Abstract:
In a method for measuring a dimension or angle of a scattering feature of an optical device, such as a photonic crystal, at least part of the array is irradiated with light. A characteristic of light scattered from the array is detected. A comparison algorithm is run on the detected characteristic of the scattered light. The comparison algorithm provides one or more numerical values indicative of the measured dimension or angle. A system for measuring a dimension or angle of a feature of an optical device includes a light source and optics for focusing light from the light source onto a target area of the optical device. A light detector is positioned to detect scattered light from the target area, with the detected light used to create a measured light characteristic. A computer linked to the light detector performs a comparison algorithm on the measured light characteristic and outputs a numerical value of the dimension or angle measured. In method for designing an optical device, such as a photonic crystal for use on an LED, an intended scattered response based on light emission characteristics desired from the optical device is simulated. One or more design parameters of the optical device are varied. An interim reflectance response of the optical device with variation of the parameters is determined. Interim scattered responses are compared to the intended scattered response. One or more scattered responses which match the intended scattered response are selected. An optical device is designed using one or more of the design parameters associated with the selected interim scattered response.

Description:
[0001]     This Application claims priority to U.S. Provisional Patent Application No. 60/669,787 filed Apr. 7, 2005. The field of the invention is optical devices and measuring features of optical devices, such as photonic crystals and LEDs. 
     
    
     TECHNICAL FIELD  
     Background  
       [0002]     Semiconductor devices, light emitting diodes (LEDs) and other optical or microelectronic devices are typically manufactured on a workpiece having a large number of individual dies (e.g., chips or devices). Each wafer undergoes several different procedures to construct the switches, capacitors, conductive interconnects, filters and other components of the device. For example, a workpiece can be processed using lithography, implanting, etching, deposition, planarization, annealing, and other procedures that are repeated to construct a high density of features. One aspect of manufacturing these devices is evaluating the workpieces to ensure that the microstructures are within the desired specifications.  
         [0003]     Photonic crystals (PCs) are optical structures that may be used to improve the performance of a micro-optical device like an LED. A photonic crystal is a device that comprises an array of scattering features in some host medium, such as air cylinders which have been etched into some material like gallium nitride (GaN) or indium phosphide (InP). The scattering structures are usually small, typically less than 1 um in width. As light interacts with a photonic crystal, its propagation characteristics are altered. For this reason, the photonic crystal can also be thought of as a synthetic lens. When a photonic crystal structure is positioned above the emission region of an LED device, for example, the output efficiency of the LED increases while the directionality of the output light is improved. Hence, the use of a photonic crystal structure with an LED is desirable.  
         [0004]     One challenge in manufacturing photonic crystals for use with LEDs is that the structure of the photonic crystal scattering features has a strong influence on the performance of the crystal itself. If the dimensions of the scattering features vary, the performance of the LED will not be precise since it will vary from workpiece to workpiece. Furthermore, if the shape or position of the scattering features is not optimal, the performance of the LED will also be less than optimal. For these reasons, characterization or metrology of the photonic crystal is important for LED device performance.  
         [0005]     Another challenge in the manufacture of photonic crystal for use with LEDs is alignment of the photonic crystal with the LED emission region. In some case, the photonic crystal layer can be manufactured directly above the LED emission region of the workpiece. In other manufacturing processes, the photonic crystal may be manufactured on a separate workpiece and bonded to the LED. In either instance, the photonic crystal must be well aligned with the LED emission region for the LED to perform optimally and reliably.  
         [0006]     Scatterometry is a technology for evaluating several parameters of microstructures and may be useful in the measurement of photonic crystal structures. With respect to semiconductor devices, scatterometry is used to evaluate film thickness, line spacing, trench depth, trench width, and other aspects of microstructures. Many semiconductor wafers, for example, include scatterometry targets in the scribe lines between the individual dies to provide a scattering structure that can be evaluated using existing scatterometry equipment. One existing scatterometry process includes illuminating such scattering structures on a workpiece and obtaining a representation of the scattered radiation returning from the periodic structure. The representation of return radiation is then analyzed to estimate one or more parameters of the microstructure.  
         [0007]     One challenge of scatterometry for the measurement of photonic crystal structures is properly locating the small scattering structures on the workpiece. Because these structures are considered a part of the device itself and not a test structure in the scribe line, the scatterometry measurement system must include a navigation system for properly positioning over the measurement area. Moreover, the spot size of the scatterometer must be appropriate for the array of features being measured. Ideally, the spot size should illuminate most of but not overfill the array of features. Because LED devices are made with different sizes of emission areas, the spot size used to measure PCs may be variable. For measurements on one LED/PC device, it may need to be small, i.e., ten microns while for measurements on another LED/PC device, it might be large, i.e., several hundred microns. This is in contrast to typical semiconductor applications, where the spot size is generally chosen to be as small as possible in order to minimize target area in the scribe line.  
