## 3 Results
### Visual Estimate Option
(**b**) Scheme of ordering in a body centered tetragonal (BCT) lattice defined by basis vectors \(\mathbf{a}_{1}\)-\(\mathbf{a}_{3}\). (**c**) Cross-section of the 3D lattice of NPs having BCT unit cell with \(N1\) = 6 and \(N3\) = 4 periods along basis vectors \(\mathbf{a}_{1}\) and \(\mathbf{a}_{3}\), respectively. GisaxStudio currently supports five basic types of the NP shape-structures: sphere, spheroid, ellipsoid, tilted ellipsoid, and core-shell spheroid NPs, as shown in Figure 8. Their parameters can be set in tab '_Nanoparticle Shape Params_', shown in Figure 8a. The shapes and structures are schematically illustrated in Figure 8b. The main parameters of the NP shape are their radii along the \(x,y,\) and \(z\) directions \(R_{\text{x,y,z}}\) (valid for _Ellipsoid_). The option _Sphere_ uses only the radius in the x direction (\(R_{\text{x}}\)) for all directions, while the option _Spheroid_ uses \(R_{\text{x}}\) for radii parallel to the surface and \(R_{\text{z}}\) for the direction vertical to the surface. The option _Ellipsoid tilted along \(a_{3}\)_ assumes the same radii values as explained for _Ellipsoid_, but the entire NP is then assumed to be tilted along the basis vector \(\mathbf{a}_{3}\), as shown in Figure 8b. The option _Core-Shell_ refers to a spheroid with core-shell structure. It consists of different core and shell materials, with radii \(R_{\text{core}}\) and \(R_{\text{shell}}\), respectively. Their origins can be shifted form each other by value \(d\), as shown in Figure 8c. Such structures are often formed by the production of core-shell QDs by thin layer deposition [7; 8; 9]. The entire system can be scaled in the \(z\) direction by factor \(F\), which enables the transition from a spherical to a spheroidal shape. Therefore, actual core-shell radii in the vertical direction are obtained by the multiplication of \(R_{\text{core}}\) and \(R_{\text{shell}}\) by factor \(F\). The distribution of all NP shapes is assumed to be gamma distribution, as described by parameter \(\gamma\), and the NP radii. All directions are assumed to have the same order of the distribution. The refraction indices of the NPs and their real and imaginary parts should also be set in the '_Nanoparticle Shape Params_'. The tab _Fixed Params_ includes the refraction indices of the matrix in which the NPs are embedded. It also includes the starting and final averaging angle, along with the step. The averaging is assumed to be performed for the rotation of the 3D lattice around the surface normal (\(z\) direction). This is needed because the regular 3D ordering usually appears in domains that are randomly rotated around the surface normal when the material is produced by the self-assembly process. If there is pre-patterning on the substrate that acts as nuclei for the 3D lattice growth, or some other mechanism that predefines the directions of basis vectors \(\mathbf{a}_{1}\) and \(\mathbf{a}_{2}\), then there is no need for averaging. Figure 7: (**a**) Tab _Deviation params_ with the corresponding parameters. (**b**) Illustration of disorder parameters \(\sigma^{1,2,3}{}_{\text{xy}}\). The disorder properties within each layer parallel to the surface (\(\sigma^{1,2}{}_{\text{xy}}\)) are usually the same (left), and they describe the deviations of each NP within a layer from the ideal positions. The parameters \(\sigma^{3}{}_{\text{xy}}\) (right) describe the disorder of each layer from the ideal position, and therefore, are a measure of the quality of the self-assembly process that leads to formation of the 3D NP lattice. (**c**) The disorder parameters in the vertical direction (perpendicular to the surface). These parameters describe the deviation of each NP within a layer (\(\sigma^{1,2}{}_{\text{z}}\)), and of each layer (\(\sigma^{3}{}_{\text{z}}\)) from the ideal positions in the vertical (\(z\)) direction.