We finally formulate the evolution of the graphene substrate. interaction and curvature energy, and the morphology of graphene on various TM substrates can be effectively estd. The most stable hBN edge corresponding to Δμ. c) Atomic configurations of the most stable edges corresponding to (b).
Research background on two-dimensional (2D) materials growth
Chemical vapor deposition (CVD) growth of single crystalline graphene on a substrate
- Graphene growth via nucleation control
- Graphene growth via seamless stitching on single-crystal substrates
- Graphene growth via seamless stitching on liquid substrates
To demonstrate the alignment of graphene islands on it, the edge of a graphene film (marked as 2 in Figure 1.7(e)) is shown in Figure 1.7(f). One year later, Ruoff's group also realized the production of single-crystalline Cu(111) foils with a size of 32 cm2 by the contact-free annealing of commercial polycrystalline Cu foils, and similarly, graphene islands that were on the obtained Cu(111 ) foils were grown also appeared to be unidirectional, as shown in Figure 1.7(g-i).67.
CVD growth of single-crystal hexagonal boron nitride (hBN) on a substrate
- hBN growth via nucleation control
- HBN growth via seamless stitching
The polarized second-harmonic generation (SHG) mapping in Figure 1.12(c) confirms the seamless stitching of the two aligned hBN domains, as there is no boundary line in the fusion area. The grown hBN islands on the obtained Cu(111) surface were found to be unidirectionally aligned with an orientational consistency ratio of more than 99.6% (see Figure 1.13(c)).
The synthesis of transition metal dichalcogenide (TMDC) films
The grown WSe2 islands on the obtained Al2O3 wafer showed a trapezoidal shape with a clear alignment along the edges of the steps (Figure 1.16(b)). Optical microscopic image of WSe2 islands on the vicinal Al2O3 (0001) wafer with inserted SEM image.
Graphene moiré superstructures on a substrate
- Structures of graphene moiré superstructures
- Applications of graphene moiré superstructures
Furthermore, many experimental and theoretical studies revealed that the degree of corrugation (height variation) of graphene moiré superstructures is highly dependent on the rotation angle of graphene. Depending on the type of substrate and the angle of rotation of the substrate, graphene moiré superstructures are different.
Conclusions
Research motivation
So far, however, a systematic understanding about the alignment of 2D islands on high-index substrates is lacking at the atomic scale and the understanding about the interactions of 2D materials and high-index surface is still far from complete. Therefore, in this thesis, we first present a systematic theoretical study on the alignment of various 2D materials on high-index substrates, with the aim of revealing the alignment mechanism at the atomic scale and providing guidelines for experimental designs on the synthesis of WSSC 2D materials.
Theoretical foundation on the growth of 2D materials
CVD growth of single-crystal graphene
- Nucleation of graphene on a substrate
- Mechanisms of graphene growing across substrate grain boundaries
- Mechanisms of alignment and coalescence of graphene islands on a TM surface
Here, we discuss the effect of graphene–substrate interaction on the orientation of graphene islands on the substrate. As shown in Figures 2.6 (d-e), the coalescence of two misaligned graphene islands results in the formation of a grain boundary between them, and the concave corner corresponds to one end of the grain boundary.
CVD growth of single-crystal hBN film
- Nucleation of hBN on a substrate
- Mechanisms of hBN alignment on a TM surface
For hBN grown on a nearby Cu(110) surface, an atomic-resolution STM image (Figure 2.11(a)) proved that the hBN island shows a ZZ edge at the interface between the grown hBN and the obtained surface and low-energy electron diffraction pattern ( LEED) confirmed that the step edges on the obtained surface are along the Cu<211> direction.84 We performed theoretical calculations to explore the formation energies of interfaces between different hBN edges with the Cu<211> step edge. As shown in Figure 2.11(b-c), where γ denotes the relative angle between an hBN ZZ direction and the Cu<211> step edge, there is only one local minimum located at γ = 0º, where the nitrogen-terminated ZZ edge of hBN is parallel to the Cu<211> step edge, confirming the unique orientation of hBN islands on the obtained vicinal Cu(110) substrate. As shown in Figure 2.11(e), the orientation of hBN islands and therefore their unidirectional alignment can only be maintained during growth if there is an inclined hBN edge which has kinks complementary to the meandering step edge.
