2D materials consist of one to a few atomic layers where the intra-layer atoms are chemically bonded and the atomic layers are weakly bonded. high bonding anisotropicity.
A high symmetric direction of a 2D materials prefers to align along a high symmetric direction of a substrate is the foundation of our main conclusion.
orientational uniformity of a 2D material on a substrate,
the symmetry group of the substrate is a subgroup of that of the 2D material.
Currently, most previous studies on the synthesis of large-sized single crystalline XXX and XXX employed vicinal (111) or (110) surfaces with parallel step edges [Nature 570, 91–95 (2019); Nature 579, 219–223 (2020); ACS Nano 14, 5036–5045 (2020)], where 2D materials tend to align along these step edges and the general study on the epitaxial 2D materials growth on various high index surface is very rare.
Besides the vicinal surfaces which are close to one of the low-index surfaces, the high-index surfaces that are largely deviated from all the low-index surfaces, like the (123) surface of an fcc material, are also ideal for the epitaxial growth of large-scale single-crystalline 2D materials.
synthesizing 2D materials with well-defined grain boundaries, for instance, polycrystalline graphene with grain boundaries of 30o misorientaation angle can be synthesized on an fcc(100) surface, similar to the case of graphene growth on a liquid Cu surface [Angew. Chem. Int. Ed. 58, 7723–7727 (2019)].
the preferential alignment of a 2D material on a substrate.
the epitaxial growth of a 2D single crystal can be realized only if the symmetry group of the substrate is a subgroup of that of the 2D materil.
Using substrates with high-index surfaces which have lower symmetry to template the epitaxial growth of various 2D materials (Nature 570, 91 (2019); Nature 579, 219 (2020); ACS nano 14, 5036 (2020), Nat. Mater. DOI 10.1038/s41563-020-0795-4 (2020))
the propagating edge of a 2D material tends to align along a high symmetry direction of the substrate.
wafer-scale single crystals
the XXX edge is generally the slowest propagrating edge because of its highest barrier for edge propagation
when we want ot grow a 2D material on a substrate, which aspects we need to condiser?
2D material-substrate interaction
alignment of a 2D material on a substrate
2D materials library (~ hundreds of) and the possible substrate types are also of the same order of magnitude.
All possible combinatins of 2D materials and substrates is greater than 100,000.
Without losing the generality,
Two sceneries of the interactons between 2D materials and various substrates.
Scenery (i) The edge of the 2D material is terminated by the substrate, like graphene or hBN on an active metal substrate, where the strong interaction between the edge of the 2D material and the pristine substrate facet determines the alignment of the 2D material and its epitaxial growth behavior;
binding energies as a function of the angle of edge alignment that is defined as the angle between the edge and a XXX〈XXX〉direction of the substrate, the difference between the binding energy minimum and maximum is significant, >0.2 eV per edge atom. a well-aligned small XXX island of ~XXX nm (which has only ~XXX atoms of which ~ XXX are at the edge) has an energy advantage of >8eV over misaligned ones. this binding energy difference is large enough to miantain a growing XXX island in a well-aligned configuration on a XXX surface. [threshold?]
plot the electron density distributions of XXX surfaces. the isosurface fluctuation in electron density is the lowest along the 〈XXX〉direction, indicating that the close-packed 〈XXX〉atomic rows form a pattern with alternative ridges and vallegs of uniform height on the surface. the less stable edge atoms form a straight line and this straight edge is prederentially passivated by either a ridge or a valley of the XXX surface instead of crossing over ridges and valleys on the surface, which results in distortion of the edge.
To further illustrate preferential passivating of the XXX edge by a close-packed atomic row, we compare the atomic structures of the interfaces and the charge density differences of teh XXX edge along both 〈XXX〉and other directions. when the XXX edge is aligned along the 〈XXX〉direction, all the edge atoms are well passivated by a 〈XXX〉atomic row and the edge remains straight. In contrast, the XXX edge is along another direction, some of the edge atoms are poorly passivated and the edge is no longer straight coz of the fluctuating ridge-valley pattern of the surface. The above analysis clearly shows the superiority of the close packed direction of a substrate in passivating a high-symmetric edge in a 2D material.