         [0008]     Another challenge of using scatterometry to evaluate PC structures is obtaining a useful representation of the radiation returning from such microstructures. Because the PC structures are typically more complicated than semiconductor structures, the returning radiation pattern may be complex. PC structures will scatter light in all angular directions, so a scatterometry measurement system that can measure in all angular directions would be advantageous for measuring PC structures. This is in contrast to semiconductor applications, where most scatterometry targets are two-dimensional line-space structures that scatter light in one plane only. Hence, a scatterometer that measures returning radiation in one plane only is sufficient for semiconductor applications, but may be inadequate for the measurement of PC structures.  
         [0009]     Another challenge of assessing PC structures using scatterometry relates to the optical properties of the materials that are used to manufacture such structures. For typical semiconductor applications, the workpiece substrate and other layers is silicon, which is typically absorbing for illumination at optical energies greater than the bandgap of the material. For PC-LED applications, the workpiece substrates and other layers can be materials like indium phosphide (InP) or gallium arsenide (GaAs), which have different bandgaps and are therefore absorbing at different wavelengths. A typical GaN LED might be made using a wide bandgap material such as sapphire or other oxide or dielectric. These materials become absorbing at extremely short wavelengths that are not typically employed in optical metrology systems. The fact that a PC-LED substrate is non-absorbing creates difficulties in managing back-reflections from the back-side of the substrate and other layers. In contrast to semiconductor applications, where there is no back-side reflection because all the radiation is absorbed, back-reflections for PC-LED applications can interfere with the incident illumination and therefore alter the returning or scattered radiation. For this reason, back-reflections in a photonic crystal scatterometry measurement must be eliminated or accounted for in the measurement process.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]      FIG. 1  is a schematic view illustrating a scatterometer in accordance with an embodiment of the invention.  
         [0011]      FIG. 2  is a schematic isometric view illustrating a portion of a three-dimensional convergence beam for irradiating microstructures on a workpiece in accordance with an embodiment of the invention.  
         [0012]      FIG. 3  is a schematic view illustrating an optical system for use in a scatterometer in accordance with an embodiment of the invention.  
         [0013]      FIG. 4  is a schematic view illustrating an optical system and an auto-focus system for use in a scatterometer in accordance with an embodiment of the invention.  
         [0014]      FIG. 5A  is a simulated intensity distribution for use in a scatterometer in accordance with an embodiment of the invention.  
         [0015]      FIG. 5B  is a measured intensity distribution provide by a scatterometer in accordance with an embodiment of the invention.  
         [0016]      FIG. 6  is a schematic view illustrating a portion of a computer system and a computational method for ascertaining parameters of photonic crystal microstructures using a scatterometer in accordance with an embodiment of the invention.  
         [0017]      FIG. 7  is a perspective representation of a photonic crystal on an LED.  
         [0018]      FIG. 8  is a schematic view showing target dimensions.  
         [0019]      FIG. 9  is schematic view of doubly periodic structure.  
         [0020]      FIGS. 10A , B, and C show measurement sensitivity to change with feature spacing S as the critical dimension.  FIG. 10A  shows the critical dimension as the spacing between the features.  FIG. 10B  is a plot of the actual data from the simulation taken with S as the critical dimension.  FIG. 10C  is a plot of the actual data from the simulation taken with S changed by 1% (3 nm).  
         [0021]      FIGS. 11A , B, and C show measurement sensitivity to change with sidewall angle A as the critical dimension.  FIG. 11A  shows the critical dimension as the sidewall angle A.  FIG. 11B  is a plot of the actual data from the simulation taken with A as the critical dimension.  FIG. 11C  is a plot of the actual data from the simulation taken with A changed by 0.5°.  
         [0022]      FIGS. 12A , B, and C show measurement sensitivity to change with feature height H as the critical dimension.  FIG. 12A  shows the critical dimension as the feature height.  FIG. 12B  is a plot of the actual data from the simulation taken with H as the critical dimension.  FIG. 12C  is a plot of the actual data from the measurement taken with H changed by 1% (2.5 nm).  
         [0023]      FIGS. 13A , B, and C are drawings of square array layouts of round, oval or elliptical, and rectangular or square scatterometry features of a photonic crystal, for use with an LED.  
         [0024]      FIGS. 14A , B, and C are drawings of rectangle array layouts of round, oval or elliptical, and rectangular or square scatterometry features of a photonic crystal, for use with an LED.  
         [0025]      FIGS. 15A , B, and C are drawings of diamond/triangle array layouts of round, oval or elliptical, and rectangular or square scatterometry features of a photonic crystal, for use with an LED.  
         [0026]      FIGS. 16A , B, and C are schematic drawings of hexagon array layouts of round, oval or elliptical, and rectangular or square scatterometry features of a photonic crystal, for use with an LED.  
         [0027]      FIGS. 17 and 18  are diagrams of optimizing an array layout with varying shapes.  
         [0028]      FIGS. 19A , B, C and D are profiles or section views of scatterometry features for use in a photonic crystal, for use with an LED.  
         [0029]      FIG. 20  is a drawing of a photonic crystal design with the scattering features formed as posts or columns with an air filler.  
