Patent Publication Number: US-10319881-B2

Title: Device including transparent layer with profiled surface for improved extraction

Description:
REFERENCE TO RELATED APPLICATIONS 
     The current application is a continuation-in-part of U.S. application Ser. No. 15/149,782, which was filed on 9 May 2016, and which is a continuation of U.S. application Ser. No. 14/297,656, which was filed on 6 Jun. 2014, now U.S. Pat. No. 9,337,387, issued on 10 May 2016, and which is continuation-in-part of U.S. application Ser. No. 13/517,711, which was filed on 14 Jun. 2012, now U.S. Pat. No. 9,142,741, issued on 22 Sep. 2015, and which claims the benefit of U.S. Provisional Application No. 61/497,489, which was filed on 15 Jun. 2011, all of which are hereby incorporated by reference. 
    
    
     GOVERNMENT LICENSE RIGHTS 
     This invention was made with Federal government support under Contract No. W911 NF-10-2-0023 awarded by Defense Advanced Research Projects Agency (DARPA). The government has certain rights in the invention. 
    
    
     TECHNICAL FIELD 
     The disclosure relates generally to emitting devices, and more particularly, to an emitting device with improved light extraction. 
     BACKGROUND ART 
     Semiconductor emitting devices, such as light emitting diodes (LEDs) and laser diodes (LDs), include solid state emitting devices composed of group III-V semiconductors. A subset of group III-V semiconductors includes group III nitride alloys, which can include binary, ternary and quaternary alloys of indium (In), aluminum (Al), gallium (Ga), and nitrogen (N). Illustrative group III nitride based LEDs and LDs can be of the form In y Al x Ga 1−x−y N, where x and y indicate the molar fraction of a given element, 0≤x, y≤1, and 0≤x+y≤1. Other illustrative group III nitride based LEDs and LDs are based on boron (B) nitride (BN) and can be of the form Ga z In y Al x B 1−x−y−z N, where 0≤x, y, z≤1, and 0≤x+y+z≤1. 
     An LED is typically composed of semiconducting layers. During operation of the LED, an applied bias across doped layers leads to injection of electrons and holes into an active layer where electron-hole recombination leads to light generation. Light is generated with uniform angular distribution and escapes the LED die by traversing semiconductor layers in all directions. Each semiconducting layer has a particular combination of molar fractions (e.g., x, y, and z) for the various elements, which influences the optical properties of the layer. In particular, the refractive index and absorption characteristics of a layer are sensitive to the molar fractions of the semiconductor alloy. 
     An interface between two layers is defined as a semiconductor heterojunction. At an interface, the combination of molar fractions is assumed to change by a discrete amount. A layer in which the combination of molar fractions changes continuously is said to be graded. Changes in molar fractions of semiconductor alloys can allow for band gap control, but can lead to abrupt changes in the optical properties of the materials and result in light trapping. A larger change in the index of refraction between the layers, and between the substrate and its surroundings, results in a smaller total internal reflection (TIR) angle (provided that light travels from a high refractive index material to a material with a lower refractive index). A small TIR angle results in a large fraction of light rays reflecting from the interface boundaries, thereby leading to light trapping and subsequent absorption by layers or LED metal contacts. 
     Roughness at an interface allows for partial alleviation of the light trapping by providing additional surfaces through which light can escape without totally internally reflecting from the interface. Nevertheless, light only can be partially transmitted through the interface, even if it does not undergo TIR, due to Fresnel losses. Fresnel losses are associated with light partially reflected at the interface for all the incident light angles. Optical properties of the materials on each side of the interface determines the magnitude of Fresnel losses, which can be a significant fraction of the transmitted light. 
     SUMMARY OF THE INVENTION 
     Aspects of the invention provide a profiled surface for improving the propagation of radiation through an interface. The profiled surface includes a set of large roughness components providing a first variation of the profiled surface having a characteristic scale approximately an order of magnitude larger than a target wavelength of the radiation. The set of large roughness components can include a series of truncated shapes. The profiled surface also includes a set of small roughness components superimposed on the set of large roughness components and providing a second variation of the profiled surface having a characteristic scale on the order of the target wavelength of the radiation. 
     A first aspect of the invention provides a device comprising: an at least partially transparent layer having a first side and a second side, wherein radiation enters the at least partially transparent layer through the first side and exits the at least partially transparent layer through the second side, and wherein at least one of the first side or the second side comprises a profiled surface, the profiled surface including: a set of large roughness components providing a first variation of the profiled surface having a characteristic scale approximately an order of magnitude larger than a target wavelength of the radiation, wherein the set of large roughness components comprise a series of truncated shapes; and a set of small roughness components providing a second variation of the profiled surface having a characteristic scale on the order of the target wavelength of the radiation, wherein the set of small roughness components are superimposed on the set of large roughness components. 
     A second aspect of the invention provides a method comprising: designing a profiled surface for an at least partially transparent layer of a device, wherein radiation passes through the profiled surface during operation of the device, wherein the profiled surface includes: a set of large roughness components providing a first non-uniform variation of the profiled surface having a characteristic scale approximately an order of magnitude larger than a target wavelength of the radiation, wherein the set of large roughness components comprise a series of truncated shapes; and a set of small roughness components providing a second non-uniform variation of the profiled surface having a characteristic scale on the order of the target wavelength of the radiation, wherein the set of small roughness components are superimposed on the set of large roughness components. 
     A third aspect of the invention provides an emitting device comprising: an active region configured to generate radiation having a peak wavelength; and an at least partially transparent layer on a first side of the active region, wherein radiation generated in the active region passes through the at least partially transparent layer, and wherein the at least partially transparent layer includes at least one profiled surface, wherein the at least one profiled surface includes: a set of large roughness components providing a first variation of the profiled surface having a characteristic scale approximately an order of magnitude larger than a target wavelength of the radiation, wherein the set of large roughness components comprise a series of truncated shapes; and a set of small roughness components providing a second variation of the profiled surface having a characteristic scale on the order of the target wavelength of the radiation, wherein the set of small roughness components are superimposed on the set of large roughness components. 
     The illustrative aspects of the invention are designed to solve one or more of the problems herein described and/or one or more other problems not discussed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other features of the disclosure will be more readily understood from the following detailed description of the various aspects of the invention taken in conjunction with the accompanying drawings that depict various aspects of the invention. 
