Atomic Bonding and Electronic Binding Energy of Two-Dimensional Bi/Li(110) Heterojunctions via BOLS-BB Model.

Combining the bond-order-length-strength (BOLS) and atomic bonding and electronic model (BB model) with density functional theory (DFT) calculations, we studied the atomic bonding and electronic binding energy behavior of Bi atoms adsorbed on the Li(110) surface. We found that the Bi atoms adsorbed on the Li(110) surface form two-dimensional (2D) geometric structures, including letter-, hexagon-, galaxy-, crown-, field-, and cobweb-shaped structures. Thus, we obtained the following quantitative information: (i) the field-shaped structure can be considered the bulk structure; (ii) the field-shaped structure of Bi atom formation has a 5d energy level of 22.727 eV, and in the letter shape structure, this energy is shifted to values greater than 0.342 eV; and (iii) the Bi/Li(110) heterojunction transfers charge from the inner Li atomic layer to the outermost Bi atomic layer. In addition, we analyzed the bonding and electronic dynamics involved in the formation of the Bi/Li(110) heterojunctions using residual density of states. This work provides a theoretical reference for the fine tuning of binding energies and chemical bonding at the interfaces of 2D metallic materials.

Introduction

With developments in nanotechnology and nanomanufacturing technologies, it has become possible to isolate synthesized materials with one (or few) atomic thickness.[1−4] Graphene was the first atomic thickness material, having been separated from graphite by Geim and Novoselov.[1] This material is called a 2D material because electrons can move only in two directions (in-plane), being confined in the third direction. Thereafter, several layered-2D materials have risen to prominence, including transition metal carbon dihalides,[5] hexagonal boron nitride,[6] and black phosphorus.[7] The confinement of this system provides graphene and other such materials with excellent electrical and optical properties, and as such they can be widely used in nanoelectronics and energy research.[8−14] Prior to the discovery of 2D semiconductor materials, the interfaces of 2D metal heterojunctions were considered to be very complex and poorly defined, rendering it difficult to quantify the active junction area and the physical properties associated with the junction.[15]

In fact, a metal heterojunction is easy to form when a metallic material is grown on a suitable substrate.[16,17] Furthermore, 2D metallic material growth requires the use of a suitable substrate material. Artificially designed and synthesized 2D metal heterojunctions, compared with bulk materials, have many peculiar physical and chemical properties.[18−23] For example, 2D metal Bi/SiC hexagon structure heterojunctions have an indirect gap of 0.67 eV.[24] However, for a heavy atom like Bi, multiple bonding patterns are possible. We calculated the multiple bonding patterns of Bi atoms on the Li(110) surface. We found that there is agglomeration of Bi atoms on the interface. The agglomeration of Bi atoms on the Li(110) interface form the 2D heterojunction (see the Supporting Information). In addition, the electronic properties of 2D metal heterojunctions can be modulated as a function of an applied gate voltage, leading to fundamentally new device phenomena and providing opportunities for the tuning of device properties.[25,26]

In this study, we calculated the energies of 2D metal Bi/Li(110) heterojunctions using first-principles methods. We found that Bi atoms were adsorbed on the surface of Li(110), forming 2D geometric structures in the shapes of letter, hexagon, galaxy, crown, field, and cobweb. Unlike the magnetic properties of the 2D metal Sc/Li(110) heterojunctions study,[27] we used the BOLS-BB model to study the atomic bonding and electronic binding of Bi/Li(110) heterojunctions. Figure shows a schematic of the BOLS–BB model. By establishing the concept of the combined BOLS–BB model, the internal mechanism of the electronic binding energy shift and chemical bond relaxation at Bi/Li(110) metal heterojunctions is revealed. The bonding and electron dynamics processes at the Bi/Li(110) heterojunction were studied, and parameter information about the related bonding and electronic structure was obtained. This work provides a new approach for the calculation of the atomic bonding and electronic binding energies of 2D metal heterojunctions.

Figure 1

Schematic of atomic bonding and binding energy (BB) model in combination with the BOLS notation. The BOLS-BB model obtains atomic bonding by quantifying the binding energy.

