In recent years, there have been many studies on the preparation of high-quality transition-metal dichalcogenides (TMDCs), which have a variety of applications including optoelectronics, spin-tronics, and valleytronics. The most attractive properties of TMDCs as candidates for such diverse applications are layer and phase dependence. Therefore, the controlled growth of various phases of TMDCs and the stacking of distinct layers have emerged as popular research realms. In previous research, people have summarized the theory of supersaturation-dependent crystal growth by continuously refining the classical BCF (Burton-Cabrera-Frank) theory. However, on the one hand, supersaturation-dependent growth theory is often employed to provide a theoretical interpretation for preparing a certain phase that lacks systematicity, and on the other hand, the parameter control involved in such theories is difficult to measure and regulate experimentally. Our study focuses on controlling the temperature distribution to affect the supersaturation degree and achieve the one-step controllable growth of three phases of WSe₂ (single layer, 3R, and 2H) directly on the different regions at the substrate under a temperature gradient. By regulating the temperature distribution, we can change the supersaturation distribution and successfully prepare spiral plates of WSe₂ by screw-dislocation-driven (SDD) growth mode, transitioning from layer-by-layer (LBL) growth mode, where we observe two orders of magnitude of second harmonic generation (SHG) signal enhancement in the spiral-stacked region. These different vertically stacked TMDCs materials will offer diverse candidates for probing the physical properties of layered materials and exploring new applications in functional electronic and optoelectronic devices.

Our experiments adopt the reverse flow method to control the growth time and growth temperature in the growth process and shorten the cooling time by a rapid cooling method. With the help of the supersaturation-dependent crystal growth theory and our experimental methods, we establish a connection between the temperature distribution, supersaturation distribution, and growth result distribution (Figs. 1 and 3). By the morphological characterization (Figs. 1 and 3) such as optic microscope (OM), atomic force microscopy (AFM), and scanning electron micrographs (SEM), we analyze the stacking mode of samples. Meanwhile, we further analyze the optical properties of the samples and demonstrate the growth of spiral structures by the spectroscopic (Figs. 2 and 4) characterization such as the Raman spectrum, photo luminescence (PL) spectrum, SHG spectrum, and spectrum mapping.

We successfully prepare monolayer, 2H-phase , and 3R-phase of WSe₂ in our supersaturation-controlled growth experiments and demonstrate their distributions [Fig. 1 (c)]. Due to the different atomic structures of the two stacking phases [Figs. 1 (d) and (e)], they exhibit different morphologies under OM, and AFM [Figs. 1 (f)-(m), Figs. 2 (a)-(c)]. Different atomic structures in different stacks will produce different electronic structures to affect the optical properties of the material. To reveal different-induced interlayer coupling in the 3R-phase and 2H-phase WSe₂, we perform PL and Raman spectroscopy on both stacking and single layer regions. The Raman spectrum of the two phases reveals different trends with increasing stacking layers, generated by different interlayer coupling [Figs. 2 (d) and (e)]. The indirect bandgap transition can be observed in the stacking area [Fig. 2 (f)], which originates from the interlayer electronic coupling. The indirect transition energy reflects the stability of the electronic structure and the strength of interlayer coupling: the lower transition energy means more stable electronic structure and stronger interlayer coupling, which is also reflected in our growth results. We show the above conclusions more vividly by spectrum mapping [Figs. 2 (g)-(i) and Figs. 2 (k)-(m)]. Symmetry also affects interlayer coupling, which will be displayed by SHG mapping. According to the supersaturation-dependent crystal growth theory, the growth mode transition from LBL to SDD is attributed to the changing supersaturation distribution. The different saturation distributions will also affect the complexity in SDD mode, which is demonstrated by OM and AFM (Fig. 3). After observing the emergence of the spiral structure, we investigate it by spectroscopy method. Similar to the Raman spectrum of 3R-phase WSe₂ under the interlayer coupling, the Raman signal of the spiral WSe₂ is also manifested as the weakened trends with the increasing number of stacking layers [Fig. 4 (a)]. In addition to interlayer coupling, the strain also has a significant influence on the optical properties of the spiral WSe₂, which is evidenced by the continuum changes of the PL spectral and aberrations in the polarization SHG [Figs. 4 (b), (i), and (l)]. According to the spectroscopic law of stacked WSe₂ discussed previously, we demonstrate the growth kinetics of the two-armd spiral structure by PL and SHG mapping [Figs. 4 (c)-(h) and Fig. 4 (k)]. Towards the armchair direction, we find two orders of magnitude SHG enhancement in the center position [Fig. 4 (j)].

By adopting the reverse flow chemical vapor deposition strategy, we accurately control the gradient distribution of the growth temperature, which determines the supersaturation distribution. The controllable growth of single layer, 2H-phase, 3R-phase, and spiral structure WSe₂ is realized. Additionally, we demonstrate the growth process of the spiral structure and elucidate the effect of interlayer coupling and strain on the optical properties of stacking WSe₂ via morphological and spectroscopic characterization. The_{supersaturation-dependent crystal growth theory is utilized to analyze the relationship between the number of screw-dislocation arms of spiral WSe2 and different supersaturation distributions. Meanwhile, we find two orders of magnitude in the center of spiral WSe2, and our study paves the way for two-dimensional semiconductor multi-phase controlling growth, structural design, stacking optical properties regulation, and optoelectronic devices.}