Intrinsic Anomalous Scaling and Long-Range Surface Correlations in SnS Thin Films Enabling High-Performance Photodetectors

Self-affine fractal morphology arising from non-equilibrium growth processes is a defining feature of low-dimensional materials and plays a crucial role in governing their electronic and optoelectronic behavior. Despite this, the impact of nanoscale fractal geometry and dynamic scaling on photodetector performance remains insufficiently explored. In this work, we present a comprehensive investigation of the morphological evolution and optoelectronic response of thermally evaporated tin(II) sulfide (SnS) thin films with thicknesses ranging from 100 to 600 nm. Atomic force microscopy reveals a systematic transition from relatively smooth, fine-grained surfaces in thinner films (Ra ≈ 21.4 nm) to rough, island-like morphologies in thicker films (Ra ≈ 144.3 nm), indicative of multiscale surface roughening. Statistical and fractal analyses─including power spectral density, autocorrelation, height–height correlation functions, lacunarity, and topographical entropy─demonstrate a progressive enhancement in surface ordering and spatial correlation with increasing thickness. The observed decrease in fractal dimension (from 2.82 to 2.12) and increase in the Hurst exponent (from 0.18 to 0.87) indicate a transition from antipersistent to strongly persistent growth behavior. Dynamic scaling analysis yields distinct global, local, and spectral roughness exponents (α ≈ 0.84 ± 0.047; αloc ≈0.7345 ± 0.0062; αs ≈ 0.7243 ± 0.031; β ≈ 0.2820 ± 0.0334; 1/z ≈ 0.2517 ± 0.0474) that confirm intrinsic anomalous scaling governed by diffusion-limited surface dynamics. Device-level studies of Ag/p-SnS/FTO-glass photodetectors reveal a strong thickness dependence of photoresponse. While the 100 nm device exhibits high responsivity and external quantum efficiency, the 250 nm film delivers the most balanced performance, achieving a responsivity of 2.425 A/W, detectivity of 9.59 × 109 jones, external quantum efficiency of 564.8%, and ultrafast rise and decay times of 0.02 and 0.06 s, respectively. Thicker films (400–600 nm) suffer from increased recombination, leading to degraded performance. Overall, this work establishes a fractal-informed morphology engineering framework that directly links nanoscale growth dynamics with macroscopic optoelectronic performance, offering a scalable strategy for designing high-performance SnS-based photodetectors.