Moore's Law, the doubling of transistors per chip every two years, necessitates the development of next-generation transistors with sub-nanometer channel thicknesses. While 2D materials offer atomically sharp surfaces and scalability to the monolayer limit, their lower charge carrier mobility and higher contact resistance compared to 3D semiconductors pose significant challenges. This research addresses these challenges by employing a high-throughput screening approach to identify high-mobility 2D materials. The primary goal is to find 2D materials capable of outperforming silicon in ultra-scaled transistors, mitigating limitations such as quantum confinement, surface roughness, and dangling bonds which severely degrade silicon's mobility at sub-nanometer scales. The use of 2D materials promises reduced gate length, lower switching capacitance, and reduced power consumption. However, reduced dimensionality intrinsically leads to higher carrier scattering rates and lower mobilities. Additionally, forming Ohmic contacts and avoiding Fermi-level pinning remain substantial obstacles. Advanced ab initio computational methods are crucial in identifying high-mobility compounds and understanding the microscopic mechanisms limiting carrier transport. Previous computational searches have identified potential high-mobility candidates, but often relied on approximations like the relaxation time approximation and neglected factors such as spin-orbit coupling. This study leverages the Materials Cloud 2D Database (MC2D), which contains experimentally synthesized 3D layered compounds amenable to exfoliation, to perform a more comprehensive high-throughput screening.

Several groups have computationally searched for high-mobility 2D materials. Some studies focused on binary borides, nitrides, and oxides, identifying candidates with mobilities exceeding 1000 cm²/Vs, but often employing approximations like the relaxation time approximation and neglecting spin-orbit coupling except in specific cases. Other research considered electron-doped and hole-doped TMDs and phosphorene, but also lacked comprehensive consideration of spin-orbit coupling. A study on elemental pnictogens predicted high hole mobility for antimonene, but again used the relaxation time approximation. Large-scale high-throughput searches have become feasible with the development of 2D materials databases like MC2D and C2DB, offering thousands of potential candidates. A previous study screened the MC2D database, but without fully considering the impact of spin-orbit coupling on the band structure and transport properties. This study aims to build upon this existing research, emphasizing a more systematic high-throughput screening approach and providing more accurate ab initio data by performing full Boltzmann transport calculations.

The methodology comprises three main steps: (i) pre-selecting high-mobility candidate materials from the MC2D database; (ii) performing high-precision carrier mobility calculations for top candidates using the ab initio Boltzmann transport equation (aiBTE); and (iii) conducting an in-depth analysis of the most promising compound, WS₂. The high-throughput screening workflow begins with the MC2D database, which contains 5619 layered materials, with a subset of 1036 deemed easily exfoliable. Dynamic stability is assessed via phonon dispersion calculations, resulting in a set of 258 dynamically stable compounds. Density functional theory (DFT) calculations are performed on 166 non-metallic compounds from this set (Set A). This involves computing ground-state structures, band structures, and conductivity effective masses (initially without spin-orbit coupling (SOC) to reduce computational cost). The selection criteria for Set B include low effective masses (<1 me) and intermediate band gaps (0.1 < Eg < 3 eV). SOC is then included in the effective mass calculations for Set B (95 compounds), resulting in Set C (50 compounds). Mobilities are estimated using both a 2D Fröhlich model (found to be inaccurate) and Emin's formula. Set D (12 compounds) is selected based on mobilities exceeding 100 cm²/Vs in Emin's model. Full aiBTE calculations are performed for these materials, with SOC included. For the most promising compounds, GW quasiparticle calculations are performed, and quadrupole corrections, as well as scattering by ionized impurities and extended defects, are included to obtain the most accurate mobility estimates. The aiBTE calculations involve solving the Boltzmann transport equation using the EPW code with Wannier-Fourier interpolation to obtain accurate carrier scattering rates and mobilities. Long-range Fröhlich electron-phonon couplings are included, along with quadrupole corrections for specific materials. Calculations include scattering by ionized impurities and extended defects. The aiBTE methodology also involves detailed convergence tests to ensure accurate results.