         FIG. 1  shows a schematic structure of an illustrative emitting device according to an embodiment. 
         FIGS. 2A and 2B  show an illustrative roughness element and an illustrative model for a roughness element, respectively, according to an embodiment. 
         FIG. 3  shows the effect of the small roughness component on transmission over a range of angles of incidence according to an embodiment. 
         FIG. 4  shows the effect of the dimensions of the small roughness component on the graded refractive index according to an embodiment. 
         FIGS. 5A and 5B  show illustrative schematics of roughness elements with a constant index of refraction and a graded index of refraction, respectively, according to an embodiment. 
         FIGS. 6A and 6B  show illustrative distributions of light and the corresponding light extraction efficiencies (LEE) for a constant index of refraction cone and a graded index of refraction cone, respectively, according to an embodiment. 
         FIGS. 7A-7C  show illustrative large roughness components and a corresponding illustrative polar plot of intensity according to embodiments. 
         FIGS. 8A-8B  show illustrative profiled surfaces according to embodiments. 
         FIGS. 9A-9B  show illustrative profiled surfaces according to embodiments. 
         FIG. 10  shows an illustrative perspective top view of a profiled surface according to an embodiment. 
         FIG. 11  shows an illustrative perspective top view of a profiled surface according to an embodiment. 
         FIG. 12  shows an illustrative top view of a profiled surface according to an embodiment. 
         FIG. 13  shows a partial view of an illustrative device according to an embodiment. 
         FIG. 14  shows a profiled surface of an illustrative substrate according to an embodiment. 
         FIG. 15  shows an illustrative plot of optimizing light extraction efficiency by layer thickness according to an embodiment. 
         FIG. 16  shows a profiled surface of an illustrative substrate according to an embodiment. 
         FIG. 17  shows an illustrative flow diagram for fabricating a circuit according to an embodiment. 
     
    
    
     It is noted that the drawings may not be to scale. The drawings are intended to depict only typical aspects of the invention, and therefore should not be considered as limiting the scope of the invention. In the drawings, like numbering represents like elements between the drawings. 
     DETAILED DESCRIPTION OF THE INVENTION 
     As indicated above, aspects of the invention provide a profiled surface for improving the propagation of radiation through an interface. The profiled surface includes a set of large roughness components providing a first variation of the profiled surface having a characteristic scale approximately an order of magnitude larger than a target wavelength of the radiation. The set of large roughness components can include a series of truncated shapes. The profiled surface also includes a set of small roughness components superimposed on the set of large roughness components and providing a second variation of the profiled surface having a characteristic scale on the order of the target wavelength of the radiation. As used herein, unless otherwise noted, the term “set” means one or more (i.e., at least one) and the phrase “any solution” means any now known or later developed solution. 
     Turning to the drawings,  FIG. 1  shows a schematic structure of an illustrative emitting device  10  according to an embodiment. In a more particular embodiment, the emitting device  10  is configured to operate as a light emitting diode (LED), such as a conventional or super luminescent LED. Alternatively, the emitting device  10  can be configured to operate as a laser diode (LD). In either case, during operation of the emitting device  10 , application of a bias comparable to the band gap results in the emission of electromagnetic radiation from an active region  18  of the emitting device  10 . The electromagnetic radiation emitted by the emitting device  10  can comprise a peak wavelength within any range of wavelengths, including visible light, ultraviolet radiation, deep ultraviolet radiation, infrared light, and/or the like. In an embodiment, a target wavelength of radiation is in the range of approximately 250 nanometers to approximately 350 nanometers. 
     The emitting device  10  includes a heterostructure comprising a substrate  12 , a buffer layer  14  adjacent to the substrate  12 , an n-type cladding layer  16  (e.g., an electron supply layer) adjacent to the buffer layer  14 , and an active region  18  having an n-type side  19 A adjacent to the n-type cladding layer  16 . Furthermore, the heterostructure of the emitting device  10  includes a p-type layer  20  (e.g., an electron blocking layer) adjacent to a p-type side  19 B of the active region  18  and a p-type cladding layer  22  (e.g., a hole supply layer) adjacent to the p-type layer  20 . 
     In a more particular illustrative embodiment, the emitting device  10  is a group III-V materials based device, in which some or all of the various layers are formed of elements selected from the group III-V materials system. In a still more particular illustrative embodiment, the various layers of the emitting device  10  are formed of group III nitride based materials. Group III nitride materials comprise one or more group III elements (e.g., boron (B), aluminum (Al), gallium (Ga), and indium (In)) and nitrogen (N), such that B W Al X Ga Y In Z N, where 0≤W, X, Y, Z≤1, and W+X+Y+Z=1. Illustrative group III nitride materials include AlN, GaN, InN, BN, AlGaN, AlInN, AlBN, AlGaInN, AlGaBN, AlInBN, and AlGaInB with any molar fraction of group III elements. 
     An illustrative embodiment of a group III nitride based emitting device  10  includes an active region  18  (e.g., a series of alternating quantum wells and barriers) composed of In y Al x Ga 1−x−y N, Ga z In y Al x B 1−x−y−z N, an Al x Ga 1−x N semiconductor alloy, or the like. Similarly, both the n-type cladding layer  16  and the p-type layer  20  can be composed of an In y Al x Ga 1−x−y N alloy, a Ga z In y Al x B 1−x−y−z N alloy, or the like. The molar fractions given by x, y, and z can vary between the various layers  16 ,  18 , and  20 . The substrate  12  can be sapphire, silicon carbide (SiC), silicon (Si), GaN, AlGaN, AlON, LiGaO 2 , or another suitable material, and the buffer layer  14  can be composed of AlN, an AlGaN/AlN superlattice, and/or the like. 
