Epitaxial growth of crystalline materials using confined directional growth and related articles and systems

Abstract

Epitaxial growth of crystalline materials using confined directional growth and related articles and systems are generally described.

Description

[0001] EPITAXIAL GROWTH OF CRYSTALLINE MATERIALS USING CONFINED

[0002] DIRECTIONAL GROWTH AND RELATED ARTICLES AND SYSTEMS

[0003] RELATED APPLICATIONS

[0004] This application claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application No. 63 / 559,063, filed February 28, 2024, and entitled “Epitaxial Growth of Crystalline Materials Using Confined Directional Growth and Related Articles and Systems,” which is incorporated herein by reference in its entirety for all purposes.

[0005] TECHNICAL FIELD

[0006] Epitaxial growth of crystalline materials using confined directional growth and related articles and systems are generally described.

[0007] SUMMARY

[0008] Epitaxial growth of crystalline materials using confined directional growth and related articles and systems are generally described. The subject matter of the present disclosure involves, in some cases, interrelated products, alternative solutions to a particular problem, and / or a plurality of different uses of one or more systems and / or articles.

[0009] According to certain embodiments, a method of forming a single-crystalline material is described. In some embodiments, the method comprises: growing multiple regions of the singlecrystalline material, each region associated with a confined well that is part of an array of confined wells, wherein each confined well has a top-view shape comprising one or more edges that seed growth of the single-crystalline material such that the crystallographic orientation of each of the regions of the single-crystalline material are substantially crystallographically aligned; and laterally growing each of the substantially crystallographically aligned regions of the single-crystalline material such that each of the substantially crystallographically aligned regions of the single-crystalline material coalesce to form a single domain of the singlecrystalline material.

[0010] In some embodiments, a method of forming a three-dimensional (3-D) single-crystalline material is described. According to certain embodiments, the method comprises growing multiple regions of the three-dimensional single-crystalline material, each region associated with a confined well that is part of an array of confined wells, wherein each confined well has a topview shape comprising one or more edges that seed growth of the three-dimensional single- crystalline material such that the crystallographic orientation of each of the regions of the three- dimensional single-crystalline material are substantially crystallographically aligned.

[0011] Other advantages and novel features of the present disclosure will become apparent from the following detailed description of various non-limiting embodiments of the disclosure when considered in conjunction with the accompanying figures. In cases where the present specification and a document incorporated by reference include conflicting and / or inconsistent disclosure, the present specification shall control.

[0012] BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Non-limiting embodiments of the present disclosure will be described by way of example with reference to the accompanying figures, which are schematic and are not intended to be drawn to scale unless otherwise indicated. In the figures, each identical or nearly identical component illustrated is typically represented by a single numeral. For purposes of clarity, not every component is labeled in every figure, nor is every component of each embodiment of the disclosure shown where illustration is not necessary to allow those of ordinary skill in the art to understand the disclosure. In the figures:

[0014] FIG. 1A is a top-view schematic illustration of an array of confined wells within a mask material on a substrate, according to certain embodiments.

[0015] FIG. IB is a cross-sectional schematic illustration of the array of confined wells within a mask material on a substrate shown in FIG. 1A, according to certain embodiments.

[0016] FIG. 1C is a top-view schematic illustration of an array of confined wells within a mask material on a substrate after growth of some crystalline material within each well, according to certain embodiments.

[0017] FIG. ID is a top-view schematic illustration of an array of confined wells within a mask material on a substrate after growth of some crystalline material seeded by multiple internal angles of each well, according to certain embodiments.

[0018] FIG. IE is a top-view schematic illustration of an array of confined wells within a mask material on a substrate after growth of additional crystalline material within each well, according to certain embodiments.

[0019] FIG. IF is a top-view schematic illustration of an array of crystalline materials on a substrate after optional removal of the mask from the substrate, according to certain embodiments. FIG. 1G is a top-view schematic illustration of a single domain of crystalline material after the crystalline materials within the confined wells of FIGS. 1A-1F have been merged, according to certain embodiments.

[0020] FIG. 1H is a cross-sectional schematic illustration of a single domain of crystalline material after the crystalline materials within the confined wells of FIG. IE have been merged, according to certain embodiments.

[0021] FIG. II is a cross-sectional schematic illustration of a single domain of crystalline material after the crystalline materials within the confined wells of FIG. IF have been merged, according to certain embodiments.

[0022] FIG. 1 J is another cross-sectional schematic illustration of a single domain of crystalline material after the crystalline materials within the confined wells of FIG. IF have been merged, according to certain embodiments.

[0023] FIG. 2A is a top-view schematic illustration of an array of confined wells within a mask material on a substrate, in which the wells contain 2-D crystalline material, according to certain embodiments.

[0024] FIG. 2B is a cross-sectional schematic illustration of the array of confined wells within a mask material on a substrate shown in FIG. 2A, according to certain embodiments.

[0025] FIG. 2C is a top-view schematic illustration of an array of confined wells within a mask material on a substrate after growth of some 3-D crystalline material over the 2-D material within each well, according to certain embodiments.

[0026] FIG. 2D is a top-view schematic illustration of an array of confined wells within a mask material on a substrate after growth of some 3-D crystalline material seeded by multiple internal angles of each well, according to certain embodiments.

[0027] FIG. 2E is a top-view schematic illustration of an array of confined wells within a mask material on a substrate after growth of additional 3-D crystalline material over the 2-D material within each well, according to certain embodiments.

[0028] FIG. 2F is a top-view schematic illustration of an array of 3-D crystalline materials on a substrate after optional removal of the mask from the substrate, according to certain embodiments.

[0029] FIG. 2G is a top-view schematic illustration of a single domain of 3-D crystalline material after the 3-D crystalline materials within the confined wells of FIGS. 2A-2F have been merged, according to certain embodiments. FIG. 2H is a cross-sectional schematic illustration of a single domain of 3-D crystalline material after the 3-D crystalline materials within the confined wells of FIG. 2E have been merged, according to certain embodiments.

[0030] FIG. 21 is a cross-sectional schematic illustration of a single domain of 3-D crystalline material after the 3-D crystalline materials within the confined wells of FIG. 2F have been merged, according to certain embodiments.

[0031] FIG. 2J is another cross-sectional schematic illustration of a single domain of 3-D crystalline material after the 3-D crystalline materials within the confined wells of FIG. 2F have been merged, according to certain embodiments.

[0032] FIG. 2K is a cross-sectional schematic illustration of a single domain of 3-D crystalline material grown over a single domain of 2-D crystalline material, according to certain embodiments.

[0033] FIG. 3 is a schematic diagram showing defect-free epitaxy on amorphous substrates, according to certain embodiments.

[0034] FIG. 4 is a schematic diagram showing materials and methods associated with confined 2-D single-crystalline material growth, according to certain embodiments.

[0035] FIG. 5 is a schematic diagram showing materials and methods associated with defect-free epitaxy, according to certain embodiments.

[0036] FIG. 6 is a schematic diagram showing monolithic integration of device layers, according to certain embodiments.

[0037] FIG. 7 is a schematic diagram showing confined 2-D single-crystalline transition-metal dichalcogenide (TMD) growth on an amorphous substrate, according to certain embodiments.

[0038] FIG. 8 is a schematic diagram showing 3-D single-crystalline growth on an amorphous substrate, according to certain embodiments.

[0039] FIG. 9A is a top-view schematic illustration of multiple regions of an epitaxial layer, each region associated with a region of a single-crystalline material that is part of an array of single-crystalline materials on a substrate, according to certain embodiments.

[0040] FIG. 9B is a top-view schematic illustration of a single domain of an epitaxial layer associated with a single domain of a single-crystalline material on a substrate, according to certain embodiments.

[0041] FIG. 9C is a cross-sectional schematic illustration of a single domain of an epitaxial layer associated with a single domain of a single-crystalline material on a mask material and a substrate, according to certain embodiments. FIG. 9D is a cross-sectional schematic illustration of a single domain of an epitaxial layer associated with a single domain of a single-crystalline material on a substrate, according to certain embodiments.

[0042] FIG. 9E is another cross-sectional schematic illustration of a single domain of an epitaxial layer associated with a single domain of a single-crystalline material on a substrate, according to certain embodiments.

[0043] FIGS. 10A-10D are top- view schematic diagrams of examples of confined wells comprising a droplet top- view shape, each droplet top-view shape having an edge angle of 10- 120°, according to certain embodiments.

[0044] FIG. 11 is a cross-sectional schematic diagram of an interface between a mask material and a substrate.

[0045] DETAILED DESCRIPTION

[0046] Epitaxial growth of crystalline materials using confined directional growth and related articles and systems are generally described. In some embodiments, for example, a method of forming a single-crystalline material (e.g., a two-dimensional single-crystalline material, a three- dimensional single-crystalline material) on an amorphous substrate is described. In certain embodiments, multiple regions of the single-crystalline material are grown, each region of the single-crystalline material associated with a confined well that is part of an array of confined wells (e.g., in a mask material associated with the amorphous substrate).

[0047] In some embodiments, each confined well has a top-view shape comprising one or more edges that seed growth of the single-crystalline material. For example, in certain embodiments, each confined well has a top-view shape comprising one or more edges, wherein an interface between the mask material and the amorphous substrate at the one or more edges seeds growth of the single-crystalline material. According to some embodiments, for example, by using an amorphous substrate that has a comparatively higher binding energy than the mask material with respect to an adatom of the single-crystalline material, the adatom of the single-crystalline material may selectively nucleate at the interface between the mask material and the amorphous substrate at the one or more edges of the confined well in the mask material, thereby seeding growth of the single-crystalline material. In some embodiments, each confined well has a topview shape comprising one or more edges that form one or more internal angles that seed growth of the single-crystalline material. For example, in certain embodiments, each confined well has a top-view shape comprising one or more edges that form one or more internal angles, wherein an interface between the mask material and the amorphous substrate at the one or more internal angles seeds growth of the single-crystalline material. According to certain embodiments, with respect to an adatom of the single-crystalline material, the interface between the mask material and the amorphous substrate at the one or more internal angles of a confined well in the mask material has a comparatively higher binding energy than other areas of the mask material and / or the amorphous substrate, resulting in the adatom of the single-crystalline material selectively nucleating at the interface between the mask material and the amorphous substrate at the one or more internal angles of the confined well, thereby seeding growth of the single-crystalline material. In certain embodiments, by seeding growth of the single-crystalline material from an interface between the mask material and the amorphous substrate at one or more edges of each confined well and / or at one or more internal angles of each confined well, the crystallographic orientations of each region of the single-crystalline material are advantageously substantially crystallographically aligned, resulting in controlled growth of an array of single-crystalline materials on the amorphous substrate. In addition, according to some embodiments, the one or more internal angles of each confined well advantageously results in the seeds of the singlecrystalline material having a particular alignment. In accordance with some embodiments, when the internal angles within the confined wells are aligned, the production of multiple domains of single-crystalline materials having substantially aligned crystal domains can be achieved.

