Using first-principles calculations, it is shown that the work function of graphene on copper can be adjusted by varying the concentration of intercalated alkali metals. Using density functional theory, we calculate the modulation of work function when Li, Na, or K are intercalated between graphene and a Cu(111) surface. The physical origins of the change in work function are explained in terms of phenomenological models accounting for the formation and depolarization of interfacial dipoles and the shift in the Fermi-level induced via charge transfer.

Epitaxial growth of graphene, a two-dimensional plane of carbon atoms in a honeycomb lattice, is one of the most promising methods of preparing monolayers as it allows for large area sheets.1–3 In addition to the great technological potential attributed to the the intrinsic electric, optical, and mechanical properties of graphene, there is a strong interest in optimizing the physical properties of graphene for various applications.4 

In this work, we will use computational tools to design a graphene substrate with desired work function (ϕW), a very important property in many applications.5–7 For example, thermionic emitters with lower operating temperatures and thus higher efficiencies are obtained with lower ϕW materials;8 photovoltaic efficiency in organic solar cells may be increased via ϕW tuning,9 and in Light Emitting Diode (LED) and FET performance depends heavily on carrier injection efficiency determined by band alignments which can be controlled via ϕW.10,11 Extensive work has been done to control ϕW of graphene via electrical gating,12 varying the number of layers,13 and chemical doping.14–18 A recent review of these efforts is available in Ref. 19.

From another viewpoint, a promising application of graphene is protective coatings.4 For example, graphene coatings have been shown to protect underlying surfaces against chemical reactions with ambient conditions.20 A common technique to modify the ϕW of a material is to introduce different atomic species onto the surface.21 One can imagine using a layer of graphene to protect such a modification, but it becomes important to know if the addition of graphene preserves the desired modifications.

Intercalation of metal atoms into the substrate–graphene interface has been one method used to alter the properties of the interface.22,23 There have been experimental studies of alkali metals (AMs) at the graphene–metal interface,24–29 where efforts are focused on synthesis and basic structural and electronic characterization. A key point is that AMs have been shown to penetrate a graphene layer grown on a metal surface.24,25

The interaction of AMs and carbon based materials has received long standing attention due to the relatively simple electronic configuration of AMs and the potential of applications in battery, fusion, and hydrogen storage applications.30–34 There is also a vast literature on AM interactions with bulk graphite and other surfaces for which reviews are available.35–37 One important result from this literature is that deposition of AMs on metal surfaces produces a coverage dependent reduction of ϕW. The general form of the coverage dependence is a reduction in ϕW as coverage is increased until an intermediate coverage is reached. As coverage is increased further, the AM layer depolarizes and ϕW increases.36,38

Many studies have investigated AM adsorption onto graphene theoretically.31,39–47 In the majority of these works, a substrate is not included in the calculations. Generally, it is found that AMs form nondestructive bonds with ionic character to graphene without altering the graphene band structure and typically serve as electron donors shifting the Fermi level up, which leads to a reduction in ϕW.28,46 Experimentally, it has been shown that the deposition of AM carbonates can reduce ϕW of few layer graphene via electron donation.18 A first-principles calculation of AM adatoms on freestanding graphene found a coverage dependence of ϕW, but only the side with adatoms showed a minimum at intermediate coverages.46 The exposed graphene showed a decrease which quickly saturated due to charge transfer,46 similar to the case of bulk graphite.48 

In this letter, we investigate alkali metals (Li, Na, and K) intercalated with graphene on a Cu(111) surface with first-principles calculations. We will show how the work function (ϕW) depends on the concentration of intercalated AMs and explain the findings using phenomenological models supported with density functional theory calculations.

Density functional theory (DFT) calculations were performed using the Vienna Ab Initio Simulation Package (VASP).49–52 Van der Waals (vdW) interactions, which are not included by standard DFT functionals, have been shown to be important for describing AM intercalated graphite.53,54 We include vdW interactions via the vdW-DF2 functional to describe exchange and correlation.55 Planewaves with an energy cutoff of 400 eV and a 5 × 5 gamma-centered grid of k-points were found to give well converged ground state properties. Since significant charge transfer is expected, we chose projector augmented-wave56,57 (PAW) potentials with valence configuration 1s22s1,2p63s1,3s23p64s1,2s22p2, and 3d104s1 for Li, Na, K, C, and Cu, respectively.

