Light emitting diodes are widely used in consumer and commercial applications.  As is well known to those having skill in the art, a light emitting diode generally includes a diode region on a microelectronic substrate.  The microelectronic substrate may comprise, for example, gallium arsenide, gallium phosphide, alloys thereof, silicon carbide and/or sapphire.  Continued developments in LEDs have resulted in highly efficient and mechanically robust light sources that can cover the visible spectrum and beyond.  These attributes, coupled with the potentially long service life of solid state devices, may enable a variety of new display applications, and may place LEDs in a position to compete with the well entrenched incandescent and fluorescent lamps. 
One measure of efficiency of LEDs is the cost per lumen.  The cost per lumen for an LED may be a function of the manufacturing cost per LED chip, the internal quantum efficiency of the LED material and the ability to couple or extract the generated light out of the device.  An overview of light extraction issues may be found in the textbook entitled High Brightness Light Emitting Diodes to Stringfellow et al.,  Academic Press, 1997, and particularly Chapter 2, entitled Overvien of Device Issues in High-Brightness Light Emitting Diodes, to Craford, at pp.  47-63. 
Light extraction has been accomplished in many ways, depending, for example, on the materials that are used to fabricate the diode region and the substrate.  For example, in gallium arsenide and gallium phosphide material systems, a thick, p-type, topside window layer may be used for light extraction.  The p-type window layer may be grown because high epitaxial growth rates may be possible in the gallium arsenide/gallium phosphide material systems using liquid and/or vapor phase epitaxy.  Moreover, current spreading may be achieved due to the conductivity of the p-type topside window layer.  Chemical etching with high etch rates and high etch selectivity also may be used to allow the removal of at least some of the substrate if it is optically absorbent.  Distributed Bragg reflectors also have been grown between an absorbing substrate and the diode region to decouple the emitting and absorbing regions. 
Other approaches for light extraction may involve mechanical shaping or texturing of the diode region and/or the substrate.  However, it may be desirable to provide other light extraction techniques that can allow further improvements in extraction efficiency.  Moreover, it may be desirable to increase the area of an LED chip from about 0.1 mm2 to larger areas, to thereby provide larger LEDs.  Unfortunately, the effectiveness of these shaping techniques may not be maintained as the chip dimensions are scaled up for higher power/intensity and/or other applications. 
Much development interest and commercial activity recently has focused on LEDs that are fabricated in or on silicon carbide, because these LEDs can emit radiation in the blue/green portions of the visible spectrum.  See, for example, U.S. Pat.  No.  5,416,342 to Edmond et al.,  entitled Blue Light-Emitting Diode With High External Quantum Efficiency, assigned to the assignee of the present application, the disclosure of which is hereby incorporated herein by reference in its entirety as if set forth fully herein.  There also has been much interest in LEDs that include gallium nitride-based diode regions on silicon carbide substrates, because these devices also may emit light with high efficiency.  See, for example, U.S. Pat.  No.  6,177,688 to Linthicum et al.,  entitled Pendeoepitaxial Gallium Nitride Semiconductor Layers On Silicon Carbide Substrates, the disclosure of which is hereby incorporated herein by reference in its entirety as if set forth fully herein. 
In such silicon carbide LEDs or gallium nitride LEDs on silicon carbide, it may be difficult to use conventional techniques for light extraction.  For example, it may be difficult to use thick p-type window layers because of the relatively low growth rate of gallium nitride.  Also, although such LEDs may benefit from the use of Bragg reflectors and/or substrate removal techniques, it may be difficult to fabricate a reflector between the substrate and the gallium nitride diode region and/or to etch away at least part of the silicon carbide substrate. 
U.S. Pat.  No.  4,966,862 to Edmond, entitled Method of Production of Light Emitting Diodes, assigned to the assignee of the present application, the disclosure of which is hereby incorporated herein by reference in its entirety as if set forth fully herein, describes a method for preparing a plurality of light emitting diodes on a single substrate of a semiconductor material.  The method is used for structures where the substrate includes an epitaxial layer of the same semiconductor material that in turn comprises layers of p-type and n-type material that define a p-n junction therebetween.  The epitaxial layer and the substrate are etched in a predetermined pattern to define individual diode precursors, and deeply enough to form mesas in the epitaxial layer that delineate the p-n junctions in each diode precursor from one another.  The substrate is then grooved from the side of the epitaxial layer and between the mesas to a predetermined depth to define side portions of diode precursors in the substrate while retaining enough of the substrate beneath the grooves to maintain its mechanical stability.  Ohmic contacts are added to the epitaxial layer and to the substrate and a layer of insulating material is formed on the diode precursor.  The insulating layer covers the portions of the epitaxial layer that are not covered by the ohmic contact, any portions of the one surface of the substrate adjacent the mesas, and the side portions of the substrate.  As a result, the junction and the side portions of the substrate of each diode are insulated from electrical contact other than through the ohmic contacts.  When the diodes are separated they can be conventionally mounted with the junction side down in a conductive epoxy without concern that the epoxy will short circuit the resulting diode.  See the abstract of U.S. Pat.  No.  4,966,862. 
U.S. Pat.  No.  5,210,051 to Carter, Jr., entitled High Efficiency Light Emitting Diodes From Bipolar Gallium Nitride, assigned to the assignee of the present application, the disclosure of which is hereby incorporated herein by reference in its entirety as if set forth fully herein, describes a method of growing intrinsic, substantially undoped single crystal gallium nitride with a donor concentration of 7×1017 cm3 or less.  The method comprises introducing a source of nitrogen into a reaction chamber containing a growth surface while introducing a source of gallium into the same reaction chamber and while directing nitrogen atoms and gallium atoms to a growth surface upon which gallium nitride will grow.  The method further comprises concurrently maintaining the growth surface at a temperature high enough to provide sufficient surface mobility to the gallium and nitrogen atoms that strike the growth surface to reach and move into proper lattice sites, thereby establishing good crystallinity, to establish an effective sticking coefficient, and to thereby grow an epitaxial layer of gallium nitride on the growth surface, but low enough for the partial pressure of nitrogen species in the reaction chamber to approach the equilibrium vapor pressure of those nitrogen species over gallium nitride under the other ambient conditions of the chamber to thereby minimize the loss of nitrogen from the gallium nitride and the nitrogen vacancies in the resulting epitaxial layer.  See the abstract of U.S. Pat.  No.  5,210,051. 
In view of the above discussion, improved light extraction techniques may be desirable for LEDs, especially LEDs that are fabricated from silicon carbide, that are fabricated from gallium nitride on silicon carbide and/or that have a relatively large area.