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We present a theoretical analysis of the electronic properties of type-IIGaAs$_{1-x}$Sb$_{x}$/GaAs quantum rings (QRs), from the perspective ofapplications in intermediate band solar cells (IBSCs). We outline theanalytical solution of Schr\"{o}dinger's equation for a cylindrical QR ofinfinite potential depth, and describe the evolution of the QR ground statewith QR morphology. Having used this analytical model to elucidate generalaspects of the electronic properties of QRs, we undertake multi-band$\textbf{k} \cdot \textbf{p}$ calculations -- including strain andpiezoelectric effects -- for realistic GaAs$_{1-x}$Sb$_{x}$/GaAs QRs. Our$\textbf{k} \cdot \textbf{p}$ calculations confirm that the large type-II bandoffsets in GaAs$_{1-x}$Sb$_{x}$/GaAs QRs provide strong confinement of holes,and further indicate the presence of resonant (quasi-bound) electron stateswhich localise in the centre of the QR. From the perspective of IBSC design thecalculated electronic properties demonstrate several benefits, including (i)large hole ionisation energies, mitigating thermionic emission from theintermediate band, and (ii) electron-hole spatial overlaps exceeding those inconventional GaAs$_{1-x}$Sb$_{x}$/GaAs QDs, with the potential to engineerthese overlaps via the QR morphology so as to manage the trade-off betweenoptical absorption and radiative recombination. Overall, our analysishighlights the flexibility offered by the QR geometry from the perspective ofband structure engineering, and identifies specific combinations of QR alloycomposition and morphology which offer optimised sub-band gap energies forQR-based IBSCs.

Electronic properties of type-II GaAs$_{1-x}$Sb$_{x}$/GaAs quantum rings for applications in intermediate-band solar cells