     As shown with respect to the emitting device  10 , a p-type metal  24  can be attached to the p-type cladding layer  22  and a p-type contact  26  can be attached to the p-type metal  24 . Similarly, an n-type metal  28  can be attached to the n-type cladding layer  16  and an n-type contact  30  can be attached to the n-type metal  28 . The p-type metal  24  and the n-type metal  28  can form ohmic contacts to the corresponding layers  22 ,  16 , respectively. In an embodiment, the p-type metal  24  and the n-type metal  28  each comprise several conductive and reflective metal layers, while the n-type contact  30  and the p-type contact  26  each comprise highly conductive metal. In an embodiment, the p-type cladding layer  22  and/or the p-type contact  26  can be at least partially transparent (e.g., semi-transparent or transparent) to the electromagnetic radiation generated by the active region  18 . For example, the p-type cladding layer  22  and/or the p-type contact  26  can comprise a short period superlattice lattice structure, such as an at least partially transparent magnesium (Mg)-doped AlGaN/AlGaN short period superlattice structure (SPSL). Furthermore, the p-type contact  26  and/or the n-type contact  30  can be at least partially reflective of the electromagnetic radiation generated by the active region  18 . In another embodiment, the n-type cladding layer  16  and/or the n-type contact  30  can be formed of a short period superlattice, such as an AlGaN SPSL, which is at least partially transparent to the electromagnetic radiation generated by the active region  18 . 
     As used herein, a layer is at least partially transparent when the layer allows at least a portion of electromagnetic radiation in a corresponding range of radiation wavelengths to pass there through. For example, a layer can be configured to be at least partially transparent to a range of radiation wavelengths corresponding to a peak emission wavelength for the light (such as ultraviolet light or deep ultraviolet light) emitted by the active region  18  (e.g., peak emission wavelength +/− five nanometers). As used herein, a layer is at least partially transparent to radiation if it allows more than approximately 0.5 percent of the radiation to pass there through. In a more particular embodiment, an at least partially transparent layer is configured to allow more than approximately five percent of the radiation to pass there through. Similarly, a layer is at least partially reflective when the layer reflects at least a portion of the relevant electromagnetic radiation (e.g., light having wavelengths close to the peak emission of the active region). In an embodiment, an at least partially reflective layer is configured to reflect at least approximately five percent of the radiation. 
     As further shown with respect to the emitting device  10 , the device  10  can be mounted to a submount  36  via the contacts  26 ,  30 . In this case, the substrate  12  is located on the top of the emitting device  10 . To this extent, the p-type contact  26  and the n-type contact  30  can both be attached to a submount  36  via contact pads  32 ,  34 , respectively. The submount  36  can be formed of aluminum nitride (AlN), silicon carbide (SiC), and/or the like. 
     Any of the various layers of the emitting device  10  can comprise a substantially uniform composition or a graded composition. For example, a layer can comprise a graded composition at a heterointerface with another layer. In an embodiment, the p-type layer  20  comprises a p-type blocking layer having a graded composition. The graded composition(s) can be included to, for example, reduce stress, improve carrier injection, and/or the like. Similarly, a layer can comprise a superlattice including a plurality of periods, which can be configured to reduce stress, and/or the like. In this case, the composition and/or width of each period can vary periodically or aperiodically from period to period. 
     It is understood that the layer configuration of the emitting device  10  described herein is only illustrative. To this extent, an emitting device/heterostructure can include an alternative layer configuration, one or more additional layers, and/or the like. As a result, while the various layers are shown immediately adjacent to one another (e.g., contacting one another), it is understood that one or more intermediate layers can be present in an emitting device/heterostructure. For example, an illustrative emitting device/heterostructure can include an undoped layer between the active region  18  and one or both of the p-type cladding layer  22  and the electron supply layer  16 . 
     Furthermore, an emitting device/heterostructure can include a Distributive Bragg Reflector (DBR) structure, which can be configured to reflect light of particular wavelength(s), such as those emitted by the active region  18 , thereby enhancing the output power of the device/heterostructure. For example, the DBR structure can be located between the p-type cladding layer  22  and the active region  18 . Similarly, a device/heterostructure can include a p-type layer located between the p-type cladding layer  22  and the active region  18 . The DBR structure and/or the p-type layer can comprise any composition based on a desired wavelength of the light generated by the device/heterostructure. In one embodiment, the DBR structure comprises a Mg, Mn, Be, or Mg+Si-doped p-type composition. The p-type layer can comprise a p-type AlGaN, AlInGaN, and/or the like. It is understood that a device/heterostructure can include both the DBR structure and the p-type layer (which can be located between the DBR structure and the p-type cladding layer  22 ) or can include only one of the DBR structure or the p-type layer. In an embodiment, the p-type layer can be included in the device/heterostructure in place of an electron blocking layer. In another embodiment, the p-type layer can be included between the p-type cladding layer  22  and the electron blocking layer. 
     Regardless, as illustrated in  FIG. 1 , the device  10  can include one or more at least partially reflective layers on a first side of the active region  18  and one or more layers having a profiled surface  40 A- 40 C on an opposing side of the active region  18  through which radiation generated in the active region  18  can leave the device  10 . As illustrated, each profiled surface  40 A- 40 C is configured to provide a boundary for an interface between two adjacent layers and/or an interface between the device  10  and the surrounding environment that is uneven or rough rather than substantially smooth. In an embodiment, the device  10  can include a profiled surface  40 A- 40 C at each interface where the refractive index changes abruptly (e.g., a difference in refractive indexes greater than or equal to approximately five percent). For example, as described herein, the substrate  12  can be made of sapphire, the buffer layer  14  can be AlN, and the cladding layer  16  can be AlGaN. For an illustrative target wavelength, these materials can have indexes of refraction of 1.8, 2.3, and 2.5, respectively. To this extent, the device  10  is shown including a profiled surface  40 A at the interface between the substrate  12  and the environment (which has an index of refraction of approximately one); a profiled surface  40 B at the interface between the buffer layer  14  and the substrate  12 ; and/or a profiled surface  40 C at the interface between the n-type cladding layer  16  and the buffer layer  14 . In this case, the buffer layer  14  can act as a light extraction film inserted between two materials with two different refraction indexes to provide a more gradual transition of refraction indexes. 
     It is understood that various embodiments of the device  10  can include a profiled surface configured as described herein at any combination of one or more interfaces. To this extent, a profiled surface can be included on any type of group III-nitride based semiconductor surface, such as AlInGaN or AlBGaN semiconductor alloys. Furthermore, a profiled surface can be included, for example, on an ultraviolet transparent glass, a polymer with a matched index deposited over a group III-nitride based semiconductor surface, and/or the like. 
