Confined growth of 2d materials and their heterostructures

Abstract

Two-dimensional (2D) materials and their heterostructures represent a promising pathway to next-generation electronics. However, challenges exist at the wafer level, including (i) controlling layer-by-layer (ML-by-ML) 2D material growth, (ii) maintaining single-domain growth, and (iii) controlling the number and crystallinity of layers. This paper discloses a deterministic confined growth technique that addresses these challenges, enabling the fabrication of wafer-level single-domain 2D monolayers and their heterostructures on any substrate. The growth of the first nucleus is confined by patterning a SiO2 mask on a 2-inch substrate to define selective or confined growth regions. Each growth region or trench is only a few micrometers wide and is filled with a single-domain monolayer before the introduction of the second set of nuclei. The second set of nuclei is grown within the trenches to create a 2-inch wafer-level array of single-domain bilayers. Devices fabricated with single-domain bilayers across the entire wafer exhibit superior performance.

Description

Technical Field

[0001] The present invention relates to confined growth of 2D materials and heterostructures thereof. This patent application claims priority under 35 USC 119(e) to U.S. application No. 63 / 374,090, filed on August 31, 2022, and the entire contents of this application are incorporated herein by reference for all purposes. Prior Art

[0002] Two-dimensional (2D) transition metal dichalcogenides (TMDs) and their heterostructures are promising platforms for next-generation electronics, spintronics, valleytronics, and optoelectronics. However, integrating semiconductor 2D heterostructures into industrial platforms has been challenging due to limited scalability. The common method for constructing 2D heterostructures is mechanical exfoliation and stacking of 2D sheets, a trial-and-error-based operation that severely limits the size of the structures that can be produced. Fabricating 2D heterostructures using mechanical exfoliation and stacking is also time-consuming.

[0003] Recent progress in achieving scalability by epitaxially growing single-crystalline monolayer (ML) TMDs on single-crystalline hexagonal substrates such as sapphire has been substantial. However, the lack of a layer-by-layer growth strategy for single-domain TMDs (TMDs) has made significant challenges in growing large-scale 2D heterostructures. Furthermore, some existing growth methods involve the undesirable step of implanting 2D materials into silicon devices when growing them on hexagonal non-silicon substrates. Single-domain TMD arrays can also be grown by laser irradiation of nucleation sites. However, this approach presents challenges because the second heterolayer is likely to nucleate on the edges of the first single-domain patches. To date, no feasible solution exists for achieving wafer-scale single-domain 2D heterostructures. Summary of the Invention

[0004] The present technology involves layer-by-layer growth of 2D materials on arbitrary substrates. This technique can be used to grow wafer-scale single-domain homojunction and heterojunction TMDs. It also includes a non-epitaxy strategy for growing single-domain TMDs on amorphous materials, enabling the formation of single-crystalline 2D materials on Si wafers coated with arbitrary layers.

[0005] The present technology addresses a fundamental kinetic issue in TMD growth. A SiO mask on an amorphous AlO or HfO layer on a silicon substrate confines the growth of a first set of TMD nuclei to an array of selective growth regions, called pockets or trenches, with lateral dimensions (width and length) no greater than a few micrometers. Density functional theory (DFT) calculations confirm higher TMD binding energies on these substrates than on the SiO mask. Consequently, TMD nucleation is concentrated on the substrate surface rather than on the SiO mask walls. Reducing the size of the pockets or trenches in the SiO mask substantially reduces the generation of fully filled first set nuclei (i.e., a single domain completely filling a pocket) during the incubation period of the second set of nuclei in the second TMD layer during growth. Consequently, the monolayer TMD (ML-TMD) layer in each trench across the entire wafer is a single crystalline domain. The confined geometry allows precise control over the number of layers so that multiple TMD monolayers (TMD MLs) can be grown on top of each other to fill the trenches.

[0006] The present technology can be used to fabricate single-domain bilayer WSe2 (BL-WSe2) at the 2-inch wafer level through subsequent confined WSe2 growth. FETs fabricated on the single-domain WSe2 array across the entire 2-inch wafer exhibit performance approaching that of mechanically exfoliated WSe2 flakes, with, for example, a maximum effective mobility of 72.8 cm2V-1s-1 for single-layer WSe2 (ML-WSe2) and 103.5 cm2V-1s-1 for bilayer WSe2.

[0007] Furthermore, these techniques can be used for the confined layer-by-layer growth of MoS2 / WSe2 heterostructures at the wafer scale. Valley lifetime measurements of single-domain MoS2 / WSe2 heterostructure arrays are comparable to those obtained for single-domain TMD flakes. The confined growth techniques of the present invention enable the fabrication of wafer-scale single-domain, single-layer-by-layer (ML-by-ML) homojunctions or heterojunctions.

[0008] The present invention provides a method for confined growth of a 2D material (e.g., a TMD such as MoS, MoSe, WS, or WSe) on a substrate (e.g., HfO or amorphous AlO) having a first binding energy for bonding with the 2D material. The method can be implemented as follows: A mask layer (e.g., SiO) having a second binding energy for bonding with the 2D material that is lower than the first binding energy is formed on the substrate. A trench having sidewalls surrounding an exposed portion of the substrate is formed on the mask layer. A core of the 2D material is disposed on the exposed portion of the substrate and grown into a single-domain monolayer of the 2D material. This single-domain monolayer can fill the trench. The single-domain monolayer can be used to form a semiconductor device, such as a valleytronics device, a forksheet field-effect transistor (FET), or a complementary field-effect transistor (FET).

[0009] The maximum lateral dimension of the trench can be approximately equal to the product of the incubation time of another nucleus of the 2D material on the single-domain monolayer and the growth rate of the 2D material. For example, the maximum lateral dimension of the trench can be approximately 2 microns. The trench can be one of a plurality of trenches in a trench array formed in the mask layer, with a single nucleus of the 2D material deposited in each trench in the trench array. When the critical trench size in each pocket is at or below a critical value, such as 2 microns, a single nucleus of the 2D material is obtained. These nuclei can grow into each single-domain monolayer of the 2D material, filling the trenches in the trench array.

[0010] In some cases, the core is a first core, and the single-domain monolayer is a first single-domain monolayer. In these cases, a second core of the 2D material can be deposited on the first single-domain monolayer and grown into a second single-domain monolayer of the 2D material, thereby forming a bilayer of the 2D material in the trench. Alternatively, in these cases, the 2D material is a first 2D material, and cores of a second 2D material, different from the first 2D material, are deposited on the single-domain monolayer and grown in the trench, thereby forming a heterostructure of the first and second 2D materials. For example, the first and second 2D materials can each be selected from the group consisting of MoS2, MoSe2, WS2, and WSe2.

[0011] In one embodiment, the present invention provides a method comprising the steps of: (a) providing a substrate of a first material; (b) depositing a mask material on the substrate; (c) forming a trench array on the mask material, the trench array comprising a plurality of trenches, each trench having a trench geometry with lateral dimensions l, x, and w, wherein each of l and w is selected to have a maximum dimension of 2 μm, and each trench having an exposed portion of the substrate surrounded by sidewalls formed of the mask material; (d) depositing adatoms of a second material on the exposed portion of the substrate, wherein a first binding energy between the first material and the second material is greater than a second binding energy between the mask material and the second material; (e) allowing the adatoms to selectively nucleate as nuclei within each trench in the trench array; and (f) growing the nuclei within each trench in the trench array; wherein the lateral dimensions associated with the trench geometry constrain the nuclei to grow into a single domain monolayer of the second material.

[0012] In one embodiment, the first material includes one of hafnium oxide (HfO 2 ), aluminum oxide (Al 2 O 3 ), hafnium zirconium oxide (HZO), titanium dioxide (TiO 2 ), zinc oxide (ZnO), iron oxide (Fe 2 O 3 ), tin oxide (SnO 2 ), nickel oxide (NiO), or copper oxide (CuO). In one embodiment, the second material includes one of graphene, carbon nanotubes (CNTs), hexagonal boron nitride (h-BN), metallic transition metal dichalcogenides (e.g., vanadium disulfide (VS2), vanadium diselenide (VSe2), cobalt disulfide (CoS2), cobalt diselenide (CoSe2), titanium disulfide (TiS2), or titanium diselenide (TiSe2)), semiconducting transition metal dichalcogenides (e.g., molybdenum disulfide (MoS2), molybdenum diselenide (MoSe2), tungsten disulfide (WS2), or tungsten diselenide (WSe2)), or high-k materials (e.g., Bi2SeO5 or Sb2O3). In one embodiment, the mask material includes at least one of amorphous silicon dioxide (a-SiO 2 ), amorphous silicon (a-Si), amorphous silicon nitride (a-SiN x ), amorphous carbon (a-C), hafnium oxide (HfO 2 ), aluminum oxide (Al 2 O 3 ), hafnium zirconium oxide (HfZrO), titanium dioxide (TiO 2 ), zinc oxide (ZnO), iron oxide (Fe 2 O 3 ), tin oxide (SnO 2 ), nickel oxide (NiO), or copper oxide (CuO).

