Source: http://www.google.com/patents/US20060192194?dq=6272333
Timestamp: 2016-09-25 02:15:08
Document Index: 265259073

Matched Legal Cases: ['Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60']

Patent US20060192194 - Electronic device contact structures - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign inPatentsElectronic device contact structures are disclosed....http://www.google.com/patents/US20060192194?utm_source=gb-gplus-sharePatent US20060192194 - Electronic device contact structuresAdvanced Patent SearchTry the new Google Patents, with machine-classified Google Scholar results, and Japanese and South Korean patents.Publication numberUS20060192194 A1Publication typeApplicationApplication numberUS 11/351,325Publication dateAug 31, 2006Filing dateFeb 9, 2006Priority dateApr 15, 2003Also published asUS7105861, US7482640, US8217415, US20050051785, US20090230545, US20130126933Publication number11351325, 351325, US 2006/0192194 A1, US 2006/192194 A1, US 20060192194 A1, US 20060192194A1, US 2006192194 A1, US 2006192194A1, US-A1-20060192194, US-A1-2006192194, US2006/0192194A1, US2006/192194A1, US20060192194 A1, US20060192194A1, US2006192194 A1, US2006192194A1InventorsAlexei Erchak, Elefterios Lidorikis, John GraffOriginal AssigneeLuminus Devices, Inc.Export CitationBiBTeX, EndNote, RefManPatent Citations (99), Referenced by (26), Classifications (24), Legal Events (4) External Links: USPTO, USPTO Assignment, EspacenetElectronic device contact structures
US 20060192194 A1Abstract
Electronic device contact structures are disclosed. Images(38) Claims(28)
1. A device, comprising: a material body designed for use in an electronic device, the material body having a surface; and a contact structure supported by the surface of the material body and extending from a conductive pad, the contact structure comprising: a patterned conductive layer having an interior portion; and a patterned insulating layer disposed between the interior portion of the patterned conductive layer and the surface of the material body, the insulating layer patterned such that the conductive layer forms an electrical contact to the material body, wherein at least a portion of the patterned insulating layer and/or the patterned conductive layer is tapered in shape. 2. The device of claim 1, wherein the device is a light-emitting diode. 3. The device of claim 1, wherein the device is a photonic lattice light-emitting diode. 4. The device of claim 1, wherein the insulating layer is patterned such that the conductive layer extends past at least one edge of the insulating layer to form an electrical contact to the material body. 5. The device of claim 1, wherein at least a portion of the patterned insulating layer is tapered in shape. 6. The device of claim 1, wherein at least a portion of the patterned conductive layer is tapered in shape. 7. The device of claim 1, wherein at least a portion of the patterned insulating layer is substantially triangular in shape. 8. The device of claim 1, wherein at least a portion of the patterned conductive layer is substantially triangular in shape. 9. The device of claim 1, wherein the patterned conductive layer comprises a metal. 10. The device of claim 1, wherein the patterned insulating layer comprises an oxide. 11. The device of claim 1, wherein the patterned insulating layer has a smaller area than the patterned conductive layer. 12. The device of claim 1, wherein the patterned insulating layer has a larger area at an end adjacent to the conductive pad than an area at a greater distance from the conductive pad. 13. The device of claim 1, wherein a length of the patterned insulating layer is about the same as a length of the patterned conductive layer. 14. The device as in claim 1, wherein the contact structure is in electrical contact to a first conductive pad and a second conductive pad. 15. A device, comprising: a material body designed for use in an electronic device, the material body having a surface; and a contact structure supported by the surface of the material body and extending from a conductive pad, the contact structure comprising: a patterned conductive layer having an interior portion; and a patterned insulating layer disposed between the interior portion of the patterned conductive layer and the surface of the material body, the insulating layer patterned such that the conductive layer forms an electrical contact to the material body, wherein the patterned insulating layer and/or the patterned conductive layer has a larger area at an end adjacent to the conductive pad than an area at a greater distance from the conductive pad. 16. The device of claim 15, wherein the device is a light emitting diode. 17. The device of claim 15, wherein the device is a photonic lattice light-emitting diode. 18. The device of claim 15, wherein the insulating layer is patterned such that the conductive layer extends past at least one edge of the insulating layer to form an electrical contact to the material body. 19. The device of claim 15, wherein at least a portion of the patterned insulating layer is tapered in shape. 20. The device of claim 15, wherein at least a portion of the patterned conductive layer is tapered in shape. 21. The device of claim 15, wherein at least a portion of the patterned insulating layer and/or the patterned conductive layer is substantially triangular in shape. 22. The device of claim 15, wherein the patterned conductive layer comprises a metal. 23. The device of claim 15, wherein the patterned insulating layer comprises an oxide. 24. The device of claim 15, wherein the patterned insulating layer has a smaller area than the patterned conductive layer. 25. The device of claim 15, wherein a length of the patterned insulating layer is about the same as a length of the patterned conductive layer. 26. The device as in claim 15, wherein the contact structure is in electrical contact to a first conductive pad and a second conductive pad. 27. The device as in claim 15, wherein the patterned insulating layer has a larger area at an end adjacent to the conductive pad than an area at a greater distance from the conductive pad. 28. The device as in claim 15, wherein the patterned conductive layer has a larger area at an end adjacent to the conductive pad than an area at a greater distance from the conductive pad.
CROSS REFERENCE TO RELATED APPLICATIONS [0001] This application is a continuation of U.S. patent application Ser. No. 10/871,877, filed Jun. 18, 2004, which claims priority under 35 U.S.C. �119 to U.S. Provisional Patent Application Ser. No. 60/553,894, filed Mar. 16, 2004, and entitled “Optical Display Systems and Methods”, and is a continuation-in-part of, and claims priority under 35 U.S.C. �120 to U.S. patent application Ser. No. 10/735,498, filed Dec. 12, 2003, and entitled “Light Emitting Systems”; U.S. patent application Ser. No. 10/794,244, filed Mar. 5, 2004, and entitled “Light Emitting Device Methods”; and U.S. patent application Ser. No. 10/794,452, filed Mar. 5, 2004, and entitled “Light Emitting Device Methods”, which claim priority under 35 U.S.C. �119 to U.S. Provisional Patent Application No. 60/462,889, filed Apr. 15, 2003; U.S. Provisional Patent Application No. 60/474,199, filed May 29, 2003; U.S. Provisional Patent Application No. 60/475,682, filed Jun. 4, 2003; U.S. Provisional Patent Application No. 60/503,653, filed Sep. 17, 2003; U.S. Provisional Patent Application No. 60/503,654, filed Sep. 17, 2003; U.S. Provisional Patent Application No. 60/503,661, filed Sep. 17, 2003; U.S. Provisional Patent Application No. 60/503,671, filed Sep. 17, 2003; U.S. Provisional Patent Application No. 60/503,672, filed Sep. 17, 2003; U.S. Provisional Patent Application No. 60/513,807, filed Oct. 23, 2003; and U.S. Provisional Patent Application No. 60/514,764, filed Oct. 27, 2003, the entire contents of each of which is hereby incorporated by reference. INCORPORATION BY REFERENCE [0002] This application incorporates by reference the following U.S. Provisional Patent Applications: 60/462,889, filed Apr. 15, 2003; 60/474,199, filed May 29, 2003; 60/475,682, filed Jun. 4, 2003; 60/503,653, filed Sep. 17, 2003; 60/503,654 filed Sep. 17, 2003; 60/503,661, filed Sep. 17, 2003; 60/503,671, filed Sep. 17, 2003; 60/503,672, filed Sep. 17, 2003; 60/513,807, filed Oct. 23, 2003; and 60/514,764, filed Oct. 27, 2003. This application also incorporates by reference the following U.S. patent applications: U.S. Ser. No. 10/723,987 entitled “Light Emitting Devices,” and filed Nov. 26, 2003; U.S. Ser. No. 10/724,004, entitled “Light Emitting Devices,” and filed Nov. 26, 2003; U.S. Ser. No. 10/724,033, entitled “Light Emitting Devices,” and filed Nov. 26, 2003; U.S. Ser. No. 10/724,006, entitled “Light Emitting Devices,” and filed Nov. 26, 2003; U.S. Ser. No. 10/724,029, entitled “Light Emitting Devices,” and filed Nov. 26, 2003; U.S. Ser. No. 10/724,015, entitled “Light Emitting Devices,” and filed Nov. 26, 2003; and U.S. Ser. No. 10/724,005, entitled “Light Emitting Devices,” and filed Nov. 26, 2003.
TECHNICAL FIELD [0003] The invention relates to electronic device contact structures. BACKGROUND [0004] A light emitting diode (LED) often can provide light in a more efficient manner than an incandescent light source and/or a fluorescent light source. The relatively high power efficiency associated with LEDs has created an interest in using LEDs to displace conventional light sources in a variety of lighting applications. For example, in some instances LEDs are being used as traffic lights and to illuminate cell phone keypads and displays. [0005] Typically, an LED is formed of multiple layers, with at least some of the layers being formed of different materials. In general, the materials and thicknesses selected for the layers determine the wavelength(s) of light emitted by the LED. In addition, the chemical composition of the layers can be selected to try to isolate injected electrical charge carriers into regions (commonly referred to as quantum wells) for relatively efficient conversion to optical power. Generally, the layers on one side of the junction where a quantum well is grown are doped with donor atoms that result in high electron concentration (such layers are commonly referred to as n-type layers), and the layers on the opposite side are doped with acceptor atoms that result in a relatively high hole concentration (such layers are commonly referred to as p-type layers). [0006] A common approach to preparing an LED is as follows. The layers of material are prepared in the form of a wafer. Typically, the layers are formed using an epitaxial deposition technique, such as metal-organic chemical vapor deposition (MOCVD), with the initially deposited layer being formed on a growth substrate. The layers are then exposed to various etching and metallization techniques to form contacts for electrical current injection, and the wafer is subsequently sectioned into individual LED chips. Usually, the LED chips are packaged. [0007] During use, electrical energy is usually injected into an LED and then converted into electromagnetic radiation (light), some of which is extracted from the LED. SUMMARY [0008] The invention relates to optical display systems and methods. [0009] In one aspect, the invention features an optical display system that includes a microdisplay having a surface and a light emitting device. The light emitting device includes a multi-layer stack of materials including a light generating region, and a first layer supported by the light generating region. A surface of the first layer is configured so that the light generated by the light generating region can emerge from the light emitting device via the surface of the first layer. The ratio of the aspect ratio of the surface of the microdisplay and the aspect ratio of the surface of the first layer is at most about two. [0010] In another aspect, the invention features an optical display system that includes a microdisplay, a light emitting device, and at least one optical component disposed along an optical path from the microdisplay to the light emitting device. The microdisplay, the light emitting device and the optical component are positioned so that, during use, an image plane of the system does not coincide with a surface of the microdisplay illuminated by light emitted by the light emitting device. [0011] In a further aspect, the invention features a method of illuminating a microdisplay using a plurality of light emitting devices. The method includes activating the plurality of light emitting devices so that at least one of the plurality of light emitting devices has an activation time that is different from an activation time of at least one of the other light emitting devices in the plurality of light emitting devices. [0012] In one aspect, the invention features an optical display system that includes a LED and a cooling system that is configured so that, during use, the cooling system regulates a temperature of the light-emitting diode. [0013] In another aspect, the invention features a light emitting device that includes a multi-layer stack of materials. The multi-layer stack of materials includes a light generating region, and a first layer supported by the light generating region. The surface of the first layer is configured so that the light generated by the light generating region can emerge from the light emitting device via the surface of the first layer. The surface of the first layer has a contact region configured so that, during use, at most about 20% an area of a microdisplay illuminated by the light emitting diode comprises dark spots formed due to the contact region. [0014] In a further aspect, the invention features an optical display system that includes a plurality of light emitting diodes, a microdisplay, at least one optical component disposed along an optical path from the microdisplay to the light emitting diode, and a beam aggregation device configured to combine light generated by the plurality of light emitting diodes. [0015] In an additional aspect, the invention features a system that includes a light emitting device. The light emitting device includes a rectangular multi-layer stack of materials including a light generating region, and a first layer supported by the light generating region. The surface of the first layer is configured so that light generated by the light generating region can emerge from the light emitting device via the surface of the first layer The light emitting device also includes at least one electrical contact pad disposed along an edge of the surface of the first layer, and a package. The package includes a plurality of plated regions for providing electrical contact to the light emitting device, a plurality of castellations to provide electrical contact from one surface of the package to the opposite surface of the package, and a plurality of wire bonds connected between the plated regions and the at least one electrical contact pad. [0016] In one aspect, the invention features a device that includes a material body designed for use in an electronic device, and a contact structure supported by the surface of the material body. The contact structure includes a patterned conductive layer and a patterned insulating layer. The patterned insulating layer is disposed between the interior portion of the patterned conductive layer and the surface of the material body. The insulating layer is patterned such that the conductive layer extends past all edges of the insulating layer to form an electrical contact to the material body. [0017] In another aspect, the invention features a device that includes a semiconductor die. The device also includes a conductive pad disposed along one side of a surface layer of the semiconductor die and another conductive pad disposed along the opposite side of the surface layer of the semiconductor die. The device further includes a plurality of conductive contacts in electrical contact with at least one of the conductive pads and extending from at least one of the conductive pads toward a central area of the semiconductor die. The device also includes an insulating layer disposed between an interior portion of at least some of the plurality of conductive contacts and the top layer of the semiconductor die. [0018] In a further aspect, the invention features a device that includes a rectangular light emitting diode (LED). The device also includes a conductive pad disposed along one side of a surface layer of the rectangular LED and another conductive pad disposed along the opposite side of the surface layer of the rectangular LED. The device further includes a plurality of conductive contacts in electrical contact with at least one of the conductive pads and extending from at least one of the conductive pads toward a central area of the rectangular LED. [0019] In an additional aspect, the invention features a device that includes a stack of materials and a contact structure disposed on the surface of the stack of materials. The contact structure includes a patterned conductive layer and a patterned insulating layer disposed between the patterned conductive layer and the surface of the stack of materials. The patterned conductive layer and the patterned insulating layer are configured such that during use a voltage drop across the patterned conductive layer is about the same at a plurality of segments disposed along the length of the patterned conductive layer. [0020] In yet another aspect, the invention features a device that includes a stack of materials and a contact structure disposed on the surface of the stack of materials. The contact structure includes a patterned conductive layer configured such that during use a heat generation across the patterned conductive layer is about the same at a plurality of segments disposed across the patterned conductive layer. [0021] Embodiments can feature one or more of the following advantages. [0022] In certain embodiments, a light-emitting system can include an LED and/or a relatively large LED chip that can exhibit relatively high light extraction. [0023] In some embodiments, a light-emitting system can include an LED and/or a relatively large LED chip that can exhibit relatively high surface brightness, relatively high average surface brightness, relatively low need for heat dissipation or relatively high rate of heat dissipation, relatively low etendue and/or relatively high power efficiency. [0024] In certain embodiments, a light-emitting system can include an LED and/or a relatively large LED chip that can be designed so that relatively little light emitted by the LED/LED chip is absorbed by packaging. [0025] In some embodiments, a light-emitting system can include a packaged LED (e.g., a relatively large packaged LED) that can be prepared without using an encapsulant material. This can result in a packaged LED that avoids certain problems associated with the use of certain encapsulant materials, such as reduced performance and/or inconsistent performance as a function of time, thereby providing a packaged LED that can exhibit relatively good and/or reliable performance over a relatively long period of time. [0026] In certain embodiments, a light-emitting system can include an LED (e.g., a packaged LED, which can be a relatively large packaged LED) that can have a relatively uniform coating of a phosphor material. [0027] In some embodiments, a light-emitting system can include an LED (e.g., a packaged LED, which can be a relatively large packaged LED) that can be designed to provide a desired light output within a particular angular range (e.g., within a particular angular range relative to the LED surface normal). [0028] In some embodiments, a light-emitting system can include an LED and/or a relatively large LED chip that can be prepared by a process that is relatively inexpensive. [0029] In certain embodiments, a light-emitting system can include an LED and/or a relatively large LED chip that can be prepared by a process that can be conducted on a commercial scale without incurring costs that render the process economically unfeasible. [0030] In some embodiments, using a rectangular shape for an LED (compared, for example, to a square) can provide certain advantages. The advantages can include one or more of the following. The rectangular LED can allow a greater number of wire bonds per unit area increasing the power that can be input into the LED. The rectangular shape can be chosen to match a particular aspect ratio of a pixel or microdisplay, thus, eliminating the need for complex beam shaping optics. The rectangular shape can also improve heat dissipation from the LED and reduce the likelihood of failure due to the device overheating. Also, because the cross section of an individual LEDs cut from a wafer is only slightly larger than the light-emitting surface area of the LED, many individual, and separately addressable LEDs can be packed closely together in an array. If one LED does not function (e.g., due to a large defect), then it does not significant diminish the performance of the array because the individual devices are closely packed. [0031] Features and advantages of the invention are in the description, drawings and claims.
