Two-dimensional (2D) materials like MoS₂ and In₂Se₃ are crucial for the semiconductor industry due to their atomic thickness, excellent physical properties, and processing compatibility. However, grain boundaries and crystallographic defects significantly impact device performance. Growing large-area single crystals of 2D materials is crucial for improving device performance and consistency. Current methods include phase transformation and epitaxial growth on single-crystal substrates. Epitaxial growth often involves substrates with surface atomic layers possessing 3-fold or 6-fold rotational symmetry. In materials with 3-fold symmetry, two locally most stable orientations (differing by 60°) can exist with a small binding energy difference. This small difference is easily disturbed during conventional chemical vapor deposition (CVD), leading to orientation inconsistencies. This paper addresses this challenge by introducing a quasi-equilibrium growth (QEG) method to synthesize inch-scale monolayer α-In₂Se₃ single crystals, a layered ferroelectric semiconductor promising for next-generation electronics due to its room-temperature ferroelectricity even at the 2D limit. Fluor-phlogopite is chosen as the substrate because its cleavage atomic surface shares the same 3-fold rotational symmetry as α-In₂Se₃, promoting uniform orientations.

The growth of large-area single-crystal 2D materials has been an active area of research. Phase transformation methods, involving the gradual transformation of polycrystalline films into single crystals using a seed crystal, have been applied to specific 2D materials. Epitaxial growth on single-crystal substrates, such as Cu and Al₂O₃, has also shown promise. However, challenges remain in achieving uniform orientation, especially when the binding energy difference between competing orientations is small, as is often the case in 3-fold symmetric 2D materials grown on similarly symmetric substrates. Previous work has demonstrated wafer-scale single-crystal growth of materials like hexagonal boron nitride and molybdenum disulfide using various methods, but these often involve specific substrate choices and stringent growth conditions. The authors highlight the need for new strategies to reliably induce oriented growth, overcoming the limitations of typical CVD processes that are susceptible to disturbances like uneven gas flow and inhomogeneous vapor distribution.

The researchers developed a quasi-equilibrium growth (QEG) method using α-In₂Se₃ as a model system. The process involves three steps: evaporation, crystallization, and film formation. A mixture of α-In₂Se₃ and KI powders is used as the precursor, with KI facilitating the evaporation of In₂Se₃ due to its ability to lower In₂Se₃'s melting temperature. The fluor-phlogopite substrate is positioned close (<1 mm) to the precursor powders in a semi-closed environment. The temperature is crucial; too high a temperature leads to large droplets sliding on the substrate and resulting in ribbons with random orientation. Optimal temperatures (720-760 °C) allow the formation of tiny clusters that evolve into uniformly oriented triangular or hexagonal α-In₂Se₃ samples. Rapid cooling after the evaporation step helps crystallization. The crystallization step involves nucleation and growth, where tiny clusters move and merge to form a continuous film. The reproducibility of the method is demonstrated by the consistent production of centimeter-scale films in five consecutive experiments. The QEG method exhibits a broad growth window, successfully producing monolayer single-crystal α-In₂Se₃ films over a wide range of temperatures (700-800 °C) and precursor ratios (30:1 to 90:1). The lateral size of a single α-In₂Se₃ flake could reach 1201 μm under optimized conditions (760 °C and 60:1 precursor ratio). The mechanism for single-crystal film growth is attributed to the lattice symmetry match between the fluor-phlogopite substrate and the α-In₂Se₃. The fluor-phlogopite (001) surface exhibits 3-fold rotational symmetry, matching that of α-In₂Se₃ (R3m). First-principles calculations confirm that the lowest binding energy state for the α-In₂Se₃ flake on fluor-phlogopite occurs at a 0° alignment angle, with a slightly higher energy minimum at a 60° angle. The QEG is maintained by minimizing fluctuations in precursor concentration and nucleation density through a semi-closed environment, small source-substrate distance, and the use of a liquid intermediate state. This near-equilibrium process allows the discrimination of the small energy difference between different orientations, resulting in robust single-orientation epitaxy. Various characterization techniques, including optical microscopy, AFM, EBSD, TEM, XRD, EDS, XPS, AES, and Raman spectroscopy, are employed to confirm the single-crystal nature, orientation, thickness, composition, and quality of the grown α-In₂Se₃ films. The wet transfer method is used to transfer films onto different substrates for further characterization and device fabrication. Monolayer MoS₂ flakes are grown by CVD and transferred onto the α-In₂Se₃ films for heterostructure device fabrication.