[0048] According to some embodiments, each of the substantially crystallographically aligned regions of the single-crystalline material may be laterally grown such that each of the substantially crystallographically aligned regions of the single-crystalline material coalesce (e.g., merge) to form a single domain of the single-crystalline material (e.g., a single domain of a two- dimensional single-crystalline material, a single domain of a three-dimensional single-crystalline material). In certain embodiments, the single domain of the single-crystalline material is advantageously defect-free. For example, in some embodiments, the single domain of the single-crystalline material comprises an advantageously low number of edge dislocations, screw dislocations, threading dislocations, and / or anti-phase boundaries (APBs), as described herein in greater detail.

[0049] As used herein, two single-crystalline domains are said to be “substantially crystallographically aligned” when common crystallographic directions between the two domains are aligned to within 5° of parallel. In some embodiments, two domains that are substantially crystallographically aligned have common crystallographic directions between the two domains that are aligned to within 3° of parallel, within 2° of parallel, within 1° of parallel, within 0.5° of parallel, within 0.2° of parallel, within 0.1° of parallel, within 0.01° of parallel, or within 0.001° of parallel. In certain embodiments, a method of forming a three-dimensional single-crystalline material on an amorphous substrate is described. In some embodiments, for example, multiple regions of a substantially crystallographically aligned two-dimensional single-crystalline material are grown, each region of the substantially crystallographically aligned two- dimensional single-crystalline material associated with a confined well that is part of an array of confined wells in a mask material associated with the amorphous substrate. In certain embodiments, multiple regions of the three-dimensional single-crystalline material are grown, each region of the three-dimensional single-crystalline material associated with a region of the substantially crystallographically aligned two-dimensional single-crystalline material such that each region of the substantially crystallographically aligned two-dimensional single-crystalline material seeds growth of the three-dimensional single-crystalline material, resulting in controlled growth of an array of substantially crystallographically aligned three-dimensional singlecrystalline materials. According to some embodiments, each region of the substantially crystallographically aligned three-dimensional single-crystalline may be laterally grown such that each of the substantially crystallographically aligned regions of the three-dimensional single-crystalline material coalesce (e.g., merge) to form a single domain the three-dimensional single-crystalline material. In certain embodiments, the single domain of the three-dimensional single-crystalline material is advantageously defect-free. For example, in some embodiments, the single domain of the three-dimensional single-crystalline material comprises an advantageously low number of edge dislocations, screw dislocations, threading dislocations, and / or anti-phase boundaries (APBs), as described herein in greater detail.

[0050] According to some embodiments, a method of forming a single-crystalline material is described. In certain embodiments, the single-crystalline material is or comprises a two- dimensional (2-D) material (e.g., a 2-D single-crystalline material). In some embodiments, the single-crystalline material is or comprises a three-dimensional (3-D) material (e.g., a 3-D singlecrystalline material). Various examples of suitable single-crystalline materials are described herein in greater detail.

[0051] As used herein, a “2-D material” (e.g., a 2-D single-crystalline material) refers to a material layer having a thickness of one molecule. In certain embodiments, for example, the 2- D material is an atomically thin material (e.g., a single monolayer of a molecule). According to some embodiments, the 2-D material has a dominant sp2orbital hybridization, e.g., the 2-D material is a material layer having a thickness of one molecule with a dominant sp2orbital hybridization. As used herein, a “3-D material” (e.g., a 3-D single-crystalline material) refers to a material layer having a thickness greater than one molecule. The 3-D material may have any of a variety of suitable thicknesses. According to certain embodiments, for example, the 3-D material has a thickness greater than or equal to 1 nanometer, greater than or equal to 5 nanometers, greater than or equal to 10 nanometers, greater than or equal to 50 nanometers, greater than or equal to 100 nanometers, greater than or equal to 500 nanometers, greater than or equal to 1 micrometer, greater than or equal to 5 micrometers, greater than or equal to 10 micrometers, greater than or equal to 50 micrometers, or greater than or equal to 100 micrometers. In certain embodiments, the 3-D material has a thickness less than or equal to 500 micrometers, less than or equal to 100 micrometers, less than or equal to 50 micrometers, less than or equal to 10 micrometers, less than or equal to 5 micrometers, less than or equal to 1 micrometer, less than or equal to 500 nanometers, less than or equal to 100 nanometers, less than or equal to 50 nanometers, less than or equal to 10 nanometers, or less than or equal to 5 nanometers. Combinations of the above recited ranges are possible (e.g., the 3-D material has a thickness greater than or equal to 1 nanometer and less than or equal to 500 micrometers). Other ranges are also possible.

[0052] In some embodiments, the method comprises providing an array of confined wells within a mask material on a substrate. FIG. 1A is a top-view schematic illustration of array of confined wells 102 (e.g., confined wells 102a-102d) within mask material 104 on a substrate (hidden from view in FIG. 1A by mask material 104), according to certain embodiments. FIG. IB is a cross- sectional schematic illustration of array of confined wells 102 (e.g., confined wells 102a- 102b) within mask material 104 on substrate 106 shown in FIG. 1A, according to certain embodiments.

[0053] Although the figures show that the array of confined wells comprises 4 confined wells, the array of confined wells may comprise any of a variety of suitable number of confined wells. In certain embodiments, for example, the array of confined wells comprises greater than or equal to 2 confined wells, greater than or equal to 4 confined wells, greater than or equal to 10 confined wells, greater than or equal to 50 confined wells, greater than or equal to 100 confined wells, greater than or equal to 500 confined wells, greater than or equal to 1,000 confined wells, or more.

[0054] In certain embodiments, the top- view shape of each confined well depends on the singlecrystalline material to be grown within the confined well. In some embodiments, for example, the top-view shape of each confined well is configured to substantially align with a crystal structure of the single-crystalline material to be grown within the confined well. As used herein, an angle in a shape of a comer of a well is said to be “substantially aligned” with an angle in a crystal structure of a crystalline domain when the angles are within 5° of each other. In some embodiments, an angle in a shape of a corner of a well and an angle in a crystal structure of a crystalline domain associated with the well are within 3° of each other, within 2° of each other, within 1° of each other, within 0.5° of each other, within 0.2° of each other, within 0.1° of each other, within 0.01° of each other, or within 0.001° of each other.

[0055] Each confined well of the array may have any of a variety of suitable top- view shapes. In some embodiments, for example, as shown in FIG. 1A, each confined well 102a- 102d comprises a triangular top-view shape. In certain embodiments, each confined well comprises a substantially equilateral triangular top-view shape, for example, having three edges with a substantially equal length and having three internal angles (e.g., internal angles 120a-120c in FIG. 1A) that are substantially equiangular (e.g., having three internal angles that are 60°, having three internal angles that are within + / - 5° of 60°). In some embodiments, each confined well comprises an obtuse triangular top-view shape, for example, having an internal angle that is greater than 90° and two internal angles that are less than 90°. In certain embodiments, each confined well comprises an acute triangular top-view shape, for example, having three internal angles that are less than 90°. According to some non-limiting embodiments, a confined well having a triangular top-view shape may advantageously be used to seed growth of a transition metal dichalcogenide single-crystalline material, as described herein in greater detail.

[0056] According to certain embodiments, although not shown in the figures, each confined well comprises a rectangular (e.g., square) top-view shape (e.g., having four internal angles that are 90°, having four internal angles that are within + / - 5° of 90°), a hexagonal top-view shape (e.g., having six internal angles totaling 720°), and / or a droplet top-view shape (e.g., having an edge angle of 10-120°). Other top-view shapes for the confined wells are also possible.

[0057] FIGS. 10A-10D show top- view schematic diagrams of examples of confined wells comprising a droplet top- view shape, each droplet top-view shape having an edge angle of 10- 120°, according to certain embodiments. As used herein, the term “edge angle” refers to an angle between two adjoining edges of a top-view shape. FIG. 10A shows a top-view schematic diagram of a confined well comprising a droplet top-view shape having edge angle 122a greater than or equal to 10° and less than or equal to 60°. FIG. 10B shows a top-view schematic diagram of a confined well comprising a droplet top-view shape having edge angle 122b greater than or equal to 30° and less than or equal to 90°. FIG. 10C shows a top-view schematic diagram of a confined well comprising a droplet top-view shape having edge angle 122c greater than or equal to 60° and less than or equal to 120°. FIG. 10D shows a top-view schematic diagram of a confined well comprising a droplet top-view shape having edge angle 122d greater than or equal to 90° and less than or equal to 120°.

[0058] According to some embodiments, the array of confined wells within the mask material on the substrate are configured such that a single-crystalline material growth surface is a surface of the substrate. Referring, for example, to FIG. IB, array of confined wells 102 (e.g., confined wells 102a- 102b) within mask material 104 on substrate 106 may be configured such that a single-crystalline material growth surface is surface 105 of substrate 106.

[0059] According to some embodiments, the mask material and the substrate are formed of different materials. In certain embodiments, for example, the confined wells are part of a mask associated with the substrate. Referring to FIGS. 1A-1B, for example, mask material 104 and substrate 106 are formed of different materials such that the confined wells (e.g., confined wells 102a- 102d) are part of mask material 104 associated with substrate 106. It may be advantageous, in certain embodiments, to use a mask material and a substrate that are formed from different materials. In some embodiments, for example, using a substrate material that has a comparatively higher binding energy than the mask material with respect to an adatom of the single-crystalline material may seed growth of the single-crystalline material from one or more edges of the confined well in the mask material (e.g., from an interface between the mask material and the substrate at the one or more edges of the confined well) and / or from one or more internal angles of the confined well in the mask material (e.g., from an interface between the mask material and the substrate at the one or more internal angles of the confined well), as explained herein in greater detail.

[0060] As used herein, “binding energy” is given its ordinary meaning in the field of physics and chemistry and refers to the smallest amount of energy required to remove an adatom from another material. To illustrate, the binding energy of a substrate with respect to an adatom would be the smallest amount of energy needed to remove the adatom from the substrate. As another example, the binding energy of a mask material with respect to an adatom would be the smallest amount of energy needed to remove the adatom from the mask material.

[0061] In some embodiments, the mask material and the substrate are formed of the same material. For example, referring to FIGS. 1A-1B, mask material 104 and substrate 106 are formed of the same material.

[0062] The mask material may have any of a variety of suitable top-view shapes. In some embodiments, for example, as shown in FIGS. 1A-1B, mask material 104 comprises a rectangular (e.g., square) top-view shape. According to some embodiments, although not shown in the figures, the mask material comprises a triangular top-view shape (e.g., an equilateral triangular top-view shape, an acute triangular top-view shape, an obtuse triangular top-view shape), a hexagonal top-view shape, a circular top-view shape, or an oval top-view shape. Other top-view shapes for the mask material are also possible.

[0063] The mask material may comprise any of a variety of suitable materials. In some embodiments, for example, the mask material comprises silicon dioxide (SiO2). In certain embodiments, the mask material comprises amorphous SiO2. According to some embodiments, the mask material comprises a metal oxide. For example, in some embodiments, the mask material comprises aluminum oxide (AI2O3) (e.g., amorphous AI2O3), hafnium zirconium oxide (HfZrO or HZO), TiCh, ZnO, Fe2O3, SnCh, NiO, and / or CuO. In certain embodiments, the mask material comprises silicon (Si). For example, in some embodiments, the mask material comprises amorphous Si, silicon nitride (SiNx), and / or SiOxNy. In some embodiments, the mask material comprises carbon (e.g., amorphous carbon). Combinations of the above recited mask materials are possible. Other materials for the mask material are also possible.