[0013] In an extended embodiment, wherein the nucleus is a first nucleus and the single-domain monolayer is a first single-domain monolayer, the method further comprises the steps of: (g) waiting for an incubation period; (h) depositing another adatom of a third material on top of the first single-domain monolayer in at least one trench in the trench array, wherein a third binding energy between the second material and the third material is greater than a second binding energy between the mask material and the third material; (i) allowing the another adatom of the third material to selectively nucleate as a second nucleus on top of the first single-domain monolayer in at least one trench in the trench array; and (j) growing the nucleus in at least one trench in the trench array; and wherein lateral dimensions associated with the trench geometry constrain the second nucleus to grow into a second single-domain monolayer of the third material, and wherein the first single-domain monolayer and the second single-domain monolayer form a bilayer.

[0014] In one embodiment, the third material includes one of graphene, carbon nanotubes (CNTs), hexagonal boron nitride (h-BN), metallic transition metal dichalcogenides (e.g., vanadium disulfide (VS2), vanadium diselenide (VSe2), cobalt disulfide (CoS2), cobalt diselenide (CoSe2), titanium disulfide (TiS2), or titanium diselenide (TiSe2)), semiconducting transition metal dichalcogenides (e.g., molybdenum disulfide (MoS2), molybdenum diselenide (MoSe2), tungsten disulfide (WS2), or tungsten diselenide (WSe2)), or a high-k material.

[0015] In one embodiment, the bilayer is a heterojunction bilayer, wherein the second material and the third material are different from each other. In another embodiment, the bilayer is a homojunction bilayer, wherein the second material and the third material are similar to each other.

[0016] In one embodiment, each of l and w is selected to have a value equal to the product of the incubation time of another nucleus of the second material on the monodomain monolayer and the growth rate of the second material. In another embodiment, each of l and w is selected to be 2 microns.

[0017] In another embodiment, the method further comprises the step of forming a semiconductor device (a valleytronic device, a forked-chip field effect transistor (FET), or a complementary field effect transistor) comprising the single-domain monolayer.

[0018] In one embodiment, before depositing the mask material on the substrate, the method includes the step of depositing at least one of hafnium oxide (HfO 2 ), aluminum oxide (Al 2 O 3 ), hafnium zirconium oxide (HZO), titanium dioxide (TiO 2 ), zinc oxide (ZnO), iron oxide (Fe 2 O 3 ), tin oxide (SnO 2 ), nickel oxide (NiO), or copper oxide (CuO) on silicon to form a substrate.

[0019] In another embodiment, the present invention provides a method comprising the steps of: (a) providing a substrate of a first material, the first material having a first Gibbs free energy; (b) depositing a mask material on the substrate, the mask material having a second Gibbs free energy, the second Gibbs free energy being higher than the first Gibbs free energy; (c) forming a groove array on the mask material, the groove array comprising a plurality of grooves, each groove having lateral dimensions of l, x, w trench geometry, wherein each of l and w is selected to have a maximum dimension of 2 μm, and each trench has an exposed portion of the substrate surrounded by sidewalls formed of a mask material; (d) depositing adatoms of a second material on the exposed portion of the substrate; (e) allowing the adatoms to selectively nucleate as first nuclei within each trench in the trench array; (f) growing the first nuclei within each trench in the trench array; wherein lateral dimensions associated with the trench geometry constrain the growth of the first nuclei to a first single-domain monolayer of the second material; (g) waiting for an incubation period; (h) depositing another adatom of a third material on top of the first single-domain monolayer in at least one trench in the trench array; (i) allowing another adatom of the third material to selectively nucleate as a second nuclei on top of the first single-domain monolayer in at least one trench in the trench array; and (j) growing the nuclei within at least one trench in the trench array; wherein lateral dimensions associated with the trench geometry constrain the growth of the second nuclei to a second single-domain monolayer of the third material, wherein the first single-domain monolayer and the second single-domain monolayer form a bilayer.

[0020] In one embodiment, the first material includes one of hafnium oxide (HfO 2 ), aluminum oxide (Al 2 O 3 ), hafnium zirconium oxide (HZO), titanium dioxide (TiO 2 ), zinc oxide (ZnO), iron oxide (Fe 2 O 3 ), tin oxide (SnO 2 ), nickel oxide (NiO), or copper oxide (CuO).

[0021] In one embodiment, the second material or the third material includes one of graphene, carbon nanotubes (CNTs), hexagonal boron nitride (h-BN), metallic transition metal dichalcogenides (e.g., vanadium disulfide (VS2), vanadium diselenide (VSe2), cobalt disulfide (CoS2), cobalt diselenide (CoSe2), titanium disulfide (TiS2), or titanium diselenide (TiSe2)), semiconducting transition metal dichalcogenides (e.g., molybdenum disulfide (MoS2), molybdenum diselenide (MoSe2), tungsten disulfide (WS2), or tungsten diselenide (WSe2)), or high-k materials (e.g., Bi2SeO5 or Sb2O3).

[0022] In one embodiment, the mask material includes at least one of amorphous silicon dioxide (a-SiO 2 ), amorphous silicon (a-Si), amorphous silicon nitride (a-SiN x ), amorphous carbon (a-C), hafnium oxide (HfO 2 ), aluminum oxide (Al 2 O 3 ), hafnium zirconium oxide (HfZrO), titanium dioxide (TiO 2 ), zinc oxide (ZnO), iron oxide (Fe 2 O 3 ), tin oxide (SnO 2 ), nickel oxide (NiO), or copper oxide (CuO).

[0023] All combinations of the aforementioned concepts and additional concepts detailed below (provided such concepts are not mutually inconsistent) are part of the subject matter disclosed herein. In particular, all combinations of patented subject matter appearing at the end of this disclosure are part of the subject matter disclosed herein. Terms used herein, and which may also appear in any references, should be given a meaning most consistent with the specific concepts disclosed herein. Simple diagram description

[0024] Those skilled in the art will understand that the drawings are primarily for illustrative purposes and are not intended to limit the scope of the subject matter described herein. The drawings are not necessarily to scale; in some instances, aspects of the various subject matter disclosed herein may be shown reduced or enlarged in the drawings to facilitate understanding of different features. In the drawings, similar reference characters generally refer to similar features (e.g., functionally similar and / or structurally similar elements).

[0025] [FIG. 1A] Illustrate a conventional method for growing transition metal dichalcogenides (TMDs).

[0026] [ FIG. 1B ] illustrates the confined growth method of the present invention for selective single-domain synthesis of single-domain monolayer TMDs, which overcomes the limitations of conventional TMD growth methods.

[0027] [Figure 1C] illustrates the fabrication of a single-domain MoS2-WSe2 heterostructure by confined growth of a second MoS2 layer on a WSe2 monolayer in each trench in a trench array.

[0028] Figure 1D shows the calculated binding energies of W3O9, Se2, and W3Se6 clusters on c-Al2O3, a-HfO2, and a-SiO2 substrates.

[0029] [Figures 2A to 2D] show the selective single-domain synthesis and monolayer-by-layer (ML-by-ML) confined growth of WSe2 in 10μm pockets (Figures 2A and 2B) and 2μm pockets (Figures 2C and 2D) on a sapphire substrate with SiO2 sidewalls.

[0030] [Figures 2E to 2H] show Raman and photoluminescence (PL) images of confined monolayer WSe2 (Figures 2E and 2F) and bilayer WSe2 (Figures 2G and 2H) in a 2 μm pocket on a sapphire substrate.

[0031] FIG2I is a cross-sectional high-resolution (HR) transmission electron microscopy (TEM) image of a confined monolayer WSe 2 in a pocket on a sapphire substrate.

[0032] [ FIG2J ] is a cross-sectional HR TEM image of confined bilayer WSe 2 in a pocket on a sapphire substrate.

[0033] FIG3A is a photograph of a confined bilayer WSe field-effect transistor (FET) array integrated on a 5.1-cm-by-5.1-cm SiO2 / Si wafer. The inset shows a micrograph of an individual FET array with 20 integrated FETs (scale bar: 10 μm).

