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Tunable high workfunction contacts: Doped graphene
Journal Pre-proofs Full Length Article Tunable High Workfunction Contacts: Doped Graphene Merid Legesse, Sergey N Rashkeev, Feras Al-Dirini, Fahhad H Alharbi PII: DOI: Reference:
S0169-4332(19)33710-9 https://doi.org/10.1016/j.apsusc.2019.144893 APSUSC 144893
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Applied Surface Science
Received Date: Revised Date: Accepted Date:
29 September 2019 11 November 2019 28 November 2019
Please cite this article as: M. Legesse, S.N. Rashkeev, F. Al-Dirini, F.H. Alharbi, Tunable High Workfunction Contacts:, Applied Surface Science (2019), doi: https://doi.org/10.1016/j.apsusc.2019.144893
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Tunable High Workfunction Contacts: Doped Graphene Merid Legesse1, Sergey N Rashkeev1, Feras Al-Dirini2, Fahhad H Alharbi2, 3 1Qatar
Environment and Energy Research Institute, Hamad Bin Khalifa University, Doha, Qatar.
2Electrical
Engineering Department, King Fahd University for Petroleum and Minerals, Dhahran, Saudi Arabia.
3K.A.CARE
Energy Research & Innovation Center, Dhahran, Saudi Arabia.
Abstract Contact electrodes with high work functions can enable significant enhancement in optoelectronic device performance due to their important role in efficient extracting/injecting carriers especially from optically active materials with high electron affinity or deep valence band edge, such as CdTe and some perovskites. With such materials becoming increasingly important in emerging solar cell technologies, the need for high work function electrodes has become of timely importance. In this work, p-doped graphene is investigated using first principle calculations, as a potential high work function contact electrode material for optoelectronic device applications. We found that chemical doping based on the adsorption of different non-metallic adatoms on graphene allows tuning the work function which can reach as high as 5.76 eV. A range of p-dopant adatoms, with varying doping concentrations, was investigated and we showed that the largest change of the work function is caused by chlorine and bromine dopants: a 4% concentration of Cl and Br dopants
results in an increase of the work function of graphene from 4.38 eV to 5.76 eV and 5.71 eV, respectively. Furthermore, the calculations show that this significant increase in graphene’s work function is mainly due to the charge transfer from graphene to p-dopant adatoms, which increases the concentration of holes at the graphene surface, and hence, increases its work function. We also analyzed the stability conditions for absorbed halogen adatoms on graphite. In particular, we found that halogen molecules formation process should be significantly inhibited by electrostatic repulsion between charged adatoms which provides additional barrier for them to get closer to react. These findings provide valuable guidance to experimental efforts towards the realization of tunable high work function graphene-based electrodes.
1. Introduction Photovoltaic devices harness the sun’s energy through the absorption of photons which results in the generation of an electron-hole pairs within the absorber material of a solar cell, with a subsequent extraction of these electrons and holes by an external electrical circuit. It is crucial that these electron-hole pairs are not given an opportunity to recombine too fast and lose the absorbed energy, and hence selective extraction of these electrons and holes by an external circuit becomes possible. This extraction process is heavily dependent on the conductivity of the external metallic electrodes as well as their interfaces with the light absorber material and window layers, which form the electron and hole selective interfaces of a solar cell, referred to as contact electrodes. Consequently, developing efficient and stable contact electrodes is essential for optimized performance and long-term stability of solar cells, and has been a challenge for a number of emerging solar cell technologies, especially those technologies that use active materials with deep valence band edge, such as CdTe and some perovskites. For any interface, a proper work function
is needed to ensure having ohmic contact (and not Schottky barrier) and to reduce voltage losses. The presence of a Schottky barrier increases the contact resistance, thereby impacting the solar cell performance detrimentally1. Currently, high work function contacts are implemented using platinum (with the work function of 5.65 eV )2, 3. However, the high cost of platinum requires the search for alternative high work function contact materials. Furthermore, due to the extremely high work function of Pt, it forms Schottky barriers with most of the known solar absorbers. In addition, having an ability to increase and tune up the work function of the contact material would open up unprecedented opportunities in enabling a range of emerging photovoltaic solar cell technologies including perovskites-based solar cells, for which the use of contact materials with high work functions is critically important4. Actually, this should find more applications in other electronic and optoelectronic devices. Being a potential candidate, graphene was implemented and reported as an alternative electrode material in solar cells5-9.
However, devices with graphene-based electrodes have mostly
underperformed in comparison to devices with metallic electrodes. One of the main reasons for this underperformance was the lower work function of graphene than the work function of some metals (e.g., Pt). Modification of the graphene’s work function by doping may increase it which will provide a chance to use graphene as a contact electrode material. Chemical doping has been reported to be efficient in modulating the work function and tailoring other electrical properties of graphene by charge transfer in and out the graphene sheet. Substitutional chemical doping of graphene is extremely challenging and has shown detrimental effects on graphene’s electrical properties, calling for alternative doping strategies such as attaching adatoms to graphene sheets. Doping of graphene with various adatoms10-30 and heteroatoms31-33 has been also extensively studied. The synthesis of nitrogen (N)-doped graphene
is feasible through a variety of different methods10, 11, 12, 13, 14, 15 , 16, 17, 18. Panchakarla10 et al. prepared nitrogen-doped graphene by carrying out arc discharge in the presence of mixtures (H2 + pyridine) or (H2 + ammonia) in the gas phase. Sheng et al.14 proposed a facile, catalyst-free thermal annealing approach for large scale synthesis of N-doped graphene using a low-cost industrial material melamine (C3H6N6) as the source of nitrogen. Yang et al.19 used SH2 gas to react with graphene oxide, in order to produce S-doped graphene. However, the resultant S-doped graphene had lower conductivity than the pristine graphene. Gao et al.20 demonstrated the growth of largearea S-doped graphene sheets on copper substrate via chemical vapor disposition (CVD) by using sulfur containing organic molecules as a precursor. Moreover, Denis21 also concluded that phosphorus doping of graphene opens a band gap larger than the one induced by sulfur, and that both P and S doped graphene can be employed for sensing applications. Furthermore, Walter et al.22 demonstrated that fluorine interaction with the carbon buffer layer on SiC leads to the formation of a strongly p-doped graphene layer that is decoupled from the substrate through intercalation, shifting the Dirac crossing point to above the Fermi energy. Zhan et al.24 synthesized I-doped graphene by a facile heat treatment method, which was then employed as an anode material for lithium ion batteries. Finally, Zhang28 et al. focused on a plasma-based chlorination process. By carefully tuning the plasma condition, they found an optimized reaction regime in which they could achieve stable single-sided chlorinated graphene with a high surface coverage (45.3 at. %, which is close to C2Cl) and with excellent carrier mobility performance (1535 cm2/V s). This result was repeatable, and the as-fabricated sample was stable at room temperature under ambient conditions. All the above work clearly highlights the extensive experimental efforts made towards modifying electronic properties of graphene through chemical doping.
In this work, we investigate the possibility of tuning (increasing) the work function of graphene by chemical doping with non-metallic adatoms (i.e. N, P, As, O, S, Se, F, Cl, Br and I) as pdopants. The effect of the p-dopant adatoms was investigated for dopant concentrations in the range of 1-4%. The structural and electronic properties as well as the work function of the proposed p-doped graphene based materials were calculated using the Density Functional Theory (DFT) methods. The results indicate that all considered p-dopant adatoms adsorbed at stable adsorption sites of graphene, increase the work function. This is due to the electron transfer from the graphene sheet to the p-dopant adatoms (Figure 1). The p-dopant adatoms are more electronegative elements than carbon and have a tendency to accept electrons from a graphene plane. It results in the depletion of electrons at the plane (i.e., increasing the concentration of holes in the plane) which results in a downward shift of the Fermi energy from the Dirac point. The magnitude of this change in graphene’s work function depends on the type of p-dopant and its concentration.
Figure 1. Schematics of the mechanism of graphene doping by p-dopant adatoms. 𝐸𝑣𝑎𝑐 corresponds to the vacuum energy level of the system, 𝐸𝑓 is the Fermi energy of the material, 𝛷𝐺 is the work function of pristine graphene, and 𝛷𝐺+𝑛𝑀 is the workfunction of graphene with attached individual non-metal adatom. Carbon atoms are shown in gray, non-metal adatom – in orange.