     Each profiled surface  40 A- 40 C can be configured to improve the extraction of radiation from a corresponding at least partially transparent layer  12 ,  14 ,  16 , respectively. For example, during operation of the device  10 , radiation can be generated in the active region  18  and travel through at least partially transparent layers  16 ,  14 ,  12 , before being emitted from the device  10 . The profiled surfaces  40 C,  40 B can be configured to increase the amount of radiation that exits a first layer  16 ,  14  and enters an adjacent layer  14 ,  12 , respectively, as compared to a device having substantially smooth boundaries between the layers  12 ,  14 ,  16 . Similarly, the profiled surface  40 A can be configured to increase the amount of radiation that exits the device  10 , e.g., via substrate  12 , and enters into the surrounding environment, as compared to a device having a substantially smooth outer surface. 
     As illustrated, a profiled surface  40 A- 40 C can be formed using a plurality of roughness elements, such as roughness elements  42 A,  42 B forming a part of the profiled surface  40 A. Each roughness element  42 A,  42 B can be configured to provide additional surfaces for reflecting and refracting light, thereby facilitating light extraction from the corresponding layer (e.g., the substrate  12 ). In an embodiment, a roughness element  42 A,  42 B is formed of a large roughness component, on which is superimposed a small roughness component as described herein. While each of the profiled surfaces  40 A- 40 C are shown including a particular number of roughness elements  42 A,  42 B, each of which is configured substantially similar to the other, it is understood that each profiled surface  40 A- 40 C can be formed of any number of roughness elements having any combination of configurations. 
     In an embodiment, the large roughness components of the roughness elements  42 A,  42 B provide variation of the profiled surface  40 A having a characteristic scale greater than a target wavelength. The target wavelength can be selected based on a peak wavelength of the radiation desired to pass through the interface during operation of the device  10  and can be within any range of wavelengths, including visible light, ultraviolet radiation, deep ultraviolet radiation, infrared light, and/or the like. In an embodiment, the target wavelength corresponds to the peak wavelength of the radiation generated in the active region  18 . In a more particular embodiment, the characteristic scale of the variation provided by the large roughness components is approximately an order of magnitude (e.g., ten times) larger than the target wavelength, and can be determined based on the average height and/or width of the large roughness components. In an embodiment, the large roughness components have comparable heights and widths, e.g., of approximately two to four micrometers. Inclusion of the large roughness components can reduce losses associated with TIR. 
     Additionally, the small roughness components of the roughness elements  42 A,  42 B can provide variation of the profiled surface  40 A having a characteristic scale on the order of the target wavelength. To this extent, the characteristic scale of the variation provided by the small roughness components can be between approximately ten to two hundred percent of the target wavelength, and can be determined based on the average height of the small roughness components. In an embodiment, the small roughness components have heights between approximately ten to one hundred nanometers. Inclusion of the small roughness components can reduce Fresnel losses. Furthermore, the small roughness components can form a photonic crystal, which is configured to guide the radiation of a target wavelength to facilitate its extraction from the layer. 
       FIGS. 2A and 2B  show an illustrative roughness element  42  and an illustrative roughness element model  50 , respectively, according to an embodiment. As illustrated in  FIG. 2A , the roughness element  42  includes a large roughness component  44  on which is superimposed a small roughness component  46 . The large roughness component  44  is shown having a truncated triangular cross section, which can correspond to a truncated cone or a truncated pyramid having any number of sides. The small roughness component  46  is illustrated as a series of peaks and valleys of material having random variations in heights and locations extending from the truncated portion  45  of the large roughness component  44 . The small roughness component  46  can reduce Fresnel losses. As illustrated in  FIG. 2B , the roughness element model  50  can include a large roughness component model  52  and a small roughness component model  54 . The large roughness component model  52  can comprise, for example, a truncated cone or a truncated pyramid shape. The small roughness component model  54  can model the small roughness component  46  as an intermediate layer having a thickness L, where the thickness corresponds to the characteristic scale of the small roughness component  46  and can be measured as the distance between the lowest valley and the highest peak on the roughness element  42 . 
     The small roughness component  46  can introduce a graded refractive index into the roughness element  42 . In particular, for a given height h along the thickness L of the intermediate layer of the small roughness component model  54 , a corresponding index of refraction can be estimated by calculating an average between the refractive index of the material forming the roughness element  42  and the material adjacent to the roughness element  42  (e.g., the layer/environment into which the radiation is transmitted after exiting the roughness element  42 ), where the average is weighted by a fractional cross sectional area of the small roughness component  46  at the given height h. 
       FIG. 3  shows the effect of the small roughness component  46  ( FIG. 2A ) on transmission (T) over a range of angles of incidence (Θ) according to an embodiment. In this case, the roughness element is included at an interface between a sapphire substrate  12  ( FIG. 1 ) having an index of refraction n=1.825 and the surrounding air (having an index of refraction approximately equal to 1) for radiation having a given wavelength in a vacuum, λ 0 . As illustrated, when the small roughness component  46  is not included (i.e., L=0λ 0 ), the transmission has a maximum of approximately 0.92 and begins to drop significantly when the angle of incidence exceeds approximately twenty degrees. When the small roughness component  46  has a thickness L of approximately 0.25λ 0 , the maximum transmission increases to approximately 0.98 and is maintained until the angle of incidence exceeds approximately twenty-eight degrees. When the small roughness component  46  has a thickness L between approximately 0.5λ 0  to 1λ 0  or greater, the transmission exceeds 0.99 until the angle of incidence exceeds approximately twenty-eight degrees. As a result, the small roughness component  46  can reduce the Fresnel losses, which results in higher radiation extraction from the sapphire substrate  12  as compared to an interface without the small roughness component  46 . 
       FIG. 4  shows the effect of the dimensions of the small roughness component  46  on the graded refractive index according to an embodiment. As illustrated, the graded refractive index gradually transitions from the refractive index of the material of the small roughness component  46  (e.g., sapphire) to the refractive index of the adjacent material (e.g., air) as the distance, z, from the large roughness component  44  ( FIG. 2A ) increases. 
       FIGS. 5A and 5B  show illustrative schematics of roughness elements  60 A,  60 B with a constant index of refraction and a graded index of refraction, respectively, according to an embodiment. In each case, a light emitting source is located at a base of the cone in the rightmost surface of the adjoining cylinder  62 . The walls of the cylinder  62  are set to be partially absorbing mirrors to mimic absorption of light in a typical light emitting diode. The roughness element  60 A comprises a cone shape with smooth sides. In contrast, the roughness element  60 B comprises a cone shape (e.g., a large roughness component) with sides having small roughness components superimposed thereon. As a result, the sides of the roughness element  60 B have a fuzzy look as compared to the sides of the roughness element  60 A. 
