Patent Publication Number: US-11384449-B2

Title: Two-stage seeded growth of large aluminum nitride single crystals

Description:
RELATED APPLICATION 
     This application is a continuation of U.S. patent application Ser. No. 16/513,796, filed Jul. 17, 2019, which is a continuation of U.S. patent application Ser. No. 16/008,407, filed Jun. 14, 2018, which claims the benefit of and priority to U.S. Provisional Patent Application No. 62/520,787, filed Jun. 16, 2017, the entire disclosure of each of which is hereby incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     In various embodiments, the present invention relates to the fabrication of single-crystal aluminum nitride (AlN). 
     BACKGROUND 
     Aluminum nitride (AlN) holds great promise as a semiconductor material for numerous applications, e.g., optoelectronic devices such as short-wavelength light-emitting diodes (LEDs) and lasers, dielectric layers in optical storage media, electronic substrates, and chip carriers where high thermal conductivity is essential, among many others. In principle, the properties of AlN may allow light emission at wavelengths down to around 200 nanometers (nm) to be achieved. Recent work has demonstrated that ultraviolet (UV) LEDs have superior performance when fabricated on low-defect AlN substrates prepared from bulk AlN single crystals. The use of AlN substrates is also expected to improve high-power radio-frequency (RF) devices made with nitride semiconductors due to the high thermal conductivity with low electrical conductivity. However, the commercial feasibility of AlN-based semiconductor devices is limited by the scarcity and high cost of large, low-defect single crystals of AlN. 
     To make large-diameter AlN substrates more readily available and cost-effective, and to make the devices built thereon commercially feasible, it is desirable to grow large-diameter (&gt;25 mm) AlN bulk crystals at a high growth rate (&gt;0.5 mm/hr) while preserving crystal quality. The most effective method of growing AlN bulk single crystals is the “sublimation-recondensation” method that involves sublimation of lower-quality (typically polycrystalline) AlN source material and recondensation of the resulting vapor to form the single-crystal AlN. U.S. Pat. No. 6,770,135 (the &#39;135 patent), U.S. Pat. No. 7,638,346 (the &#39;346 patent), U.S. Pat. No. 7,776,153 (the &#39;153 patent), and U.S. Pat. No. 9,028,612 (the &#39;612 patent), the entire disclosures of which are incorporated by reference herein, describe various aspects of sublimation-recondensation growth of AlN, both seeded and unseeded. 
     During seeded growth of AlN, single crystals of AlN are nucleated on a high-quality single-crystal seed, and the growing crystals replicate the crystalline order of the exposed face of the seed. Moreover, the diameter of the growing crystal is often allowed to expand beyond the diameter of the seed; such “diameter expansion” enables the growth of large crystals while obviating the need to utilize seed crystals with large diameters, which is beneficial since large-area AlN seeds are often prohibitively expensive or simply unavailable. Such diameter expansion may be enabled via control of the radial and/or axial thermal gradients within the growth chamber during crystal growth, as detailed in the &#39;612 patent. Growth of single-crystal AlN boules is often initiated from AlN seeds having an exposed c-plane face with Al polarity, as the subsequent growth of AlN crystals with the Al-polarity orientation proceeds at a high growth rate—higher than growth rates enabled at other crystalline orientations. While such techniques produce boules of high-quality material, they are susceptible to parasitic, or “secondary” nucleation at the edges of the crystals. Parasitic nucleation events can result in higher defect densities, or even polycrystalline crystals, and thus the usable, high-quality area of the AlN crystal boule is often limited. Parasitic nucleation is a particular problem during diameter expansion of Al-polarity AlN crystals, as the radial thermal gradients that enable diameter expansion from small seeds may increase the frequency of parasitic nucleation events. Therefore, there is a need for improved crystal growth sequences that enable the formation of high-quality large single crystals of AlN. 
     SUMMARY 
     In various embodiments of the present invention, growth of large, high-quality single crystals of AlN is enabled via a two-stage process utilizing seeds of different crystalline orientations. In the first stage of the process, a small-diameter single-crystal AlN seed having a c-face, N polarity is utilized to seed growth therefrom of a high-quality AlN crystal via sublimation-recondensation or another growth technique based on physical vapor transport (PVT). While only slow growth rates on the N-polarity orientation of the first seed are possible (this orientation has the slowest growth rate of all of the various possible AlN growth modes), the growth on the first seed suppresses or substantially eliminates parasitic nucleation events at the edge of the growing crystal. It is believed that the suppression of parasitic nucleation events is enabled via the relatively high spreading rate of a properly oriented island on the N-polarity AlN crystal in the lateral direction. That is, while the growth of the AlN single crystal proceeds slowly in the growth, or “axial” direction, the high spreading rate in the lateral direction results in the “coating” of any parasitic nuclei that form on the (0001) facet (i.e., the (000-1) facet) of the crystal, and thus such nuclei do not grow into parasitic crystals that deleteriously impact the quality of the AlN boule. This very desirable feature is maintained so long as the growth rate is sufficiently slow. However, if one attempts to increase the growth rate by driving the (000-1) facet too far out of equilibrium, misoriented nuclei will form and grow quickly in the [0001] direction (i.e., the [000-1] direction) because of the resulting supersaturation of growth species within the crystal-growth system. Under these circumstances, these misoriented nuclei will not have a chance to be overgrown by properly oriented nuclei that are expanding in the lateral direction. 
     Thus, while growth of the AlN crystal could, in theory, simply proceed via diameter expansion from an N-polarity seed, such growth also has disadvantages. As mentioned above, the N-polarity growth rate is the slowest growth rate for AlN crystals, rendering N-polarity growth time-consuming and therefore expensive in a commercial context. In addition, prolonged N-polarity growth may result in the formation of slow-growing growth facets within the crystal, and the growing crystal may transition from substantially circular to hexagonal in cross-section. Specifically, m-plane facets that are perpendicular to the (000-1) tend to form during prolonged N-polarity growth, and such facets retard or substantially stop the lateral expansion of the AlN crystal. Thus, embodiments of the present invention utilize a second stage of crystal growth that preserves the high crystalline quality of the first growth stage while enabling higher growth rates and continued diameter expansion. The diameter of the AlN single crystal is allowed to expand during the first growth stage to a “transition diameter” larger than the diameter of the initial N-polarity seed, whereupon the growth process is halted before the formation of slow-growing facets in the crystal (for example). The diameter expansion of the AlN single crystal may be controlled by control of the radial thermal gradient within the growth crucible, as detailed in the &#39;612 patent. For example, the radial thermal gradient may be increased to promote diameter expansion until a desired diameter is obtained, whereupon the radial thermal gradient may be decreased (but typically not to zero) to slow or substantially eliminate further diameter expansion and to promote axial growth. 
     Because quality of the AlN single crystal may be compromised (via, e.g., formation of large-angle grain boundaries, polycrystalline growth, and/or other defects resulting from parasitic nucleation) if lateral growth (and concomitant diameter expansion) proceeds too rapidly (i.e., for a given amount of axial growth, which may be limited by the dimensions of the growth crucible or other aspects of the growth apparatus), the first growth stage may be repeated one or more times in order to obtain AlN single crystal having the desired transition diameter via N-polarity growth—after each first growth stage, a new, larger N-polarity seed may be cut from the resulting boule and utilized as the seed for the subsequent iteration. For example, diameter expansion of the AlN single crystal may be limited to a value ranging from approximately 0.5 mm to approximately 2 mm for each iteration of the first growth stage. In various embodiments, the diameter expansion during an iteration of N-polarity growth is limited to a value of less than or equal to approximately 2 mm for each 20 mm of axial growth of the crystalline boule. 
     After the one or more iterations of the first growth stage, the now-larger AlN single crystal is sliced to form a new growth seed for the second stage of the growth process. The new seed has a c face and an Al polarity and is utilized to form an even larger AlN single-crystal boule via the high growth rate enabled by the Al-polarity crystal face in combination with continued diameter expansion. The orientation of the new seed (and all seeds described herein) may be selected from a boule or other crystal during slicing via, for example, x-ray diffraction measurements and/or other materials characterization enabling identification of the orientation of the crystal; such techniques are known to those of skill in the art and may be performed without undue experimentation. In accordance with embodiments of the invention, a newly sliced seed may be polished to reduce surface roughness and remove cutting artifacts and/or damage. 
     The polarity of the seed may also be identified and selected chemically. For example, the seed polarity may be identified and selected via exposure of the seed to a basic or acidic solution, which will roughen an N-polarity face while leaving an Al-polarity face smooth. Examples of such treatments include exposing the seed for, e.g., 10-30 seconds to a KOH—NaOH eutectic melt at approximately 500° C., exposing the seed for, e.g., 30-90 seconds to a KOH aqueous solution at a temperature ranging from approximately 200° C. to approximately 350° C., or exposing the seed for, e.g., 30-90 seconds to a phosphoric acid aqueous solution at a temperature ranging from approximately 200° C. to approximately 300° C. After exposure, an N-polarity face will be roughened while an Al-polarity face will remain smooth and shiny. In this manner, an Al-polarity face may be selected and mounted within the crystal-growth chamber as the growth face of the seed for the second growth stage in accordance with embodiments of the present invention. Similarly, an N-polarity face of a seed may be identified in this fashion (e.g., for the first growth stage), and the roughness resulting from the chemical treatment may be removed (e.g., via a polishing technique such as CMP) before epitaxial growth on the seed, if desired. 
     In various embodiments of the invention, parasitic nucleation during the second growth stage is reduced or substantially eliminated via the greater control of the radial thermal gradient afforded by the use of the larger seed produced during the first growth stage. That is, the use of a seed having a diameter of at least the transition diameter surprisingly results in less (or substantially no) parasitic nucleation during diameter expansion, even at higher growth rates and/or diameter-expansion rates. For example, the radial thermal gradient in the growth crucible may be increased to enable diameter expansion during the second growth stage (or each iteration thereof) of at least 4 mm, at least 5 mm, at least 10 mm, or even more; such large radial thermal gradients would result in defective and/or polycrystalline growth (and/or deleterious facet formation) during the first growth stage. As with the first growth stage, the second growth stage may be repeated one or more times in order to obtain AlN single crystal having the desired final diameter via Al-polarity growth. In various embodiments of the invention, the diameter expansion during Al-polarity growth may be at least approximately 10 mm to approximately 20 mm (or more) for each 20 mm of axial growth of the crystalline boule. (As utilized herein, diameter expansion rates “for each X mm of axial growth” apply even if the amount of axial growth is less than X mm and may be scaled accordingly based on the actual or desired amount of axial growth. For example, a diameter expansion of approximately 20 mm for each 20 mm of axial growth corresponds to a diameter expansion of approximately 1 mm for each 1 mm of axial growth.) 
     Thus, in embodiments of the invention the transition diameter of the AlN crystal at which the growth process is transitioned from the first stage to the second stage may be (1) smaller than that at which N-polarity growth results in formation of slow-growth facets and formation of non-circular crystals, and (2) sufficiently large to support formation thereon of a radial thermal gradient having a magnitude adequate to suppress parasitic edge nucleation (and/or, e.g., formation of large-angle grain boundaries and/or other defects) during Al-polarity growth. In various embodiments of the invention, the transition diameter ranges from approximately 10 mm to approximately 40 mm, or even from approximately 15 mm to approximately 25 mm. The second growth stage may involve continued diameter expansion to crystal diameters of, for example, 100 mm, 150 mm, or even larger. In some embodiments, diameter expansion is halted during the second growth stage via manipulation (e.g., flattening, or even substantial elimination) of the radial thermal gradient within the growth chamber and/or because the diameter of the crystal increases to match the inner diameter of the growth chamber. The length of the crystal boule produced by the second growth stage may be quite large. In various embodiments, the length of the boule may be limited only by the inner dimensions of the growth chamber and/or by the size of the furnace utilized to produce the thermal growth environment within the growth chamber. 
