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In recent years, neural networks have achieved phenomenal success across a wide range of applications. They have also proven useful for solving differential equations. The focus of this work is on the Poisson–Boltzmann equation (PBE) that governs the electrostatics of a metal–oxide–semiconductor capacitor. We were motivated by the question of whether a neural network can effectively learn the solution of PBE using the methodology pioneered by Lagaris et al. [IEEE Trans. Neural Netw. 9 (1998)]. In this method, a neural network is used to generate a set of trial solutions that adhere to the boundary conditions, which are then optimized using the governing equation. However, the challenge with this method is the lack of a generic procedure for creating trial solutions for intricate boundary conditions. We introduce a novel method for generating trial solutions that adhere to the Robin and Dirichlet boundary conditions associated with the PBE. Remarkably, by optimizing the network parameters, we can learn an optimal trial solution that accurately captures essential physical insights, such as the depletion width, the threshold voltage, and the inversion charge. Furthermore, we show that our functional solution can extend beyond the sampling domain. [ABSTRACT FROM AUTHOR]

Borophene, the lightest member of mono-elemental 2D materials family, has attracted much attention due to its intriguing polymorphism. Among many polymorphs, digitally discovered 8-Pmmn stands out owing to its unique tilted-Dirac fermions. However, the property of interfaces between 8-Pmmn and metal substrates has so far remained unexplored, which has critical importance of its application in any electronic devices. Here, with the help of density functional theory, we show that the unique tilted-Dirac property is completely lost when 8-Pmmn borophene is interfaced with common electrode materials such as Au, Ag, and Ti. This is attributed to the high chemical reactivity of borophene as observed from crystal orbital Hamilton population and electron localization function analysis. In an effort to restore the Dirac property, we insert a graphene/hexagonal-boron-nitride (hBN) layer between 8-Pmmn and metal, a technique used in recent experiments for other 2D materials. We show that while the insertion of graphene successfully restores the Dirac nature for all three metals, hBN fails to do so while interfacing with Ti. The quantum chemical insights presented in this work may aid in to access the Dirac properties of 8-Pmmn in experiments. [ABSTRACT FROM AUTHOR]

A recent demonstration of nonvolatile resistive switching in monolayer hexagonal boron nitride (h-BN) has paved the way for the development of the thinnest memory devices feasible. Nevertheless, the exact mechanism of such remarkable resistive switching has remained obscure, which may hinder the optimization of such attractive technology. Here, we present the first dynamic description of the resistive switching process in a Ni/monolayer h-BN/Ni device at an atomistic level by employing reactive molecular dynamics simulations. We show that with the application of a suitable bias, the h-BN layer moves vertically and peels off Ni ions from the electrode, which gets adsorbed in the N vacancy center. From density-functional-theory based electron-localization-function calculations, we confirm that N vacancy generates highly delocalized electrons around the vacancy location resulting in the adsorption of Ni ions, though such a phenomenon is not likely in case of B vacancy due to the absence of electronic states around the defect center. We demonstrate the restoration of Ni ions with the application of reverse bias in case of bipolar switching, and by rising temperature in case of unipolar switching, which agrees with the experimental observations. Finally, we conduct ab initio quantum transport calculation to find an increase in zero-bias conductivity of about 7.4 times after the Ni ion adsorption. This atomistic insight enables precise defect-engineering in 2D materials for the realization of h-BN based high-performance memristive crossbar array. [ABSTRACT FROM AUTHOR]

The insertion of a graphene (or h-BN) layer in a two-dimensional (2D) MoS2–metal interface to de-pin the Fermi level has been a common strategy in experiments. Recently, however, the 2D material space has expanded much beyond transition metal dichalcogenides, and it is not clear if the same strategy will work for other materials. Here, we select a family of twelve emerging, commercially available 2D semiconductors with the work function range of 3.8–6.1 eV and study their interfaces with metals in the presence and absence of the graphene buffer layer. Using the density functional theory, we show that the graphene buffer layer preserves the ideal Schottky–Mott rule to a great extent when the interfaces are made with Ag and Ti. However, the h-BN buffer layer does not yield a similar performance since its electrons are not as localized as graphene. It is further observed that even graphene is not very effective in preserving the ideal Schottky–Mott rule while interfacing with high work function metals (Au, Pd, and Pt). The quantum chemical insights presented in this paper could aid in the design of high-performance electronic devices with low contact resistance based on newly developed 2D materials. [ABSTRACT FROM AUTHOR]