[0064] The substrate may have any of a variety of suitable top-view shapes. In some embodiments, for example, as shown in FIGS. 1A-1B, the substrate (hidden from view in FIG.1A by mask material 104) comprises a rectangular (e.g., square) top-view shape. According to some embodiments, although not shown in the figures, the substrate comprises a triangular top-view shape (e.g., an equilateral triangular top-view shape, an acute triangular top-view shape, an obtuse triangular top-view shape), a hexagonal top-view shape, a circular top-view shape, or an oval top-view shape. Other top-view shapes for the substrate are also possible.

[0065] The substrate may comprise any of a variety of suitable materials. In some embodiments, the substrate is an amorphous substrate. In certain embodiments, the substrate comprises a semiconducting material, an insulating material, and / or a metallic material. In certain embodiments, for example, the substrate comprises glass (e.g., SiO2), diamond, Si(100), a metal oxide, SiNx, and / or combinations thereof. Suitable metal oxides may include, but are not limited to, hafnium(IV) oxide (HfO2), AI2O3, HZO, BaHfo.6Tio.4O3 (BHTO), and / or combinations thereof. Other materials for the substrate, including other semiconducting materials, insulating materials, and / or metallic materials, are also possible.

[0066] In some embodiments, the method comprises growing multiple regions of the singlecrystalline material. FIG. 1C is a top-view schematic illustration of array of confined wells 102 (e.g., confined wells 102-102d) within mask material 104 on a substrate (hidden from view in FIG. 1C by mask material 104) after growth of some crystalline material 108 within each well, according to certain embodiments. According to some embodiments, each region of the singlecrystalline material is associated with a confined well that is part of the array of confined wells. Referring, for example, to FIG. 1C, each region of single-crystalline material 108 is associated with a confined well (e.g., confined wells 102a- 102d) that is part of array of confined wells 102.

[0067] In certain embodiments, the multiple regions of the single-crystalline material are grown over the substrate. Referring, for example, to FIG. 1C, each region of single-crystalline material 108 associated with a confined well (e.g., confined wells 102a-102d) is grown over the substrate (hidden from view in FIG. 1C by mask material 104). In certain embodiments, the multiple regions of the single-crystalline material are grown directly over the substrate.

[0068] In certain embodiments, each confined well has a top-view shape comprising one or more edges that seed growth of the single-crystalline material. For example, in certain embodiments, each confined well has a top-view shape comprising one or more edges, wherein an interface between the mask material and the substrate at the one or more edges seeds growth of the single-crystalline material. Referring, for example, to FIG. 1C, each confined well (e.g., confined wells 102a- 102d) has a top-view shape (e.g., as described herein in greater detail) comprising one or more edges (e.g., edges 132a and / or 132b) that seed growth of singlecrystalline material 108. In certain embodiments, each confined well (e.g., confined wells 102a- 102d) has a top-view shape (e.g., as described herein in greater detail) comprising one or more edges (e.g., edges 132a and / or 132b), wherein the interface between mask material 104 and the substrate (hidden from view in FIG. 1C by mask material 104) at the one or more edges (e.g., edges 132a and / or 132b) seeds growth of single-crystalline material 108. In some embodiments, the mask material and the substrate are formed of different materials, and the substrate has a comparatively higher binding energy than the mask material with respect to an adatom of the single-crystalline material. In certain embodiments, an interface between the mask material and the substrate at one or more edges of the confined well within the mask material has a comparatively higher binding energy than the mask material and / or the substrate material with respect to an adatom of the single-crystalline material, which advantageously seeds growth of the single-crystalline material from the interface between the mask material and the substrate at the one or more edges of the confined well in the mask material. According to some embodiments, by seeding growth of the single-crystalline material from the interface between the mask material and the substrate at the one or more edges of each confined well, the crystallographic orientations of each region of the single-crystalline material are advantageously substantially crystallographically aligned. For example, referring to FIG. 1C, the crystallographic orientations of each region of single-crystalline material 108 are substantially crystallographically aligned. In certain embodiments, each confined well has a top-view shape comprising one or more edges that form one or more internal angles that seed growth of the single-crystalline material. For example, in some embodiments, each confined well has a top-view shape comprising one or more edges that form one or more internal angles, wherein an interface between the mask material and the substrate at the one or more internal angles seeds growth of the single-crystalline material. Referring, for example, to FIG. 1C, each confined well (e.g., confined wells 102a- 102d) has a top-view shape (e.g., as described herein in greater detail) comprising one or more edges (e.g., edges 132a and / or 132b) that form one or more internal angles (e.g., internal angle 120a shown in FIG.1A) that seed growth of single-crystalline material 108. In some embodiments, each confined well (e.g., confined wells 102a- 102d) has a top-view shape (e.g., as described herein in greater detail) comprising one or more edges (e.g., edges 132a and / or 132b) that form one or more internal angles (e.g., internal angle 120a shown in FIG.1A), wherein an interface between mask material 104 and the substrate (hidden from view in FIG. 1C by mask material 104) at the one or more internal angles (e.g., internal angle 120a shown in FIG.1A) seeds growth of single-crystalline material 108. In certain embodiments, with respect to an adatom of the single-crystalline material, an interface between the mask material and the substrate at the one or more internal angles of a confined well has a comparatively higher binding energy than other areas of the mask material and / or the substrate material, which advantageously seeds growth of the single-crystalline material from the interface between the mask material and the substrate at the one or more internal angles of the confined well. According to some embodiments, by seeding growth of the single-crystalline material from the interface between the mask material and the substrate at one or more internal angles of one or more edges of each confined well, the crystallographic orientations of each region of the single-crystalline material are advantageously substantially crystallographically aligned. For example, referring to FIG. 1C, the crystallographic orientations of each region of singlecrystalline material 108 are substantially crystallographically aligned. In some embodiments, by seeding growth of the single-crystalline material from the interface between the mask material and the substrate at one or more internal angles of one or more edges of each confined well, the production of multiple domains of single-crystalline material (e.g., an array of single-crystalline materials) having substantially aligned crystal domains can advantageously be achieved.

[0069] FIG. 11 shows a cross-sectional schematic diagram of interface 130 between mask material 104 and substrate 106 taken along line 11 in FIG. 1C. In some embodiments, the interface (e.g., interface 130) corresponds to a point in a confined well (e.g., confined well 102a) where the mask material (e.g., mask material 104) and the substrate (e.g., substrate 106) interconnect. As described herein in greater detail, interface 130 between mask material 104 and substrate 106 at one or more edges of confined well 102a and / or at one or more internal angles of confined well 102a may, in certain embodiments, advantageously seed growth of singlecrystalline material 108.

[0070] In certain embodiments, each confined well has a top-view shape comprising multiple internal angles that seed growth of the single-crystalline material. For example, in certain embodiments, each confined well has a top-view shape comprising multiple internal angles, wherein the interfaces between the mask material and the substrate at the multiple internal angles seed growth of the single-crystalline material. According to certain embodiments, for example, each confined well has a top-view shape (e.g., as described herein in greater detail) comprising at least two internal angles, at least three internal angles, at least four internal angles, etc., that seed growth of the single-crystalline material. In some embodiments, each confined well has a top-view shape (e.g., as described herein in greater detail) comprising at least two internal angles, at least three internal angles, at least four internal angles, etc., wherein the interfaces between the mask material and the substrate at the internal angles seed growth of the single-crystalline material. FIG. ID is a top-view schematic illustration of an array of confined wells 102 (e.g., confined wells 102a-102d) within mask material 104 on a substrate (hidden from view in FIG. ID by mask material 104) after growth of some crystalline material 108 (e.g., crystalline material 108a- 108c) seeded by multiple internal angles of each well, according to certain embodiments. In some embodiments, growth of crystalline material 108 (e.g., crystalline material 108a- 108c) is seeded by multiple interfaces between mask material 104 and the substrate (hidden from view in FIG. ID by mask material 104) at multiple internal angles of each well. In some embodiments, as shown in FIG. ID, each of confined wells 102a- 102d comprise at least two internal angles (e.g., three internal angles) that seed growth of singlecrystalline material 108a- 108c. In certain embodiments, each of confined wells 102a- 102d comprise at least two internal angles (e.g., three internal angles), wherein the interfaces between mask material 104 and the substrate (hidden from view in FIG. ID by mask material 104) at the at least two internal angles (e.g., three internal angles) seed growth of single-crystalline material 108a- 108c. According to some embodiments, by seeding growth of the single-crystalline material from multiple interfaces between the mask material and the substrate at multiple internal angles of each confined well, the crystallographic orientations of each nuclei of the single-crystalline material are advantageously substantially crystallographically aligned. For example, referring to FIG. ID, the crystallographic orientations of each nuclei of singlecrystalline materials 108a- 108c are substantially crystallographically aligned. This substantial crystallographic alignment can lead to defect-free single crystalline materials when multiple nuclei merge, as described herein in greater detail.

[0071] In some embodiments, the method comprises growing each region of the singlecrystalline material such that each region of the single-crystalline material fills or substantially fills each confined well associated with each region of the single-crystalline material. FIG. IE is a top-view schematic illustration of array of confined wells (hidden from view in FIG. IE by single-crystalline material 108) within mask material 104 on a substrate (hidden from view in FIG. IE by mask material 104) after growth of additional crystalline material 108 within each confined well, according to certain embodiments. In certain embodiments, as shown in FIG. IE, each region of single-crystalline material 108 has filled or substantially filled each confined well (e.g., hidden from view in FIG. IE by single-crystalline material 108) associated with each region of single-crystalline material 108. In certain embodiments, as described herein in greater detail, the crystallographic orientations of each region of single-crystalline material 108 are substantially crystallographically aligned. In some embodiments, each region of singlecrystalline material 108 is part of an array of single-crystalline materials (e.g., an array of crystallographically aligned single-crystalline materials).

[0072] According to some embodiments, the method comprises optionally removing the mask material. In some embodiments, for example, the mask material may be removed if the mask material and the substrate are formed of different materials. FIG. IF is a top-view schematic illustration of an array of crystalline materials 108 on substrate 106 after optional removal of the mask material (e.g., mask material 104 shown in FIG. IE) from substrate 106, according to certain embodiments.