We use the vdW-DF2 optimized lattice constant a=2.474Å for graphene and fix the supercell accordingly. Experimentally, graphene on copper surfaces exhibits long range Moiré patterns;58–60 however, ab initio treatment of these geometries is not computationally feasible. The use of a 1 × 1 configuration where the copper is strained is justified in our case as ΔϕW50meV when the graphene is shifted relative to the Cu(111) surface.61 We also checked our results by straining the graphene and keeping the copper surface fixed, and find our physical description holds.61 Additionally, our use of a 1 × 1 configuration allows to compare more directly with previous theoretical results.62 To optimize the geometry, we allow the AM, graphene, and top layer of Cu atoms to move until all forces are less than 0.04eV/Å. A symmetric slab with adsorbates added to both the top and bottom is used to prevent a spurious dipole interaction between periodic images, and at least 19 Å of vacuum is included in the supercell. We choose the three-fold hollow site as the initial position of the alkali metals as previous works show this to be the most energetically favorable configuration.63 Seven layers in the Cu slab were found to give converged results. Supercells corresponding to alkali coverages of θ=1/16, 2/16, 3/16, 4/16, 6/16, 8/16, and 16/16 are constructed on Cu(111) 4 × 4 slabs.61 We note that some coverages can be represented on smaller supercells but by using an initially identical Cu slab we ensure no ambiguities due to Brillouin zone sampling, charge symmetrization or FFT wrap-around error.

Our results may be understood in the context of three effects: (i) a shift in the graphene Fermi energy due to charge transfer from the AM, (ii) a shift in graphene Fermi energy due to the Cu surface, and (iii) the formation of an interfacial dipole and its weakening through depolarization due to dipole-dipole interactions. In the following text, we describe how these effects combine when different AMs are intercalated.

First, we consider our results in terms of a model for the shift in Fermi-level for graphene interacting with a metal surface.62 We begin by noting that the electronic structure of graphene is not altered apart from energy shifts by the presence of Cu(111) or AMs.46,62 The work function of graphene-covered metal is ϕ(d)=ϕMΔV(d), where ϕM is the metal work function and d is the graphene–metal separation. The key feature of the model is that the shift in potential ΔV(d) is decomposed into two terms: one describing the electron transfer in terms of a plane capacitor and another accounting for the wave function overlap. Assuming linear bands, the shift in Fermi-level is

ΔEF(d)=sgn(x)1+2(α/κ)D0(dd0)|x|1(α/κ)D0(dd0),
(1)

where x=ϕMϕGΔc(d), work-function of graphene is ϕG, shift due to wave function overlap is described by Δc(d)=eγd(a0+a1d+a2d2),α=e2/ϵ0A, A is the area of graphene, D0 and d0 are constants coming from the density of states and equilibrium separations, κ is the effective dielectric in the plane-capacitor model, and ai are constants obtained via fitting to ab initio data. We refer readers to Ref. 62 for the derivation of the model. In the case of graphene on Cu(111), the work function of this system is expected to decrease, Δϕ0.5eV, at an equilibrium separation of d0=2.4Å, which agrees very well with our calculated result of Δϕ0.4eV (see Fig. 1). At separations of d5Å, the work function is expected to increase, Δϕ0.3eV (Ref. 62) (with intercalated AM the distance between graphene and Cu(111) in our simulations is d5Å).

FIG. 1.

Work function for different coverages of AMs. In the case of Cu(111), we find ϕ=5.19eV, and for graphene on Cu(111), we find ϕ=4.77eV.

FIG. 1.

Work function for different coverages of AMs. In the case of Cu(111), we find ϕ=5.19eV, and for graphene on Cu(111), we find ϕ=4.77eV.

Close modal

In our case, we have AMs intercalated between the graphene and Cu(111) surface. At low coverages, we expect the model to work well. However, as more AM adatoms are added, the following modifications should be made to the picture: κ will describe an effective dielectric constant for the layer of AM, ϕM will be modulated (reduced) depending on the coverage of AMs on Cu, and the Δc(d) term should be modified to reflect the distance between graphene and AM layer. We now examine the effects of each of these modifications.