     In various embodiments of the present invention, the radial and/or axial thermal gradients within the crystal-growth crucible utilized to promote and control the axial growth and diameter expansion of the AlN material may be controlled in various different manners. For example, individual heating elements arranged around the crucible may be powered to different levels (and thus different temperatures) to establish thermal gradients within the crucible. In addition or instead, thermal insulation may be selectively arranged around the crucible such that thinner and/or less insulating insulation is positioned around areas of higher desired temperature. As detailed in the &#39;612 patent, thermal shields may also be arranged around the crucible, e.g., above and/or below the crucible, in any of a multitude of different arrangements in order to establish desired thermal gradients within the crucible. In various embodiments, isotherms of the thermal gradient may be concave (viewed along the axial growth direction) during diameter expansion and substantially flat during axial growth with diameter expansion minimized or substantially eliminated. 
     Although embodiments of the invention have been presented herein utilizing AlN as the exemplary crystalline material fabricated in accordance therewith, embodiments of the invention may also be applied to other crystalline materials such as silicon carbide (SiC) and zinc oxide (ZnO); thus, herein, all references to AlN herein may be replaced, in other embodiments, by SiC or ZnO. As utilized herein, the term “diameter” refers to a lateral dimension (e.g., the largest lateral dimension) of a crystal, growth chamber, or other object, even if the crystal, growth chamber, or other object is not circular and/or is irregular in cross-section. 
     As utilized herein, a “substrate” or a “wafer” is a portion of a previously grown crystalline boule having top and bottom opposed, generally parallel surfaces. Substrates typically have thicknesses ranging between 200 μm and 1 mm and may be utilized as platforms for the epitaxial growth of semiconductor layers and the fabrication of semiconductor devices (e.g., light-emitting devices such as lasers and light-emitting diodes, transistors, power devices, etc.) thereon. As utilized herein, “room temperature” is 25° C. 
     In an aspect, embodiments of the invention feature a method of forming single-crystal aluminum nitride (AlN). A first seed crystal is provided or disposed within a first growth chamber. The first seed crystal includes, consists essentially of, or consists of AlN (e.g., doped or undoped AlN). The first seed crystal has a growth face having an N polarity. The first growth chamber is heated, whereby a first radial thermal gradient and a first axial thermal gradient are formed within the first growth chamber. Vapor including, consisting essentially of, or consisting of aluminum and nitrogen is condensed within the first growth chamber, thereby forming on the growth face of the first seed a first AlN single crystal that (a) increases in size along a growth direction in response to the first axial thermal gradient and (b) increases in size along a radial direction substantially perpendicular to the growth direction in response to the first radial thermal gradient. Condensation of the vapor within the first growth chamber is ceased after a diameter of the first AlN single crystal increases to a transition diameter greater than a diameter of the first seed crystal. A second seed crystal is separated from the first AlN single crystal. The second seed crystal includes, consists essentially of, or consists of AlN (e.g., doped or undoped AlN). The second seed crystal has a diameter larger than a diameter of the first seed crystal. The second seed crystal has a growth face having an Al polarity. The second seed crystal is provided or disposed within a second growth chamber. The second growth chamber is heated, whereby a second radial thermal gradient and a second axial thermal gradient are formed within the second growth chamber. Vapor including, consisting essentially of, or consisting of aluminum and nitrogen is condensed within the second growth chamber, thereby forming on the growth face of the second seed a second AlN single crystal that increases in size along the growth direction in response to the second axial thermal gradient. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. The first growth chamber may be the same as the second growth chamber. The first growth chamber may be different from the second growth chamber. During at least a portion of the formation of the second AlN single crystal, the second AlN single crystal may increase in size along the radial direction in response to the second radial thermal gradient. The second AlN single crystal may be separated into one or more AlN substrates. Each of the AlN substrates may have a diameter larger than the diameter of the first seed crystal and/or larger than the diameter of the first seed crystal. The second radial thermal gradient may be larger than the first radial thermal gradient. A growth rate of the second AlN single crystal may be larger than a growth rate of the first AlN single crystal. The transition diameter may range from approximately 10 mm to approximately 40 mm, from approximately 10 mm to approximately 15 mm, from approximately 10 mm to approximately 20 mm, from approximately 10 mm to approximately 30 mm, from approximately 20 mm to approximately 40 mm, from approximately 20 mm to approximately 30 mm, from approximately 25 mm to approximately 40 mm, from approximately 30 mm to approximately 40 mm, or may be less than approximately 40 mm, less than approximately 35 mm, less than approximately 30 mm, less than approximately 25 mm, less than approximately 20 mm, or less than approximately 15 mm. The transition diameter may be at least 5 mm, at least 6 mm, at least 7 mm, at least 8 mm, at least 9 mm, or at least 10 mm. 
     A single-crystal AlN substrate may be separated from the second AlN single crystal. A light-emitting device structure may be formed over the single-crystal AlN substrate to form a light-emitting device. The light-emitting device may be configured to emit visible or ultraviolet light. After forming at least a portion of the light-emitting device structure, at least a portion of the single-crystal AlN substrate may be removed from the light-emitting device. The light-emitting device may include, consist essentially of, or consist of a light-emitting diode or a laser. 
     In another aspect, embodiments of the invention feature a method of forming single-crystal aluminum nitride (AlN). In a step (a), a first seed crystal is provided. The first seed crystal includes, consists essentially of, or consists of AlN (e.g., doped or undoped AlN). The first seed crystal has a growth face having an N polarity. In a step (b), single-crystal AlN is deposited on the first seed crystal (e.g., on the growth face of the first seed crystal) within a first growth chamber. In a step (c), during at least some of the deposition of single-crystal AlN on the first seed crystal, diameter expansion is induced such that at least a portion of the single-crystal AlN has a diameter greater than a diameter of the first seed crystal. In a step (d), a new first seed crystal is separated from the single-crystal AlN after deposition of the single-crystal AlN on the first seed crystal. The new first seed crystal has a diameter greater than the diameter of the first seed crystal. The new first seed crystal has a growth face having an N polarity. In a step (e), steps (b) and (c) are repeated using the new first seed crystal produced in step (d). In a step (f), after step (e), a second seed crystal is separated from the single-crystal AlN deposited on the new first seed crystal. The second seed crystal includes, consists essentially of, or consists of AlN (e.g., doped or undoped AlN). The second seed crystal has a growth face having an Al polarity. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. In a step (g), single-crystal AlN may be deposited on the second seed crystal within a second growth chamber. The first growth chamber may be the same as the second growth chamber. The first growth chamber may be different from the second growth chamber. During a step (h), during at least some of the deposition of single-crystal AlN on the second seed crystal, diameter expansion may be induced such that at least a portion of the single-crystal AlN has a diameter greater than a diameter of the second seed crystal. The diameter expansion during step (h) may be, for each 20 mm of axial growth of the single-crystal AlN, at least approximately 10 mm, at least approximately 15 mm, at least approximately 20 mm, or at least approximately 25 mm. The diameter expansion during step (h) may be, for each 20 mm of axial growth of the single-crystal AlN, at most approximately 50 mm, at most approximately 35 mm, at most approximately 30 mm, at most approximately 25 mm, or at most approximately 20 mm. In a step (i), after deposition of the single-crystal AlN on the second seed crystal, a new second seed crystal may be separated from the single-crystal AlN. The new second seed crystal may have a diameter greater than the diameter of the second seed crystal. In a step (j), steps (g) and (h) may be repeated using the new second seed crystal produced in step (i). Steps (i) and (j) may be repeated one or more times. 
     A single-crystal AlN substrate may be separated from the single-crystal AlN produced during steps (g) and (h). A light-emitting device structure may be formed over the single-crystal AlN substrate to form a light-emitting device. The light-emitting device may be configured to emit visible or ultraviolet light. After forming at least a portion of the light-emitting device structure, at least a portion of the single-crystal AlN substrate may be removed from the light-emitting device. The light-emitting device may include, consist essentially of, or consist of a light-emitting diode or a laser. 
     Steps (d) and (e) may be repeated one or more times before step (f). The diameter expansion in step (c) may be, for each 20 mm of axial growth of the single-crystal AlN, at most approximately 5 mm, at most approximately 4 mm, at most approximately 3 mm, at most approximately 2 mm, at most approximately 1.5 mm, at most approximately 1 mm, or at most approximately 0.5 mm. In step (f) the diameter of the second seed crystal may range from approximately 10 mm to approximately 40 mm, from approximately 10 mm to approximately 15 mm, from approximately 10 mm to approximately 20 mm, from approximately 10 mm to approximately 30 mm, from approximately 20 mm to approximately 40 mm, from approximately 20 mm to approximately 30 mm, from approximately 25 mm to approximately 40 mm, from approximately 30 mm to approximately 40 mm, or may be less than approximately 40 mm, less than approximately 35 mm, less than approximately 30 mm, less than approximately 25 mm, less than approximately 20 mm, or less than approximately 15 mm. The diameter of the second seed crystal in step (f) may be at least 5 mm, at least 6 mm, at least 7 mm, at least 8 mm, at least 9 mm, or at least 10 mm. 
     In yet another aspect, embodiments of the invention feature a method of forming single-crystal aluminum nitride (AlN). In a step (a), a first seed crystal is provided. The first seed crystal includes, consists essentially of, or consists of AlN (e.g., doped or undoped AlN). The first seed crystal has a growth face having an N polarity. In a step (b), single-crystal AlN is deposited on the first seed crystal (e.g., on the growth face of the first seed crystal) within a first growth chamber. In a step (c), during at least some of the deposition of single-crystal AlN on the first seed crystal, diameter expansion is induced such that at least a portion of the single-crystal AlN has a diameter greater than a diameter of the first seed crystal. In a step (d), after step (c), a second seed crystal is separated from the single-crystal AlN deposited on the first seed crystal. The second seed crystal includes, consists essentially of, or consists of AlN (e.g., doped or undoped AlN). The second seed crystal has a growth face having an Al polarity. The second seed crystal has a diameter greater than the diameter of the first seed crystal. In a step (e), single-crystal AlN is deposited on the second seed crystal within a second growth chamber. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. In a step (f), during at least some of the deposition of single-crystal AlN on the second seed crystal, diameter expansion may be induced such that at least a portion of the single-crystal AlN has a diameter greater than a diameter of the second seed crystal. During a step (g), after deposition of the single-crystal AlN on the second seed crystal, a new second seed crystal may be separated from the single-crystal AlN. The new second seed crystal may have a diameter greater than the diameter of the second seed crystal. During a step (h), steps (e) and (f) may be repeated using the new second seed crystal produced in step (g). The diameter expansion during step (f) may be, for each 20 mm of axial growth of the single-crystal AlN, at least approximately 10 mm, at least approximately 15 mm, at least approximately 20 mm, or at least approximately 25 mm. The diameter expansion during step (f) may be, for each 20 mm of axial growth of the single-crystal AlN, at most approximately 50 mm, at most approximately 35 mm, at most approximately 30 mm, at most approximately 25 mm, or at most approximately 20 mm. Steps (g) and (h) may be repeated one or more times. 