This paper is organized as follows. Section 2 outlines the details of computational methods used. This is followed by a description of the systems under investigation and an in-depth analysis of their structural properties (Section 3). Section 4 presents the results for the calculated work functions for different systems under consideration, and an analysis of their charge density distribution. Section 5 analyses the electronic properties of these systems, with a focus on their band structure. Finally, Section 6 summarizes the findings.
2. Methods In this work, DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP)34, 35. The approach is based on an iterative solution of the Kohn-Sham equations of the DFT in a plane-wave basis set with the Projector Augmented Wave (PAW)36, 37 pseudopotentials. The semicore 2p states of N, O and F, 3p states of P, S and Cl, and 4p and 3d states of As, Se, Br, and I were treated explicitly as valence states. The Perdew, Burke, and Ernzernhof (PBE)38 exchange-correlation (XC) functional of the generalized gradient approximation (GGA) was adopted. A plane-wave basis set with a maximum plane-wave cutoff energy of 400 eV was used. The Monkhorst-Pack mesh39 for sampling the Brillouin zone with a Gaussian broadening of 0.1 eV was used. In the calculations, the structures were fully relaxed with a Γ– centered 8x8x1 kmesh. A semi-empirical van der Waals correction term vdW-DF40, 41, 42, 43 was included which is known to have a significant impact on the adsorption energies at graphene surfaces. We also performed charge transfer analysis between the p-dopant adatoms and graphene sheet using the Bader44 and DDEC (Density Derived Electrostatic and Chemical) charge analysis approaches45, 46.
Graphene has two C atoms arranged in a two-dimensional honeycomb lattice with a hexagonal primitive unit cell. We used the calculated graphene lattice constant of 2.47 Å for a pristine graphene supercell, which is in-line with the experimental value of 2.46 Å47. For notation, we let x and y to be the in-plane directions and z to be perpendicular to the graphene plane. A twodimensional 7 × 7 supercell (consisting of 98 carbon atoms) was used to simulate the graphene sheet, and the neighboring sheets were separated by at least 15 Å of vacuum in the 𝑧 −direction to prevent interlayer interactions (See more details in Ref.[48]). Different types of non-metallic adatoms (namely, N, P, As, O, S, Se, F, Cl, Br and I) were used as p-dopants. In order to explore the effect of the p-dopant concentration, three different concentrations (1%, 2%, and 4%) for each adatom were considered. Equilibrium atomic positions were determined for fully relaxed supercells (with relaxed cell volume, lattice vectors and atomic positions). Self-consistent total energy calculations were stopped when the successive energy difference between the two iterations became less than 10–4 eV, and the Hellmann-Feynman forces acting on each atom became less than 0.01 eV/Å.
3. Results & discussion 3.1
Structural properties of p-doped graphene
To study the structural properties of p-doped graphene, p-dopant adatoms were placed at graphene sheet in the three adsorption sites shown in Figure 2: (i) above the center of the graphene hexagonal ring (hollow site, or H-site); (ii) above the C-C bond (bridge site, or B site) and; (iii) above the carbon atom (top site, or T site). Of the three considered adsorption sites, the site with the highest adsorption energy (minimal total energy) is referred to as the favored site.
(a)
Pristine Graphene
(c)
Top –site
(b)
Hollow –site
(d)
Bridge–site
Figure 2. Structural properties of p-doped graphene. Carbon atoms are shown in gray, the p-dopant adatom (i.e., 𝑁, 𝑃 𝐴𝑠, 𝑂, 𝑆, 𝑆𝑒, 𝐹, 𝐶𝑙, 𝐵𝑟 and 𝐼) - in orange.
The most favorable adsorption sites for different nonmetal adatoms at graphene plane are calculated (Figure 3). The result shows that for Group V and VI nonmetal elements, the 𝐵 − site indicated by vertical blue bars in Figures 3 (a) and (b) is the most stable adsorption site. In the previous work,48 we showed that Group I, II, and III metal adatoms prefer to be adsorbed in the H − sites above the graphene sheet. However, for the Group VII adatoms (F, Cl, Br and I), the T − site indicated by vertical green bars in Figure 3 (c) is the most stable adsorption site. These results are consistent with previous reports49. The distances between graphene and the nonmetal adatoms are also shown in Figure 3. It shows that within each group the distance between the nonmetal adatom and graphene plane grows with the atomic number of the element.
4
4
4
3
…
3
3
2
2
2
1
1
1
0
0
0
-1
-1
-1
-2
-2
-2
-3
-3
-3
-4
-4
-4
N
P
As
(a)
O
S
Se
F
(b)
Cl
Br
I
(c)
Figure 3. Calculated distance (𝑑𝐺−𝐴𝑑 ) between the adatom and graphene plane (Top: y- axes, vertical bars) and adsorption energy for an individual adatom (Bottom: y- axes, filled red circles) for the most stable adsorption sites of adatoms at graphene plane for: (a) Group V elements; (b) Group VI elements and; (c) Group VII elements. The most stable adsorption sites are the B- sites for the Group V and Group VI elements (blue vertical bars for 𝑑𝐺−𝐴𝑑 ) and the T- sites for the Group VII elements (green vertical bars).
3.2
Adsorption energy of p-doped graphene
The adsorption energy of individual adatom on graphene, ∆𝐸𝑎𝑑 , is defined as ∆𝐸𝑎𝑑
=
𝐸𝐺+𝑛𝑀 − 𝐸𝐺 − 𝐸𝑛𝑀
(1)
Here 𝐸𝐺+𝑛𝑀 is the total energy of graphene supercell with adatom, 𝐸𝐺 is the total energy of the pristine graphene supercell and 𝐸𝑛𝑀 is the total energy of the isolated nonmetal adatom in vacuum. The adsorption geometry is obtained by relaxation. The adsorption energy of adatoms on graphene is shown in Figure 3 in red circles. For example, the N adatom adsorbs strongly on pristine graphene at the B − site, and its adsorption energy is -3.23 eV, the F adatom binds shrongly at the T – site (-2.68 eV), while other halogen Cl, Br and I adatoms weakly adsorb at the T − site, with an adsorption energy of -1.19, -1.05 and -0.87 eV respectively (Figure 3). More detailed examination of electron charge density associated with the Cl, Br and I adatoms reveals that
interaction between these adatoms and graphene is weak which is related to the lack of substantial overlap between these adatoms and graphene states (see more details in section 4.1). In other words, Cl, Br and I adatoms form charged covalent bonds with graphene. In experiment, adsorption of Cl, Br and I on graphene surface is wildly studied and shows that the Cl and Br adatoms could be successfully adsorbed on graphene surfaces. For example, Zhang28 et al. found an optimized reaction regime in the plasma-based chlorination process and achieved stable singlesided chlorinated graphene with a high surface coverage (45.3 at. %). The as-fabricated sample was stable at room temperature under ambient conditions. Meanwhile, the stability of halide adatom adsorption at the graphene surface is still an open question (Refs. [27-30]). To get a better insight into this problem, we calculated the value of Ediff = (Eb,mol – 2 Ead ) for each of the four halogen atoms (F, Cl, Br, and I). Here Eb,mol is the bond energy (F-F, Cl-Cl, Br-Br, and I-I) in free, neutral F2, Cl2, Br2, and I2 molecules. We took these values (-1.61, 2.52, -1.97 and -1.53 eV for F2, Cl2, Br2, and I2) from Ref.[50]. The positive value of Ediff means that configuration with two absorbed individual adatoms at the graphene surface is energetically more favorable than the formation of a diatomic molecule. The negative value of Ediff means that halogen molecule will be formed, and adatoms will not bind to the surface. For fluorine adsorption, the value of Ediff is +3.75 eV, i.e., formation ot F2 molecule is thermodynamically unfavorable. For other halogens (Cl, Br, and I), the situation is not that clear, i.e., more research should be performed. Table 1 shows that the absolute value of Ediff is much lower than both Eb,mol and Ead for all three halogens. In addition to that, several calculations [27, 51] indicated that barrier for the migration between nearest T- sites is extremely low ( < 0.005 eV according to Ref. [51]) which means that even at moderate temperatures, individual absorbant will continuously migrate around the surface. At the same time, the bonding between adatom and
