ABSTRACT

We study graphene electrodes that can be used for contacting single molecules. The nanometer-scale gap is made by feedback controlled electroburning in few-layer graphene sheets. We analyze the time stability, and the influence of the temperature and gate voltage on the current flowing through the empty gaps. The electrodes are stable at room temperature for long periods of time. We show statistics of the relation between the initial resistance of the few-layer graphene flakes and the final size of the gaps. We find that thicker flakes are more suitable for the fabrication of the electrodes.

1. Introduction

Graphene, extensively studied in the last years, has emerged as a material of special interest for spintronics. Being an all organic material, it displays unique electronic transport properties [1] such as high carrier mobility, high flexibility and very low spin-orbit coupling which allows the injection of spin-polarized currents in graphene with very long coherence lengths even at room temperatures [2]. Several prototypes of graphene-based spintronics devices have been proposed such as spin valves [3].

A different approach is to exploit the exceptional properties of graphene for the fabrication of electrodes for molecular spintronics. Molecular spintronics [4] proposes to use the spin state of individual magnetic molecules to process and storage information. Electrical control of the spin is preferred over other stimuli like the magnetic field because it is faster and can be done locally. Such an electric control can be achieved in three-terminal spin transistors, where a single molecule is attached to two nanometer-spaced electrodes. A third electrode is used to gate the different orbitals of the molecule. The most used electrode material is gold due to its noble character. However, gold atoms are highly mobile at room temperature making the electrodes unstable and therefore hindering any possible application at ambient conditions. Some alternatives explore the use of platinum electrodes [5], which are more stable at room temperature. Graphene, however, offers additional advantages over metallic electrodes. The covalent-bond structure of graphite promise stable electrodes at room temperatures and for long periods of time. In addition, few-layer graphene (FLG) electrodes can be made much thinner than their metallic counterparts, thereby enhancing the coupling of the molecules with the gate. The versatility of graphene moreover, allows for combination with ferromagnetic materials enabling the injection of spin-polarized electrons into the molecule. With spin-polarized currents, additional control of the molecular spin is predicted [6,7]. However, this has been out of reach with ferromagnetic metallic electrodes which oxidize during junction fabrication, preventing the injection of current in the molecule.

Recent advances [8] show that it is possible to open nanometer-sized gaps (1 - 2 nm) in ultrathin graphite flakes suitable for trapping molecules. Knowledge on the influence of external parameters, like temperature or gate voltage, on the electrical transport through the empty electrodes, is of fundamental importance for molecular spintronics. This permits to discriminate the electrode contribution to the electronic transport from the features originating from the magnetic molecule once deposited. In this paper we present a detailed study on the stability of FLG electrodes and the dependence of the tunnel current through the empty gap with the temperature, the gate voltage and time. We also present a statistical study on the dependence of the controllability of the electroburning process and the final size of the gap with the initial resistance of the FLG flake.

2. Fabrication of the Electrodes

We first briefly describe the fabrication technique of the electrodes. More details can be found in [8]. Figure 1(a) shows a schematic design of a three-terminal transistor made of graphene source and drain electrodes. Graphene flakes are deposited by mechanical exfoliation of graphite onto a silicon substrate covered with 285 nm of silicon oxide. Few-layer graphene flakes are selected under the optical microscope. Suitable flakes for molecular spintronics need to be thin to maximize the gate coupling with the linking molecule. On the other hand, the electrodes have to be thick enough to act as a continuous reservoir of electrons without discrete level structure and no gate dependence [9,10]. We select flakes of 3 to 18 nm thickness corresponding to approximately 10 to 60 layers of graphene. The initial resistance of the flake ranges between 100 Ω and 2 kΩ.

Afterwards, gold pads are defined on top of the selected flakes by electron-beam lithography and subsequent gold evaporation. The underlying silicon substrate is used as back-gate electrode. The nanogap in the few-layer graphene is opened by using a feedback controlled electroburning technique [8] at room temperature and in air. The experimental procedure is analogous to that used for electromigration of metallic wires [11,12]: a voltage is applied between the gold leads that induces a current through the flake. Graphene heats up by the Joule effect and carbon atoms react with atmospheric oxygen. The opening of the gap begins at an edge around the centre of the flake where the heat removal to the gold pads is minimal and reactivity of the edge atoms with oxygen is maximal. The current through the flake is continuously recorded while ramping the voltage. As soon as the conductance drops 10 % within the last 200 mV of the ramp, the voltage is swept to zero in milliseconds (see [8] for more details of the process). The fast feedback is essential to avoid the sudden breaking of the flake which may then originate a large gap unsuitable for contacting molecules. Several voltage ramps are repeated until the resistance reaches the MΩ range. Figure 1(b) shows a typical current-voltage curve during the electroburning process. Figure 1(c) shows an AFM picture of a flake before and after electroburning. The size of the gap appears larger than a few nanometers. Note, however, that the edges may not be vertical. The upper graphene layers are expected to be more reactive with oxygen and in addition the lower layers can dissipate heat more easily through the substrate. The nanometric gap may therefore be closer to the substrate, which cannot be probed by the AFM tip. We also observe rests of the resist used during the fabrication process in the image taken before electroburning. Interestingly, these impurities disappear after the current annealing of the sample as seen in Figure 1(c).

3. Characterization of the Empty Gap

We start characterizing the time-stability of the electrodes by measuring the tunnel current through the gap when sweeping a bias voltage between source and drain electrodes. The tunnel current depends exponentially on the width of the gap [13] and thus it is very sensitive to small changes in the electrode distance or more generally in its geometry.

Figure 2(a) shows the current through the gap measured within V = ± 0.4 V (blue solid line). The width of the gap is estimated by fitting the tunnelling current to a Simmons model [13]. The current depends on the width of the gap w and the height of the tunnel barrier φ that depends on the work function of the conductor. The best fitting (red dashed line in Figure 2(b)) is obtained with φ = 0.92 eV and w ~ 1.95 nm.