What distinguishes the work from most previous theoretical models is its scope. Earlier density functional theory calculations on ZnO typically examined one dopant at a time, substituting a single impurity atom into the lattice to tune the band gap, electron density, or defect chemistry. Those models clarified individual dopant behavior but ignored the intricacies that arise when two or more dopants share the same crystal. The new study breaks with that tradition by investigating multiple and mixed-dopant cases under equivalent computational conditions, enabling a direct, apples-to-apples comparison of doping strategies that the literature, with its inconsistent methods across studies, has never provided.

The computational framework is rigorous. All calculations were performed with the DMol³ package in Materials Studio, based on the all-electron numerical atomic orbital method. A pristine wurtzite ZnO structure from the Materials Project was expanded into a 2 × 2 × 1 supercell, large enough to represent realistic doping concentrations while avoiding spurious interactions between periodic dopant images. Geometry optimizations used the generalized gradient approximation with Perdew–Burke–Ernzerhof exchange-correlation, a Fermi-level smearing of 0.5 electron volts, and stringent convergence criteria: total energy within 1 × 10⁻⁵ Hartree and forces below 0.002 Hartree per angstrom. Because conventional GGA-PBE methods systematically underpredict semiconductor band gaps, electronic and optical properties were additionally evaluated with a hybrid functional that includes exact Hartree–Fock exchange, eliminating the self-interaction error and producing band-gap predictions in far better agreement with experimental measurements. All reported band gaps in the study rest on these hybrid-functional results.

Dopants were introduced by substituting zinc atoms in the supercell with aluminum, gallium, indium, magnesium, or silver. The Zn site was chosen deliberately: in wurtzite ZnO, cation substitution is energetically favorable, and comparisons of ionic radii and oxidation states with Zn²⁺ confirm that Zn-site incorporation carries lower energy than interstitial or oxygen-site modes. Spin-polarized calculations were included for doped systems to capture possible localized magnetic moments or unpaired electronic states, while pristine ZnO remained non-magnetic. Brillouin-zone sampling used a Monkhorst–Pack k-point mesh verified through convergence testing, and the same converged sampling was applied to every model to maintain consistency. The pseudopotential treatment paid special attention to the Zn 3d and 4s states together with the O 2p states, the orbitals that dominate the valence-band maximum, conduction-band minimum, and overall band-gap behavior.

The single-doping results are striking. Pristine ZnO shows a calculated band gap of 3.21 electron volts, matching experimental values of 3.37 to 3.44 electron volts. Every dopant narrows the gap: aluminum reduces it to 2.46 electron volts, gallium to 2.41, indium to 2.61, magnesium to 2.71, and silver to 2.75. Gallium produces the largest narrowing, aluminum the second largest. Mechanistically, aluminum and gallium form donor-like couplings to the conduction band, indium’s extended 5s orbitals interact with the s-type conduction band of ZnO, magnesium modifies local Zn–O bonds, and silver’s 4d states hybridize with O 2p states near the valence band, potentially shifting the valence-band edge upward and extending absorption into the visible range.

Increasing the concentration of a single dopant produces far more dramatic narrowing. With two dopant atoms in the supercell, the gaps fall below 2 electron volts across the board: 1.61 electron volts for ZnO–2Al, 1.52 for ZnO–2Ga, 1.72 for ZnO–2In, 1.81 for ZnO–2Mg, and 1.91 for ZnO–2Ag. These values reflect a transition from isolated donor levels to broadened conduction-edge or impurity-band levels as dopant wavefunctions begin to overlap. Such gaps would permit solar photon absorption across a much broader range, but the same high density of electronically active centers can increase scattering and non-radiative loss, so the predicted optical benefit must be tested against carrier lifetime and mobility before any efficiency claim is made.