graphene surface is not purely covalent, and charge transfer between halogen adatoms and graphene surface occurs (see also Figure 6 below) which causes an appearance of a significant negative charge ( QAd-G) at the halogen dopant. Let us assume that two halogen adatoms get closer to each other while migrating around the surface. Interaction between them includes two components: (i) Coulomb repulsion between two negatively charged atoms; (ii) Covalent bonding between them. Coulomb repulsion is a long-range interaction while covalent bonding plays any role at short distances only. Calculations for Cl adsorbants positioned at one side of a graphene sheet indicated that Cl2 molecule starts to form when the distance between the two adsorbed Cl adatoms is less that the distance between the fourth nearest T-site neighbors (3.6 Å) [27]. The covalent bonding between two atoms positioned at such distance (calculated by continuously increasing the interatomic distance in free, neutral molecule) is very low for all three halogens (Table 1). The Coulomb repulsion between the two charged adatoms is quite high which means that there is a reasonably high barrier for two absorbed halogen atoms to come closer on graphene surface. This Coulomb repulsion energy could be considered as a qualitative estimate of the value of the barrier. Now we could try to describe the behavior of halogen adatoms positioned on one side of the graphene sheet. When two halogen atoms randomly migrate around the graphene surface, at some point they could get closer. The Coulomb repulsion between them turns on at much larger distance than covalent attraction which forms a barrier for them to get closer. Meanwhile, these atoms can easily migrate (with nearly zero barrier) in the directions for which the distance between them is not reducing. Apparently the statistical probability to migrate in these directions is much higher than to migrate in directions for which the distance reduces. Such a dynamic behavior could explain the stability of halogen adatoms adsorbed at graphene surfaces. This picture should be
valid at least for low concentration of adatoms at the surface. For higher concentrations, however, one should also take into account the delicate balance between the electrostatic repulsion between adatoms and covalent bonding between them. Recent experiment with plasma-based chlorination process, in which stable single-sided chlorinated graphene with a high surface coverage (45.3 at. %) was achieved [28], partly confirms this picture. Table 1. Adsorption energy (Ead), molecular binding energy (Eb,mol), the value of Ediff, the value of charge at the absorbed adatom ( QAd-G), Coulomb and covalent energies (ECoul and Ecov ) for Cl, Br, and I adatoms at graphene surface positioned at the fourth nearest neighbor T-site positions (at distance of 3.6 Å). Element
Ead (eV)
Eb,mol (eV)
Ediff (eV)
QAd-G (e)
ECoul (eV)
Ecov (eV)
Cl
-1.19
-2.52
-0.14
-0.5
+0.99
< 0.05
Br
-1.05
-1.97
+0.13
-0.46
+0.91
< 0.05
I
-0.87
-1.53
+0.23
-0.39
+0.77
< 0.05
3.3
Work function of p-doped graphene
In general, adatom adsorption on graphene is expected to alter Fermi level and dipole moment of the system. Also, there can be a noticeable change in work function of such system relative to the pristine graphene. The electron work function (Φ) is the minimal energy required to extract an electron from the surface of the solid defined as Φ = 𝐸𝑣𝑎𝑐 − 𝐸𝑓 , where 𝐸𝑣𝑎𝑐 is the reference vacuum energy and 𝐸𝑓 is the Fermi level of the system graphene plus adsorbed adatoms52. In our calculations, 𝐸𝑣𝑎𝑐 is determined from the electrostatic potential in the vacuum region, far enough from the adatom-graphene system in the 𝑧 −direction that the value is converged (see Figures 4
and S1 from Supporting Information section). Figure 4 shows the electrostatic potential < 𝑉 > averaged inside the supercell over the planes parallel to the graphene layer as a function of the distance from the layer of chlorine-doped graphene. This computational method method has been widely used in previous studies for calculating the work function48,
53, 54
. Similarly, 𝐸𝑓 is
determined by the upper limit of the integral of the density of states from the lowest calculated energy level to the energy that gives the total number of electrons per the unit cell.
Figure 4. The electrostatic potential < 𝑉 > averaged inside the supercell over the planes parallel to the graphene layer as a function of the distance from Cl-doped graphene surface.
The main target of this work is to determine the change of the work function of p-doped graphene as a function of dopant concentration. Figure 5 shows the work function of doped graphene for different p-dopants and different dopant concentration. For pristine graphene, the calculated work function is 4.38 eV which is in good agreement with both previous experimental and theoretical
results48,
53, 54
. A presence of p–dopant adatoms always has a tendency to increase the work
function of the system (see Figure 5). This is consistent with experimental and previous theoretical work26, 57. For example, nitrogen doped graphene exhibits higher work function than pristine graphene (Figure 5 (a)). This is related to the fact that electronegativity of nitrogen atom is higher than electronegativity of carbon atom at the graphene plane. Therefore, N atom has a tendency to grab electrons from the graphene plane which causes depletion of the electron density at the plane. Consequently, the Fermi energy of the system is shifted down from the Dirac-point which increases its work function. The magnitude of the Fermi energy shift from the Dirac-point towards deep valence bands depends on the electronegativity of nonmetal adatoms and their concentration. For Cl–doped graphene, the work function increases from 4.38 eV to 5.76 eV for 4% doping, which is the largest effect for all nonmetal adatoms considered here (and the dopant concentrations not exceeding 4%). Other Group VII adatoms (F, Br, and I) also significantly increase the work function of the graphene plane. If the number of atoms per supercell is larger than one (for 7 x 7 graphene supercell with 98 atoms, 1% concentration approximately corresponds to 1 adatom per cell, 2% - to 2 atoms, 4 % - to 4 atoms), different mutual arrangements of adatoms at the plane are possible. To take these arrangements into account, we performed calculations for five different configurations for each dopant. For a supercell with two adatoms (2% doping), the configurations differ by the distance between the two adatoms starting from the configuration where the two atoms are positioned at two neighboring stable sites. For a four dopant supercell (4% doping), we also started from the configuration where the four atoms are positioned at neighboring sites; other structures with 4 adatoms were randomly generated. This approach allowed perform a statistical analysis and evaluate the error bar for the work function at different adatom concentrations. Figure 5 clearly
indicates that error bars of the work function are quite small (below 0.02 eV), i.e., the result does not depend strongly on the dopant arrangement.
7
7
7
5
5
5
3
3
3
1
1 N
P
As
WF ( 1%)
WF (2%)
WF (4%)
1 O
S
Se
F
Cl
Br
I
(b) (c) Figure 5. The work function ( ) for different concentration of nonmetal adatoms at p-doped graphene: (a) Group V adatoms, (b) Group VI adatoms, and (c) Group VII adatoms. Results for 1% adatoms concentration are shown in cyan, for 2% concentration - in indigo, and for 4% concentration – in green. The error bars are shown in red.
(a)
3.4
Charge density analysis of p-doped graphene
In this section, calculations of charge transfer in p-doped graphene are performed based on the Bader and the Density Derived Electrostatic and Chemical (DDEC) charge analysis methods. For the most stable adsorption sites previously identified in Section 3 (B − sites for the Groups V and VI elements and T − sites for the Group VII elements), the results are shown in Figure 6. The Bader charges were calculated from the charge densities generated by the VASP codes using the program developed by G. Henkelman et al44.
0
0
-0.2
-0.2
-0.2
-0.4
-0.4
-0.4
-0.6
-0.6
-0.6 N
P
As
(a)
DDEC
O
S
Bader
Se
0
F
(b)
Cl
Br
I
(c)
Figure 6. Charge transfer (the charge difference between an isolated atom and atom at the graphene plane) from graphene to individual nonmetal adatom (𝒬𝐴𝑑−𝐺 ) for: (a) Group V elements; (b) Group VI elements, and; (c) Group VII elements. Charge transfers calculated by both Bader and DDEC analysis methods are shown.
