The optical properties of a vertical multilayer stack of semiconductor self-assembled quantum dots (QDs) depend on the coupling status. We present an improved modeling method for analysis of QD stacks, consisting of several separate steps in the elastic strain analysis, to reproduce the realistic unidirectional strain accumulation along the QD growth direction from lower and upper dots. Based on this modeling method, by varying the spacer thickness, we systematically study a large variety of QD stack structures, for better understanding the influence of strain and electronic coupling mechanisms. A “quasi continuum band” or highly degenerate excited state (ES) is found in the closely multi-stacked QDs, probably accounting for the occurrence of distinct blueshifting of the photoluminescence peak wavelength for the decreasing spacer thickness. The enhanced ES emission from this type of stacking QD modeled by using rate equations may pave a way for designing potential high-performance laser devices operating on ES.

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Background No study had directly compared the reliability, correlation with clinical symptoms, and surgical outcomes of dural sac cross-sectional area (DCSA), nerve root sedimentation sign (SedSign), and morphological grade for lumbar spinal stenosis (LSS). Methods From January 2017 to December 2020, 202 patients with LSS were retrospectively analyzed. The narrowest segments were assessed via T2-weighted cross-sectional images using DCSA, morphological grade, and SedSign by two independent observers. Three classifications’ reliabilities were evaluated. Correlations between three classifications and between each of the classifications and symptoms or surgical outcomes 12 months postoperatively were evaluated. Results There were 144 males and 58 females; 23, 52, and 127 patients had the narrowest segment in L2–3, L3–4, and L4–5, respectively. The intra-observer reliability of DCSA ranged from 0.91 to 0.93, and the inter-observer reliability was 0.90. The intra-observer reliability of SedSign ranged from 0.83 to 0.85, and the inter-observer reliability was 0.75. The intra-observer reliability of morphological grade ranged from 0.72 to 0.78, and the inter-observer reliability was 0.61. Each of these classifications was correlated with the other two (P < 0.01). For preoperative symptoms, DCSA was correlated with leg pain (LP) (r =  − 0.14), Oswestry Disability Index (ODI) (r =  − 0.17), and claudication (r =  − 0.19). Morphological grade was correlated with LP (r = 0.19) and claudication (r = 0.27). SedSign was correlated with ODI (r = 0.23). For postoperative outcomes, morphological grade was correlated with LP (r =  − 0.14), and SedSign was correlated with ODI (r = 0.17). Conclusions Substantial to almost perfect intra and inter-observer reliabilities for the three classifications were found; however, these classifications had either weak correlations with symptoms and surgical outcomes or none at all. Based on our findings, using one of them without conducting other tests for LSS will have limited or uncertain value in surgical decision-making or evaluating the prognostic value.

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