[0034] Figure 3B shows the transfer characteristics of a confined bilayer WSe 2FET at a drain-source voltage V DS = -1 V, with a channel length L CH of 0.7 μm. The results show a maximum on-current density of 155.8 μA μm −1 and a field-effect mobility of 103.5 cm 2V −1s −1.

[0035] [Figure 3C] shows the output characteristics of the confined bilayer WSe 2FET.

[0036] FIG3D shows a plot of the on-state current density Ion versus the effective mobility μeff for various WSe2FETs, including the present invention FET (star; upper right), a FET with 1-3 monolayers of single-crystal WSe2 grown by chemical vapor deposition (CVD) (solid dark squares), a polycrystalline 1-3 monolayer WSe2 film grown by chemical vapor deposition (CVD) (open squares), and an exfoliated WSe2 wafer (pentagons). The drain-source voltage and channel length are -1 V and approximately 1 μm, respectively.

[0037] [Figure 3E] is a histogram of the on-state current density I on (left) and effective mobility μ eff (right) of FETs fabricated using exfoliated single / double WSe 2 flakes and confined single / double WSe 2 films.

[0038] [Figure 3F] is a statistical distribution diagram of the on-state current density and effective mobility of a confined double-layer WSe2FET array (different triangles represent the location of the double-layer WSe2 film on the wafer).

[0039] FIG4A shows a photograph and schematic diagram of HfO2 deposited on a Si wafer in a pocket with a lateral size of 1 μm (scale bar: 5 μm).

[0040] [Figure 4B] shows the nucleation of single-domain MoS2 in a 1μm HfO2 pocket with SiO2 sidewalls.

[0041] [FIG. 4C] Shows an array of confined single-domain MoS2 in 1 μm HfO2 pockets with SiO2 sidewalls.

[0042] [Figure 4D] is a graph showing the transfer characteristics of 16 FETs fabricated using confined monolayer MoS2 (8 FETs, lower trace) or confined bilayer MoS2 (8 FETs, upper trace) on a HfO2 substrate.

[0043] [Figure 4E] is a histogram of the average and maximum values ​​of the on-state current density I on (left) and the effective mobility μ eff (right) of single-layer MoS 2 and double-layer MoS 2 FETs.

[0044] FIG4F is a cross-sectional high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of the heterointerface [MoS2 (upper layer) and WSe2 (lower layer)] covered with energy-dispersive X-ray (EDX) spectra of Mo Kα (upper left peak), S Kα (upper right peak), W Lα (lower left peak), and Se Kα (lower right peak).

[0045] [Figure 4G] Time-resolved circular dichroism (CD) plots of the responses of monolayer WSe2 at 300K (lower trace) and heterobilayer (MoS2 / WSe2) at 300K (middle trace) and 77K (upper trace).

[0046] [Figure 5] A graph showing the relationship between the lateral growth rate and the second nucleation time of confined growth.

[0047] [Figures 6A to 6E] illustrate the comparison of the formation of the WSe2 second layer with increasing H2 content. Implementation Method

[0048] FIG1A shows a conventional method for growing transition metal dichalcogenides (TMDs). Initially, a first group of TMD adsorbates is deposited.

[12] Introduced in the substrate

[10] (left) TMD adsorbed atoms on the surface.

[12] On the substrate

[10] Nucleation

[14] . These cores

[14] is randomly oriented, because the core

[14] Usually no

[10] Alignment. When the core

[14] When the lateral growths touch each other (in the middle), they merge to form particles

[16] , resulting in nuclear

[14] have continuous polycrystalline layers with random orientation. This polycrystalline growth will eventually degrade the intrinsic properties of TMD. In addition, in some particles

[16] (right) Additional nucleation may occur

[18] Repeating this process without controlling additional nucleation results in

[16] overlap and in the particles

[16] The initial layer of nuclei has a second group of nuclei

[18] and grew a TMD layer with irregular thickness.

[0049] Figure 1B illustrates a confined growth method that addresses these issues by precisely controlling the thickness and crystallization of TMD growth. First, c-plane Al2O3, HfO2, or another material with relatively low Gibbs free energy, such as an amorphous or crystalline metal oxide, is deposited on a Si wafer to form the substrate on which the TMDs will grow.

[0100] Other suitable substrate materials include graphene, hexagonal boron nitride (hBN), hafnium zirconium oxide (HZO), TiO2, ZnO, Fe2O3, SnO2, NiO, CuO, or TMD-coated materials.

[0050] Then, the mask material

[0110] A thin layer (e.g. 5 nm, 10 nm, 50 nm, 100 nm, or even hundreds of nanometers thick; possibly up to 250 nm, 500 nm, 750 nm, or 1 µm thick) is applied to the substrate.

[0100] on a c-plane Al2O3 or HfO2 surface. Suitable mask materials include materials with relatively high Gibbs free energy, such as amorphous SiO2 (a-SiO2), a-Si, a-SiNx, and a-carbon.

[0051] Next, the restricted growth region

[0102] , also known as recess, pocket, trench, well, or cavity, each with lateral dimensions ranging from tens of nanometers to a maximum of about 2 microns, in a thin layer of a-SiO2

[0110] Patterned. Patterned a-SiO 2 layer

[0110] Also called a mask or mask layer. These pockets

[0102] The pockets may be of any suitable shape (e.g., square, rectangular, triangular, or circular) and may be formed in a 1D or 2D array (e.g., a square, rectangular, or hexagonal array).

[0102] Extending all the way through the a-SiO2 layer

[0110] , to expose the sidewall of a-SiO2

[0112] Surrounding substrate

[0100] A portion of the Al 2 O 3 or HfO 3 surface. Pocket

[0102] It can even partially extend into the c-plane Al2O3 or HfO3 (for example, a few nanometers) (Figure 1B, left).

[0052] Once in the a-SiO2 layer Forming a pocket

[0102] , the 2D material adsorbs atoms

[0120] Introduced into each pocket (left). For example, note that within a 1nm x 1nm area, there are 42 adatoms (W and Se). Therefore, within a 2µm x 2µm trench, a monolayer requires 84,000 adatoms, and a bilayer requires 168,000 adatoms for each pocket. Suitable 2D materials include semiconducting TMDs such as WSe2 (in this example), MoS2, MoSe2, and WS2. Other suitable 2D materials include, but are not limited to, graphene, carbon nanotubes (CNTs), hBN, metallic TMDs (e.g., VS2, VSe2, CoS2, CoSe2, TiS2, TiSe2), and high-k 2D materials (e.g., Bi2SeO5, Sb2O3).

[0053] Each bag The size is small enough that only a single nucleation occurs in each pocket (in the middle)

[0122] (Represented by a single triangle in Figure 1B). In its pocket

[0102] grows on the exposed c-plane Al2O3 or HfO2 at the bottom until it reaches the a-SiO2 sidewall

[0112] and fill the entire groove To form a TMD film

[0124] (Right). Individual TMD films

[0124] is a single domain and also a single layer (right, inset).

[0054] FIG1C shows how the steps of adatom introduction, nucleation, and single crystal growth in the method of FIG1B can be repeated to obtain a single-domain MoS2 / WSe2 heterostructure or a single-domain homogeneous bilayer (BL) of WSe2. (A bilayer can be viewed as two monolayers combined by van der Waals interactions.) Once the WSe2 monolayer In the bag

[0102] is formed, then MoS2 adsorption atoms

[0130] Introduced into WSe2 monolayer

[0124] The hole on

[0102] (Fig. 1C, left). These MoS2 adsorbed atoms

[0130] After nucleation to form a core

[0132] (middle), and in WSe 2 monolayer

[0124] Growth (right) to form a single crystal MoS2 monolayer

[0134] (right illustration), resulting in

[0102] There is a MoS2 / WSe2 heterostructure

[0140] DFT calculations confirm this growth selectivity. Alternatively, WSe2 adatoms can be deposited on a WSe2 monolayer and nucleate and grow to form a single-domain bilayer of WSe2.

[0055] Figure 1D shows the DFT-calculated binding of the WSe precursor WO3 and Se, as well as the resulting WSe2 clusters, on c-Al2O3, a-HfO2, and a-SiO2. These DFT calculations reveal that the WO3 clusters (W3O9, left), Se clusters (Se2, center), and WSe2 clusters (W3Se6, right) have stronger binding interactions with c-Al2O3 and a-HfO2 than with the SiO2 surface. This suggests that the clusters preferentially bind to the substrate surface at the bottom of the pockets, rather than to the a-SiO2 sidewalls of the pockets, leading to selective WSe2 growth within the pockets.