Figure 6 indicates a negative charge transfer from graphene to any p- dopant adatom, i.e., the electron density at the graphene plane at the vicinity of the adatom defect is depleted which shifts the Fermi level from the Dirac point deeper into the valence band. In general, the charge transfer values calculated by both Bader and DDEC are in close agreement. However, DDEC fails to predict the value for charge transfer for fluorine, as shown in Fig. 5(c). It happens because the differential electron charge density distribution plot for the F-doped graphene (see Figure 7 (g) below) clearly indicates a significant electron density depletion at the graphene sheet and electron density accumulation at the F adatom. The differential charge densities for different p-dopants given by the equation, ∆𝜌 = 𝜌𝐺+𝑛𝑀 − 𝜌𝐺 − 𝜌𝑛𝑀
(2)
are shown in Figure 7. Here 𝜌𝐺+𝑛𝑀 is the charge density of graphene with adsorbed nonmetal adatom, 𝜌𝐺 is the charge density of the pristine graphene sheet, and 𝜌𝑛𝑀 is the charge density of an isolated nonmetal adatom.
Figure 7. Differential electron charge density distribution for the graphene sheet that has been pdoped through an adsorption of different nonmetal adatoms: (a) N; (b) P; (c) As; (d) O; (e) S; (f) Se; (g) F; (h) Cl; (i) Br, and; (j) I. Carbon atoms are shown in gray; the nonmetal adatom located within the charge density cloud - in red. The gold color corresponds to negative differential charge accumulated around the nonmetal adatom, while the cyan color – to the electron charge depletion (excess of the positive charge) at the graphene plane.
In Figure 7, the cyan color corresponds to an excess of positive charge (electron depletion) which occurs at the graphene sheet at the vicinity of the adatom. For Cl, Br and I atoms, the differential charge density plots clearly show the highest depletion of electrons at the graphene plane and the
highest degree of localization of the electron charge at the adatom. This accumulation significantly reduces the hybridization between electronic states of the adatom and the rest of graphene plane which explains why the shift of the Fermi level down from the Dirac point is the highest for Group VII elements.
3.5
Electronic structure of p-doped graphene
To study the effects of adatom adsorption on the electronic properties of graphene even further, we calculated the band structure of graphene supercells with different types of p-dopants and different concentrations. The band structure of the pristine graphene supercell is shown in Figure 8 (a). In the planar hexagonal structure of graphene, the 𝑝𝑥 and 𝑝𝑦 orbitals of carbon are degenerated. They hybridize with the 𝑠 orbital and form the 𝑠𝑝2 𝜎 bond states. The 𝑝𝑧 orbitals form the bonding (𝜋) and antibonding (𝜋 ∗ ) orbitals oriented normally to the graphene sheet. The corresponding two electronic bands touch at high symmetry 𝐾 point of the Brillouin zone, i.e., the bandgap in the pristine graphene is zero (Figure 8 (a)). The band energies are changing linearly near the Dirac point which leads to a vanishing effective masses for the charge carriers. These features of the electronic properties of graphene are responsible for the observed ballistic transport, Dirac-type quasiparticles, and anomalous quantum Hall effect 58, 59, 60, 61, 62 .
Figure 8. The band structure of: (a) Pristine graphene supercell; (b) Graphene supercell with 1% of nitrogen dopant; (c) Same for 2% of nitrogen dopant; (d) Same for 4% of nitrogen dopant. Electronic bands with dominant contribution of C atoms are shown in red, and bands with dominant contribution of N atoms – in green. Fermi energy for each system is indicated by horizontal dashed line. Zero energy corresponds to the Fermi level of the pristine graphene.
The band structures of nitrogen doped graphene, with different adatom concentrations, are shown in Figures 8 (b-d). Figure 8 (b) shows the band structure of N-doped graphene with nitrogen concentration of 1% (one N adatom in 98 atoms graphene supercell). The band structure shows that the 2𝑝 orbitals of nitrogen strongly hybridize with the 𝑠𝑝2 orbitals of graphene, which corresponds to the chemisorption of nitrogen atom at the graphene plane. It results in distortion of the two-dimensional lattice structure of graphene which breaks its symmetry and opens a gap of 0.11 eV between the 𝜋 and 𝜋 ∗ graphene bands. The higher concentration of nitrogen adatoms increases not only the work function of graphene but also the 𝜋 – 𝜋 ∗ gap (which becomes 0.32 eV at nitrogen concentration of 4%). This result is consistent with previously reported experimental results63.
(a)
(b)
(c)
Figure 9. Band structure of Cl-doped graphene supercells with dopant concentration of: (a) 1%; (b) 2%; (c) 4%. Electronic bands with dominant contribution of C atoms are shown in red, and bands with dominant contribution of Cl atoms – in green. Fermi energy for each system is indicated by horizontal dashed line. Zero energy corresponds to the Fermi level of the pristine graphene.
Unlike nitrogen, chlorine adatom couples to graphene plane weakly. Therefore, the adsorption of Cl to graphene causes insignificant distortion of the two-dimensional hexagonal honeycomb graphene lattice only. The 𝜋 and 𝜋 ∗ electronic bands are still linear near the Dirac point and have a zero gap between them (Figure 9). Bromine and iodine doped graphene shows the behavior similar to the Cl doped material (see Supporting Information, Figures S2 and S3). Table 1. The 𝜋 – 𝜋 ∗ gaps of p-doped graphene for different adatom dopants at two dopant concentrations (1% and 4%). Adatom 𝜋 – 𝜋 ∗ gap for 1% of dopants (eV) 𝜋 – 𝜋 ∗ gap for 4% of dopants (eV)
F 0.15
Cl Br I N 0.00 0.00 0.00 0.10
P 0.20
As 0.15
O S Se 0.30 0.22 0.10
0.25
0.00 0.00 0.00 0.32
0.30
0.34
0.35 0.25 0.30
Opening a 𝜋 – 𝜋 ∗ gap in graphene has been an endeavor of great importance in the graphene research community, since most envisioned applications for graphene in electronic devices require the presence of a bandgap. In this work, we have reported the possibility of opening a 𝜋 – 𝜋 ∗ gap in graphene by doping, We also found that this band gap may be tuned by varying the concentration of dopant adatoms. Table 1 shows the 𝜋 – 𝜋 ∗ gaps for different types of non-metal adatoms and two different dopant concentrations. Notably, the gaps of oxygen, nitrogen and phosphors doped graphene could reach above 0.3 eV at dopant concentration of 4%.
4. Conclusion We investigated possibilities for increasing the work function of graphene by adsorption of nonmetal adatoms (p- dopants), in order to use such systems as a back-contact electrode for emerging photovoltaic technologies. We performed this study for different adatom dopants and different dopant concentrations. For all the nonmetal Group V and Group VI adatoms considered, we showed that the bridge (B) site at the graphene plane is the most stable site, while for Group VII elements prefer to be adsorbed at the graphene top (T) sites. We found that p-doping of graphene by adatoms is highly efficient in modulating the 𝜋 – 𝜋 ∗ gap of graphene and increasing its work function. We found that the work function of graphene can increased from 4.38 eV for pristine material to 5.76 eV and to 5.71 eV for Cl–doped and Br-doped graphene respectively (at the dopant concentration of 4%). Using the band structure analysis and differential charge density mapping, we conclude that charge transfer from graphene to non-metal adatoms causes the depletion of electrons at the graphene plane and lowering the Fermi level thus increasing the work function of the system. We also analyzed the stability conditions for absorbed halogen adatoms on graphite. We found that halogen molecules formation process should be significantly inhibited by
electrostatic repulsion between charged adatoms which provides additional barrier for adatoms to get closer to react. These results pave the way towards the experimental realization of high work function graphene contact electrodes, which are of timely importance for emerging photovoltaic technologies. ACKNOWLEDGMENT Funding for this research was provided by Qatar National Research Foundation (QNRF), grant numbers NPRP 7-317-1-055 and NPRP X-107-1-027. Computational resources are provided by research computing at Texas A&M University at Qatar.
Conflict of interest
This paper has not been submitted to any other journal, there are no conflicts of interest and all co-authors are aware of and approve submission of this paper.
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Highlights High workfunction contacts play an important role in efficiently extracting carriers Different p-dopants adatoms on graphene tune the workfunction as high as 5.76 eV Rising workfunction is mainly due to the charge transfer from graphene to pdopants Distortion of the lattice structure of graphene breaks its symmetry and opens a gap p-doped graphene is promising for use of graphene-based contact electrodes
Author contribution
M.L. performed calculations, data analysis and writing paper. S.R. and F.A.D. participated in data analysis and writing the paper. F.H.A. participated in data analysis. All authors contributed to discussions.
