Dislocation-driven growth of WS2/WSe2 quantum well superlattices

The synthesis of two-dimensional lateral heterojunctions with nanoscale characteristic width and sharp interfaces remains challenging. The quantum confinement effects are still difficult to create on 2D materials since widths smaller than 5 nm are necessary for quantum confinement effects and quantum well applications. In this study, we demonstrated the growth of a sub-2-nm tungsten sulfide quantum well array in a monolayer of tungsten selenide, driven by the climb of mismatch dislocation in a heterointerface due to the lattice mismatch. Width-controllable 2D quantum well superlattices are theoretically formed by the mismatch dislocation-driven growth mechanism, according to our analysis. Thus, abundant photonic electronic properties can be obtained in 2D quantum well superlattices formed at varied lateral heterointerfaces, which will support the study of topological insulators and superconductors.


Introduction
Two-dimensional (2D) lateral heterojunctions and superlattices with a series of novel properties have been generated and reported recently (Geim and Grigorieva, 2013;Liu et al., 2014;Gong et al., 2015;Li et al., 2015;Zhang et al., 2017;Chen et al., 2018;Liu et al., 2019;Shi et al., 2020;Zhang et al., 2021). Available growth methods produce featured widths in the scale of hundreds of nanometers or, at best, at micrometer scale and commonly result in rough and defective interfaces with extensive chemical intermixing Liu et al., 2015;Zhang et al., 2017;Shi et al., 2020). Quantum wells in conventional semiconductors with their unique electronic structure and quantum confinement have important applications in quantum cascade lasers, solar cells, high-electron mobility transistors, and infrared photodetectors (Faist et al., 1994;Gudiksen et al., 2002). In a 2D system, quantum well structures may be best generated by laterally sandwiching a nanoscale strip of a 2D semiconductor between two strips of another 2D semiconductor with a different band gap. It is theoretically necessary to control the width of the 2D quantum well comparable to the de Broglie wavelength of the carrier (the sub-10-nm regime and, ideally, less than 5 nm) so that quantum size effects occur. However, available growth methods only produce features with widths in the micrometer or, at best, 100 nm scale. Therefore, implementing quantum confinement effects in 2D systems remains challenging. In recent years, several studies have reported observations of quantum wells in 2D systems. Han et al. (2018) and Zhu et al. (2020) reported the fabrication methods of onedimensional MoS 2 quantum channels in WSe 2 -MoS 2 and MoSe 2 -MoS 2 hetero-systems, respectively.
Here, we report the growth of high-quality sub-2-nm-wide quantum wells within semiconductor monolayers, making use of the lattice mismatch between two semiconducting materials in the 2D lateral heterojunctions. The growth was controlled by individual misfit dislocations formed at the lateral heterointerface between a WSe 2 and a WS 2 . Atomic resolution scanning transmission electron microscopy (STEM) images revealed that these tungsten sulfide quantum wells were less than 2 nm in width and formed fully coherent lateral interfaces with the tungsten selenium monolayer matrix without extended defects.
These results showed that the insertion of metal and S atoms into the dislocation cores induced dislocation climb, with concomitant selective substitution of Se atoms around the dislocation core by S atoms. The substitution process, driven by the local strain field, led to the growth of WS 2 quantum well arrays laterally sandwiched in the WSe 2 monolayers.
Theoretically, the mismatch dislocation at the interface needed to be formed in intervals to release strain. Repetition of the misfit dislocationdriven growth mechanism formed parallel WS 2 quantum wells, and these parallel 2D narrow nano-bands were quantum well superlattices. Considering the large variety of 2D materials, 2D quantum well superlattices in varied lateral heterojunctions will display diverse photonic electronic properties; therefore, controllable width 2D quantum well superlattices are expected to be fabricated.
2 Experimental details 2.1 Growth of monolayer WSe 2 A quartz boat loaded with WSe 2 powder (~1 g) was located at the center heating zone of the furnace, as shown in Figure 1A, and a clean silica (~300 nm)/Si substrate was located at the terminal of the furnace as the growth substrate. The horizontal distance between the powder and the silicon wafer was kept between 11 and 15 cm. During the process of temperature increase, the growth substrate was placed upstream of the source, and the airflow was set to 300 sccm (along the "step 1" arrow in Figure 1A) for 15 min to remove the undesired oxygen and water from the tube. The Ar airflow was then kept at 50 sccm. When the central heating zone reached the target temperature of 1150°C, the 50 sccm airflow with the transferred direction (along the "step 2" arrow in Figure 1A) ensured the growth substrate was located downstream of the source and then maintained for 10 min for growth. Next, the airflow direction was reversed (along the "step 1" arrow in Figure 1A) to stop the growth process and allow it to naturally cool down to room temperature. The entire process occurred under ambient pressure in an argon atmosphere.