Results and Discussion

We used first-principles methods to calculate Bi/Li(110) heterostructures, which are obtained by adsorption of Bi atoms at different positions on the Li(110) surface. The optimized geometry of Bi/Li(110) heterostructures is shown in Figure . We found that Bi atoms adsorbed on the Li(110) surface formed various 2D geometric structures, namely, letter, hexagon, galaxy, crown, field, and cobweb shapes. This is similar to the 2D structure formed by the adsorption of Sc[27] and Y[28] atoms on the Li(110) surface. In addition, the height h between the Bi and Li(110) layers is the distance between the Bi atomic layer and Li(110) atomic layer in the direction of the thickness of the slab. The calculated interlayer heights h of these structures are 0.95, 2.09, 1.10, 1.59, 2.36, and 1.76 Å, respectively, as shown in Table .

Figure 2

Optimized geometric structures of Bi atoms adsorbed on the Li(110) surface: (a) letter shape, (b) hexagon shape, (c) galaxy shape, (d) crown shape, (e) field shape, and (f) cobweb shape. In each panel, the upper image is a side-on view of the structure and the lower image is a top-down view of the same. The height h is the shortest distance between the Bi atoms layer and Li(110) atoms layer.

Table 1

Geometric and Energy Parameters for Different Shaped Heterojunctions as Obtained via First-Principles Calculationsa

		work function (eV)			total energy (eV)
geometric structures	hx (Å)	Bi	Li	Bi/Li(110)	EBi	ELi	EBi/Li	Eform (eV)
letter shape	0.95	4.183	2.903	3.266	–10630.71	–5460.24	–16097.72	–6.77
hexagon shape	2.09	4.429	3.019	3.423	–12757.54	–5460.38	–18225.79	–7.87
galaxy shape	1.10	4.256	3.037	3.366	–14883.39	–5459.5	–20352.67	–9.78
crown shape	1.59	4.188	3.016	3.255	–17011.06	–5460.09	–22479.13	–7.98
field shape	2.36	4.224	3.070	3.354	–19135.4	–5460.42	–24603.65	–7.83
cobweb shape	1.76	4.314	3.030	3.328	–14884.11	–5460.3	–20352.29	–7.88

Table gives the corresponding values of the work function (eV), the height h (Å) and the total energy(eV) of the relaxed Bi/Li(110) heterostructure, isolated Bi, and Li monolayers, corresponding formation energy Eform of the listed each heterostructure. The shortest distance between the Bi atoms adsorbed on the Li(110) surface of height h (Å).

We calculated the total energy of Bi and Li(110) and that of Bi/Li(110) in the letter-, hexagon-, galaxy-, crown-, field-, and cobweb-shaped structures. Thus, the formation energy Eform was calculated as the energy difference between these values, using the equation[29−31]Eform = EBi/Li – EBi – ELi, where EBi/Li, EBi, and ELi are the total energies of the relaxed Bi/Li(110) heterostructure, isolated Bi, and Li monolayers, respectively. These values are presented in Table . The formation energies of the letter-, hexagon-, galaxy-, crown-, field-, and cobweb-shaped heterojunctions are −6.77, −7.87, −9.78, −7.98, −7.83, and −7.88 eV, respectively. The ab initio molecular dynamics calculations show that the structure is stable, as shown in the Supporting Information. Therefore, we confirm that both the Bi/Li(110) heterojunctions are stable geometric structures.

The work function is the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface or the energy needed to move an electron from the fermi energy level to the vacuum. The value of the work function is an indication of the strength of the binding energy of the electrons in the metal. The larger the work function, the less likely it is for the electrons to leave the metal. We calculated the work functions of Bi, Li(110), and Bi/Li(110) heterojunctions, as shown in Table . For the same structure, we found that the work functions are in the order Bi > Bi/Li(110) > Li(110). The results show that Bi/Li(110) heterojunctions effectively reduce the work function of Bi metal.

