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An amphoteric dopant can act as a donor impurity or an acceptor impurity according to its incorporated lattice site or defect configuration. Silicon in gallium arsenide is the standard example: substitution on the gallium sublattice gives a shallow donor, while substitution on the arsenic sublattice gives a shallow acceptor. Its electrical effect therefore depends on growth conditions as well as total silicon concentration.^[ref]

Substitutional arsenic has one more valence electron than germanium, so it acts as a donor impurity. Thermal ionization of its shallow bound state supplies mobile conduction-band electrons and leaves fixed positive donor charge. The resulting n-type semiconductor can have $n_e\gg n_i$ even when only a small fraction of host atoms are replaced. Its electrical conductivity then rises because the mobile carrier count increases; the opposite donor charge preserves macroscopic charge neutrality.

This argument assumes that the donors are substantially ionized at the measurement temperature and that the added impurity scattering does not overwhelm the carrier increase. The screened bound-donor picture and its departures from a simple hydrogenic model are described in institutional semiconductor spectroscopy notes.^[ref]

Retain the inferred mobilities and assume one ionized donor per added arsenic atom, negligible compensation, the same band gap, and the nondegenerate semiconductor mass-action law. Relative to the intrinsic sample, a conductivity factor $f$ requiresFor complete donor ionization, charge neutrality gives $N_D=n_e-n_h$, soThe host atom density, using $M_{\mathrm{Ge}}\simeq 72.63\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$, isThus the required atomic fraction isapproximately one donor per $5.8\times 10^4$ host atoms. The electron density must rise to about $2000n_i$, not $1000n_i$, because the original intrinsic sample conducted through both electrons and holes. This is an estimate under unchanged mobility: impurity scattering, incomplete ionization, compensation and band-edge changes can alter it. Here $n_e/N_c\simeq 0.12$, so the nondegenerate treatment is an approximation rather than an arbitrarily dilute limit.

Arsenic has five valence electrons, one more than silicon. As a substitutional donor impurity, it supplies a weakly bound extra electron which is largely thermally released into the conduction band at room temperature, leaving an ionized positive donor.

Consequently the mobile electron density increases far above the intrinsic value, so the conductivity increases substantially even at ppm dopant levels. The crystal remains macroscopically neutral: fixed donor charge compensates the added mobile charge.

Arsenic has five valence electrons, whereas silicon has four. A substitutional arsenic atom can therefore supply an extra electron after participating in the silicon bonding network. It acts as a shallow donor impurity, introducing a localized level $E_D$ just below the conduction band. Ionizing that donor costs much less energy than excitation across the full band gap.

At the lowest temperatures, donor electrons remain bound and the valence band is filled. Mobile-carrier populations are negligible: this is dopant freeze-out. Initial heating releases donor electrons into the conduction band, producing a rapid rise in conductivity governed by the shallow-donor energy scale. The positive ionized donor charge compensates the released electronic charge; the bulk need not acquire net charge.

At intermediate temperatures, nearly all donors are ionized but intrinsic electron–hole generation is still small. In an uncompensated sample,where $N_D$ is donor number density. The supply of donor electrons is finite, so further heating cannot keep creating them. This is the extrinsic plateau under the approximation of weakly varying mobility, and its carrier density is much larger than that of the undoped sample at the same temperature. In real material, scattering changes mobility, so donor exhaustion alone predicts a carrier-density plateau rather than guaranteeing perfectly flat conductivity.

At higher temperatures, intrinsic generation becomes comparable to and then exceeds the donor contribution. Once $n_i\gg N_D$, the populations approach $n\simeq p\simeq n_i$, and activation across the main gap causes the steeper rise. The relevant regimes are therefore freeze-out, donor exhaustion, and intrinsic excitation, not three successive types of dopant.

Clean the exposed silicon and grow a thin, high-quality SiO2 gate dielectric by controlled dry thermal oxidation. Deposit polycrystalline silicon, conventionally by low-pressure chemical vapour deposition from silane, dope it in situ or by subsequent implantation and activation, and pattern/etch it to define the two gates. Phosphorus or arsenic gives n+ polysilicon; boron gives p+ polysilicon where the selected gate-work-function process requires it. A traditional single-poly process may use a common gate doping instead; gate and source/drain doping need not be identical.

The patterned gates subsequently serve as self-alignment masks for donor-doped nMOS source/drain and acceptor-doped pMOS source/drain regions. Annealing activates these dopants. Keep the oxide thin and uniform enough for strong electrostatic control but free from pinholes and excessive leakage. A high-permittivity dielectric deposited by atomic layer deposition with a metal gate is a modern alternative, rather than the conventional polysilicon/SiO2 stack drawn.

Semiconductor doping introduces electrically active impurities. In gallium arsenide, silicon has one more valence electron than gallium but one fewer than arsenic. Silicon on a gallium site can therefore supply a shallow donor electron, while silicon on an arsenic site can accept an electron and leave a mobile hole. It is an amphoteric dopant, so its net effect depends on site occupation and growth conditions.^[ref]

For isotropic parabolic bands, shift the energy origin in the given free-electron density of states to the appropriate band edge and use its effective mass:and, for valence electron states,The stated normalization includes the two spin states and assumes one effective valley. In a nondegenerate semiconductor, the conduction occupation is approximately $e^{-(E-\mu )/(k_{B}T)}$ and the probability of a valence hole is approximately $e^{(E-\mu )/(k_{B}T)}$. Substituting $x=(E-{ϵ}_c)/(k_{B}T)$ in the first integral, and the corresponding hole energy in the second, giveswhere the effective density of states values are $N_c=2[m_e{k}_{B}T/(2\pi {\hslash }^2){]}^{3/2}$ and $N_v=2[m_h{k}_{B}T/(2\pi {\hslash }^2){]}^{3/2}$. The factor $\sqrt{\pi }/2$ comes from the supplied Gaussian-weighted integral. Multiplying cancels the shared thermodynamic equilibrium chemical potential and proves the semiconductor mass-action law:For the given sample $N_D=2\times 10^{21}{\mathrm{m}}^{-3}$ and $N_A=10^{21}{\mathrm{m}}^{-3}$. With complete donor ionization and occupied acceptors, charge neutrality gives $n-p=N_D-N_A=10^{21}{\mathrm{m}}^{-3}$. At $293\mathrm{K}$ the given masses and gap giveSolving the compensated semiconductor equations, or using $n_i\ll N_D-N_A$, yieldsThe very small minority density is consistent with the wide gap and the strongly n-type balance. Also $n/N_c\simeq 2.6\times 10^{-3}\ll 1$ and $p/N_v\ll 1$, checking the nondegenerate approximation. The acceptor levels are occupied in this n-type regime; complete acceptor ionization in the compensation equation is appropriate to the model.

At low temperature dopant freeze-out reduces the conduction-electron population; a quantitative curve would require dopant binding energies and occupation factors. Once donors are ionized while intrinsic excitation is negligible, $n\simeq N_D-N_A$ gives an extrinsic plateau. At higher temperature intrinsic pairs eventually dominate, so $n\simeq p\simeq n_i(T)\propto T^{3/2}{e}^{-E_g/(2k_{B}T)}$ if the gap and masses are treated as constant. Real gap and mass changes modify that last expression.