The mixed co-doping results reveal that band-gap engineering in ZnO is neither additive nor monotonic. At 1:1 ratios, gaps range from 2.1 to 2.7 electron volts; at 2:2 ratios, from 1.6 to 2.6. The final gap emerges from local lattice relaxation, orbital hybridisation, charge redistribution, dopant–dopant separation, and the position of dopant-derived states relative to the ZnO band edges. Some pairs show strong narrowing as concentration increases—Al–Mg falls from 2.2 to 1.6 electron volts, In–Mg from 2.3 to 1.6, In–Ag from 2.7 to 1.7—while Ga–In remains constant at 2.1 and Al–Ga actually rises slightly from 2.4 to 2.6. These deviations prove that the relaxed electronic structure, not merely dopant content, governs the outcome. When dopants occupy nearby or electronically connected positions, relaxation around one site changes the bonding environment of the other through shared oxygen neighbors and overlapping strain fields, altering metal–oxygen distances, bond angles, local electrostatic potential, and orbital overlap.

The density of states analysis explains why. In pristine ZnO, deep Zn 3d states appear at low energy, O 2p states dominate the valence band, and the conduction band is formed primarily from Zn 4s states, confirming the wide gap and limited visible-light absorption. Aluminum, gallium, and indium form s donor-like states that overlap with the Zn 4s orbitals at the conduction-band minimum, with indium producing broader and more delocalized conduction-band features that enhance electronic mobility. Magnesium modifies the conduction band while maintaining a clean gap, improving band alignment without creating deep defects. Silver adds density of states near the valence-band edge through Ag 4d and O 2p hybridization, which may improve hole participation but also raises the possibility of deep state formation and greater recombination.

From a solar-cell perspective, the study is careful to note that the smallest calculated gap is not automatically the best material. A wider spectral response can raise the photogeneration rate and short-circuit current density when the absorption coefficient is sufficiently high, but strong narrowing may enhance current while reducing the maximum open-circuit voltage, and deep impurity states can trap carriers and support non-radiative recombination. Band-edge positions must remain compatible with adjacent transport layers, electrodes, dyes, or redox couples in heterojunction or sensitized devices. The most promising candidates identified are ZnO–2Al–2Mg and ZnO–2In–2Mg at 1.6 electron volts, followed by ZnO–2Ga–2Mg and ZnO–2In–2Ag at 1.7 and ZnO–2Al–2Ag at 2.0, compositions that provide substantial visible-light gap reduction while remaining within the approximate 1 to 2 electron volt photovoltaic design window, unlike ultra-narrow sub-1 electron volt systems that would suffer from reduced photovoltage and stronger defect-assisted recombination.

The study also proposes experimental pathways to validate the computational predictions. Photoluminescence spectroscopy can determine defect emissions and doping-induced energy levels within the gap; Hall effect tests give direct indications of carrier concentration and mobility; ultraviolet-visible spectroscopy can measure the optical absorption edge and band-gap energies. Synthesis routes such as sol–gel, hydrothermal, pulsed laser deposition, and magnetron sputtering are already established for ZnO thin films and nanostructures, while X-ray diffraction and scanning electron microscopy can verify phase purity and crystallinity. Formation-energy calculations under Zn-rich and O-rich limits, together with spectroscopy and lifetime measurements, are needed to distinguish useful dopant states from harmful trap states. The work establishes a mechanistic framework showing why some co-dopant combinations are substantially more effective than others, demonstrating that successful optimisation of ZnO requires deliberate control of dopant chemistry, concentration, and atomic configuration rather than indiscriminate increases in dopant loading or pursuit of the smallest possible gap.

Subject of Research: Density functional theory comparison of single, mixed, and multi-doping strategies in ZnO for enhanced solar energy conversion

Article Title: Computational investigation of single, multi and mixed doping strategies in ZnO for enhanced solar energy conversion

Article References: Nyangiwe, N. N. (2026). Computational investigation of single, multi and mixed doping strategies in ZnO for enhanced solar energy conversion. Results in Physics, Article 108769. https://doi.org/10.1016/j.rinp.2026.108769

Image Credits: AI Generated

DOI: 10.1016/j.rinp.2026.108769

Keywords: solar energy, zinc oxide, density functional theory, doping, photovoltaics, band gap engineering, semiconductors, co-doping, visible light absorption, materials science, Computational, investigation