(Invited) Challenges and Opportunities in the Modeling of Novels Devices and Materials for Logic Applications
Authors: Luisier Mathieu , Szabo Aron , Klinkert Cedric , Stieger Christian , Rau Martin , Agarwal Tarun , Lee Youseung 
Published: February 2020

In the search for post Si CMOS transistors, different device geometries (FinFETs-on-oxide, nanowires, nanosheets), materials (III-V, Ge, carbon nanotubes), and combination of them have been receiving a lot of attention from the semiconductor industry and from academia. Recently, very promising experimental results have put 2-D single-layer crystals under the spotlight, starting from graphene in 2005 and followed by transition metal dichalcogenides (TMDs), e.g. MoS2 in 2011. Their excellent electrostatic properties, absence of surface dangling bonds, tuneable effective masses and band gaps, and possibility to be stacked on top of each other to form van der Waals heterostructures make 2-D materials particularly appealing for future logic applications, especially at gate lengths below 20 nm. A recent theoretical study based on density functional theory (DFT) [1] predicted that more than 1,800 2-D monolayer compounds might exist, with about 1,000 of them that could be relatively easily exfoliated from their 3-D parents. Among them, some exhibit semiconducting, other metallic or insulating behaviours. Still, it can be expected that hundreds could be suitable as channel material of future ultra-scaled transistors. Exploring the "current vs. voltage" characteristics of all of them to identify the ones that might eventually challenge the current Si FinFET technology is currently not possible at the experimental level: this would require the fabrication of very high number of samples that it would be difficult to compare to each other. Furthermore, the results might strongly depend on the crystal quality, processing techniques, measurement setups, or experimental conditions. All these effects do not allow to properly and unambiguously determine the intrinsic potential of each considered 2-D material.
As an alternative, device simulation could be used to support the on-going experimental activity and guide it towards the best material-structure configurations. For that purpose, an accurate, physics-based modelling approach is necessary that does not take fitting parameters as inputs. Ab initio quantum transport solvers lend themselves perfectly to this type of exploratory studies. Such an advanced computer aided design (CAD) tool has been developed to evaluate the figures of merits (ON-current, injection velocity, inversion charge, sub-threshold slope, scalability, energy-delay product...) of future transistors relying on 2-D channel materials [2]. It combines plane-wave DFT calculations, transformations into maximally localised Wannier functions, constructions of device Hamiltonian matrices, and quantum transport simulations. By doing so, a full-band treatment of any single- or multi-layer 2-D compound is possible, without the need for a model parameterisation, as encountered in (semi-)empirical methods such as tight-binding or pseudo-potentials.
Here, the properties of conventional TMDs and black phosphorus will be first simulated at the ab initio level and compared to those of strained-Si and III-V FinFETs. Since all theses device configurations will be investigated with the same tool (self-consistent Schrödinger and Poisson solver) and set of approximations, the results do not depend on the simulator features, but only on the intrinsic characteristics of each structure. As next step, the study will be extended by adding the data obtained for 100 other 2-D materials. It will be shown (i) that samples with both high n- and p-type ON-currents can be found, (ii) that they can theoretically outperform Si FinFETs, and (iii) that some of them can be scaled down to gate lengths of 5 nm, while still keeping a decent device behaviour. Finally, since contacting 2-D materials remains an important issue that has not yet been fully resolved, the proposed simulation approach will be employed to highlight the physical mechanisms controlling the transfer of electrons from a metallic layer into a 2-D monolayer.
[1] N. Mounet, M. Gilbertini, Ph. Schwaller, D. Campi, A. Merkys, A. Marrazzo, T. Sohier, I. E. Castelli, A. Cepellotti, G. Pizzi, and N. Marzari, "Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds", Nature Nano. 13, 246 (2018).
[2] A. Szabo, Reto Rhyner, and Mathieu Luisier, "Ab initio simulation of single- and few-layer MoS2 transistors: effect of electron-phonon scattering", Phys. Rev. B 92, 035435 (2015).