       FIGS. 6A and 6B  show illustrative distributions of light and the corresponding light extraction efficiencies (LEE) for the cones  60 A,  60 B of  FIGS. 5A and 5B , respectively, according to an embodiment. As illustrated, the LEE (shown in  FIG. 6B ) for the transmission of light through the cone  60 B having a graded index of refraction is clearly higher than the LEE (shown in  FIG. 6A ) for the transmission of light through the cone  60 A having a constant index of refraction, e.g., an improvement of over ten percent. 
       FIGS. 7A-7C  show illustrative large roughness components  70 A,  70 B and a corresponding illustrative polar plot of intensity, respectively, according to embodiments. In  FIG. 7A , the large roughness component  70 A is in the shape of a truncated cone, while the large roughness component  70 B of  FIG. 7B  is in the shape of a truncated pyramid. Each large roughness component  70 A,  70 B can comprise an inverse truncated element, where the base B, which is the portion of the large roughness component  70 A,  70 B adjacent to the corresponding layer (e.g., substrate  12 ), is smaller than the top T. While not shown, it is understood that each large roughness component  70 A,  70 B can be used to form a roughness element by superimposing a small roughness component on, for example, the top surface of the truncated shape. Furthermore, while the truncated pyramid of the large roughness component  70 B is shown having a base and top with four sides, it is understood that the base and top of the pyramid can be a polygon with any number of sides. 
     Such a configuration for the large roughness components  70 A,  70 B can be used, for example, for light focusing in order to facilitate extraction of light from the layer, e.g., by designing the large roughness components  70 A,  70 B to determine an emission cone angle for radiation of the target wavelength. To this extent, the sides of the truncated cone shape of the large roughness component  70 A can form an angle Θ of less than ninety degrees. Similarly, the sides of the truncated pyramid shape of the large roughness component  70 B and the sides of the truncated cone shape of the large roughness component  44 A can form an angle with respect to the normal of less than forty-five degrees. In this manner, an increased amount of light reflections will result in the light being directed out from the layer.  FIG. 7C  shows an illustrative polar plot of intensity distribution for the large roughness component  70 A. 
       FIGS. 8A-8B  show illustrative profiled surfaces  400 A,  400 B according to embodiments. In each case, it is understood that while only the set of large roughness components of each profiled surface  400 A,  400 B are shown for clarity, each profiled surface  400 A,  400 B can include a set of small roughness components (e.g., the set of small roughness components  46  in  FIG. 2A ) superimposed on the set of large roughness components as described herein. As illustrated in the figures and described herein, the set of large roughness components can include a series of truncated shapes. 
     In  FIG. 8A , the profiled surface  400 A includes a set of large roughness components  80 A- 80 E. A first portion of the set of large roughness components (e.g., components  80 A- 80 D) includes a series of truncated triangular cross sections, each of which can correspond to a truncated cone or a truncated pyramid having any number of sides. A second portion of the set of large roughness components (e.g., component  80 E) includes one or more inverse truncated triangular cross sections. For example, the large roughness components  80 A- 80 D each include a base B 1  that is larger than a top T 1 . The base B 1  is the portion of the large roughness component  80 A- 80 D that is adjacent to the corresponding layer (e.g., substrate  12 ), and is smaller than the top T 1 . Conversely, the inverse truncated large roughness component  80 E includes a base B 2  that is smaller than a top T 2 . 
     In  FIG. 8B , the profiled surface  400 B includes a first portion of the set of large roughness components including one or more truncated components (e.g., component  82 A) and a second portion of the set of large roughness components including a series of inverse truncated large roughness components (e.g., components  82 B- 82 E). It is understood that the profiled surfaces  400 A,  400 B can include any number of truncated large roughness components and any number of inverse truncated large roughness components. In an embodiment, the truncated large roughness components can be at least approximately twenty percent of the large roughness components located on the profiled surface. In another embodiment, the inverse truncated large roughness components can be at least approximately twenty percent of the large roughness components located on the profiled surface. 
       FIGS. 9A-9B  show illustrative profiled surfaces  402 A,  402 B according to embodiments. In each case, it is understood that while only the set of large roughness components of each profiled surfaces  402 A,  402 B are shown for clarity, each profiled surface  402 A,  402 B can include a set of small roughness components (e.g., the set of small roughness components  46  in  FIG. 2A ) superimposed on the set of large roughness components as described herein. As illustrated in the figures and described herein, the set of large roughness components can concurrently include a series of truncated shapes and a series of non-truncated shapes. This configuration can be useful, for example, as a parameter for light scattering. 
     In  FIG. 9A , the profiled surface  402 A includes a set of large roughness components  90 A- 90 E. A first portion of the set of large roughness components (e.g., component  90 A) includes one or more components having truncated triangular cross sections, which can correspond to a truncated cone or a truncated pyramid having any number of sides. A second portion of the set of large roughness components (e.g.,  90 B- 90 E) includes components having non-truncated triangular cross sections. In  FIG. 9B , the profiled surface  402 B includes a first portion of the set of large roughness components including one or more non-truncated large roughness components (e.g., component  92 A) and a second portion of the set of large roughness components including truncated large roughness components (e.g., components  92 B- 92 E). It is understood that the profiled surfaces  402 A,  402 B can include any number of truncated large roughness components and any number of non-truncated large roughness components. In an embodiment, for example, the truncated large roughness components can be at least approximately twenty percent of the large roughness components located on the profiled surface. In another embodiment, for example, the non-truncated large roughness components can be at least approximately twenty percent of the large roughness components located on the profiled surface. 
     In each case shown in  FIGS. 8A-8B and 9A-9B , the first portion of the set of large roughness components (e.g., components  80 A- 80 D in  FIG. 8A ) can be interspersed with the second portion of the set of large roughness components (e.g., component  80 E in  FIG. 8A ) on the profiled surface in any one or two dimensional pattern. Although the first portion of the set of large roughness components in  FIGS. 8A-8B  are shown as grouped together, it is understood that the first and the second portion of the set of large roughness components can be anywhere along the profiled surface and are not necessarily grouped together. For example, in  FIG. 8A , component  80 E can be placed between component  80 A and component  80 B, between component  80 B and component  80 C; between component  80 C and component  80 D, and/or the like. Furthermore, if more than one component is in both the first portion and the second portion of the set of large roughness components, it is understood that the first portion and the second portion can be interspersed in any regular, semi-regular, or random pattern. To this extent, the first portion and the second portion of the set of large roughness components can form an alternating pattern of large roughness components. 