[0097] Like reference symbols in the various drawings indicate like elements. DETAILED DESCRIPTION [0098] FIG. 1 is a schematic representation of a light-emitting system 50 that has an array 60 of LEDs 100 incorporated therein. Array 60 is configured so that, during use, light that emerges from LEDs 100 (see discussion below) emerges from system 50 via surface 55. [0099] Examples of light-emitting systems include projectors (e.g., rear projection projectors, front projection projectors), portable electronic devices (e.g., cell phones, personal digital assistants, laptop computers), computer monitors, large area signage (e.g., highway signage), vehicle interior lighting (e.g., dashboard lighting), vehicle exterior lighting (e.g., vehicle headlights, including color changeable headlights), general lighting (e.g., office overhead lighting), high brightness lighting (e.g., streetlights), camera flashes, medical devices (e.g., endoscopes), telecommunications (e.g. plastic fibers for short range data transfer), security sensing (e.g. biometrics), integrated optoelectronics (e.g., intrachip and interchip optical interconnects and optical clocking), military field communications (e.g., point to point communications), biosensing (e.g. photo-detection of organic or inorganic substances), photodynamic therapy (e.g. skin treatment), night-vision goggles, solar powered transit lighting, emergency lighting, airport runway lighting, airline lighting, surgical goggles, wearable light sources (e.g. life-vests). An example of a rear projection projector is a rear projector television. An example of a front projection projector is a projector for displaying on a surface, such as a screen or a wall. In some embodiments, a laptop computer can include a front projection projector. [0100] Typically, surface 55 is formed of a material that transmits at least about 20% (e.g., at least about 30%, at least about 40%, at least about 50%, at least about 60%, at least about 70%, at least about 80%, at least about 90%, at least about 95%) of the light that emerges from LEDs 100 and impinges on surface 55. Examples of materials from which surface 55 can be formed include glass, silica, quartz, plastic, and polymers. [0101] In some embodiments, it may be desirable for the light that emerges (e.g., total light intensity, light intensity as a function of wavelength, and/or peak emission wavelength) from each LED 100 to be substantially the same. An example is time-sequencing of substantially monochromatic sources (e.g. LEDs) in display applications (e.g., to achieve vibrant full-color displays). Another example is in telecommunications where it can be advantageous for an optical system to have a particular wavelength of light travel from the source to the light guide, and from the light guide to the detector. A further example is vehicle lighting where color indicates signaling. An additional example is in medical applications (e.g., photosensitive drug activation or biosensing applications, where wavelength or color response can be advantageous). [0102] In certain embodiments, it may be desirable for the light that emerges (e.g., total light intensity, light intensity as a function of wavelength, and/or peak emission wavelength) from at least some of LEDs 100 to be different from the light that emerges (e.g., total light intensity, light intensity as a function of wavelength, and/or peak emission wavelength) from different LEDs 100. An example is in general lighting (e.g., where multiple wavelengths can improve the color rendering index (CRI)). CRI is a measurement of the amount of color shift that objects undergo when lighted by the light-emitting system as compared with the color of those same objects when seen under a reference lighting system (e.g., daylight) of comparable correlated temperature. Another example is in camera flashes (e.g., where substantially high CRI, such as substantially close to the CRI of noontime sunlight, is desirable for a realistic rendering of the object or subject being photographed). A further example is in medical devices (e.g., where substantially consistent CRI is advantageous for tissue, organ, fluid, etc. differentiation and/or identification). An additional example is in backlighting displays (e.g., where certain CRI white light is often more pleasing or natural to the human eye). [0103] Although depicted in FIG. 1 as being in the form of an array, LEDs 100 can be configured differently. As an example, in some embodiments, system 50 includes a single LED 100. As another example, in certain embodiments, the array is curved to help angularly direct the light from various sources onto the same point (e.g., an optic such as a lens). As a further example, in some embodiments, the array of devices is hexagonally distributed to allow for close-packing and high effective surface brightness. As an additional example, in certain embodiments, the devices are distributed around a mirror (e.g., a dichroic mirror) that combines or reflects light from the LEDs in the array. [0104] In FIG. 1 the light that emerges from LEDs 100 is shown as traveling directly from LEDs 100 to surface 55. However, in some embodiments, the light that emerges from LEDs 100 can travel an indirect path from LEDs 100 to surface 55. As an example, in some embodiments, system 50 includes a single LED 100. As another example, in certain embodiments, light from LEDs 100 is focused onto a microdisplay (e.g., onto a light valve such as a digital light processor (DLP) or a liquid crystal display (LCD)). As a further example, in some embodiments, light is directed through various optics, mirrors or polarizers (e.g., for an LCD). As an additional example, in certain embodiments, light is projected through primary or secondary optics, such as, for example, a lens or a set of lenses. [0105] FIG. 2A shows an optical display system 1100 (see discussion above) including a non-Lambertian LED 1110 (see discussion below), a lens 1120 and a microdisplay 1130. LED 1110 is spaced a distance L1 from lens 1120, and microdisplay 1130 is spaced a distance L2 from lens 1120. Distances L1 and L2 are selected so that, for light emitted by LED 1110 that impinges on lens 1120, the image plane of lens 1120 coincides with the surface of microdisplay 1130 on which the light emitted by LED 1110 impinges. [0106] With this arrangement, system 1100 can use the light emitted by LED 1110 to relatively efficiently illuminate the surface of microdisplay 1130 with the shape of the surface of LED 1110 that emits light being about the same as the shape of the surface of 1130 that is illuminated by the light emitted by LED 1110. For example, in some embodiments, the ratio the aspect ratio of LED 1110 to the aspect ratio of microdisplay 1130 can be from about 0.5 to about 2 (e.g., from about 9/16 to about 16/9, from about 3/4 to about 4/3, about 1). The aspect ratio of microdisplay 1130 can be, for example, 1920�1080, 640�480, 800�600, 1024�700, 1024�768, 1024�720, 1280�720, 1280�768, 1280�960, or 1280�1064. [0107] In general, the surface of microdisplay 1130 and/or the surface of LED 1110 can have any desired shape. Examples of such shapes include square, circular, rectangular, triangular, trapezoidal, and hexagonal. [0108] In some embodiments, an optical display system can relatively efficiently illuminate the surface of microdisplay 1130 without a lens between LED 1110 and microdisplay 1130 while still having the shape of the surface of LED 1110 that emits light being about the same as the shape of the surface of 1130 that is illuminated by the light emitted by LED 1110. For example, FIG. 2B shows a system 1102 in which a square LED 1110 is imaged onto a square microdisplay 1130 without having a lens between LED 1110 and microdisplay 1130. As another example, FIG. 2C shows an optical display system 1104 in which a rectangular LED 1110 can be imaged onto a rectangular microdisplay 1130 (with a similarly proportioned aspect ratio) without having a lens between LED 1110 and microdisplay 1130. [0109] In certain embodiments, an anamorphic lens can be disposed between LED 1110 and microdisplay 1130. This can be desirable, for example, when the aspect ratio of LED 1110 is substantially different from the aspect ratio of microdisplay 1130. As an example, FIG. 2D shows a system 1106 that includes LED 1110 having a substantially square shaped surface, microdisplay 1130 having a substantially rectangular shaped surface (e.g., an aspect ratio of about 16:9 or about 4:3), and an anamorphic lens 1120 disposed between LED 1110 and microdisplay 1130. In this example, anamorphic lens 1120 can be used to convert the shape of the light emitted by LED 1110 to substantially match the shape of the surface of microdisplay 1130. This can enhance the efficiency of the system by increasing the amount of light emitted by the surface of LED 1110 that impinges upon the surface of microdisplay 1130. [0110] FIG. 3 shows an optical display system 1200 including LED 1110, lens 1120, and microdisplay 1130. The light emitting surface of LED 1110 has contact regions to which electrical leads 1115 are attached (see discussion below). LED 1110 is spaced a distance L3 from lens 1120, and microdisplay 1130 is spaced a distance L4 from lens 1120. Leads 1115 block light from being emitted from the contact regions of LED 1110. If the plane of the surface of microdisplay 1130 on which the light emitted by LED 1110 impinges coincides with the image plane of lens 1120, a set of dark spots 1202 corresponding to the contact region of the light emitting surface of LED 1110 can appear on this surface of microdisplay 1130. To reduce the area of this surface of microdisplay 1130 that is covered by the dark spots, distances L3 and L4 are selected so that, for light emitted by LED 1110 that impinges on lens 1120, the image plane of lens 1120 does not coincide with the plane of the surface of microdisplay 1130 on which the light emitted by LED 1110 impinges (i.e., there exists a distance, ΔL, between the image plane of lens 1120 and the plane of the surface of microdisplay 1130 on which the light emitted by LED 1110 impinges). With this arrangement, the light from LED 1110 is defocused in the plane of the surface of microdisplay 1130 on which the light emitted by LED 1110 impinges, and the resulting intensity of light is more uniform on this surface of microdisplay 1130 than in the image plane of lens 1120. The total distance between the LED and the microdisplay 1130 can be represented as the distance between the LED 1110 and the image plane 1120 (L5) plus the distance, ΔL. In general, as ΔL is increased by increasing the distance between the LED 1110 and the microdisplay 1130, the intensity of dark spots decreases but the intensity of light emitted by LED 1110 that impinges on the surface of microdisplay 1130 decreases. Alternately, when the microdisplay is translated such that the distance between the LED 1110 and the microdisplay 1130 is decreased, the intensity is greater than the intensity at the image plane, but the microdisplay may be only partially illuminated. In some embodiments, the absolute value of ΔL/L5 is from about 0.00001 to about 1 (e.g., from about 0.00001 to about 0.1, from about 0.00001 to about 0.01, from about 0.00001 to about 0.001), or from about .00001 to about .0001) In some embodiments, multiple LEDs may be used to illuminate a single microdisplay (e.g., a 3�3 matrix of LEDs). Such a system can be desirable because, when multiple LEDs are arranged to illuminate a single microdisplay, if one LEDs fails, the system would still be useable (however a dark spot may occur due to the absence of light from the particular LED). If multiple LEDs are used to illuminate a single microdisplay, the optical system can be configures so that dark spots do not appear on the surface of the microdisplay. For example, the microdisplay can be translated outside of the image plane such that the area between the LEDs does not result in a dark spot. [0111] In some embodiments, the intensity of dark spots on the surface of microdisplay 1130 can be reduced by appropriately configuring the contact region of the surface of LED 1110. For example, FIG. 4A shows a top view of an LED 1110 with a contact region disposed around the perimeter of LED 1110. With this arrangement, with or without the presence of a lens (with or without defocusing), the optical display system can be configured (e.g., by properly sizing the area of the surface of microdisplay 1130) so that the intensity of the dark spots created by the contact region of the surface of LED 1110 on surface 1130 is relatively small. This approach may be used with systems that include multiple LEDs (e.g., a 3�3 matrix of LEDs). [0112] As another example, FIG. 4B shows an optical display system 300 that includes LED 1110 and microdisplay 1130. LED 1110 includes a contact region formed by leads 1115 that is selected so that dark spots 1202 appear at a region not imaged on the surface of microdisplay 1130. In this example, the surface of microdisplay 1130 can be located at the image plane of lens 1120 because the dark spots fall outside of the area imaged on the microdisplay at the image plane of lens 1120. If the shape of LED 1110 is matched to the shape of microdisplay 1130, leads 1115 can be disposed, for example, on the surface of LED 1110 around its perimeter. In this example, the area inside the contact region of surface 1110 matches (e.g., the aspect ratio is similar) to the surface of microdisplay 1130. This approach may be used with systems that include multiple LEDs (e.g., a 3�3 matrix of LEDs). [0113] As a further example, FIG. 5 shows an optical display system 1700 that includes LED 1110 and microdisplay 1130. LED 1110 also includes a contact region formed by leads 1115 and a homogenizer 1702 (also referred to as a light tunnel or light pipe) that guides light emitted from LED 1110 to a lens 1120. Total internal reflection of the light emitted by LED 1110 off the inside surfaces of homogenizer 1702 can generate a substantially uniform output distribution of light and can reduce the appearance of dark spots caused by leads 1115 so that microdisplay 1130 is substantially uniformly illuminated by LED 1110 (e.g., an image generated in an image plane 1131 is substantially uniform). [0114] Optionally, system 1700 can include one or more additional optical components. For example, in some embodiments, optical display system 1700 can also include a lens disposed in the path prior to the homogenizer to focus light into the homogenizer. In certain embodiments, the aspect ratio of the aperture of homogenizer 1702 matches that of LED 1110 such that when LED 1110 is mounted in close proximity to homogenizer 1702, additional lenses may not be necessary or such that more efficient coupling of light into homogenizer 1702 is possible with a lens prior to homogenizer 1702. [0115] As an additional example, FIG. 6 shows an optical display system 1710 that includes LED 1110 and microdisplay 1130. LED 1110 also includes a contact region formed by leads 1115 and a set of multiple lenses 1712 that are disposed between LED 1110 and lens 1120. Lenses 1712 can vary in size, shape, and number. For example, the number and size of lenses 1712 can be proportional to the cross-sectional area of LED 1110. In some embodiments, lenses 1712 include a set of between about 1 and about 100 lenses with sizes varying of, for example, from about 1 mm to about 10 cm. The light emitted by LED 1110, enters lenses 1712 and is refracted. Since the surfaces of lenses 1712 are curved, the light refracts at different angles causing the beams emerging from lenses 1712 to overlap. The overlapping of the beams reduces the appearance of dark spots caused by leads 1115 so that microdisplay 1130 is substantially uniformly illuminated by LED 1110 (e.g., an image generated in an image plane 1131 is substantially uniform). [0116] While optical display systems have been described as including a single lens, in some embodiments, multiple lenses can be used. Further, in certain embodiments, one or more optical components other than lens(es) can be used. Examples of such optical components include mirrors, reflectors, collimators, beam splitters, beam combiners, dichroic mirrors, filters, polarizers, polarizing beam splitters, prisms, total internal reflection prisms, optical fibers, light guides and beam homogenizers. The selection of appropriate optical components, as well as the corresponding arrangement of the components in the system, is known to those skilled in the art. [0117] Moreover, although optical display systems have been described as including one non-Lambertian LED, in some embodiments, more than one non-Lambertian LED can be used to illuminate microdisplay 1130. For example, FIG. 7 shows a system 1500 that includes a blue LED 1410 (an LED with a dominant output wavelength from about 450 to about 480 nm), a green LED 1420 (an LED with a dominant output wavelength from about 500 to about 550 nm), and a red LED 1430 (an LED with a dominant output wavelength from about 610 to about 650 nm) which are in optical communication with the surface of microdisplay 1130. LEDS 1410, 1420, and 