First-principles-based device models are in demand in the semiconductor industry to assess the impact of new materials at very early phases of the technology development. Existing models for the 2D metal–oxide–semiconductor field-effect transistor work under quasi-static limit and can only be used for designing circuits operating under half of the transistor's intrinsic cut-off frequency. Here, we develop a compact device model for phosphorene-based transistor that takes into account its band structure anisotropy as well as the carrier inertia, which is crucial for high-frequency operation. In a multi-scale approach, density functional theory based calculation is first carried out to obtain the material specific parameters, which are then used to develop a continuity equation based non-quasi-static model to gain insight into the high-frequency behaviors. We find that channel orientation has a strong impact on both the low and high frequency conductances; however, it affects only the high-frequency component of capacitances. The model is then implemented in an industry-standard circuit simulator using relaxation-time-approximation technique and simulations are conducted to demonstrate its applicability for near cut-off frequency circuit operation. The proposed modeling methodology, which connects material to circuit, thus helps us to expand the design space, where technology downscaling could be very challenging and expensive. [ABSTRACT FROM AUTHOR]

Electron-phonon coupling limited transport in phosphorene metal oxide semiconductor field effect transistors (MOSFETs) is studied along the armchair (AC) and zigzag (ZZ) directions. In a multiscale approach, the unit cell of phosphorene is first relaxed, and the band structure is calculated using hybrid density functional theory (DFT). The transport equations are then solved quantum mechanically under the nonequilibrium Green's function formalism using DFT-calibrated two-band k ⋅ p hamiltonian. The treatment of electron-phonon scattering is done under the self-consistent Born approximation in conjunction with deformation potential theory. It is found that optical phonon modes are largely responsible for degradation of ON-current apart from p-channel AC MOSFET where acoustic phonon modes play a stronger role. It is further observed that electron-phonon scattering is more pronounced in the ZZ direction, whereas the diffusive ON-current of p-MOSFET in a given direction is higher than n-MOSFET. Further study on the complex band structure of phosphorene reveals band wrapping within the bandgap region in the AC direction and multiple crossings in the ZZ direction. This signifies strong phonon-assisted tunneling in the ZZ direction in comparison with the AC direction. For completeness, drain current in the AC tunnel field effect transistor is calculated, and electron-phonon scattering is observed only in the near vicinity of the OFF-current. [ABSTRACT FROM AUTHOR]

Two dimensional (2D) materials demonstrate several novel electrical, mechanical, and thermal properties which are quite distinctive to those of their bulk form. Among many others, one important potential application of the 2D material is its use in the field of energy harvesting. Owing to that, here we present a detailed study on electrical as well as thermal transport of monolayer MoS2, in quasi ballistic regime. Besides the perfect monolayer in its pristine form, we also consider various line defects which have been experimentally observed in mechanically exfoliated MoS2 samples. For calculating various parameters related to the electrical transmission, we employ the non-equilibrium Green's function-density functional theory combination. However, to obtain the phonon transmission, we take help of the parametrized Stillinger-Weber potential which can accurately delineate the inter-atomic interactions for the monolayer MoS2. Due to the presence of line defects, we observed significant reductions in both the charge carrier and the phonon transmissions through a monolayer MoS2 flake. Moreover, we also report a comparative analysis showing the temperature dependency of the thermoelectric figure of merit values, as obtained for the perfect as well as the other defective 2D samples. [ABSTRACT FROM AUTHOR]

A low Schottky barrier height (SBH) at source/drain contact is essential for achieving high drive current in atomic layer MoS2-channel-based field effect transistors. Approaches such as choosing metals with appropriate work functions and chemical doping are employed previously to improve the carrier injection from the contact electrodes to the channel and to mitigate the SBH between the MoS2 and metal. Recent experiments demonstrate significant SBH reduction when graphene layer is inserted between metal slab (Ti and Ni) and MoS2. However, the physical or chemical origin of this phenomenon is not yet clearly understood. In this work, density functional theory simulations are performed, employing pseudopotentials with very high basis sets to get insights of the charge transfer between metal and monolayer MoS2 through the inserted graphene layer. Our atomistic simulations on 16 different interfaces involving five different metals (Ti, Ag, Ru, Au, and Pt) reveal that (i) such a decrease in SBH is not consistent among various metals, rather an increase in SBH is observed in case of Au and Pt; (ii) unlike MoS2-metal interface, the projected dispersion of MoS2 remains preserved in any MoS2- graphene-metal system with shift in the bands on the energy axis. (iii) A proper choice of metal (e.g., Ru) may exhibit ohmic nature in a graphene-inserted MoS2-metal contact. These understandings would provide a direction in developing high-performance transistors involving heteroatomic layers as contact electrodes. [ABSTRACT FROM AUTHOR]