Growth of WSe 2 /WS 2 2D quantum well superlattices
To obtain the WSe 2 /WS 2 2D quantum well, the monolayer WSe 2 was chosen as a seed to further the epitaxial growth of the monolayer WS 2 . At the same time, quantum wells started forming at the interfaces of WSe 2 /WS 2 lateral heterojunctions. For the epitaxial growth of WS 2 , the WS 2 powder and prepared monolayer WSe 2 (substituted for clean substrate and WSe 2 powder) were placed at the same position in another specified CVD system similar to the system used for WSe 2 growth. Likewise, during the period of temperature increase, the growth substrate was placed upstream of the source and the airflow (along the "step 1" arrow in Figure 1A) was set to 300 sccm for 15 min, and then reduced to 100 sccm and kept at that airflow rate. When the central heating zone reached the target temperature of 1120°C, the airflow was set to 100 sccm in the transferred direction (along the "step 2" arrow in Figure 1A), ensuring the growth substrate was located downstream of the source, and then maintained for 5 min for WS 2 epitaxial growth. After that, the airflow direction was reversed (along the "step 1" arrow in Figure 1A) to stop the epitaxial growth process and allow it to naturally cool down to room temperature. The entire process occurred under ambient pressure in an argon atmosphere.

Characterization
Optical microscopy and STEM were used to characterize the morphologies of the nano-heterojunctions. The Raman spectra were performed using a Renishaw confocal Raman system excited by a 488nm laser at room temperature. The applied laser power was set to 5%, and the exposure time was approximately 0.1 s. STEM imaging and EELS analysis were carried out using a Thermo Scientific Themis Z 3.2 system equipped with a cold field-emission gun and a mirror lens corrector operating at 300 kV. All STEM experiments were completed at room temperature. The strain distribution of the nanostructure was calculated based on the geometric phase analysis method using the FRWRtools plugin for DigitalMicrograph (www.physik.hu-berlin.de/ en/sem/software/software_frwrtools).
The STEM samples were prepared using a poly-methylmethacrylate (PMMA)-assisted method. PMMA was spin-coated onto the heterojunction sample until the PMMA layer fully covered the heterojunction sample and then baked at 180°C for 3 min. Afterward, the wafer was immersed in a saturated 0.2 M NaOH solution to etch the SiO 2 layer. After the sample coated with PMMA was separated from the silicon wafer, it was transferred into fresh deionized water, repeatedly, to wash away residual contaminants and then fished by a conventional lacey carbon film TEM grid. The astransferred sample was dried naturally in the ambient environment and then immersed in acetone overnight to clean up the PMMA coating layers. All the STEM samples were baked at 150°C for 6 h to avert unexpected contamination from hydrocarbon.