1430 can be arranged to be activated simultaneously, in sequence or both. In other embodiments, at least some of the LEDs may be in optical communication with separate microdisplay surfaces. [0118] In some embodiments, LEDs 1410, 1420, and 1430 are activated in sequence. In such embodiments, a viewer's eye generally retains and combines the images produced by the multiple colors of LEDs. For example, if a particular pixel (or set of pixels) or microdisplay (or portion of a microdisplay) of a frame is intended to be purple in color, the surface of the microdisplay can be illuminated with red LED 1430 and blue LED 1410 during the appropriate portions of a refresh cycle. The eye of a viewer combines the red and the blue and “sees” a purple microdisplay. In order for a human not to notice the sequential illumination of the LEDs, a refresh cycle having an appropriate frequency (e.g., a refresh rate greater than 120 Hz) can be used. [0119] LEDs 1410, 1420 and 1430 may have varying intensities and brightness. For example, green LED 1420 may have a lower efficiency than red LED 1430 or blue LED 1410. Due to a particular LED (e.g., green LED 1420) having a lower efficiency, it can be difficult to illuminate the surface of the microdisplay with a sufficiently high brightness of the color of light (e.g., green) emitted by the relatively low efficiency LED (e.g., LED 1420). To compensate for this disparity in efficiency (to produce an image that is not distorted due to the difference in light brightness), the activation cycles for the multiple LEDs can be adjusted. For example, the least efficient LED may be allocated a longer activation time (i.e., on for a longer period of time) than the more efficient LEDs. In a particular example, for a red/green/blue projection system instead of a 1/3:1/3:1/3 duty cycle allocation, the cycle may be in the ratio of 1/6:2/3:1/6 (red:green:blue). In another example, the cycle may be in the ratio of 0.25:0.45:0.30 (red:green:blue). In other examples, the duty cycle dedicated to the activation of the green LED may be further increased. For example, the duty cycle dedicated to imaging the green LED 1420 can be greater than about 40% (e.g., greater than about 45%, greater than about 50%, greater than about 60%, greater than about 70%, greater than about 80%, greater than about 90%). In some embodiments, the duty cycle for each LED is different. As an example, the duty cycle for red LED 1430 can be greater than the duty cycle for blue LED 1410. While systems have been described in which the activation cycle is selected based on the intensity and/or brightness of an LED, in some systems the activation time of an LED may be selected based on one or more other parameters. In some examples, the activation time of the least efficient light emitting device is at least about 1.25 times (e.g., at least about 1.5 times, at least about 2 times, at least about 3 times) the activation time of another light emitting device. [0120] FIG. 8A shows an embodiment of a liquid crystal display (LCD) based optical display system 1720 including blue LED 1410, green LED 1420, and red LED 1430 (e.g., as described above) which are in optical communication with the surface of associated LCD panels 1728, 1730, and 1732. Optical display system 1720 also includes lenses 1722, 1724, and 1726 in a corresponding optical path between LEDs 1410, 1420, and 1430 and associated LCD panels 1728, 1730, and 1732. Lenses 1722, 1724, and 1726 focus the light onto associated LCD panels 1728, 1730, and 1732. Optical display system 1720 further includes a device 1734 (e.g., an x-cube) that combines multiple beams of light from LCD panels 1728, 1730, and 1732 into a single beam 1736 (indicated by arrows) that can be directed to a projection lens 1735 or other display Optionally, optical display system 1720 can include a polarizer that transmits a desired polarization (e.g. the ‘p’ polarization) while reflecting another polarization (e.g. the ‘s’ polarization). The polarizer can be disposed in the path between LEDs 1410, 1420, and 1430 and associated lenses 1722, 1724, and 1726, between lenses 1722, 1724, and 1726 and the associated LCD panels 1728, 1730, and 1732, or in other locations along the optical path. As shown in FIG. 8B, in some embodiments the aspect ratio of an LED (e.g., LED 1430) can be matched to the aspect ratio of the microdisplay (e.g., microdisplay 1732) as described above. [0121] FIG. 9 shows an embodiment of a digital light processor (DLP) based optical display system 1750 including blue LED 1410, green LED 1420, and red LED 1430 (as described above) which are each in optical communication with associated lenses 1722, 1724, and 1726 (as described above). Light emitted from LEDs 1410, 1420, and 1430 passes through the associated lenses 1722, 1724, and 1726 and is collected by a device 1734 (e.g., an x-cube) that combines multiple beams of light emitted by LEDs 1410, 1420, and 1430 into a single beam that can be directed to a total internal reflection (TIR) prism 1752. For example, the light emerging from x-cube 1734 can be directed to TIR prism 1752 by a mirror 1754 or other device such as a light guide. TIR prism 1752 reflects light and directs the light to a DLP panel 1756. DLP panel 1756 includes a plurality of mirrors that can be actuated to generate a particular image. For example, a particular mirror can either reflect light 1760 (indicated by arrows) such that the light is directed to a projection 1755 or can cause the light to be reflected away from projection lens 1755. The combination of the LEDs 1410, 1420, and 1430 and DLP panel 1756 allow greater control of the signal. For example, the amount of data sent to DLP panel 1756 can be reduced (allowing greater switching frequency) by switching on and off LEDs 1410, 1420, and 1430 in addition to the mirrors in DLP panel 1756. For example, if no red is needed in a particular image, red LED 1430 can be switched off eliminating the need to send a signal to DLP 1752 to switch the associated mirror. The ability to modulate the LEDs can improve for example color quality, image quality, or contrast. [0122] FIG. 10 shows a particular embodiment of a liquid crystal on silicon (LCOS) based optical display system 1770 including blue LED 1410, green LED 1420, and red LED 1430 (as described above) which are each in optical communication with an associated polarizing beam splitter 1774, 1778, and 1782. Light emitted from LEDs 1410, 1420, and 1430 passes through the associated polarizing beam splitters 1774, 1778, and 1782 and is projected onto an associated LCOS panel 1772, 1776, or 1780. Since LCOS panels 1772, 1776, and 1780 are not sensitive to all polarizations of light, the polarizing beam splitters 1774, 1778, and 1782 polarize the light to a particular polarization (e.g., by transmitting a desired polarization (e.g., the ‘p’ polarization) while reflecting another polarization (e.g., the ‘s’ polarization) the polarization of some light and pass other polarizations) based on the sensitivity of LCOS panels 1772, 1776, and 1780. The light reflected from LCOS panels 1772, 1776, and 1780 is collected by a device 1734 (e.g., an x-cube) that combines the beams of light from the multiple LCOS panels 1772, 1776, and 1780 to generate a beam 1790 (indicated by arrows) that is directed to a projection lens 1795. [0123] While in the above examples, the optical display system includes red, green, and blue light emitting devices, other colors and combinations are possible. For example, the system need not have only three colors. Additional colors such as yellow may be included and allocated a portion of the duty cycle. Alternately, multiple LEDs having different dominant wavelengths may be optically combined to produce a resulting color. For example, a blue-green LED (e.g., an LED with a dominant wavelength between the wavelength of blue and green) can be combined with a yellow LED to produce ‘green’ light. In general, the number of LEDs and the color of each LED can be selected as desired. Additional microdisplays can also be included. [0124] In some embodiments, the duty cycle for the lesser efficient LED (e.g. green) can be increased by various data compression techniques and algorithms. For example, sending only the difference in image information from the previous image rather than the total information required to reconstruct each image allows an increase in the data rate. Using this method, less data needs to be sent allowing for higher data rates and reduced duty cycles for complementary colors for a given refresh cycle. [0125] In embodiments in which multiple LEDs are used to illuminate a given microdisplay, optical componentry may or may not be present along the light path between one or more of the LEDs and the microdisplay. For example, an x-cube or a set of dichroic mirrors may be used to combine light from the multiple LEDs onto a single microdisplay. In embodiments in which optical componentry is present along the light path, different optical componentry can be used for each LED (e.g. if the surface of the LEDs are of different size or shape), or the same optical componentry can be used for more than one LED. [0126] In some embodiments, differing brightness for a particular color based on the desired chromaticity of an image may be obtained by illuminating the display for a portion of the activation time allocated to the particular LED. For example, to obtain an intense blue, the blue LED can be activated for the entire activation time and for a less intense blue, the blue LED is activated for only a portion of the total allocated activation time. The portion of the activation time used to illuminate the display can be modulated, for example, by a set of mirrors that can be positioned to either pass light to the microdisplay or reflect the light away from the microdisplay. [0127] In certain embodiments, an array of moveable microdisplays (e.g., a moveable mirror) is actuated to produce a desired intensity. For example, each micromirror can represent a pixel and the intensity of the pixel can be determined by the positioning of the microdisplay. For example, the micromirror can be in an on or an off state and the proportion of the time spent in the on state during the activation time of a particular color of LED determines the intensity of the image. [0128] In general, in embodiments in which multiple LEDs are used, one or more of the LEDs (e.g., each LED) can have the aspect ratio relationship described above with respect to the aspect ratio of microdisplay 1130. [0129] FIG. 11 shows an optical display system 1600 that includes LED 1110, microdisplay 1130, a cooling system 1510, and a sensor 1520 that is in thermal communication with LED 1110 and electrical communication with cooling system 1510 so that, during use of system 1600, sensor 1520 and cooling system 1510 can be used to regulate the temperature of LED 1110. This can be desirable, for example, when LED 1110 is a relatively large are LED (see discussion below) because such an LED can generate a significant amount of heat. With the arrangement shown in FIG. 11, the amount of power input to LED 1110 can be increased with (primarily, increased operational efficiency at higher drive currents) reduced risk of damaging LED 1110 via the use of sensor 1520 and cooling system 1510 to cool LED 1110. Examples of cooling systems include thermal electric coolers, fans, heat pipes, and liquid cooling systems. Sensor 1520 can be, for example, manually controlled or computer controlled. In some embodiments, the system may not include a sensor (e.g., cooling system 1510 can be permanently on, or can be manually controlled). The use of a cooling system can provide multiple advantages such as reducing the likelihood of damage to the LED resulting from an excess temperature and increasing the efficiency of the LED at higher drive currents. The cooling system may also reduce the shift in wavelength induced by temperature. [0130] In some embodiments, using a non-lambertian LED results in non-uniform angular distribution of light. In such embodiments, the microdisplay can be translated away from the image plane to reduce the appearance of the angular non-uniformity. In certain embodiments, information flow to the microdisplay can be achieved using an electrical or optical connection. In some examples, the rate of information flow can be increased using an optical connection. [0131] In some embodiments, the size of a PLLED or other non-lambertian source can be increased and the light can be collected at a smaller angle. This can increase the brightness of the image 6 n a display. [0132] FIG. 12 shows a side view of an LED 100 in the form of a packaged die. LED 100 includes a multi-layer stack 122 disposed on a submount 120. Multi-layer stack 122 includes a 320 nm thick silicon doped (n-doped) GaN layer 134 having a pattern of openings 150 in its upper surface 110. Multi-layer stack 122 also includes a bonding layer 124, a 100 nm thick silver layer 126, a 40 nm thick magnesium doped (p-doped) GaN layer 128, a 120 nm thick light-generating region 130 formed of multiple InGaN/GaN quantum wells, and a AlGaN layer 132. An n-side contact pad 136 is disposed on layer 134, and a p-side contact pad 138 is disposed on layer 126. An encapsulant material (epoxy having an index of refraction of 1.5) 144 is present between layer 134 and a cover slip 140 and supports 142. Layer 144 does not extend into openings 150. [0133] Light is generated by LED 100 as follows. P-side contact pad 138 is held at a positive potential relative to n-side contact pad 136, which causes electrical current to be injected into LED 100. As the electrical current passes through light-generating region 130, electrons from n-doped layer 134 combine in region 130 with holes from p-doped layer 128, which causes region 130 to generate light. Light-generating region 130 contains a multitude of point dipole radiation sources that emit light (e.g., isotropically) within the region 130 with a spectrum of wavelengths characteristic of the material from which light-generating region 130 is formed. For InGaN/GaN quantum wells, the spectrum of wavelengths of light generated by region 130 can have a peak wavelength of about 445 nanometers (nm) and a full width at half maximum (FWHM) of about 30 nm. [0134] It is to be noted that the charge carriers in p-doped layer 126 have relatively low mobility compared to the charge carriers in the n-doped semiconductor layer 134. As a result, placing silver layer 126 (which is conductive) along the surface of p-doped layer 128 can enhance the uniformity of charge injection from contact pad 138 into p-doped layer 128 and light-generating region 130. This can also reduce the electrical resistance of device 100 and/or increase the injection efficiency of device 100. Because of the relatively high charge carrier mobility of the n-doped layer 134, electrons can spread relatively quickly from n-side contact pad 136 throughout layers 132 and 134, so that the current density within the light-generating region 130 is substantially uniform across the region 130. It is also to be noted that silver layer 126 has relatively high thermal conductivity, allowing layer 126 to act as a heat sink for LED 100 (to transfer heat vertically from the multi-layer stack 122 to submount 120). [0135] At least some of the light that is generated by region 130 is directed toward silver layer 126. This light can be reflected by layer 126 and emerge from LED 100 via surface 110, or can be reflected by layer 126 and then absorbed within the semiconductor material in LED 100 to produce an electron-hole pair that can combine in region 130, causing region 130 to generate light. Similarly, at least some of the light that is generated by region 130 is directed toward pad 136. The underside of pad 136 is formed of a material (e.g., a Ti/Al/Ni/Au alloy) that can reflect at least some of the light generated by light-generating region 130. Accordingly, the light that is directed to pad 136 can be reflected by pad 136 and subsequently emerge from LED 100 via surface 110 (e.g., by being reflected from silver layer 126), or the light that is directed to pad 136 can be reflected by pad 136 and then absorbed within the semiconductor material in LED 100 to produce an electron-hole pair that can combine in region 130, causing region 130 to generate light (e.g., with or without being reflected by silver layer 126). [0136] As shown in FIGS. 12 and 13, surface 110 of LED 100 is not flat but consists of a modified triangular pattern of openings 150. In general, various values can be selected for the depth of openings 150, the diameter of openings 150 and the spacing between nearest neighbors in openings 150 can vary. Unless otherwise noted, for purposes of the figures below showing the results of numerical calculations, openings 150 have a depth 146 equal to about 280 nm, a non-zero diameter of about 160 nm, a spacing between nearest neighbors or about 220 nm, and an index of refraction equal to 1.0. The triangular pattern is detuned so that the nearest neighbors in pattern 150 have a center-to-center distance with a value between (a−Δa) and (a+Δa), where “a” is