{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T05:17:15Z","timestamp":1787807835451,"version":"build-2784847793"},"reference-count":85,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T00:00:00Z","timestamp":1787616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004837","name":"Spanish Ministry of Science and Innovation","doi-asserted-by":"crossref","award":["PID2023-150663NB-C21"],"award-info":[{"award-number":["PID2023-150663NB-C21"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"crossref"}]},{"award":["PID2023-150663NB-C21"],"award-info":[{"award-number":["PID2023-150663NB-C21"]}],"id":[{"id":"https:\/\/ror.org\/023ktd084","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>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 \u03c3R=0.02, a model-dependent crossover around \u03c3R=0.03\u20130.04, 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.<\/jats:p>","DOI":"10.3390\/mi17091005","type":"journal-article","created":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T15:01:07Z","timestamp":1787670067000},"page":"1005","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Degradation of the Intermediate Band Caused by Disorder in Quantum-Dot Intermediate-Band Solar Cells"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6399-1356","authenticated-orcid":false,"given":"Lucas","family":"Cuadra","sequence":"first","affiliation":[{"name":"Department of Signal Processing and Communications, University of Alcal\u00e1, 28805 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4456-9886","authenticated-orcid":false,"given":"Jorge","family":"P\u00e9rez-Aracil","sequence":"additional","affiliation":[{"name":"Department of Signal Processing and Communications, University of Alcal\u00e1, 28805 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4048-1676","authenticated-orcid":false,"given":"Sancho","family":"Salcedo-Sanz","sequence":"additional","affiliation":[{"name":"Department of Signal Processing and Communications, University of Alcal\u00e1, 28805 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5014","DOI":"10.1103\/PhysRevLett.78.5014","article-title":"Increasing the efficiency of ideal solar cells by photon induced transitions at intermediate levels","volume":"78","author":"Luque","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"013001","DOI":"10.1088\/2516-1083\/ab0fa8","article-title":"Photovoltaic technology and visions for the future","volume":"1","author":"Green","year":"2019","journal-title":"Prog. Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1038\/nmat4676","article-title":"Energy conversion approaches and materials for high-efficiency photovoltaics","volume":"16","author":"Green","year":"2017","journal-title":"Nat. Mater."},{"key":"ref_4","first-page":"1548305","article-title":"Silicon solar cells: Toward the efficiency limits","volume":"4","author":"Andreani","year":"2019","journal-title":"Adv. Phys. X"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"083505","DOI":"10.1063\/1.2034090","article-title":"Experimental analysis of the quasi-Fermi level split in quantum dot intermediate-band solar cells","volume":"87","author":"Luque","year":"2005","journal-title":"Appl. Phys. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"247701","DOI":"10.1103\/PhysRevLett.97.247701","article-title":"Production of photocurrent due to intermediate-to-conduction-band transitions: A demonstration of a key operating principle of the intermediate-band solar cell","volume":"97","author":"Stanley","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ramiro, I., Antolin, E., Linares, P., Lopez, E., Artacho, I., Datas, A., Marti, A., Luque, A., Steer, M., and Stanley, C. (2014). Two-photon photocurrent and voltage up-conversion in a quantum dot intermediate band solar cell. Proceedings of the 2014 IEEE 40th Photovoltaic Specialist Conference (PVSC), IEEE.","DOI":"10.1109\/PVSC.2014.6925629"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1109\/JPHOTOV.2014.2368712","article-title":"Spectrally resolved interband and intraband transitions by two-step photon absorption in InGaAs\/GaAs quantum dot solar cells","volume":"5","author":"Tamaki","year":"2014","journal-title":"IEEE J. Photovolt."