The intermediate-band solar cell concept, first proposed by Luque and Martí in 1997, has been demonstrated experimentally in expensive III-V compound semiconductor systems, but its compatibility with mainstream silicon manufacturing has remained an open question. The new work addresses this by simulating a periodic superlattice of cubic silicon quantum dots, each under tensile strain, embedded in a relaxed silicon-germanium matrix. When quantum dots are packed close enough together, their confined electron wave functions overlap and isolated energy levels broaden into minibands, which could serve as the intermediate band. Crucially, the team replaced the simplified single effective mass used in their earlier work with the full anisotropic effective mass tensor of the strain-split silicon Delta-2 valleys, with transverse masses of 0.19 and a longitudinal mass of 0.916 times the free electron mass, oriented along the growth axis.

That change turned out to matter enormously. The researchers scanned 495 different geometries, varying the dot size from 3.0 to 8.0 nanometres, the barrier thickness between dots from 1.0 to 5.0 nanometres, and the germanium fraction in the matrix from 0.20 to 0.38, solving the anisotropic BenDaniel-Duke Hamiltonian on a fine finite-difference grid with Bloch boundary conditions at 132 high-symmetry wave-vector points. Their central finding is that mass anisotropy alters the dispersion and isolation of the minibands far more strongly than it shifts the band minimum itself. The light transverse masses amplify spreading in the plane of the dots, while the heavy longitudinal mass suppresses it along the stacking direction, so bandwidths and inter-band overlaps change in ways a scalar mass simply cannot capture.

To qualify as a usable intermediate band, the lowest electron miniband had to satisfy four criteria simultaneously: it must remain fully bound below the barrier, carry a thermal margin exceeding one thermal energy unit at room temperature, span at least 5 millielectronvolts to form a genuine band rather than a flat level, and sit at least 5 millielectronvolts away from the next higher miniband to avoid parasitic hybridisation. Under these core conditions, 171 of the 495 geometries passed; adding an upper width limit of 50 millielectronvolts, designed to prevent the band from becoming too delocalised, trimmed the strict set to 170. Notably, no geometry survived at barrier thicknesses of 1.5 nanometres or below. In all 110 of those thin-barrier cases, the isolation criterion failed because strong tunnelling broadens adjacent bands until they overlap, and in 22 cases the lowest band even lost full confinement.

Perhaps the most consequential revision is compositional. The earlier scalar-mass model had pointed to a single optimum germanium fraction near 0.30. The tensor calculation instead reveals a favourable plateau at higher germanium contents, roughly x = 0.35 to 0.38, where the stronger electron barrier balances the increased in-plane coupling introduced by the lighter transverse masses. The comparison between models is striking: only 66 structures, about a third of the scalar core, survive in both models. One hundred five geometries enter the tensor core because anisotropic broadening lifts their bandwidth above the minimum threshold, while 138 scalar survivors drop out, mostly because their inter-miniband separation falls below 5 millielectronvolts. Median changes across the full scan included a 35.78 millielectronvolt reduction in inter-band separation, underscoring why density-of-states-equivalent masses are inadequate for directional kinetic modelling.

The team also resolved a subtle band-alignment question that has puzzled researchers in this material system: how adding germanium to the matrix can still create a barrier for electrons. The answer lies in strain. Tensile strain in the silicon dot splits the conduction valleys, and for the Si-rich compositions studied, the relevant strained alignment places the matrix conduction edge above the dot edge, with the offset given by 0.64 times the germanium fraction. The valence-band alignment, meanwhile, is type II: the highest heavy-hole state sits in the silicon-germanium matrix while the electron miniband resides in the strained silicon dot. This spatial separation makes the valence-band-to-intermediate-band transition spatially indirect, a fact with real implications for optical strength that the authors flag as requiring future phonon-assisted treatment.

To connect these electronic structures to actual sunlight, the researchers integrated the ASTM G173-03(2020) AM1.5G reference solar spectrum, using its full tabulated 2002 wavelengths from 280 to 4000 nanometres at an integrated power of 1000.371 watts per square metre without renormalisation. Because a miniband has finite width, the position chosen within it, bottom, centre or top, changes the two sub-gap photon thresholds. The spectrum was partitioned into three disjoint energy windows corresponding to the two-step and direct transitions, and the matched two-photon flux was taken as the smaller of the two sub-gap channels. In every one of the 170 strict geometries and at every placement, the valence-band-to-intermediate-band channel was the limiting one, a structural consequence of the fact that the width of that spectral window equals the second transition energy, which is bounded by the conduction-band offset and never exceeds 0.2432 electronvolts across the studied range.

The placement sensitivity analysis delivered another practical lesson. Moving the assumed intermediate state from the bottom to the top of the miniband changed the matched two-step photon flux by a median of 5.91 percent and by more than 51 percent in the extreme case, with 31 of 170 geometries shifting by over 20 percent. The ideal total spectral current bound, by contrast, moved by less than 3.9 percent because the direct above-gap contribution dominates that aggregate. The authors stress that their photon counts are upper bounds assuming perfect absorption and collection: phonon-assisted optical matrix elements, carrier occupations, recombination, escape mechanisms, and device electrostatics are all excluded from the present calculation, so the numbers should guide material screening rather than efficiency claims.

The study also probes robustness. Because a periodic unit cell cannot represent the random disorder of real self-assembled dot arrays, the team examined what happens when each retained design is nudged by a single 0.5-nanometre grid step in dot size or barrier thickness. Only about 41 percent of core geometries kept their classification across all nearest-neighbour changes, with median shifts as large as 6.10 millielectronvolts in isolation energy. The practical message for experimentalists is clear: choose candidate structures from the interior of the high-germanium design region, never from its staircase-shaped boundary, and subject the survivors to fuller models incorporating phonon-assisted absorption, disorder, recombination kinetics and device fields before any efficiency prediction can be trusted. In doing so, the work delivers exactly what screening studies are meant to provide, a defensible shortlist of silicon-compatible nanostructures worth the investment of more expensive simulation and, eventually, growth.

Subject of Research: Anisotropic electron minibands and solar spectral usability in tensile-strained Si/SiGe quantum-dot superlattices for intermediate-band solar cells

Article Title: Anisotropic electron minibands and AM1.5G spectral usability windows in tensile-strained Si/relaxed Si 1-x Ge x quantum-dot superlattices

Article References: Lassina, D., Soumaïla, D., Michel, K. O., Alain, D., Raguilignaba, S., & François, Z. (2026). Anisotropic electron minibands and AM1.5G spectral usability windows in tensile-strained Si/relaxed Si1-xGex quantum-dot superlattices. Results in Physics, Article 108754. https://doi.org/10.1016/j.rinp.2026.108754

Image Credits: AI Generated

DOI: 10.1016/j.rinp.2026.108754

Keywords: intermediate-band solar cell, silicon quantum dots, SiGe superlattice, miniband dispersion, effective mass anisotropy, AM1.5G spectrum, tensile strain, band alignment, photovoltaics, Si1-xGex, Anisotropic, electron