the lattice constant for an ideal triangular pattern and “Δa” is a detuning parameter with dimensions of length and where the detuning can occur in random directions. To enhance light extraction from LED 100 (see discussion below), detuning parameter, Δa, is generally at least about one percent (e.g., at least about two percent, at least about three percent, at least about four percent, at least about five percent) of ideal lattice constant, a, and/or at most about 25% (e.g., at most about 20%, at most about 15%, at most about 10%) of ideal lattice constant, a. In some embodiments, the nearest neighbor spacings vary substantially randomly between (a−Δa) and (a+Δa), such that pattern 150 is substantially randomly detuned. [0137] For the modified triangular pattern of openings 150, it has been found that a non-zero detuning parameter enhances the extraction efficiency of an LED 100. For LED 100 described above, as the detuning parameter Δa increases from zero to about 0.15 a, numerical modeling (described below) of the electromagnetic fields in the LED 100 has shown that the extraction efficiency of the device increases from about 0.60 to about 0.70, as shown in FIG. 14. [0138] The extraction efficiency data shown in FIG. 14 are calculated by using a three-dimensional finite-difference time-domain (FDTD) method to approximate solutions to Maxwell's equations for the light within and outside of LED 100. See, for example, K. S. Kunz and R. J. Luebbers, The Finite-Difference Time-Domain Methods (CRC, Boca Raton, Fla., 1993); A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, London, 1995), both of which are hereby incorporated by reference. To represent the optical behavior of LED 100 with a particular pattern 150, input parameters in a FDTD calculation include the center frequency and bandwidth of the light emitted by the point dipole radiation sources in light-generating region 130, the dimensions and dielectric properties of the layers within multilayer stack 122, and the diameters, depths, and nearest neighbor distances (NND) between openings in pattern 150. [0139] In certain embodiments, extraction efficiency data for LED 100 are calculated using an FDTD method as follows. The FDTD method is used to solve the full-vector time-dependent Maxwell's equations: ∇ → � E → = - μ ∂ H → ∂ t , ∇ → � H → = ɛ ∞ ∂ E → ∂ t + ∂ P → ∂ t , where the polarizability {right arrow over (P)}={right arrow over (P)}1+{right arrow over (P)}2+ . . . +{right arrow over (P)}m captures the frequency-dependent response of the quantum well light-generating region 130, the p-contact layer 126 and other layers within LED 100. The individual {right arrow over (P)}m terms are empirically derived values of different contributions to the overall polarizability of a material (e.g., the polarization response for bound electron oscillations, the polarization response for free electron oscillations). In particular, ⅆ 2 P → m ⅆ t 2 + γ m ⅆ P → m ⅆ t + ω m 2 P → m = ɛ ( ω ) E → , where the polarization corresponds to a dielectric constant ɛ ( ω ) = ɛ ∞ + ∑ m s m ω m 2 - ω 2 - ⅈγ m ω . [0140] For purposes of the numerical calculations, the only layers that are considered are encapsulant 144, silver layer 126 and layers between encapsulant 144 and silver layer 126. This approximation is based on the assumption that encapsulant 144 and layer 126 are thick enough so that surrounding layers do not influence the optical performance of LED 100. The relevant structures within LED 100 that are assumed to have a frequency dependent dielectric constant are silver layer 126 and light-generating region 130. The other relevant layers within LED 100 are assumed to not have frequency dependent dielectric constants. It is to be noted that in embodiments in which LED 100 includes additional metal layers between encapsulant 144 and silver layer 126, each of the additional metal layers will have a corresponding frequency dependent dielectric constant. It is also to be noted that silver layer 126 (and any other metal layer in LED 100) has a frequency dependent term for both bound electrons and free electrons, whereas light-generating region 130 has a frequency dependent term for bound electrons but does not have a frequency dependent term for free electrons. In certain embodiments, other terms can be included when modeling the frequency dependence of the dielectric constant. Such terms may include, for example, electron-phonon interactions, atomic polarizations, ionic polarizations and/or molecular polarizations. [0141] The emission of light from the quantum well region of light-generating region 130 is modeled by incorporating a number of randomly-placed, constant-current dipole sources within the light-generating region 130, each emitting short Gaussian pulses of spectral width equal to that of the actual quantum well, each with random initial phase and start-time. [0142] To cope with the pattern of openings 150 in surface 110 of the LED 100, a large supercell in the lateral direction is used, along with periodic boundary conditions. This can assist in simulating relatively large (e.g., greater than 0.01 mm on edge) device sizes. The full evolution equations are solved in time, long after all dipole sources have emitted their energy, until no energy remains in the system. During the simulation, the total energy emitted, the energy flux extracted through top surface 110, and the energy absorbed by the quantum wells and the n-doped layer is monitored. Through Fourier transforms both in time and space, frequency and angle resolved data of the extracted flux are obtained, and therefore an angle- and frequency-resolved extraction efficiency can be calculated. By matching the total energy emitted with the experimentally known luminescence of light-generating region 130, absolute angle-resolved extraction in lumens/per solid angle/per chip area for given electrical input is obtained. [0143] Without wishing to be bound by theory, it is believed that the detuned pattern 150 can enhance the efficiency with which light generated in region 130 emerges from LED 100 via surface 110 because openings 150 create a dielectric function that varies spatially in layer 134 according to pattern 150. It is believed that this alters the density of radiation modes (i.e., light modes that emerge from surface 110) and guided modes (i.e., light modes that are confined within multi-layer stack 122) within LED 100, and that this alteration to the density of radiation modes and guided modes within LED 100 results in some light that would otherwise be emitted into guided modes in the absence of pattern 150 being scattered (e.g., Bragg scattered) into modes that can leak into radiation modes. In certain embodiments, it is believed that pattern 150 (e.g., the pattern discussed above, or one of the patterns discussed below) can eliminate all of the guided modes within LED 100. [0144] It is believed that the effect of detuning of the lattice can be understood by considering Bragg scattering off of a crystal having point scattering sites. For a perfect lattice arranged in lattice planes separated by a distance d, monochromatic light of wavelength λ is scattered through an angle θ according to the Bragg condition, nλ=2dsinθ, where n is an integer that gives the order of the scattering. However, it is believed that for a light source having a spectral bandwidth Δλ/λ and emitting into a solid angle ΔΘ, the Bragg condition can be relaxed by detuning the spacing of between lattice sites by a detuning parameter Δa. It is believed that detuning the lattice increases the scattering effectiveness and angular acceptance of the pattern over the spectral bandwidth and spatial emission profile of the source. [0145] While a modified triangular pattern 150 having a non-zero detuning parameter Δa has been described that can enhance light extraction from LED 100, other patterns can also be used to enhance light extraction from LED 100. When determining whether a given pattern enhances light extraction from LED 100 and/or what pattern of openings may be used to enhance light extraction from LED 100, physical insight may first be used to approximate a basic pattern that can enhance light extraction before conducting such numerical calculations. [0146] The extraction efficiency of LED 100 can be further understood (e.g., in the weak scattering regime) by considering the Fourier transform of the dielectric function that varies spatially according to pattern 150. FIG. 15 depicts the Fourier transform for an ideal triangular lattice. Extraction of light into a particular direction with in-plane wavevector k is related to the source emission Sk′ into all those modes with in-plane wavevector k′ (i.e. parallel to pattern 150) that are compatible to k by the addition or subtraction of a reciprocal lattice vector G, i.e k=k′�G. The extraction efficiency is proportional to the magnitude of the corresponding Fourier component (Fk) of the dielectric function εG given by F k → = c k → ∑ G -> ɛ G → S k → - G → , ɛ G → = ∫ ɛ ( r → ) ⅇ - ⅈ G → r → ⅆ r → [0147] Since light propagating in the material generally satisfies the equation k2(in-plane)+k2 (normal)=ε(ω/c)2, the maximum G to be considered is fixed by the frequency (ω) emitted by the light-generating region and the dielectric constant of the light-generating region. As shown in FIG. 15, this defines a ring in reciprocal space which is often called the light line. The light line will be an annulus due to the finite bandwidth of the light-generating region but for sake of clarity we illustrate the light line of a monochromatic source. Similarly, light propagating within the encapsulant is bounded by a light line (the inner circle in FIG. 15). Therefore, the extraction efficiency is improved by increasing Fk for all directions k that lie within the encapsulant light-line which amounts to increasing the number of G points within the encapsulant light line and increasing the scattering strength εG for G points which lie within the material light line. This physical insight can be used when selecting patterns that can improve extraction efficiency. [0148] As an example, FIG. 16 shows the effect of increasing lattice constant for an ideal triangular pattern. The data shown in FIG. 16 are calculated using the parameters given for LED 100 shown in FIG. 12, except that the emitted light has a peak wavelength of 450 nm, and the depth of the holes, the diameter of the holes, and the thickness of the n-doped layer 134 scale with the nearest neighbor distance, a, as 1.27 a, 0.72 a, and 1.27 a+40 nm, respectively. Increasing the lattice constant, increases the density of G points within the light-line of the encapsulant. A clear trend in extraction efficiency with NND is observed. It is believed that the maximum extraction efficiency occurs for NND approximately equal to the wavelength of light in vacuum. The reason a maximum is achieved, is that as the NND becomes much larger than the wavelength of light, the scattering effect is reduced because the material becomes more uniform. [0149] As another example, FIG. 17 shows the effect of increasing hole size or filling factor. The filling factor for a triangular pattern is given by (2π/√3)*(r/a)2, where r is the radius of a hole. The data shown in FIG. 17 are calculated using the parameters given for the LED 100 shown in FIG. 12, except that the diameter of the openings is changed according the filling factor value given on the x-axis of the graph. The extraction efficiency increases with filling factor as the scattering strengths (εG) increase. A maximum is observed for this particular system at a filling factor of �48%. In certain embodiments, LED 100 has a filling factor of at least about 10% (e.g., at least about 15%, at least about 20%) and/or at most about 90% (e.g., at most about 80%, at most about 70%, at most about 60%). [0150] While a modified triangular pattern has been described in which a detuning parameter relates to positioning of openings in the pattern from the positions in an ideal triangular lattice, a modified (detuned) triangular pattern may also be achieved by modifying the holes in an ideal triangular pattern while keeping the centers at the positions for an ideal triangular pattern. FIG. 18 shows an embodiment of such a pattern. The enhancement in light extraction, the methodology for conducting the corresponding numerical calculation, and the physical explanation of the enhanced light extraction for a light-emitting device having the pattern shown in FIG. 18 is generally the same as described above. In some embodiments, a modified (detuned) pattern can have openings that are displaced from the ideal locations and openings at the ideal locations but with varying diameters. [0151] In other embodiments, enhanced light extraction from a light-emitting device can be achieved by using different types of patterns, including, for example, complex periodic patterns and nonperiodic patterns. As referred to herein, a complex periodic pattern is a pattern that has more than one feature in each unit cell that repeats in a periodic fashion. Examples of complex periodic patterns include honeycomb patterns, honeycomb base patterns, (2�2) base patterns, ring patterns, and Archimidean patterns. As discussed below, in some embodiments, a complex periodic pattern can have certain openings with one diameter and other openings with a smaller diameter. As referred to herein, a nonperiodic pattern is a pattern that has no translational symmetry over a unit cell that has a length that is at least 50 times the peak wavelength of light generated by region 130. Examples of nonperiodic patterns include aperiodic patterns, quasicrystalline patterns, Robinson patterns, and Amman patterns. [0152] FIG. 19 shows numerical calculations for LED 100 for two different complex periodic patterns in which certain openings in the patterns have a particular diameter, and other openings in the patterns have smaller diameters. The numerical calculations represented in FIG. 19 show the behavior of the extraction efficiency (larger holes with a diameter of 80 nm) as the diameter of the smaller holes (dR) is varied from zero nm to 95 nm. The data shown in FIG. 17 are calculated using the parameters given for the LED 100 shown in FIG. 12 except that the diameter of the openings is changed according the filling factor value given on the x-axis of the graph. Without wishing to be bound by theory, multiple hole sizes allow scattering from multiple periodicities within the pattern, therefore increasing the angular acceptance and spectral effectiveness of the pattern. The enhancement in light extraction, the methodology for conducting the corresponding numerical calculation, and the physical explanation of the enhanced light extraction for a light-emitting device having the pattern shown in FIG. 19 is generally the same as described above. [0153] FIG. 20 shows numerical calculations for LED 100 having different ring patterns (complex periodic patterns). The number of holes in the first ring surrounding the central hole is different (six, eight or 10) for the different ring patterns. The data shown in FIG. 20 are calculated using the parameters given for the LED 100 shown in FIG. 12, except that the emitted light has a peak wavelength of 450 nm. The numerical calculations represented in FIG. 20 show the extraction efficiency of LED 100 as the number of ring patterns per unit cell that is repeated across a unit cell is varied from two to four. The enhancement in light extraction, the methodology for conducting the corresponding numerical calculation, and the physical explanation of the enhanced light extraction for a light-emitting device having the pattern shown in FIG. 20 is generally the same as described above. [0154] FIG. 21 shows numerical calculations for LED 100 having an Archimidean pattern. The Archimedean pattern A7 consists of hexagonal unit cells 230 of 7 equally-spaced holes with a nearest neighbor distance of a. Within a unit cell 230, six holes are arranged in the shape of a regular hexagon and the seventh hole is located at the center of the hexagon. The hexagonal unit cells 230 then fit together along their edges with a center-to-center spacing between the unit cells of a′=a*(1+√{square root over (3)}) to pattern the entire surface of the LED. This is known as an A7 tiling, because 7 holes make up the unit cell. Similarly, the Archimidean tiling A19 consists of 19 equally-spaced holes with a NND of a. The holes are arranged in the form of an inner hexagon of seven holes, and outer hexagon of 12 holes, and a central hole within the inner hexagon. The hexagonal unit cells 230 then fit together along their edges with a center-to-center spacing between the unit cells of a′=a*(3+√{square root over (3)}) to pattern the entire surface of the LED. The enhancement in light extraction, the methodology for conducting the corresponding numerical calculation, and the physical explanation of the enhanced light extraction for a light-emitting device having the pattern shown in FIG. 21 is generally the same as described above. As shown in FIG. 21 the extraction efficiency for A7 and A19 is about 77%. The data shown in FIG. 21 are