Declaration of interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
S0169-4332(19)33710-9 https://doi.org/10.1016/j.apsusc.2019.144893 APSUSC 144893
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Applied Surface Science
Received Date: Revised Date: Accepted Date:
29 September 2019 11 November 2019 28 November 2019
Please cite this article as: M. Legesse, S.N. Rashkeev, F. Al-Dirini, F.H. Alharbi, Tunable High Workfunction Contacts:, Applied Surface Science (2019), doi: https://doi.org/10.1016/j.apsusc.2019.144893
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Tunable High Workfunction Contacts: Doped Graphene Merid Legesse1, Sergey N Rashkeev1, Feras Al-Dirini2, Fahhad H Alharbi2, 3 1Qatar
Environment and Energy Research Institute, Hamad Bin Khalifa University, Doha, Qatar.
2Electrical
Engineering Department, King Fahd University for Petroleum and Minerals, Dhahran, Saudi Arabia.
3K.A.CARE
Energy Research & Innovation Center, Dhahran, Saudi Arabia.
Abstract Contact electrodes with high work functions can enable significant enhancement in optoelectronic device performance due to their important role in efficient extracting/injecting carriers especially from optically active materials with high electron affinity or deep valence band edge, such as CdTe and some perovskites. With such materials becoming increasingly important in emerging solar cell technologies, the need for high work function electrodes has become of timely importance. In this work, p-doped graphene is investigated using first principle calculations, as a potential high work function contact electrode material for optoelectronic device applications. We found that chemical doping based on the adsorption of different non-metallic adatoms on graphene allows tuning the work function which can reach as high as 5.76 eV. A range of p-dopant adatoms, with varying doping concentrations, was investigated and we showed that the largest change of the work function is caused by chlorine and bromine dopants: a 4% concentration of Cl and Br dopants
results in an increase of the work function of graphene from 4.38 eV to 5.76 eV and 5.71 eV, respectively. Furthermore, the calculations show that this significant increase in graphene’s work function is mainly due to the charge transfer from graphene to p-dopant adatoms, which increases the concentration of holes at the graphene surface, and hence, increases its work function. We also analyzed the stability conditions for absorbed halogen adatoms on graphite. In particular, we found that halogen molecules formation process should be significantly inhibited by electrostatic repulsion between charged adatoms which provides additional barrier for them to get closer to react. These findings provide valuable guidance to experimental efforts towards the realization of tunable high work function graphene-based electrodes.
1. Introduction Photovoltaic devices harness the sun’s energy through the absorption of photons which results in the generation of an electron-hole pairs within the absorber material of a solar cell, with a subsequent extraction of these electrons and holes by an external electrical circuit. It is crucial that these electron-hole pairs are not given an opportunity to recombine too fast and lose the absorbed energy, and hence selective extraction of these electrons and holes by an external circuit becomes possible. This extraction process is heavily dependent on the conductivity of the external metallic electrodes as well as their interfaces with the light absorber material and window layers, which form the electron and hole selective interfaces of a solar cell, referred to as contact electrodes. Consequently, developing efficient and stable contact electrodes is essential for optimized performance and long-term stability of solar cells, and has been a challenge for a number of emerging solar cell technologies, especially those technologies that use active materials with deep valence band edge, such as CdTe and some perovskites. For any interface, a proper work function
is needed to ensure having ohmic contact (and not Schottky barrier) and to reduce voltage losses. The presence of a Schottky barrier increases the contact resistance, thereby impacting the solar cell performance detrimentally1. Currently, high work function contacts are implemented using platinum (with the work function of 5.65 eV )2, 3. However, the high cost of platinum requires the search for alternative high work function contact materials. Furthermore, due to the extremely high work function of Pt, it forms Schottky barriers with most of the known solar absorbers. In addition, having an ability to increase and tune up the work function of the contact material would open up unprecedented opportunities in enabling a range of emerging photovoltaic solar cell technologies including perovskites-based solar cells, for which the use of contact materials with high work functions is critically important4. Actually, this should find more applications in other electronic and optoelectronic devices. Being a potential candidate, graphene was implemented and reported as an alternative electrode material in solar cells5-9.
However, devices with graphene-based electrodes have mostly
underperformed in comparison to devices with metallic electrodes. One of the main reasons for this underperformance was the lower work function of graphene than the work function of some metals (e.g., Pt). Modification of the graphene’s work function by doping may increase it which will provide a chance to use graphene as a contact electrode material. Chemical doping has been reported to be efficient in modulating the work function and tailoring other electrical properties of graphene by charge transfer in and out the graphene sheet. Substitutional chemical doping of graphene is extremely challenging and has shown detrimental effects on graphene’s electrical properties, calling for alternative doping strategies such as attaching adatoms to graphene sheets. Doping of graphene with various adatoms10-30 and heteroatoms31-33 has been also extensively studied. The synthesis of nitrogen (N)-doped graphene
is feasible through a variety of different methods10, 11, 12, 13, 14, 15 , 16, 17, 18. Panchakarla10 et al. prepared nitrogen-doped graphene by carrying out arc discharge in the presence of mixtures (H2 + pyridine) or (H2 + ammonia) in the gas phase. Sheng et al.14 proposed a facile, catalyst-free thermal annealing approach for large scale synthesis of N-doped graphene using a low-cost industrial material melamine (C3H6N6) as the source of nitrogen. Yang et al.19 used SH2 gas to react with graphene oxide, in order to produce S-doped graphene. However, the resultant S-doped graphene had lower conductivity than the pristine graphene. Gao et al.20 demonstrated the growth of largearea S-doped graphene sheets on copper substrate via chemical vapor disposition (CVD) by using sulfur containing organic molecules as a precursor. Moreover, Denis21 also concluded that phosphorus doping of graphene opens a band gap larger than the one induced by sulfur, and that both P and S doped graphene can be employed for sensing applications. Furthermore, Walter et al.22 demonstrated that fluorine interaction with the carbon buffer layer on SiC leads to the formation of a strongly p-doped graphene layer that is decoupled from the substrate through intercalation, shifting the Dirac crossing point to above the Fermi energy. Zhan et al.24 synthesized I-doped graphene by a facile heat treatment method, which was then employed as an anode material for lithium ion batteries. Finally, Zhang28 et al. focused on a plasma-based chlorination process. By carefully tuning the plasma condition, they found an optimized reaction regime in which they could achieve stable single-sided chlorinated graphene with a high surface coverage (45.3 at. %, which is close to C2Cl) and with excellent carrier mobility performance (1535 cm2/V s). This result was repeatable, and the as-fabricated sample was stable at room temperature under ambient conditions. All the above work clearly highlights the extensive experimental efforts made towards modifying electronic properties of graphene through chemical doping.
In this work, we investigate the possibility of tuning (increasing) the work function of graphene by chemical doping with non-metallic adatoms (i.e. N, P, As, O, S, Se, F, Cl, Br and I) as pdopants. The effect of the p-dopant adatoms was investigated for dopant concentrations in the range of 1-4%. The structural and electronic properties as well as the work function of the proposed p-doped graphene based materials were calculated using the Density Functional Theory (DFT) methods. The results indicate that all considered p-dopant adatoms adsorbed at stable adsorption sites of graphene, increase the work function. This is due to the electron transfer from the graphene sheet to the p-dopant adatoms (Figure 1). The p-dopant adatoms are more electronegative elements than carbon and have a tendency to accept electrons from a graphene plane. It results in the depletion of electrons at the plane (i.e., increasing the concentration of holes in the plane) which results in a downward shift of the Fermi energy from the Dirac point. The magnitude of this change in graphene’s work function depends on the type of p-dopant and its concentration.
Figure 1. Schematics of the mechanism of graphene doping by p-dopant adatoms. 𝐸𝑣𝑎𝑐 corresponds to the vacuum energy level of the system, 𝐸𝑓 is the Fermi energy of the material, 𝛷𝐺 is the work function of pristine graphene, and 𝛷𝐺+𝑛𝑀 is the workfunction of graphene with attached individual non-metal adatom. Carbon atoms are shown in gray, non-metal adatom – in orange.