Results and discussion
3.1 Lateral heterojunction with 2D quantum wells Figure 1B is the synthesis strategy diagrammatic sketch of the WSe 2 /WS 2 2D quantum well, and Figure 1B① and Figure 1B② show the idealized schematic sketch of the monolayer WSe 2 and the WSe 2 / WS 2 2D quantum well, respectively. The WS 2 quantum well was inserted into the monolayer WSe 2 , which started to grow from the WSe 2 /WS 2 interface, as depicted in Figure 1B②. The width of the quantum well in Figure 1B② is exaggerated to make the display easy to recognize and understand. Figure 1C is the optical image of the monolayer WSe 2 /WS 2 lateral heterojunction synthesized on a silica/ silicon substrate; it shows two concentric regions with slightly different optical contrast due to the refractive index and thickness difference between tungsten selenide and tungsten sulfide (Henrie et al., 2004;Blake et al., 2007). Here, the nanoscale WS 2 2D quantum wells formed at the WSe 2 /WS 2 interface but were difficult to recognize in the optical image due to the low enlargement factor of optical microscopy. To further explore the spatial modulation of structural and optical properties in WSe 2 /WS 2 lateral heterostructures, the confocal Raman microscope was used to characterize the nanostructure. We picked up three points marked ''1,″ ''2,″ and ''3″ in Figure 1C for the Raman study, where ''1'' (black point), ''2'' (red point), and ''3'' (blue point) are located at the internal tungsten selenium, the WSe 2 /WS 2 interface, and the epitaxial tungsten sulfide area, respectively. The Raman spectra at different locations showed distinct differences: the internal region Raman spectrum had a significant peak at 250 cm −1 (black line in Figure 1D), consistent with the A 1g resonance pattern of WSe 2 , and the peripheral region Raman spectrum had two significant peaks, at 350 cm −1 and 419 cm −1 (blue line in Figure 1D), corresponding to the E 1 2g and A 1g resonance patterns of WS 2 . Significantly, the Raman spectrum of the WSe 2 /WS 2 interface showed both the resonance modes of WSe 2 and the resonance modes of WS 2 (red line in Figure 1D), which indicate that tungsten selenium and tungsten sulfide coexist well within the same triangular domain.

Strain analysis in a WSe 2 /WS 2 2D quantum well
These WS 2 quantum wells extending from the WSe 2 /WS 2 interface, mostly distributed in parallel, were generally observed in the lateral WSe 2 /WS 2 heterojunction samples, as shown in the STEM image in Figure 2A. Figure 2B is the enlarged view of Figure 2A, and the clear boundaries between WSe 2 and WS 2 in the WSe 2 /WS 2 2D quantum well are apparent. Also, the strain distribution corresponding to Figure 2B is given in Figure 2C. The perfect lattice from the monolayer WSe 2 was used as a reference for calculating the strain. In the perfect monolayer, the lattice constant of WSe 2 was~4% larger than that of WS 2 , which indicates that the WS 2 quantum well had high and uniform tensile strain along its growth direction, leading to the observed dislocationfree transverse interface. However, the situation was different in the direction perpendicular to the growth direction, where there was a comparatively larger lattice mismatch between WS 2 and WSe 2 (~4.3 ± 0.5%), as revealed by the calculated strain distribution spectrum. Figure 3A shows a 2D quantum well in which the monolayer of the WS 2 nanoribbons is laterally sandwiched between two monolayer WSe 2 nanoribbons. As shown in the STEM image in Figure 3A, the Se and S atomic sites are distinguished from the image contrast due to different atomic numbers (Krivanek et al., 2010;Zhou et al., 2012), where the WS 2 quantum well shows a lower image intensity than the surrounding monolayer WSe 2 , and the WS 2 /WSe 2 interface is marked by red dashed lines.