calculated using the parameters given for the LED 100 shown in FIG. 12, except that the emitted light has a peak wavelength of 450 and except that the NND is defined as the distance between openings within an individual cell. [0155] FIG. 22 shows numerical calculation data for LED 100 having a quasicrystalline pattern. Quasicrystalline patterns are described, for example, in M. Senechal, Quasicrystals and Geometry (Cambridge University Press, Cambridge, England 1996), which is hereby incorporated by reference. The numerical calculations show the behavior of the extraction efficiency as the class of 8-fold based quasi-periodic structure is varied. It is believed that quasicrystalline patterns exhibit high extraction efficiency due to high degree of in-plane rotational symmetries allowed by such structures. The enhancement in light extraction, the methodology for conducting the corresponding numerical calculation, and the physical explanation of the enhanced light extraction for a light-emitting device having the pattern shown in FIG. 22 is generally the same as described above. Results from FDTD calculations shown in FIG. 22 indicate that the extraction efficiency of quasicrystalline structures reaches about 82%. The data shown in FIG. 22 are calculated using the parameters given for the LED 100 shown in FIG. 12, except that the emitted light has a peak wavelength of 450 and except that the NND is defined as the distance between openings within an individual cell. [0156] While certain examples of patterns have been described herein, it is believed that other patterns can also enhance the light extraction from LED 100 if the patterns satisfy the basic principles discussed above. For example, it is believed that adding detuning to quasicrystalline or complex periodic structures can increase extraction efficiency. [0157] In some embodiments, at least about 45% (e.g., at least about 50%, at least about 55%, at least about 60%, at least about 70%, at least about 80%, at least about 90%, at least about 95%) of the total amount of light generated by light-generating region 130 that emerges from LED 100 emerges via surface 110. [0158] In certain embodiments, the cross-sectional area of LED 100 can be relatively large, while still exhibiting efficient light extraction from LED 100. For example, one or more edges of LED 100 can be at least about one millimeter (e.g., at least about 1.5 millimeters, at least about two millimeters, at least about 2.5 millimeters, at least about three millimeters), and at least about 45% (e.g., at least about 50%, at least about 55%, at least about 60%, at least about 70%, at least about 80%, at least about 90%, at least about 95%) of the total amount of light generated by light-generating region 130 that emerges from LED 100 emerges via surface 110. This can allow for an LED to have a relatively large cross-section (e.g., at least about one millimeter by at least about one millimeter) while exhibiting good power conversion efficiency. [0159] In some embodiments, the extraction efficiency of an LED having the design of LED 100 is substantially independent of the length of the edge of the LED. For example, the difference between the extraction efficiency of an LED having the design of LED 100 and one or more edges having a length of about 0.25 millimeter and the extraction efficiency of LED having the design of LED 100 and one or more edges having a length of one millimeter can vary by less than about 10% (e.g., less than about 8%, less than about 5%, less than about 3%). As referred to herein, the extraction efficiency of an LED is the ratio of the light emitted by the LED to the amount of light generated by the device (which can be measured in terms of energy or photons). This can allow for an LED to have a relatively large cross-section (e.g., at least about one millimeter by at least about one millimeter) while exhibiting good power conversion efficiency. [0160] In certain embodiments, the quantum efficiency of an LED having the design of LED 100 is substantially independent of the length of the edge of the LED. For example, the difference between the quantum efficiency of an LED having the design of LED 100 and one or more edges having a length of about 0.25 millimeter and the quantum efficiency of LED having the design of LED 100 and one or more edges having a length of one millimeter can vary by less than about 10% (e.g., less than about 8%, less than about 5%, less than about 3%). As referred to herein, the quantum efficiency of an LED is the ratio of the number of photons generated by the LED to the number of electron-hole recombinations that occur in the LED. This can allow for an LED to have a relatively large cross-section (e.g., at least about one millimeter by at least about one millimeter) while exhibiting good performance. [0161] In some embodiments, the wall plug efficiency of an LED having the design of LED 100 is substantially independent of the length of the edge of the LED. For example, the difference between the wall plug efficiency of an LED having the design of LED 100 and one or more edges having a length of about 0.25 millimeter and the wall plug efficiency of LED having the design of LED 100 and one or more edges having a length of one millimeter can vary by less than about 10% (e.g., less than about 8%, less than about 5%, less than about 3%). As referred to herein, the wall plug efficiency of an LED is the product of the injection efficiency of the LED (the ratio of the numbers of carriers injected into the device to the number of carriers that recombine in the light-generating region of the device), the radiative efficiency of the LED (the ratio of electron-hole recombinations that result in a radiative event to the total number of electron-hole recombinations), and the extraction efficiency of the LED (the ratio of photons that are extracted from the LED to the total number of photons created). This can allow for an LED to have a relatively large cross-section (e.g., at least about one millimeter by at least about one millimeter) while exhibiting good performance. [0162] In some embodiments, it may be desirable to manipulate the angular distribution of light that emerges from LED 100 via surface 110. To increase extraction efficiency into a given solid angle (e.g., into a solid angle around the direction normal to surface 110) we examine the Fourier transform of the dielectric function that varies spatially according to pattern 150 (as described earlier). FIG. 23 shows the Fourier transform construction for two ideal triangular lattices of different lattice constant. To increase the extraction efficiency, we seek to increase the number of G points within the encapsulant light line and scattering strengths of G points (εG) within the material light line. This would imply increasing the NND so as to achieve the effect depicted in FIG. 16. However, here we are concerned with increasing the extraction efficiency into a solid angle centered around the normal direction. Therefore, we would also like to limit the introduction of higher order G points by reducing the radius of the encapsulant light line, such that the magnitude of G>(ω(ne))/c. We can see that by decreasing the index of refraction of the encapsulant (the bare minimum of which is removing the encapsulant all together) we allow larger NND and therefore increase the number of G points within the material light line that are available to contribute to extraction in the normal direction (Fk=0) while simultaneously avoiding diffraction into higher order (oblique angles) in the encapsulant. The above described trends are depicted in FIG. 24 which shows extraction efficiency into a solid angle (given by the collection half-angle in the diagram). The data shown in FIG. 24 are calculated using the parameters given for the LED 100 shown in FIG. 12, except that the emitted light has a peak wavelength of 530 nm and a bandwidth of 34 nm, the index of refraction of the encapsulant was 1.0, the thickness of the p-doped layer was 160 nm, the light generating layer was 30 nm thick, the NND (a) for the three curves is shown on FIG. 24, and the depth, hole diameter, and n-doped layer thickness scaled with a, as 1.27 a, 0.72 a, and 1.27 a+40 nm, respectively. As the lattice constant is increased, the extraction efficiency at narrow angles increases as well as the overall extraction efficiency into all angles. However, for even larger lattice constant, diffraction into higher order modes in the encapsulant limits the extraction efficiency at narrow angles even though the overall extraction efficiency increases into all angles. For a lattice constant of 460 nm, we calculate greater than 25% extraction efficiency into a collection half-angle of 30�. That is, about half of the extracted light is collected within only about 13.4% of the upper hemisphere of solid angle demonstrating the collimation effect of the pattern. It is believed that any pattern that increases the number of G points within the material light line while limiting the number of G points within the encapsulant light line to only the G points at k=0 can improve the extraction efficiency into a solid angle centered around the normal direction. [0163] The approach is especially applicable for reducing the source etendue which is believed to often be proportional to n2, where n is the index of refraction of the surrounding material (e.g., the encapsulant). It is therefore believed that reducing the index of refraction of the encapsulating layer for LED 100 can lead to more collimated emission, a lower source etendue, and therefore to a higher surface brightness (here defined as the total lumens extracted into the etendue of the source). In some embodiments then, using an encapsulant of air will reduce the source etendue while increasing extraction efficiency into a given collection angle centered around the normal direction. [0164] In certain embodiments, when light generated by region 130 emerges from LED 100 via surface 110, the distribution of light is more collimated than a lambertian distribution. For example, in some embodiments, when light generated by region 130 emerges from LED 100 via surface 110, at least about 40% (e.g., at least about 50%, at least about 70%, at least about 90%) of the light emerging via the surface of the dielectric layer emerges within at most about 30� (e.g., at most about 25�, at most about 20�, at most about 15�) of an angle normal to surface 110. [0165] The ability to extract a relatively high percentage of light from a desired angle alone or coupled with a relatively high light extraction can allow for a relatively high density of LEDs to be prepared on a given wafer. For example, in some embodiments, a wafer has at least about five LEDs (e.g., at least about 25 LEDs, at least about 50 LEDs) per square centimeter. [0166] In some embodiments, it may be desirable to modify the wavelength(s) of light that emerge(s) from a packaged LED 100 relative to the wavelength(s) of light generated by light-generating region 130. For example, as shown in FIG. 25, an LED 300 having a layer containing a phosphor material 180 can be disposed on surface 110. The phosphor material can interact with light at the wavelength(s) generated by region 130 to provide light at desired wavelength(s). In some embodiments, it may be desirable for the light that emerges from packaged LED 100 to be substantially white light. In such embodiments, the phosphor material in layer 180 can be formed of, for example, a (Y,Gd)(Al,Ga)G:Ce3+ or “YAG” (yttrium, aluminum, garnet) phosphor. When pumped by blue light emitted from the light-generating region 130, the phosphor material in layer 180 can be activated and emit light (e.g., isotropically) with a broad spectrum centered around yellow wavelengths. A viewer of the total light spectrum emerging from packaged LED 100 sees the yellow phosphor broad emission spectrum and the blue InGaN narrow emission spectrum and typically mixes the two spectra to perceive white. [0167] In certain embodiments, layer 180 can be substantially uniformly disposed on surface 110. For example, the distance between the top 151 of pattern 150 and the top 181 of layer 180 can vary by less than about 20% (e.g., less than about 10%, less than about 5%, less than about 2%) across surface 110. [0168] In general, the thickness of layer 180 is small compared to the cross-sectional dimensions of surface 130 of LED 100, which are typically about one millimeter (mm) by one mm. Because layer 180 is substantially uniformly deposited on surface 110, the phosphor material in layer 180 can be substantially uniformly pumped by light emerging via surface 110. The phosphor layer 180 is relatively thin compared to the dimensions of the surface 110 of the LED 100, such that light emitted by the light-generating region 130 is converted into lower wavelength light within the phosphor layer 180 approximately uniformly over the entire surface 110 of LED 100. Thus, the relatively thin, uniform phosphor layer 180 produces a uniform spectrum of white light emitted from the LED 100 as a function of position on surface 110. [0169] In general, LED 100 can be fabricated as desired. Typically, fabrication of LED 100 involves various deposition, laser processing, lithography, and etching steps. [0170] For example, FIG. 26 shows a LED wafer 500 containing an LED layer stack of material deposited on a substrate (e.g., sapphire, compound semiconductor, zinc oxide, silicon carbide, silicon) 502. Such wafers are commercially available. Exemplary commercial suppliers include Epistar Corporation, Arima Optoelectronics Corporation and South Epitaxy Corporation. On substrate 502 are disposed, consecutively, a buffer layer 504 (e.g., a nitride-containing layer, such as a GaN layer, an AlN layer, an AlGaN layer), an n-doped semiconductor layer (e.g., an n-doped Si:GaN) layer 506, a current spreading layer 508 (e.g., an AlGaN/GaN heterojunction or superlattice), a light-emitting region 510 (e.g., an InGaN/GaN multi-quantum well region), and a semiconductor layer 512 (e.g., a p-doped Mg:GaN layer). Wafer 500 generally has a diameter of at least about two inches (e.g., from about two inches to about 12 inches, from about two inches to about six inches, from about two inches to about four inches, from about two inches to about three inches). [0171] FIG. 27 shows a multi-layer stack 550 including layers 502, 504, 506, 508, 510 and 512, as well as layers 520, 522, 524 and 526, which are generally formed of materials capable of being pressure and/or heat bonded as described below. For example, layer 520 can be a nickel layer (e.g., electron-beam evaporated), layer 522 can be a silver layer (e.g., electron-beam evaporated), layer 524 can be a nickel layer (e.g., electron-beam evaporated), and layer 526 can be a gold layer (e.g., electron-beam evaporated). In some embodiments, layer 520 can be a relatively thin layer, and layer 524 can be a relatively thick layer. Layer 524 can act, for example, as diffusion barrier to reduce the diffusion of contaminants (e.g., gold) into layers 520, 522 and/or 524 itself. After deposition of layers 520, 522, 524 and 526, multi-layer stack 550 can be treated to achieve an ohmic contact. For example, stack 550 can be annealed (e.g., at a temperature of from about 400� C. to about 600� C.) for a period of time (e.g., from about 30 seconds to about 300 seconds) in an appropriate gas environment (e.g., nitrogen, oxygen, air, forming gas). [0172] FIG. 28 shows a multi-layer stack 600 that includes a submount (e.g., germanium (such as polycrystalline germanium), silicon (such as polycrystalline silicon), silicon-carbide, copper, copper-tungsten, diamond, nickel-cobalt) 602 having layers 604, 606, 608 and 610 deposited thereon. Submount 602 can be formed, for example, by sputtering or electroforming. Layer 604 is a contact layer and can be formed, for example, from aluminum (e.g., electron evaporated). Layer 606 is a diffusion barrier and can be formed, for example, from Ni (e.g. electron evaporated). Layer 608 can be a gold layer (e.g., electron-beam evaporated), and layer 610 can be a AuSn bonding layer (e.g., thermal evaporated, sputtered) onto layer 608. After deposition of layers 604, 606, 608 and 610, multi-layer stack 600 can be treated to achieve an ohmic contact. For example, stack 600 can be annealed (e.g., at a temperature of from about 350� C. to about 500� C.) for a period of time (e.g., from about 30 seconds to about 300 seconds) in an appropriate gas environment (e.g., nitrogen, oxygen, air, forming gas). [0173] FIG. 29 shows a multi-layer stack 650 formed by bonding together layers 526 and 610 (e.g., using a solder bond, using a eutectic bond, using a peritectic bond). Layers 526 and 610 can be bonded, for example, using thermal-mechanical pressing. As an example, after contacting layers 526 and 610, multi-layer stack 650 can be put in a press and pressurized (e.g., using a pressure of up to about 5 MPa, up to about 2 MPa) heated (e.g., to a temperature of from about 200� C. to about 400� C.). Stack 650 can then be cooled (e.g., to room temperature) and removed from the press. [0174] Substrate 502 and buffer