[0056] This selectivity was demonstrated by the simultaneous growth of WSe2 on Al2O3, HfO2, and SiO2 substrates under the same CVD growth conditions. Atomic force microscopy (AFM) images showed that during the 20-minute growth period, WSe2 nucleated only on Al2O3 and HfO2, but not on SiO2. This resulted in the successful selective confined growth of WSe2 on the exposed substrate surface of the micropatterned SiO2 trench array.

[0057] The trench size is chosen to allow only a single domain of WSe2 to form a monolayer, and the trench size is determined by both the lateral growth rate of WSe2 and the incubation period for the second nucleation. The measured lateral growth rate and incubation period for the second nucleation of WSe2 were approximately 0.4 μm / minute and 5 minutes, respectively. This means that each trench should be no wider than approximately 2 μm to prevent nucleation of a second layer of WSe2. By varying the TMD powder content, the gas ratio (Ar / H2), and the growth temperature, the lateral growth rate or incubation period (and therefore the maximum trench width) can be controlled. For example, this control can be achieved by varying the S / Se powder content between 100 mg and 1500 mg, or the MoO3 / WO3 powder content between 10 mg and 100 mg. Furthermore, the gas ratio of argon (Ar) to hydrogen (H2) can be adjusted between Ar-100% / H2-0% and Ar-0% / H2-100%. At the same time, the growth temperature can be adjusted between 200℃ and 1000℃.

[0058] Figure 5 depicts a graph showing the relationship between the lateral growth rate of confined growth and the second nucleation time. In this non-limiting example, after an initial incubation time of 5 minutes, WSe2 grew laterally for up to 10 minutes, and a second nucleation occurred after maintaining the confined monolayer (ML) for an additional 2 minutes (i.e., a second incubation time of 2 minutes starting from the 10-minute time point).

[0059] Figures 6A to 6E compare the formation of the second layer of WSe2 as the H2 content increases. Scanning electron micrographs of the second layer of WSe2 are shown before (see Figure 6A) and after (see Figure 6B) a 15% increase in the H2 content. Figure 6C depicts an optical micrograph of the AA' stacking structure in Figure 6B. The addition of H2 saturates the nucleation density on the first WSe2 monolayer, allowing the second layer of WSe2 to begin nucleating in the middle of the first monolayer. Therefore, after the layer-by-layer confined growth of WSe2 monolayers at different H2 contents, the SEM morphology of the confined monolayer is compared with that of the bilayer (BL) (see Figures 6A and 6B). When compared to polycrystalline WSe2, the surface of the confined WSe2 is extremely smooth, and the contrast between the confined monolayer (see Figure 6(d)) and the confined bilayer (see Figure 6(e)) is similar.

[0060] In one embodiment, the present invention provides a method comprising the steps of: (a) providing a substrate of a first material; (b) depositing a mask material on the substrate; (c) forming a trench array on the mask material, the trench array comprising a plurality of trenches, each trench having a trench geometry with lateral dimensions l, x, and w, wherein each of l and w is selected to have a maximum dimension of 2 μm, and each trench having an exposed portion of the substrate surrounded by sidewalls formed of the mask material; (d) depositing adatoms of a second material on the exposed portion of the substrate, wherein a first binding energy between the first material and the second material is greater than a second binding energy between the mask material and the second material; (e) allowing the adatoms to selectively nucleate as nuclei within each trench in the trench array; and (f) growing the nuclei within each trench in the trench array; and wherein the lateral dimensions associated with the trench geometry constrain the nuclei to grow into a single domain monolayer of the second material.

[0061] In one embodiment, the first material includes one of hafnium oxide (HfO 2 ), aluminum oxide (Al 2 O 3 ), hafnium zirconium oxide (HZO), titanium dioxide (TiO 2 ), zinc oxide (ZnO), iron oxide (Fe 2 O 3 ), tin oxide (SnO 2 ), nickel oxide (NiO), or copper oxide (CuO). In one embodiment, the second material includes one of graphene, carbon nanotubes (CNTs), hexagonal boron nitride (h-BN), metallic transition metal dichalcogenides (e.g., vanadium disulfide (VS2), vanadium diselenide (VSe2), cobalt disulfide (CoS2), cobalt diselenide (CoSe2), titanium disulfide (TiS2), or titanium diselenide (TiSe2)), semiconducting transition metal dichalcogenides (e.g., molybdenum disulfide (MoS2), molybdenum diselenide (MoSe2), tungsten disulfide (WS2), or tungsten diselenide (WSe2)), or high-k materials (e.g., Bi2SeO5 or Sb2O3). In one embodiment, the mask material includes at least one of amorphous silicon dioxide (a-SiO 2 ), amorphous silicon (a-Si), amorphous silicon nitride (a-SiN x ), amorphous carbon (a-carbon), hafnium oxide (HfO 2 ), aluminum oxide (Al 2 O 3 ), hafnium zirconium oxide (HfZrO), titanium dioxide (TiO 2 ), zinc oxide (ZnO), iron oxide (Fe 2 O 3 ), tin oxide (SnO 2 ), nickel oxide (NiO), or copper oxide (CuO).

[0062] In an extended embodiment, wherein the nucleus is a first nucleus and the single-domain monolayer is a first single-domain monolayer, the method further comprises the steps of: (g) waiting for an incubation period; (h) depositing another adatom of a third material on top of the first single-domain monolayer in at least one trench in the trench array, wherein a third binding energy between the second material and the third material is greater than a second binding energy between the mask material and the third material; (i) allowing the another adatom of the third material to selectively nucleate as a second nucleus on top of the first single-domain monolayer in at least one trench in the array of trenches; and (j) growing the nucleus in at least one trench in the trench array; and wherein lateral dimensions associated with the trench geometry constrain the growth of the second nucleus into a second single-domain monolayer of the third material, and wherein the first single-domain monolayer and the second single-domain monolayer form a bilayer.

[0063] In one embodiment, the third material includes one of graphene, carbon nanotubes (CNTs), hexagonal boron nitride (h-BN), metallic transition metal dichalcogenides (e.g., vanadium disulfide (VS2), vanadium diselenide (VSe2), cobalt disulfide (CoS2), cobalt diselenide (CoSe2), titanium disulfide (TiS2), or titanium diselenide (TiSe2)), semiconducting transition metal dichalcogenides (e.g., molybdenum disulfide (MoS2), molybdenum diselenide (MoSe2), tungsten disulfide (WS2), or tungsten diselenide (WSe2)), or a high-k material.

[0064] In one embodiment, the bilayer is a heterojunction bilayer, wherein the second material and the third material are different from each other. In another embodiment, the bilayer is a homojunction bilayer, wherein the second material and the third material are similar to each other.

[0065] In one embodiment, l and w are each selected to have a value equal to the product of the incubation time of another nucleus of the second material on the single-domain monolayer and the growth rate of the second material. For example, when the measured lateral growth rate and second nucleation incubation time of WSe are approximately 0.4 μm / minute and 5 minutes, respectively, l and w are each selected to have a value equal to 5 minutes multiplied by 0.4 μm / minute, which is 2 μm. In this embodiment, l and w are selected to be 2 microns.

[0066] In another embodiment, the method further comprises the step of forming a semiconductor device (a valleytronic device, a forked-chip field effect transistor (FET), or a complementary field effect transistor) comprising the single-domain monolayer.

[0067] In one embodiment, before depositing the mask material on the substrate, the method includes the step of depositing at least one of hafnium oxide (HfO 2 ), aluminum oxide (Al 2 O 3 ), hafnium zirconium oxide (HZO), titanium dioxide (TiO 2 ), zinc oxide (ZnO), iron oxide (Fe 2 O 3 ), tin oxide (SnO 2 ), nickel oxide (NiO), or copper oxide (CuO) on silicon to form a substrate.

[0068] In another embodiment, the present invention provides a method comprising the steps of: (a) providing a substrate of a first material, the first material having a first Gibbs free energy; (b) depositing a mask material on the substrate, the mask material having a second Gibbs free energy, the second Gibbs free energy being higher than the first Gibbs free energy; (c) forming a groove array on the mask material, the groove array comprising a plurality of grooves, each groove having lateral dimensions of l, x, w trench geometry, wherein each of l and w is selected to have a maximum dimension of 2 μm, and each trench has an exposed portion of the substrate surrounded by sidewalls formed by a mask; (d) depositing adatoms of a second material on the exposed portion of the substrate; (e) allowing the adatoms to selectively nucleate into nuclei within each trench in the trench array; (f) growing nuclei within each trench in the trench array; and wherein lateral dimensions associated with the trench geometry constrain the growth of the first nuclei into single-domain monolayers of the second material; (g) waiting for an incubation period; (h) depositing another adatom of a third material on top of the first single-domain monolayer in at least one trench in the trench array; (i) allowing another adatom of the third material to selectively nucleate into second nuclei on top of the first single-domain monolayer in at least one trench in the trench array; and (j) growing the nuclei within at least one trench in the trench array; and wherein lateral dimensions associated with the trench geometry constrain the growth of the second nuclei into second single-domain monolayers of the third material, and wherein the first single-domain monolayer and the second single-domain monolayer form a bilayer.