[0073] In certain embodiments, the method comprises laterally growing each of the substantially crystallographically aligned regions of the single-crystalline material. Referring to FIGS. IE- IF, for example, each of the substantially crystallographically aligned regions of single-crystalline material 108 may be laterally grown. According to some embodiments, by laterally growing each of the substantially crystallographically aligned regions of single-crystalline material 108, each of the substantially crystallographically aligned regions of single-crystalline material 108 coalesce (e.g., merge) to form a single domain of single-crystalline material 108. FIG. 1G is a top-view schematic illustration of single domain 110 of single-crystalline material 108 after crystalline materials 108 within the confined wells of FIGS. 1A-1F have been merged, according to certain embodiments. FIG. 1H is a cross-sectional schematic illustration of single domain 110 of single-crystalline material 108 after crystalline materials 108 within the confined wells of FIG. IE have been merged, according to certain embodiments. As shown in FIG. 1H, each of the substantially crystallographically aligned regions of single-crystalline material 108 (as shown in FIG. IE) and / or single domain 110 of single-crystalline material 108 may laterally grow over mask material 104, according to certain embodiments. FIG. II is a cross-sectional schematic illustration of single domain 110 of single-crystalline material 108 after crystalline materials 108 within the confined wells of FIG. IF have been merged, according to certain embodiments. As shown in FIG. II, each of the substantially crystallographically aligned regions of single-crystalline material 108 (as shown in FIG. IF) and / or single domain 110 of single-crystalline material 108 may laterally grow over void 124 previously occupied by a mask material, according to certain embodiments. In other embodiments each of the substantially crystallographically aligned regions of the single-crystalline material and / or the single domain of the single-crystalline material laterally grows such that the single-crystalline material fills or substantially fills one or more voids previously occupied by a mask material. For example, FIG. 1J is another cross-sectional schematic illustration of single domain 110 of single-crystalline material 108 after the crystalline materials 108 within the confined wells of FIG. IF have been merged, according to certain embodiments. As shown in FIG. 1J, each of the substantially crystallographically aligned regions of single-crystalline material 108 (as shown in FIG. IF) and / or single domain 110 of single-crystalline material 108 may laterally grow such that singlecrystalline material 108 fills or substantially fills one or more voids previously occupied by a mask material.

[0074] The single domain of the single-crystalline material may have any of a variety of suitable top-view shapes. According to some embodiments, the top-view shape of the single domain of the single-crystalline material depends on the top-view shape of the substrate and / or the mask material over (e.g., on) which the single domain of the single-crystalline material is grown. In some embodiments, for example, as shown in FIG. 1G, single domain 110 of single-crystalline material 108 comprises a rectangular (e.g., square) top-view shape. According to some embodiments, although not shown in the figures, the single domain of the single-crystalline material comprises a triangular top-view shape (e.g., an equilateral triangular top-view shape, an acute triangular top-view shape, an obtuse triangular top-view shape), a hexagonal top-view shape, a circular top-view shape, or an oval top-view shape. Other top-view shapes for the single domain of the single-crystalline material are also possible.

[0075] The single domain of the single-crystalline material may have any of a variety of suitable lateral dimensions. In certain embodiments, the single domain of the single-crystalline material has a first lateral dimension and a second lateral dimension that is perpendicular to the first lateral dimension. Referring, for example, to FIG. 1G, single domain 110 of single-crystalline material 108 has first lateral dimension 202a and second lateral dimension 202b that is perpendicular to first lateral dimension 202a.

[0076] The first lateral dimension of the single domain of the single-crystalline material may be a maximum length or a maximum diameter of the single domain of the single-crystalline material. In some embodiments, for example, referring to FIG. 1G, single domain 110 of singlecrystalline material 108 comprises a rectangular (e.g., square) top-view shape having first lateral dimension 202a corresponding to a maximum length of single domain 110 of single-crystalline material 108. In other embodiments, although not shown in the figures, the single domain of the single-crystalline material comprises a triangular top-view shape having a first lateral dimension corresponding to a maximum length of the single domain of the single-crystalline material, a hexagonal top-view shape having a first lateral dimension corresponding to a maximum length of the single domain of the single-crystalline material, a circular top-view shape having a first lateral dimension corresponding to a maximum diameter of the single domain of the singlecrystalline material, or an oval top-view shape having a first lateral dimension corresponding to a maximum diameter of the single domain of the single-crystalline material.

[0077] The second lateral dimension of the single domain of the single-crystalline material may be a length or a diameter of the single domain of the single-crystalline material that is perpendicular to the first lateral dimension of the single domain of the single-crystalline material. In certain embodiments, for example, as shown in FIG. 1G, single domain 110 of single-crystalline material 108 comprises a rectangular (e.g., square) top-view shape having second lateral dimension 202b corresponding to a length of single domain 110 of singlecrystalline material 108 that is perpendicular to first lateral dimension 202a. In other embodiments, although not shown in the figures, the single domain of the single-crystalline material comprises a triangular top-view shape having a second lateral dimension corresponding to a length of the single domain of the single-crystalline material that is perpendicular to the first lateral dimension of the single domain of the single-crystalline material, a hexagonal top-view shape having a second lateral dimension corresponding to a length of the single domain of the single-crystalline material that is perpendicular to the first lateral dimension of the single domain of the single-crystalline material, a circular top-view shape having a second lateral dimension corresponding to a diameter of the single domain of the single-crystalline material that is perpendicular to the first lateral dimension of the single domain of the single-crystalline material, or an oval top-view shape having a second lateral dimension corresponding to a diameter of the single domain of the single-crystalline material that is perpendicular to the first lateral dimension of the single domain of the single-crystalline material. The first lateral dimension (e.g., first lateral dimension 202a) of the single domain (e.g., single domain 110) of the single-crystalline material (e.g., single-crystalline material 108) may have any of a variety of suitable lengths. In certain embodiments, for example, the first lateral dimension of the single domain of the single-crystalline material has a length greater than or equal to 100 micrometers, greater than or equal to 500 micrometers, greater than or equal to 1 millimeter, greater than or equal to 5 millimeters, greater than or equal to 1 centimeter, greater than or equal to 5 centimeters, greater than or equal to 10 centimeters, greater than or equal to 50 centimeters, or greater. In some embodiments, the first lateral dimension of the single domain of the single-crystalline material has a length less than or equal to 1 meter, less than or equal to 50 centimeters, less than or equal to 10 centimeters, less than or equal to 5 centimeters, less than or equal to 1 centimeter, less than or equal to 5 millimeters, less than equal to 1 millimeter, or less than or equal to 500 micrometers. Combinations of the above recited ranges are possible (e.g., the first lateral dimension of the single domain of the single-crystalline material has a length greater than or equal to 100 micrometers and less than or equal to 1 meter). Other ranges are also possible.

[0078] The second lateral dimension (e.g., second lateral dimension 202b) of the single domain (e.g., single domain 110) of the single-crystalline material (e.g., single-crystalline material 108) may have any of a variety of suitable lengths. In certain embodiments, for example, the second lateral dimension of the single domain of the single-crystalline material has a length greater than or equal to 100 micrometers, greater than or equal to 500 micrometers, greater than or equal to 1 millimeter, greater than or equal to 5 millimeters, greater than or equal to 1 centimeter, greater than or equal to 5 centimeters, greater than or equal to 10 centimeters, greater than or equal to 50 centimeters, or greater. In some embodiments, the second lateral dimension of the single domain of the single-crystalline material has a length less than or equal to 1 meter, less than or equal to 50 centimeters, less than or equal to 10 centimeters, less than or equal to 5 centimeters, less than or equal to 1 centimeter, less than or equal to 5 millimeters, less than equal to 1 millimeter, or less than or equal to 500 micrometers. Combinations of the above recited ranges are possible (e.g., the second lateral dimension of the single domain of the single-crystalline material has a length greater than or equal to 100 micrometers and less than or equal to 1 meter). Other ranges are also possible.

[0079] The single domain of the single-crystalline material may have any of a variety of suitable facial surface areas. In some embodiments, for example, the facial surface area of the single domain of the single-crystalline material is greater than or equal to 0.01 millimeters2, greater than or equal to 0.25 millimeters2, greater than or equal to 1 millimeter2, greater than or equal to 25 millimeters2, greater than or equal to 1 centimeter2, greater than or equal to 25 centimeters2, greater than or equal to 100 centimeters2, greater than or equal to 2500 centimeters2, or greater. In certain embodiments, the facial surface area of the single domain of the single-crystalline material is less than or equal to 1 meter2, less than or equal to 2500 centimeters2, less than or equal to 100 centimeters2, less than or equal to 25 centimeters2, less than or equal to 1 centimeter2, less than or equal to 25 millimeters2, less than or equal to 1 millimeter2, or less than or equal to 0.25 millimeters2. Combinations of the above recited ranges are possible (e.g., the facial surface area of the single domain of the single-crystalline material is greater than or equal to 0.01 millimeters2and less than or equal to 1 meter2). Other ranges are also possible.

[0080] The single domain of the single-crystalline material may have any of a variety of suitable thicknesses. Referring, for example, to FIGS. 1H-1J, single domain 110 of single-crystalline material 108 has thickness 904. In certain embodiments, the thickness of the single domain of a 2-D single-crystalline material is one molecule (e.g., an atomically thin material, such as a single monolayer of a molecule), as described herein in greater detail. In some embodiments, the thickness of the single domain of a 3-D single-crystalline material is greater than one molecule (e.g., greater than or equal to 1 nanometer and less than or equal to 500 micrometers), as described herein in greater detail.

[0081] In certain embodiments, the single domain of the single-crystalline material is advantageously defect-free. In some embodiments, the single-domain of the single-crystalline material comprises substantially no (or no) edge dislocations, screw dislocations, threading dislocations, APBs, and / or other defects. In certain embodiments, for example, the single domain of the single-crystalline material comprises fewer than 2 x 1013defects / cm2, fewer than 1013defects / cm2, fewer than 1012defects / cm2, fewer than 1011defects / cm2, fewer than 1010defects / cm2, fewer than 109defects / cm2, fewer than 108defects / cm2, fewer than 107defects / cm2, fewer than 106defects / cm2, fewer than 105defects / cm2, fewer than 104defects / cm2, fewer than 1000 defects / cm2, fewer than 100 defects / cm2, or fewer than 10 defects / cm2. In some embodiments, the single domain of the single-crystalline material comprises greater than or equal to 1 defect / cm2, greater than or equal to 10 defects / cm2, greater than or equal to 100 defects / cm2, greater than or equal to 1000 defects / cm2, greater than or equal to 104defects / cm2, greater than or equal to 105defects / cm2, greater than or equal to 106defects / cm2, greater than or equal to 107defects / cm2, greater than or equal to 108defects / cm2, greater than or equal to 109defects / cm2, greater than or equal to 1010defects / cm2, greater than or equal to 1011defects / cm2, greater than or equal to 1012defects / cm2, or greater than or equal to 1013defects / cm2. Combinations of the above recited ranges are possible (e.g., the single domain of the single- crystalline material comprises fewer than 2 x 1013defects / cm2and greater than or equal to 1 defect / cm2). Other ranges are also possible.

[0082] According to certain embodiments, the number of defects in a single domain of 2-D single-crystalline material is calculated from the point defects as measured by scanning transmission electron microscopy (STEM). In some embodiments, the number of defects in a single domain of 3-D single-crystalline material is measured by X-ray diffraction techniques, Electron Channeling Contrast Imaging (ECCI) from scanning electron microscopy (SEM), and / or transmission electron microscopy (TEM).

[0083] According to certain embodiments, growing the single-crystalline material comprises chemical vapor deposition (CVD). In some embodiments, growing the single-crystalline material comprises metal-organic chemical vapor deposition (MOCVD), atmospheric pressure chemical vapor deposition (APCVD), plasma-enhanced chemical vapor deposition (PECVD), and / or liquid phase chemical vapor deposition (LPCVD).

