First principles study of the voltage-dependent conductance properties of n-type and p-type graphene–metal contacts
Introduction
Graphene is considered to be an advantageous candidate for the future nanoelectronics technology owing to its high electrical [1] and thermal conductivity [2], mechanical performance [3] and novel production methods [4]. Graphene is a zero-gap semiconductor with a linear dispersion relationship near the K-point in the Brillouin zone [5]. Measured high carrier density of 3 × 1012 cm−2 [6] and the conductivity as high as conductance quantum [7], which is the highest conductance per quantum channel at the nanoscale [8], enables to use graphene in nanoscale circuits as interconnects [9] and as the channels of graphene field effect transistors (FETs) [10]. Although graphene is internally a zero-gap ambipolar semiconductor [11] with high mobility, its interaction with metals alters its electrical behaviour [12]. The contact of graphene with metals is inescapable since various metallic interconnects are expected to be present in the nanoscale electronic technology such as aluminium, copper, gold, silver and platinum [13] which make contacts with graphene. The effects of the different types of metals on the conductance properties of graphene–metal interface clearly have to be investigated in order to model these contacts accurately.
There are various studies treating the graphene–metal contact with both theoretical and experimental discussions. Khomyakov et al. [14] investigated the doping of graphene with the contact metal using first-principles methods. They found out that graphene is doped either n-type or p-type when it comes into contact with a metal depending on the work function differences of graphene and the contact metal. Metals which have lower work functions than graphene dope graphene as n-type near the interface and vice versa. Graphene is doped n-type with Al, Ag and Cu while Au and Pt dope graphene as p-type [14]. Liu et al. [15] studied graphene–metal contact preparation methods, asymmetric conductances and annealing effects. They also show that charge transfer between metal and graphene dope graphene depending on the work function differences and this leads to asymmetric conductance characteristics. Huard et al. [16] measured the electrical transport of graphene–metal interface for various geometries. They show that the asymmetry of graphene–metal contact conductance arises from the pinning of the charge density in the graphene part. Nagashio et al. [17], [18] also performed graphene–metal interface measurements with different metals such as Ni, Cr/Au and Ti/Au. They have shown that the intrinsic conductance of graphene in graphene FETs is highly affected with the contact resistance and the graphene–metal contact resistance is around 500–1000 Ω μm [17]. In another study, Stokbro et al. [19] modelled the contact resistance of graphene–nickel interface using first-principles methods and have shown that ab initio methods can be used to model graphene–metal contacts accurately. Barraza-Lopez et al. [20] studied graphene–aluminium contacts using ab initio simulations and obtained the potential profile at the interface to interpret contact conductance. The temperature dependence of palladium–graphene contacts are investigated experimentally by Xia et al. [21] where mean-free path of electrons in graphene is used in the modelling of the contact resistance. There are also other several experimental studies in the literature regarding the transport behaviour of graphene–metal contacts. In one of these studies, Heersche et al. investigated the resistance of graphene–superconductor metal contacts and have given evidence of phase coherent electronic transport [22]. Shot noise of graphene–metal interfaces are studied in [23], [24]. Transport barriers at the metal–graphene interfaces are experimentally investigated in [25]. Russo et al. modelled charge transfer from the metal to graphene for several layer graphene [26]. In another study, taking practical applications into consideration, Robinson et al. implemented a method to produce graphene–metal contacts with ultra-low resistance [27]. The experimental measurements of the graphene–Pd contacts are performed by Jiao et al. where it is found out that graphene is doped p-type by Pd and there is an asymmetric resistance–voltage dependency [28]. Ballistic transport in graphene with metal contacts is discussed in the seminal paper of Novoselov et al. [29]. The electrical measurements of field effect transistors, which use graphene as the channel and various contact metals as the source and drain contacts, is another method to investigate the metal–graphene interfaces. In [30], [31], [32], this method is used to obtain the variation of the graphene–metal contact resistance with the change of the gate potential.