As shown in Figure 2.12, the STM image shows that the step edges on the obtained Cu(111) surface consist of two typical step edge terminations (A and B).
CVD growth of single-crystal monolayer TMDC films
- Nucleation barrier of TMDC on a substrate
- Mechanisms of TMDC alignment on a substrate
However, research on the alignment of different TMDC islands on substrates has been quite limited so far. Very recently, motivated by the success of well-aligned hBN islands on high-index Cu surfaces, unidirectionally aligned MoS2 islands were realized for the first time on a vicinal Au(111) surface (see Figure 1.17). The obtained vicinal Au(111) surface is shown in Figure 2.15.179. Similar to a strongly stepped Cu(111) surface, there are also two types of Au<110> step edges on an Au(111) surface and the stability of different MoS2 edges joining these two steps and on the Au( 111) terrace are confirmed are compared by DFT calculations. Nevertheless, a systematic understanding of the mechanism of TMDC alignment is still lacking on both low and high index TM surfaces to date.
In contrast, high-index TM surfaces show great potential in shaping the growth of unidirectionally aligned low-symmetry 2D materials due to the existence of stepped edges on such substrates.
Conclusions and unsolved research problems
Currently, C6V Cu (111) and C2V Ge (110) surfaces have been proven to be a good substrate for the growth of single-sided C6V graphene islands. C3V 2D materials are found to show at least two orientations on all low-index TM surfaces. An experimental investigation on the extent of 2D islands on all high-index TM substrates is impossible.
Therefore, a systematic theoretical study on the alignment mechanism of 2D materials on various high-index TM substrates is urgent, which is very useful for screening suitable substrates for the growth of unidirectionally aligned 2D islands and thus various WSSC 2D- materials.
Methodology
Introduction
Introduction of Density functional theory (DFT)
- The Born-Oppenheimer approximation
- The Hohenberg-Kohn theorem
- The Kohn-Sham method
- Approximation to the exchange-correlation functional
The first Hohenberg-Kohn theorem states that the external potential and therefore the ground state electronic energy is a unique function of the electron density, 𝐸0= 𝐸0[𝑛0(𝑟⃑)]. Therefore, the ground state electron density uniquely determines the external potential and also the electronic Hamiltonian, which means that the ground state electronic energy is a unique function of the electron density and depends on the external potential. The second Hohenberg-Kohn theorem states that the electron density that minimizes the energy of the overall functional element is the true ground state electron density, and the proof is as follows.
Since the exchange-correlation potential is also a function of the electron density, the Kohn-Sham equation can be solved by a self-consistent field calculation, and the Kohn-Sham scheme is shown in Figure 3.1.
Introduction to classical molecular dynamics (MD) simulation
- Interactions between atoms
- Boundary conditions
- Ensemble
- Time integration algorithm
During MD simulations, choosing an appropriate potential to describe the interactions between atoms is crucial for the accuracy of the simulated results. However, the periodic boundary condition is not always applicable in all directions of the system, especially the low-dimensional materials. For the μVT ensemble, μ, V and T of the system are kept constant, and are usually used for the system that can exchange both energy and mass with the surroundings.
A safe time step is usually set to be about 1/10 of the vibrational period of the atoms in the simulated system.