[0084] The single-crystalline material may comprise any of a variety of suitable materials. In some embodiments, the single-crystalline material comprises a transition-metal dichalcogenide (TMD) represented by the formula MX2 wherein M is a transition-metal atom and X is a chalcogen atom. In certain embodiments, the TMD is a metallic and / or semiconducting TMD. Suitable TMDs include, but are not limited to, tungsten diselenide (WSe2), tungsten disulfide (WS2), molybdenum diselenide (MoSe2), molybdenum disulfide (M0S2), vanadium diselenide (VSe2), vanadium disulfide (VS2), cobalt diselenide (CoSe2), cobalt disulfide (C0S2), titanium diselenide (TiSe2), titanium disulfide (TiS2), and / or combinations thereof. Other TMDs are also possible. In some embodiments, the single-crystalline material comprises a high-K dielectric material. Suitable high-K dielectric materials include, but are not limited to, dibismuth selenium pentoxide (EfeSeOs), antimony oxide (Sb2O3), and / or combinations thereof. Other high-K dielectric materials are also possible. In certain embodiments, the single crystalline material comprises graphene, hexagonal boron nitride (hBN), a carbon nanotube (CNT), and / or combinations thereof. Combinations of any of the above recited single-crystalline materials are possible. Other materials for the single-crystalline material are also possible.

[0085] According to some embodiments, a method of forming a 3-D single-crystalline material over regions of 2-D material is described.

[0086] In certain embodiments, the method comprises growing multiple regions of a 2-D singlecrystalline material, each region of the 2-D single-crystalline material associated with a confined well that is part of an array of confined wells, as described herein in greater detail, for example, with respect to FIGS. 1A-1E. FIG. 2A is a top-view schematic illustration of an array of confined wells (hidden from view in FIG. 2A by 2-D material 108’) within mask material 104 on a substrate (hidden from view in FIG. 2A by mask material 104), in which the wells contain 2-D material 108’, according to certain embodiments. FIG. 2B is a cross-sectional schematic illustration of the array of confined wells 102 (e.g., confined wells 102a- 102b) within mask material 104 on substrate 106 shown in FIG. 2A, according to certain embodiments.

[0087] According to certain embodiments, the method comprises growing multiple regions of the 3-D single-crystalline material. FIG. 2C is a top-view schematic illustration of an array of confined wells (hidden from view in FIG. 2C by 2-D material 108’) within mask material 104 on a substrate (hidden from view in FIG. 2C by mask material 104) after growth of some 3-D crystalline material 108” over the 2-D material 108’ within each well, according to certain embodiments. According to some embodiments, each region of the 3-D single-crystalline material is associated with a confined well that is part of the array of confined wells. Referring, for example, to FIG. 2C, each region of 3-D single-crystalline material 108” is associated with a confined well that is part of the array of confined wells (hidden from view in FIG. 2C by 2-D material 108’).

[0088] According to some embodiments, the multiple regions of the 3-D single-crystalline material are grown over (e.g., directly over) a 2-D single-crystalline material. In certain embodiments, for example, each region of the 2-D single-crystalline material associated with a confined well seeds the growth of the 3-D single-crystalline material. Referring, for example, to FIG. 2C, multiple regions of 3-D single-crystalline material 108” are grown over 2-D singlecrystalline material 108’ using 2-D single-crystalline material 108’ as a seed. In some embodiments, growing the 3-D single-crystalline material over the 2-D single-crystalline material comprises epitaxial growth. For example, referring to FIG. 2C, growing 3-D singlecrystalline material 108” over 2-D single-crystalline material 108’ comprises epitaxial growth.

[0089] As described herein in greater detail with respect to FIG. 1C, the crystallographic orientations of each region of the 2-D single-crystalline material 108’ may be substantially crystallographically aligned. According to certain embodiments, by seeding growth of the 3-D single crystalline material using the substantially crystallographically aligned 2-D singlecrystalline material, the crystallographic orientations of each region of the 3-D single-crystalline material are advantageously substantially crystallographically aligned. For example, referring to FIG. 2C, the crystallographic orientations of each region of 3-D single-crystalline material 108” are substantially crystallographically aligned.

[0090] As described herein in greater detail with respect to FIG. ID, each confined well may have a top-view shape comprising multiple internal angles that seed growth of the single- crystalline material. FIG. 2D is a top-view schematic illustration of an array of confined wells (e.g., hidden from view in FIG. 2D by 2-D material 108’) within mask material 104 on a substrate (hidden from view in FIG. 2D by mask material 104) after growth of some 3-D crystalline material 108” (e.g., crystalline material 108a”-108c”) seeded by multiple internal angles of each well, according to certain embodiments. In certain embodiments, growth of 3-D crystalline material 108” (e.g., crystalline material 108a”-108c”) is seeded by multiple interfaces between mask material 104 and the substrate (hidden from view in FIG. 2D by mask material 104) at the multiple internal angles of each well. In some embodiments, as shown in FIG. 2D, each of the confined wells comprise at least two internal angles (e.g., three internal angles) that seed growth of 3-D single-crystalline material 108a”-108c”. In certain embodiments, each of the confined wells comprise at least two internal angles (e.g., three internal angles), wherein the interfaces between mask material 104 and the substrate (hidden from view in FIG. 2D by mask material 104) at the at least two internal angles (e.g., three internal angles) seed growth of 3-D single-crystalline material 108a”- 108c”. According to some embodiments, by seeding growth of the 3-D single-crystalline material from multiple interfaces between the mask material and the substrate at multiple internal angles of each confined well, the crystallographic orientations of each nuclei of the 3-D single-crystalline material are advantageously substantially crystallographically aligned. For example, referring to FIG. 2D, the crystallographic orientations of each nuclei of 3-D single-crystalline materials 108a” -108c” are substantially crystallographically aligned. This substantial crystallographic alignment can lead to defect-free 3-D single crystalline materials when multiple nuclei merge, as described herein in greater detail.

[0091] In certain embodiments, the method comprises growing each region of the 3-D singlecrystalline material such that each region of the 3-D single-crystalline material fills or substantially fills each confined well. FIG. 2E is a top-view schematic illustration of an array of confined wells (hidden from view in FIG. 2E by 3-D single-crystalline material 108”) within mask material 104 on a substrate (hidden from view in FIG. 2E by mask material 104) after growth of additional 3-D crystalline material 108” over the 2-D material (hidden from view in FIG. 2E by 3-D crystalline material 108”) within each well, according to certain embodiments. In certain embodiments, as shown in FIG. 2E, each region of 3-D single-crystalline material 108” has filled or substantially filled each confined well (hidden from view in FIG. 2E by 3-D single-crystalline material 108”). In some embodiments, as described herein in greater detail, the crystallographic orientations of each region of 3-D single-crystalline material 108” are substantially crystallographically aligned. In certain embodiments, each region of 3-D single- crystalline material 108” is part of an array of 3-D single-crystalline materials (e.g., an array of crystallographically aligned 3-D single-crystalline materials).

[0092] In certain embodiments, the method comprises optionally removing the mask material. In some embodiments, for example, the mask material may be removed if the mask material and the substrate are formed of different materials. FIG. 2F is a top-view schematic illustration of an array of 3-D crystalline materials 108” on substrate 106 after optional removal of the mask (e.g., mask material 104 shown in FIG. 2E) from substrate 106, according to certain embodiments.

[0093] According to some embodiments, the method comprises laterally growing each of the substantially crystallographically aligned regions of the 3-D single-crystalline material. Referring to FIGS. 2E-2F, for example, each of the substantially crystallographically aligned regions of 3-D single-crystalline material 108” may be laterally grown. In some embodiments, by laterally growing each region of the substantially crystallographically aligned regions of the 3-D single-crystalline material, each of the substantially crystallographically aligned regions of the 3-D single-crystalline material 108” coalesce (e.g., merge) to form a single domain of the 3- D single-crystalline material 108”. FIG. 2G is a top-view schematic illustration of single domain 110’ of 3-D crystalline material 108” after 3-D crystalline materials 108” within the confined wells of FIGS. 2A-2F have been merged, according to certain embodiments. FIG. 2H is a cross-sectional schematic illustration of single domain 110’ of 3-D crystalline material 108” after 3-D crystalline materials 108” within the confined wells of FIG. 2E have been merged, according to certain embodiments. As shown in FIG. 2H, each of the substantially crystallographically aligned regions of 3-D crystalline material 108” (as shown in FIG. 2E) and / or single domain 110’ of 3-D crystalline material 108” may laterally grow over mask material 104, according to certain embodiments. FIG. 21 is a cross-sectional schematic illustration of single domain 110’ of 3-D crystalline material 108” after 3-D crystalline materials 108” within the confined wells of FIG. 2F have been merged, according to certain embodiments. As shown in FIG. 21, each of the substantially crystallographically aligned regions of 3-D crystalline material 108” (as shown in FIG. 2F) and / or single domain 110’ of 3D crystalline material 108” may laterally grow over void 124 previously occupied by a mask material, according to certain embodiments. In other embodiments, each of the substantially crystallographically aligned regions of the 3-D crystalline material and / or the single domain of the 3-D crystalline material laterally grows such that the 3-D crystalline material fills or substantially fills one or more voids previously occupied by a mask material. For example, FIG. 2J is another cross-sectional schematic illustration of single domain 110’ of 3-D crystalline material 108” after 3-D crystalline materials 108” within the confined wells of FIG. 2F have been merged, according to certain embodiments. As shown in FIG. 2J, each of the substantially crystallographically aligned regions of 3-D single- crystalline material 108” (as shown in FIG. 2F) and / or single domain 110’ of 3-D single-crystalline material 108” may laterally grow such that the 3-D single-crystalline material 108 fills or substantially fills one or more voids previously occupied by a mask material.

[0094] According to certain embodiments, a method of forming a single domain of a 3-D singlecrystalline material over a single domain of a 2-D single-crystalline material is described. FIG. 2K is a cross-sectional schematic illustration of single domain 110’ of 3-D single-crystalline material 108” grown over single domain 110 of 2-D single-crystalline material 108’, according to certain embodiments. In some embodiments, single domain 110 of 2-D single-crystalline material 108’ may be grown, e.g., as described herein in greater detail with respect to FIGS. 1A- 1J. In certain embodiments, single domain 110’ of 3-D single-crystalline material 108” is grown over single domain 110 of 2-D single-crystalline material 108’ using 2-D singlecrystalline material 108’ as a seed. In some embodiments, growing the single domain of the 3-D single-crystalline material comprises epitaxial growth.

[0095] The single domain of the 3-D single-crystalline material may have any of a variety of suitable top-view shapes. According to some embodiments, the top-view shape of the single domain of the 3-D single-crystalline material depends on the top-view shape of the substrate, the mask material, and / or the single domain of the 2-D single-crystalline material over (e.g., on) which the single domain of the 3-D single-crystalline material is grown. In some embodiments, for example, as shown in FIG. 2G, single domain 110’ of 3-D single-crystalline material 108” comprises a rectangular (e.g., square) top-view shape. According to some embodiments, although not shown in the figures, the single domain of the 3-D single-crystalline material comprises a triangular top-view shape (e.g., an equilateral triangular top-view shape, an acute triangular top-view shape, an obtuse triangular top-view shape), a hexagonal top-view shape, a circular top-view shape, or an oval top-view shape. Other top-view shapes for the single domain of the 3-D single-crystalline material are also possible.