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Antolin, E., Mart\u00ed, A., Linares, P.G., Ramiro, I., Hern\u00e1ndez, E., Farmer, C., Stanley, C., and Luque, A. (2010). Advances in quantum dot intermediate band solar cells. Proceedings of the 2010 35th IEEE Photovoltaic Specialists Conference, IEEE.","DOI":"10.1109\/PVSC.2010.5614224"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.solmat.2015.12.031","article-title":"Demonstration of the operation principles of intermediate band solar cells at room temperature","volume":"149","author":"Datas","year":"2016","journal-title":"Sol. Energy Mater. Sol. Cells"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"157701","DOI":"10.1103\/PhysRevLett.114.157701","article-title":"Intermediate band solar cell with extreme broadband spectrum quantum efficiency","volume":"114","author":"Datas","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"125422","DOI":"10.1103\/PhysRevB.96.125422","article-title":"Analysis of the intermediate-band absorption properties of type-II GaSb\/GaAs quantum-dot photovoltaics","volume":"96","author":"Ramiro","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ekins-Daukes, N., Honsberg, C., and Yamaguchi, M. (2005). Signature of intermediate band materials from luminescence measurements. Proceedings of the Conference Record of the Thirty-First IEEE Photovoltaic Specialists Conference, 2005, IEEE.","DOI":"10.1109\/PVSC.2005.1488066"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2118","DOI":"10.1109\/16.944204","article-title":"Thermodynamic consistency of sub-bandgap absorbing solar cell proposals","volume":"48","author":"Luque","year":"2001","journal-title":"IEEE Trans. Electron Devices"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S1386-9477(02)00366-1","article-title":"Thermodynamics of solar energy conversion in novel structures","volume":"14","author":"Luque","year":"2002","journal-title":"Phys. E Low-Dimens. Syst. Nanostruct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0927-0248(94)90209-7","article-title":"Absolute limiting efficiencies for photovoltaic energy conversion","volume":"33","year":"1994","journal-title":"Sol. Energy Mater. Sol. Cells"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1038\/s41928-021-00632-7","article-title":"Colloidal quantum dot electronics","volume":"4","author":"Liu","year":"2021","journal-title":"Nat. Electron."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Harrison, P., and Valavanis, A. (2016). Quantum Wells, Wires and Dots: Theoretical and Computational Physics of Semiconductor Nanostructures, John Wiley & Sons.","DOI":"10.1002\/9781118923337"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4920","DOI":"10.1021\/acsanm.0c01386","article-title":"Quantum Dots and Their Applications: What Lies Ahead?","volume":"3","author":"Cotta","year":"2020","journal-title":"ACS Appl. Nano Mater."},{"key":"ref_20","first-page":"46","article-title":"Quantum dot analysis of the space charge region of intermediate band solar cell","volume":"Volume 2001","author":"Cuadra","year":"2001","journal-title":"Proceedings of the Photovoltaics for the 21st Century II: Proceedings of the International Symposium"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.solener.2020.03.011","article-title":"Internal polarization electric field effects on the efficiency of InN\/InxGa1\u2212xN multiple quantum dot solar cells","volume":"201","author":"Bikerouin","year":"2020","journal-title":"Sol. Energy"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"064513","DOI":"10.1063\/1.3468520","article-title":"Reducing carrier escape in the InAs\/GaAs quantum dot intermediate band solar cell","volume":"108","author":"Farmer","year":"2010","journal-title":"J. Appl. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Ramiro, I., Antolin, E., Steer, M., Linares, P., Hernandez, E., Artacho, I., Lopez, E., Ben, T., Ripalda, J., and Molina, S. (2012). InAs\/AlGaAs quantum dot intermediate band solar cells with enlarged sub-bandgaps. Proceedings of the 2012 38th IEEE Photovoltaic Specialists Conference, IEEE.","DOI":"10.1109\/PVSC.2012.6317694"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1038\/nphoton.2012.1","article-title":"Understanding intermediate-band solar cells","volume":"6","author":"Luque","year":"2012","journal-title":"Nat. Photonics"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"044502","DOI":"10.1063\/1.3684968","article-title":"Understanding the operation of quantum dot intermediate band solar cells","volume":"111","author":"Luque","year":"2012","journal-title":"J. Appl. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1002\/pip.3351","article-title":"Intermediate band solar cells: Present and Future","volume":"29","author":"Ramiro","year":"2021","journal-title":"Prog. Photovolt. Res. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1038\/s41467-020-20835-4","article-title":"Spin blockade and phonon bottleneck for hot electron relaxation observed in n-doped colloidal quantum dots","volume":"12","author":"Wang","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4532","DOI":"10.1038\/s41467-019-12558-y","article-title":"Observation of a phonon bottleneck in copper-doped colloidal quantum dots","volume":"10","author":"Wang","year":"2019","journal-title":"Nat. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2107888","DOI":"10.1002\/adma.202107888","article-title":"Colloidal Quantum Dot Solar Cells: Progressive Deposition Techniques and Future Prospects on Large-Area Fabrication","volume":"34","author":"Zhao","year":"2022","journal-title":"Adv. Mater."