     In one embodiment, the large roughness components or large truncated roughness components (herein referred to as large components or large elements) may be collocated in a different portion of the profiled surface than a portion of the profiled surface on which the inverse truncated large roughness elements (herein referred to as inverse components or elements) are located. Such a configuration can be utilized, e.g., in order to affect the distribution of intensity of radiation emitted from the corresponding device (e.g., a UV LED). For example, the large elements may be collocated in a centrally located (e.g., middle) portion of an exit face of the LED device, occupying approximately 20-50% of the surface area of the exit face, and the inverse components can surround the region containing large elements. 
     It is understood that other collocations of large elements and inverse elements are possible. One approach for designing a collocation pattern uses ray tracing simulation and an optimization algorithm to obtain a target distribution of intensity of radiation emitted from the device. Such a process can be roughly understood as a series of steps, where in order to obtain or approximate a target intensity distribution over polar angles, the collocation pattern is adjusted until a local or global optimum condition corresponding to the target intensity distribution is found. It is further understood that in order to optimize the intensity distribution over polar angles with respect to a target intensity distribution, as well as an overall efficiency of the device, not only collocation of large and inverted components can be varied, but also the collocation of elements containing small roughness scale. For example, the large elements positioned in the central portion of the exit face may contain small scale roughness elements, whereas the inverse elements may not contain such small scale roughness elements. 
       FIG. 10  shows an illustrative top view of a profiled surface  502  according to an embodiment. As illustrated, the profiled surface  502  can include a plurality of roughness elements  542 A,  542 B,  542 C located in various locations along the profiled surface  502 . While each of the plurality of roughness elements  542 A,  542 B,  542 C are shown as structures with a circular base (e.g., a cone or a cylinder), it is understood that each of the plurality of roughness elements  542 A,  542 B,  542 C can include any combination of truncated and/or non-truncated shape. In addition, it is understood that any of the plurality of roughness elements  542 A,  542 B,  542 C can be inversely truncated. In an embodiment, each of the plurality of roughness elements  542 A,  542 B,  542 C can vary in lateral size. For example, if the plurality of roughness elements  542 A,  542 B,  542 C are structures with a circular base, the plurality of roughness elements  542 A,  542 B,  542 C can vary in diameter. In an embodiment, the variation in lateral size of the plurality of roughness elements  542 A,  542 B,  542 C can be radially dependent and/or radially monotonic. In an embodiment, the shape and/or the characteristic diameter (e.g., the square root of the shape&#39;s area) of the plurality of roughness elements  542 A,  542 B,  542 C can be random. In an embodiment, the plurality of roughness elements  542 A,  542 B,  542 C can include a combination of pyramids with triangular, rectangular, and/or hexagonal cross-sections.  FIG. 11  shows an illustrative perspective top view of a profiled surface  602  according to an embodiment. The profiled surface  602  is similar to the profiled surface  502  shown in  FIG. 10  and the plurality of roughness elements  642 A,  642 B,  642 C can include any combination of truncated and/or non-truncated shape, include cone, cylinder, pyramids with any shaped cross-section, and/or the like. In addition to the variation in lateral size discussed in  FIG. 10 , the plurality of roughness elements  642 A,  642 B,  642 C can vary in height. The variation in the height of the plurality of roughness elements  642 A,  642 B,  642 C can be random, radial, radially monotonic, or have a particular pattern in the lateral direction that results in a distribution and manipulation of light emitted or absorbed by the device. Although the plurality of roughness elements  642 A,  642 B,  642 C are shown to include variation in lateral size and height, it is understood that only the height or lateral size can vary in embodiments. Regardless of whether the variation is in the lateral size, height, or both, it is understood that the lateral variation is selected to result in a target polar distribution of the emitted light. Also, it is understood that the plurality of roughness elements shown in both  FIGS. 10 and 11  can include large roughness components and small roughness components, as discussed herein. Furthermore, in an embodiment, the plurality of roughness elements shown in  FIGS. 10 and 11  can include a set of very large roughness elements and a set of large roughness elements, where the set of very large roughness elements are larger than the set of large roughness elements by at least 100%. The set of very large roughness elements can be designed to result in optical manipulation of the light through lensing. 
       FIG. 12  shows an illustrative perspective top view of a profiled surface  702  according to an embodiment. As illustrated, the profiled surface  702  can include a plurality of roughness elements  742 . Each roughness element  742  can include a plurality of layers and the diameter of each of the plurality of layers can decrease from the bottom of the roughness element  742  to the top. The bottom layer of each roughness element  742  can include a large roughness component  744 , while the top of each roughness element  742  can include a small roughness component  746 . In an embodiment, the large roughness component  744  can be designed for light manipulation, and can result in structure with a Fresnel lens effect. It is understood that the other layers between the small roughness component  746  and the large roughness component  744  can have a small roughness component. 
       FIG. 13  shows a partial view of an illustrative device  800  according to an embodiment. In an embodiment, the device  800  can include a partially transparent substrate  812  that includes tapered edges  813  to form a truncated shape. In an embodiment, the tapered edges  813  can be at angle of approximately 10 to approximately 80 degrees. In another embodiment, the angle of the tapered edges  813  is between approximately 30 degrees and approximately 60 degrees. In another embodiment, the angle of the tapered edges  813  is approximately 30 degrees with a +/−10 degree spread. A partially transparent semiconductor heterostructure  814  is grown over the partially transparent substrate  812 . The heterostructure  814  can comprise a group III nitride semiconductor layer, such as a buffer layer. In an embodiment, the heterostructure layer  814  can comprise a semiconductor laminate structure including a buffer layer located adjacent to the substrate  812 , a cladding layer located over the buffer layer, and then followed by an active region comprising a plurality of quantum wells and barriers. 