[0096] The single domain of the 3-D single-crystalline material may have any of a variety of suitable lateral dimensions. In certain embodiments, the single domain of the 3-D singlecrystalline material has a first lateral dimension and a second lateral dimension that is perpendicular to the first lateral dimension. Referring, for example, to FIG. 2G, single domain 110’ of 3-D single-crystalline material 108” has first lateral dimension 202a’ and second lateral dimension 202b’ that is perpendicular to first lateral dimension 202a’. The first lateral dimension of the single domain of the 3-D single-crystalline material may be a maximum length or a maximum diameter of the single domain of the 3-D singlecrystalline material. In some embodiments, for example, referring to FIG. 2G, single domain 110’ of 3-D single-crystalline material 108” comprises a rectangular (e.g., square) top-view shape having first lateral dimension 202a’ corresponding to a maximum length of single domain 110’ of 3-D single-crystalline material 108”. In other embodiments, although not shown in the figures, the single domain of the 3-D single-crystalline material comprises a triangular top-view shape having a first lateral dimension corresponding to a maximum length of the single domain of the 3-D single-crystalline material, a hexagonal top-view shape having a first lateral dimension corresponding to a maximum length of the single domain of the 3-D single-crystalline material, a circular top-view shape having a first lateral dimension corresponding to a maximum diameter of the single domain of the 3-D single-crystalline material, or an oval top-view shape having a first lateral dimension corresponding to a maximum diameter of the single domain of the 3-D single-crystalline material.

[0097] The second lateral dimension of the single domain of the 3-D single-crystalline material may be a length or a diameter of the single domain of the 3-D single-crystalline material that is perpendicular to the first lateral dimension of the single domain of the 3-D single-crystalline material. In certain embodiments, for example, as shown in FIG. 2G, single domain 110’ of 3-D single-crystalline material 108” comprises a rectangular (e.g., square) top-view shape having second lateral dimension 202b’ corresponding to a length of single domain 110’ of 3-D singlecrystalline material 108” that is perpendicular to first lateral dimension 202a’ . In other embodiments, although not shown in the figures, the single domain of the 3-D single-crystalline material comprises a triangular top-view shape having a second lateral dimension corresponding to a length of the single domain of the 3-D single-crystalline material that is perpendicular to the first lateral dimension of the single domain of the 3-D single-crystalline material, a hexagonal top-view shape having a second lateral dimension corresponding to a length of the single domain of the 3-D single-crystalline material that is perpendicular to the first lateral dimension of the single domain of the 3-D single-crystalline material, a circular top-view shape having a second lateral dimension corresponding to a diameter of the single domain of the 3-D single-crystalline material that is perpendicular to the first lateral dimension of the single domain of the 3-D single-crystalline material, or an oval top-view shape having a second lateral dimension corresponding to a diameter of the single domain of the 3-D single-crystalline material that is perpendicular to the first lateral dimension of the single domain of the 3-D single-crystalline material. The first lateral dimension (e.g., first lateral dimension 202a’) of the single domain (e.g., single domain 110’) of the 3-D single-crystalline material (e.g., 3-D single-crystalline material 108”) may have any of a variety of suitable lengths. In certain embodiments, for example, the first lateral dimension of the single domain of the 3-D single-crystalline material has a length greater than or equal to 100 micrometers, greater than or equal to 500 micrometers, greater than or equal to 1 millimeter, greater than or equal to 5 millimeters, greater than or equal to 1 centimeter, greater than or equal to 5 centimeters, greater than or equal to 10 centimeters, greater than or equal to 50 centimeters, or greater. In some embodiments, the first lateral dimension of the single domain of the 3-D single-crystalline material has a length less than or equal to 1 meter, less than or equal to 50 centimeters, less than or equal to 10 centimeters, less than or equal to 5 centimeters, less than or equal to 1 centimeter, less than or equal to 5 millimeters, less than equal to 1 millimeter, or less than or equal to 500 micrometers. Combinations of the above recited ranges are possible (e.g., the first lateral dimension of the single domain of the 3-D single-crystalline material has a length greater than or equal to 100 micrometers and less than or equal to 1 meter). Other ranges are also possible.

[0098] The second lateral dimension (e.g., second lateral dimension 202b’) of the single domain (e.g., single domain 110’) of the 3-D single-crystalline material (e.g., single-crystalline material 108”) may have any of a variety of suitable lengths. In certain embodiments, for example, the second lateral dimension of the single domain of the 3-D single-crystalline material has a length greater than or equal to 100 micrometers, greater than or equal to 500 micrometers, greater than or equal to 1 millimeter, greater than or equal to 5 millimeters, greater than or equal to 1 centimeter, greater than or equal to 5 centimeters, greater than or equal to 10 centimeters, greater than or equal to 50 centimeters, or greater. In some embodiments, the second lateral dimension of the single domain of the 3-D single-crystalline material has a length less than or equal to 1 meter, less than or equal to 50 centimeters, less than or equal to 10 centimeters, less than or equal to 5 centimeters, less than or equal to 1 centimeter, less than or equal to 5 millimeters, less than equal to 1 millimeter, or less than or equal to 500 micrometers. Combinations of the above recited ranges are possible (e.g., the second lateral dimension of the single domain of the 3-D single-crystalline material has a length greater than or equal to 100 micrometers and less than or equal to 1 meter). Other ranges are also possible.

[0099] The single domain of the 3-D single-crystalline material may have any of a variety of suitable facial surface areas. In some embodiments, for example, the facial surface area of the single domain of the 3-D single-crystalline material is greater than or equal to 0.01 millimeters2, greater than or equal to 0.25 millimeters2, greater than or equal to 1 millimeter2, greater than or - 1 - equal to 25 millimeters2, greater than or equal to 1 centimeter2, greater than or equal to 25 centimeters2, greater than or equal to 100 centimeters2, greater than or equal to 2500 centimeters2, or greater. In certain embodiments, the facial surface area of the single domain of the 3-D single-crystalline material is less than or equal to 1 meter2, less than or equal to 2500 centimeters2, less than or equal to 100 centimeters2, less than or equal to 25 centimeters2, less than or equal to 1 centimeter2, less than or equal to 25 millimeters2, less than or equal to 1 millimeter2, or less than or equal to 0.25 millimeters2. Combinations of the above recited ranges are possible (e.g., the facial surface area of the single domain of the 3-D single-crystalline material is greater than or equal to 0.01 millimeters2and less than or equal to 1 meter2). Other ranges are also possible.

[0100] The single domain of the 3-D single-crystalline material may have any of a variety of suitable thicknesses. Referring, for example, to FIGS. 2H-2I, single domain 110’ of singlecrystalline material 108” has thickness 904’. In certain embodiments, the thickness of the single domain of the 3-D single-crystalline material is greater than one molecule (e.g., greater than or equal to 1 nanometer and less than or equal to 500 micrometers), as described herein in greater detail.

[0101] In certain embodiments, the single domain of the 3-D single-crystalline material is advantageously defect-free. In some embodiments, the single-domain of the 3-D singlecrystalline material comprises substantially no (or no) edge dislocations, screw dislocations, threading dislocations, APBs, and / or other defects. In certain embodiments, for example, the single domain of the 3-D single-crystalline material comprises fewer than 109defects / cm2, fewer than 108defects / cm2, fewer than 107defects / cm2, fewer than 106defects / cm2, fewer than 105defects / cm2, fewer than 104defects / cm2, fewer than 1000 defects / cm2, fewer than 100 defects / cm2, or fewer than 10 defects / cm2. In some embodiments, the single domain of the 3-D single-crystalline material comprises greater than or equal to 1 defect / cm2, greater than or equal to 10 defects / cm2, greater than or equal to 100 defects / cm2, greater than or equal to 1000 defects / cm2, greater than or equal to 104defects / cm2, greater than or equal to 105defects / cm2, greater than or equal to 106defects / cm2, greater than or equal to 107defects / cm2, or greater than or equal to 108defects / cm2. Combinations of the above recited ranges are possible (e.g., the single domain of the 3-D single-crystalline material comprises fewer than 109defects / cm2and greater than or equal to 1 defect / cm2). Other ranges are also possible.

[0102] As described elsewhere herein, the number of defects in the single domain of 3-D single crystalline material is measured by X-ray diffraction techniques, ECCI from SEM, and / or TEM. According to certain embodiments, a method comprises growing an epitaxial layer (e.g., a single-crystalline epitaxial layer) on (e.g., directly on) the single-crystalline material (e.g., the 2-D single-crystalline material and / or the 3-D single-crystalline material). In certain embodiments, multiple regions of an epitaxial layer are grown, each region associated with a region of a single-crystalline material that is part of an array of single-crystalline materials, thereby forming an array of epitaxial layers. FIG. 9A is a top-view schematic illustration of multiple regions of epitaxial layer 902, each region associated with a region of a singlecrystalline material (e.g., a region of a 2-D single-crystalline material, a region of a 3-D singlecrystalline material) that is part of an array of single-crystalline materials on substrate 106, according to certain embodiments. In FIG. 9A, the array of single-crystalline materials is hidden from view by the multiple regions of epitaxial layer 902. In other embodiments, an epitaxial layer is grown over a single-domain of a single-crystalline material, thereby forming a singledomain of an epitaxial layer. FIG. 9B is a top-view schematic illustration of single domain 110” of epitaxial layer 902 associated with a single domain of a single-crystalline material (e.g., a single domain of a 2-D single-crystalline material, a single domain of a 3-D single-crystalline material) on a substrate, according to certain embodiments. In FIG. 9B, the single domain of the single-crystalline material and the substrate are hidden from view by single domain 110” of epitaxial layer 902. FIG. 9C is a cross-sectional schematic illustration of single domain 110” of epitaxial layer 902 associated with single domain 110 of single-crystalline material 108 (e.g., a single domain of a 2-D single-crystalline material, a single domain of a 3-D single-crystalline material) on mask material 104 and substrate 106 (e.g., as shown in FIG. 1H), according to certain embodiments. FIG. 9D is a cross-sectional schematic illustration of single domain 110” of epitaxial layer 902 associated with single domain 110 of single-crystalline material 108 (e.g., a single domain of a 2-D single-crystalline material, a single domain of a 3-D single-crystalline material) on substrate 106 (e.g., as shown in FIG. II), according to certain embodiments. FIG. 9E is another cross-sectional schematic illustration of single domain 110” of epitaxial layer 902 associated with single domain 110 of single-crystalline material 108 (e.g., a single domain of a 2-D single-crystalline material, a single domain of a 3-D single-crystalline material) on substrate 106 (e.g., as shown in FIG. 1J), according to certain embodiments.

[0103] The single domain of the epitaxial layer may have any of a variety of suitable top-view shapes. According to some embodiments, the top- view shape of the single domain of the epitaxial layer depends on the top-view shape of the single domain of the single-crystalline material (e.g., single domain of 2-D single-crystalline material, single domain of 3-D singlecrystalline material) over (e.g., on) which the single domain of the epitaxial layer is grown. In some embodiments, for example, as shown in FIG. 9B, single domain 110” of epitaxial layer 902 comprises a rectangular (e.g., square) top-view shape. According to some embodiments, although not shown in the figures, the single domain of the epitaxial layer comprises a triangular top-view shape (e.g., an equilateral triangular top-view shape, an acute triangular top-view shape, an obtuse triangular top-view shape), a hexagonal top-view shape, a circular top-view shape, or an oval top-view shape. Other top-view shapes for the single domain of the epitaxial layer are also possible.