layer 504 are then at least partially removed from stack 650. In general, this can be achieved using any desired methods. For example, as shown in FIG. 30, in some embodiments, substrate 502 is removed by exposing stack 650 (e.g., through surface 501 of substrate 502) to electromagnetic radiation at an appropriate wavelength to partially decompose layer 504. It is believed that this results in local heating of layer 504, resulting in the partial decomposition of the material of layer 504 adjacent the interface of layer 504 and substrate 502, thereby allowing for the removal of substrate 502 from stack 650 (see discussion below). For example, in embodiments in which layer 504 is formed of gallium nitride, it is believed that constituents including gallium and gaseous nitrogen are formed. In some embodiments, stack 650 can be heated during exposure of surface 501 to the electromagnetic radiation (e.g., to reduce strain within stack 650). Stack 650 can be heated, for example, by placing stack 650 on a hot plate and/or by exposing stack 650 to an additional laser source (e.g. a CO2 laser). Heating stack 650 during exposure of surface 501 to electromagnetic radiation can, for example, reduce (e.g., prevent) liquid gallium from re-solidifying. This can reduce the build up of strain within stack 650 which can occur upon the re-solidification of the gallium [0175] In certain embodiments, after exposure to the electromagnetic radiation, residual gallium is present and keeps substrate 502 bonded in stack 650. In such embodiments, stack 650 can be heated to above the melting temperature of gallium to allow substrate 502 to be removed from the stack. In certain embodiments, stack 650 may be exposed to an etchant (e.g., a chemical etchant, such as HCl) to etch the residual gallium and remove substrate 502. Other methods of removing the residual gallium (e.g., physical methods) may also be used. [0176] As an example, in certain embodiments, surface 501 is exposed to laser radiation including the absorption wavelength of layer 504 (e.g., about 248 nanometers, about 355 nanometers). Laser radiation processes are disclosed, for example, in U.S. Pat. Nos. 6,420,242 and 6,071,795, which are hereby incorporated by reference. The multi-layer stack is then heated to above the melting point of gallium, at which point substrate 502 and buffer layer 504 are removed from the stack by applying a lateral force to substrate 502 (e.g., using a cotton swab). [0177] In some embodiments, multiple portions of surface 501 are simultaneously exposed to the electromagnetic radiation. In certain embodiments, multiple portions of surface 501 are sequentially exposed to electromagnetic radiation. Combinations of simultaneous and sequential exposure can be used. Further, the electromagnetic radiation can be exposed on surface 501 in the form of a pattern (e.g., a serpentine pattern, a circular pattern, a spiral pattern, a grid, a grating, a triangular pattern, an elementary pattern, a random pattern, a complex pattern, a periodic pattern, a nonperiodic pattern). In some embodiments, the electromagnetic radiation can be rastered across one or more portions of surface 501. In certain embodiments, surface 501 is exposed to overlapping fields of electromagnetic radiation. [0178] In some embodiments, the electromagnetic radiation passes through a mask before reaching surface 501. As an example, the electromagnetic radiation can pass through an optical system that includes a mask (e.g., a high thermal conductivity mask, such as a molybdenum mask, a copper-beryllium mask) before reaching surface 501. In some embodiments, the mask is an aperture (e.g., for truncating or shaping the beam). The optical system can include, for example, at least two lenses having the mask disposed therebetween. As another example, the mask can be formed as a pattern of material on surface 501, with the mask leaving certain portions of surface 501 exposed and some portions of surface 501 unexposed. Such a mask can be formed, for example, via a lithography process. In some embodiments, the electromagnetic radiation can be rastered across one or more portions of the mask. [0179] Without wishing to be bound by theory, it is believed that reducing at least one dimension of the region on surface 501 exposed to electromagnetic radiation within a given area of surface 501 can limit undesired crack propagation, such as crack propagation into layer 504, layer 506 or other layers of stack 650 during removal of substrate 502, while still allowing for crack propagation at the interface between substrate 502 and buffer layer 504. It is believed that, if the size of the feature of the electromagnetic radiation on surface 501 is too large, then a gaseous bubble (e.g., a nitrogen bubble) may form that can create a localized pressure that can cause undesired cracking. For example, in embodiments in which surface 501 is exposed to laser radiation that forms a spot or a line on surface 501, at least one dimension of the spot or line can be a maximum of at most about one millimeter (e.g., at most about 500 microns, at most about 100 microns, at most about 25 microns, at most about 10 microns). In some embodiments, the spot size is from about five microns to about one millimeter (e.g., from about five microns to about 100 microns, from about five microns to about 25 microns, from about five microns to about 10 microns). [0180] In certain embodiments, stack 650 is vibrated while surface 501 is exposed to the electromagnetic radiation. Without wishing to be bound by theory, it is believed that vibrating stack 650 while exposing stack 650 to the electromagnetic radiation can enhance crack propagation along the interface between layer 504 and substrate 502. Generally, the conditions are selected to limit the propagation of cracks into layer 504 (e.g., so that substantially no cracks propagate into layer 504, 506, and the rest of stack 650). [0181] After removal of substrate 502, a portion of buffer layer 504 typically remains on at least a portion of the surface of layer 506. A residue of material from substrate 502 (e.g., containing aluminum and/or oxygen) can also be present on the remaining portion of buffer layer 504 and/or on the surface of layer 506. It is generally desirable to remove the remaining portions of buffer layer 504 and any residue from substrate 502, to expose the surface of layer 506, and to clean the exposed surface of layer 506 because layer 506 (which is typically formed of an n-doped semiconductor material) can exhibit good electrical properties (e.g., desirable contact resistance) for subsequent formation of an electrical contact. One or more process steps are usually used to remove any residue and/or remaining portion of buffer layer 504 present, and to clean the surface of layer 506 (e.g., to remove impurities, such as organics and/or particles). The process(es) can be performed using a variety of techniques and/or combinations of techniques. Examples include chemical-mechanical polishing, mechanical polishing, reactive ion etching (e.g., with a substantially chemically etching component), physical etching, and wet etching. Such methods are disclosed, for example, in Ghandhi, S., VLSI Fabrication Principles: Silicon & Gallium Arsenide (1994), which is hereby incorporated by reference. In certain embodiments, buffer layer 504 is not completely removed. Instead, in such embodiments, these processes can be used to remove only on portions of buffer layer 504 that correspond to locations where electrical leads will subsequently be disposed (e.g., by using a self-aligned process). [0182] Often, when substrate 502 is removed, the amount of strain in stack 650 (e.g., due to the lattice mismatch and/or thermal mismatch between the layers in stack 650) can change. For example, if the amount of strain in stack 650 is decreased, the peak output wavelength of region 510 can change (e.g., increase). As another example, if the amount of strain in stack 650 is increased, the peak output wavelength of region 510 can change (e.g., decrease). [0183] To limit undesired cracking during removal of substrate 502, in some embodiments, consideration is given to the coefficient of thermal expansion of both substrate 502, the coefficient of thermal expansion of submount 602, the combined thickness of layers 504, 506, 508, 510, and 512, and/or the coefficient of thermal expansion of one or more of layers 504, 506, 508, 510, and 512. As an example, in some embodiments, substrate 502 and submount 602 are selected so that the coefficient of thermal expansion of submount 602 differs from a coefficient of thermal expansion of substrate 502 by less than about 15% (e.g., less than about 10%, less than about 5%). As another example, in certain embodiments, substrate 502 and submount 602 are selected so that the thickness of submount 602 is substantially greater than the thickness of substrate 502. As an additional example, in some embodiments, semiconductor layers 504, 506, 508, 510, 512 and submount 602 are selected so that the coefficient of thermal expansion of submount 602 differs from a coefficient of thermal expansion of one or more of layers 504, 506, 608, 510, and 512 by less than about 15% (e.g., less than about 10%, less than about 5%). [0184] In general, substrate 502 and submount 602 can have any desired thickness. In some embodiments, substrate 502 is at most about five millimeters (e.g., at most about three millimeters, at most about one millimeter, about 0.5 millimeter) thick. In certain embodiments, submount 602 is at most about 10 millimeters (e.g., at most about five millimeters, at most about one millimeter, about 0.5 millimeter) thick. In some embodiments, submount 602 is thicker than substrate 502, and, in certain embodiments, substrate 502 is thicker than submount 602. [0185] After removal of buffer layer 504 and exposing/cleaning the surface of layer 506, the thickness of layer 506 can be reduced to a desired final thickness for use in the light-emitting device. This can be achieved, for example, using a mechanical etching process, alone or in combination with an etching process. In some embodiments, after etching/cleaning the exposed surface of layer 506, the surface of layer 506 has a relatively high degree of flatness (e.g., a relatively high degree of flatness on the scale of the lithography reticle to be used). As an example, in some embodiments, after etching/cleaning the exposed surface of layer 506, the surface of layer 506 has a flatness of at most about 10 microns per 6.25 square centimeters (e.g., at most about five microns per 6.25 square centimeters, at most about one micron per 6.25 square centimeters). As another example, in certain embodiments, after etching/cleaning the exposed surface of layer 506, the surface of layer 506 has a flatness of at most about 10 microns per square centimeter (e.g., at most about five microns per square centimeter, at most about one microns per square centimeter). In certain embodiments, after etching/cleaning the exposed surface of layer 506, the surface of layer 506 has an RMS roughness of at most about 50 nanometers (e.g., at most about 25 nanometers, at most about 10 nanometers, at most about five nanometers, at most about one nanometer). [0186] In some embodiments, prior to forming the dielectric function that varies spatially according to a pattern in the surface of layer 506, the exposed surface of layer 506 may be too rough and/or insufficiently flat to use nanolithography to form the pattern with sufficient accuracy and/or reproducibility. To enhance the ability to accurately and/or reproducibly form the pattern in the surface of layer 506, the nanolithography process may include depositing a planarization layer on the surface of layer 506 and a lithography layer on the surface of the planarization layer. For example, FIG. 31 shows an embodiment in which a planarization layer 702 is disposed on the surface of layer 506, and a lithography layer 704 is disposed on the surface of layer 702, an exposed surface 505 of layer 506 may be relatively rough (e.g., RMS roughness of about 10 nanometers or more) after cleaning/etching layer 506. In some embodiments, planarization layer 702 is formed of multiple layers (e.g., of the same material) that are sequentially deposited. [0187] Examples of materials from which planarization layer 702 can be selected include polymers (e.g., DUV-30J from Brewer Sciences, anti-reflection coatings, high viscosity formable polymers), and examples of materials from which lithography layer 704 can be selected include UV-curable polymers (e.g., low viscosity MonoMat™ available from Molecular Imprints, Inc.). Layers 702 and 704 can be formed using any desired technique, such as, for example, spin coating, vapor deposition, and the like. [0188] Layer 702 can be, for example, at least about 100 nanometers thick (e.g., at least about 500 nanometers thick) and/or at most about five microns thick (e.g., at most about one micron thick). Layer 704 can be, for example, at least about one nanometer thick (e.g., at least about 10 nanometers thick) and/or at most about one micron thick (e.g., at most about 0.5 micron thick). [0189] A mold that defines a portion of the desired pattern is then pressed into lithography layer and (typically with heating or UV-curing of the mold and/or layer 704), and stepped across the surface of layer 704 in a portion-by-portion manner to form indentions in layer 704 (FIG. 32) that correspond to the desired pattern in the surface of layer 506. In some embodiments, a single step covers the entire wafer (e.g., full wafer nanolithography techniques). Layer 704 is then etched (e.g., using reactive ion etching, wet etching) to expose portions of the surface of layer 702 corresponding to what were the indented portions of layer 704 (FIG. 33). Examples of such imprint/etch processes are disclosed, for example, in U.S. Pat. No. 5,722,905, and Zhang et al., Applied Physics Letters, Vol. 83, No. 8, pp. 1632-34, both of which are hereby incorporated by reference. Typically, the pattern in layer 704 also leaves regions for depositing n-contacts later on in the process flow. In alternate embodiments, other techniques (e.g., x-ray lithography, deep ultraviolet lithography, extreme ultraviolet lithography, immersion lithography, interference lithography, electron beam lithography, photolithography, microcontact printing, self-assembly techniques) may be used to create the pattern in layer 704. [0190] As shown in FIG. 34, patterned layer 704 is used as a mask to transfer the pattern into the planarization layer 702 (e.g., dry etching, wet etching). An example of a dry etching method is reactive ion etching. Referring to FIG. 35, layers 702 and 704 are subsequently used as a mask to transfer the pattern into the surface of layer 506 (e.g., using dry etching, wet etching). As shown in FIG. 36, following etching of layer 506, the layers 702 and 704 are removed (e.g., using an oxygen-based reactive ion etch, a wet solvent etch). [0191] Referring to FIG. 37, in some embodiments, the process can include, disposing a material 708 (e.g., a metal, such as aluminum, nickel, titanium, tungsten) in the etched portions of layers 702 and 704 (e.g., by evaporation) and on the surface of layer 704. As shown in FIG. 38, layers 702 and 704 are then etched (e.g., using reactive ion etching, wet etching), leaving behind etch-resistant material 708 on the surface of layer 506, which can serve as a mask for etching the pattern into the surface of layer 506 (FIG. 39). Referring to FIG. 40, etch resistant material 708 can then be removed (e.g., using dry etching, wet etching). [0192] In some embodiments, the process can include, after forming the indents in layer 704, disposing (e.g., spin coating) an etch resistant material (e.g., a Si-doped polymer) 710 on the surface of layer 704 and in the indents in layer 704, and material 710 is then etched back (e.g., using dry etching) so that to expose the surface of layer 704 while maintaining the etch-resistant material in the indents in layer 704 (FIG. 41). As shown in FIG. 42, portions of layers 702 and 704 are then etched (e.g., using reactive ion etching, dry etching, wet etching), leaving behind etch-resistant material 708 and the portions of layers 702 and 704 under material 708, which serve as a mask for etching the pattern into the surface of layer 506 (FIG. 43). Referring to FIG. 44, the remaining portions of layers 702 and 704, as well as etch resistant material 708, can then be removed (e.g., using reactive ion etching, dry etching, wet etching). In some embodiments, removing layer 708 can involve the use of a plasma process (e.g., a fluorine plasma process). [0193] After the pattern has been transferred to n-doped layer 506, a layer of phosphor material can optionally be disposed (e.g., spin-coated) onto the patterned surface of n-doped layer 506. In some embodiments, the phosphor can conformally coat the patterned surface (coat with substantially no voids present along the bottoms and sidewalls of the openings in the patterned surface). Alternatively, a layer of encapsulant material can be disposed on the surface of patterned n-doped