Past exam of the chemistry course of the year 1 of the natural sciences course of the University of Cambridge / 2025 / 6 / b

Gallium phosphide forms a tetrahedral network of polar covalent bonds, with electron density displaced toward phosphorus. The alternating diamond-related structure is the zinc blende structure: each Ga has four P neighbours and each P has four Ga neighbours. A local orbital hybridization picture combines outward-pointing s,p-derived orbitals into four approximately $s{p}^3$ bond directions; in the crystal these interactions form extended occupied bonding bands.

Since ${\chi }_{\mathrm{Allen}}(\mathrm{P})-{\chi }_{\mathrm{Allen}}(\mathrm{Ga})=2.25-1.76=0.49>0$, P attracts shared electron density more strongly. Write ${\mathrm{Ga}}^{\delta +}-{\mathrm{P}}^{\delta -}$ to indicate an ionic contribution superposed on covalent bonds. Formal oxidation states Ga($+3$) and P($-3$) are electron-assignment labels, not proof of completely transferred charges or a purely ionic crystal.

Neither atom requires $3d$ hybrids for these four bonds. The Ga $3d^{10}$ shell is filled and relatively core-like; the relevant Ga valence orbitals are $4s,4p$. P uses principally $3s,3p$; its empty $3d$ orbitals are too high in energy to be a necessary bonding set. Detailed band calculations may include d-state mixing or core–valence effects, but that does not turn the tetrahedral bonding into an expanded-valence d-hybrid construction.

A $2.24\mathrm{eV}$ band gap is consistent with a semiconductor. In pure gallium phosphide, the valence band is essentially full and the conduction band essentially empty at low temperature; thermal or optical excitation can produce mobile electrons and electron holes.

At room temperature, $k_{B}T\approx 0.026\mathrm{eV}$ is much smaller than the band gap, so intrinsic excitation is strongly suppressed. Pure material consequently has a low intrinsic carrier density, while semiconductor doping can markedly increase its electrical conductivity.

Sulfur substituting for phosphorus acts as a donor impurity, giving n-type semiconductor behaviour and usually increasing electrical conductivity. A P site normally supplies five valence electrons; S supplies six. After forming the surrounding bonds, the extra electron can occupy a donor level below the conduction band and be thermally ionized into that band. The donor impurity then carries positive charge.

This assignment is supported experimentally: infrared transmission measurements on S-doped gallium phosphide resolved bound-donor transitions and determined a sulfur donor optical ionization energy of about $0.104\mathrm{eV}$, far smaller than the host band gap.^[ref]

The effect depends on substitution on P sites, donor ionization, compensation by acceptors and charge carrier mobility. A dilute active donor population increases the electron term in $\sigma =e(n{\mu }_n+p{\mu }_p)$; not every dopant must donate a mobile electron at room temperature. Sulfur's larger Allen electronegativity does not overturn this electron-counting argument or make a P-site sulfur atom an acceptor.