This paper is organized as follows. Section 2 outlines the details of computational methods used. This is followed by a description of the systems under investigation and an in-depth analysis of their structural properties (Section 3). Section 4 presents the results for the calculated work functions for different systems under consideration, and an analysis of their charge density distribution. Section 5 analyses the electronic properties of these systems, with a focus on their band structure. Finally, Section 6 summarizes the findings.
2. Methods In this work, DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP)34, 35. The approach is based on an iterative solution of the Kohn-Sham equations of the DFT in a plane-wave basis set with the Projector Augmented Wave (PAW)36, 37 pseudopotentials. The semicore 2p states of N, O and F, 3p states of P, S and Cl, and 4p and 3d states of As, Se, Br, and I were treated explicitly as valence states. The Perdew, Burke, and Ernzernhof (PBE)38 exchange-correlation (XC) functional of the generalized gradient approximation (GGA) was adopted. A plane-wave basis set with a maximum plane-wave cutoff energy of 400 eV was used. The Monkhorst-Pack mesh39 for sampling the Brillouin zone with a Gaussian broadening of 0.1 eV was used. In the calculations, the structures were fully relaxed with a Γ– centered 8x8x1 kmesh. A semi-empirical van der Waals correction term vdW-DF40, 41, 42, 43 was included which is known to have a significant impact on the adsorption energies at graphene surfaces. We also performed charge transfer analysis between the p-dopant adatoms and graphene sheet using the Bader44 and DDEC (Density Derived Electrostatic and Chemical) charge analysis approaches45, 46.
Graphene has two C atoms arranged in a two-dimensional honeycomb lattice with a hexagonal primitive unit cell. We used the calculated graphene lattice constant of 2.47 Å for a pristine graphene supercell, which is in-line with the experimental value of 2.46 Å47. For notation, we let x and y to be the in-plane directions and z to be perpendicular to the graphene plane. A twodimensional 7 × 7 supercell (consisting of 98 carbon atoms) was used to simulate the graphene sheet, and the neighboring sheets were separated by at least 15 Å of vacuum in the 𝑧 −direction to prevent interlayer interactions (See more details in Ref.[48]). Different types of non-metallic adatoms (namely, N, P, As, O, S, Se, F, Cl, Br and I) were used as p-dopants. In order to explore the effect of the p-dopant concentration, three different concentrations (1%, 2%, and 4%) for each adatom were considered. Equilibrium atomic positions were determined for fully relaxed supercells (with relaxed cell volume, lattice vectors and atomic positions). Self-consistent total energy calculations were stopped when the successive energy difference between the two iterations became less than 10–4 eV, and the Hellmann-Feynman forces acting on each atom became less than 0.01 eV/Å.
3. Results & discussion 3.1
Structural properties of p-doped graphene
To study the structural properties of p-doped graphene, p-dopant adatoms were placed at graphene sheet in the three adsorption sites shown in Figure 2: (i) above the center of the graphene hexagonal ring (hollow site, or H-site); (ii) above the C-C bond (bridge site, or B site) and; (iii) above the carbon atom (top site, or T site). Of the three considered adsorption sites, the site with the highest adsorption energy (minimal total energy) is referred to as the favored site.
(a)
Pristine Graphene
(c)
Top –site
(b)
Hollow –site
(d)
Bridge–site
Figure 2. Structural properties of p-doped graphene. Carbon atoms are shown in gray, the p-dopant adatom (i.e., 𝑁, 𝑃 𝐴𝑠, 𝑂, 𝑆, 𝑆𝑒, 𝐹, 𝐶𝑙, 𝐵𝑟 and 𝐼) - in orange.
The most favorable adsorption sites for different nonmetal adatoms at graphene plane are calculated (Figure 3). The result shows that for Group V and VI nonmetal elements, the 𝐵 − site indicated by vertical blue bars in Figures 3 (a) and (b) is the most stable adsorption site. In the previous work,48 we showed that Group I, II, and III metal adatoms prefer to be adsorbed in the H − sites above the graphene sheet. However, for the Group VII adatoms (F, Cl, Br and I), the T − site indicated by vertical green bars in Figure 3 (c) is the most stable adsorption site. These results are consistent with previous reports49. The distances between graphene and the nonmetal adatoms are also shown in Figure 3. It shows that within each group the distance between the nonmetal adatom and graphene plane grows with the atomic number of the element.
4
4
4
3
…
3
3
2
2
2
1
1
1
0
0
0
-1
-1
-1
-2
-2
-2
-3
-3
-3
-4
-4
-4
N
P
As
(a)
O
S
Se
F
(b)
Cl
Br
I
(c)
Figure 3. Calculated distance (𝑑𝐺−𝐴𝑑 ) between the adatom and graphene plane (Top: y- axes, vertical bars) and adsorption energy for an individual adatom (Bottom: y- axes, filled red circles) for the most stable adsorption sites of adatoms at graphene plane for: (a) Group V elements; (b) Group VI elements and; (c) Group VII elements. The most stable adsorption sites are the B- sites for the Group V and Group VI elements (blue vertical bars for 𝑑𝐺−𝐴𝑑 ) and the T- sites for the Group VII elements (green vertical bars).
3.2
Adsorption energy of p-doped graphene
The adsorption energy of individual adatom on graphene, ∆𝐸𝑎𝑑 , is defined as ∆𝐸𝑎𝑑
=
𝐸𝐺+𝑛𝑀 − 𝐸𝐺 − 𝐸𝑛𝑀
(1)
Here 𝐸𝐺+𝑛𝑀 is the total energy of graphene supercell with adatom, 𝐸𝐺 is the total energy of the pristine graphene supercell and 𝐸𝑛𝑀 is the total energy of the isolated nonmetal adatom in vacuum. The adsorption geometry is obtained by relaxation. The adsorption energy of adatoms on graphene is shown in Figure 3 in red circles. For example, the N adatom adsorbs strongly on pristine graphene at the B − site, and its adsorption energy is -3.23 eV, the F adatom binds shrongly at the T – site (-2.68 eV), while other halogen Cl, Br and I adatoms weakly adsorb at the T − site, with an adsorption energy of -1.19, -1.05 and -0.87 eV respectively (Figure 3). More detailed examination of electron charge density associated with the Cl, Br and I adatoms reveals that
interaction between these adatoms and graphene is weak which is related to the lack of substantial overlap between these adatoms and graphene states (see more details in section 4.1). In other words, Cl, Br and I adatoms form charged covalent bonds with graphene. In experiment, adsorption of Cl, Br and I on graphene surface is wildly studied and shows that the Cl and Br adatoms could be successfully adsorbed on graphene surfaces. For example, Zhang28 et al. found an optimized reaction regime in the plasma-based chlorination process and achieved stable singlesided chlorinated graphene with a high surface coverage (45.3 at. %). The as-fabricated sample was stable at room temperature under ambient conditions. Meanwhile, the stability of halide adatom adsorption at the graphene surface is still an open question (Refs. [27-30]). To get a better insight into this problem, we calculated the value of Ediff = (Eb,mol – 2 Ead ) for each of the four halogen atoms (F, Cl, Br, and I). Here Eb,mol is the bond energy (F-F, Cl-Cl, Br-Br, and I-I) in free, neutral F2, Cl2, Br2, and I2 molecules. We took these values (-1.61, 2.52, -1.97 and -1.53 eV for F2, Cl2, Br2, and I2) from Ref.[50]. The positive value of Ediff means that configuration with two absorbed individual adatoms at the graphene surface is energetically more favorable than the formation of a diatomic molecule. The negative value of Ediff means that halogen molecule will be formed, and adatoms will not bind to the surface. For fluorine adsorption, the value of Ediff is +3.75 eV, i.e., formation ot F2 molecule is thermodynamically unfavorable. For other halogens (Cl, Br, and I), the situation is not that clear, i.e., more research should be performed. Table 1 shows that the absolute value of Ediff is much lower than both Eb,mol and Ead for all three halogens. In addition to that, several calculations [27, 51] indicated that barrier for the migration between nearest T- sites is extremely low ( < 0.005 eV according to Ref. [51]) which means that even at moderate temperatures, individual absorbant will continuously migrate around the surface. At the same time, the bonding between adatom and