Figure shows the density of states (DOS) diagram for the Bi 5d and Li 1s orbitals of the letter-, hexagon-, galaxy-, crown-, field-, and cobweb-shaped structures calculated by DFT. Figure a shows that the Bi 5d orbital has negative binding energy shifts. Comparing the data in Figure and Table , we observe that the Bi 5d orbital binding energies of the letter-, hexagonal-, galaxy-, crown-, field-, and cobweb-shaped structures are 22.385, 22.491, 22.669, 22.671, 22.727, and 22.521 eV, respectively, and the binding energy of the structures increases in the order field shape > crown shape > galaxy shape > cobweb shape > hexagon shape > letter shape.

Figure 3

(a) Bi 5d and (b) Li 1s DOS for 2D metal Bi/Li(110) letter-, hexagon-, galaxy-, crown-, field-, and cobweb-shaped heterojunction structures.

Table 2

Electronic Binding Energy of the Bi 5d Level is Written E5d(x) (eV); the Energy Shifts Are Computed as ΔE5d(x) = E5d(x) – E5d(B) (eV); Potential Energy of Inter-Surface ; Values of the Charges of the Bi and Li Atoms; is Bond Energy Density; the Relative Bond Energy Ratio (RBER) δγx = γ – 1; the Relative Bond Energy Density (RBED) δEd = γ4 – 1; and Relative Local Bond Strain (RLBS) δε = γ–1 – 1 Are Given

geometric structures	E5d(x)	ΔE5d(x)	δγx	δεx (%)	δEd (%)	chargea (Bi) (e/atom)	chargea (Li) (e/atom)	Vsurface
letter shape	22.385	–0.342	–0.342	0.434	–0.764	–0.482	0.326	–4.762
hexagon shape	22.491	–0.236	–0.236	0.264	–0.608	–0.490	0.405	–2.734
galaxy shape	22.669	–0.058	–0.058	0.054	–0.190	–0.466	0.424	–5.171
crown shape	22.671	–0.056	–0.056	0.052	–0.184	–0.307	0.368	–2.046
field shape	22.727	0	0	0	0	–0.382	0.440	–2.050
cobweb shape	22.521	–0.206	–0.206	0.223	–0.553	–0.417	0.397	–2.708

Negative signs indicate charge gain; otherwise, charge loss occurs.

To calculate the change in the interface bonding at Bi/Li(110) heterojunctions caused by Bi metal doping, we should obtain the interface binding energy shift ΔEv(i) = Ev(x) – Ev(B) and the energy level width of the bulk ΔE5d(wB) = 1.13 eV. For the value of E5d(B), we used the peak value of the binding energy of the field-shaped structure as a reference. Using eqs –15, we calculated the relative bond energy density (RBED) δEd, local bond strain (RLBS) δε, and relative bond energy ratio (RBER) δγ of the letter-, hexagon-, galaxy-, crown-, field-, and cobweb-shaped structures, as shown in Table and Figure . By calculating the atomic bond parameters, we found that compared to the field-shaped structure, the letter-, hexagon-, galaxy-, crown-, and cobweb-shaped structures have negative values of the RBED δEd and RBER δγ and positive values of the RLBS δε. This indicates the properties of these shaped structures compared to those of a layer of Bi atoms adsorbed on the Li(110) surface.

Figure 4

Trends for energy shift ΔE5d(x), RBED δEd, RLBS δε, and RBER δγ as predicted by the BOLS–BB model and DFT calculations.

Using DFT calculations to calculate the energies and structures of Bi/Li(110) heterojunctions, we found that electron transfer occurs within the valence electron band after Bi is adsorbed onto the Li(110) surface. The residual DOS (RDOS) results are obtained as the difference between DOS collected from a surface before and after it is physically or chemically adsorbed.[32] From the RDOS data, we can obtain the distribution of the electronic structure and bonding near the valence band at the Fermi level (EF). Figure shows the RDOS data for the letter-, hexagon-, galaxy-, crown-, field-, and cobweb-shaped structures. Bi atoms are adsorbed on the Li(110) surface (Figure ). Consistent with the prediction of the BBB theory,[33] there are four characteristic regions of the DOS plot: Bi–Li bonding states (from −4 to −6 eV), nonbonding states (from −2 to −4 eV), electron (Liδ−)–hole (Biδ+) (−1 and 1 eV), and antibonding states (from +2 to +4 eV). For the valence band, charge is transferred from a lower energy level to a higher energy level, and the atomic polarization is an important parameter for electrons and holes.