         [0030]      FIG. 21  is a drawing of a photonic crystal design with the scattering features formed as air holes with an optical material filler.  
         [0031]      FIG. 22  is an enlarged section view of a single scattering feature from the photonic crystal shown in  FIG. 21 , with an air hole surrounded by gallium nitride filler.  
         [0032]      FIG. 23  is an enlarged section view of a single scattering feature formed from an oxide material with a gallium nitride filler, for use in a photonic crystal.  
         [0033]      FIG. 24  is an enlarged section view of a single gallium nitride scattering feature and an oxide filler, for use in a photonic crystal. 
     
    
     DETAILED DESCRIPTION  
       [0000]     A. Overview  
         [0034]     The present invention is directed toward evaluating photonic crystal (PC) microstructures on optical workpieces and other types of substrates. Many applications of the present invention are directed toward scatterometers and methods of using scatterometry to determine several parameters of periodic microstructures, pseudo-periodic structures, and other very small structures having features sizes as small as 100 nm or less. Several specific embodiments of the present invention are particularly useful in the semiconductor industry to determine the width, depth, line edge roughness, wall angle, film thickness, and many other parameters of the features formed in microprocessors, memory devices, and other semiconductor devices. The scatterometers and methods of the invention, however, are not limited to semiconductor applications and can be applied equally well in other applications.  
         [0035]     One embodiment of the invention is directed toward a scatterometer for evaluating PC microstructures on workpieces. In this embodiment, the scatterometer comprises an irradiation source, such as a laser, a first optics assembly, and an object lens assembly. The irradiation source produces a first beam of radiation at a first wavelength. The first optics assembly is aligned with the path of the beam and configured to condition the beam (e.g., shape, randomize, select order, diffuse, converge, diverge, collimate, etc.). The object lens assembly is aligned with the path of the beam and positioned between the first optics assembly and a workpiece site. The object lens assembly is configured to focus the conditioned beam to a spot at an object focal plane. The lens assembly or other optics of the scatterometer is also configured to receive scattered radiation reflecting from a workpiece at a workpiece processing site and to present an intensity distribution of the scattered radiation in a second focal plane. The scatterometer of this embodiment can further include a detector, a navigation system, and an auto-focus system. The detector is positioned to receive at least a portion of the scattered radiation distribution and configured to produce a representation of the scattered radiation distribution. The navigation system is operatively coupled to the lens assembly or a support structure holding the workpiece, and it is configured to identify and locate the desired PC microstructure on the workpiece. The auto-focus system is operatively coupled to one of the lens assembly or the workpiece site, and it is configured to position the microstructure at the object focal plane.  
         [0036]     Another embodiment of a scatterometer in accordance with the invention comprises a laser configured to produce a beam of radiation having a first wavelength, an optical system having a first optics assembly configured to condition the beam of radiation, and a lens assembly. The lens assembly is configured to focus the beam at an area of an object focal plane having a small spot size such that the beam has angles of incidence through a range of altitude angles of at least approximately 0°-45° and azimuth angles of at least approximately 0° to 90°. The altitude angle (Θ) is the angle between a vector normal to the object focal plane, and the azimuth angle (Ψ) is the angle normal to the reference vector in a plane parallel to the object focal plane. The beam more preferably has angles of incidence through altitude angles of 0° to greater than 70° through azimuth angles of 0°-360°. The scatterometer is further configured to collect and present the scattered radiation reflected from the microstructure in a second focal plane. In one embodiment, the lens assembly itself presents the scattered light in the second focal plane, but in other embodiments the optical system has another optic member that presents the scattered radiation distribution in the second focal plane. The scatterometer of this invention further includes a detector positioned to receive the scattered radiation distribution of the scattered radiation and configured to produce a representation of the scattered radiation distribution. The scatterometer also includes a computer operatively coupled to the detector to receive the representation of the scattered radiation distribution. The computer includes a database and a computer-operable medium. The database has a plurality of simulated scattered radiation distributions corresponding to different sets of parameters of the microstructure. The computer-operable medium contains instructions that cause the computer to identify a simulated scattered radiation distribution that adequately fits the representation of the measured scattered radiation distribution.  
         [0037]     Another embodiment of the invention is a scatterometer for evaluating a PC microstructure on a workpiece comprising an irradiation system, an optical system, and a detector. The irradiation system includes a laser and or lamp, and the irradiation system is configured to produce a first beam of radiation having a first wavelength and a second beam of radiation having a second wavelength. The optical system has a first unit configured to condition the first and second beams. The optical system further includes a second unit configured to (a) focus the first and second beams at an area of an object focal plane having an appropriate spot size, and (b) present a distribution of scattered radiation returning from a PC microstructure in a second focal plane. The detector is positioned to receive the distribution of the scattered radiation, and the detector is configured to produce a representation of the scattered radiation distribution.  