     In an embodiment, the semiconductor heterostructure  814  is formed of a material that is different from the material of the partially transparent substrate  812 , so that a refractive index of the heterostructure  914  is at least 2% different from a refractive index of the substrate  812 . In an embodiment, the refractive index of the heterostructure  814  is less than the refractive index of the substrate  812 . In another embodiment, the refractive index of the heterostructure  814  is approximately square root of the refractive index of the substrate  812 . The heterostructure  814  can be formed of a group III nitride semiconductor material, such as Al x Ga 1−x N, Al x In y Ga 1−x−y , and/or the like. In an embodiment, the heterostructure  814  comprises a material having light scattering at the target wavelength. The light scattering can be due to a presence of polycrystalline ultraviolet transparent layer within the heterostructure  814 . In an embodiment, a thickness of the heterostructure  814  is less than the characteristic height of the plurality of large roughness elements  842 A,  842 B. 
     The substrate  812  can include one or more profiled surfaces  840 A,  840 B. As shown, the substrate  812  include a first profiled surface  840 A along a side opposing the semiconductor heterostructure  814  and a second profiled surface  840 B along one of the tapered edges  813 . Each profiled surface  840 A,  840 B can be formed by a plurality of roughness elements  842 A,  842 B, respectively. Although it is not shown, it is understood each of the plurality of roughness elements  842 A,  842 B can include both large and small roughness components, as discussed herein. It is also understood that each profiled surface  840 A,  840 B can include different shapes and sizes (lateral size and height) for the plurality of roughness elements  842 A,  842 B. The combination of the tapered edges  813  of the substrate  812  with the profiled surface  840 B, in addition to the profiled surface  840 A, results in increased light extraction from the device. 
       FIG. 14  shows a profiled surface  940  of an illustrative partially transparent substrate  912  according to an embodiment. It is understood that the profiled surface  940  shown in  FIG. 14  can include any side of the substrate  912 . The profiled surface  940  can be formed by a plurality of roughness elements  942 . Although it is not shown, it is understood that any of the plurality of roughness elements  942  can include a small roughness component, in addition to the large roughness component, as discussed herein. In an embodiment, the plurality of roughness elements  942  can be separated by a region  950  that is filled with a set of layers  952 ,  954 . Although only two layers  952 ,  954  are shown, it is understood that any number of layers  952 ,  954  can be deposited over the substrate  912  into the regions  950 . 
     In an embodiment, the set of layers  952 ,  954  are partially transparent to the target wavelength of the device and include an index of refraction that is different than the index of refraction of the material of the substrate  912 . In an embodiment, the set of layers  952 ,  954  can include an index of refraction that is between the index of refraction of the material of the substrate  912  and the index of refraction for the ambient. In an embodiment, the set of layers  952 ,  954  can include an index of refraction that is approximately the square root of the index of refraction of the material of the substrate  912 . For example, if the substrate  912  is formed of sapphire, with an index of refraction of approximately 1.821 for ultraviolet radiation, the set of layers  952 ,  954  can have an index of refraction of approximately 1.35. In general, the index of refraction for each of the set of layers  952 ,  954  can be approximately 1.2 to approximately 1.6. In an embodiment, the set of layers  952 ,  954  can be formed of a fluoropolymer film, such as calcium fluoride (CaF 2 ), magnesium fluoride (MgF 2 ), anodic aluminum oxide (AAO), aluminum oxide (Al 2 O 3 ), hafnium oxide (HfO 2 ), and/or the like. In an embodiment, the set of layers  952 ,  954  can include roughness components, scattering and/or reflective domains, and/or the like. 
     The thickness of each of the set of layers  952 ,  954  can be designed to improve the light extraction efficiency (LEE) of the device. For example,  FIG. 15  illustrates that a thickness of one or more of the layers  952 ,  954  can significantly impact the LEE of the device by providing the particular changes in index of refraction across the interface. The average index of refraction as a function of the thickness of the set of layers  952 ,  954  and the plurality of roughness elements  942 , depends on the height of the plurality of roughness elements  942 , the type and the thickness of the set of layers  952 ,  954 , and the shape of the plurality of roughness elements  942 . The thicknesses of each of these layers  952 ,  954  and the plurality of roughness elements  942  can be similar to the wavelength of the emitted radiation, and can be in the range of approximately 10 to approximately 1000 nanometers. In an embodiment, the plurality of roughness elements  942  can reach several microns in characteristic height. 
       FIG. 16  shows a profiled surface  1040  of an illustrative partially transparent substrate  1012  according to an embodiment. As discussed herein, the profiled surface  1040  is formed by a plurality of roughness elements  1042 . The profiled surface  1040  can include a plurality of nanostructures  1048 A,  1048 B located in one or more of the regions  1050  between the plurality of roughness elements  1042 . In an embodiment, the plurality of nanostructures  1048 A,  1048 B can comprise nanowires, as shown in  FIG. 16 . In an embodiment, the plurality of nanostructures  1048 A,  1048 B can each be oriented differently. For example, the first plurality of nanostructures  1048 A are oriented orthogonally, while the second plurality of nanostructures  1048 B are oriented at a target angle to the profiled surface  1040 . The plurality of nanostructures  1048 A,  1048 B can be designed to have a required index of refraction, e.g., by careful tailoring of optical properties of the plurality of nanostructures  1048 A,  1048 B. In an embodiment, the index of refraction for the plurality of nanostructures  1048 A,  1048 B can vary with the thickness of the plurality of nanostructures  1048 B,  1048 B. Although the plurality of roughness elements  1042  are shown as truncated, it is understood that any number of the plurality of roughness elements  1042  can be non-truncated. Also, although it is not shown, it is understood that any of the plurality of roughness elements  1042  can include a small roughness component, in addition to the large roughness component, as discussed herein. 
     Returning to  FIG. 1 , it is understood that a device  10 , or a heterostructure used in forming a device  10 , including one or more layers having a profiled surface, such as layers  12 ,  14 , and  16 , can be fabricated using any solution. For example, an emitting device/heterostructure can be manufactured by obtaining (e.g., forming, preparing, acquiring, and/or the like) a substrate  12 , forming (e.g., growing, depositing, adhering, and/or the like) a buffer layer  14  thereon, and forming an n-type cladding layer  16  over the buffer layer  14 . Furthermore, the active region  18 , e.g., including quantum wells and barriers, can be formed over the n-type cladding layer  16  using any solution. The p-type layer  20  can be formed over the active region  18  and the p-type cladding layer  22  can be formed on the p-type layer  20  using any solution. Additionally, one or more metal layers, contacts, and/or additional layers can be formed using any solution. Furthermore, the heterostructure/device can be attached to a submount via contact pads. 