     During at least some of the deposition of single-crystal AlN on the second seed crystal, diameter expansion may be induced such that at least a portion of the single-crystal AlN has a diameter greater than a diameter of the second seed crystal. The diameter expansion during deposition of single-crystal AlN on the second seed crystal may be, for each 20 mm of axial growth of the single-crystal AlN, at least approximately 10 mm, at least approximately 15 mm, at least approximately 20 mm, or at least approximately 25 mm. The diameter expansion during deposition of single-crystal AlN on the second seed crystal may be, for each 20 mm of axial growth of the single-crystal AlN, at most approximately 50 mm, at most approximately 35 mm, at most approximately 30 mm, at most approximately 25 mm, or at most approximately 20 mm. 
     A single-crystal AlN substrate may be separated from the single-crystal AlN deposited on the second seed crystal. A light-emitting device structure may be formed over the single-crystal AlN substrate to form a light-emitting device. The light-emitting device may be configured to emit visible or ultraviolet light. After forming at least a portion of the light-emitting device structure, at least a portion of the single-crystal AlN substrate may be removed from the light-emitting device. The light-emitting device may include, consist essentially of, or consist of a light-emitting diode or a laser. 
     The diameter of the second seed crystal may range from approximately 10 mm to approximately 40 mm, from approximately 10 mm to approximately 15 mm, from approximately 10 mm to approximately 20 mm, from approximately 10 mm to approximately 30 mm, from approximately 20 mm to approximately 40 mm, from approximately 20 mm to approximately 30 mm, from approximately 25 mm to approximately 40 mm, from approximately 30 mm to approximately 40 mm, or may be less than approximately 40 mm, less than approximately 35 mm, less than approximately 30 mm, less than approximately 25 mm, less than approximately 20 mm, or less than approximately 15 mm. The diameter of the second seed crystal may be at least 5 mm, at least 6 mm, at least 7 mm, at least 8 mm, at least 9 mm, or at least 10 mm. 
     The diameter expansion in step (c) may be, for each 20 mm of axial growth of the single-crystal AlN, at most approximately 5 mm, at most approximately 4 mm, at most approximately 3 mm, at most approximately 2 mm, at most approximately 1.5 mm, at most approximately 1 mm, or at most approximately 0.5 mm. The first growth chamber may be the same as the second growth chamber. The first growth chamber may be different from the second growth chamber. In step (c), the diameter of the at least a portion of the single-crystal AlN may not exceed a transition diameter. The transition diameter may range from approximately 10 mm to approximately 40 mm, from approximately 10 mm to approximately 15 mm, from approximately 10 mm to approximately 20 mm, from approximately 10 mm to approximately 30 mm, from approximately 20 mm to approximately 40 mm, from approximately 20 mm to approximately 30 mm, from approximately 25 mm to approximately 40 mm, from approximately 30 mm to approximately 40 mm, or may be less than approximately 40 mm, less than approximately 35 mm, less than approximately 30 mm, less than approximately 25 mm, less than approximately 20 mm, or less than approximately 15 mm. The transition diameter may be at least 5 mm, at least 6 mm, at least 7 mm, at least 8 mm, at least 9 mm, or at least 10 mm. 
     In another aspect, embodiments of the invention feature a method of forming single-crystal aluminum nitride (AlN). In a step (a), a first seed crystal is provided. The first seed crystal includes, consists essentially of, or consists of AlN (e.g., doped or undoped AlN). In a step (b), single-crystal AlN is deposited on the first seed crystal (e.g., on a growth face of the first seed crystal) within a first growth chamber. In a step (c), during at least some of the deposition of single-crystal AlN on the first seed crystal, diameter expansion is induced such that at least a portion of the single-crystal AlN has a diameter greater than a diameter of the first seed crystal. The diameter expansion proceeds at a first expansion rate. In a step (d), after step (c), a second seed crystal is separated from the single-crystal AlN deposited on the first seed crystal. The second seed crystal includes, consists essentially of, or consists of AlN (e.g., doped or undoped AlN). The second seed crystal has a diameter greater than the diameter of the first seed crystal. In a step (e), single-crystal AlN is deposited on the second seed crystal within a second growth chamber. In a step (f), during at least some of the deposition of single-crystal AlN on the second seed crystal, diameter expansion is induced such that at least a portion of the single-crystal AlN has a diameter greater than a diameter of the second seed crystal. The diameter expansion proceeds at a second expansion rate larger than the first expansion rate. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. The first seed crystal and/or the second seed crystal may have a c growth face. The first seed crystal may have a growth face having an N polarity. The second seed crystal may have a growth face having an Al polarity. The diameter of the second seed crystal may range from approximately 10 mm to approximately 40 mm, from approximately 10 mm to approximately 15 mm, from approximately 10 mm to approximately 20 mm, from approximately 10 mm to approximately 30 mm, from approximately 20 mm to approximately 40 mm, from approximately 20 mm to approximately 30 mm, from approximately 25 mm to approximately 40 mm, from approximately 30 mm to approximately 40 mm, or may be less than approximately 40 mm, less than approximately 35 mm, less than approximately 30 mm, less than approximately 25 mm, less than approximately 20 mm, or less than approximately 15 mm. The diameter of the second seed crystal may be at least 5 mm, at least 6 mm, at least 7 mm, at least 8 mm, at least 9 mm, or at least 10 mm. 
     The first expansion rate may be, for each 20 mm of axial growth of the single-crystal AlN, at most approximately 5 mm, at most approximately 4 mm, at most approximately 3 mm, at most approximately 2 mm, at most approximately 1.5 mm, at most approximately 1 mm, or at most approximately 0.5 mm. The second expansion rate may be, for each 20 mm of axial growth of the single-crystal AlN, at least approximately 10 mm, at least approximately 15 mm, at least approximately 20 mm, or at least approximately 25 mm. The second expansion rate may be, for each 20 mm of axial growth of the single-crystal AlN, at most approximately 50 mm, at most approximately 35 mm, at most approximately 30 mm, at most approximately 25 mm, or at most approximately 20 mm. The first growth chamber may be the same as the second growth chamber. The first growth chamber may be different from the second growth chamber. 
     In step (c), the diameter of the at least a portion of the single-crystal AlN may not exceed a transition diameter. The transition diameter may range from approximately 10 mm to approximately 40 mm, from approximately 10 mm to approximately 15 mm, from approximately 10 mm to approximately 20 mm, from approximately 10 mm to approximately 30 mm, from approximately 20 mm to approximately 40 mm, from approximately 20 mm to approximately 30 mm, from approximately 25 mm to approximately 40 mm, from approximately 30 mm to approximately 40 mm, or may be less than approximately 40 mm, less than approximately 35 mm, less than approximately 30 mm, less than approximately 25 mm, less than approximately 20 mm, or less than approximately 15 mm. The transition diameter may be at least 5 mm, at least 6 mm, at least 7 mm, at least 8 mm, at least 9 mm, or at least 10 mm. 
     A single-crystal AlN substrate may be separated from the single-crystal AlN deposited on the second seed crystal. A light-emitting device structure may be formed over the single-crystal AlN substrate to form a light-emitting device. The light-emitting device may be configured to emit visible or ultraviolet light. After forming at least a portion of the light-emitting device structure, at least a portion of the single-crystal AlN substrate may be removed from the light-emitting device. The light-emitting device may include, consist essentially of, or consist of a light-emitting diode or a laser. 
     In yet another aspect, embodiments of the invention feature a crystal assemblage that includes, consists essentially of, or consists of a first seed crystal having a growth surface, a first single-crystal AlN boule extending from the growth surface of the first seed crystal, a second seed crystal having a growth surface, and a second single-crystal AlN boule extending from the growth surface of the second seed crystal. The first seed crystal includes, consists essentially of, or consists of AlN (e.g., doped or undoped AlN). The growth face of the first seed crystal has an N polarity. The first seed crystal has a first diameter. A diameter of at least a portion of the first boule exceeds the first diameter and increases, for each 20 mm of axial length, at most approximately 5 mm, at most approximately 4 mm, at most approximately 3 mm, at most approximately 2 mm, at most approximately 1.5 mm, at most approximately 1 mm, or at most approximately 0.5 mm. The second seed crystal includes, consists essentially of, or consists of AlN (e.g., doped or undoped AlN). The growth face of the second seed crystal has an Al polarity. The second seed crystal has a second diameter greater than the first diameter. A diameter of at least a portion of the second boule exceeds the second diameter and increases, for each 20 mm of axial length, at least approximately 10 mm, at least approximately 15 mm, at least approximately 20 mm, or at least approximately 25 mm. The diameter of the at least a portion of the second boule may increase, for each 20 mm of axial growth of the single-crystal AlN, at most approximately 50 mm, at most approximately 35 mm, at most approximately 30 mm, at most approximately 25 mm, or at most approximately 20 mm. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. The second seed crystal may have been a portion of the first single-crystal AlN boule. The second seed crystal may have been or may be separated from the first single-crystal AlN boule. A maximum diameter of the first boule may not exceed a transition diameter. The transition diameter may range from approximately 10 mm to approximately 40 mm, from approximately 10 mm to approximately 15 mm, from approximately 10 mm to approximately 20 mm, from approximately 10 mm to approximately 30 mm, from approximately 20 mm to approximately 40 mm, from approximately 20 mm to approximately 30 mm, from approximately 25 mm to approximately 40 mm, from approximately 30 mm to approximately 40 mm, or may be less than approximately 40 mm, less than approximately 35 mm, less than approximately 30 mm, less than approximately 25 mm, less than approximately 20 mm, or less than approximately 15 mm. The transition diameter may be at least 5 mm, at least 6 mm, at least 7 mm, at least 8 mm, at least 9 mm, or at least 10 mm. A minimum diameter of the second boule may be no less than the transition diameter. 
     A minimum diameter of the second boule may be at least equal to a transition diameter. The transition diameter may range from approximately 10 mm to approximately 40 mm, from approximately 10 mm to approximately 15 mm, from approximately 10 mm to approximately 20 mm, from approximately 10 mm to approximately 30 mm, from approximately 20 mm to approximately 40 mm, from approximately 20 mm to approximately 30 mm, from approximately 25 mm to approximately 40 mm, from approximately 30 mm to approximately 40 mm, or may be less than approximately 40 mm, less than approximately 35 mm, less than approximately 30 mm, less than approximately 25 mm, less than approximately 20 mm, or less than approximately 15 mm. The transition diameter may be at least 5 mm, at least 6 mm, at least 7 mm, at least 8 mm, at least 9 mm, or at least 10 mm. 
     The first diameter may not exceed a transition diameter. The transition diameter may range from approximately 10 mm to approximately 40 mm, from approximately 10 mm to approximately 15 mm, from approximately 10 mm to approximately 20 mm, from approximately 10 mm to approximately 30 mm, from approximately 20 mm to approximately 40 mm, from approximately 20 mm to approximately 30 mm, from approximately 25 mm to approximately 40 mm, from approximately 30 mm to approximately 40 mm, or may be less than approximately 40 mm, less than approximately 35 mm, less than approximately 30 mm, less than approximately 25 mm, less than approximately 20 mm, or less than approximately 15 mm. The transition diameter may be at least 5 mm, at least 6 mm, at least 7 mm, at least 8 mm, at least 9 mm, or at least 10 mm. The second diameter may be no less than the transition diameter. 
