diffusion currents, represented by $J = \sigma E + q(D_e\nabla n - D_h\nabla p)$.

Mean lifetime ($\tau_n, \tau_p$)

The average time that a carrier (electron or hole) exists in the free state before recombining.

Majority carrier

The most abundant charge carrier in a semiconductor material (electrons in N-type, holes in P-type).

Minority carrier

The least abundant charge carrier in a semiconductor material (holes in N-type, electrons in P-type).

Intrinsic semiconductor

A pure semiconductor material where the electron concentration equals the hole concentration ($n = p = n_i$).

Extrinsic semiconductor

A semiconductor material that has been doped with impurities to alter its electrical properties.