The high-throughput screening identifies monolayer WS₂ as the most promising p-type 2D semiconductor. Initial calculations (without all refinements) predict very high hole and electron mobilities for several compounds: antimonene (h-Sb) with high hole mobility, WSe₂ with high hole mobility, and WS₂ with exceptionally high hole mobility; bismuthene (h-Bi) and Bi₂Te₃Se₂ (skippenite) show high electron mobility. For WS₂, the calculated room-temperature hole mobility is initially extremely high (3021 cm²/Vs at low carrier concentration), significantly exceeding previously reported theoretical values. The exceptionally high hole mobility in WS₂ is attributed to the significant role of SOC. SOC splits the valence band maximum at K, suppressing inter-valley and intra-valley scattering, leading to low scattering rates and ultimately high mobility. The impact of various factors on the WS₂ hole mobility is thoroughly investigated. Using DFT without SOC yields a drastically reduced mobility (99 cm²/Vs). GW quasiparticle calculations increase the mobility slightly (3309 cm²/Vs). A higher carrier concentration (10¹³ cm⁻²) reduces mobility considerably (2087 cm²/Vs). Quadrupole corrections further reduce the mobility (1342 cm²/Vs). Ionized impurity scattering, using a typical defect concentration of 10¹² cm⁻², significantly reduces the mobility (509 cm²/Vs). Scattering by extended defects (grain boundaries or ripples), considered for sizes ranging from 30 to 500 nm, also dramatically reduces the mobility (240 cm²/Vs for 30 nm defects). In contrast to the hole mobility, the electron mobility in WS₂ is primarily governed by electron-phonon scattering, and the calculated values align reasonably well with experimental data. The study also reports mobilities for other materials in Set D (Sb, GeSe, SnTe, ZrSe₂, HfSe₂, WTe₂, SiH, Tl₂O, Bi₂Te₃Se₂, TiNCl, and TiNBr), alongside MoS₂, Bi, GeS, and WSe₂, providing a comprehensive comparison.

The findings highlight that while WS₂ possesses inherently ultra-high hole mobility, its practical performance is significantly limited by defects and interfaces. The discrepancy between the predicted intrinsic hole mobility and experimental results is attributed to factors like DFT band structure accuracy limitations, carrier concentration variations, quadrupole couplings, various scattering mechanisms (impurity and extended defects), contact resistance, and gate dielectric/substrate effects. The importance of Ohmic contacts is emphasized, as Schottky contacts introduce high contact resistance, lowering the apparent mobility. The use of doped TMDs as contacts is suggested as a promising strategy to reduce contact resistance. The influence of the dielectric environment is also considered, with remote phonon scattering potentially playing a significant role. The study emphasizes the need for comprehensive ab initio calculations to accurately predict carrier mobilities in 2D materials, as simplified approaches can lead to inaccurate results, especially for materials with weak electron-phonon coupling where extrinsic effects can dominate. The results suggest that future research should focus on minimizing defect density and optimizing channel, contacts, and dielectrics, rather than solely searching for novel materials, to achieve high mobility in 2D-based transistors.

This research demonstrates that WS₂ is an inherently ultra-high mobility semiconductor. However, its full potential is currently hampered by defects and interfacial effects. The study strongly suggests that controlling defect density and optimizing the interaction between the channel material, contacts, and gate dielectric are crucial for realizing the potential of WS₂ in ultra-scaled electronics. Future research should focus on addressing these extrinsic factors to unlock the high mobility of WS₂ in practical devices.

The study acknowledges several limitations. The calculations do not fully account for free-carrier screening of piezoacoustic and polar optical phonon scattering. Higher-order phonon scattering processes, such as electron-two-phonon scattering, are also not explicitly included and could influence the mobility. The model used for extended defect scattering is a simplification, and more sophisticated models might be necessary for a more precise estimation of the impact of extended defects. Lastly, the effects of the gate dielectric and substrate, including remote phonon scattering, are not comprehensively addressed in the calculations but only qualitatively estimated. This might underestimate the ultimate achievable performance in actual devices.