[0069] In one embodiment, the first material includes one of hafnium oxide (HfO 2 ), aluminum oxide (Al 2 O 3 ), hafnium zirconium oxide (HZO), titanium dioxide (TiO 2 ), zinc oxide (ZnO), iron oxide (Fe 2 O 3 ), tin oxide (SnO 2 ), nickel oxide (NiO), or copper oxide (CuO).

[0070] In one embodiment, the second material or the third material includes one of graphene, carbon nanotubes (CNTs), hexagonal boron nitride (h-BN), metallic transition metal dichalcogenides (e.g., vanadium disulfide (VS2), vanadium diselenide (VSe2), cobalt disulfide (CoS2), cobalt diselenide (CoSe2), titanium disulfide (TiS2), or titanium diselenide (TiSe2)), semiconducting transition metal dichalcogenides (e.g., molybdenum disulfide (MoS2), molybdenum diselenide (MoSe2), tungsten disulfide (WS2), or tungsten diselenide (WSe2)), or high-k materials (e.g., Bi2SeO5 or Sb2O3).

[0071] In one embodiment, the mask material includes at least one of amorphous silicon dioxide (a-SiO 2 ), amorphous silicon (a-Si), amorphous silicon nitride (a-SiN x ), amorphous carbon (a-C), hafnium oxide (HfO 2 ), aluminum oxide (Al 2 O 3 ), hafnium zirconium oxide (HfZrO), titanium dioxide (TiO 2 ), zinc oxide (ZnO), iron oxide (Fe 2 O 3 ), tin oxide (SnO 2 ), nickel oxide (NiO), or copper oxide (CuO).

[0072] All combinations of the aforementioned and additional concepts described in more detail below (provided such concepts are not mutually inconsistent) are part of the subject matter disclosed herein. In particular, all combinations of patented subject matter appearing at the end of this disclosure are part of the subject matter disclosed herein. Terms used herein, and which may also appear in any references, should be given a meaning most consistent with the specific concepts disclosed herein.

[0073] Figures 2A to 2D show images of WSe2 grown in arrays of confined areas (trench) of varying widths using the method of Figure 1B for varying durations. Figures 2A and 2B show WSe2 grown in 10μm-wide trenches for 20 minutes and 30 minutes, respectively. Figures 2C and 2D show WSe2 grown in 2μm-wide trenches for 7 minutes and 10 minutes, respectively.

[0074] As shown in Figure 2A, WSe2 growth in a 10μm-wide trench for 20 minutes (considerably longer than the five-minute second nucleation incubation time) resulted in some trenches with multiple nuclei. While approximately 70% of the trenches in Figure 2A contained only a single WSe2 triangle, other trenches contained multiple nuclei. Increasing the growth time by 30 minutes resulted in the formation of multi-domain polycrystalline WSe2, as shown in Figure 2B. A substantial reduction in photoluminescence (PL) intensity was observed in the multi-domain regions compared to the single-domain regions. Twenty-five percent of the trenches with multiple nuclei contained more than two nuclei at the edges, while the remaining trenches had nuclei in the center. However, as shown in Figures 2C and 2D, reducing the trench width to 2μm resulted in only a single nucleus per trench, regardless of whether the nucleation occurred homogeneously at the center or heterogeneously at the edges.

[0075] Without being bound by any particular theory, confined growth effectively suppresses additional heterogeneous nucleation in the trenches by reducing the size of the possible nucleation region. As shown in Figures 2C and 2D, further growth of the nuclei produces single-crystalline monolayers that fill the entire corresponding trench. Because each confined WSe2 monolayer originates from a single nucleus, each WSe2 monolayer in the trench array is single-crystalline throughout the wafer. During the growth of the second nucleus on top of the first WSe2 layer, approximately 97% of the 2μm-wide trenches were completely filled with WSe2.

[0076] Figures 2E and 2F show, respectively, Raman images at the E 1 2g peak and photoluminescence (PL) images at 1.65 eV of WSe 2 grown in 2 μm-wide trenches. The height of each trench can range from 5 to 100 nm. These measurements confirm that the WSe 2 grown in these trenches is indeed a monolayer WSe 2. At room temperature, the full width at half maximum (FWHM) of the PL spectrum of the monodomain WSe 2 in the trenches was measured to be approximately 55 meV on average, which is similar to that of high-quality monodomain WSe 2 flakes mechanically separated from bulk WSe 2.

[0077] Measurements show that a second WSe2 layer can be grown on these single-monolayer WSe2 arrays to form a uniform, homogeneous bilayer with superior electrical properties to a monolayer. As shown in Figure 1B, each pocket in each trench is allowed to fill with only a single domain. Further increasing the growth time results in the formation of a single-domain bilayer WSe2 that completely fills the trench. In each trench, regardless of the nucleation mode, only a single additional WSe2 nucleus is present; in other words, approximately 60% of the secondary nuclei are heterogeneous nucleations derived from the SiO2 mask sidewalls. This is further confirmed by a Raman spectral shift from the A1g peak (approximately 259.6 cm-1) of the confined monolayer to the B12g peak (approximately 308.5 cm-1) of the confined bilayer. Furthermore, a shift in the PL spectral peak from 1.65 eV to 1.6 eV confirms the shift from a direct to an indirect band gap.

[0078] Figures 2G and 2H show Raman imaging of the B12g peak and PL imaging at 1.6 eV, respectively, confirming the presence of uniform wafer-level bilayer 2D material in the trenches across the entire wafer. Figures 2I and 2J show high-resolution transmission electron microscopy (HRTEM) images of a 0.8 nm thick single-layer WSe2 and a 1.6 nm thick bilayer WSe2, respectively. Scanning tunneling electron microscopy (STEM) images confirm that the bilayer WSe2 grows unrestricted at the center or edge of the SiO2 trench. Furthermore, planar HAADF-STEM analysis reveals that the bilayer WSe2 is epitaxially aligned in an AA' stack.

[0079] Confined growth of single-domain TMD homo- or hetero-bilayers at precisely defined locations on a wafer makes TMDs feasible for use as CMOS channel materials. Figure 3A shows a bi-layer WSe2 field-effect transistor (FET) array grown on a 2-inch wafer using the confined growth method illustrated in Figures 1B and 1C. The wafer in Figure 3A is a sapphire wafer with back-gated devices fabricated using metal-induced transfer. Other substrates, including Si wafers with suitable masking materials, and other top gating solutions can also be used.

[0080] Figure 3B shows representative drain-source current-gate-source voltage (I ds - V gs) characteristics measured from one of the bilayer WSe 2FET arrays. At V ds = -1 V, the FET exhibits an on / off current ratio greater than 10 8 , a subthreshold swing (SS) of 240.5 mV / dec, a maximum on-state current density ( I on ) of up to 155.8 μA μm − 1 , and a field-effect mobility (μ eff = gm L ⁄ WC g V ds , C g = 11.6 nF cm − 2 ) of up to 103.5 cm − 2 V − 1 s − 1 . Figure 3C shows a maximum saturation current of 465 μA μm − 1 .

[0081] Figure 3D shows the turn-on current / effective mobility characteristics of the WSe 2FET array in Figure 3A compared to WSe 2FET arrays fabricated using other methods. The electrical properties of the FETs fabricated using confined-growth monolayer / bilayer WSe 2 are comparable to the best reported properties for single-crystal WSe 2-based FETs and are similar to (or better than) the electrical properties of the exfoliated wafer-based monolayer / bilayer WSe 2FETs shown in Figure 3E.

[0082] Figure 3F shows a statistical analysis of the on-current Ion and effective mobility μeff per unit width of the FET array. Both Ion and μeff per unit width of the FETs have a Gaussian distribution; the mean and variance of Ion density are 89.9 μA μm-1 and 17.3%, respectively, and the mean and variance of μeff are 79.1 cm-2 V-1 s-1 and 24.1%, respectively. The 213 FETs fabricated using confined bilayer WSe2 had an estimated yield of 93.9%. Furthermore, FETs fabricated using confined single-layer WSe2 exhibited comparable electrical performance to those fabricated using confined bilayer WSe2. FETs fabricated using confined bilayer WSe2 exhibited comparable performance to wafer-based FETs uniformly distributed across the entire array.

