Theoretical study of scattering in graphene ribbons in the presence of structural and atomistic edge roughness

We investigate the diffusive electron-transport properties of charge-doped graphene ribbons and nanoribbons with imperfect edges. We consider different regimes of edge scattering, ranging from wide graphene ribbons with (partially) diffusive edge scattering to ribbons with large width variations and nanoribbons with atomistic edge roughness. For the latter, we introduce an approach based on pseudopotentials, allowing for an atomistic treatment of the band structure and the scattering potential, on the self-consistent solution of the Boltzmann transport equation within the relaxation-time approximation and taking into account the edge-roughness properties and statistics. The resulting resistivity depends strongly on the ribbon orientation, with zigzag (armchair) ribbons showing the smallest (largest) resistivity and intermediate ribbon orientations exhibiting intermediate resistivity values. The results also show clear resistivity peaks, corresponding to peaks in the density of states due to the confinement-induced subband quantization, except for armchair-edge ribbons that show a very strong width dependence because of their claromatic behavior. Furthermore, we identify a strong interplay between the relative position of the two valleys of graphene along the transport direction, the correlation profile of the atomistic edge roughness, and the chiral valley modes, leading to a peculiar strongly suppressed resistivity regime, most pronounced for the zigzag orientation.Comment: 13 pages, 7 figure

Generalized phonon-assisted Zener tunneling in indirect semiconductors with non-uniform electric fields : a rigorous approach

A general framework to calculate the Zener current in an indirect semiconductor with an externally applied potential is provided. Assuming a parabolic valence and conduction band dispersion, the semiconductor is in equilibrium in the presence of the external field as long as the electronphonon interaction is absent. The linear response to the electron-phonon interaction results in a non-equilibrium system. The Zener tunneling current is calculated from the number of electrons making the transition from valence to conduction band per unit time. A convenient expression based on the single particle spectral functions is provided, enabling the numerical calculation of the Zener current under any three-dimensional potential profile. For a one dimensional potential profile an analytical expression is obtained for the current in a bulk semiconductor, a semiconductor under uniform field and a semiconductor under a non-uniform field using the WKB (Wentzel-Kramers-Brillouin) approximation. The obtained results agree with the Kane result in the low field limit. A numerical example for abrupt p - n diodes with different doping concentrations is given, from which it can be seen that the uniform field model is a better approximation than the WKB model but a direct numerical treatment is required for low bias conditions.Comment: 29 pages, 7 figure

Image-Force Barrier Lowering of Schottky Barriers in Two-Dimensional Materials as a Function of Metal Contact Angle

Two-dimensional (2D) semiconductors are a promising solution for the miniaturization of electronic devices and for the exploration of novel physics. However, practical applications and demonstrations of physical phenomena are hindered by high Schottky barriers at the contacts to 2D semiconductors. While the process of image-force barrier lowering (IFBL) can considerably decrease the Schottky barrier, IFBL is not fully understood for the majority of prevalent contact geometries. We introduce a novel technique to determine the IFBL potential energy with application spanning far beyond that of any existing method. We do so by solving Poisson's equation with the boundary conditions of two metal surfaces separated by an angle Omega. We then prove that our result can also be obtained with the method of images provided a non-Euclidean, cone-manifold space is used. The resulting IFBL is used to calculate the expected contact resistance of the most prevalent geometric contacts. Finally, we investigate contact resistance and show how the stronger IFBL counteracts the effect of larger depletion width with increasing contact angle. We find that top contacts experience lower contact resistance than edge contacts. Remarkably, our results identify tunable parameters for reducing Schottky barriers and likewise contact resistance to edge-contacted 2D materials, enhancing potential applications.Comment: 22 pages, 6 figure

Numerical Implementation of the Barrier Lowering Effect at Metal Surfaces

When a charged particle in vacuum or a semiconductor is in the proximity of a grounded metal, the Coulombic interaction between the charged particle and electrons inside the metal results in the formation of a thin charged layer of opposite polarity near the metal surface. The oppositely charged surface layer in turn exerts an attractive force on the charged particle, reducing the potential barrier seen by the charged particle in the presence of an electric field. This complex many-body phenomenon at the metal surface, known as the image-force barrier lowering (IFBL) effect, is particularly relevant to carrier transport at metal-semiconductor interfaces, which are ubiquitous across all transistor architectures. An accurate treatment of this effect requires invoking density functional theory (DFT) at the GW level, which becomes computationally expensive when considering large simulation domains involving non-uniform dielectric setups. Furthermore, beyond a few simple grounded metal geometries, it is difficult to derive analytical expressions of IFBL in arbitrary structures. Many quantum transport studies in the literature have therefore ignored the effect or relied on the one-dimensional analytical expression for IFBL corresponding to a 1D metal plate to incorporate IFBL into their calculations. In this work, we present a novel numerical approach to calculate the image force potential in arbitrary metal geometries and with non-uniform dielectric environments. Our approach, based on the method of images on a non-Euclidean manifold and eigenvalue decomposition of the Laplacian matrix, can handle large simulation domains with complex dielectric setups, a regime typically inaccessible to DFT based approaches. We will compare and contrast our numerical approach with the closed-form expressions of IFBL reported recently for top and side contacts to transition-metal dichalogenides (TMDs). Lastly, the numerically evaluated image force potential will be imported into our open-source quantum transport solver and the effect of IFBL on the Schottky barrier height (ϕB) and contact resistance (RC) of metal-MoS2 contact will be demonstrated.Texas Advanced Computing Center (TACC