The key findings of this research include the successful development and demonstration of a quasi-equilibrium growth (QEG) method for synthesizing inch-scale single-crystal monolayer α-In₂Se₃ films on fluor-phlogopite substrates. The QEG method leverages the 3-fold rotational symmetry match between the substrate and the material to achieve uniform orientation and large-area single-crystal growth. The method is robust and reproducible, yielding high-quality films with a broad growth window. Various characterization techniques confirm the single-crystal nature, high crystallinity, and atomically flat monolayer nature of the α-In₂Se₃ films. The high crystal quality translates into superior device performance. The grown α-In₂Se₃ films exhibit high electron mobility (up to 117.2 cm²V⁻¹s⁻¹) as demonstrated in fabricated Fe-FET devices. These devices show remarkable nonvolatile memory performance, with a large hysteresis window, long retention time (over 8000 s), and robust cycling endurance (over 8000 write/erase cycles). The researchers also fabricated a vertical heterostructure device comprising monolayer α-In₂Se₃ and monolayer MoS₂, which demonstrated an even larger hysteresis window (~100 V) and exceptional retention time (over 20,000 s) and cycling endurance (over 10,000 cycles). The excellent performance is attributed to the single-crystalline nature of the α-In₂Se₃ eliminating grain boundaries and the resulting improved carrier mobility and polarization uniformity. The uniformity of the synthesized α-In₂Se₃ films is further supported by the fabrication and testing of an array of 32 α-In₂Se₃/MoS₂ heterostructure FETs, all showing high performance with hysteresis windows exceeding 95 V and on/off ratios greater than 10². This work demonstrates a significant improvement in the size and quality of single-crystal 2D α-In₂Se₃ compared to previous methods. The achieved inch-scale single crystals represent an order-of-magnitude improvement in the lateral size compared to previously reported methods.

The successful synthesis of inch-scale single-crystal monolayer α-In₂Se₃ using the QEG method significantly advances the field of 2D material growth and device fabrication. The method effectively addresses the challenge of achieving uniform orientation in epitaxial growth, particularly for materials with small energy differences between competing orientations. The high quality of the resulting films translates into superior device performance, surpassing the performance of materials obtained by previously reported methods. The demonstrated long retention times and high endurance of the Fe-FET devices highlight the potential of this material for use in high-performance non-volatile memory applications. The results from the α-In₂Se₃/MoS₂ heterostructure device showcase the versatility of this material and its compatibility for integration into complex device structures. The QEG method presented offers a new pathway towards the scalable production of high-quality 2D materials, opening avenues for diverse applications in electronics and beyond.

This research presents a novel quasi-equilibrium growth (QEG) method for producing high-quality, inch-scale single-crystal monolayer α-In₂Se₃ films. The method successfully overcomes the challenges of achieving uniform orientation in 2D material epitaxy. The resulting films exhibit superior electronic properties and exceptional nonvolatile memory performance in fabricated devices, exceeding the capabilities of previously reported methods. This work opens up opportunities for large-scale integration of high-performance 2D ferroelectric devices and lays the groundwork for future research in this exciting area.

While the QEG method shows significant advantages, some limitations exist. The current study primarily focuses on α-In₂Se₃; further investigations are needed to assess its applicability to other 2D materials. The semi-closed environment used might limit scalability for truly large-scale wafer-level production. Although the method demonstrates a wide process window, optimizing the growth parameters for specific applications or different substrates may be required. The long-term stability of the devices under various operating conditions also needs to be extensively evaluated.