As more adsorbates are added to the layer between graphene and Cu, the effective dielectric constant, κ, increases resulting in a larger shift in Fermi-level. This picture is consistent with the increase of ϕW as coverage is increased from θ=1/16 to θ=4/16 shown in Fig. 1.

A well known effect of AM adsorption on a metal surface is the lowering of the work function with a very strong dependence on the alkali coverage36,38 with a minimum typically at coverages of θ0.10.25.64 In the case of Cu and Li, the measured work function, ϕ, varies by up to 2 eV depending on the Li coverage.65 With full coverage of Na atoms, ϕW of Cu(111) is lowered from 4.94eV to 2.77eV.66,67 This change in work function (ϕM) leads to an increased |ϕMϕGΔc(d)|, leading to a larger shift in Fermi-level and thus an initial increase in ϕ(d).

This effect is balanced by the interaction with the new adsorbate layer as the coverage is increased. This is accounted for by an increased Δc(d)=eγd(a0+a1d+a2d2), where d is now reflecting the distance between graphene and AM not graphene and Cu(111). However, note that there is some variation in layer spacing. Generally, the model is not very sensitive to these changes as the variation in layer spacing at different coverages is minimal, except in the case of Li.61 

These considerations account for the general trend of the ϕW curves shown in Fig. 1. At all coverages, ϕW is reduced from ϕ=4.77eV of graphene on Cu(111). For all AMs considered, ϕW initially increases again with the increase in coverage, drops dramatically at an intermediate coverage, and then increases again with further increases in coverage. In particular, the initial increase in ϕW when coverage is increased from θ=1/16 to θ=4/16 is well accounted for by the change in effective dielectric constant.

However, the model fails to elucidate an essential physical process at intermediate coverages. For AMs on Cu(111), the basic mechanism for modification of ϕ at low coverages is the creation of a surface dipole via partial ionization of the alkali atom. As the coverage is increased, the strength of this dipole is reduced as it is energetically more favorable to maintain electrons in a layer of AM atoms.36 This explanation works satisfactorily in the case of AMs on Cu(111) or graphene alone, but should be modified for the present situation.

To this end, a Bader charge analysis of the all-electron density is done to quantify charge transfer.68 The Bader volumes are assigned using the all-electron density, calculated on a fine grid (140 × 140 × 576 grid points), while the values reported are the usual valence charge density. At low coverages, the ionization of alkali atoms is high and the electron density is distributed between both the Cu and graphene, resulting in a suppression of the surface dipole at low coverages. This is illustrated in Fig. 2, where the difference in valence and Bader charge per adatom is plotted as a function of coverage. In the top panel, the ionization of the AMs is shown to decrease as the coverage is increased. The lower panels show the amount of charge per adatom which has transferred to the graphene and copper.

FIG. 2.

Electrons transferred per adatom from Bader analysis. Positive (negative) values indicate a loss (gain) of electrons.

FIG. 2.

Electrons transferred per adatom from Bader analysis. Positive (negative) values indicate a loss (gain) of electrons.

Close modal

As the coverage is increased, the charge transferred per AM adatom is decreasing, consistent with the picture of a depolarization effect where the adsorbates interact and form a decoupled layer. In fact, in the case of Li, the total charge transferred peaks at θ=4/16 and is decreasing with increased coverage. The charge from AM atoms is distributed to the both the graphene and Cu surface, with the graphene receiving more of the charge. We define the charge density difference, Δρ(r)=ρCu+X+grapheneρCuρXρgraphene, where X = Li,Na,K. In Fig. 3, we show the plane averaged charge density difference normalized by the number of AM adatoms. The depolarization effect is also clearly illustrated by the decrease in charge density difference per adatom with increasing coverage.

FIG. 3.

Plane averaged charge density difference per adatom for different coverages of Li (top), Na (middle), and K (bottom). The copper slab is indicated in gray, and the approximate positions of alkali metal and graphene are indicated by dashed green and blue lines, respectively.

FIG. 3.