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The high-resolution STEM-annular dark-field (ADF) image of a WS 2 quantum well is shown in Figure 3B; the yellow and red circles mark Se and S atoms, respectively. It was observed that the~1.2 nm WS 2 quantum well was embedded in a single layer of WSe 2 and growing along the hexagonal armchair orientation. Correspondingly, Figure 3C is the idealized atomic structural model of the WS 2 quantum well according to Figure 3B. The interface is highlighted by the red and black dashed lines in Figures 3B,C, respectively. It is obvious that there are no mismatches or defects at the interface, which means a fully coherent lateral interface was formed.
3.4 Formation mechanism of WS 2 quantum wells at the WSe 2 /WS 2 lateral interface Similar to film growth, strain relaxation at the epitaxial interface with intrinsic lattice mismatch produces mismatch dislocation once the critical width is exceeded (Matthews and Blakeslee, 1974;Jain et al., 1997). For the lateral WSe 2 /WS 2 heterostructures, the mismatch dislocation array spaced~8 nm in the zigzag orientation was expected to alleviate the lattice strain due to the presence of~4% lattice mismatch between WSe 2 and WS 2 . Through careful observation, it was found that WS 2 quantum wells relied on a dislocation core for growth at the lateral WSe 2 /WS 2 heterointerface in general, and further growth was considered driven by misfit dislocation climb. As shown in Figure 4A, the insertion of one W atom and two S atoms from the gas source was considered initiation of the dislocation-driven growth as such dislocation drove the W and S atoms to invade the WSe 2 along the hexagonal zigzag orientation, which is consistent with our experimental results. According to statistical analysis, the width of WS 2 quantum wells is about 1.2 nm, which is equivalent to the width of the four WS 2 unit cells. A four-unit-cell-width and a one-unit-cell-width WS 2 nanoseed, shaded in light red in Figure 4B,are shown penetrating to the WSe 2 monolayer to propagate the quantum well.
Theoretically, the formation of the mismatch dislocation at the interface was required per each~8 nm interval to release strain. After repeating the aforementioned growth mechanism, parallel WS 2 quantum wells were formed, and these parallel 2D narrow nano-bands were quantum well superlattices, as shown in Figure 4C.

Promising 2D quantum well superlattices with atomically sharp lateral interfaces
According to the aforementioned results, there is potential to generate a 2D quantum superlattice, consisting of equally spaced 2D quantum wells, if growth conditions are precisely controlled. The WS 2 quantum well grown by this mechanism formed a type II band arrangement with the surrounding monolayer WSe 2 , as shown in Figure 4B.
Meanwhile, the n-type doped ultranarrow WS 2 nanoribbons were expected to be conductors due to the type II band alignment. Nanoribbons of higher carrier concentrations can be obtained by this process of modulation doping as ionizing donors are distributed in the WSe 2 region and thus reduce Coulomb scattering in WS 2 . Furthermore, the quantum wells shown in Figure 5A are not evenly spaced, and such a phenomenon could be attributed to the periodic array that was not initially formed at the interface. The bottom area in Figure 5B is an enlarged display of the red dotted frame in Figure 5A. There are different energy band distributions in the region of tungsten sulfide and tungsten selenide. From Figure 5A and Figure 5B, it can be concluded that the length distribution of quantum wells ranges from ten nanometers to a few microns, while the spacing between the quantum wells is about 8 nm, which is basically consistent with the previous theoretical analysis results. High-quality 2D semiconductor quantum well superlattices may be prepared by a misalignment drive mechanism if the growth parameters of the chemical vapor deposition (CVD) system are stably controlled.

Conclusion
To summarize, we successfully synthesized sub-2-nm quantum well arrays in WSe 2 /WS 2 lateral heterojunctions. High-resolution STEM images showed the atomically sharp lateral interfaces between the  Frontiers in Materials frontiersin.org WS 2 quantum well and monolayer WSe 2 . Among them,~4% lattice mismatch between WSe 2 and WS 2 monolayers led to misfit dislocation arrays with an average spacing of 8 nm at the lateral heterointerface. After that, dislocations drove the corresponding atoms to penetrate along the hexagonal armchair orientation, which plays a key role in the efficient growth of quantum wells. According to the results of the WSe 2 /WS 2 lateral heterojunction system, such quantum well superlattice structures are expected to be formed in varied lateral heterojunctions. Considering the large variety of 2D materials, 2D quantum well superlattices in varied lateral heterojunctions will display abundant photonic electronic properties, which provide new roads for the study of topological insulators and superconductors.