     The second diameter may be at least equal to a transition diameter. The transition diameter may range from approximately 10 mm to approximately 40 mm, from approximately 10 mm to approximately 15 mm, from approximately 10 mm to approximately 20 mm, from approximately 10 mm to approximately 30 mm, from approximately 20 mm to approximately 40 mm, from approximately 20 mm to approximately 30 mm, from approximately 25 mm to approximately 40 mm, from approximately 30 mm to approximately 40 mm, or may be less than approximately 40 mm, less than approximately 35 mm, less than approximately 30 mm, less than approximately 25 mm, less than approximately 20 mm, or less than approximately 15 mm. The transition diameter may be at least 5 mm, at least 6 mm, at least 7 mm, at least 8 mm, at least 9 mm, or at least 10 mm. 
     A lateral surface of the first boule may be substantially free of planar facets (e.g., facets defining planes substantially parallel to the axial direction of the boule). A lateral surface of the second boule may be substantially free of planar facets (e.g., facets defining planes substantially parallel to the axial direction of the boule). A lateral surface of the first boule may be substantially free of polycrystalline material (e.g., polycrystalline AlN). A lateral surface of the second boule may be substantially free of polycrystalline material (e.g., polycrystalline AlN). 
     The axial length of the first boule may range from approximately 10 mm to approximately 25 mm, from approximately 10 mm to approximately 20 mm, from approximately 10 mm to approximately 15 mm, from approximately 15 mm to approximately 25 mm, or from approximately 15 mm to approximately 20 mm. The axial length of the second boule may range from approximately 20 mm to approximately 50 mm, from approximately 25 mm to approximately 50 mm, from approximately 30 mm to approximately 50 mm, or from approximately 25 to approximately 35 mm. The axial length of the second boule may be greater than the axial length of the first boule. 
     A concentration of carbon and/or oxygen within at least a portion of the first boule, within substantially the entire first boule, or within the entire first boule may be (e.g., for each of carbon and oxygen or collectively) at least approximately 10 19  cm −3 , at least approximately 10 20  cm −3 , or at least approximately 10 21  cm −3 . A concentration of carbon and/or oxygen within at least a portion of the first boule, within substantially the entire first boule, or within the entire first boule may be (e.g., for each of carbon and oxygen or collectively) at most approximately 10 22  cm −3  or at most approximately 10 21  cm −3 . A concentration of carbon and/or oxygen within at least a portion of the second boule, within substantially the entire second boule, or within the entire second boule may be (e.g., for each of carbon and oxygen or collectively) at most approximately 5×10 cm −3 , at most approximately 10 18  cm −3 , at most approximately 5×10 17  cm −3 , or at most approximately 10 17  cm −3 . A concentration of carbon and/or oxygen within at least a portion of the second boule, within substantially the entire second boule, or within the entire second boule may be (e.g., for each of carbon and oxygen or collectively) at least approximately 10 14  cm −3 , at least approximately 10 15  cm −3 , or at least approximately 10 16  cm −3 . A concentration of carbon and/or oxygen within at least a portion of the second seed crystal, within substantially the entire second seed crystal, or within the entire second seed crystal may be (e.g., for each of carbon and oxygen or collectively) at least approximately 10 19  cm −3 , at least approximately 10 20  cm −3 , or at least approximately 10 21  cm −3 . A concentration of carbon and/or oxygen within at least a portion of the second seed crystal, within substantially the entire second seed crystal, or within the entire second seed crystal may be (e.g., for each of carbon and oxygen or collectively) at most approximately 10 22  cm −3  or at most approximately 10 21  cm −3 . A concentration of carbon and/or oxygen within the second boule may be less than A concentration of carbon and/or oxygen within the second seed crystal. A concentration of carbon and/or oxygen within at least a portion of the second boule may decrease along the axial length of the second boule in a direction away from the second seed crystal. A concentration of carbon and/or oxygen within a first portion of the second boule adjoining the second seed crystal may be larger than a concentration of carbon and/or oxygen within a second portion of the second boule farther away from the second seed crystal than the first portion. A concentration of carbon and/or oxygen within the first portion of the second boule may decrease within increasing distance away from the second seed crystal. 
     These and other objects, along with advantages and features of the present invention herein disclosed, will become more apparent through reference to the following description, the accompanying drawings, and the claims. Furthermore, it is to be understood that the features of the various embodiments described herein are not mutually exclusive and may exist in various combinations and permutations. As used herein, the terms “approximately,” “about,” and “substantially” mean±10%, and in some embodiments, ±5%. All numerical ranges specified herein are inclusive of their endpoints unless otherwise specified. The term “consists essentially of” means excluding other materials that contribute to function, unless otherwise defined herein. Nonetheless, such other materials may be present, collectively or individually, in trace amounts. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the drawings, like reference characters generally refer to the same parts throughout the different views. Also, the drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the invention. In the following description, various embodiments of the present invention are described with reference to the following drawings, in which: 
         FIG. 1A  is a schematic of an AlN unit cell; 
         FIG. 1B  is a schematic cross-section of a crystal-growth chamber utilized for crystal growth in accordance with various embodiments of the invention; 
         FIG. 1C  depicts the crystal-growth chamber of  FIG. 1B  after growth of a single-crystalline boule controlled to induce diameter expansion of the boule in accordance with various embodiments of the invention; 
         FIG. 1D  is a photograph of an exemplary AlN crystal grown on an N-polarity seed crystal to a diameter past the transition diameter, whereupon edge facets have formed in the crystal; 
         FIG. 1E  is a schematic cross-section of a seed crystal separated from the boule illustrated in  FIG. 1C  in accordance with various embodiments of the invention; 
         FIG. 2A  is a schematic cross-section of a crystal-growth chamber utilized for crystal growth in accordance with various embodiments of the invention; 
         FIG. 2B  depicts the crystal-growth chamber of  FIG. 2A  after growth of a single-crystalline boule controlled to induce diameter expansion of the boule in accordance with various embodiments of the invention; 
         FIGS. 3A and 3B  are schematic cross-sections of light-emitting devices in accordance with various embodiments of the invention; and 
         FIGS. 4A and 4B  are schematic cross-sections of light-emitting devices after substrate removal in accordance with various embodiments of the invention. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1A  is a simple schematic of the AlN unit cell, in which the two crystallographic directions [0001] and [000 1 ] corresponding to +c (i.e., Al-polar) and −c (i.e., N-polar) orientations are also indicated. According to common convention, and as utilized herein, the Al face or Al-polarity face corresponds to the (0001) plane, while the N face or N-polarity face corresponds to the (000 1 ) plane. As shown in  FIG. 1A , both the Al and N faces may each be Al-terminated or N-terminated. However, likely due to lower formation energies, the Al-terminated (0001) surface and the N-terminated (000 1 ) surface tend to be more stable, and this arrangement is assumed in the present disclosure. 
       FIG. 1B  is a cross-sectional view of a crystal-growth apparatus  100  in accordance with various embodiments of the present invention. As shown, apparatus  100  contains therewithin a first AlN seed (or “seed,” or “seed crystal”)  110  mounted within a crystal-growth chamber  120 . AlN source material  130  may be disposed within and at the bottom of the growth chamber  120 . For example, the source material  130  may include, consist essentially of, or consist of high-purity AlN polycrystalline ceramic. (In other embodiments of the invention, gaseous vapor may be pumped into the growth chamber  120  and utilized directly as source material.) For example, the source material  130  may include, consist essentially of, or consist of AlN polycrystalline ceramic fabricated in accordance with U.S. Pat. No. 8,012,257, filed on Mar. 30, 2007, or U.S. Pat. No. 9,034,103, filed on Jun. 30, 2010, the entire disclosure of each of which is incorporated by reference herein. 
     The crystal-growth furnace that typically surrounds the growth chamber  120  is not shown in  FIG. 1B . Examples of such details may be found in the &#39;346 patent. In various embodiments, the furnace may include a radio-frequency (RF) heating coil, and the growth chamber (or “crucible”)  120  moves vertically relative to the heating coil (i.e., either the growth chamber  120  or the heating coil, or both, may move) in order to help form and maintain an axial thermal gradient along the direction of crystal growth from the first seed  110 . The first seed  110  may include, consist essentially of, or consist of a single-crystal AlN plate and has an exposed face having an N-polarity facing the source material  130 . Seed  110  may have any of a variety of cross-sectional shapes; in various embodiments, the cross-sectional shape of the seed crystal  110  is approximately the same as that of the growth chamber  120 , e.g., circular. 
     The first seed  110  may be produced by any of several suitable techniques, for example techniques described in U.S. Pat. No. 6,719,843, filed on Sep. 20, 2002 (the &#39;843 patent), and U.S. Pat. No. 8,123,859, filed on Jul. 22, 2010 (the &#39;859 patent), the entire disclosure of each of which is incorporated herein by reference. For example, an AlN single crystal may be grown seedlessly (or “unseeded,” e.g., within the conical tip of a crystal-growth crucible, which localizes the preferred nucleation point for the crystal), and the first seed  110  may be sliced or cut from the crystal with the desired orientation and shape. Alternatively, the first seed  110  may be produced by spontaneous nucleation of AlN within a growth crucible or apparatus, as described in C. Hartmann, et al., “Bulk AlN growth by physical vapour transport,” Semicond. Sci. Technol. Vol. 29, 084002 (2014), the entire disclosure of which is incorporated by reference herein, followed by slicing of a seed crystal having the desired orientation and shape. The thickness of the first seed  110  may range from, for example, approximately 0.2 mm to approximately 2 mm. 
     The crucible  120  may include, consist essentially of, or consist of one or more refractory materials, such as W, rhenium (Re), and/or tantalum nitride (TaN). As described in the &#39;135 patent and the &#39;153 patent, the crucible  120  may have one or more surfaces (e.g., walls) configured to selectively permit the diffusion of N therethrough and selectively prevent the diffusion of Al therethrough. In some embodiments, the apparatus  100  for growth of single-crystal AlN boules includes a crucible  120  such as the one disclosed in the &#39;843 patent, consisting essentially of W and fabricated by a CVD process. Multiple grain layers within the wall of the crucible may be obtained by interrupting the W deposition several times before the final wall thickness is obtained. Other crucible materials may be used, such as W—Re alloys; Re; tantalum monocarbide (TaC); a mixture of Ta 2 C and TaC; a mixture of Ta 2 C, TaC and Ta; Ta 2 N); a mixture of Ta and Ta 2 N; hafnium nitride (HfN); a mixture of Hf and HfN; a mixture of W and Ta; W; and combinations thereof. 
     In various embodiments of the invention, the crucible  120  is placed into a furnace (e.g., an inductively heated furnace) so that the temperature gradient between the source material  130  and the seed  110  drives vapor to move from the hotter high-purity AlN ceramic source to the cooler seed crystal  110 . The temperature at the seed interface and the temperature gradients may be monitored and carefully adjusted, if necessary, in order to nucleate high-quality monocrystalline material on the seed  110  and not destroy the AlN seed  110 . The single-crystalline AlN material may be formed at temperatures of, e.g., greater than about 2000° C. The axial and/or radial thermal gradients within the crucible  120  may be controlled via any of a variety of techniques, e.g., via the arrangement of thermal shields outside of the crucible  120 , as detailed in the &#39;612 patent. 