graphene surface is not purely covalent, and charge transfer between halogen adatoms and graphene surface occurs (see also Figure 6 below) which causes an appearance of a significant negative charge ( QAd-G) at the halogen dopant. Let us assume that two halogen adatoms get closer to each other while migrating around the surface. Interaction between them includes two components: (i) Coulomb repulsion between two negatively charged atoms; (ii) Covalent bonding between them. Coulomb repulsion is a long-range interaction while covalent bonding plays any role at short distances only. Calculations for Cl adsorbants positioned at one side of a graphene sheet indicated that Cl2 molecule starts to form when the distance between the two adsorbed Cl adatoms is less that the distance between the fourth nearest T-site neighbors (3.6 Å) [27]. The covalent bonding between two atoms positioned at such distance (calculated by continuously increasing the interatomic distance in free, neutral molecule) is very low for all three halogens (Table 1). The Coulomb repulsion between the two charged adatoms is quite high which means that there is a reasonably high barrier for two absorbed halogen atoms to come closer on graphene surface. This Coulomb repulsion energy could be considered as a qualitative estimate of the value of the barrier. Now we could try to describe the behavior of halogen adatoms positioned on one side of the graphene sheet. When two halogen atoms randomly migrate around the graphene surface, at some point they could get closer. The Coulomb repulsion between them turns on at much larger distance than covalent attraction which forms a barrier for them to get closer. Meanwhile, these atoms can easily migrate (with nearly zero barrier) in the directions for which the distance between them is not reducing. Apparently the statistical probability to migrate in these directions is much higher than to migrate in directions for which the distance reduces. Such a dynamic behavior could explain the stability of halogen adatoms adsorbed at graphene surfaces. This picture should be
valid at least for low concentration of adatoms at the surface. For higher concentrations, however, one should also take into account the delicate balance between the electrostatic repulsion between adatoms and covalent bonding between them. Recent experiment with plasma-based chlorination process, in which stable single-sided chlorinated graphene with a high surface coverage (45.3 at. %) was achieved [28], partly confirms this picture. Table 1. Adsorption energy (Ead), molecular binding energy (Eb,mol), the value of Ediff, the value of charge at the absorbed adatom ( QAd-G), Coulomb and covalent energies (ECoul and Ecov ) for Cl, Br, and I adatoms at graphene surface positioned at the fourth nearest neighbor T-site positions (at distance of 3.6 Å). Element
Ead (eV)
Eb,mol (eV)
Ediff (eV)
QAd-G (e)
ECoul (eV)
Ecov (eV)
Cl
-1.19
-2.52
-0.14
-0.5
+0.99
< 0.05
Br
-1.05
-1.97
+0.13
-0.46
+0.91
< 0.05
I
-0.87
-1.53
+0.23
-0.39
+0.77
< 0.05
3.3
Work function of p-doped graphene
In general, adatom adsorption on graphene is expected to alter Fermi level and dipole moment of the system. Also, there can be a noticeable change in work function of such system relative to the pristine graphene. The electron work function (Φ) is the minimal energy required to extract an electron from the surface of the solid defined as Φ = 𝐸𝑣𝑎𝑐 − 𝐸𝑓 , where 𝐸𝑣𝑎𝑐 is the reference vacuum energy and 𝐸𝑓 is the Fermi level of the system graphene plus adsorbed adatoms52. In our calculations, 𝐸𝑣𝑎𝑐 is determined from the electrostatic potential in the vacuum region, far enough from the adatom-graphene system in the 𝑧 −direction that the value is converged (see Figures 4
and S1 from Supporting Information section). Figure 4 shows the electrostatic potential < 𝑉 > averaged inside the supercell over the planes parallel to the graphene layer as a function of the distance from the layer of chlorine-doped graphene. This computational method method has been widely used in previous studies for calculating the work function48,
53, 54
. Similarly, 𝐸𝑓 is
determined by the upper limit of the integral of the density of states from the lowest calculated energy level to the energy that gives the total number of electrons per the unit cell.
Figure 4. The electrostatic potential < 𝑉 > averaged inside the supercell over the planes parallel to the graphene layer as a function of the distance from Cl-doped graphene surface.
The main target of this work is to determine the change of the work function of p-doped graphene as a function of dopant concentration. Figure 5 shows the work function of doped graphene for different p-dopants and different dopant concentration. For pristine graphene, the calculated work function is 4.38 eV which is in good agreement with both previous experimental and theoretical
results48,
53, 54
. A presence of p–dopant adatoms always has a tendency to increase the work
function of the system (see Figure 5). This is consistent with experimental and previous theoretical work26, 57. For example, nitrogen doped graphene exhibits higher work function than pristine graphene (Figure 5 (a)). This is related to the fact that electronegativity of nitrogen atom is higher than electronegativity of carbon atom at the graphene plane. Therefore, N atom has a tendency to grab electrons from the graphene plane which causes depletion of the electron density at the plane. Consequently, the Fermi energy of the system is shifted down from the Dirac-point which increases its work function. The magnitude of the Fermi energy shift from the Dirac-point towards deep valence bands depends on the electronegativity of nonmetal adatoms and their concentration. For Cl–doped graphene, the work function increases from 4.38 eV to 5.76 eV for 4% doping, which is the largest effect for all nonmetal adatoms considered here (and the dopant concentrations not exceeding 4%). Other Group VII adatoms (F, Br, and I) also significantly increase the work function of the graphene plane. If the number of atoms per supercell is larger than one (for 7 x 7 graphene supercell with 98 atoms, 1% concentration approximately corresponds to 1 adatom per cell, 2% - to 2 atoms, 4 % - to 4 atoms), different mutual arrangements of adatoms at the plane are possible. To take these arrangements into account, we performed calculations for five different configurations for each dopant. For a supercell with two adatoms (2% doping), the configurations differ by the distance between the two adatoms starting from the configuration where the two atoms are positioned at two neighboring stable sites. For a four dopant supercell (4% doping), we also started from the configuration where the four atoms are positioned at neighboring sites; other structures with 4 adatoms were randomly generated. This approach allowed perform a statistical analysis and evaluate the error bar for the work function at different adatom concentrations. Figure 5 clearly
indicates that error bars of the work function are quite small (below 0.02 eV), i.e., the result does not depend strongly on the dopant arrangement.
7
7
7
5
5
5
3
3
3
1
1 N
P
As
WF ( 1%)
WF (2%)
WF (4%)
1 O
S
Se
F
Cl
Br
I
(b) (c) Figure 5. The work function ( ) for different concentration of nonmetal adatoms at p-doped graphene: (a) Group V adatoms, (b) Group VI adatoms, and (c) Group VII adatoms. Results for 1% adatoms concentration are shown in cyan, for 2% concentration - in indigo, and for 4% concentration – in green. The error bars are shown in red.
(a)
3.4
Charge density analysis of p-doped graphene
In this section, calculations of charge transfer in p-doped graphene are performed based on the Bader and the Density Derived Electrostatic and Chemical (DDEC) charge analysis methods. For the most stable adsorption sites previously identified in Section 3 (B − sites for the Groups V and VI elements and T − sites for the Group VII elements), the results are shown in Figure 6. The Bader charges were calculated from the charge densities generated by the VASP codes using the program developed by G. Henkelman et al44.
0
0
-0.2
-0.2
-0.2
-0.4
-0.4
-0.4
-0.6
-0.6
-0.6 N
P
As
(a)
DDEC
O
S
Bader
Se
0
F
(b)
Cl
Br
I
(c)
Figure 6. Charge transfer (the charge difference between an isolated atom and atom at the graphene plane) from graphene to individual nonmetal adatom (𝒬𝐴𝑑−𝐺 ) for: (a) Group V elements; (b) Group VI elements, and; (c) Group VII elements. Charge transfers calculated by both Bader and DDEC analysis methods are shown.
