Monte Carlo Study of Electronic Transport in Monolayer InSe

Abstract

The absence of a band gap in graphene makes it of minor interest for field-effect transistors. Layered metal chalcogenides have shown great potential in device applications thanks to their wide bandgap and high carrier mobility. Interestingly, in the ever-growing library of two-dimensional (2D) materials, monolayer InSe appears as one of the new promising candidates, although still in the initial stage of theoretical studies. Here, we present a theoretical study of this material using density functional theory (DFT) to determine the electronic band structure as well as the phonon spectrum and electron-phonon matrix elements. The electron-phonon scattering rates are obtained using Fermi’s Golden Rule and are used in a full-band Monte Carlo computer program to solve the Boltzmann transport equation (BTE) to evaluate the intrinsic low-field mobility and velocity-field characteristic. The electron-phonon matrix elements, accounting for both long- and short-range interactions, are considered to study the contributions of different scattering mechanisms. Since monolayer InSe is a polar piezoelectric material, scattering with optical phonons is dominated by the long-range interaction with longitudinal optical (LO) phonons while scattering with acoustic phonons is dominated by piezoelectric scattering with the longitudinal (LA) branch at room temperature (T = 300 K) due to a lack of a center of inversion symmetry in monolayer InSe. The low-field electron mobility, calculated considering all electron-phonon interactions, is found to be 110 cm2V−1s−1, whereas values of 188 cm2V−1s−1 and 365 cm2V−1s−1 are obtained considering the long-range and short-range interactions separately. Therefore, the calculated electron mobility of monolayer InSe seems to be competitive with other previously studied 2D materials and the piezoelectric properties of monolayer InSe make it a suitable material for a wide range of applications in next generation nanoelectronics.

Understanding high-field electron transport properties and strain effects of monolayer transition metal dichalcogenides

“…The electron transport in various 2D materials and devices have been widely studied using different theoretical/computational methods, including Monte Carlo (MC), Wigner equation, nonequilibrium Green's functions, and master equation for the density matrix [14][15][16]. Particularly, the MC method has been applied to study silicene and germanene, [17] InSe, [18] and graphene. [19][20][21][22][23] Regarding the high-field electron transport in MX2, Ferry [24] studied MoS2 and WS2 using MC method: the electron band structure and the scattering rates approximated by analytic models with parameters taken from first-principles calculations and experiments; MoS2 is found to have a higher saturation velocity than WS2.…”

Layered Semiconducting 2D Materials for Future Transistor Applications

“…Each I EFF data point is obtained with an applied V DD = 0.75 V after aligning all I D ‐ V GS curves at I OFF = 2 × 10 −3 μA μm −1 ( V GS = 0 V). Filled symbols (circle [ 42 ] and square [ 43 ] ) refer to the theoretical phonon‐limited mobility of monolayer 2D materials solved by the BTE with EPC matrix elements from first‐principles calculations. Open symbols refer to the theoretical phonon‐limited mobility of monolayer 2D materials calculated by Takagi formula [ 48 ] with effective deformation potential and mass extracted from first‐principles (triangles, [ 44 ] cross, [ 45 ] square, [ 46 ] and diamonds [ 47 ] ).…”

“…[ 46,101 ] However, due to the lack of center of inversion symmetry, a recent full‐band Monte–Carlo calculation has shown that the mobility of monolayer InSe is around 100 cm 2 V −1 s −1 with the long‐range electron–phonon interaction considered. [ 43 ] Even with this electron mobility, monolayer InSe still keeps good performance contributed to its small effective mass for short gate length transistors. But, a “Mexican hat” shape‐like valence band structure with low dispersion leading to a very large hole effective mass makes the monolayer InSe unsuitable for p‐type transistor applications.…”

“…The data points in Figure 3c for various 2D monolayer materials are based on the theoretical predicted effective masses and mobility. [42][43][44][45][46][47] The effective mass is extracted from the lowest energy valley from the band structure calculated by DFT. The mobility for the data points is the phonon-limited mobility, which is the highest mobility a material can achieve.…”

“…It ignores the wave function overlap, anisotropism of the deformation potential, and intervalley scatterings, and thus the mobility value may often be overestimated. [49] A higher level electron-phonon coupling (EPC) matrix elements from ab initio calculations integrated into Boltzmann transport equation (BTE) is a more rigorous way to calculate the phonon-limited mobility (filled symbols in Figure 3c) [42,43,[49][50][51][52][53] but only a few 2D materials had been studied using such calculation-intensive method.…”