Advanced techniques for analysis of XRD patterns and optical absorption spectra were employed to derive in-depth physical insights into the structure and properties of quantum nanocrystals of the cubic modification of CuInS 2 synthesized by a sonochemical route. Three-dimensional assemblies of the synthesized nanocrystals deposited as thin films exhibit multifractal surface morphology, with the multifractal singularity spectral widths being far above the monofractal limit. The widths of the multifractal spectra indicate that films grown by the conventional chemical method are structurally richer and at the same time characterized by higher complexity of the surface than those grown under sonochemical conditions, while the values of the Holder exponent corresponding to their maxima are rather close. In both cases, the multifractal spectra are right-skewed, with a positive asymmetry parameter a s and domination of high fractal exponents. The right-skewness is more pronounced in the case of sonochemically deposited films. Lacunarity in the chemically deposited samples is smaller than in the sonochemically deposited ones, regardless of the particular scale on which the comparison is carried out, indicating a higher homogeneity and, in parallel, higher translational invariance in the former case. Somewhat larger heterogeneity and wider distribution of gap sizes in the sonochemically deposited samples are attributed to acoustic streaming phenomena that take place within the ultrasonically irradiated reactor under heterogeneous sonochemical conditions. The average particle size as well as the size distribution and the degree of structural disorder can be controlled by an appropriate control of the reactor content and its exposure to ultrasonic irradiation in the course of deposition process. This, in turn, allows appropriate tuning of the material's band gap energy, which is physically based on both intradot size-quantization effects and the interdot charge carrier coupling phenomena. Considering the substantial relevance of the title material in optoelectronics and solar cell technology, the physically based design of the material's properties demonstrated in the present study can open certain new directions in the development of solar cells based on inorganic semiconductor systems.