Experimental evidence of p-type doping of graphene in graphene–Au contacts is shown by Malec and Davidovic together with the variation of the drain current by the gate voltage [33]. In another experimental study, n-type and p-type doping of graphene with various metals is experimentally observed [34]. In [34], asymmetric resistance–voltage variation is also reported. Graphene–Cu contacts are experimentally studied in [35] showing that graphene is doped n-type with Cu and it is also shown that annealing can increase contact conductivity. Knoch et al. utilized dual-gate field effect transistor structure to measure graphene–metal contact properties. They found out that Pd contacts dope graphene as p-type and extracted doping concentration from experiments [36].
Liu et al. used first-principles approach to investigate the contact resistance of graphene–Ni and graphene–Cu contacts and concluded that graphene–Ni contacts have lower conductance than graphene–Cu contacts [37]. In [38], Do and Li considered the coupling between π-bands and sd bands and then modelled the resistance behaviours of graphene–metal contacts. Takagi and Okada also used first-principles methods to study the contacts of graphene with Pd, Au, Ag and Pt pillars and found out that the geometry of the contacts are also effective on the resistance value [39]. In [40], Barraza-Lopez et al. used DFT–NEGF transport calculations of graphene–metal contacts with covalent bonds. In another study, tight-binding parameters for the dispersion curve of graphene–Ti contacts are obtained [41]. The self-energy parameters, which describe graphene–metal coupling, is used to model the conductance of graphene–metal interface in [42] and their model represents the asymmetric behaviour of the graphene–metal conductance. Maassen et al. used first-principles simulations to obtain the transport properties of the contact of graphene with Cu(1, 1, 1) crystal and they also found out that graphene is doped n-type by copper [43].
In this work, we investigate (i) voltage dependent transmissions, (ii) current–voltage variations and, (iii) voltage dependency of the resistances of p-type and n-type graphene–metal contacts. Self-consistent quantum mechanical simulations employing density functional theory (DFT) in conjunction with non-equilibrium Green’s function formalism (NEGF) are used to obtain current–voltage variations of graphene–Cu and graphene–Au contacts. Voltage-dependent resistances of these graphene–metal contacts are then calculated. Asymmetry in their resistances is discussed and it is shown that obtained resistance behaviours are in consistent with the interpretations existing in the literature. Finally, a polynomial model for representing the current–voltage characteristics of both p-type and n-type graphene–metal contacts is given which is essential for the nanoelectronics designer.
Section snippets
Simulated p-type and n-type graphene–metal contacts
In [13], the charge transfer at the graphene–metal interface is investigated in detail and it is concluded that graphene is doped n-type if the work function of the interface metal is lower than the work function of the graphene. Similarly, graphene is doped p-type if the work function of the contact metal is higher than the work function of graphene. This is also verified by [14], [16], [17]. According to [44], the work function of graphene is 4.6 eV. In order to obtain n-type graphene–metal
Simulation results/calculation
The polarity of the contacts during the application of the bias voltage is shown schematically in Fig. 2. Applied voltage is swept from −2 V to 2 V in 0.1 V steps and DFT–NEGF simulations are performed for each step in order to obtain the variation of the transmission spectrum. (−2 V, 2 V) voltage range is selected taking International Technology Roadmap for Semiconductors (ITRS) [51] into consideration. Obtained transmission spectra for graphene–Cu and graphene–Au contacts are shown in Fig. 3a,
Discussion and the proposed polynomial model
As it can be seen from Fig. 4a, the I–V variation of graphene–Cu interface shows a current limit meaning a rapid increase in the resistance as the applied voltage increases in the positive direction. According to the work function differences, graphene is expected to be doped n-type when it comes into contact with Cu. The obtained I–V and R–V plots verify this fact. Graphene is doped n-type and as the voltage increases in the positive direction, the graphene–Cu contact starts to limit the
Conclusions
Electronic transport properties of p-type and n-type graphene–metal contacts are investigated from nanoelectronics point of view in this study. The variation of the transmission spectra of graphene–Cu and graphene–Au interfaces are obtained using self-consistent quantum mechanical simulations for the applied voltage range of (−2 V, 2 V). It is observed that the change of the transmission spectrum of n-type graphene–Cu contact is negligible when the voltage is increased in the negative voltage
Acknowledgement
The author would like to thank Quantumwise A.S. and Dr. Anders Blom for their valuable support.
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