         [0038]     Another embodiment of a scatterometer in accordance with the invention comprises a laser configured to produce a beam of radiation having a first wavelength, an optical system, a detector, a calibration unit, and a computer. The optical system has a first optics assembly configured to condition the beam of radiation such that the beam is a diffuse and randomized beam. The optical system also includes an object lens assembly configured to (a) focus the beam at an area of an object focal plane and (b) present a distribution of scattered radiation reflected or otherwise returning from a PC microstructure in a second focal plane. The detector is positioned to receive the distribution of the scattered radiation and configured to produce a representation of the scattered radiation distribution. The calibration unit of one embodiment includes a first calibration member having a first reflectivity of the first wavelength and a second calibration member having a second reflectivity different than the first reflectivity. The first and second calibration members are located to be irradiated by the beam during a setup procedure to determine a reference reflectance. The computer is operatively coupled to the detector and includes a computer-operable medium that determines the reference reflectance using a first reflectance from the first calibration member and a second reflectance from the second calibration member.  
         [0039]     Since PC and other optical element microstructures scatter in all directions, in yet another embodiment, the illumination optical system and detection optics are positioned on different sides of the sample piece being measured. This arrangement allows for a transmissive, as opposed to reflective, scattering measurement. For this type of transmissive scattering measurement, transmissive calibration samples having known transmissivities are used instead of reflective samples.  
         [0040]     The present invention is also directed toward several methods for evaluating a PC microstructure on a workpiece. One embodiment of such a method comprises generating a laser beam or a beam from a lamp having a first wavelength or range of wavelengths and irradiating a microstructure on a workpiece by passing the beam through a lens assembly that focuses the beam to a focus area in an object focal plane. The focus area should have a dimension not greater than the array of scattering structures such that the incident illumination does not overall the scattering array, and the beam has a range of incidence angles having altitude angles of 0° to at least 45° and azimuth angles of 0° to greater than 90°. The method further includes detecting an actual distribution of scattered radiation returning from the microstructure.  
         [0041]     In another embodiment of a method in accordance with the invention the procedure of irradiating a microstructure comprises irradiating the focus area with a laser beam having a first wavelength and irradiating the focus area with a laser beam having a second wavelength different than the first wavelength. For example, the first wavelength can be approximately 244 nm and the second wavelength can be approximately 457 nm. The workpieces are irradiated with one or more beams having one or more wavelengths less than 500 nm in several specific embodiments, but longer wavelengths like 532 nm or 633 nm, or infrared wavelengths, may be used in other embodiments. Another aspect in accordance with another embodiment of the invention includes calibrating the detector by providing a first calibration member having a first reflectivity and a second calibration member having a second reflectivity. The system can be calibrated by determining a reference reflectance using a first reflectance from the first calibration member and a second reflectance from the second calibration member. Other embodiments can use only a single calibration member.  
         [0042]     The invention resides in the systems and methods described, as well as in sub-systems and sub-combinations of their elements and steps. The elements or steps of one embodiment may be equivalently used as well in other embodiments.  
         [0000]     B. Embodiments of Scatterometers and Methods for Evaluating Microstructures on Workpieces  
         [0043]      FIG. 1  is a schematic illustration of a scatterometer  10  in accordance with an embodiment of the invention. In this embodiment, the scatterometer  10  includes an irradiation source  100  that generates a beam  102  at a desired wavelength. The irradiation source  100  can be a monochromatic light source, such as a laser system and/or lamp capable of producing (a) a beam  102  at a single wavelength, (b) a plurality of beams at different wavelengths, or (c) any other output having a single wavelength or a plurality of wavelengths. In many applications directed toward assessing microstructures on semiconductor workpieces, the irradiation source  100  is a laser that produces a beam having a wavelength less than 500 nm, and more preferably in the range of approximately 150 nm-500 nm. In a different embodiment, the irradiation source  100  can include a plurality of different lasers and/or filters to produce a first beam having a first wavelength of approximately 244 nm and a second beam having a second wavelength of approximately 457 nm. For applications directed towards PC structures, the desired wavelength will typically be larger, preferably in the range of 400-800 nm. It will be appreciated that the irradiation source  100  can produce additional wavelengths having shorter or longer wavelengths in the UV spectrum, visible spectrum, and/or other suitable spectrum. The irradiation source  100  can further include a fiber optic cable to transmit the beam  102  through a portion of the apparatus.  
         [0044]     The scatterometer  10  further includes an optical system  200  between the irradiation source  100  and a workpiece W. In one embodiment, the optical system  200  includes a first optics assembly  210  that conditions the beam  102  to form a conditioned beam  212 . The first optics assembly  210 , for example, can include a beam diffuser/randomizer that diffuses and randomizes the radiation to reduce or eliminate the coherence of the beam  102 . The first optics assembly  210  can also include a beam element that shapes the beam to have a desired cross-sectional dimension, shape, and/or convergence-divergence. The beam element, for example, can shape the beam  212  to have a circular, rectilinear, or other suitable cross-sectional shape for presentation to additional optic elements downstream from the first optics assembly  210 . The first optics assembly may also include optical components whose positions may be varied to produce different beam conditions, such as a spot size or shape which may be optimized for the one particular photonic crystal measurement.  
