Multiscale Analysis for Field-Effect Penetration through Two-Dimensional Materials

Gate-tunable two-dimensional (2D) materials-based quantum capacitors (QCs) and van der Waals heterostructures involve tuning transport or optoelectronic characteristics by the field effect. Recent studies have attributed the observed gate-tunable characteristics to the change of the Fermi level in the first 2D layer adjacent to the dielectrics, whereas the penetration of the field effect through the one-molecule-thick material is often ignored or oversimplified. Here, we present a multiscale theoretical approach that combines first-principles electronic structure calculations and the Poisson–Boltzmann equation methods to model penetration of the field effect through graphene in a metal–oxide–graphene–semiconductor (MOGS) QC, including quantifying the degree of “transparency” for graphene two-dimensional electron gas (2DEG) to an electric displacement field. We find that the space charge density in the semiconductor layer can be modulated by gating in a nonlinear manner, forming an accumulation or inversion layer at the semiconductor/graphene interface. The degree of transparency is determined by the combined effect of graphene quantum capacitance and the semiconductor capacitance, which allows us to predict the ranking for a variety of monolayer 2D materials according to their transparency to an electric displacement field as follows: graphene > silicene > germanene > WS2 > WTe2 > WSe2 > MoS2 > phosphorene > MoSe2 > MoTe2, when the majority carrier is electron. Our findings reveal a general picture of operation modes and design rules for the 2D-materials-based QCs.

Production of Highly Monolayer Enriched Dispersions of Liquid-Exfoliated Nanosheets by Liquid Cascade Centrifugation

While liquid exfoliation is a powerful technique to produce defect-free nanosheets in large quantities, its usefulness is limited by broad nanosheet thickness distributions and low monolayer contents. Here we demonstrate liquid processing techniques, based on iterative centrifugation cascades, which can be designed to achieve either highly efficient nanosheet size-selection and/ or monolayer enrichment. The resultant size-selected dispersions were used to establish quantitative metrics to determine monolayer volume fraction, as well as mean nanosheet size and thickness, from standard spectroscopic measurements. Such metrics allowed us to design and optimize centrifugation cascades to enrich liquid exfoliated WS2 dispersions up to monolayer contents of 75%. Monolayer-rich dispersions show relatively bright photoluminescence with narrow line widths (