The lattice constant of XXX edge matches that of the 〈XXX〉direction of XXX substrate well.
condiering lattice-mismatch, the lattice constant of XXX edge is about 12.6% smaller than that of 〈XXX〉direction.
The lowest propagating (also high-symmetric) edge of a 2D material prefers to align along the high-symmetric direction of an active metal substrate, regardless of the lattice-match between the 2D material and the substrate.
Scenery (ii) The edge of the 2D material is self-passivated or terminated by active atoms from the environment of its growth, such as H or OH groups, where the weak inetraction between the bulk of the 2D material and the pristine substrate facet dominates the alignment of the 2D material.
The General Theoretical framework
DFT calculations of edge binding energies
DFT calculations are carried out via the Vienna ab initio simulation Package (VASP). The exchange-correlation effect is treated by the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA). The interaction between valence electrons and ion cores was described by the projected augmented wave (PAW) method and the k-point mesh was sample by a separation of 0.03 Å−1.
the binding energy of a graphene ZZ edge to certain surfaces. Graphene nanoribbons alon the ZZ direction, which were three hexagons wide and one of the two ZZ edges passivated by hydrogen.
the incommensurate lattice constants
low-index Cu surfaces
a small number of periodic structures
DFT can handle how many the number of atoms to calculate.
The initial distane between the material and substrate is set to ~Å, which was estimated from DFT-D2 calculations [J. Comput. Chem. 27, 1787–1799 (2006)], and it is the typical euqilibrium distance between material and the underlying substrate surface.
Structure optimization is conducted with the atomic positions of the lowest XXX atomic layer fixed. In addition, the vertical possitions of carbon atoms that are passivated by hydrogen were also fixed during structure optimization.
To eliminate the imaginary interaction between periodic images along the vertical direction, a vacuum layer with a 15Å thickness was used to separate the XXX slabs. All the structures were relaxed until the force on each unfixed atom was <0.01eV/Å, with an energy convergence of 10-4eV.
To calculate the binding energies between the materiasl and substrate surface. The binding energy of a XX edge of XXX to the substrate is defined as:
Eb = Et-Es-EM/l
To calculate the weak interaction between XXX wall and XXX surface, a XXX layer was stacked to a XXX slab consisting of three atomic layers under periodic boundary condition and with different alignment angles. during structure optimization, the bottom atomic layer of the metal slab was fixed. The binding energy between the XXX wall and the metal substrate is defined as
Eb = Et-Em-Es/NXX
N is the number of XXX of XXX layer in the unit cell of the whole system.
To calculate the weak interaction between WS2 and XXX layer, a triangular XXX cluster consisting of XXX atoms and XXX atoms was placed on a XXX layer woth different orientations. Because the edges of the XXX cluster are passivated by XXX and the XXX layer is chemically insert, the interaction between the XXX cluster and XXX should be dominated by XXX wall and the XXX layer. The binding energy between the XXX cluster and the XXX layer is defined as
Eb = Et-EXXX-Exxx/Nw
the slowest propagating edge coz of its heighest barrier for propagation.
the kinetic Wulff construction
Cu substrate with tailored step edges
transition metal dichalocogenides with 3-fold summetry
the alignment of a 2D material on a substrate depends on both qits symmetry and that of the substrate
2D polycrystalline materials with designed grain boundaries
DFT calculations of edge binding energies
the intra-layer atoms
One edge of each island is passivated by a high-symmetric step edge of the substrate.
low-index ~ surface; high-index ~surface
the expitaxial growth relationship
numbers of alignments and misalignment angles of 2D materials on the substrate.
Experimental observations
Experimental details
Ar Sputtering
1. Flushing Ar gas line
(1) When TMP-1 (V150) is running , V1 close, V2 close.
(2) If TMP-4 (V50) is not running, run it.
(3) Close V12. V8 , V10 , V13 should be close.
(4) Slowly open the V14, pull the Ar gas line with TMP4. Ensure that the reading of TC2 does not exceed 2V.
(5) When the reading of TC2 is close to 7.3V, close V14.
(6) Open V15 (value of Ar gas cylinder), set Ar gas line to 1 atm, close V14.
(7) Open V14 carefully while read TC2. In this case, the reading of TC2 should never be less than 2V. When TC2 is close to 7.3V, close V14.