layer 506 (e.g. by CVD, sputtering, suspension by liquid binder that is subsequently evaporated). In some embodiments, the encapsulant can contain one or more phosphor materials. In some embodiments, the phosphor can be compressed to achieve thickness uniformity less than about 20%, less than about 15%, less than about 10%, less than about 5%, or less than about 2% of the average thickness of the phosphor. In some embodiments, the phosphor-containing encapsulant can conformally coat the patterned surface. [0194] After the dielectric function pattern has been created in the n-doped layer 506, individual LED dice can be cut from the wafer. Once wafer processing and wafer testing is complete, individual LED dice are separated and prepared for packaging and testing. A sidewall passivation step and/or a pre-separation deep mesa etching step may be used to reduce potential damage to the electrical and/or optical properties of the patterned LED incurred during wafer cutting. The individual LEDs can be any size up to the size of the wafer itself, but individual LEDs are typically square or rectangular, with sides having a length between about 0.5 mm to 5 mm. To create the dice, standard photolithography is used to define the location of contact pads on the wafer for energizing the device, and ohmic contacts are evaporated (e.g. using electron beam evaporation) onto the desired locations. [0195] In some embodiments, as shown in FIG. 45A, a contact layout for an LED 1802 includes two conductive pads 1804 a and 1804 b and conductive bars (or fingers) 1806 extending from conductive pads 1804 a and 1804 b toward a central area of LED 1802. Wire bonds (not shown) connected to conductive pads 1804 a and 1804 b provide current and voltage to LED 1802. Conductive bars 1806 spread the current from the conductive pads 1804 a and 1804 b to a top surface 1808 of LED 1802. Bars 1806 allow the current to be spread sufficiently across top surface 1808 while limiting the amount of surface 1808 covered by the contacts. [0196] FIG. 45B shows a top view of LED 1802 including conductive pads 1804 a and 1804 b and conductive bars 1806. In some embodiments, the width of conductive pads 1804 a and 1804 b can be larger than the width of conductive bars 1806. The larger width of pads 1804 a and 1804 b can allow pads 1804 a and 1804 b to function as power busses and spread a relatively large amount of power down the bus to bars 1806. The width of pads 1804 a and 1804 b and bars 1806 can be relative to the size of LED 1802 and/or can be based on other factors such as lithography and processing parameters. [0197] For example, an LED may range in size from about 0.5 mm to about 1 cm on a side. As described above, the aspect ratio of LED 1802 can also vary. The width of conductive pads 1804 a and 1804 b can be, for example, about 50 um to about 500 um and the width of bars 1806 can be, for example, about 1 um to about 50 um. The height of conductive pads 1804 a and 1804 b and bars 1806 can vary based on, for example, current and power to be supplied to the LED or based on deposition and processing parameters. For example, conductive pads 1804 a and 1804 b and bars 1806 can be about 0.1 um to about 10 um in height. [0198] In general, bars 1806 can vary as desired in both length and shape. As shown in FIG. 45B, bars 1806 can be rectangular and extend from conductive pads 1804 a and 1804 b toward a central region of LED 1802. Alternatively, bars 1806 could have a different shape such as square, triangular, or trapezoidal. [0199] FIGS. 46A to 46C show another example of a contact structure. In this example, multiple bars 1812 extend across the entire length of LED 1810, connecting conductive pad 1804 a to conductive pad 1804 b. Contact bars 1812 have an associated resistivity rm, thickness tb, and a length l. Current distribution properties for LED 1810 based on conductive pads 1804 a and 1804 b and contact bars 1812 can be estimated by simplifying the structure into an equivalent circuit model as shown in FIG. 46C. [0200] The aspect ratio of LED 1810 can influence the current dissipation of the system. The aspect ratio ‘L’ of LED 1810 can be calculated according to the following equation as shown below: L=√{square root over (Ab/a)}
[0201] where A is the die's surface area (e.g., length multiplied by width) and a and b are the aspect ratios of the die. For example for an LED with a 16�9 aspect ratio, a=16 and b=9. [0202] As described above, in order to allow light generated in the LED to be emitted through the surface, contact bars 1812 do not cover the entire surface of LED 1810. Since the contacts cover only a portion of the surface of LED 1810, the contact resistance is divided by the surface coverage ratio f as shown in the following equation ρn-c→ρn-c/f [0203] The current density across the junction can be estimated according to the following equation as shown below: J=J 0(e eV j /KT−1), [0204] where J0 is the junction saturation current and T the absolute temperature. The above estimates neglect the contribution of the n-type material in lateral current spreading. However, in general the current spreading is predominantly occurring in the metal contact because the conductivity of the contact is much greater than the conductivity of the n-type material. For example, the ratio of the contact conductivity to the n-type material conductivity can be in the range of from about 100 to about 500. [0205] In a similar system (but with infinite separation between the pads), if the calculation is performed in a forward bias (e.g., Vj>>kT/e) and if the voltage drop across the series resistance is much larger than kT/e (e.g., (ρp-c+ρn-c/f+ρptp+ρntn)J0eeV j /kT>>kT/e), then a linear approximation of the current density distribution at the junction can be estimated according to the following equation J(x)=J 1(e −x/L s +e −(L−x)/L s ) [0206] where J1 is the current density beneath a pad, x is the distance from a pad, and Ls is the current spreading length as shown in the following equation L s=√{square root over ((ρp-c+ρn-c /f+ρ p t p+ρn t n)t m/ρm)}
[0207] This estimation assumes an infinite separation between the pads. However, for a linear approximation with non-infinite separation, the solutions for individual pads can be added together. The procedure described above introduces an error close to the die center, but is not believed to significantly alter the physical trends. [0208] The minimum current density can appear at the center of the device x=L/2 and can be estimated according to the following the following equation Jmin=2J1e−L/2L s [0209] where the uniformity factor is estimated as shown in equation U = J ( L / 2 ) J ( 0 ) = 2 ⅇ - L / 2 L s 1 + ⅇ - L / L s . [0210] For a die with the same surface area, switching from a square shape into a rectangular shape with aspect ratios a,b where the contact bars are along the small side, the minimum current density increases and the uniformity factor is modified as shown in the following equations J min ′ = 2 J 1 ⅇ - Ab / a 2 L s U ′ = J ( L ′ / 2 ) J ( 0 ) = 2 ⅇ - Ab / a / 2 L s 1 + ⅇ - Ab / a / L s [0211] Thus, a uniformity increase factor can be estimated as shown in equation S = U ′ / U = 1 + ⅇ - A / L s 1 + ⅇ - Ab / a / L s ⅇ A 2 L s ( 1 - b / a ) [0212] For example, the uniformity increase factor ‘S’ has a minimum value S=1 for the square case (e.g., a=b). For a 16�9 rectangle, assuming the following values: ρm=2.2�10−6 Ωcm (gold), ρp-c=1.0�10−3 Ωcm2, ρp=5.0 Ωcm, ρn-c=1.0�10−4 Ωcm2, ρn=5.0�10−3 Ωcm, n-contact surface coverage 10%, and thicknesses for p-, n-, and metal 0.3 μm, 3.0 μm and 2 μm (at a 10% coverage). Then Ls equals 1.4 mm. If the die has a surface area of A=25 mm2. In the square case U=0.325, while in the 16�9 case U′=0.5, or a uniformity increase factor S=1.54, i.e. a 54% increase of current uniformity. [0213] Thus, without wishing to be bound by theory, it is believed that using a rectangular shape for an LED can provide benefits in the current spreading. The contact resistivity can alternatively or additionally be altered to enhance the current spreading by including an insulating layer 1820 (e.g., an oxide layer, FIG. 47A) underneath a portion of the contact. As shown in FIGS. 47A and 47B, insulating layer 1820 (indicated by dashed lines) is included under a portion of bar 1812. Insulating layer 1820 has a greater width at the top of the bar (e.g., close to pads 1804) and gets thinner towards the central area of the die. An equivalent circuit diagram is shown in FIG. 47B. [0214] Contact resistivity is generally proportional to the contact area. For example, the contact resistivity increases as the contact area decreases as shown in the following equation ρ n - c eff = ρ n - c f eff = ρ n - c W 2 w = ρ n - c WL 2 xw b = ρ n - c f L 2 x [0215] where W is the repetition rate of the bars (e.g., the number of bars per unit area). Due to underlying insulating layer 1820, the area of the contact is smaller at the edge of the contact closest to pads 1804 a and 1804 b and increases as the distance from pads 1804 a and 1804 b increases. Due to the difference in contact area, the contact resistivity is higher close to pads 1804 a and 1804 b and decreases gradually towards the center of the LED. The difference in contact resistivity can force the current to travel further, reducing current crowding, increasing uniformity of light emission through the surface, and reducing performance degradation. The current spreading length can be estimated according to the following equation L s(x)=√{square root over ((ρp-c+(ρn-c /f)(L/2x)+ρp t p+ρn t n)t m/ρm)}
[0216] The junction current density along the die can be estimated by the following equation J ( x ) = J 1 ⅇ - ∫ 0 x ⅆ x / L s ( x ) + J 1 ⅇ - ∫ L x ⅆ x / L s ( L - x ) and [0217] the minimum current is at the center of the device (e.g., at x=L/2) can be estimated according to the following equation J min = 2 J 1 ⅇ - ∫ 0 L / 2 ⅆ x / L s ( x ) [0218] The current uniformity factor for the structure shown in FIG. 47B can be estimated according to the following equation U = J ( L / 2 ) J ( 0 ) = 2 ⅇ - ∫ 0 L / 2 ⅆ x / 2 L s ( x ) 1 + ⅇ - ∫ 0 L ⅆ x / 2 L s ( x ) . [0219] As described above, oxide layer 1820 can force current towards the ends of the contacts (e.g., toward the central area of the die) increasing the current spreading. Oxide layer 1820 can also reduce the light generation underneath the light absorbing contacts allowing greater percentage of the generated light to emerge from the surface of the LED. [0220] FIGS. 48A and 48B show a further configuration of pads 1804 a and 1804 b, contact 1830, and oxide layer 1820 (indicated by dashed lines and disposed under a portion of contact 1830). Here, contacts 1830 are also tapered. While shown in FIG. 48A as being linearly tapered, other tapering could be used. The linear tapering maintains a similar total contact area to the contact area of contact 1812 shown in FIG. 47A, with the contact width at the die center being approximately half of the width of bars 1812 (FIG. 47A), while the contact width at the pads is 3 times larger than the width shown in FIG. 47A. The oxide can be tapered at higher angle so that the contact resistance is maximum at the pad and minimum at the die center. The contact resistance decreases towards the die center, and the bar resistance decreases closer to the pad. The tapering of both the contact and the insulating layer contribute to forcing the current towards the die center. The local spreading length can be estimated according to the following equation L s(x)=√{square root over ((ρp-c+(ρn-c /f)(L/x)+ρp t p+ρn t n)t m/(2ρm/(3−4x/L)))}. [0221] Similar integration formulas for the current distribution as described above can be used to estimate the current distribution for the structure shown in FIGS. 48A and 48B. [0222] FIG. 49A shows a top view and FIGS. 49B and 49C show cross-sectional views of an additional contact structure 1801. Conductive contacts 1836 extend toward the center of the die, but do not continuously cover the upper surface of the LED between bars 1804 a and 1804 b. An insulating layer 1834 is located between the top of the LED and metal contact 1836 in an interior portion of the contact. Both the contact 1836 and the insulating layer 1834 are tapered. Arrows 1837 represent the current spreading from the metal contact 1836 into the surface of the die. [0223] FIG. 50 shows a graph 1850 of estimated normalized junction current density as a function of the normalized distance between bars 1804 a and 1804 b for various contact and die configurations based on the forgoing equations. Line 1856 represents the current density for square die with rectangular bars and no oxide, line 1858 represents the current density for rectangular die with rectangular bars and no oxide, line 1860 represents the current density for a rectangular die with rectangular bars and tapered oxide, and line 1862 represents the current density for rectangular die with tapered bars and tapered oxide. Graph 1850 shows the improvement in the current density distribution for both a rectangular chip and an oxide layer under a portion of the contact. [0224] FIG. 51A shows a top view and FIG. 51B shows a cross-sectional view of an additional contact structure 1803. Insulating layers 1805 a and 1805 b are located between the top of the LED and metal pads 1804 a and 1804 b, respectively. Insulating layers 1805 a and 1805 b are located under a portion of metal pads 1804 a and 1804 b, respectively, toward the edge of the die such that a portion of metal pads 1804 a and 1804 b are supported by insulating layers 1805 a and 1805 b, respectively, and a portion of metal pads 1804 a and 1804 b are supported by the top surface of the light emitting diode. Oxide layers 1805 a and 1805 b reduce the light generation underneath the light absorbing metal pads 1804 a and 1804 b allowing greater percentage of the generated light to emerge from the surface of the LED. [0225] While embodiments described above include a single set of contacts extending from metal pads 1804 a and 1804 b, multiple sets of contacts could be used. For example, a second set of contacts could extend from the set of contacts connected to metal pads 1804 and so forth. Further, while oxide layers have been described, most generally, the layers can be formed of any appropriate electronically insulating material (e.g., nitride). [0226] FIG. 52 shows the dimensions of an example of a contact 1899 and can be used to estimate electrical transport inside the n-contact. It is assumed contact 1899 distributes a uniform current density J0 within contact period D 1870. The total current to be carried by the contact can be estimated as shown in the following equation Imax=J0DL. [0227] This maximum current is flowing at the top of the contact (at the pad) corresponding to a current density that can be estimated as shown in the following equation J max = J 0 D WT L [0228] At any distance x from the bar's end, the current density can be estimated as shown in the following equation J = J 0 D WT x [0229] The voltage drop per unit length can be estimated as shown in the following equation ⅆ V c ⅆ x = J 0 DRx WT [0230] and the heat generated per unit length can be estimated as shown in the following equation ⅆ Q c ⅆ x = 2 J 0 2 D 2 Rx 2 WT [0231] Integrating the above equation the total voltage drop can be estimated as shown in the following equation V c = J 0 DRL 2 2 WT [0232] and the total heat generated in the bar can be estimated as shown in the following equation Q c = 2 J 0 2 D 2 RL 3 3 WT [0233] When the total heat generated becomes significant, uniform current assumption can break down, as can the device's performance (e.g., the device overheats). Therefore, it can be desirable to minimize the maximum current density (current density generally scales linearly with length), the voltage drop (voltage drop generally scales with the square length), and/or the heat generated (heat generated generally scales with the cube of the length). Based on the above relationships, a rectangular 9�16 die having more but shorter bars has a, b and c reduced by a factor of �, 9/16, and 27/64 respectively. Since the number of bars is increased by a factor of 4/3, it is believed that the total heat generated can be reduced by a factor of 9/16. [0234] FIG. 53 shows a packaged LED device 1890. In general, the package should be capable of facilitating light collection while also providing mechanical and environmental protection of the die and allowing heat generated in the die to be dissipated. As described above, LED 1890 includes conductive pads 1804 a and 1804 b that allow current to be spread to multiple contact fingers 1812 and dissipated to the LED surface. Multiple wire bonds 1892 provide an electrical current path between the LED and the package. Wire bonds 1892 can be made of various conductive materials such as gold, aluminum, silver, platinum, copper, and other metals or metal alloys. The package also includes multiple castellations 1894 to transport current from a bottom surface of the package to a top surface of the package to facilitate surface mounting on a circuit board. Castellations 1894 include a central region and a plating