     The diameter (or other lateral dimension) of the first seed  110  may be relatively small to enable more effective suppression of parasitic nucleation events at the edges of the growing crystal. For example, the diameter of the seed  110  may range from approximately 5 mm to approximately 20 nm. As shown in  FIG. 1C , during the first stage of crystal growth, an AlN single crystal  140  nucleates and grows from the exposed N-polarity face of the seed  110 . As shown, the diameter (or other lateral dimension) of the crystal  140  expands beyond that of the seed  110 , during at least a portion of the growth of the crystal  140 , via imposition of a radial thermal gradient within the crucible  120 . As detailed herein, in general, increasing the radial thermal gradient increases the growth rate of a growing crystal in the radial (or “lateral”) direction and thus increases the rate of diameter expansion of the crystal due to the larger lateral growth component. 
     In addition, as described in U.S. Pat. No. 9,034,103, dopants such as Si,  0 , and/or C may be incorporated within the source material  130  for the growth of crystal  140  and may thus be incorporated within the crystal  140  as it is formed. The present inventors have discovered that incorporation of such dopants may advantageously reduce the amount of parasitic edge nucleation during growth on the seed  110 . Incorporation of the dopant(s) into the crystal  140  may result in reduced UV transparency of crystal  140  and seed crystals formed therefrom; however, lesser optical performance of such seeds may be acceptable since the seeds are merely utilized to form even larger crystals in the second growth stage. In various embodiments, the concentration of one or more dopants (e.g., Si, O, C) within the source material  130  and/or within the crystal  140  after formation is at least approximately 10 19  cm −3 . In various embodiments, the concentration of the one or more dopants is limited to approximately 10 21  cm −3  or less, e.g., to prevent deleterious segregation in crystal  140 . 
     Once the diameter of the crystal  140  reaches a transition diameter, the first stage of crystal growth is halted, and the apparatus  100  and the various elements therewithin are cooled down to approximately room temperature. In various embodiments of the invention, the transition diameter ranges from approximately 10 mm to approximately 40 nm, from approximately 10 mm to approximately 35 mm, from approximately 10 mm to approximately 30 mm, from approximately 10 mm to approximately 25 mm, from approximately 25 mm to approximately 40 mm, or from approximately 25 mm to approximately 35 mm. In various embodiments, the crystal  140  is cooled down to room temperature at a relatively high rate, e.g., approximately 300° C./hour or faster, for at least the initial stage of cooling from the growth temperature. In various embodiments, the cooling of crystal  140  is not “controlled,” i.e., not slowed via application of heat from the furnace surrounding the crucible  120 . In various embodiments, the rapid cooling of crystal  140  results in reduced UV transparency of crystal  140  and seed crystals formed therefrom; however, lesser optical performance of such seeds may be acceptable since the seeds are merely utilized to form even larger crystals in the second growth stage. For example, rapid cooling may result in increased concentrations of point defects and concomitant decreases in UV transparency, as described in U.S. Pat. No. 9,034,103. 
     The growth of the crystal  140  typically proceeds due to a relatively large axial thermal gradient (e.g., ranging from approximately 5° C./cm to approximately 100° C./cm) formed within the growth chamber  120 . A heating apparatus (not shown for clarity), e.g., an RF heater, one or more heating coils, and/or other heating elements or furnaces, heats the growth chamber  120  to an elevated temperature typically ranging between approximately 1800° C. and approximately 2300° C. The apparatus  100  may feature one or more sets of thermal shields disposed above and/or below the growth chamber  120 , arranged to create the large axial thermal gradient (by, e.g., better insulating the bottom end of growth chamber  120  and the source material  130  from heat loss than the top end of growth chamber  120  and the growing crystal  140 ), as detailed in the &#39;612 patent. During the growth process, the growth chamber  120  may be translated within the heating zone created by the heating apparatus (or, equivalently, the heating apparatus itself may be translated relative to the growth chamber  120 ) via a drive mechanism in order to maintain the axial thermal gradient near the surface of the growing crystal  140 . 
     In various embodiments, for example if the crystal  140  has not achieved the desired transition diameter during the growth process, the crystal  140  may be removed from the growth chamber and sectioned to form a new seed  110  having a larger diameter and an N-polarity surface, and the above-described growth process may be repeated. The growth process may be repeated one or more times until a crystal  140  having a diameter no less than the desired transition diameter is grown. In various embodiments, the length of crystal  140  is limited by the inner dimensions of growth chamber  120 , allowing for the presence of source material  130 . That is, in embodiments of the invention the growth of crystal  140  is halted before the crystal  140  grows to a length sufficient to contact any remaining source material  130  within the growth chamber  120 . In exemplary embodiments, the length of crystal  140  ranges from approximately 10 mm to approximately 25 mm, from approximately 10 mm to approximately 20 mm, from approximately 10 mm to approximately 15 mm, or from approximately 15 mm to approximately 20 mm. 
     The radial thermal gradient during the growth process of crystal  140  on seed  110  may be kept relatively small (e.g., non-zero) to avoid the formation of large (1-100) facets (i.e., m-plane facets) that may easily form during N-polarity growth. For example, the radial thermal gradient during the growth on seed  110  may range from approximately 0.5° C./cm to approximately 5° C./cm, from approximately 0.5° C./cm to approximately 4° C./cm, from approximately 0.5° C./cm to approximately 3° C./cm, from approximately 1° C./cm to approximately 5° C./cm, from approximately 1° C./cm to approximately 4° C./cm, or from approximately 1° C./cm to approximately 3° C./cm. Utilization of larger radial gradients (to, e.g., expand the diameter of crystal  140  more quickly) may result in defect formation in crystal  140  (due to, e.g., excessive supersaturation of the gaseous growth precursor species over the (000-1) facet). Thus, diameter expansion of crystal  140  may be relatively slow as a function of the amount of axial growth in order to maintain high crystal quality. As also detailed in the &#39;612 patent, the radial thermal gradient within the growth chamber  120  may be controlled via, e.g., selection of thickness, spacing, and/or opening size of one or more thermal shields arranged around (e.g., above and/or below) the growth chamber  120 . 
     In various embodiments of the invention, the axial growth rate of crystal  140  is limited due to difficulties related to maintaining a large axial thermal gradient in conjunction with a low radial thermal gradient. That is, the axial thermal gradient and the resulting axial growth rate may be limited in order to maintain the low radial thermal gradient. In various embodiments, the axial growth rate of the crystal  140  ranges from approximately 0.1 mm/h to approximately 0.5 mm/h, from approximately 0.1 mm/h to approximately 0.4 mm/h, from approximately 0.1 mm/h to approximately 0.3 mm/h, from approximately 0.2 mm/h to approximately 0.4 mm/h, or from approximately 0.2 mm/h to approximately 0.3 mm/h. In various embodiments of the invention, the axial growth rate of crystals grown as detailed herein may be controlled via, e.g., selection of the initial starting position of the growth chamber  120  with respect to the heating coil disposed outside of the growth chamber  120 , use of higher power to the heating coil (and therefore higher growth temperature) to increase the growth rate, selecting a smaller distance between the seed crystal and the source material to increase the growth rate, and increasing the axial thermal gradient (e.g., via selection and arrangement of thermal shields outside of the growth chamber  120 ). 
     In various embodiments, the rate of diameter expansion during growth on the first seed  110  and the transition diameter at which the growth is concluded are limited in order to prevent or substantially minimize parasitic nucleation and facet formation at the edges of crystal  140 . Applicants have discovered that application of larger radial thermal gradients during growth on N-polarity seeds such as first seed  110  may result in strong competition of crystal nuclei of different orientations at the edges of the growing crystal, and this phenomenon results in parasitic nucleation and formation of crystal regions having different domains and crystalline textures. Limiting the rate of diameter expansion results in time-consuming, uneconomical growth processes. In addition, Applicants have discovered that limiting the diameter expansion via minimization of the radial thermal gradient during crystal growth may result in the formation of slow-growing growth facets within the crystal, and the growing crystal may transition from substantially circular to hexagonal in cross-section. 
       FIG. 1D  is a photograph of an AlN single-crystal boule grown on an N-polarity seed crystal in which large m-plane {1 1 00} facets have developed during the latter stages of growth, transitioning the crystal to a hexagonal cross-sectional shape. (In  FIG. 1D , the boule has been flipped from the orientation illustratively shown in  FIG. 1C , and the original seed crystal is at the bottom.) Various embodiments of the present invention limit N-polarity growth to form crystals  140  substantially free of such facets, limit the rate of diameter expansion of growth on first seed  110 , and limit the ultimate diameter of crystal  140  to the transition diameter in order to minimize or eliminate the opposing phenomena of parasitic nucleation and edge-facet formation in crystal  140 . For example, diameter expansion of the crystal  140  may be limited to a value ranging from approximately 0.5 mm to approximately 2 mm for each iteration of growth on a first seed  110 . In various embodiments, the diameter expansion during an iteration of N-polarity growth is limited to a value of less than or equal to approximately 2 mm for each 20 mm of axial growth of the crystal  140 . 
     As shown in  FIG. 1E , the crystal  140  may be removed from the growth chamber  120  and sectioned to produce a second AlN seed crystal  150  having an exposed c face having an Al polarity. For example, after being oriented at a specific crystallographic orientation (selected via, e.g., x-ray Laue diffraction techniques as known in the art), the crystal  140  may be cut with, e.g., a diamond saw, and any resulting surface roughness and/or damage may be reduced or substantially eliminated via a polishing and/or planarization process. For example, the seed  150  may be polished in accordance with processes detailed in U.S. Pat. No. 7,037,838, the entire disclosure of which is incorporated by reference herein. An exemplary method includes performing a chemical-mechanical planarization (CMP) step by applying an abrasive suspension in a solution consisting essentially of a hydroxide. Another exemplary method is a CMP process that includes polishing a substrate using a slurry including an abrasive suspension in a solution capable of modifying the surface material of the substrate and creating a finished surface suitable for epitaxial growth. The active solution chemically modifies the surface of the substrate, forming a compound softer than the underlying substrate material. The abrasive is selected to be harder than the newly created compound, but softer than the substrate material, so that it polishes away the newly formed layer, while leaving the native substrate surface pristine and highly polished. The thickness of the second seed  150  may range from, for example, approximately 0.2 mm to approximately 2 mm. 
     In the event that the crystal  140  has developed facets over a portion of its length, exhibits parasitic edge nucleation and/or associated defects (e.g., dislocations, domain formation, phase boundaries, etc.) at its edge over a portion of its length, or otherwise was grown beyond the desired transition diameter, such portions of the crystal  140  may be removed, and the new seed  150  may be separated from a substantially facet-free portion of the crystal  140  at a length of the crystal  140 , measured from the seed  110 , not exceeding the desired transition diameter. 
       FIG. 2A  depicts an exemplary crystal-growth apparatus  200  utilized for a second growth stage during formation of AlN single crystals with accordance of embodiments of the present invention. As shown, apparatus  200  features growth chamber  120  containing the second seed  150  and source material  130  therein. While growth chamber  120  may be utilized for both the first growth stage (i.e., growth utilizing the N-polarity seed  110 ) and the second growth stage (i.e., growth utilizing the Al-polarity seed  150 ), in embodiments of the invention different growth chambers may be utilized for each of the growth stages. For example, a smaller growth chamber may be utilized for the first growth stage, as the seed and the grown crystal are smaller. A smaller growth chamber may be more easily and rapidly heated and cooled, thereby enabling higher throughput. Smaller growth chambers may also facilitate the formation and maintenance of smaller radial thermal gradients within the growth chamber. In various embodiments, the diameter (or other lateral dimension) of the growth chamber utilized for growth on the N-polarity seed  110  may be limited to approximately the transition diameter selected for the crystal (e.g., approximately 2 mm, approximately 5 mm, or approximately 10 mm greater than the transition diameter), while the diameter (or other lateral dimension) of the growth chamber utilized for growth on the Al-polarity seed  150  may be larger (e.g., at least twice, or at least three times larger). 