[0083] The confined growth technique of the present invention can also be used to fabricate logic memory. Figure 4A shows a single-crystalline TMD (here, MoS) fabricated on a 10nm amorphous HfO layer deposited on a Si wafer, using a SiO mask to define a trench approximately 1µm wide. DFT calculations confirm that the TMD's binding on HfO is higher than on SiO. However, the difference between the binding on sapphire and SiO is greater than the difference between the binding on HfO and SiO. This may result in a shorter incubation time between the first and second nucleations when the TMD is grown in a SiO mask on the HfO surface. This shortened incubation time can be alleviated by reducing the trench size to 1µm and adjusting the carrier gas and growth conditions to further increase the selectivity between HfO and SiO.

[0084] As shown in Figures 4B and 4C, only a single nucleation event occurred within each 1μm trench. Further growth successfully filled the trench, yielding single-crystalline monolayer MoS2 within a confined region on the amorphous HfO2 surface. Layer-by-layer growth is also possible. FETs were fabricated using confined monolayer / bilayer MoS2 on HfO2 substrates to verify the electrical properties of confined monolayer / bilayer MoS2. Figure 4D shows the transfer characteristics (Ids-Vds) measured from these fabricated monolayer / bilayer MoS2 FETs. The FETs achieved maximum I on densities of up to 86.7 μA μm −1 (single-layer MoS 2) and 129.3 μA μm −1 (bilayer MoS 2), with μ eff of up to 62.2 cm 2 V −1 s −1 (single-layer MoS 2) and 88.61 cm 2 V −1 s −1 (bilayer MoS 2) ( FIG. 4E ), with C g_HfO 2 of 600 nF cm −2 and V ds of 1 V. These MoS 2 FETs exhibit electrical properties similar to those of single-crystal MoS 2-based FETs fabricated using other technologies.

[0085] Heterobilayer TMD semiconductors can be fabricated using the continuous confined growth of single-domain monolayers. For example, a single MoS2 layer can be grown on an array of single-domain WSe2 layers. A single MoS2 nucleus can be confined within a fully covered WSe2-filled trench and grow to form a single-domain MoS2 / WSe2 heterobilayer. Raman imaging and PL spectroscopy confirm the uniform formation of the MoS2 / WSe2 heterobilayer. Furthermore, the cross-sectional HAADF-STEM image in Figure 4F shows a sharp van der Waals (vdW) heterointerface between the confined MoS2 monolayer and the WSe2 monolayer, without any alloy formation. A uniform heterointerface without secondary nucleation can be observed in the low-magnification HAADF-STEM image.

[0086] Figure 4 illustrates the valley electron efficiency of MoS2 / WSe2 heterobilayer arrays. Specifically, Figure 4G shows the valley-polarized carrier dynamics of confined WSe2 monolayers and heterobilayers (MoS2 / WSe2) arrays, characterized by ultrafast circular dichroism (CD) based on time-resolved pump-probe spectroscopy. In confined WSe2 monolayers, valley lifetimes (e.g., on the order of tens of picoseconds) are observed due to rapid valley depolarization due to altered interactions, whereas in confined heterobilayers, longer valley lifetimes (e.g., on the order of hundreds of picoseconds) are observed at 300K due to ultrafast charge separation. Furthermore, an increase in valley lifetime (on the order of nanoseconds) is confirmed by a reduction in phonon scattering at 77K.

[0087] Confined growth techniques can be used to synthesize wafer-scale single-domain 2D TMD arrays. These confined growth techniques exploit key Gibbs free energy differences to achieve layer-by-layer synthesis, enabling the fabrication of homobilayer (WSe2 / WSe2) and heterobilayer (MoS2 / WSe2) array structures. Furthermore, arrays of confined-growth bilayer WSe2 transistor devices exhibit wafer-scale performance comparable to devices fabricated from exfoliated WSe2. Thus, confined growth techniques address the difficulty of controlling the dynamics of 2D materials at the wafer scale, a major hurdle in 2D TMDs, and can be applied to large-scale single-crystal vdW integration, providing a new approach to constructing electronic platforms based on 2D materials.

[0088] [Simulation, fabrication, and measurement results] [] []

[0089] DFT calculations of the selectively confined growth of TMDs were performed using the Vienna Ab initio Simulation Package (VASP), employing projector augmented wave (PAW) pseudopotentials and a plane-wave basis set. The generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) function was used to describe the electron-change related interactions. The valence electron configurations of W, Se, O, Al, and Si are 6s 25d 4, 4s 24p 4, 2s 22p 4, 3s 23p 1, and 3s 23p 2, respectively. The energy cutoff for the plane-wave expansion was set at 420 eV. When performing DFT calculations on large lattices (lattice constant >10 Å), the Brillouin zone is sampled using a k-point grid with only Γ-points. Surface bonding interactions are studied by placing WO3, Se, and WSe2 clusters atop a-HfO2, Al2O3 (0001), and a-SiO2 slabs, respectively. The HfO2, SiO2, and Al2O3 surfaces are passivated with H atoms to simulate an Ar / H2 growth environment. The atomic structures of amorphous HfO2 and SiO2 are obtained using a melt-quenching method with ab-initio molecular dynamics simulations of the crystal structures. The structures are optimized by relaxing the top adatoms using fixed substrate atoms. The structural relaxation criterion is that the forces acting on the atoms are less than 0.01 eV / Å. When the system energy difference between two consecutive repetitions is less than 10-5 eV, electronic minimization occurs. The surface binding of adsorbent A on substrate B is calculated as Eb = EA / BE AE B, where EA / B, EA, and EB are the energies of the adsorption system A / B, the separated adsorbent A, and substrate B, respectively.

[0090] Confined Pattern Fabrication. For confined TMD growth, LOR 3A and photoresist (PR, S1805) were coated on a sapphire substrate and patterned using an AS200 i-ray stepper (AutoStep 200). An approximately 25 nm thick a-SiO2 layer was deposited on the PR-patterned sapphire substrate using an e-beam evaporator. To create sapphire pockets (trench) in the sapphire, the SiO2 pattern was stripped using a PG stripper (Kayaku Advanced Materials) and rinsed in acetone and isopropyl alcohol for 15 minutes each.

[0091] Synthesis of WSe2 and MoS2. Confined TMDs were synthesized in a quartz tube with a 4-inch diameter. 300 mg of Se or S powder was placed in (Region I) and 30 mg of WO3 or MoO3 powder was placed in (Region II), with the distance between regions fixed at 33 cm. A SiO2-patterned sapphire substrate was vertically placed 6 cm behind the WO3 or MoO3 powder, and the front and back surfaces of the substrate were covered with quartz plates to reduce or minimize direct reaction.

[0092] Prior to synthesizing confined WSe2 monolayers, a vacuum pump was used to remove air from the quartz tube. After closing the vacuum valve, the tube was filled with a carrier gas ratio of Ar (50 sccm) / H2 (50 sccm), and the atmospheric valve was then opened. The Ar / H2 ratio was maintained. The growth temperatures of (Region I) and (Region II) were heated at ramp rates of 15°C min⁻¹ and 30°C min⁻¹, respectively. Region I was maintained at 450°C and Region II at 890°C for 10 minutes, followed by natural cooling to room temperature.

[0093] For confined bilayer WSe2, the second layer of WSe2 was synthesized using a carrier gas ratio of Ar (35 sccm) / H2 (65 sccm). For confined heterostructures (MoS2 / WSe2), MoS2 synthesis was performed at 200°C (Zone I) and 750°C (Zone II), with ramp rates of 8°C min⁻¹ and 30°C min⁻¹, respectively. Specifically, to improve growth selectivity on HfO2 substrates, the SiO2 trench size was reduced to 1 μm, and the overall Ar / H2 flow rate was increased from 100 sccm (Ar (50 sccm) / H2 (50 sccm)) to 200 sccm (Ar (100 sccm) / H2 (100 sccm)). All reactions were performed at atmospheric pressure, and the TMDs exhibited a purity exceeding 99.99%.

[0094] Characterization of confined TMDs. Raman and PL spectra were measured using a Renishaw InVia Reflex microspectrometer with a 532 nm pump laser. Light was dispersed using a 2,400-groove mm-1 holographic grating. For Raman and PL mapping, the sample was scanned using laser illumination on an xy piezo stage. SEM images were measured using a high-resolution scanning electron microscope (ZEISS Merlin) with an in-lens detector. The working distance was 6 mm at an accelerating voltage of 2 kV and a probe current of 70 pA. TEM characterization was performed using a transmission electron microscope (JEOL JEM-2100F) at an accelerating voltage of 200 kV and a STEM (Titan Themis Z G3 Cs-Corrected) at an accelerating voltage of 60 kV. EDX line profiles were obtained using Velox software in STEM mode using the characteristic Mo Kα, S Kα, W Lα, and Se Kα X-ray signals. XPS spectra were measured using a magnesium Kα source (MultiLab 2000, Thermo VG), and the peak energy was corrected by the C 1s peak at 284.8 eV. AFM morphology analysis was performed using an XE 100 (Park Systems Corp.).