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1844","DOI":"10.1002\/adma.200305395","article-title":"Colloidal PbS nanocrystals with size-tunable near-infrared emission: Observation of post-synthesis self-narrowing of the particle size distribution","volume":"15","author":"Hines","year":"2003","journal-title":"Adv. Mater."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"12732","DOI":"10.1021\/acs.chemrev.5b00063","article-title":"Colloidal quantum dot solar cells","volume":"115","author":"Carey","year":"2015","journal-title":"Chem. Rev."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4819","DOI":"10.1021\/acs.chemrev.8b00733","article-title":"The role of ligands in the chemical synthesis and applications of inorganic nanoparticles","volume":"119","author":"Feliu","year":"2019","journal-title":"Chem. Rev."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.1021\/acs.accounts.0c00765","article-title":"The future of ligand engineering in colloidal semiconductor nanocrystals","volume":"54","author":"Zito","year":"2021","journal-title":"Acc. Chem. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3694","DOI":"10.1021\/acs.nanolett.0c00638","article-title":"Ligand-assisted reconstruction of colloidal quantum dots decreases trap state density","volume":"20","author":"Sun","year":"2020","journal-title":"Nano Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1038\/nmat4526","article-title":"The surface science of nanocrystals","volume":"15","author":"Boles","year":"2016","journal-title":"Nat. Mater."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5209","DOI":"10.1021\/acs.jpclett.7b02193","article-title":"Surface traps in colloidal quantum dots: A combined experimental and theoretical perspective","volume":"8","author":"Giansante","year":"2017","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1021\/acs.chemmater.6b04648","article-title":"On the origin of surface traps in colloidal II\u2013VI semiconductor nanocrystals","volume":"29","author":"Houtepen","year":"2017","journal-title":"Chem. Mater."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1021\/acsenergylett.8b01669","article-title":"Rationalizing and controlling the surface structure and electronic passivation of cesium lead halide nanocrystals","volume":"4","author":"Bodnarchuk","year":"2018","journal-title":"ACS Energy Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1126\/science.aax5825","article-title":"Resurfacing halide perovskite nanocrystals","volume":"364","author":"Almeida","year":"2019","journal-title":"Science"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1126\/science.1116703","article-title":"PbSe nanocrystal solids for n- and p-channel thin film field-effect transistors","volume":"310","author":"Talapin","year":"2005","journal-title":"Science"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1021\/cr900137k","article-title":"Prospects of colloidal nanocrystals for electronic and optoelectronic applications","volume":"110","author":"Talapin","year":"2010","journal-title":"Chem. Rev."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"10085","DOI":"10.1021\/ja1024832","article-title":"Expanding the chemical versatility of colloidal nanocrystals capped with molecular metal chalcogenide ligands","volume":"132","author":"Kovalenko","year":"2010","journal-title":"J. Am. Chem. Soc."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"aac5523","DOI":"10.1126\/science.aac5523","article-title":"Building devices from colloidal quantum dots","volume":"353","author":"Kagan","year":"2016","journal-title":"Science"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1021\/acsphyschemau.2c00018","article-title":"The Rise and Future of Discrete Organic\u2013Inorganic Hybrid Nanomaterials","volume":"2","author":"Brett","year":"2022","journal-title":"ACS Phys. Chem. Au"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1038\/s41578-020-00274-9","article-title":"Colloidal quantum dot lasers","volume":"6","author":"Park","year":"2021","journal-title":"Nat. Rev. Mater."},{"key":"ref_46","unstructured":"Qu, J. (2021). Colloidal Semiconductor Nanocrystals for Optoelectronic Applications: Photodetectors and Light Emitting Diodes. [Ph.D. Thesis, Sorbonne Universit\u00e9]."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Kubo, T., Wang, H., and Segawa, H. (2022). Solution-Processed Quantum-Dot Solar Cells. Springer Handbook of Inorganic Photochemistry, Springer.","DOI":"10.1007\/978-3-030-63713-2_40"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"e01521","DOI":"10.1002\/adom.202501521","article-title":"Quantum-Dot Intermediate Band Semiconductors: From Materials to Applications","volume":"13","author":"Xu","year":"2025","journal-title":"Adv. Opt. Mater."