Energy distributions of field emitted electrons from carbon nanosheets: Manifestation of the quantum size effect

Abstract

We emphasize the importance of experiments with voltage dependent field emission energy distribution analysis in carbon nanosheets. Our analysis shows the crucial influence of the band structure on the energy distribution of field emitted electrons in few-layer graphene. In addition to the main peak we found characteristic sub-peaks in the energy distribution. Their positions strongly depend on the number of layers and the inter-layer interaction. The discovery of these peaks in field emission experiments from carbon nanosheets would be a clear manifestation of the quantum size effect in these new materials. Recently, freestanding carbon nanosheets (CNSs) have been synthesized on a variety of substrates by radio frequency plasma enhanced chemical vapor deposition [1,2]. The sheets are consisting of several graphene layers and stand roughly vertical to the substrate. It has been found that CNSs have good field emission characteristics with promising applications in vacuum microelectronic devices [3,4,5,6]. High emission total current at low threshold field enables using CNSs as an effective cold cathode material.Until now only the current-voltage characterization was used in studies of CNSs. At the same time, voltage dependent field emission energy distribution (V-FEED) analysis is known as a powerful experimental method to interrogate the field emission. As compared to classical I-V characterization, V-FEED analysis can provide more information related to both inherent properties of the emitter and to the basic tunneling process [7]. In particular, in single-walled carbon nanotubes (CNTs) the FEED has shown characteristic peaks originated from the stationary waves in the cylindrical part of the nanotube [8]. Their number and sharpness were found to increase with the length of the tubes. Notice that short periodic variations were also observed in the thickness-dependent field emission current from ultrathin metal films (UMF) [9]. The calculated electron energy distribution curve characteristic of UMF was found to have "steps" which correspond with the quantized "normal" energies [10]. The resonant-tunneling peaks with specific microscopic tunneling mechanisms were also observed in field emission from nanostructured semiconductor cathodes [11]. A different example of the quantum size effect in CNTs, which originates from the intrinsic properties of the energy band structure, was revealed in field emission [12]. It is reasonable to expect manifestation of quantum size effects in subnanometer CNSs.

The evolution of electronic structure in few-layer graphene revealed by optical spectroscopy

“…Graphene's few-layer counterparts have also recently been the subject of much interest, since this broader class of materials offers the potential for further control of electronic states by interlayer interactions (2)(3)(4)(5)(6). Indeed, theoretical investigations have predicted dramatic changes in the electronic properties in few-layer graphene (FLG) compared with single-layer graphene (SLG) (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17): When two or more layers of graphene are present in ordered FLG, the characteristic linearly dispersing bands of the single layer are either replaced or augmented by pairs of split hyperbolic bands. These new bands correspond to fermions of finite mass, unlike the electrons present in SLG that behave as massless fermions.…”

Influence of tip geometry on the field emission law from axisymmetric and wall-like emitters

“…It has been found that CNSs have good field emission characteristics with promising applications in vacuum microelectronic devices [6][7][8]. Our theoretical analysis revealed the crucial influence of the band structure on the field emission characteristics of CNSs, in particular, on the energy distribution of field emitted electrons [9]. In that consideration we have explored a planar FN-like model based on the independent channel method suggested recently in [10].…”

Edge field emission of large-area single layer graphene

“…A theoretical study has shown that due to quantization of electron momentum, emission from graphene sheets follow the ln(J/F 3 ) ~ 1/F 2 law for dependence of emission current density, J, on applied electric field, F, in contrast to the conventional Fowler-Nordheim (FN) law of M a n u s c r i p t ln(J/F 2 ) ~ 1/F which is valid for three-dimensional materials [13]. Theoretical considerations which take into account a specific band structure of graphene and the field penetration effect also predict deviations from FN law [14] and reveal additional peaks in energy distribution of emitted electrons [15]. Moreover, relativistic [16] and electron interference [17,18] effects can in principle be identified in the study of FE patterns and currentvoltage characteristics of graphene emitters.…”