         [0045]     The optical system  200  can further include an object lens assembly  300  that focuses the conditioned beam  212  for presentation to the workpiece W and receives radiation reflected from the workpiece W. The object lens assembly  300  is configured to receive the conditioned beam  212  and form a convergent beam  310  focused at a discrete focus area S on an object focal plane  320 . The convergent beam  310  can have a conical shape when the conditioned beam  212  has a circular cross-section, but in other embodiments the convergent beam  310  can have other shapes. For example, when the conditioned beam  212  has a rectilinear cross-section, the convergent beam  310  has a pyramidal shape. As explained in more detail below with reference to Section C, the convergent beam  310  can have a range of incidence angles having altitude angles of 0° to greater than approximately 70° and having azimuth angles of 0° to greater than 90° and more preferably 0-360°. The altitude angle is the angle from a reference vector normal to the object focal plane  320 , and the azimuth angle is the angle in a plane parallel to the object focal plane  320  and normal to the reference vector. The large range of incidence angles generates a large number of scattered angles and hence unique data points that enable accurate evaluations of several parameters of the photonic crystal microstructure.  
         [0046]     The focus area at the object focal plane  320  preferably has a size and shape suitable for evaluating the particular photonic crystal microstructure, and as has been previously discussed, should fill a large region of the photonic crystal array but not exceed it. For example, when the photonic crystal on the workpiece has a maximum dimension of approximately 100-200 μm, then the focus area is also approximately 100-200 μm. The size of the focal area is preferably not greater than the size of the photonic crystal array so that the radiation does not scatter from features outside of the PC. In many applications, therefore, the object lens assembly  300  is configured to produce a spot size generally less than 200 μm, and more preferably less than 100 μm. The scatterometer  10  can have larger focus areas in other embodiments, such as when the LED emission area is large  
         [0047]     The object lens assembly  300  is further configured to collect the scattered radiation reflecting from the workpiece W and present the scattered radiation on a second focal plane  340 . The object lens assembly  300 , more particularly, presents the scattered radiation in a manner that provides a distribution of the scattered radiation at the second focal plane  340 . In one embodiment, the object lens assembly  300  directs the scattered radiation coming at particular angles from the object focal plane  320  to corresponding points on the second focal plane  340 . Additional aspects of specific embodiments of the object lens assembly  300  are described below with reference to Section C.  
         [0048]     The optical system  200  can further include a beam splitter  220  through which the conditioned beam  212  can pass to the object lens assembly  300  and from which a portion of the return beam propagating away from the second focal plane  340  is split and redirected. The optical system  200  can optionally include a second optics assembly  230  that receives the split portion of the return beam from the beam splitter  220 . The second optics assembly is configured to prepare the return beam for imaging by an imaging device. Additional aspects of specific embodiments of the second optics assembly  230  are described below with reference to Section C.  
         [0049]     The scatterometer  10  further includes a detector  400  positioned to receive the intensity distribution propagating back from the second focal plane  340 . The detector  400  can be a CCD array, CMOS imager, other suitable cameras, or other suitable energy sensors for accurately measuring the scattered radiation distribution. The detector  400  is further configured to provide or otherwise generate a representation of the scattered radiation distribution. For example, the representation of the distribution can be data stored in a database, an image suitable for representation on a display, or other suitable characterizations of the scattered radiation distribution. Several embodiments of the detector  400  are described below in greater detail with reference to Section D.  
         [0050]     The scatterometer  10  can further include a navigation system  500  and an auto-focus system  600 . The navigation system  500  can include a light source  510  that illuminates a portion of the workpiece W and optics  520  that view the workpiece W. As explained in more detail below, the navigation system  500  can have a low magnification capability for locating the general region of the PC structure on the workpiece (e.g., global alignment), and a high magnification capability for precisely identifying the location of the PC structure to be measured. Several embodiments of the navigation system can use the irradiation source  100  and components of the optical system  200 . The navigation system  500  provides information to move the object lens assembly  300  and/or a workpiece site  510  to accurately position the focus area of the object lens assembly  300  at the desired PC structure on the workpiece W.  
         [0051]     The auto-focus system  600  can include a focus array  610 , and the optical system  200  can include an optional beam splitter  240  that directs radiation returning from the workpiece W to the focus array  610 . The auto-focus system  600  is operatively coupled to the object lens assembly  300  and/or the workpiece site  510  to accurately position the PC structure on the workpiece W at the object focal plane  320  of the object lens assembly  300 . As explained in more detail below with reference to Section E, the navigation system  500  and the auto-focus system  600  enable the scatterometer  10  to evaluate the highly variable size and positions of photonic crystal arrays on a workpiece.  
         [0052]     The scatterometer  10  further includes a calibration system for monitoring the properties of the input beam  102  and maintaining the accuracy of the other components. The calibration system (a) monitors the intensity, phase, polarization, wavelength or other beam property of the beam  102  in real time, (b) provides an accurate reference reflectance for the detector  400  to ensure the accuracy of the scatterometer, and/or (c) provides angular calibration of the system. In one embodiment, the calibration system includes a detector  700  and a beam splitter  702  that directs a portion of the initial beam  102  to the detector  700 . The detector  700  monitors changes in the intensity of the beam  102  in real-time to continuously maintain the accuracy of the measured intensity distribution of the radiation from the workpiece W. The detector  700  can also or alternatively detect phase changes, polarization, beam shape and directionality, or a differential intensity.  