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1038\/nature14563","article-title":"Quantum-dot-in-perovskite solids","volume":"523","author":"Ning","year":"2015","journal-title":"Nature"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"345402","DOI":"10.1088\/0957-4484\/24\/34\/345402","article-title":"Self-organized colloidal quantum dots and metal nanoparticles for plasmon-enhanced intermediate-band solar cells","volume":"24","author":"Mendes","year":"2013","journal-title":"Nanotechnology"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"6882","DOI":"10.1021\/acsnano.5b00332","article-title":"Colloidal nanoparticles for intermediate band solar cells","volume":"9","author":"Voros","year":"2015","journal-title":"ACS Nano"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Hahn, R.V., Rodr\u00edguez-Bol\u00edvar, S., Rodosthenous, P., Skibinsky-Gitlin, E.S., Califano, M., and G\u00f3mez-Campos, F.M. (2022). Optical Absorption in N-Dimensional Colloidal Quantum Dot Arrays: Influence of Stoichiometry and Applications in Intermediate Band Solar Cells. Nanomaterials, 12.","DOI":"10.3390\/nano12193387"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"102884","DOI":"10.1016\/j.mtcomm.2021.102884","article-title":"Key photovoltaic parameters of organohalide lead perovskite quantum dot intermediate band solar cell: A numerical investigation","volume":"29","author":"Roy","year":"2021","journal-title":"Mater. Today Commun."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1038\/s41467-018-07655-3","article-title":"Solution-processed intermediate-band solar cells with lead sulfide quantum dots and lead halide perovskites","volume":"10","author":"Hosokawa","year":"2019","journal-title":"Nat. Commun."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1021\/acs.jpclett.8b03657","article-title":"Interaction between colloidal quantum dots and halide perovskites: Looking for constructive synergies","volume":"10","author":"Ngo","year":"2019","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1038\/nphoton.2016.11","article-title":"Highly efficient quantum dot near-infrared light-emitting diodes","volume":"10","author":"Gong","year":"2016","journal-title":"Nat. Photonics"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"14757","DOI":"10.1038\/ncomms14757","article-title":"Field-emission from quantum-dot-in-perovskite solids","volume":"8","author":"Gong","year":"2017","journal-title":"Nat. Commun."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1801016","DOI":"10.1002\/smll.201801016","article-title":"Hybrid PbS quantum-dot-in-perovskite for high-efficiency perovskite solar cell","volume":"14","author":"Han","year":"2018","journal-title":"Small"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1038\/s41586-019-1239-7","article-title":"Lattice anchoring stabilizes solution-processed semiconductors","volume":"570","author":"Liu","year":"2019","journal-title":"Nature"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Ribeiro, G., Ferreira, G., Menda, U., Alexandre, M., Brites, M.J., Barreiros, M.A., Jana, S., \u00c1guas, H., Martins, R., and Fernandes, P. (2023). Sub-bandgap sensitization of perovskite semiconductors via colloidal quantum dots incorporation. Nanomaterials, 13.","DOI":"10.3390\/nano13172447"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"3647","DOI":"10.1021\/acsphotonics.3c00738","article-title":"Thermal-carrier-escape mitigation in a quantum-dot-In-perovskite intermediate band solar cell via bandgap engineering","volume":"10","author":"Menda","year":"2023","journal-title":"ACS Photonics"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1038\/s41377-021-00671-x","article-title":"Light management with quantum nanostructured dots-in-host semiconductors","volume":"10","author":"Alexandre","year":"2021","journal-title":"Light Sci. Appl."},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Li, M.F. (1994). Modern Semiconductor Quantum Physics, World Scientific.","DOI":"10.1142\/9789814261517"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"1492","DOI":"10.1103\/PhysRev.109.1492","article-title":"Absence of diffusion in certain random lattices","volume":"109","author":"Anderson","year":"1958","journal-title":"Phys. Rev."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1088\/0034-4885\/56\/12\/001","article-title":"Localization: Theory and experiment","volume":"56","author":"Kramer","year":"1993","journal-title":"Rep. Prog. Phys."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1103\/RevModPhys.80.1355","article-title":"Anderson Transitions","volume":"80","author":"Evers","year":"2008","journal-title":"Rev. Mod. Phys."},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Cuadra, L., Salcedo-Sanz, S., and Nieto-Borge, J.C. (2023). Carrier Transport in Colloidal Quantum Dot Intermediate Band Solar Cell Materials Using Network Science. Int. J. Mol. Sci., 24.","DOI":"10.3390\/ijms24043797"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"16701","DOI":"10.1038\/s41598-020-73578-z","article-title":"Quantum transport in a chain of quantum dots with inhomogeneous size distribution and manifestation of 1D Anderson localization","volume":"10","author":"Cha","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1021\/acsaelm.1c01011","article-title":"Effect of Positional Disorders on Charge Transport in Nanocrystal Quantum Dot Thin Films","volume":"4","author":"Xing","year":"2022","journal-title":"ACS Appl. Electron. Mater."