[0104] The single domain of the epitaxial layer may have any of a variety of suitable lateral dimensions. In certain embodiments, the single domain of the epitaxial layer has a first lateral dimension and a second lateral dimension that is perpendicular to the first lateral dimension. Referring, for example, to FIG. 9B, single domain 110” of epitaxial layer 902 has first lateral dimension 202a” and second lateral dimension 202b” that is perpendicular to first lateral dimension 202a’ ’ .

[0105] The first lateral dimension of the single domain of the epitaxial layer may be a maximum length or a maximum diameter of the single domain of the epitaxial layer. In some embodiments, for example, referring to FIG. 9B, single domain 110” of epitaxial layer 902 comprises a rectangular (e.g., square) top-view shape having first lateral dimension 202a” corresponding to a maximum length of single domain 110” of epitaxial layer 902. In other embodiments, although not shown in the figures, the single domain of the epitaxial layer comprises a triangular top-view shape having a first lateral dimension corresponding to a maximum length of the single domain of the epitaxial layer, a hexagonal top-view shape having a first lateral dimension corresponding to a maximum length of the single domain of the epitaxial layer, a circular top-view shape having a first lateral dimension corresponding to a maximum diameter of the single domain of the epitaxial layer, or an oval top-view shape having a first lateral dimension corresponding to a maximum diameter of the single domain of the epitaxial layer.

[0106] The second lateral dimension of the single domain of the epitaxial layer may be a length or a diameter of the single domain of the epitaxial layer that is perpendicular to the first lateral dimension of the single domain of the epitaxial layer. In certain embodiments, for example, as shown in FIG. 9B, single domain 110” of epitaxial layer 902 comprises a rectangular (e.g., square) top-view shape having second lateral dimension 202b” corresponding to a length of single domain 110” of epitaxial layer 902 that is perpendicular to first lateral dimension 202a”. In other embodiments, although not shown in the figures, the single domain of the epitaxial layer comprises a triangular top-view shape having a second lateral dimension corresponding to a length of the single domain of the epitaxial layer that is perpendicular to the first lateral dimension of the single domain of the epitaxial layer, a hexagonal top-view shape having a second lateral dimension corresponding to a length of the single domain of the epitaxial layer that is perpendicular to the first lateral dimension of the single domain of the epitaxial layer, a circular top-view shape having a second lateral dimension corresponding to a diameter of the single domain of the epitaxial layer that is perpendicular to the first lateral dimension of the single domain of the epitaxial layer, or an oval top-view shape having a second lateral dimension corresponding to a diameter of the single domain of the epitaxial layer that is perpendicular to the first lateral dimension of the single domain of the epitaxial layer.

[0107] The first lateral dimension (e.g., first lateral dimension 202a”) of the single domain (e.g., single domain 110”) of the epitaxial layer (e.g., epitaxial layer 902) may have any of a variety of suitable lengths. In certain embodiments, for example, the first lateral dimension of the single domain of the epitaxial layer has a length greater than or equal to 100 micrometers, greater than or equal to 500 micrometers, greater than or equal to 1 millimeter, greater than or equal to 5 millimeters, greater than or equal to 1 centimeter, greater than or equal to 5 centimeters, greater than or equal to 10 centimeters, greater than or equal to 50 centimeters, or greater. In some embodiments, the first lateral dimension of the single domain of the epitaxial layer has a length less than or equal to 1 meter, less than or equal to 50 centimeters, less than or equal to 10 centimeters, less than or equal to 5 centimeters, less than or equal to 1 centimeter, less than or equal to 5 millimeters, less than equal to 1 millimeter, or less than or equal to 500 micrometers. Combinations of the above recited ranges are possible (e.g., the first lateral dimension of the single domain of the epitaxial layer has a length greater than or equal to 100 micrometers and less than or equal to 1 meter). Other ranges are also possible.

[0108] The second lateral dimension (e.g., second lateral dimension 202b”) of the single domain (e.g., single domain 110”) of the epitaxial layer (e.g., epitaxial layer 902) may have any of a variety of suitable lengths. In certain embodiments, for example, the second lateral dimension of the single domain of the epitaxial layer has a length greater than or equal to 100 micrometers, greater than or equal to 500 micrometers, greater than or equal to 1 millimeter, greater than or equal to 5 millimeters, greater than or equal to 1 centimeter, greater than or equal to 5 centimeters, greater than or equal to 10 centimeters, greater than or equal to 50 centimeters, or greater. In some embodiments, the second lateral dimension of the single domain of the epitaxial layer has a length less than or equal to 1 meter, less than or equal to 50 centimeters, less than or equal to 10 centimeters, less than or equal to 5 centimeters, less than or equal to 1 centimeter, less than or equal to 5 millimeters, less than equal to 1 millimeter, or less than or equal to 500 micrometers. Combinations of the above recited ranges are possible (e.g., the second lateral dimension of the single domain of the epitaxial layer has a length greater than or equal to 100 micrometers and less than or equal to 1 meter). Other ranges are also possible.

[0109] The single domain of the epitaxial layer may have any of a variety of suitable facial surface areas. In some embodiments, for example, the facial surface area of the single domain of the epitaxial layer is greater than or equal to 0.01 millimeters2, greater than or equal to 0.25 millimeters2, greater than or equal to 1 millimeter2, greater than or equal to 25 millimeters2, greater than or equal to 1 centimeter2, greater than or equal to 25 centimeters2, greater than or equal to 100 centimeters2, greater than or equal to 2500 centimeters2, or greater. In certain embodiments, the facial surface area of the single domain of the epitaxial layer is less than or equal to 1 meter2, less than or equal to 2500 centimeters2, less than or equal to 100 centimeters2, less than or equal to 25 centimeters2, less than or equal to 1 centimeter2, less than or equal to 25 millimeters2, less than or equal to 1 millimeter2, or less than or equal to 0.25 millimeters2. Combinations of the above recited ranges are possible (e.g., the facial surface area of the single domain of the epitaxial layer is greater than or equal to 0.01 millimeters2and less than or equal to 1 meter2). Other ranges are also possible.

[0110] The single domain of the epitaxial layer may have any of a variety of suitable thicknesses. Referring, for example, to FIGS. 9C-9E, single domain 110” of epitaxial layer 902 has thickness 904”. In certain embodiments, the thickness of the single domain of the epitaxial layer is greater than or equal to 50 nm, greater than or equal to 100 nm, greater than or equal to 500 nm, greater than or equal to 1 micrometer, or greater than or equal to 5 micrometers. In some embodiments, the thickness of the single domain of the epitaxial layer is less than or equal to 10 micrometers, less than or equal to 5 micrometers, less than or equal to 1 micrometer, less than or equal to 500 nm, or less than or equal to 100 nm. Combinations of the above recited ranges are possible (e.g., the thickness of the single domain of the epitaxial layer is greater than or equal to 50 nm and less than or equal to 10 micrometers). Other ranges are also possible.

[0111] In some embodiments, an epitaxial layer may be grown on the single-crystalline material (e.g., on a region of a single-crystalline material that is part of an array of single-crystalline materials, on a single domain of a single crystalline material) via epitaxial growth. In certain embodiments, epitaxial growth of the epitaxial layer may use the single-crystalline material as a seed.

[0112] In some embodiments, the epitaxial layer is advantageously defect-free. In some embodiments, the epitaxial layer comprises substantially no (or no) edge dislocations, screw dislocations, threading dislocations, APBs, and / or other defects. In certain embodiments, for example, the epitaxial layer comprises fewer than 109defects / cm2, fewer than 108defects / cm2, fewer than 107defects / cm2, fewer than 106defects / cm2, fewer than 105defects / cm2, fewer than 104defects / cm2, fewer than 1OOO defects / cm2, fewer than 100 defects / cm2, or fewer than 10 defects / cm2. In some embodiments, the epitaxial layer comprises greater than or equal to 1 defect / cm2, greater than or equal to 10 defects / cm2, greater than or equal to 100 defects / cm2, greater than or equal to 1000 defects / cm2, greater than or equal to 104defects / cm2, greater than or equal to 105defects / cm2, greater than or equal to 106defects / cm2, greater than or equal to 107defects / cm2, or greater than or equal to 108defects / cm2. Combinations of the above recited ranges are possible (e.g., the epitaxial layer comprises fewer than 109defects / cm2and greater than or equal to 1 defect / cm2). Other ranges are also possible.

[0113] According to certain embodiments, the number of defects in the epitaxial layer is measured by X-ray diffraction techniques, ECO from SEM, and / or TEM.

[0114] The epitaxial layer may comprise any of a variety of suitable materials. In certain embodiments, the epitaxial layer (e.g., the single-crystalline epitaxial layer) comprises a III- nitride material. The term “Ill-nitride material” is used herein to refer to any Group III elementnitride compound. Non-limiting examples of Ill-nitride materials include boron nitride (BN), aluminum nitride (AIN), gallium nitride (GaN), indium nitride (InN), and thallium nitride (TIN), as well as any alloys including Group III elements and Group V elements (e.g., AlxGa(i-x)N, AlxInyGa(i-x.y)N, InxGa(i-x)N, AlxIn(i-x)N, GaAsaPbN(i-a-b), AlxInyGa(i-x.y)AsaPbN(i-a-b), and the like). Ill- nitride materials may be doped n-type or p-type, or may be intrinsic.

[0115] The phrase “aluminum nitride material” refers to aluminum nitride (AIN) and any of its alloys, such as aluminum gallium nitride (AlxGa(i-x)N), aluminum indium nitride (Alxhi(i-x)N), aluminum indium gallium nitride (AlxInyGa(i-x-y)N), aluminum indium gallium arsenide phosphoride nitride (AlxInyGa(i-x-y)AsaPbN(i-a-b)), and the like. In certain embodiments, the aluminum nitride material comprises AIN.

[0116] The phrase “gallium nitride material” refers to gallium nitride (GaN) and any of its alloys, such as aluminum gallium nitride (AlxGa(i-x)N), indium gallium nitride (InyGa(i-y)N), aluminum indium gallium nitride (AlxInyGa(i-x-y)N), gallium arsenide phosphoride nitride (GaAsaPbN(i-a-b)), aluminum indium gallium arsenide phosphoride nitride (AlxInyGa(i.x. y)AsaPbN(i-a-b)), and the like. In certain embodiments, the gallium nitride material comprises GaN.

[0117] According to certain embodiments, the epitaxial layer (e.g., the single-crystalline epitaxial layer) comprises a III-phosphide material. The term “III-phosphide material” is used herein to refer to any Group III element-pho sphide compound. Non-limiting examples of III- phosphide materials include gallium phosphide (GaP), boron phosphide (BP), aluminum phosphide (A1P), indium phosphide (InP), and thallium phosphide (TIP), as well as any alloys including Group III elements and Group V elements (e.g., AlxGa(i-x)P, AlxInyGa(i-x-y)P, InxGa(i-x)P, AlxIn(i-x)P, GaAsaPbN(i-a-b), AlxInyGa(i-x.y)AsaPbN(i-a-b), and the like). III-phosphide materials may be doped n-type or p-type, or may be intrinsic.