A general theory of 2D materials alignment on crystalline substrates with different
- Introduction
- The symmetries of 2D materials and substrate surfaces
- Alignment of 2D materials on low-index high symmetric substrates
- Alignment of C 6V -2D materials on high-symmetric substrates
- Alignment of 3-fold symmetric 2D materials on high-symmetric substrates
- Alignment of 2D materials on low symmetric substrates
- Alignment of 6-fold symmetric 2D materials on low symmetric substrates
- Alignment of C 3V -2D materials on low symmetric substrates
- Summary
The mirror planes of the 2D material and the substrates along different directions are indicated by dashed lines. The lower the interface formation energy, the more stable the orientation orientation of the 2D material on the substrate. On a low-index high-symmetry substrate, 2D materials usually exhibit multiple orientations depending on both the symmetries of the substrate and the 2D material.
On CS symmetric surfaces, islands of 2D materials show one or two orientations, depending on the configuration of the interfaces.
Alignment of graphene islands on low symmetric Cu substrates
- Introduction
- Structures of low symmetric Cu substrates
- Modeling and simulation methods
- Modeling
- Simulation methods
- Results and Discussions
- Alignment of graphene islands on Cu{111}-based low symmetric surfaces
- Alignment of graphene islands on Cu{100}-based high-index low symmetric substrates
- Alignment of graphene islands on Cu{110}-based high-index low symmetric surfaces
- Summary
Since all low symmetric surfaces have the exact Cu[110] direction, the Cu[110] step edge is chosen here as a reference. Figures 5.2 (b) and (e) show the structure of Cu{100}-based high-index low symmetric substrates and the buckling density profile as a function of Cu step edge orientation, respectively. In summary, the orientation of graphene is not sensitive to the step edge variation on Cu{111}-based high-index low-symmetric substrate.
For the Cu<110> step edge, the lattices of graphene ZZ edge and Cu step edge match very well.
Single-crystal graphene grown on twinned Cu substrates
- Introduction
- Experimental methods and results
- Preparation of twinned Cu foils
- Synthesis of unidirectional graphene islands on twinned Cu foils
- Theoretical modeling and discussions
- Modeling of twinned Cu foils
- Alignment of graphene islands on twinned Cu substrates
- Application to other 2D materials
- Anticipation of graphene alignment on twined hexagonal close-packed (HCP) metal substrate
- Summary
In Figure 6.2(e), a high-resolution transmission electron microscope (HRTEM) image of the grain boundary shows that the two grains with (116) and (111) surfaces are mirror symmetric with respect to their grain boundary, which is the double characteristic of the grain boundary indicates. annealed Cu foil. To investigate the orientations of graphene islands on the Cu surface, the grain texture of the Cu surfaces must first be determined. The map in Figure 6.7 shows the misorientation angles of graphene islands on the two sides of the <111>/60o Cu twin along all orientations, and the misorientation angle values are indicated by colors.
Moreover, it is worth noting that the misorientation angles are exactly 0º along the dashed line on the map, indicating perfect alignment of graphene islands on the Cu foils with these twin grain boundaries.
Alignment of hBN islands on low symmetric Cu substrates
- Introduction
- Modeling and simulation methods
- Modeling
- Simulation methods
- Results and discussions
- Alignment of hBN islands on Cu{111}-based high-index low symmetric substrates
- Alignment of hBN islands on Cu{100}-based low symmetric substrates
- Alignment of hBN islands on Cu{110}-based low symmetric surfaces
- Experimental evidence
- Summary
Clearly, aligned hBN islands can only be synthesized on Cu{111}-based high-index low-symmetry substrates with SE<211>i×<110>step edges when -9.61 𝑒𝑉 <. We further calculated the orientations of hBN islands attached to beveled step edges of Cu{100}-based high-index low-symmetry substrates. Following the above analysis, we further investigated the alignment of hBN islands on Cu{110}-based high-index low-symmetry substrates.
We found that the alignment of hBN islands on high-index, low-symmetric Cu substrates is largely determined by the structures of the substrate step edges.
The effect of surface roughness on the alignment of grown 2D materials
Introduction
Modeling and discussions
As shown in Figure 8.2(b), the edges of the steps are no longer aligned in a constant direction, but start to wiggle due to the roughness of the surface. So the step edges on the cone are the intercepts of the cone surface and the planes of the terraces, and they are curved lines. Moreover, from Figure 8.2(e), we can also qualitatively reveal the effect of the density of step edges on the change of their direction under the same 𝜃.