(8) repeat (6) and (7) about 3 times.
(9) when TMP-1 is running and TC2 is 7.3V, open V2. When the vacuum level of TC2 deteriorates and becomes 7.3V again, open V1.
2. Ar sputtering
(1) Open V15. When Ar gas line is 2 atm, close V15.
(2) Cool the Ar gas line in LN2 of a dewar bottle (fix it with an Aluminum plate).
(3) Ion gun holder electrode (H) to GND, sample electrode (S) to tester (20 mA range).
(4) Place the sample holder on the annealing base and place the annealing base in front of the annealing base (it is advisable to tilt it slightly in the direction in which the beam will be easily hit).
(5) Close GV2.
(6) Open VLV1 gradually while looking at the vacuum level of the Chamber. Set it yo 5×10-5 Torr (6.43V).
(7) Turn on the power of Ion gun controller.
(8) Turn the Filament knob to the right and inject IF = 25 mA.
(9) The acceleration voltage is set to 1kV.
(10) Turn on the switch Remote (this starts sputtering).
(11) Adjust the FOCUS, position, and Angle of the sample to maximize the sample current. It usually has a current 2 mA.
(12) Turn off Remote, Fila turn to 0 mA.
(13) Close VLV1, it turns back about 2.8 until see a black marker.
(14) The vacuum level should be better to 1×10-9 Torr (2V) in 1-2 min. Open GV2.
(15) In another 10 min, the vacuum level should improve to less than 5×10-10 Torr.
Note: The order (1) and (1) must never be reversed. Ar liquefies at LN2 temp, so when LN2 is gone, the pressure in the gas line increases and is very dangerous.
Annealing
(1) Make sure that the Imax knob on the control panel is left (Imax = 0) and the switch is Imax. Also, confirm that the terminal of C.C. OUTPUT on control panel 1 is connected to a DC power supply (it should be normally connected).
(2) Adjust dI/dV knob on the control panel 1 (this is the speed at which the current is dropped at the end of the annealing). It is usually set to 0.5×10-2 A/s. The actual speed of the current drop is different from the display of control panel 1.
(3) Place the sample holder on the annealing base and check that the current transfer terminal of the annealing base is in contact with the sample holder by the tester. At this point, the resistance value is from Pt(111) (10-5 Ω・cm).
(4) Connnect the DC power supply to the current introduction terminal of the annealing base with a cable. Verify that no current draw pin is connected to the sputtering pin.
(5) Fix the radiation thermometer with a stand where the center of the sample is visible.
(6) Connect the radiation thermometer and the control panel 1 with a cable. Turn on the TM switch.
TM OUTPUT D-OUT
TM INPUT A-OUT
(7) Gradually turn the knob of Imax to the right while looking at the value of the radiation thermometer, and raise it up to the target Temp. For the sample with a large resistivity. it is recommended to use a power supply with a higher maximum voltage and raise the temp slightly, then turn off the power supply and switch to the original power supply.
(8) The temp may vary from 10 to 20 in the progress of annealing. Turn the Imax knob to adjust the temp appropariately.
(9) Switch control panel 1 from Imax to START, after annealing.
(10) Turn off the direct current, when the current is 0.
(11) Turn the Imax Knob to the left. Switch back to Imax.
Deposition Methods
(1) Make sure that the vacuum level (UHV2 reading) is good (usually around 1×10-10 Torr).
(2) The sample holder attached the tip of the transfer rod and the surface is directed upward. Place the thinnest part of the transfer rod directly above the deposited part so that the deposited part is fully visible from the Membrane Pressure Gauge.
(3) Wire as follows
- Connect the membrane pressure gauge and the membrane pressure controller.
- Connect the output of the high voltage power supply to the crucible through the tester (200 mA range) (Ag-Ta crucible, Au-W crucible).
- Connect the DC power supply (KIKUSUI PAD35-20L) to the fila and drop one side to GND.
(4) Turn on the power of the MPG controller and set up MPG parameter (density, Zvalue) depending on the vapor deposition source material. The distance between the vapor deposiiton and MPG is twice the root of the vapor deposition and the sample distance. Set up density value as a half of real value.
(5) Make sure the toggle switch on control panel 1 is Imax and the Imax knob is full to the left.