Figure 6 indicates a negative charge transfer from graphene to any p- dopant adatom, i.e., the electron density at the graphene plane at the vicinity of the adatom defect is depleted which shifts the Fermi level from the Dirac point deeper into the valence band. In general, the charge transfer values calculated by both Bader and DDEC are in close agreement. However, DDEC fails to predict the value for charge transfer for fluorine, as shown in Fig. 5(c). It happens because the differential electron charge density distribution plot for the F-doped graphene (see Figure 7 (g) below) clearly indicates a significant electron density depletion at the graphene sheet and electron density accumulation at the F adatom. The differential charge densities for different p-dopants given by the equation, ∆𝜌 = 𝜌𝐺+𝑛𝑀 − 𝜌𝐺 − 𝜌𝑛𝑀
(2)
are shown in Figure 7. Here 𝜌𝐺+𝑛𝑀 is the charge density of graphene with adsorbed nonmetal adatom, 𝜌𝐺 is the charge density of the pristine graphene sheet, and 𝜌𝑛𝑀 is the charge density of an isolated nonmetal adatom.
Figure 7. Differential electron charge density distribution for the graphene sheet that has been pdoped through an adsorption of different nonmetal adatoms: (a) N; (b) P; (c) As; (d) O; (e) S; (f) Se; (g) F; (h) Cl; (i) Br, and; (j) I. Carbon atoms are shown in gray; the nonmetal adatom located within the charge density cloud - in red. The gold color corresponds to negative differential charge accumulated around the nonmetal adatom, while the cyan color – to the electron charge depletion (excess of the positive charge) at the graphene plane.
In Figure 7, the cyan color corresponds to an excess of positive charge (electron depletion) which occurs at the graphene sheet at the vicinity of the adatom. For Cl, Br and I atoms, the differential charge density plots clearly show the highest depletion of electrons at the graphene plane and the
highest degree of localization of the electron charge at the adatom. This accumulation significantly reduces the hybridization between electronic states of the adatom and the rest of graphene plane which explains why the shift of the Fermi level down from the Dirac point is the highest for Group VII elements.
3.5
Electronic structure of p-doped graphene
To study the effects of adatom adsorption on the electronic properties of graphene even further, we calculated the band structure of graphene supercells with different types of p-dopants and different concentrations. The band structure of the pristine graphene supercell is shown in Figure 8 (a). In the planar hexagonal structure of graphene, the 𝑝𝑥 and 𝑝𝑦 orbitals of carbon are degenerated. They hybridize with the 𝑠 orbital and form the 𝑠𝑝2 𝜎 bond states. The 𝑝𝑧 orbitals form the bonding (𝜋) and antibonding (𝜋 ∗ ) orbitals oriented normally to the graphene sheet. The corresponding two electronic bands touch at high symmetry 𝐾 point of the Brillouin zone, i.e., the bandgap in the pristine graphene is zero (Figure 8 (a)). The band energies are changing linearly near the Dirac point which leads to a vanishing effective masses for the charge carriers. These features of the electronic properties of graphene are responsible for the observed ballistic transport, Dirac-type quasiparticles, and anomalous quantum Hall effect 58, 59, 60, 61, 62 .
Figure 8. The band structure of: (a) Pristine graphene supercell; (b) Graphene supercell with 1% of nitrogen dopant; (c) Same for 2% of nitrogen dopant; (d) Same for 4% of nitrogen dopant. Electronic bands with dominant contribution of C atoms are shown in red, and bands with dominant contribution of N atoms – in green. Fermi energy for each system is indicated by horizontal dashed line. Zero energy corresponds to the Fermi level of the pristine graphene.
The band structures of nitrogen doped graphene, with different adatom concentrations, are shown in Figures 8 (b-d). Figure 8 (b) shows the band structure of N-doped graphene with nitrogen concentration of 1% (one N adatom in 98 atoms graphene supercell). The band structure shows that the 2𝑝 orbitals of nitrogen strongly hybridize with the 𝑠𝑝2 orbitals of graphene, which corresponds to the chemisorption of nitrogen atom at the graphene plane. It results in distortion of the two-dimensional lattice structure of graphene which breaks its symmetry and opens a gap of 0.11 eV between the 𝜋 and 𝜋 ∗ graphene bands. The higher concentration of nitrogen adatoms increases not only the work function of graphene but also the 𝜋 – 𝜋 ∗ gap (which becomes 0.32 eV at nitrogen concentration of 4%). This result is consistent with previously reported experimental results63.
(a)
(b)
(c)
Figure 9. Band structure of Cl-doped graphene supercells with dopant concentration of: (a) 1%; (b) 2%; (c) 4%. Electronic bands with dominant contribution of C atoms are shown in red, and bands with dominant contribution of Cl atoms – in green. Fermi energy for each system is indicated by horizontal dashed line. Zero energy corresponds to the Fermi level of the pristine graphene.
Unlike nitrogen, chlorine adatom couples to graphene plane weakly. Therefore, the adsorption of Cl to graphene causes insignificant distortion of the two-dimensional hexagonal honeycomb graphene lattice only. The 𝜋 and 𝜋 ∗ electronic bands are still linear near the Dirac point and have a zero gap between them (Figure 9). Bromine and iodine doped graphene shows the behavior similar to the Cl doped material (see Supporting Information, Figures S2 and S3). Table 1. The 𝜋 – 𝜋 ∗ gaps of p-doped graphene for different adatom dopants at two dopant concentrations (1% and 4%). Adatom 𝜋 – 𝜋 ∗ gap for 1% of dopants (eV) 𝜋 – 𝜋 ∗ gap for 4% of dopants (eV)
F 0.15
Cl Br I N 0.00 0.00 0.00 0.10
P 0.20
As 0.15
O S Se 0.30 0.22 0.10
0.25
0.00 0.00 0.00 0.32
0.30
0.34
0.35 0.25 0.30
Opening a 𝜋 – 𝜋 ∗ gap in graphene has been an endeavor of great importance in the graphene research community, since most envisioned applications for graphene in electronic devices require the presence of a bandgap. In this work, we have reported the possibility of opening a 𝜋 – 𝜋 ∗ gap in graphene by doping, We also found that this band gap may be tuned by varying the concentration of dopant adatoms. Table 1 shows the 𝜋 – 𝜋 ∗ gaps for different types of non-metal adatoms and two different dopant concentrations. Notably, the gaps of oxygen, nitrogen and phosphors doped graphene could reach above 0.3 eV at dopant concentration of 4%.
4. Conclusion We investigated possibilities for increasing the work function of graphene by adsorption of nonmetal adatoms (p- dopants), in order to use such systems as a back-contact electrode for emerging photovoltaic technologies. We performed this study for different adatom dopants and different dopant concentrations. For all the nonmetal Group V and Group VI adatoms considered, we showed that the bridge (B) site at the graphene plane is the most stable site, while for Group VII elements prefer to be adsorbed at the graphene top (T) sites. We found that p-doping of graphene by adatoms is highly efficient in modulating the 𝜋 – 𝜋 ∗ gap of graphene and increasing its work function. We found that the work function of graphene can increased from 4.38 eV for pristine material to 5.76 eV and to 5.71 eV for Cl–doped and Br-doped graphene respectively (at the dopant concentration of 4%). Using the band structure analysis and differential charge density mapping, we conclude that charge transfer from graphene to non-metal adatoms causes the depletion of electrons at the graphene plane and lowering the Fermi level thus increasing the work function of the system. We also analyzed the stability conditions for absorbed halogen adatoms on graphite. We found that halogen molecules formation process should be significantly inhibited by
electrostatic repulsion between charged adatoms which provides additional barrier for adatoms to get closer to react. These results pave the way towards the experimental realization of high work function graphene contact electrodes, which are of timely importance for emerging photovoltaic technologies. ACKNOWLEDGMENT Funding for this research was provided by Qatar National Research Foundation (QNRF), grant numbers NPRP 7-317-1-055 and NPRP X-107-1-027. Computational resources are provided by research computing at Texas A&M University at Qatar.
Conflict of interest
This paper has not been submitted to any other journal, there are no conflicts of interest and all co-authors are aware of and approve submission of this paper.
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Highlights High workfunction contacts play an important role in efficiently extracting carriers Different p-dopants adatoms on graphene tune the workfunction as high as 5.76 eV Rising workfunction is mainly due to the charge transfer from graphene to pdopants Distortion of the lattice structure of graphene breaks its symmetry and opens a gap p-doped graphene is promising for use of graphene-based contact electrodes
Author contribution
M.L. performed calculations, data analysis and writing paper. S.R. and F.A.D. participated in data analysis and writing the paper. F.H.A. participated in data analysis. All authors contributed to discussions.
Declaration of interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.