Figure 5

Valence band of Bi/Li(110) heterostructures. The profiles exhibit four valence RDOS features: antibonding, electron–hole, nonbonding, and bonding states. The dotted line in the figure is the Fermi level.

Regarding the deformation charge density values (Table and Figure ), it should be noted that a positive sign indicates that electrons are accepted, and the charge is transferred from Li atoms to Bi atoms. Figures and 7 present the electron dynamics of the bonding at the heterojunctions. The low coordination Biδ+ atom on the surface causes the Liδ− atom to produce an electronic nonbonding state. The nonbonding lone pair of electrons polarizes the Biδ+ electrons to form Biδ+–Liδ− dipole moments. Simultaneously, the polarization appears as Bi 5d core bands. The electron binding energy of the core band has a negative shift, as shown in Figure . The characteristic electron (Liδ−)–hole (Biδ+) bands in the DOS, at −1.0 and 1.0 eV, are produced by the Biδ+–Liδ− dipole moment, which produces a bond between the heteroatoms that is stronger than either the Li–Li or Bi–Bi bonds. The stronger electronic interaction reduces the energy of the surface work function, and the electron binding energy of the Bi 5d core band balances the electron distribution at the interface. The antibonding state (+2 to +4 eV) arises as a result of the polarization of Bi electrons by the isolated Biδ+–Liδ− dipole moment. In addition, it should be emphasized that the RDOS results not only provide an effective numerical calculation method for quantitatively studying atomic bonding and electronic behavior at Bi/Li(110) heterojunctions but also provide a new method for the formation of Bi/Li(110) heterostructures.

Figure 6

Deformation charge density of (a) letter-, (b) hexagon-, (c) galaxy-, (d) crown-, (e) field-, and (f) cobweb-shaped structures of Bi atoms.

Figure 7

Schematics showing (a) 2D metal PN junctions and (b) electronic energy shift of core band structure.

Unlike the valence band, in which charge mixing and atomic s-, p-, and d- orbital mixing occur after the formation of the heterojunctions, the electron transfer in the core bands of the atomic energy levels in the DOS distribution occurs as a result of the effects of potential energy or bonding state. Because of weak hybridization (polarization), the bonding state is ligand-like (Bi atoms), and the antibonding state mostly metal-like (Li atoms). Our calculations revealed that the Millikan charge of the first layer of Li atoms is positive, indicating that electrons are lost. The negative charge of the Bi atoms implies that electrons are obtained. The electronic structure of the Bi/Li(110) heterojunctions calculated here is similar to that of the PN junction structure of the semiconductor, as shown in Figure a.

We calculated the potential energy functions of the surfaces as a function of the positive and negative charges, .. The calculated potential energies of the surfaces are all negative, indicating that chemical bonds are formed between the Li and Bi atoms. The more negative the potential energy, the better the interface bonding performance, and the formation of the PN junction structure will strengthen the bonding performance of the interface atoms. As both Bi and Li are metals, they are not the same as semiconductors, and thus they have no band gap. Therefore, here, we present the energy band structure of the core band, as shown in Figure b. The PN junction structure of the metal heterojunctions allows a part of the excess electron density from the Li atoms to be transferred to different energy levels of the Bi atoms. The filling of different Bi atomic energy levels causes a negative shift in the binding energy of electrons. Therefore, the formation of the PN junction structure of the metal heterojunctions will cause a shift in the electron binding energy.

Conclusions

We investigated the geometric, electronic, energetic, and bonding properties of Bi/Li(110) heterojunctions. The results are summarized below:

We calculated multiple bonding patterns of Bi atoms on the Li(110) surface. Our results show that a small number of Bi atoms can also agglomerate on the surface to form a 2D heterostructure.