         [0053]     The calibration system can further include a calibration unit  704  having one or more calibration members for calibrating the detector  400 . In one embodiment, the calibration unit  704  includes a first calibration member  710  having a first reflectance of the wavelength of the beam and a second calibration member  720  having a second reflectance of the wavelength of the beam. The first calibration member  710  can have a very high reflectance, and the second calibration member  720  can have a very low reflectance to provide two data points for calibrating the detector  400 .  
         [0054]     The scatterometer  10  further includes a computer  800  operatively coupled to several of the components. In one embodiment, the computer  800  is coupled to the irradiation source  100 , the detector  400 , the navigation system  500 , the auto-focus system  600 , and the reference detector  700 . The computer  800  is programmed to operate the irradiation source  100  to produce at least a first beam having a first wavelength and preferably to also produce a second beam having a second wavelength, as described above. The computer  800  can also control the source  100  to control the output intensity of the beam. The computer  800  further includes modules to operate the navigation system  500  and auto-focus system  600  to accurately position the focus area of the convergent beam  310  at a desired location on the wafer W and in precise focus.  
         [0055]     In several embodiments, the computer  800  further includes a computer-operable medium for processing the measured scattered radiation distribution to provide an evaluation of the PC structure on the workpiece W. For example, the computer  800  can include a database having a plurality of simulated intensity distributions corresponding to known parameters of the photonic crystal structure. The computer  800  can include computer-operable media to process the measured intensity distribution in conjunction with the database of simulated intensity distributions in a manner that selects the simulated intensity distribution that best fits the measured intensity distribution. Based upon the selected simulated intensity distribution, the computer stores and/or presents the parameters of the microstructure corresponding to those of the simulated intensity distribution, or an extrapolation or interpolation of such parameters. Several aspects of the computer  800  and methods for processing the measured intensity distribution are set forth below in greater detail with reference to Section G.  
         [0000]     C. Embodiments of Optics and Lens Assemblies  
         [0056]     The scatterometer  10  can have several different embodiments of optics assemblies and lens assemblies for optimizing the scatterometer for use with specific types of photonic crystal structures. The object lens assembly  300 , for example, can be achromatic to accommodate a plurality of beams at different wavelengths, or it can have a plurality of individual assemblies of lenses that are each optimized for a specific wavelength. Such individual lens assemblies can be mounted on a turret that rotates each lens assembly in the path of the beam according to the wavelength of the particular beam. In either case, the object lens assembly  300  is useful for applications that use different wavelengths of radiation to obtain information regarding the radiation returning from the workpiece.  
         [0057]     The object lens assembly  300  can also include reflective lenses that are useful for laser beams or lamp illumination in the UV spectrum. Certain types of glass may filter or attenuate UV radiation. As such, when the beam has a short wavelength in the UV spectrum, the object lens assembly  300  and other optic members can be formed from reflective materials that transmit the UV radiation. In another embodiment, the first optics assembly  210  or the object lens assembly  300  may have a polarizing lens that polarizes the radiation for the convergent beam  310  ( FIG. 1 ).  
         [0058]      FIG. 2  illustrates one embodiment of the convergent beam  310  explained above with reference to  FIG. 1  formed by an embodiment of the object lens assembly  300 . The convergent beam  310  illustrated in  FIG. 2  has a frusto-conical configuration that results in a focus area S. The focus area S is smaller than the area of the microstructure under evaluation. In several particular applications for the LED industry, the focus area S is approximately 10-200 μm in diameter, and more preferably approximately 20-30 μm in diameter. The focus area S, however, is not limited to these ranges in other embodiments. The focus area S may not necessarily be circular, and thus the convergent beam  310  is typically configured such that the focus area S has a maximum dimension less than 30 μm (e.g., approximately 50 nm to approximately 30 μm).  
         [0059]     The convergent beam  310  simultaneously illuminates a microfeature M through a wide range of incidence angles having large ranges of altitude angles Θ and azimuth angles Φ. Each incidence angle has an altitude angle Θ and an azimuth angle Φ. In general, the incidence angles have altitude angles Θ of 0° to at least 45°, and more preferably from 0° to greater than 70°. The range of azimuth angles Φ can be 0° to greater than approximately 90°, and more preferably throughout the entire range of 0° to 360°. As a result, the object lens assembly  300  can form a conical beam having a large range of incidence angles (Θ, Φ) to capture a significant amount of data in a single measurement of the workpiece W. This is expected to enhance the utility and throughput of scatterometry for measuring photonic crystal structures, which due to their complexity will produce a complicated scattering pattern.  