     It is understood that the fabrication of the emitting device/heterostructure can include the deposition and removal of a temporary layer, such as mask layer, the patterning one or more layers, the formation of one or more additional layers not shown, and/or the like. To this extent, a profiled surface  40 A- 40 C (or profiled surfaces  400 A,  400 B,  402 A,  402 B) can be fabricated using any combination of deposition and/or etching. For example, the fabrication can include selective deposition and/or etching of nanoscale objects, such as nanodots and/or nanorods, of the material to form the large and/or small roughness components. Such deposition and/or etching can be used to form periodic and/or non-periodic random patterns. 
     In fabricating the profiled surfaces discussed herein, a simulation using ray tracing and an optimization algorithm, such as a genetic algorithm, can be performed. An illustrative embodiment of the process of simulation can comprise: 
     a) Modeling an optical structure of a light emitting diode (LED), which can include incorporating domains with their respective optical properties and assigning volumes or surfaces for emission of light; 
     b) Evaluating an efficiency of the LED and intensity of radiated light by collecting emitted rays on the surface of a control detecting sphere surrounding the LED; 
     c) Incorporating a set of roughness elements on a set of LED surfaces as described herein; 
     d) Establishing a set of optimization parameters for modeling roughness, such as roughness shape, size, location, reflective/transmittal properties of roughness surfaces (which model the reflective/transparent properties of such roughness in the presence of small sub-wavelength roughness elements), and/or the like; and
 
e) Re-evaluating the efficiency of LED by varying optimization parameters describing roughness where the variation of any one parameter in the set of parameters can be either random, or continuous (wherein continuous variation includes also no variation). The parameter variation can be performed, for example, according to a genetic algorithm where models with sets of improved parameters are allowed to “cross-breed”, wherein “cross-breeding” includes overlapping a parameter space of one model with a parameter space of another model in various combinations to create one or more new sets of optimization parameters for evaluation. Furthermore, the “cross-breeding” can include introducing randomness into one or more parameters of the new sets of optimization parameters.
 
     While shown and described herein as a method of designing and/or fabricating an emitting device to improve extraction of light from the device, it is understood that aspects of the invention further provide various alternative embodiments. For example, aspects of the invention can be implemented to facilitate the transmission of light within the device, e.g., as part of optical pumping of a laser light generating structure, excitation of a carrier gas using a laser pulse, and/or the like. Similarly, an embodiment of the invention can be implemented in conjunction with a sensing device, such as a photosensor or a photodetector. In each case, a profiled surface can be included in an exterior surface of the device and/or an interface of two adjacent layers of the device in order to facilitate the transmission of light through the interface in a desired direction. 
     In one embodiment, the invention provides a method of designing and/or fabricating a circuit that includes one or more of the devices designed and fabricated as described herein. To this extent,  FIG. 17  shows an illustrative flow diagram for fabricating a circuit  126  according to an embodiment. Initially, a user can utilize a device design system  110  to generate a device design  112  for a semiconductor device as described herein. The device design  112  can comprise program code, which can be used by a device fabrication system  114  to generate a set of physical devices  116  according to the features defined by the device design  112 . Similarly, the device design  112  can be provided to a circuit design system  120  (e.g., as an available component for use in circuits), which a user can utilize to generate a circuit design  122  (e.g., by connecting one or more inputs and outputs to various devices included in a circuit). The circuit design  122  can comprise program code that includes a device designed as described herein. In any event, the circuit design  122  and/or one or more physical devices  116  can be provided to a circuit fabrication system  124 , which can generate a physical circuit  126  according to the circuit design  122 . The physical circuit  126  can include one or more devices  116  designed as described herein. 
     In another embodiment, the invention provides a device design system  110  for designing and/or a device fabrication system  114  for fabricating a semiconductor device  116  as described herein. In this case, the system  110 ,  114  can comprise a general purpose computing device, which is programmed to implement a method of designing and/or fabricating the semiconductor device  116  as described herein. Similarly, an embodiment of the invention provides a circuit design system  120  for designing and/or a circuit fabrication system  124  for fabricating a circuit  126  that includes at least one device  116  designed and/or fabricated as described herein. In this case, the system  120 ,  124  can comprise a general purpose computing device, which is programmed to implement a method of designing and/or fabricating the circuit  126  including at least one semiconductor device  116  as described herein. 
     In still another embodiment, the invention provides a computer program fixed in at least one computer-readable medium, which when executed, enables a computer system to implement a method of designing and/or fabricating a semiconductor device as described herein. For example, the computer program can enable the device design system  110  to generate the device design  112  as described herein. To this extent, the computer-readable medium includes program code, which implements some or all of a process described herein when executed by the computer system. It is understood that the term “computer-readable medium” comprises one or more of any type of tangible medium of expression, now known or later developed, from which a stored copy of the program code can be perceived, reproduced, or otherwise communicated by a computing device. 
     In another embodiment, the invention provides a method of providing a copy of program code, which implements some or all of a process described herein when executed by a computer system. In this case, a computer system can process a copy of the program code to generate and transmit, for reception at a second, distinct location, a set of data signals that has one or more of its characteristics set and/or changed in such a manner as to encode a copy of the program code in the set of data signals. Similarly, an embodiment of the invention provides a method of acquiring a copy of program code that implements some or all of a process described herein, which includes a computer system receiving the set of data signals described herein, and translating the set of data signals into a copy of the computer program fixed in at least one computer-readable medium. In either case, the set of data signals can be transmitted/received using any type of communications link. 
     In still another embodiment, the invention provides a method of generating a device design system  110  for designing and/or a device fabrication system  114  for fabricating a semiconductor device as described herein. In this case, a computer system can be obtained (e.g., created, maintained, made available, etc.) and one or more components for performing a process described herein can be obtained (e.g., created, purchased, used, modified, etc.) and deployed to the computer system. To this extent, the deployment can comprise one or more of: (1) installing program code on a computing device; (2) adding one or more computing and/or I/O devices to the computer system; (3) incorporating and/or modifying the computer system to enable it to perform a process described herein; and/or the like. 
     The foregoing description of various aspects of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously, many modifications and variations are possible. Such modifications and variations that may be apparent to an individual in the art are included within the scope of the invention as defined by the accompanying claims.