[0095] Device Fabrication and Electrical Measurement Results. For device fabrication using confined single-layer / double-layer WSe2, a 600nm-thick gold film was deposited on confined WSe2 / sapphire using e-beam evaporation. The Au / WSe2 stack was exfoliated using thermal release tape as a handle layer and transferred to a 300nm-thick SiO2 / heavily p-doped silicon wafer. The thermal release tape was removed on a 120°C hotplate, followed by an oxygen plasma treatment to remove any remaining tape from the Au film. The Au film was then etched using a gold etchant and rinsed with deionized water. (To compare electrical properties, a few-layer WSe2 flake was also transferred in the same manner.)

[0096] After transferring confined monolayer / bilayer WSe onto a SiO substrate, alignment marks for electron beam lithography (EBL) were patterned on the SiO substrate using optical lithography. Ti (2.5 nm thick) and Au (7.5 nm thick) were then deposited using an electron beam evaporator. EBL was then used to pattern 2 μm-wide drain and source contact regions. Polymethyl methacrylate (PMMA) A4 and PMMA A6 were spin-coated at 3000 rpm for the EBL photoresist and baked at 180°C for 150 seconds. After developing the PMMA, 10 nm-thick Pt and 80 nm-thick Au layers were deposited using an electron beam evaporator. Finally, lift-off was used to remove all areas except the source / drain contact metal. The same process, from patterning the alignment marks for EBL to developing the PMMA, was followed for device fabrication using confined monolayer / bilayer MoS on HfO. Then, a 10 nm thick Ni layer and an 80 nm thick Au layer were deposited using an electron beam evaporator, followed by lift-off.

[0097] Current-voltage characteristics were measured using an Agilent B2900A source / measure unit. All measurements were performed in air at room temperature. Furthermore, a 2-inch confined bilayer WSe2 was transferred onto a 300 nm thick SiO2 / Si substrate measuring 5.1 x 5.1 cm2. Kelvin probe force microscopy (KPFM) confirmed a highly uniform work function (5.08 eV) across the confined bilayer WSe2. Platinum was then used to integrate the source and drain electrodes with a 0.7 μm channel length (LCH). A hole barrier height of 0.31 eV was estimated using a modified Richardson plot.

[0098] Time-resolved pump-probe spectroscopy. Ultrafast CD (CD) measurements were performed using time-resolved pump-probe spectroscopy to investigate valley-polarized carrier dynamics. A 100 kHz Yb-based regenerative amplification system (Photoconversion PHAROS) provided femtosecond laser pulses, and a sequential optical parametric amplifier (ORPHEUS) generated wavelength-tunable pump and probe pulses that resonated with the WSe2 A exciton resonance with a pulse duration of 50 fs and a spectral bandwidth of 50 meV. The sample on the cryostat was illuminated by the pump pulses with a 40x objective. The pump-induced changes in the probe reflectivity were recorded as a function of the time delay introduced by a mechanical translation stage and a lock-in amplifier. The polarization profiles of the pump and probe pulses were controlled by half-wavelength plates and quarter-wavelength plates, respectively. The pump and probe pulses were measured to produce signals with the same circular polarization helicity (co-polarization) and opposite circular polarization helicities (cross-polarization). Valley-dependent ultrafast CD responses, as shown in FIG. 4F and FIG. 4G , are obtained by the difference between the co-polarization pump-probe response and the cross-polarization pump-probe response. in conclusion

[0099] Although various inventive embodiments have been described and illustrated herein, those skilled in the art will readily envision various other methods and / or structures for performing the functions and / or obtaining the results and / or one or more advantages described herein, and each such variation and / or configuration is considered within the scope of the inventive embodiments described herein. More generally, those skilled in the art will readily recognize that all parameters, dimensions, materials, and configurations described herein are intended to be exemplary, and that actual parameters, dimensions, materials, and / or configurations will depend on the specific application or applications in which the teachings of the present invention are used. Those skilled in the art will recognize or be able to ascertain many equivalents to the specific inventive embodiments described herein without more than routine experimentation. Therefore, it should be understood that the foregoing embodiments are presented by way of example only, and that, within the scope of the appended claims and their equivalents, the inventive embodiments may be practiced otherwise than as specifically described and protected. The inventive embodiments disclosed herein are directed to each individual feature, system, article, material, kit, and / or method described herein. In addition, any combination of two or more of the features, systems, articles, materials, kits and / or methods is within the scope of the present invention if they are not mutually inconsistent.

[0100] Similarly, various inventive concepts can be embodied as methods provided in one or more examples. The actions performed as part of a method can be performed in any order suitable for the method. Thus, embodiments can be constructed in an order that performs actions differently from that described, and may include performing some actions simultaneously, even though actions are shown as sequential in the illustrated embodiments.

[0101] All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and / or ordinary meanings of the defined terms.

[0102] Unless expressly stated to the contrary, the indefinite articles "a" and "an" as used herein in the specification and claims should be understood to mean "at least one."

[0103] It should be understood that the phrase "and / or" as used herein means that the elements so combined are "either or both," i.e., elements that are combined in some cases and not combined in other cases. Multiple elements listed with "and / or" should be interpreted in the same manner, i.e., the elements so combined are "one or more." Whether related or unrelated to the elements specifically identified by the phrase "and / or," other elements may optionally be present in addition to these elements. Thus, as a non-limiting example, reference to "A and / or B," when used in conjunction with an open-ended term such as "comprising," can mean that in one embodiment, only A (optionally including elements other than B); in another embodiment, only B (optionally including elements other than A); in yet another embodiment, both A and B (optionally including other elements); and so on.

[0104] It should be understood that the term "or" used in this specification and claims has the same meaning as the term "and / or" as described above. For example, when there are separate items in a list, "or" or "and / or" should be interpreted as inclusive, meaning including at least one of the plurality of elements or listed elements, but may also include more than one and, if necessary, additional unlisted items. Only terms that clearly indicate the contrary, such as "only one of" or "exactly one of," or when used in the claims, "consisting of," will refer to the inclusion of exactly one of the plurality of elements or listed elements. Generally, when preceded by an exclusive term, such as "either," "one of," "only one of," or "exactly one of," the term "or" as used herein should only be read to indicate an exclusive option (i.e., "one or the other but not both"). When used in a patent claim, the phrase "consisting essentially of" should have its ordinary meaning as used in patent law.

[0105] As used herein and in the claims, in reference to a list of one or more elements, the phrase "at least one" should be understood to mean at least one element selected from any one or more elements in the list of elements, but does not necessarily include at least one of each or every element specifically listed in the list of elements, and does not exclude any combination of elements in the list of elements. The phrase "at least one" is defined to also allow for the presence of additional elements, whether or not related to the elements specifically identified in the list of elements. Thus, as a non-limiting example, “at least one of A and B” (or equivalent to “at least one of A or B” or equivalent to “at least one of A and / or B”) may, in one embodiment, mean at least one A, and optionally more than one A, with no B present (and optionally including elements other than B); in another embodiment, mean at least one B, and optionally more than one B, with no A present (and optionally including elements other than A); in yet another embodiment, mean at least one A, and optionally more than one A, and at least one B, and optionally more than one B (and optionally including other elements); and so on.

[0106] In the foregoing claims and the specification, all transitional terms such as "comprising," "including," "carrying," "having," "containing," "involving," "holding," "composed of," and similar terms should be understood to be open-ended, meaning, but not limited to, including. As provided in Section 2111.03 of the U.S. Patent Office Manual of Patent Examining Procedures, only the transitional terms "consisting of" and "consisting essentially of" are considered closed or semi-open transitional terms, respectively.