layer. The central region can be composed of a refractory metal, for example, tungsten and can be relatively thick (e.g., about 100 um to about 1 mm). The central region can be plated with an electrically conductive material such as gold. The plating can range in thickness from about 0.5 um to about 10 um and provides a current path that supports relatively high power levels. In addition, the package includes a transparent cover 1896 packaged on the LED die to protect the patterned surface 506 (FIG. 36) when an encapsulant is not used. The transparent cover 1896 is attached to the package, for example, using a glassy frit that is melted in a furnace. Alternatively, cover 1896 can be connected using a cap weld or an epoxy for example. The transparent cover 1896 can be further coated with one or more anti-reflection coatings to increase light transmission. Without wishing to be bound by theory, it is believed that the absence of an encapsulant layer allows higher tolerable power loads per unit area in the patterned surface LED 100. Degradation of the encapsulant can be a common failure mechanism for standard LEDs and is avoided not using an encapsulant layer. Packaged device 1890 can be mounted on a circuit board, on another device, or directly on a heat sink. [0235] FIG. 54 shows a model of the heat dissipation for a packaged device 1890 placed on a heat sink device. The packaged device 1890 is supported by a core board 1900 that includes insulating and electrically conductive regions (e.g., conductive regions using metals such as Al or Cu) attached to the heat sink. For example, packaged device 1890 can be attached to core board 1900 using solder (examples of solder include AuSn solder, PbSn solder, NiSn solder, InSn solder, InAgSn solder, and PbSnAg solder) or using an electrically conductive epoxy (e.g., silver filled epoxy). Core board 1900 is supported by a layer of heat sink metal 1902 and heat sink fins 1904. For example, core board 1900 can be attached to heat sink metal 1902 using solder (examples of solder include AuSn solder, PbSn solder, NiSn solder, InSn solder, InAgSn solder, and PbSnAg solder) or using epoxy (e.g., silver filled epoxy). In this model it is assumed that heat spreads from packaged device 1890 as the heat dissipates towards the heat sink. Spreading angle 1906 represents the angle at which heat dissipates out of packaged device 1890. Spreading angle 1906 generally varies depending on the material properties and the vertical layout of the system. Spreading angle 1906 can vary for different layers in the heat sink. The thermal resistance of a slice with thickness dx can be estimated according to the following equation dR th = dx K 0 1 S x ″2 = dx K 0 1 ( S ′ + 2 x tan θ ) 2 [0236] where K0 is the thermal conductivity and S′ is the dimensions of the heat front at the top of the element. Integrating produces the following equation for resistivity R = d K 0 1 S ′ ( S ′ + 2 d tan θ ) [0237] In the case of a rectangle, this resistivity can be calculated generating the results shown in FIG. 55. FIG. 55 shows a calculated ratio of Rth—rectangle/Rth—square (where Rth is the thermal resistance) for a system of large thickness and spreading angle of 45�. As the aspect ratio increases, the thermal resistance can drop. For example, if a square die system has a thermal resistance of 20� C./W and it is desired to dissipate 3 W of power, then the junction temperature (assuming an ambient temperature of 25� C.) can be 25+20*3=85� C. A rectangular die of the same area and same dissipated heat, however, will typically have a lower junction temperature. FIG. 56 shows a graph of junction temperature as a function of aspect ratio. It is believed that a lower junction temperature is desirable for reduced wavelength shift and higher device efficiency. [0238] As described above, using a rectangular shape for an LED (compared, for example, to a square) can provide certain advantages. The advantages can include one or more of the following. The rectangular LED can allow a greater number of wire bonds per unit area increasing the power that can be input into the LED. The rectangular shape can be chosen to match a particular aspect ratio of a pixel or microdisplay, thus, eliminating the need for complex beam shaping optics. The rectangular shape can also improve heat dissipation from the LED and reduce the likelihood of failure due to the device overheating. [0239] Because the cross section of an individual LEDs cut from a wafer is only slightly larger than the light-emitting surface area of the LED, many individual, and separately addressable LEDs can be packed closely together in an array. If one LED does not function (e.g., due to a large defect), then it does not significant diminish the performance of the array because the individual devices are closely packed. [0240] While certain embodiments have been described, other embodiments are possible. [0241] As an example, while certain thickness for a light-emitting device and associated layers are discussed above, other thicknesses are also possible. In general, the light-emitting device can have any desired thickness, and the individual layers within the light-emitting device can have any desired thickness. Typically, the thicknesses of the layers within multi-layer stack 122 are chosen so as to increase the spatial overlap of the optical modes with light-generating region 130, to increase the output from light generated in region 130. Exemplary thicknesses for certain layers in a light-emitting device include the following. In some embodiments, layer 134 can have a thickness of at least about 100 nm (e.g., at least about 200 nm, at least about 300 nm, at least about 400 nm, at least about 500 nm) and/or at most about 10 microns (e.g., at most about five microns, at most about three microns, at most about one micron). In certain embodiments, layer 128 has a thickness of at least about 10 nm (e.g., at least about 25 nm, at least about 40 nm) and/or at most about one micron (e.g., at most about 500 nm, at most about 100 nm). In some embodiments, layer 126 has a thickness of at least about 10 nm (e.g., at least about 50 nm, at least about 100 nm) and/or at most about one micron (e.g., at most about 500 nm, at most about 250 nm). In certain embodiments, light-generating region 130 has a thickness of at least about 10 nm (e.g., at least about 25 nm, at least about 50 nm, at least about 100 nm) and/or at most about 500 nm (e.g., at most about 250 nm, at most about 150 nm). [0242] As an example, while a light-emitting diode has been described, other light-emitting devices having the above-described features (e.g., patterns, processes) can be used. Such light-emitting devices include lasers and optical amplifiers. [0243] As another example, while current spreading layer 132 has been described as a separate layer from n-doped layer 134, in some embodiments, a current spreading layer can be integral with (e.g., a portion of) layer 134. In such embodiments, the current spreading layer can be a relatively highly n-doped portion of layer 134 or a heterojunction between (e.g. AlGaN/GaN) to form a 2D electron gas. [0244] As a further example, while certain semiconductor materials have been described, other semiconductor materials can also be used. In general, any semiconductor materials (e.g., III-V semiconductor materials, organic semiconductor materials, silicon) can be used that can be used in a light-emitting device. Examples of other light-generating materials include InGaAsP, AlInGaN, AlGaAs, InGaAlP. Organic light-emitting materials include small molecules such as aluminum tris-8-hydroxyquinoline (Alq3) and conjugated polymers such as poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-vinylenephenylene] or MEH-PPV. [0245] As an additional example, while large area LEDs have been described, the LEDs can also be small area LEDs (e.g., LEDs smaller than the standard about 300 microns on edge). [0246] As another example, while a dielectric function that varies spatially according to a pattern has been described in which the pattern is formed of holes, the pattern can also be formed in other ways. For example, a pattern can be formed continuous veins and/or discontinuous veins in the appropriate layer. Further, the pattern in varying dielectric function can be achieved without using holes or veins. For example, materials having different dielectric functions can be patterned in the appropriate layer. Combinations of such patterns can also be used. [0247] As a further example, while layer 126 has been described as being formed of silver, other materials can also be used. In some embodiments, layer 126 is formed of a material that can reflect at least about 50% of light generated by the light-generating region that impinges on the layer of reflective material, the layer of reflective material being between the support and the multi-layer stack of materials. Examples of such materials include distributed Bragg reflector stacks and various metals and alloys, such as aluminum and aluminum-containing alloys. [0248] As another example, support 120 can be formed of a variety of materials. Examples of materials from which support 120 can be formed include copper, copper-tungsten, aluminum nitride, silicon carbide, beryllium-oxide, diamonds TEC, and aluminum. [0249] As an additional example, while layer 126 has been described as being formed of a heat sink material, in some embodiments, a light-emitting device can include a separate layer (e.g., disposed between layer 126 and submount 120) that serves as a heat sink. In such embodiments, layer 126 may or may hot be formed of a material that can serve as a heat sink. [0250] As a further example, while the varying pattern in dielectric function has been described as extending into n-doped layer 134 only (which can substantially reduce the likelihood of surface recombination carrier losses) in addition to making use of the entire light-generating region, in some embodiments, the varying pattern in dielectric function can extend beyond n-doped layer (e.g., into current spreading layer 132, light-generating region 130, and/or p-doped layer 128). [0251] As another example, while embodiments have been described in which air can be disposed between surface 110 can cover slip 140, in some embodiments materials other than, or in an addition to, air can be disposed between surface 110 and cover slip 140. Generally, such materials have an index of refraction of at least about one and less than about 1.5 (e.g., less than about 1.4, less than about 1.3, less than about 1.2, less than about 1.1). Examples of such materials include nitrogen, air, or some higher thermal conductivity gas. In such embodiments, surface 110 may or may not be patterned. For example, surface 110 may be non-patterned but may be roughened (i.e., having randomly distributed features of various sizes and shapes less than λ/5). [0252] As another example, while embodiments involving the deposition and etching of planarization and lithography layers have been described, in some embodiments, a pre-patterned etch mask can be laid down on the surface of the n-doped semiconductor layer. [0253] As a further example, in some embodiments, an etch mask layer can be disposed between the n-doped semiconductor layer and the planarization layer. In such embodiments, the method can include removing at least a portion of the etch mask layer (e.g., to form a pattern in the etch stop layer corresponding to the pattern in the n-doped semiconductor layer). [0254] As an additional example, while embodiments, have been disclosed in which surface 110 is patterned and smooth, in some embodiments, surface 110 may be patterned and rough (i.e., having randomly distributed features of various sizes and shapes less than λ/5, less than λ/2, less than λ). Further, in certain embodiments, the sidewalls of openings 150 can be rough (i.e., having randomly distributed features of various sizes and shapes less than λ/5, less than λ/2, less than λ), with or without surface 110 being rough. Moreover, in some embodiments, the bottom surface of openings 150 can be rough (i.e., having randomly distributed features of various sizes and shapes less than λ/5, less than λ/2, less than λ). Surface 110, the sidewalls of openings 150, and/or the bottom surfaces of openings 150 can be roughened, for example, by etching (e.g., wet etching, dry etching, reactive ion etching). Without wishing to be bound by theory, it is believed that roughening surface 110 and/or the sidewalls of openings 150 may increase the probability, with respect to a atomically smooth surface, that a light ray will eventually strike at an angle that less than the critical angle given by Snell's law and will be extracted. [0255] As another example, in some embodiments, the submount can be machined to include spring-like structures. Without wishing to be bound by theory, it is believed that such spring-like structures may reduce cracking during removal of the substrate. [0256] As a further example, in some embodiments, the submount can be supported by an acoustically absorbing platform (e.g., a polymer, a metallic foam). Without wishing to be bound by theory, it is believed that such acoustically absorbing structures may reduce cracking during removal of the substrate. [0257] As an additional example, in some embodiments, the substrate is treated (e.g., etched, ground, sandblasted) before being removed. In certain embodiments, the substrate may be patterned before it is removed. In some embodiments, the thickness of the layers is selected so that, before removing the substrate and buffer layers, the neutral mechanical axis of the multi-layer stack is located substantially close (e.g., less than about 500 microns, less than about 100 microns, less than about 10 microns, less than about five microns) to the interface between the p-doped semiconductor layer and a bonding layer. In certain embodiments, portions of the substrate are separately removed (e.g., to reduce the likelihood of cracking). [0258] As another example, while embodiments have been described in which a buffer layer is separate from an n-doped semiconductor layer (e.g., a buffer layer grown on the substrate, with an n-doped semiconductor layer separately grown on the buffer), in some embodiments, there can be a single layer instead. For example, the single layer can be formed by first depositing a relatively low doped (e.g., undoped) semiconductor material on the substrate, followed by (in one process) depositing a relatively high doped (n-doped) semiconductor material. [0259] As a further example, while embodiments have been described in which a substrate is removed by a process that includes exposing a surface of the substrate to electromagnetic radiation (e.g., laser light), in some embodiments other methods can be used to remove the substrate. For example, removal of the substrate can involve etching and/or lapping the substrate. In certain embodiments, the substrate can be etched and/or lapped, and then subsequently exposed to electromagnetic radiation (e.g., laser light). [0260] As an additional example, in some embodiments, after depositing the planarization layer but before depositing the lithography layer, the upper surface of the planarization layer can be flattened. For example, a flat object, such as an optical flat, can be placed on the upper surface of the planarization layer while heating the planarization layer (e.g., with a hot plate). In some embodiments, a pressure can be applied (e.g., using a physical weight or press) to assist with the flattening process. [0261] As another example, in some embodiments the substrate can be treated before being removed. For example, the substrate can be exposed to one or more processes selected from etching, polishing, grinding, and sandblasting. In certain embodiments, treating the substrate can include patterning the substrate. In some embodiments, treating the substrate includes depositing an antireflective coating on the substrate. Such an antireflective coating can, for example, allow relatively large regions of the substrate to be removed when using a substrate removal process that involves exposing the substrate to electromagnetic radiation because the coating can reduce reflection of the electromagnetic radiation. In certain embodiments, a pattern on the surface of the substrate can also be used to achieve an anti-reflection effect. [0262] In some embodiments, a light-emitting device can include a layer of a phosphor material coated on surface 110, cover layer 140 and supports 142. [0263] In certain embodiments, a light-emitting device can include a cover layer 140 that has a phosphor material disposed therein. In such embodiments, surface 110 may or may not be patterned. [0264] In an alternative implementation, the light emitted by the light-generating region 130 is UV (or violet, or blue) and the phosphor layer 180 includes a mixture of a red phosphor material (e.g., L2O2S:Eu3+), a green phosphor material (e.g, ZnS:Cu,Al,Mn), and blue phosphor material (e.g, (Sr,Ca,Ba,Mg)10(PO4)6Cl:Eu2+). [0265] Other embodiments are in the claims. 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