Therefore, a high step edge density can effectively weaken the effect of surface roughness on the change of step edge directions.
Summary
Alignment of TMDC islands on vicinal Au(111) substrates
- Introduction
- Calculation methods
- Results and Discussions
- Summary
Because 𝜇𝑆 is equal to -4.32 eV or -5.47 eV using S bulk or W bulk as reference, it is clear that the growth of WS2 film on the pristine Au(111) surface is always energetically favored in the 𝜇𝑆 range between two values, indicating that the Au(111) surface can remain its pristine configuration with the WS2 film cover. Along the Au<110> step edge, the ZZS and ZZW edges are more superior than the AC edge, but there is no obvious binding energy difference for the interfaces on the Au<110> step edge pinned by ZZS and ZZW edges because both WS2 ZZ- edges have been well passivated by S atoms. However, the different compositions of ZZS and such S-terminated ZZW edges should result in different formation energies of ZZS and such S-terminated ZZW edges, which will lead to only one preferred orientation of the WS2 island along the Au<110> step edge.
It should be noted that, due to the unbalanced stoichiometry, the edge formation energies of the WS2 edges as well as the interfacial formation energies between these edges and the Au step edges are highly dependent on the environmental condition.
Formation mechanisms of large single-crystal Cu(111) foil by contact free annealing
- Introduction
- Experimental setups and results
- Theoretical methods and discussions
- Calculation methods
- Modeling and discussions
- Summary
The EBSD maps in Figure 10.2(c) on different areas of the Cu sheet also suggest its single crystallinity. The in-plane orientation of the various areas of the Cu sheet is then examined, as shown in Figure 10.2(d). To understand the formation process of Cu sheet with {111}<112> surface during annealing, the texture evolution with respect to annealing time was further explored.
To investigate the movement of vacancies in the Cu slot, classical MD simulations were performed, as shown in Figure 10.6.
Rotated graphene moiré superstructures on various transition metal surfaces
- Introduction
- Modeling and calculation methods
- Modeling
- Calculation methods
- Rotation-dependent graphene on the Ru(0001) surface
- Structural evolution of graphene on the Ru(0001) surface
- Electronic properties of graphene/Ru(0001) superstructures
- Applications of graphene/Ru(0001) superstructures as templates
- Formation mechanisms of graphene moiré superstructures on the Ru(0001) surface
- Rotated graphene moiré superstructures on other transition metal surfaces
- Summary
Here, the rotation angles of the graphene/Ru(0001) superstructures can be restricted to the range of 0–30°, and the graphene/Ru(0001) supercells have mirror symmetry with respect to 30° because both graphene and the Ru(0001) surface are C6V symmetric. Therefore, the binding energy of graphene on the Ru (0001) surface can be estimated by summing the energy at the four highly symmetric sites of the Ru (0001) surface. The curvature energy of the graphene/Ru(0001) superstructure is mainly from the bumpy part of the graphene layer, and for graphene, its curvature energy (𝐸𝐶) and radius of curvature (R) satisfy the ratio 𝐸𝐶 ∝ 1.
By comparing the differences of graphene on the Ir(111) and Pt(111) surfaces, we find that the difference in the binding energies of graphene at different places on the Ir(111) surface is greater than the difference on the Pt(111) surface. , resulting in a slightly larger height fluctuation of the graphene layer on the Ir (111) surface than that on the Pt (111) surface.
Conclusions and further research plans
Epitaxial chemical vapor deposition Growth of single layer graphene over cobalt film crystallized on sapphire. Epitaxial growth of large-area single-layer graphene over Cu(111)/sapphire by atmospheric pressure CVD. Growth of large area single and bilayer graphene by controlled carbon deposition on polycrystalline Ni surfaces.
The role of surface oxygen in the growth of large single crystal graphene on copper.