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"23703","DOI":"10.5488\/cmp.29.23703","article-title":"Effect of weak positional disorder on the miniband structure of spherical quantum dot chains","volume":"29","author":"Leshko","year":"2026","journal-title":"Condens. Matter Phys."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"2728","DOI":"10.1021\/nl061684x","article-title":"The Peculiar Electronic Structure of PbSe Quantum Dots","volume":"6","author":"An","year":"2006","journal-title":"Nano Lett."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"127406","DOI":"10.1103\/PhysRevLett.110.127406","article-title":"Measurement of Electronic States of PbS Nanocrystal Quantum Dots Using Scanning Tunneling Spectroscopy: The Role of Parity Selection Rules in Optical Absorption","volume":"110","author":"Diaconescu","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Ridley, B.K. (2013). Quantum Processes in Semiconductors, Oxford University Press. [5th ed.].","DOI":"10.1093\/acprof:oso\/9780199677214.001.0001"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"23028","DOI":"10.1039\/D0NR06892F","article-title":"The Role of Ligands in Electron Transport in Nanocrystal Solids","volume":"12","author":"Khabibullin","year":"2020","journal-title":"Nanoscale"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"17725","DOI":"10.1039\/D2NR04244D","article-title":"Electronic Transport in Quantum-Dot-in-Perovskite Solids","volume":"14","author":"Erwin","year":"2022","journal-title":"Nanoscale"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"2852","DOI":"10.1038\/s41467-020-16560-7","article-title":"Charge Transport in Semiconductors Assembled from Nanocrystal Quantum Dots","volume":"11","author":"Yazdani","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"3023","DOI":"10.1021\/nn900863a","article-title":"Size-Dependent Optical Properties of Colloidal PbS Quantum Dots","volume":"3","author":"Moreels","year":"2009","journal-title":"ACS Nano"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1021\/acs.nanolett.6b04201","article-title":"Charge Carrier Hopping Dynamics in Homogeneously Broadened PbS Quantum Dot Solids","volume":"17","author":"Gilmore","year":"2017","journal-title":"Nano Lett."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"3077","DOI":"10.1088\/0022-3719\/6\/21\/012","article-title":"Density of states from moments. Application to the impurity band","volume":"6","author":"Gaspard","year":"1973","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"015012","DOI":"10.1088\/1367-2630\/16\/1\/015012","article-title":"Critical Exponent for the Anderson Transition in the Three-Dimensional Orthogonal Universality Class","volume":"16","author":"Slevin","year":"2014","journal-title":"New J. Phys."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"134209","DOI":"10.1103\/PhysRevB.84.134209","article-title":"Multifractal Finite-Size Scaling and Universality at the Anderson Transition","volume":"84","author":"Rodriguez","year":"2011","journal-title":"Phys. Rev. B"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"156801","DOI":"10.1103\/PhysRevLett.95.156801","article-title":"Coulomb Blockade and Hopping Conduction in PbSe Quantum Dots","volume":"95","author":"Romero","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"1800082","DOI":"10.1002\/adma.201800082","article-title":"Lead-Chalcogenide Colloidal-Quantum-Dot Solids: Novel Assembly Methods, Electronic Structure Control, and Application Prospects","volume":"30","author":"Balazs","year":"2018","journal-title":"Adv. Mater."},{"key":"ref_84","doi-asserted-by":"crossref","unstructured":"Datta, S. (2005). Quantum Transport: Atom to Transistor, Cambridge University Press.","DOI":"10.1017\/CBO9781139164313"},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"7845","DOI":"10.1063\/1.365394","article-title":"Single and multiband modeling of quantum electron transport through layered semiconductor devices","volume":"81","author":"Lake","year":"1997","journal-title":"J. Appl. Phys."}],"container-title":["Micromachines"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-666X\/17\/9\/1005\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T04:19:05Z","timestamp":1787804345000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-666X\/17\/9\/1005"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,25]]},"references-count":85,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["mi17091005"],"URL":"https:\/\/doi.org\/10.3390\/mi17091005","relation":{},"ISSN":["2072-666X"],"issn-type":[{"value":"2072-666X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,25]]}}}