         [0060]      FIG. 3  is a schematic diagram illustrating a specific embodiment of the optical system  200  in accordance with the invention. In this embodiment, the first optics assembly  210  includes a beam conditioner  214  that produces a conditioned beam  212  including diffused and randomized radiation. The beam conditioner  214  can be a fiber optic line that transmits the beam from the irradiation source (not shown in  FIG. 3 ) and an actuator that moves the fiber optic line to randomize the laser beam. The actuator can move the beam conditioner  214  in such a way that it does not repeat its movement over successive iterations to effectively randomize the radiation.  
         [0061]     The beam conditioner  214  can further include or alternatively be an order sorter for removing undesired diffraction orders from the output. For example, the beam conditioner  214  may form a conditioned beam that provides a limited input to the object lens assembly  300  so that only a single, specific diffraction illuminates pre-selected parts of the detector. The beam conditioner  214  may include a carousel of apertures placed at the input of the optical system  200  so that different input apertures may be selected according to the desired diffraction order of the conditioned beam  212 .  
         [0062]     The first optics assembly  210  can further include a field stop  216  and an illumination lens  218 . The field stop  216  is positioned in the first focal plane of the illumination lens  218 , and the field stop  216  can have an aperture in a desired shape to influence the spot size and spot shape in conjunction with the illumination lens  218 . In general, the illumination lens  218  collimates the radiation for presentation to the object lens assembly  300 .  
         [0063]     The embodiment of the object lens  300  illustrated in  FIG. 3  can include a plurality of separate lenses. For example, the object lens assembly  300  can include a divergent lens  302 , a first convergent lens  304 , and a second convergent lens  306 . The first convergent lens  304  can have a first maximum convergence angle, and the second convergent lens  306  can have a second maximum convergence angle (see  FIG. 4 ). In operation, the object lens assembly  300  (a) focuses the conditioned beam  212  to form the convergent beam  310  and (b) presents the return radiation from the workpiece W on the second focal plane  340 . The location of the second focal plane  340  depends upon the particular configurations of the lenses  302 ,  304  and  306 . For purposes of illustration, the second focal plane  340  is shown as coinciding with the location of the first convergent lens  304 .  
         [0064]     The embodiments of the first optics assembly  210  or object lens  300  may include elements whose position may be varied or altered so as to produce different input beam conditions, such as a variable spot size or shape. This particular embodiment is expected to have great utility to photonic crystal measurements, where the overall array size of the PC structure may vary from one device to another.  
         [0065]     The embodiments of the first optics assembly  210  or object lens  300  may include elements whose position may be varied or altered so as to project a near field or far field scattered radiation distribution at the detector  400 .  
         [0066]     The object lens assembly  300  is configured such that the angle (Θ x , Φ y ) of rays within the convergent beam  310  will pass through corresponding points (x, y) in the second focal plane  340 . As a result, radiation passing through any given point (x, y) in the second focal plane  340  toward the workpiece W will pass through the object focal plane  320  at a particular corresponding angle (Θ x , Φ y ), and similarly radiation reflecting from the object focal plane  320  at a particular angle (Θ x , Φ y ) will pass through a unique point (x, y) on the second focal plane  340 . The reflected radiation passing through the second focal plane  340  propagates to the beam splitter  220  where it is directed toward the second optics assembly  230 .  
         [0067]     The second optics assembly  230  includes a relay lens  232 , an output beam splitter  234 , and an image-forming lens  236 . The relay lens  232  and output beam splitter  234  present the reflected and/or diffracted radiation (i.e., return radiation) from the beam splitter  220  to the image-forming lens  236 , and the image-forming lens  236  “maps” the angular distribution of reflectance and/or diffraction (i.e., the scattered radiation distribution) from the second focal plane  340  to the imaging array of the detector  400 . In a particular embodiment, the image-forming lens  236  preferably presents the image to the detector  400  such that the pixels of the imager in the detector  400  can be mapped to corresponding areas in the second focal plane  340 .  
         [0000]     D. Embodiments of Detectors  
         [0068]     The detector  400  can have several different embodiments depending upon the particular application. In general, the detector is a two-dimensional array of sensors, such as a CCD array, a CMOS imager array, or another suitable type of “camera” or energy sensor that can measure the scattered radiation from the workpiece W corresponding to the distribution at the second focal plane  340 . The detector  400  may be configured to measure intensity, phase, polarization or cross-polarization, or wavelength of the scattered radiation. The detector may be a reflectometer, polarimeter or ellipsometer. In one embodiment, the detector  400  further includes a polarizer such as a rotating polarizer or a sheet polarizer to change the polarization of the light. The orthogonally polarized radiation can be used together or separately to measure certain characteristics that are otherwise undetectable from non-polarized light. As such, polarizing the reflected radiation can optimize the response to increase the resolution and accuracy of the scatterometer  10 .  