     In accordance with embodiments of the invention, crystal growth via PVT (e.g., sublimation-recondensation) is initiated using apparatus  200  in order to form on seed  150  an AlN single crystal  210 , as shown in  FIG. 2B . Because the seed  150  has an exposed c face having an Al polarity, the growth rate of the crystal  210  in the axial direction (i.e., toward the source material  130 ) may be increased to a rate faster than the growth rate utilized during the first growth stage. For example, the rate at which the growth chamber  120  is moved relative to the axial thermal gradient (formed via, e.g., arrangement of thermal shields relative to the growth chamber  120  and/or heating elements exterior to the growth chamber  120 ) may be faster than that utilized during the first growth stage while maintaining good crystal quality. In various embodiments of the invention, the axial growth rate of the crystal  210  may range from approximately 0.6 mm/h to approximately 1.5 mm/hr, from approximately 0.6 mm/h to approximately 1 mm/hr, from approximately 0.6 mm/h to approximately 0.8 mm/hr, from approximately 0.8 mm/h to approximately 1.5 mm/hr, or from approximately 0.8 mm/h to approximately 1 mm/hr. 
     In addition, because the seed  150  has a diameter of at least the transition diameter, parasitic nucleation at the edges of crystal  210  is suppressed or substantially eliminated. Due to the Al polarity of the seed  150 , the radial thermal gradient during growth of crystal  210  may be increased to a level beyond that utilized during the growth of crystal  140  on seed  110 . While the present inventors do not wish to be bound by any physical theory, growth on the seed  150  in the [0001] direction may proceed under larger radial thermal gradients (and thus larger resulting diameter expansion) due to the existence of relatively low energy facets between the (0001) facet and the m-plane facet (e.g., corresponding to {1-100} or {1-103} planes)—such facets may have surface energies close to the surface energy of the (0001) facet; thus, even under larger radial thermal gradients, the (0001) facet remains small and less defect introduction may occur due to supersaturation. In addition, perimeter portions of crystal  210  undergoing diameter expansion may not be subject to strong selective nucleation but will instead grow smoothly (relative to (0001) growth), resulting in high-quality material. 
     In various embodiments of the invention, the source material  130  is undoped (e.g., substantially free of dopants such as Si, O, and/or C) for the second stage of growth, and thus the crystal  210  may also be substantially free of such dopants. For example, the concentration of one or more dopants such as Si, O, and/or C within the source material  130  and the resulting crystal  210  may be less than approximately 10 19  cm −3 , less than approximately 5×10 18  cm −3 , less than approximately 10 18  cm −3 , less than approximately 5×10 17  cm −3 , or less than approximately 10 17  cm −3 . In this manner, the crystal  210  and portions thereof (e.g., wafers therefrom) may exhibit advantageously high UV transparency. 
     While the lateral surface of portions of the crystal in  FIG. 2B  (as well as crystal  140  shown in in  FIGS. 1C and 1E ) are depicted as straight and linear (in cross-section), this is not limiting, as the rate of diameter expansion during crystal growth may vary. Thus, embodiments of the present invention include crystal boules having lateral surfaces that are at least partially curved and/or at least partially composed of straight linear segments each forming a different angle with respect to the growth surface of the seed crystal (in cross section). 
     In various embodiments of the invention, the radial thermal gradient within the growth chamber  120  may be controlled to, e.g., reduce the possibility of parasitic nucleation at the edge of crystal  210  and/or to promote diameter expansion via, e.g., placement and configuration of one or more thermal shields as detailed in the &#39;612 patent. 
     As shown in  FIG. 2B  and as discussed above, the diameter of crystal  210  may also expand during growth via, e.g., control of (e.g., increasing) the radial thermal gradient within the growth chamber  120 . In various embodiments, the diameter of crystal  210  may expand to be approximately equal to the inner diameter of growth chamber  120 . That is, the diameter of crystal  210  may expand until the crystal  210  encounters the wall of growth chamber  120 , at which time axial growth of crystal  210  may continue at a substantially constant lateral diameter. At such time, or when a desired final diameter of crystal  210  has been achieved by diameter expansion, the radial thermal gradient within the growth chamber  120  may be decreased (although typically not eliminated entirely). In various embodiments, the final diameter of the crystal  210  may be at least approximately 2×, at least approximately 3×, at least approximately 4×, or at least approximately 5× the transition diameter, or even larger. For example, the final diameter of the crystal  210  may be at least 50 mm, at least 60 mm, at least 70 mm, at least 80 mm, at least 90 mm, or at least 100 mm. 
     In various embodiments, the length of crystal  210  is limited by the inner dimensions of growth chamber  120 , allowing for the presence of source material  130 . That is, in embodiments of the invention the growth of crystal  210  is halted before the crystal  210  grows to a length sufficient to contact any remaining source material  130  within the growth chamber  120 . In various embodiments, the length of crystal  210  is greater than the as-grown length of the crystal  140 . For example, the length of crystal  210  may range from approximately 20 mm to approximately 50 mm, from approximately 25 mm to approximately 50 mm, from approximately 30 mm to approximately 50 mm, or from approximately 25 to approximately 35 mm. 
     After formation of the crystal  210 , crystal  210  may be segmented into multiple AlN single-crystal wafers (e.g., as detailed for crystal  140  above) for, e.g., fabrication of electronic and/or optoelectronic devices thereon. For example, portions of crystal  210  may be utilized as substrates for subsequent epitaxial growth and processing for the formation of light-emitting diodes (LEDs) and/or lasers that emit light in the ultraviolet wavelength range. 
       FIG. 3A  schematically depicts a light-emitting device structure  300  in accordance with embodiments of the present invention. Light-emitting device structures  300  in accordance with embodiments of the invention may include, consist essentially of, or consist of, for example, light-emitting diodes or lasers. As shown, the device structure  300  includes a substrate  305 , which in various embodiments includes, consists essentially of, or consists of aluminum nitride, e.g., single-crystal aluminum nitride. In various embodiments, substrate  305  is a single-crystal substrate separated from crystal  210  after formation thereof. In various embodiments, the substrate  305  may not be transparent (at least not fully transparent) to radiation emitted by the device structure  300  (e.g., UV radiation). Substrate  305  may be miscut such that the angle between its c-axis and its surface normal is between approximately 0° and approximately 4°. In various embodiments, the misorientation of the surface of substrate  305  is less than approximately 0.3°, e.g., for substrates  305  that are not deliberately or controllably miscut. In other embodiments, the misorientation of the surface of substrate  305  is greater than approximately 0.3°, e.g., for substrates  305  that are deliberately and controllably miscut. In various embodiments, the direction of the miscut is towards the a-axis. 
     The surface of substrate  305  may have a group-III (e.g., Al—) polarity, and may be planarized, e.g., by chemical-mechanical polishing. The RMS surface roughness of substrate  305  may be less than approximately 0.5 nm for a 10 μm×10 μm area. In some embodiments, atomic-level steps are detectable on the surface when probed with an atomic-force microscope. The threading dislocation density of substrate  305  may be measured using, e.g., etch pit density measurements after a 5 minute KOH—NaOH eutectic etch at 450° C. In various embodiments, the threading dislocation density is less than approximately 2×10 3  cm −3 . In some embodiments substrate  305  has an even lower threading dislocation density. Substrate  305  may be topped with a homoepitaxial layer (not shown) that may include, consist essentially of, or consist of doped or undoped AlN. 
     The various layers of device structure  300  disposed over substrate  305  may be formed by any of a variety of different techniques, e.g., epitaxial growth techniques such as chemical vapor deposition (CVD) methods such as metallorganic CVD (MOCVD). 
     In accordance with embodiments of the invention, a release layer  310  may be disposed over the substrate  305  to facilitate later removal of all or a portion of the substrate  305  from the rest of device structure  300 , for example as described in U.S. patent application Ser. No. 15/977,031, filed on May 11, 2018 (the &#39;031 patent application), the entire disclosure of which is incorporated by reference herein. In various embodiments, the release layer  310  is substantially lattice-matched to the substrate  305 . Minimizing the lattice mismatch between the release layer  310  and the substrate  305  advantageously reduces or eliminates, for example, cracking and/or defect introduction in the release layer  310  and island formation (i.e., three-dimensional growth) during growth of the release layer  310 . (As used herein, a layer that is “substantially lattice-matched” to a substrate or another layer has an unstrained lattice parameter sufficiently close to that of the substrate or other layer to enable epitaxial growth of the layer thereover such that the layer is approximately lattice-relaxed, or tensilely or compressively strained without significant strain relaxation (e.g., less than 20% relaxation, or even less than 10% relaxation), and/or to enable epitaxial growth of the layer without introduction of cracks and/or defects (e.g., dislocations) at densities exceeding those, if any, present in the underlying substrate or layer.) In various embodiments, the lattice mismatch between the release layer  310  and the substrate  305  is less than ±5%, less than ±3%, less than ±2%, less than ±1%, less than ±0.5%, less than ±0.2%, or less than ±0.1%. In various embodiments, it may be preferable to reduce the lattice mismatch when the release layer  310  is tensilely strained (i.e., the unstrained, innate in-plane lattice spacing of the release layer  310  is smaller than that of substrate  305 ) in order to minimize or eliminate stress-relieving cracking in the release layer  310 . In various embodiments, when the release layer  310  is compressively strained, the lattice mismatch to the substrate  305  may be larger but may be a function of the thickness of release layer  310 . For example, compressively strained release layers  310  having too much lattice mismatch to the substrate  305  and too large a thickness may island during layer growth. Thus, in various embodiments, a release layer  310  having a compressive lattice mismatch with substrate  305  of approximately 3% may have a thickness no more than approximately 10 nm. For layers with less lattice mismatch, the thickness may be larger. 
     In various embodiments, the release layer  310  includes, consists essentially of, or consists of AlN or AlGaN doped with one or more impurities that form an absorption band within the release layer  310  for a wavelength of light not strongly absorbed by the substrate  305  itself. For example, the release layer  310  may include, consist essentially of, or consist of AlN doped with oxygen, which has an absorption band at approximately 310 nm. Since an AlN substrate  305  does not strongly absorb light having wavelengths larger than approximately 300 nm, absorption of light within, and concomitant local heating of, the release layer  310  may be utilized to remove the substrate  305  from the device structure  300 . In various embodiments, the release layer  310  may be doped with oxygen (O) and/or one or more other dopants, for example, carbon (C), iron (Fe), manganese (Mn), or gadolinium (Gd). Such dopants may be introduced (e.g., as an additional gaseous species) during epitaxial growth of the release layer  310 . In other embodiments, some or all of the dopant may be introduced after epitaxial growth of at least a portion of the release layer  310  by techniques such as ion implantation or dopant diffusion (e.g., from a solid or gaseous source). In various embodiments of the invention, one or more of the dopants may be introduced into and/or present within the release layer  310  at a concentration of at least for example, approximately 10 17  cm −3 , at least approximately 10 18  cm −3 , or even at least 10 19  cm −3 . In various embodiments of the invention, one or more of the dopants may be introduced into and/or present within the release layer  310  at a concentration of at most for example, approximately 10 20  cm −3 , or at most approximately 10 21  cm −3 . 