Atomically thin layered black phosphorous (BP) has recently appeared as an alternative to the transitional metal dichalcogenides for future channel material in a metal-oxide-semiconductor transistor due to its lower carrier effective mass. Investigation of the electronic property of source/drain contact involving metal and two-dimensional material is essential as it impacts the transistor performance. In this paper, we perform a systematic and rigorous study to evaluate the Ohmic nature of the side-contact formed by the monolayer BP (mBP) and metals (gold, titanium, and palladium), which are commonly used in experiments. Employing the Density Functional Theory, we analyse the potential barrier, charge transfer and atomic orbital overlap at the metal-mBP interface in an optimized structure to understand how efficiently carriers could be injected from metal contact to the mBP channel. Our analysis shows that gold forms a Schottky contact with a higher tunnel barrier at the interface in comparison to the titanium and palladium. mBP contact with palladium is found to be purely Ohmic, where as titanium contact demonstrates an intermediate behaviour. [ABSTRACT FROM AUTHOR]

In this work, we present a study on the negative differential resistance (NDR) behavior and the impact of various deformations (like ripple, twist, wrap) and defects like vacancies and edge roughness on the electronic properties of short-channel MoS2 armchair nanoribbon MOSFETs. The effect of deformation (3°-7° twist or wrap and 0.3-0.7 Å ripple amplitude) and defects on a 10 nm MoS2 ANR FET is evaluated by the density functional tight binding theory and the non-equilibrium Green`s function approach. We study the channel density of states, transmission spectra, and the ID-VD characteristics of such devices under the varying conditions, with focus on the NDR behavior. Our results show significant change in the NDR peak to valley ratio and the NDR window with such minor intrinsic deformations, especially with the ripple. [ABSTRACT FROM AUTHOR]

We theoretically analyze the performance of transition metal dichalcogenide (MX2) single wall nanotube (SWNT) surround gate MOSFET, in the 10 nm technology node. We consider semiconducting armchair (n, n) SWNT of MoS2, MoSe2, WS2, and WSe2 for our study. The material properties of the nanotubes are evaluated from the density functional theory, and the ballistic device characteristics are obtained by self-consistently solving the Poisson-Schrödinger equation under the non-equilibrium Green's function formalism. Simulated ON currents are in the range of 61-76 μA for 4.5 nm diameter MX2 tubes, with peak transconductance ∼175-218 μS and ON/OFF ratio ∼0.6 × 105-0.8 × 105. The subthreshold slope is ∼62.22 mV/decade and a nominal drain induced barrier lowering of ∼12-15 mV/V is observed for the devices. The tungsten dichalcogenide nanotubes offer superior device output characteristics compared to the molybdenum dichalcogenide nanotubes, with WSe2 showing the best performance. Studying SWNT diameters of 2.5-5 nm, it is found that increase in diameter provides smaller carrier effective mass and 4%-6% higher ON currents. Using mean free path calculation to project the quasi-ballistic currents, 62%-75% reduction from ballistic values in drain current in long channel lengths of 100, 200 nm is observed. [ABSTRACT FROM AUTHOR]

We present a simplified yet analytical formulation of the carrier backscattering coefficient for zig-zag semiconducting single walled carbon nanotubes under diffusive regime. The electron-phonon scattering rate for longitudinal acoustic, optical, and zone-boundary phonon emissions for both inter- and intrasubband transition rates have been derived using Kane's nonparabolic energy subband model. The expressions for the mean free path and diffusive resistance have been formulated incorporating the aforementioned phonon scattering. Appropriate overlap function in Fermi's golden rule has been incorporated for a more general approach. The effect of energy subbands on low and high bias zones for the onset of longitudinal acoustic, optical, and zone-boundary phonon emissions and absorption have been analytically addressed. 90% transmission of the carriers from the source to the drain at 400 K for a 5 μm long nanotube at 105 V m-1 has been exhibited. The analytical results are in good agreement with the available experimental data. [ABSTRACT FROM AUTHOR]

