Degradation of the Intermediate Band Caused by Disorder in Quantum-Dot Intermediate-Band Solar Cells

Intermediate band solar cells require in-gap electronic states that remain sufficiently extended to sustain collective electronic coupling and facilitate carrier motion. We investigate how structural disorder affects an intermediate band formed by coupled colloidal quantum dots embedded in a perovskite-like matrix. The system is represented by a single-orbital tight-binding Hamiltonian on a dilated face-centered-cubic lattice containing 4000 quantum dots, with system sizes between 1372 and 5324 in the finite-size analysis. Radius dispersion modifies on-site energies and hopping amplitudes, whereas positional disorder acts mainly through variations in interdot separation. Eigenstate extension is quantified using the normalized participation ratio. To distinguish spectral broadening from the loss of useful extended states, we also evaluate the mean participation of a contiguous threshold-defined spectral core, its relative energy width, and their product as a combined robustness descriptor. For the adopted baseline parameter set, degradation is energy selective: states near the spectral edges lose participation before states near the band center. At equal nominal amplitudes, radius disorder produces a stronger response than positional disorder, although the two amplitudes do not represent equal realized variances. A positional-disorder amplitude of 0.05 retains approximately 86% of the ordered-reference value of the combined descriptor, whereas a radius-disorder amplitude of 0.05 reduces it to about 22%; when both amplitudes are 0.05, about 14% remains. The model displays a comparatively robust regime near σR=0.02, a model-dependent crossover around σR=0.03-0.04, and strong degradation at larger values. Finite-size results are consistent with near-extensive scaling of the effective core participation number over the simulated sizes, but do not establish a thermodynamic mobility edge. These findings identify quantum-dot size uniformity as the more restrictive model control variable for preserving an extended intermediate-band core.