Semiconductor doping

The controlled introduction of impurities to change a semiconductor's charge carrier populations. Donor impurities and acceptor impurities can produce an n-type semiconductor or a p-type semiconductor, respectively; compensation and temperature also matter.

Substitutional semiconductor doping replaces selected host atoms with impurity atoms on ordinary lattice sites. A shallow donor impurity can supply a mobile conduction electron and remain positively charged; a shallow acceptor impurity can capture an electron and leave a mobile valence hole, remaining negatively charged. In nondegenerate, substantially ionized material, donor-dominated doping raises the chemical potential toward the conduction edge and acceptor-dominated doping lowers it toward the valence edge. Dopants do not create net bulk charge in a neutral sample: fixed impurity charge compensates the mobile carrier charge. Freeze-out, compensation and degeneracy qualify the simplest relation between dopant and carrier densities.

An intrinsic semiconductor has electron and hole densities $n=p=n_i$, so ${\sigma }_i=e{n}_i({\mu }_e+{\mu }_h)$. In a fully ionised, uncompensated n-type sample with $N_D\gg n_i$, $n\simeq N_D$, $p\simeq n_i^2/N_D$, andThus a carrier-density ratio alone is not generally the electrical conductivity ratio. If electron mobility is unchanged and electron transport dominates the intrinsic conductivity, it reduces to $N_D/n_i$; equal electron and hole mobilities instead give $N_D/(2n_i)$. Ionised-impurity scattering can change the doped mobility.

At sufficiently low temperature, donor or acceptor ionization becomes energetically unfavourable. Carriers remain bound to dopants rather than contributing to conduction, reducing the mobile carrier density. This dopant freeze-out is distinct from the high-temperature intrinsic regime, where thermal excitation across the band gap overwhelms the net dopant contribution.

An impurity level is an electronic energy level associated with a dopant or defect in a semiconductor. A shallow donor impurity introduces a level just below the conduction band, and a shallow acceptor impurity introduces one just above the valence band. Under electrostatic band bending, these levels shift with the local band edges in the same material; their occupation is determined relative to the equilibrium chemical potential.

An n-type semiconductor has more mobile Electrons than electron holes. The letter describes the predominant mobile charge carriers, not a net negative electric charge of the whole material.

A p-type semiconductor has more mobile electron holes than Electrons; it can nevertheless be electrically neutral overall.

A semiconductor whose mobile charge carrier population requires Fermi-Dirac statistics rather than a dilute Maxwell-Boltzmann distribution. In a strongly degenerate n-type semiconductor, the Fermi level lies inside the conduction band; in a strongly degenerate p-type semiconductor, it lies inside the valence band. The occupied and empty quantum states on opposite sides of a tunnel diode can then overlap in energy. Heavy semiconductor doping both changes these occupations and narrows the depletion region; a narrow barrier and accessible final quantum states serve different roles.