     In exemplary embodiments, a release layer  310  including, consisting essentially, or consisting of AlN doped with oxygen may exhibit an absorption band at a wavelength of approximately 310 nm, and a release layer  310  including, consisting essentially, or consisting of AlN doped with carbon may exhibit an absorption band at a wavelength of approximately 265 nm. In such embodiments, radiation for substrate separation may be applied via, for example, a KrF laser (emission wavelength of approximately 248 nm) or a XeCl laser (emission wavelength of approximately 308 nm). 
     In various embodiments, release layer  310  may include, consist essentially of, or consist of a semiconductor other than AlN (e.g., AlGaN), and which may contain one or more dopants forming one or more absorption bands for light that is not strongly absorbed by substrate  305 . In various embodiments, the release layer  310  may include, consist essentially of, or consist of a nitride alloy containing one or more of boron, aluminum, gallium, and/or indium. The release layer  310  may even include, consist essentially of, or consist of silicon carbide or a metal nitride (in which the metal is, e.g., one or more of Sc, Y, La, Ti, or Ta). For example, a release layer  310  including, consisting essentially, or consisting of silicon carbide may exhibit an absorption band at a wavelength of approximately 376 nm, and a release layer  310  including, consisting essentially, or consisting of titanium nitride may exhibit an absorption band at a wavelength of approximately 365 nm. In various embodiments, the release layer  310  is substantially lattice-matched to substrate  305 . 
     In various embodiments, multiple release layers  310  may be present within device structure  300 , and each release layer  310  may have one or more absorption bands different from one or all absorption bands in the other release layer(s)  310 . For example, multiple release layers  310  including, consisting essentially of, or consisting of AlN or AlGaN may be formed (e.g., epitaxially grown), where each release layer  310  is doped with a different one of the dopants referred to above. In various embodiments, one or more release layers  310  may be tensilely strained with respect to the substrate  305 , and/or one or more release layers  310  may be compressively strained with respect to the substrate  305 . In various embodiments of the invention, release layer  310  is not present within the device structure  300 . 
     Device structure  300  also includes an active light-emitting structure  315  disposed over the release layer  310 , if the release layer  310  is present, as shown in  FIG. 3A . For example, the active structure  315  may include a bottom contact layer  320 . In various embodiments, the bottom contact layer  320  is n-type doped, e.g., doped with an impurity such as P, As, Sb, C, H, F, O, Mg, and/or Si. The bottom contact layer  320  may include, consist essentially of, or consist of, for example, AlN or Al x Ga 1-x N. In an embodiment, an optional graded buffer layer (not shown) is disposed above substrate  305  and below bottom contact layer  320  (and, in various embodiments, below the release layer  310 , if the release layer  310  is present). The graded buffer layer may include, consist essentially of, or consist of one or more semiconductor materials, e.g., Al x Ga 1-x N. In various embodiments, the graded buffer layer has a composition approximately equal to that of substrate  305  at the bottom interface of the graded buffer layer in order to promote two-dimensional growth and avoid deleterious islanding (such islanding may result in undesired elastic strain relief and/or surface roughening in the graded buffer layer and subsequently grown layers). The composition of the graded buffer layer at an interface with bottom contact layer  320  (or release layer  310 , if present) may be chosen to be close to (e.g., approximately equal to) that of the desired active region of the device (e.g., the Al x Ga 1-x N concentration that will result in the desired wavelength emission from the light-emitting device). In an embodiment, the graded buffer layer includes, consists essentially of, or consists of doped or undoped Al x Ga 1-x N graded from an Al concentration x of approximately 100% to an Al concentration x ranging from approximately 60% to approximately 85%. 
     The bottom contact layer  320  may have a thickness sufficient to prevent current crowding after device fabrication and/or to stop on during etching to fabricate contacts. For example, the thickness of bottom contact layer  320  may range from approximately 100 nm to approximately 500 nm, or from approximately 100 nm to approximately 2 μm. When utilizing a bottom contact layer  320 , the final light-emitting device may be fabricated with back-side contacts. In various embodiments, bottom contact layer  320  will have high electrical conductivity even with a small thickness due to the low defect density maintained when the layer is pseudomorphic. As utilized herein, a pseudomorphic film is one where the strain parallel to the interface between the film and an underlying layer or substrate is approximately that needed to distort the lattice in the film to match that of the substrate (or a relaxed, i.e., substantially unstrained, layer over the substrate and below the pseudomorphic film). Thus, the parallel strain in a pseudomorphic film will be nearly or approximately equal to the difference in lattice parameters between an unstrained substrate parallel to the interface and an unstrained epitaxial layer parallel to the interface. 
     Active structure  315  is configured for the emission of light in response to an applied voltage. Thus, the active structure  315  may include a multiple-quantum well (“MQW”) layer  325  disposed above bottom contact layer  320 . In various embodiments, MQW layer  325  is disposed directly on the bottom contact layer  320 . In other embodiments, an optional layer (e.g., an undoped layer including, consisting essentially of, or consisting of an undoped semiconductor material such as AlGaN) may be disposed between the bottom contact layer  320  and the MQW layer  325 . The MQW layer  325  may be doped with the same doping polarity as the bottom contact layer  320 , e.g., n-type doped. The MQW layer  325  may include, consist essentially of, or consist of one or more quantum wells separated by (or surrounded on both sides by) barriers. For example, each period of MQW layer  325  may feature an Al x Ga 1-x N quantum well and an Al y Ga 1-y N barrier, where x is different from y. Typically, y is greater than 0.4 for light-emitting devices designed to emit light having a wavelength less than 300 nm and may be greater than 0.7 for shorter-wavelength emitters. It may even be greater than 0.9 for devices designed to emit at wavelengths shorter than 250 nm. The value of x will, at least in part, determine the emission wavelength of the device. For emission wavelengths longer than 280 nm, x may be as low as 0.2. For wavelengths between 250 nm and 280 nm, x may vary between 0.2 and 0.7. For wavelengths shorter than 250 nm, x may be greater than 0.6. In various embodiments, the difference between x and y is large enough to obtain good confinement of the electrons and holes in the active region, thus enabling high ratio of radiative recombination to non-radiative recombination. In an embodiment, the difference between x and y is approximately 0.25, e.g., x is approximately 0.5 and y is approximately 0.75. MQW layer  325  may include a plurality of such periods, and may have a total thickness ranging from 20 nm to 100 nm, or less than approximately 50 nm. In various embodiments of the invention, the active light-emitting structure  315  is configured to (e.g., has a MQW layer  325  having layer composition(s) selected to) emit ultraviolet light. 
     In various embodiments of the invention, an electron-blocking layer  330  may be disposed over MQW layer  325 . The electron-blocking layer  330  typically has a wider band gap than that of a band gap within the MQW layer  325  (e.g., a band gap of the barrier layers therewithin). In various embodiments, the electron-blocking layer  330  may include, consist essentially of, or consist of e.g., Al x Ga 1-x N, and electron-blocking layer  330  may be doped. For example, the electron-blocking layer  330  may be doped with the same doping polarity as that of bottom contact layer  320  and/or MQW layer  325  (e.g., n-type doped). In various embodiments, the value of x in the electron-blocking layer  330  is greater than the value of the Al mole fraction in the barrier layers used in the MQW layer  325 . For longer wavelength devices with emission wavelengths greater than 300 nm, x may be as low as 0.4 and may be greater than 0.7 for shorter wavelength devices. It may even be greater than 0.9 for devices designed to emit at wavelengths shorter than 250 nm. Electron-blocking layer  330  may have a thickness that may range, for example, between approximately 10 nm and approximately 50 nm, or even between approximately 10 nm and approximately 30 nm. In various embodiments of the invention, the electron-blocking layer  330  is sufficiently thin (e.g., thickness less than about 30 nm, or less than about 20 nm) so as to facilitate carrier (e.g., hole) tunneling through the electron-blocking layer  330 . In various embodiments of the invention, the electron-blocking layer  330  is omitted from device structure  300 . 
     As shown in  FIG. 3A , device structure  300  may also include a graded layer  335  disposed above the electron-blocking layer  330  (or above the MQW layer  325  in embodiments in which electron-blocking layer  330  is omitted), and a cap layer (or “top contact layer”)  340  may be disposed over the graded layer  335 . The cap layer  340  may be doped with a doping polarity opposite of that of the bottom contact layer  320 , e.g., p-type doped with one or more dopants such as Mg, Be, and/or Zn. In other embodiments, the cap layer  340  may be undoped, as carriers (e.g., holes) may be injected from an electrode into a two-dimensional carrier gas disposed at the interface between the cap layer  340  and the graded layer  335 . (While in exemplary embodiments described herein the cap layer  340  is doped p-type and the bottom contact layer  320  is doped n-type, embodiments in which the doping polarities of these layers are switched are within the scope of the present invention; in such embodiments, the electron-blocking layer  330 , if present, may be considered to be a “hole-blocking layer,” as understood by those of skill in the art.) The cap layer  340  may have a thickness ranging from, e.g., approximately 1 nm to approximately 100 nm, or approximately 1 nm to approximately 50 nm, or approximately 1 nm to approximately 20 nm. In various embodiments, the cap layer  340  includes, consists essentially of, or consists of Al x Ga 1-x N, and in various embodiments the aluminum concentration x may range from 0 (i.e., pure GaN) to approximately 0.2. 
     The device structure  300  may also incorporate one or more metallic contacts to facilitate electrical contact to the device. For example, one metallic contact may include or consist essentially of an electrode layer  345  disposed above or on the cap layer  340 . The composition and/or shape of the electrode layer  345  are not particularly limited as long as it enables the injection of carriers (e.g., holes) into the cap layer  340 . In embodiments in which holes are injected into a p-type doped nitride-based semiconductor cap layer  340 , the electrode layer  345  may include, consist essentially of, or consist of one or more metals having large work functions, e.g., Ni, Au, Pt, Ag, Rh, and/or Pd, alloys or mixtures of two or more of these metals, or oxide-based and/or transparent electrode materials such as indium tin oxide (ITO). In embodiments in which electrons are injected into an n-type doped nitride-based semiconductor cap layer  340 , the electrode layer  345  may include, consist essentially of, or consist of one or more metals, e.g., Ti, Al, Au, Pt, Ni, and/or V, alloys or mixtures of two or more of these metals, or oxide-based and/or transparent electrode materials such as indium tin oxide (ITO). Electrode layers  345  in accordance with embodiments of the invention are not limited to these materials. The thickness of the electrode layer  345  may be, for example, between approximately 10 nm and approximately 100 nm, or between approximately 10 nm and approximately 50 nm, or between approximately 10 nm and approximately 30 nm, or between approximately 25 nm and approximately 40 nm. In various embodiments, the electrode layer  345  is formed after removal of all or a portion of the substrate  305 . 