[0107] 10: Base material 12: TMD Adsorption Atoms 14: Nuclear 16: Particles 18: Nuclear 100: base material 102: Restricted growth area / pocket / groove / hole 110:a-SiO 2 layers 112: a-SiO 2 sidewall 120:2D material adsorption atoms 122: Nuclear 124:TMD film / single layer 130:MoS2 adsorbate 132: Nuclear 134: Single crystal MoS2 monolayer 140:MoS2 / WSe2 heterostructure

Claims

1. A method for confined growth of a 2D material on a substrate, comprising the steps of: (a) providing a substrate of a first material; (b) depositing a masking material on the substrate; (c) forming a trench array on the masking material, the trench array comprising a plurality of trenches, each trench having a trench geometry with a lateral dimension of l × w, wherein l and w are each selected to have a maximum dimension of 2 µm, and each trench having an exposed portion of the substrate surrounded by sidewalls formed of the masking material; (d) depositing adatoms of a second material on the exposed portion of the substrate, wherein a first binding energy between the first material and the second material is greater than a second binding energy between the masking material and the second material; (e) allowing the adatoms to selectively nucleate within each trench in the trench array; and (f) growing the nuclei within each trench in the trench array; The lateral dimension associated with the trench geometry restricts the growth of the nucleus into a single domain monolayer of the second material, and each of l and w is selected to have a value equal to the product of the cultivation time of another nucleus of the second material on the single domain monolayer and the growth rate of the second material.

2. The method of claim 1, wherein the first material comprises one of hafnium oxide (HfO2), aluminum oxide (Al2O3), hafnium zirconium oxide (HZO), titanium dioxide (TiO2), zinc oxide (ZnO), iron oxide (Fe2O3), tin oxide (SnO2), nickel oxide (NiO), or copper oxide (CuO).

3. The method of claim 1, wherein the second material comprises one of graphene, carbon nanotubes (CNTs), hexagonal boron nitride (h-BN), metallic transition metal dichalcogenides, semiconducting transition metal dichalcogenides, or high-k materials.

4. The method of claim 3, wherein the metallic transition metal dichalcogenide is one of vanadium disulfide (VS2), vanadium diselenide (VSe2), cobalt disulfide (CoS2), cobalt diselenide (CoSe2), titanium disulfide (TiS2), or titanium diselenide (TiSe2).

5. The method of claim 3, wherein the semiconducting transition metal dichalcogenide is one of molybdenum disulfide (MoS2), molybdenum diselenide (MoSe2), tungsten disulfide (WS2), or tungsten diselenide (WSe2).

6. The method of claim 3, wherein the high-k material is either Bi2SeO5 or Sb2O3.

7. The method of claim 1, wherein the masking material comprises at least one of amorphous silicon dioxide (a-SiO2), amorphous silicon (a-Si), amorphous silicon nitride (a-SiNx), amorphous carbon (a-carbon), hafnium oxide (HfO2), aluminum oxide (Al2O3), hafnium zirconium oxide (HfZrO), titanium dioxide (TiO2), zinc oxide (ZnO), iron oxide (Fe2O3), tin oxide (SnO2), nickel oxide (NiO), or copper oxide (CuO).

8. The method of claim 1, wherein the core is a first core and the monolayer is a first monolayer, the method further comprising the steps of: (g) during a waiting period for cultivation; (h) depositing another adsorbed atom of a third material on top of the first monolayer in at least one trench in the trench array, wherein a third binding energy between the second material and the third material is greater than a second binding energy between the masking material and the third material; (i) allowing the other adsorbed atom of the third material to selectively nucleate as a second core on top of the first monolayer in at least one trench in the array trenches; and (j) growing the core in the at least one trench in the trench array; wherein the lateral dimension associated with the trench geometry restricts the growth of the second core into a second monolayer of the third material, wherein the first monolayer and the second monolayer form a bilayer.

9. The method of claim 8, wherein the third material comprises one of graphene, carbon nanotubes (CNTs), hexagonal boron nitride (h-BN), metallic transition metal dichalcogenides, semiconducting transition metal dichalcogenides, or high-k materials.

10. The method of claim 9, wherein the metallic transition metal dichalcogenide is one of vanadium disulfide (VS2), vanadium diselenide (VSe2), cobalt disulfide (CoS2), cobalt diselenide (CoSe2), titanium disulfide (TiS2), or titanium diselenide (TiSe2).

11. The method of claim 9, wherein the semiconducting transition metal dichalcogenide is one of molybdenum disulfide (MoS2), molybdenum diselenide (MoSe2), tungsten disulfide (WS2), or tungsten diselenide (WSe2).

12. The method of claim 8, wherein the double layer is a heterogeneous interface double layer, wherein the second material and the third material are different from each other.

13. The method of claim 8, wherein the double layer is a homogeneous interface double layer, wherein the second material and the third material are similar to each other.

14. The method of claim 1, wherein forming the trench comprises etching through the masking material and partially into the substrate.

15. The method of request item 1, wherein each of l and w is selected as 2 micrometers.

16. The method of claim 1, further comprising: forming a semiconductor device comprising the single domain single layer.

17. The method of claim 16, wherein the semiconductor device comprises one of a valleytronics device, a fork-type field-effect transistor (FET), or a complementary FET.

18. The method of claim 1, further comprising, before depositing the masking material on the substrate, depositing at least one of hafnium oxide (HfO2), aluminum oxide (Al2O3), hafnium zirconium oxide (HZO), titanium dioxide (TiO2), zinc oxide (ZnO), iron oxide (Fe2O3), tin oxide (SnO2), nickel oxide (NiO), or copper oxide (CuO) on silicon to form the substrate.

19. A method for confined growth of a 2D material on a substrate, comprising the steps of: (a) providing a substrate of a first material having a first Gibbs free energy; (b) depositing a masking material on the substrate having a second Gibbs free energy higher than the first Gibbs free energy; (c) forming an array of trenches on the masking material, the array comprising a plurality of trenches, each trench having a trench geometry with a lateral dimension of l × w, wherein l and w are each selected to have a maximum dimension of 2 µm, and each trench having an exposed portion of the substrate surrounded by sidewalls formed of the masking material; (d) depositing adsorbed atoms of a second material on the exposed portion of the substrate; and (e) allowing the adsorbed atoms to selectively nucleate into first nuclei within each trench in the array of trenches. (f) Growing the first nucleus within each trench in the trench array, wherein the lateral dimension associated with the trench geometry restricts the growth of the first nucleus into a first monolayer of the second material; (g) During the incubation period; (h) Depositing another adsorbed atom of the third material on top of the first monolayer of the third material in at least one trench in the trench array; (i) Allowing the other adsorbed atom of the third material to selectively nucleate into a second nucleus on top of the first monolayer of the third material within at least one trench in the array trenches; and (j) Growing the nucleus within the at least one trench in the trench array; wherein the lateral dimension associated with the trench geometry restricts the growth of the second nucleus into a second monolayer of the third material, wherein the first monolayer and the second monolayer form a bilayer, and wherein each of l and w is selected to have a value equal to the product of the incubation time of the other nucleus of the second material on the monolayer and the growth rate of the second material.

20. The method of claim 19, wherein the first material comprises one of hafnium oxide (HfO2), aluminum oxide (Al2O3), hafnium zirconium oxide (HZO), titanium dioxide (TiO2), zinc oxide (ZnO), iron oxide (Fe2O3), tin oxide (SnO2), nickel oxide (NiO) or copper oxide (CuO).

21. The method of claim 19, wherein the second material or the third material comprises one of graphene, carbon nanotubes (CNTs), hexagonal boron nitride (h-BN), metallic transition metal dichalcogenides, semiconducting transition metal dichalcogenides, or high-k materials.

22. The method of claim 21, wherein the metallic transition metal dichalcogenide is one of vanadium disulfide (VS2), vanadium diselenide (VSe2), cobalt disulfide (CoS2), cobalt diselenide (CoSe2), titanium disulfide (TiS2), or titanium diselenide (TiSe2).

23. The method of claim 21, wherein the semiconducting transition metal dichalcogenide is one of molybdenum disulfide (MoS2), molybdenum diselenide (MoSe2), tungsten disulfide (WS2), or tungsten diselenide (WSe2).

24. The method of claim 21, wherein the high-k material is one of Bi2SeO5 or Sb2O3.

25. The method of claim 19, wherein the masking material comprises at least one of amorphous silicon dioxide (a-SiO2), amorphous silicon (a-Si), amorphous silicon nitride (a-SiNx), amorphous carbon (a-carbon), hafnium oxide (HfO2), aluminum oxide (Al2O3), hafnium zirconium oxide (HfZrO), titanium dioxide (TiO2), zinc oxide (ZnO), iron oxide (Fe2O3), tin oxide (SnO2), nickel oxide (NiO), or copper oxide (CuO).

26. The method of claim 19, wherein the double layer is a heterogeneous interface double layer, wherein the second material and the third material are different from each other.

27. The method of claim 19, wherein the double layer is a homogeneous interface double layer, wherein the second material and the third material are similar to each other.

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