(6) Turn on KIKUSUI PAD35-20L power supply.
(7) Looking at the value of UHV2 and PAD35-20L, turn the Imax knob to the right gradually and draw 5A current, at this time, the voltage is about 5V.
(8) Until the UHV2 is good enough (usually around 3×10-10 Torr), degas continues. it usually lasts about 5 min.
(9) Make sure the HV power supply porality is positive. Set the current limit (normally 30 mA is fine).
(10) Reading UHV2, MPG controller, and tester, the deposition speed is got by applying the HV gradually. The evaporation rate of 0.1A/sec can be got by regulate I and V.
(11) Once the melting pot has warmed uniformly and the evaporation rate has stabilized, the sample is directed downward and brought directly above the evaporator. Once teh required amount has been deposited, the sample is quickly moved and pointed upward.
(12) Set the high voltage power supply to 0V. Turn off the power supply.
(13) Turn the Imax knob of the Control panel 1 to the left, Imax =0.
(14) Turn off the power (KIKUSUI PAD35-20L).
(15) Turn off the Membrane Pressure Meter.
1. Three-fold symmetry
(1) hBN
C3V aymmetry of hBN. Three of its six ZZ edges are nitrogen terminated and the other three are boron terminated (namsed as ZZN and ZZB edges hereafter).
The ZZN edge has been proven to be the slowest propagating and kinetic Wulff construction leads to triangular hBN islands enclosed by three ZZN edges.
Recent works have shown that well-aligned hBN islands can be successfully achieved by using a Cu substrate with railored step edges.
(2) Reansition Metal Dischcogenides (TMDCs)
2. Six-fold Symmetry
Moire Pattern
Two periodic structures are overlaid with a slight misalignment or rotation.
charge spilling at interface
free energy
interface strain
strain relaxation-magnetic mismatch like HCT models
Pressure/strain: structure phase transition + Magnetic ground state induce effective trimerizationn of the Mn atoms control exchange frustraton induce helical modulation.
Mn3Sn built in even layers
weakly bound in the lattice planes.
The shortest distance between the Mn atoms of two neighboring layers is ~, whereas the nearest-neighbor atoms in the same layer are only ~. The weak binding between the lattice planes is a big advantage.
The lattice parameter from electron diffraction.
A stoichiometric trarget
The target to substrate distance was XXX?
One monolayer (ML) is defined by the atomic density of the substrate.
The area density of XXX atoms on ~ is ~ atom/cm2.
Extra effects from L-T phase.
A subtle change to the magnetic ground state.
Low energy magnetism in the commnesurate phase of Mn3Sn described Models of interacting local moments.
BZ almost 0.1 eV.
epitaxial islands
chemical bonds
kagome-based Moire system
Moire potentials are induced by a 2D irreducible corepresentation engenvalve fragile phases.
A moire system formed by stacking 2 graphe-like layers with similar lattice constants but opposite signs of the Dirac Fermi velovity.
potential energy surface
ordered honeycomb-kagome network
unpassivated dangling bonds
monolayer limit
structural recontruction-modulated electronic properties
strain relaxation
interface polarity can tailor the behavior of strain relaxation
prinstine surface
~ desorption
the moire periodicity determins the electron progation length on the lattice and the interlayer electron-electron interactions.
A moire pattern from the projection of one periodic pattern to another with relative lattice constant or misalignment.-periodic potential to modify the electronic properties.
Van Hove sigularities at the cross point of 2 sets of Dirac cones.
Mott-like insulating behavior at half filling state.
A multiple-Q Spin state, Q is the wave vector of the magentic modulation.
A superpostion of several of single-Q spin states.
120 structure of Mn1 spins: a sum of 3 Single-Q states with Q vectors along the 3 equivalent directions of the hexagonal lattice.
Multiple-Q spin state induce CDW modulation, coz the spin-charge coupling in itinerant magnets.
the CDW modulation in Mn3Sn weak-It is not clear whether STM can visualize the SDW annd CDW modualtions. Several factors: surface termination. the tunneling conditions the interference effects between different modulations. STM not is sensitive enough to detect the subtle CDW modulation induced by the multiple-Q spin state.
Wetting layer
wearly interacting substrates
self-assembled molecular layers
QING SHI 