     In various embodiments, a second electrode layer  350  may be formed in electrical contact with (and, in various embodiments, direct mechanical contact with) the bottom contact layer  320 , even if the substrate  305  is not removed, as shown in  FIG. 3B ; such an electrode layer  350  may be considered to be a “bottom electrode layer.” For example, a portion of the active structure  315  may be removed by, e.g., conventional photolithography and wet and/or dry etching, in order to reveal at least a portion of the bottom contact layer  320 . The second electrode layer  350  may then be deposited on the bottom contact layer. The composition and/or shape of the bottom electrode layer  350  are not particularly limited as long as it enables the injection of carriers (e.g., electrons) into the bottom contact layer  320 . In embodiments in which electrons are injected into an n-type doped nitride-based semiconductor bottom contact layer  320 , the bottom electrode layer  350  may include, consist essentially of, or consist of one or more metals such as one or more metals, e.g., Ti, Al, Au, Pt, Ni, and/or V, alloys or mixtures of two or more of these metals, or oxide-based and/or transparent electrode materials such as indium tin oxide (ITO). In embodiments in which holes are injected into a p-type doped nitride-based semiconductor bottom contact layer  320 , the bottom electrode layer  350  may include, consist essentially of, or consist of one or more metals having large work functions, e.g., Ni, Au, Pt, Ag, Rh, and/or Pd, alloys or mixtures of two or more of these metals, or oxide-based and/or transparent electrode materials such as indium tin oxide (ITO). Bottom electrode layers  350  in accordance with embodiments of the invention are not limited to these materials. The thickness of the bottom electrode layer  350  may be, for example, between approximately 10 nm and approximately 100 nm, or between approximately 10 nm and approximately 50 nm, or between approximately 10 nm and approximately 30 nm, or between approximately 25 nm and approximately 40 nm. 
     As mentioned above, embodiments of the present invention feature a graded layer  335  disposed between the cap layer  340  and the electron-blocking layer  330  (or the MQW layer  315  in embodiments in which the electron-blocking layer  330  is omitted). The graded layer  335  typically includes, consists essentially of, or consists of a nitride semiconductor, e.g., a mixture or alloy of Ga, In, and/or Al with N. The compositional gradient within graded layer  335  may be substantially continuous or stepped, and the grading rate within the graded layer  335  may be substantially constant or may change one or more times within the thickness of graded layer  335 . The graded layer  335  may be undoped. In other embodiments, the graded layer  335  is doped n-type or p-type with one or more dopants, e.g., C, H, F, O, Mg, Be, Zn, and/or Si. The thickness of the graded layer  335  may be, for example, between approximately 5 nm and approximately 100 nm, between approximately 10 nm and approximately 50 nm, or between approximately 20 nm and approximately 40 nm. In various embodiments, the epitaxial growth process utilized to form the various layers of the device structure  300  may be temporarily halted between growth of the graded layer  335  and the underlying layer and/or the overlying layer. In various embodiments, the graded layer  335  is pseudomorphically strained to one or more of the underlying layers and/or to the substrate  305 . 
     In various embodiments of the invention, one or more (or even all) of the layers of device structure  300  formed over substrate  305  may be pseudomorphically strained, similar to device layers described in U.S. Pat. No. 9,437,430, filed on Jan. 25, 2008, U.S. Pat. No. 8,080,833, filed on Apr. 21, 2010, and U.S. Pat. No. 9,299,880, filed on Mar. 13, 2014, the entire disclosure of each of which is incorporated by reference herein. Thus, as detailed therein, in various embodiments, one or more of the layers of device structure  300  may be pseudomorphic and may have a thickness greater than its predicted (e.g., via the Maxwell-Blakeslee theory) critical thickness. Moreover, the collective layer structure of device structure  300  may have a total thickness greater than the predicted critical thickness for the layers considered collectively (i.e., for a multiple-layer structure, the entire structure has a predicted critical thickness even when each individual layer would be less than a predicted critical thickness thereof considered in isolation). In other embodiments, one or more layers of device structure  300  are pseudomorphically strained and cap layer  340  is partially or substantially fully relaxed. For example, the lattice mismatch between cap layer  340  and substrate  305  and/or MQW layer  335  may be greater than approximately 1%, greater than approximately 2%, or even greater than approximately 3%. In an exemplary embodiment, cap layer  340  includes, consists essentially of, or consists of undoped or doped GaN, substrate  305  includes, consists essentially of, or consists of doped or undoped single-crystalline AlN, and MQW layer  325  includes, consists essentially of, or consists of multiple Al 0.55 Ga 0.45 N quantum wells interleaved with Al 0.75 Ga 0.25 N barrier layers, and cap layer  340  is lattice mismatched by approximately 2.4%. Cap layer  340  may be substantially relaxed, i.e., may have a lattice parameter approximately equal to its theoretical unstrained lattice constant. A partially or substantially relaxed cap layer  340  may contain strain-relieving dislocations having segments threading to the surface of cap layer  340  (such dislocations may be termed “threading dislocations”). The threading dislocation density of a relaxed cap layer  340  may be larger than that of substrate  305  and/or layers underlying cap layer  340  by, e.g., one, two, or three orders of magnitude, or even more. 
     In accordance with embodiments of the present invention, application of light (e.g., laser light) and/or heat may be utilized to separate the substrate  305  from the rest of device structure  300 , as detailed in the &#39;031 patent application. Before such substrate separation, the device structure  300  may be attached to a handle wafer (not shown) by, for example, wafer bonding or an adhesive material. In various embodiments, the device structure  300  may be wafer bonded to the handle wafer via use of an intermediate material such as, for example, photoresist (e.g., SU-8), glass frit, an organic material such as benzocyclobutene (BCB), etc. Wafer bonding techniques, including reversible ones (i.e., techniques in which the handle wafer is straightforwardly removed after bonding and processing) are known to those of skill in the art and may be accomplished without undue experimentation. The handle wafer may be at least substantially transparent to light emitted by the active structure  315  and/or to light utilized to separate substrate  305  (e.g., via absorption within release layer  310 ). The handle wafer may include, consist essentially of, or consist of, for example, one or more semiconductor materials, sapphire, quartz, etc. For substrate separation, heat and/or light having a wavelength corresponding to an absorption band within release layer  310  (e.g., approximately 310 nm for oxygen-doped AlN) may be emitted into the device structure  300  (e.g., from below the substrate  105  and/or from one or more sides of the bonded structure). (As utilized herein, a wavelength “corresponding to” an absorption band is sufficiently close to the absorption band such that an amount of the light sufficient to effect at least partial release of an underlying substrate and/or layer is absorbable within the layer having the absorption band.) In various embodiments, the light is primarily composed of or contains a wavelength that is within ±20 nm, within ±10 nm, within ±5 nm, within ±2 nm, or within ±1 nm of the wavelength of an absorption band within the release layer  310 . In various embodiments, the release layer  310  may have more than one absorption band (due to, e.g., introduction of two or more different dopants), and the light may be primarily composed of or contain one or more wavelengths that are within ±20 nm, within ±10 nm, within ±5 nm, within ±2 nm, or within ±1 nm of the wavelength of one or more of the absorption bands within the release layer  310 . Absorption of the light and/or heat within the release layer  310  results in local heating within the release layer  310 , which may be magnified for release layers  310  having lower thermal conductivity. The local heating results in crack formation and subsequent fracture within the release layer  310  and/or at the interface between release layer  310  and substrate  305 , thereby removing the substrate  305  (or at least a portion thereof) from device structure  300 . In various embodiments of the invention, the light may be applied at a fluence ranging from, for example, approximately 500 mJ/cm 2  to approximately 1000 mJ/cm 2 . In various embodiments of the invention, the light may be applied as one or more pulses. Such pulses may have durations ranging from, for example, approximately 10 ms to approximately 100 ms. 
     In various embodiments, at least a portion of the release layer  310  remains attached to the device structure  300  upon removal of the substrate  305 . After removal of the substrate  305 , any remaining portion of the release layer  310  may be removed (e.g., by selective etching or grinding and/or polishing). A metallic contact may be formed in contact with the bottom contact layer  320 , and the device structure  300  may be utilized to emit light without absorption thereof by substrate  305 . The metallic contact may be formed on the “bottom” surface of the bottom contact layer  320  (i.e., the surface of the bottom contact layer  320  opposite the top contact layer), or a portion of the structure may be etched away so that the metallic contact may be formed on a thusly revealed “top” surface of the bottom contact layer (i.e., the surface of the bottom contact layer  320  opposite the prior location of substrate  305 ). In various embodiments, any handle wafer used in the substrate-separation process is removed from the device structure  300 , while in other embodiments, the handle wafer remains attached to the device structure  300 . 
     As mentioned, after removal of all or a portion of the substrate  305 , electrical contacts may be made to the bottom contact layer  320  and the cap layer  340  so that power may be applied to the device structure  300 , resulting in light emission therefrom.  FIGS. 4A and 4B  depict different device structures  400  in accordance with various embodiments, in which a bottom electrode layer  410  is formed below the newly exposed bottom contact layer  120  after removal of the substrate  305  ( FIG. 4A ) and on top of a portion of bottom contact layer  320  after removal of the substrate  305  and masking and removal of a portion of the active structure  315  ( FIG. 4B ). The composition and/or shape of the bottom electrode layer  410  are not particularly limited as long as it enables the injection of carriers (e.g., electrons) into the bottom contact layer  320 . In embodiments in which electrons are injected into an n-type doped nitride-based semiconductor bottom contact layer  320 , the bottom electrode layer  410  may include, consist essentially of, or consist of one or more metals such as one or more metals, e.g., Ti, Al, Au, Pt, Ni, and/or V, alloys or mixtures of two or more of these metals, or oxide-based and/or transparent electrode materials such as indium tin oxide (ITO). In embodiments in which holes are injected into a p-type doped nitride-based semiconductor bottom contact layer  320 , the bottom electrode layer  410  may include, consist essentially of, or consist of one or more metals having large work functions, e.g., Ni, Au, Pt, Ag, Rh, and/or Pd, alloys or mixtures of two or more of these metals, or oxide-based and/or transparent electrode materials such as indium tin oxide (ITO). Bottom electrode layers  410  in accordance with embodiments of the invention are not limited to these materials. The thickness of the bottom electrode layer  410  may be, for example, between approximately 10 nm and approximately 100 nm, or between approximately 10 nm and approximately 50 nm, or between approximately 10 nm and approximately 30 nm, or between approximately 25 nm and approximately 40 nm. 
     After formation of the electrodes  345  and/or  410 , the resulting light-emitting device may be electrically connected to a package, for example as detailed in U.S. Pat. No. 9,293,670, filed on Apr. 6, 2015 (the &#39;670 patent), the entire disclosure of which is incorporated by reference herein. A lens may also be positioned on the device to transmit (and, in various embodiments, shape) the light emitted by the device. For example, a rigid lens may be disposed over the device as described in the &#39;670 patent or in U.S. Pat. No. 8,962,359, filed on Jul. 19, 2012, or in U.S. Pat. No. 9,935,247, filed on Jul. 23, 2015, the entire disclosure of each of which is incorporated by reference herein. After packaging, any handle wafer remaining on the active structure  315  may be removed. 
     The growth of bulk single crystals has been described herein primarily as being implemented by what is commonly referred to as a “sublimation” or “sublimation-recondensation” technique wherein the source vapor is produced at least in part when, for production of AlN, crystalline solids of AlN or other solids or liquids containing AlN, Al or N sublime preferentially. However, the source vapor may be achieved in whole or in part by the injection of source gases or the like techniques that some would refer to as “high-temperature CVD.” Also, other terms are sometimes used to describe these and techniques that are used to grow bulk single AlN crystals in accordance with embodiments of the invention. Therefore, the terms “depositing,” “growing,” “depositing vapor species,” and like terms are used herein to generally cover those techniques by which the crystal may be grown pursuant to embodiments of this invention. 
     The terms and expressions employed herein are used as terms of description and not of limitation, and there is no intention, in the use of such terms and expressions, of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention claimed.