We found that the interface of the Bi/Li(110) heterojunction will form a PN junction. The results show that the PN junction formed by the metal heterojunction will result in a core level shift.

We used a combined BOLS–BB model to calculate parameter information for the atomic bonding and electronic properties of the Bi/Li(110) heterojunctions. The results of the BOLS–BB model provide an effective numerical calculation for studying the quantitative information about the bonding and electronic behavior of Bi/Li(110) heterostructures.

Principles and Methods

Tight Binding Approximation

In the tight binding approximation, the Hamiltonian is given by[34]where, A(r⃗) ∝ 1/r⃗ is the vector potential, m is electron mass, ℏ is the Planck’s constant, c is speed of light, and q is the electron charge. The electronic binding energy of the vth energy band Ev(x) is

In this definition, Ev(B) and Ev(0) are the energy levels of bulk atoms and an isolated atom, respectively; αv is the overlap integral; and βv is the exchange integral, which contributes to the width of the energy band. |v,i⟩ represents the wave function, with a periodic factor f(k) in the form of e–, while k is the wave vector. Vatom(r) is the intra-atomic potential of the atom, Vcrys(r) is the potential of the crystal, and the interaction potential changes with the coordination environment and during chemical reactions. In the localized band of core levels, βv is very small, so αv determines the energy shift of the core levels.

BOLS–BB Model

In the BOLS–BB model, the bond energy uniquely determines the impurity-induced core-level binding energy shift[20]where z is the atomic coordination number of an atom in the xth atomic layer from the surface. The energy level of an isolated atom Ev(0) is the unique reference energy, from which the electronic binding energy of the core energy levels is considered. The bulk component Ev(B) is obtained from X-ray photoelectron spectroscopy (XPS) results and DFT calculations.

In this definition, p is the momentum, r is the electron radius, and zzz is the atomic fractional coordination number. Z is the initial atom charge (neutral Z = 0, positively Z = +1, and negatively Z = −1). Thus, the core-electron binding energy shifts will be , , and , initially neutral, singly charged negative and positive atoms, respectively.[35]Equation provides estimates for the bond energy E, bond length d and ΔEv(wB) ≈ ΔEv(B) is the spectral full width of the bulk component (wB) of the vth energy level; actual spectral intensities and shapes, however, are subject to polarization effects and measurement artifacts. The width of the binding energy shift for the surface component (w) of the vth energy level is ΔEv(w) = ΔEv(B) + ΔEv(x). We can calculate the chemisorption and defect-induced interface bond energy ratio γ with the known reference value of ΔEv′(x) = Ev(x) – Ev(B), ΔEv(B) = Ev(B) – Ev(0) and ΔEv(x) = Ev(x) – Ev(0) derived from the surface via DFT calculations and XPS analysis. Hence, we obtain

Thus, one can drive the interface RBER parameter δγ and elucidate via XPS analysis whether the bond energy strength determines the interface performance. If δγ < 0, the bond energy E is reduced and the bond is weakened. Conversely, if δγ > 0, the bond energy increases and the bond becomes stronger. The RLBS δε indicates the relative contraction of the atomic bond length d. The RBED δEd is the energy density of the atomic bond with energy E.

DFT Calculations

We calculated the geometric structure, atomic bonding, charge transfer, binding energy shifts, and electronic distribution of Bi/Li (110) heterojunctions by using DFT calculations. The Vienna ab initio simulation package and plane-wave pseudopotentials are used in the calculations.[36,37] We also employed the Perde–Burke–Ernzerhof exchange–correlation potentials;[38] the plane-wave cutoff was 400 eV, and the vacuum space was 18 Å. The Brillouin zone was calculated with special k-points generated in an 8 × 8 × 1 mesh grid. In the calculations, the energy converged to 10–6 eV and the force on each atom converged to <0.01 eV/Å. To consider long-range van der Waals interaction, DFT-D3 calculation was used.