Plane averaged charge density difference per adatom for different coverages of Li (top), Na (middle), and K (bottom). The copper slab is indicated in gray, and the approximate positions of alkali metal and graphene are indicated by dashed green and blue lines, respectively.

Close modal

Next, we relate these charge density difference plots to the formation and suppression of a surface dipole. The dipole moment normal to the surface can be estimated via

μN=[rΔρ(r)d3r]z=bulkvaczΔλN(z)dz,
(2)

where ΔλN(z) is Δρ(r) averaged over the xy plane.69 Calculated net dipole moments normal to the surface are shown in Fig. 4. The magnitude of the net moment is at a maximum at intermediate coverages of θ=4/16 to θ=8/16. At lower coverages, the moment is suppressed because the AM shares electrons with both the Cu and graphene. At higher coverages, the magnitude of the dipole moment is decreasing due to the depolarization of the AM layer.

FIG. 4.

Net surface dipole moment (see Eq. (2)).

FIG. 4.

Net surface dipole moment (see Eq. (2)).

Close modal

To illustrate the depolarization effect, we consider a uniform layer of dipoles, each feeling a field due to the adjacent dipoles. The field in this case is given by E=8.89N3/2μ, where 8.89 is a geometric factor, N is the number of adatoms, and μ is the dipole moment.70 Expressing the dipole moment as μ=μ0+αE, where α is the polarizability, and substituting with the Helmholtz equation, Δϕ=4πμN, the change in work function can be written as Δϕ=4πμ0N1+8.89αN3/2.46,70,71 This function is characterized by a minimum at N0=(2/889α)(3/2), showing a clear dip corresponding to the intermediate coverages.

Finally, we discuss the potential for tuning ϕW of graphene in these systems. A DFT calculation46 studied suspended graphene with AM adatoms of various coverages applied to one face of the graphene. The main difference is that they did not include a substrate in their calculations. They found that the dependence of ϕW on adatom coverage for both the graphene layer side and the adatom layer side was different. For the graphene layer side, as the adatom coverage is increased, ϕW sharply declines and then plateaus. On the adatom side, they found a behavior similar to our results, little change in ϕW at very low coverages, a pronounced drop at intermediate coverages, and a subsequent increase as coverage is increased. The main feature to note in their calculation is that ϕW of the exposed graphene surface is only reduced when AM atoms are adsorbed on the opposite side.

Compared to tuning via gating, which has been shown to induce a change in work function up to Δϕ0.3eV,12 intercalation is a passive method which does not require active electronics and can induce a greater change in work function, Δϕ0.9eV (Fig. 1). Chemical doping via deposition of alkali metal carbonates achieves similar changes in work function (Δϕ0.8eV),18 but the exposed surface modifications may show increased reactivity. The inclusion of a substrate in our calculations shows that ϕW of the exposed graphene layer can exhibit a more complex dependence. In cases with substrates known to significantly alter the electronic structure of graphene, the physics may differ substantially from the present results. With intercalation of AMs, one can tune ϕW of the exposed graphene layer through varying the concentration of intercalated atoms. We note that in practice, a precise control of the concentration of AM may prove difficult, though one may consider advanced techniques for patterning adsorbates such as positioning atoms with an STM tip.72 

In conclusion, we have shown that ϕW of a graphene monolayer on a Cu(111) surface can be modulated by varying the concentration of intercalated AM atoms. The change in ϕW was found to be driven by the formation and depolarization of an interfacial dipole and the dynamics of Fermi-level shifts induced by the metal surface. We found that the bonding and charge transfer dynamics are altered from the case of AM on freestanding graphene and graphene on metal surfaces. In particular, we find that the exposed graphene surface exhibits the change in ϕW when the Cu(111) substrate is present in contrast to previous results showing that the effect would only be visible in suspended graphene systems on the side to which the AM atoms are adsorbed.46 Our results indicate that the metal–AM–graphene platform can be useful in applications requiring engineered work functions, such as field emission applications where the graphene can also serve as a protective layer.

We thank Jonathan Jarvis for many useful conversations. This work has been supported by the National Science Foundation (NSF) under Grant Nos. PHY1314463, ECCS1307378, and IIA126117. Additional support was from NSF Award No. OCI-1226258.

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Supplementary Material