We have investigated analytically the influence of band non-parabolicity on the quantized gate capacitance in n-channel inversion layers of AlxGa1-xAs|GaAs, In1-xAsxSb|InSb, and In1-xAlxAs|In1-xGaxAsyP1-x δ-doped modulation field effect devices, whose channel electrons obey the three, two, and the parabolic energy band models of Kane. The quantized gate capacitance has been investigated by including the effects of electric subbands under quantum mechanical treatment on GaAs, InSb, and In1-xGaxAsyP1-y lattices matched to InP as channel materials. The oscillatory dependence of the quantized gate capacitance as a function of surface electric field and gate bias signatures directly the two-dimensional quantum confinement of the carriers. The influence of the band non-parabolicity of the confined carriers significantly influences the value of the gate capacitance. The result of the gate capacitances for the parabolic energy band model forms a special case of our generalized theoretical formalism. [ABSTRACT FROM AUTHOR]

Recent experimental demonstration on the coexistence of metallic and semiconducting phases in the same monolayer MoS2 crystal has attracted much attention for its use in ultra-low contact resistance-MoS2 transistors. However, the electronic structures of the metallic-to-semiconducting phase boundaries, which appear to dictate the carrier injection in such transistors, are not yet well understood. In this letter, interfacing the 2H and 1T′ polytypes appropriately, we first model the "beta" (β) and the "gamma" (γ) phase boundaries, and demonstrate good agreement with experiential results. We then apply first-principles based density functional theory to calculate the electronic structures for those optimized geometries. We further employ non equilibrium Green's function formalism to evaluate the transmission spectra and the local density of states (LDOS) in order to assess the Schottky barrier nature of the phase boundaries. Our study reveals that while the γ boundary yields p-type Schottky barrier, the β boundary leads to the distinct symmetric Schottky barrier with an atomically sharp transition region. This understanding could be useful for designing high performance transistors using phase-engineered MoS2 crystals. [ABSTRACT FROM AUTHOR]

Recent experimental demonstration on the coexistence of metallic and semiconducting phases in the same monolayer MoS2 crystal has attracted much attention for its use in ultra-low contact resistance-MoS2 transistors. However, the electronic structures of the metallic-to-semiconducting phase boundaries, which appear to dictate the carrier injection in such transistors, are not yet well understood. In this letter, interfacing the 2H and 1T′ polytypes appropriately, we first model the "beta" (β) and the "gamma" (γ) phase boundaries, and demonstrate good agreement with experiential results. We then apply first-principles based density functional theory to calculate the electronic structures for those optimized geometries. We further employ non equilibrium Green's function formalism to evaluate the transmission spectra and the local density of states (LDOS) in order to assess the Schottky barrier nature of the phase boundaries. Our study reveals that while the γ boundary yields p-type Schottky barrier, the β boundary leads to the distinct symmetric Schottky barrier with an atomically sharp transition region. This understanding could be useful for designing high performance transistors using phase-engineered MoS2 crystals. [ABSTRACT FROM AUTHOR]

In this paper we show the effect of electron-phonon scattering on the performance of monolayer (1L) MoS2 and WSe2 channel based n-MOSFETs. Electronic properties of the channel materials are evaluated using the local density approximation (LDA) in density functional theory (DFT). For phonon dispersion we employ the small displacement/frozen phonon calculations in DFT. Thereafter using the non-equilibrium Green's function (NEGF) formalism, we study the effect of electron-phonon scattering and the contribution of various phonon modes on the performance of such devices. It is found that the performance of the WSe2 device is less impacted by phonon scattering, showing a ballisticity of 83% for 1L-WSe2 FET for channel length of 10 nm. Though 1L-MoS2 FET of similar dimension shows a lesser ballisticity of 75%. Also in the presence of scattering there exist a 21-36% increase in the intrinsic delay time (τ) and a 10-18% reduction in peak transconductance (gm) for WSe2 and MoS2 devices respectively. [ABSTRACT FROM AUTHOR]