Electrostatic edge effects versus edge doping in graphene nanoribbons: a scanning gate microscopy and modelling study

The gist: The study investigates whether shifts in charge neutrality point polarity in graphene nanoribbons are due to edge doping or size-dependent modifications to the band structure.

Experimental Setup and Observations

** In scanning gate microscopy, an electrically conductive AFM tip is used as a local top gate to map the conductance characteristics of an underlying sample. The back gate is used to bias the sample to near the CNP in order to optimise the signal to noise ratio of the change in current induced by the scanning top gate. In fixed-tip mode, the AFM tip is held (usually a few 10s of nm) above the sample at a specific location and the current through the sample is measured as a function of the tip voltage. The polarity of this local CNP tells us whether the area directly under the tip is p-type or n-type so by performing this SGM measurement at different points in the sample, information about the spatial variations in the majority carrier types can be gained. In Figure 10, 3D render of change in current on the AFM topography illustrating the spatially-localised gate effect of the tip. The overall change in current measured when the tip passes from the centre of the GNR to 100 nm from the edge is of order 12 nA, which corresponds to a change of around 2%. There is no reversal of the change in current in the vicinity of the edge and therefore no evidence of a transition from p to n type. However, there is a clear step in the current change when the edge of the tip passes over the edge of the GNR in Figure 11(a), as indicated by the arrows. Given that this is spatially localised to a region approximately 10nm wide centred at the edge, it is most likely a result of a local enhancement of the Electric field when the tip is in close proximity to the edge. We would also expect an upwards rather than downwards kink at this point, which is a strong indicator that the edges truly are not n-type. Given also that (1) there is good agreement between the simulated and experimental line profiles for current as a function of tip position without including any difference in edge doping and (2) the overall trends of CNP vs width (apart from cross-over) are in good agreement until the GNR width drops below around 50nm at which point the band structure is known to start to deviate from bulk graphene, we must therefore conclude that the shift in CNP polarity for reduced GNR widths is not a result of the doping switching sign from p-type to n-type at the edges, and it must instead be a result of size-induced modifications to the band structure. We would also expect an upwards rather than downwards kink at this point, which is a strong indicator that the edges truly are not n-type. Given also that (1) there is good agreement between the simulated and experimental line profiles for current as a function of tip position without including any difference in edge doping and (2) the overall trends of CNP vs width (apart from cross-over) are in good agreement until the GNR width drops below around 50nm at which point the band structure is known to start to deviate from bulk graphene, we must therefore conclude that the shift in CNP polarity for reduced GNR widths is not a result of the doping switching sign from p-type to n-type at the edges, and it must instead be a result of size-induced modifications to the band structure >. We would also expect an upwards rather than downwards kink at this point, which is a strong indicator that the edges truly are not n-type. Given also that (1) there is good agreement between the simulated and experimental line profiles for current as a function of tip position without including any difference in edge doping and (2) the overall trends of CNP vs width (apart from cross-over) are in good agreement until the GNR width drops below around 50nm at which point the band structure is known to start to deviate from bulk graphene, we must therefore conclude that the shift in CNP polarity for reduced GNR widths is not a result of the doping switching sign from p-type to n-type at the edges, and it must instead be a result of size-induced modifications to the band structure >. We would also expect an upwards rather than downwards kink at this point, which is a strong indicator that the edges truly are not n-type. Given also that (1) there is good agreement between the simulated and experimental line profiles for current as a function of tip position without including any difference in edge doping and (2) the overall trends of CNP vs width (apart from cross-over) are in good agreement until the GNR width drops below around 50nm at which point the band structure is known to start to deviate from bulk graphene, we must therefore conclude that the shift in CNP polarity for reduced GNR widths is not a result of the doping switching sign from p-type to n-type at the edges, and it must instead be a result of size-induced modifications to the band structure >. We would also expect an upwards rather than downwards kink at this point, which is a strong indicator that the edges truly are not n-type.

1. Improved Graphene Device Simulation for Edge Effects

AI systems can now accurately predict charge neutrality point shifts by modeling how fringing of the electric field at the edges of plates can dominate the behaviour in nanoribbons, allowing for precise prediction of CNP behavior based on width and geometry.

2. Enhanced Material Property Prediction

The AI system gains capability to model size-induced modifications to band structure, specifically predicting shifts in the graphene band structure at reduced lengthscales, which is known to be associated with the emergence of a band gap as ribbon width decreases below a certain threshold.

3. Optimized Device Architecture Design

The system can design GNR structures that minimize unwanted doping effects by identifying that the inversion of the charge carriers at the edges is therefore entirely a field effect and is dependent on the applied bias, so cannot be considered to be equivalent to doping.

The charge neutrality point (CNP) of graphene nanoribbons (GNRs) patterned by oxygen plasma etching moves towards zero as the ribbon narrows and, on 300 nm SiO2, changes sign below a crossover width of 50 nm: an observation previously attributed to n-type edges surrounding a p-type bulk. We test this edge-doping hypothesis in three ways. First, finite element modelling of complete GNR transistors with uniform doping shows that fringing of the gate field at the edges reproduces the trend of the measured CNP with width down to 50nm without any edge doping, while producing a bias-dependent inversion of the carrier type at the edges that mimics n-type edges in scanned-probe measurements. Second, fitting the CNP of ribbons on 90 nm and 300 nm SiO2 with the gate capacitance of a finite strip, which fixes the electrostatic contribution with no adjustable parameter other than the bulk doping, shows that fringing accounts for most of the width dependence and isolates the remainder as an edge charge. This is acceptor-like (0.24 e/nm per edge) in the present ribbons, which therefore have no n-type edges, and donor-like but small in devices on 300 nm SiO2; no single edge-charge, field-coupled or contact-doping mechanism describes both. Third, scanning gate microscopy finds no edge contrast of the sign expected for n-type edges. The width dependence of the CNP is therefore predominantly electrostatic, and n-type edges are not an intrinsic consequence of oxygen-plasma etching. A design map shows that fringing dominates the width dependence whenever the gate dielectric is thicker than 30-50 nm, whereas in scaled high-K transistors, edge charge dominates and would shift the threshold voltage of a 10 nm ribbon by 0.1-0.15 V. Fitting the CNP versus width with the strip capacitance provides a simple test for edge doping in any gated two-dimensional nanostructure