[0118] In some embodiments, the epitaxial layer (e.g., the single-crystalline epitaxial layer) comprises a III-arsenide material. The term “III-arsenide material” is used herein to refer to any Group III element- arsenide compound. Non-limiting examples of III-arsenide materials include gallium arsenide (GaAs), boron arsenide (BAs), aluminum arsenide (AlAs), indium arsenide (InAs), and thallium arsenide (TlAs), as well as any alloys including Group III elements and Group V elements (e.g., AlxGa(i-x)As, AlxInyGa(i-x.y)As, InxGa(i-x)As, AlxIn(i-x)P, GaAsaAsbN(i-a-b), AlxInyGa(i-x.y)AsaPbN(i-a-b), and the like). III-arsenide materials may be doped n-type or p-type, or may be intrinsic.

[0119] In some embodiments, the epitaxial layer (e.g., the single-crystalline epitaxial layer) comprises an oxide (e.g., a metal oxide). The metal oxide may be, in certain embodiments, zinc oxide (ZnO). Other oxides are also possible, according to some embodiments, such as barium titanate (BaTiOa or BTO), barium strontium titanate (BaxSri-xTiO3 or BST), strontium titanate (SrTiOa or STO), strontium ruthenium oxide (SrRuOa or SRO), lanthanum aluminate (LaAIOs or LAO), lead magnesium niobate-lead titanate (Pb(Mgi / 3Nb2 / 3)O3-PbTiO3 or PMN-PT), yttrium iron garnet (Y3FC5O12 or YIG), lithium niobate (LiNbOs), lithium titanate (Li2TiO3), and the like. In some embodiments, the single-crystalline semiconductor material comprises a perovskite.

[0120] In certain embodiments, the epitaxial layer (e.g., the single-crystalline epitaxial layer) comprises Si, Ge, GaAs, GaP, InP, InAs, GaN, AIN, InGaN, AlGaN, and / or combinations thereof. Other materials for the epitaxial layer are also possible.

[0121] In some embodiments, a method comprises growing a device layer on the singlecrystalline material (e.g., the 2-D single-crystalline material and / or the 3-D single-crystalline material) and / or on the epitaxial layer (e.g., the single-crystalline epitaxial layer). In certain embodiments, multiple regions of a device layer are grown, each region associated with a region of a single crystalline material that is part of an array of single-crystalline materials and / or a region of an epitaxial layer that is part of an array of epitaxial layers, thereby forming an array of device layers. In other embodiments, a device layer is grown over a single-domain of a singlecrystalline material and / or a single-domain of an epitaxial layer, thereby forming a singledomain of a device layer. The device layer may comprise any of a variety of suitable materials. In some embodiments, the device layer comprises a light-emitting diode (LED) and / or a photonic layer. In certain embodiments, the LED is a micro-LED or an ultra-violet (UV) LED. In some embodiments, the photonic layer is a laser and / or sensor. In certain embodiments, the device layer comprises a high-electron-mobility transistor (HEMT) and / or an electronic layer. Other device layers are also possible. In certain embodiments, the device layer comprises any of the materials described herein with respect to the epitaxial layer.

[0122] FIG. 3 is a schematic diagram showing defect-free epitaxy on amorphous substrates, according to certain embodiments. In accordance with certain embodiments, as shown in FIG. 3, an array of substantially crystallographically aligned 2-D single-crystalline materials may be grown, each region of the substantially crystallographically aligned 2-D single-crystalline material associated with a confined well that is part of an array of confined wells within a mask material on a substrate (e.g., an amorphous substrate). FIG. 7 is a schematic diagram showing confined 2-D single-crystalline TMD growth on an amorphous substrate, according to certain embodiments. In accordance with certain embodiments, as shown in FIG. 7, an array of substantially crystallographically aligned 2-D single-crystalline TMD material may be grown, each region of the substantially crystallographically aligned 2-D single-crystalline TMD material associated with a confined well that is part of an array of confined wells within a mask material on a substrate (e.g., an amorphous substrate, such as a Si wafer).

[0123] Referring to FIG. 3, in certain embodiments, each region of the substantially crystallographically aligned 2-D single-crystalline material is grown via van der Waals (vdW) epitaxy. In certain embodiments, each region of the substantially crystallographically aligned 2- D single-crystalline material may coalesce (e.g., merge) to form a single domain of 2-D singlecrystalline material. In some embodiments, each region of the substantially crystallographically aligned 2-D single-crystalline material may be used to seed the growth of an array of substantially crystallographically aligned 3-D single-crystalline materials. In some embodiments, each region of the substantially crystallographically aligned 3-D single-crystalline material may coalesce (e.g., merge) to form a single domain of 3-D single-crystalline material. FIG. 8 is a schematic diagram showing 3-D single-crystalline growth on an amorphous substrate, according to certain embodiments.

[0124] FIG. 4 is a schematic diagram showing materials and methods associated with confined 2-D single-crystalline material growth, according to certain embodiments. In accordance with some embodiments, as shown in FIG. 4, a method may comprise patterning a trench (e.g., a confined well) on an amorphous substrate via geometric engineering, growing a single nucleus of a 2-D single-crystalline material within the trench, and growing additional single-crystalline 2-D material within the trench.

[0125] FIG. 5 is a schematic diagram showing materials and methods associated with defect-free epitaxy, according to certain embodiments. In accordance with some embodiments, as shown in FIG. 5, a method may comprise growing a single nucleus of an epitaxial material on a 2-D single-crystalline material within a trench (e.g., a confined well) on a substrate (e.g., an amorphous substrate) and growing additional epitaxial material on the 2-D single-crystalline material (e.g., via van der Waals epitaxy) to form a defect-free epitaxial layer.

[0126] FIG. 6 is a schematic diagram showing monolithic integration of device layers, according to certain embodiments. In accordance with certain embodiments, as shown in FIG. 6, a method may comprise growing a device layer (e.g., a photonic and / or an electronic layer) on an epitaxial layer.

[0127] U.S. Provisional Patent Application No. 63 / 559,063, filed February 28, 2024, and entitled “Epitaxial Growth of Crystalline Materials Using Confined Directional Growth and Related Articles and Systems,” is incorporated herein by reference in its entirety for all purposes.

[0128] While several embodiments of the present invention have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and / or structures for performing the functions and / or obtaining the results and / or one or more of the advantages described herein, and each of such variations and / or modifications is deemed to be within the scope of the present invention. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and / or configurations will depend upon the specific application or applications for which the teachings of the present invention is / are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments of the invention described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, the invention may be practiced otherwise than as specifically described and claimed. The present invention is directed to each individual feature, system, article, material, and / or method described herein. In addition, any combination of two or more such features, systems, articles, materials, and / or methods, if such features, systems, articles, materials, and / or methods are not mutually inconsistent, is included within the scope of the present invention. The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.”

[0129] The phrase “and / or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Other elements may optionally be present other than the elements specifically identified by the “and / or” clause, whether related or unrelated to those elements specifically identified unless clearly indicated to the contrary. Thus, as a non-limiting example, a reference to “A and / or B,” when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A without B (optionally including elements other than B); in another embodiment, to B without A (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.

[0130] As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and / or” as defined above. For example, when separating items in a list, “or” or “and / or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to 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 element of a number or list of elements. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e. “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of.” “Consisting essentially of,” when used in the claims, shall have its ordinary meaning as used in the field of patent law.

[0131] As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and / or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.

[0132] As used herein, “wt%” is an abbreviation of weight percentage. As used herein, “at%” is an abbreviation of atomic percentage.

[0133] Some embodiments may be embodied as a method, of which various examples have been described. The acts performed as part of the methods may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include different (e.g., more or less) acts than those that are described, and / or that may involve performing some acts simultaneously, even though the acts are shown as being performed sequentially in the embodiments specifically described above.

[0134] Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements.

[0135] In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of’ and “consisting essentially of’ shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.

Claims

CLAIMSWhat is claimed is:

1. A method of forming a single-crystalline material, comprising: growing multiple regions of the single-crystalline material, each region associated with a confined well that is part of an array of confined wells, wherein each confined well has a top-view shape comprising one or more edges that seed growth of the single-crystalline material such that the crystallographic orientation of each of the regions of the single-crystalline material are substantially crystallographically aligned; and laterally growing each of the substantially crystallographically aligned regions of the single-crystalline material such that each of the substantially crystallographically aligned regions of the single-crystalline material coalesce to form a single domain of the single-crystalline material.

2. A method of forming a three-dimensional (3-D) single-crystalline material, comprising: growing multiple regions of the three-dimensional single-crystalline material, each region associated with a confined well that is part of an array of confined wells, wherein each confined well has a top-view shape comprising one or more edges that seed growth of the three-dimensional single-crystalline material such that the crystallographic orientation of each of the regions of the three-dimensional single-crystalline material are substantially crystallographically aligned.

3. The method of claim 2, wherein the growing occurs such that each of the substantially crystallographically aligned regions of the three-dimensional singlecrystalline material coalesce to form a single domain of the three-dimensional singlecrystalline material.

4. The method of any one of claims 1-3, comprising, prior to growing the multiple regions of the single-crystalline material, growing multiple regions of two-dimensional (2-D) single-crystalline material within the confined wells.

5. The method of any one of claims 1-4, wherein the multiple regions of the singlecrystalline material are grown over a substrate.

6. The method of claim 5, wherein the substrate is an amorphous substrate.

7. The method of any one of claims 1-6, wherein the confined wells are part of a mask associated with a substrate.

8. The method of claim 7, wherein the mask and the substrate are formed of different materials.

9. The method of any one of claims 5-8, wherein the substrate comprises glass, diamond, and / or Si(100).

10. The method of any one of claim 1-9, wherein the one or more edges form one or more internal angles that seed the growth of the single-crystalline material such that the crystallographic orientation of each of the regions of the single-crystalline material are substantially crystallographically aligned.

11. The method of any one of claim 1-10, wherein the top-view shape comprises a triangular top-view shape, a rectangular top-view shape, a hexagonal top-view shape, and / or a droplet top-view shape.

12. The method of any one of claim 1-11, wherein the mask comprises silicon dioxide, amorphous AI2O3, HfZrO, TiC , ZnO, Fe2<D3, SnCh, NiO, CuO, amorphous Si, SiNx, SiOxNy, amorphous carbon, and / or combinations thereof.

13. The method of any one of claim 1 or 3-12, wherein the single domain of the single-crystalline material has fewer than 2 x 1013defects / cm2.

14. The method of any one of claim 1-13, wherein the single-crystalline material comprises a transition metal dichalcogenide, EfeSeOs, Sb2O3, graphene, hexagonal boron nitride, a carbon nanotube, and / or combination thereof.

15. The method of any one of claim 1-14, further comprising growing an epitaxial layer on the single-crystalline material.

16. The method of claim 15, wherein the epitaxial layer comprises a Ill-nitride material, a III-phosphide material, a III-arsenide material, and / or a metal oxide.

17. The method of any one of claims 15-16, wherein the epitaxial layer comprises Si, Ge, GaAs, GaP, InP, InAs, GaN, AIN, InGaN, AlGaN, and / or combinations thereof.

18. The method of any one of claims 15-17, wherein the epitaxial layer comprises fewer than 109defects / cm2.

19. The method of any one of claims 15-18, further comprising growing a device layer on the epitaxial layer.

20. The method of claim 19, wherein the device layer comprises a light-emitting diode (LED), a photonic layer, a high-electron-mobility transistor (HEMT), and / or an electronic layer.

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