         [0000]     E. Navigation and Auto-Focus Systems  
         [0069]     The navigation system  500  accurately aligns the beam  310  with a desired area on the workpiece W, and the auto-focus system  600  adjusts the object lens assembly  300  or workpiece site  510  so that the object focal plane  320  is at the microstructure. In one embodiment, the navigation system  500  has a separate illumination source, lens and measurement optics for determining the precise location of the microstructure on the workpiece W. The light source of the navigation system  500  can be a LED, and the lens and optics can be a two-stage system having low and high magnifications. The low magnification stage identifies the general area on the wafer where the microstructure is located, and the high magnification stage refines the location. In other embodiments, the navigation system  500  can include additional relay optics introduced to image the surface directly through the object lens assembly  300 .  
         [0070]     The auto-focus system  600  can be a camera correlation focus system having a dihedral mirror that simultaneously splits the illumination pupil in two and redirects the light from the two halves of the dihedral mirror to different sections of a CCD array. The displacement between the two images is used to automatically determine the focus. A field stop can be incorporated to prevent overlap of the two images on the focus camera. The field stop is included in the illumination beam of the microscope of the auto-focus system.  
         [0071]      FIG. 4  is a schematic illustration of an embodiment of the navigation system  500  and auto-focus system  600  for use in the scatterometer. Several aspects of  FIG. 4  are similar to those explained above with reference to  FIGS. 1 and 3 , and thus like reference numbers refer to like components in these figures. The navigation system  500  can have a high magnification system associated with the metrology system. For example, the high magnification system includes a light source  550 , such as an LED, that injects light via a beam splitter  552  and is focused on the second focal plane by a relay lens  553  via beam splitter  240 . This light illuminates the workpiece and is reflected back through the object lens assembly  300 . The reflected light is directed by beam splitter  220  and through lenses  232  and  554  to camera  560 . The lenses  232  and  554  form an image of the PC structure on the camera  560 .  
         [0072]     The auto-focus system  600  in this embodiment shares the relay lens  553  and the beam splitter  552  with the navigation system. The beam splitter  552  directs a beam  620  to a dihedral mirror  630 , an image lens  632 , and a steering mirror  634 . The first beam  620  is then received by an auto-focus detector  640 , such as a CCD array or other type of camera.  
         [0000]     F. Calibration  
         [0073]     The calibration system is used to monitor the properties of the initial beam  102  ( FIG. 1 ) and calibrate the system efficiency for accurately detecting the scattered radiation distribution. The beam properties are monitored by a reference detector  700  that receives a portion of the beam  102  in real time. As the beam fluctuates, the reference detector  700  detects the changes in the beam  102  and sends a signal to the computer  800 . The computer  800  accordingly adjusts the measured intensity distribution by the variances in the intensity of the initial beam  102  to eliminate errors caused by small changes in the beam  102 . Unlike some systems that do this periodically, the computer  800  continuously receives signals from the reference detector  700  to maintain the accuracy of the system in real time. This is expected to significantly enhance the accuracy and precision with which the scatterometer  10  can evaluate extremely complex features in PC structures.  
         [0074]     The calibration system can also include a calibration unit, such as the calibration unit  704  ( FIG. 1 ) with one or more calibration members, for providing photometric calibration of the system. In one embodiment, the first calibration member  710  can be a highly reflective mirror having a reflectance greater than 95%, and more preferably a reflectance of approximately 99.99%. The first calibration member  710  can be configured to have a consistent reflectance through a wide range of altitude angles. The second calibration member  720  is preferably a black glass having a low reflectance (e.g., 0% to 10%). In operation, the detector  400  is calibrated by measuring the reflectance of the beam from the first calibration member  710  and from the second calibration member  720  to provide two data points corresponding to the known 99.99% reflectance of the first calibration member  710  and the known 0% reflectance of the second calibration member  720 . Using these two data points, a straight line can be obtained to provide a reference reflectance of the detector  400 .  
         [0075]     The scatterometer can be calibrated further using several different methods. For example, a known grating with a known intensity distribution can be measured using the scatterometer  10  to determine whether the detector  400  accurately produces a representation of the intensity distribution. In another embodiment, a thin film having a known thickness can be irradiated to determine whether the detector  400  provides an accurate representation of the intensity distribution from such a thin film. Both of these techniques can also be combined for yet another calibration method.  
         [0000]     G. Computational Analyses  
         [0076]     The computer  800  can use several different processes for determining one or more parameters of the microstructure based on the measured intensity distribution from the detector  400 . In general, the computer  800  compares the measured intensity distribution with one or more simulated intensity distributions corresponding to selected parameters of the features and materials of the microstructure (e.g., height, width, line edge roughness, roundness of edge corners, spacing, film thickness, refraction index, reflection index, and/or other physical properties). Based on the comparison, the computer  800  then stores and/or provides an output of one or more parameters of the microstructure.  
         [0077]      FIG. 5A  is an image illustrating a simulated scattered radiation intensity distribution  810  having a first interference pattern  812  including a plurality of thin arcs, a second interference pattern  814  including a plurality of different arcs, and a third interference pattern  816  in a configuration of a “bulls-eye.” The first interference pattern  812  can correspond to the specular reflections, the second interference pattern  814  can correspond to higher order diffractions, and the interference pattern  816  can correspond to the film thickness. The interference patterns of the simulated intensity distribution  810  are unique to each set of feature parameters, and thus changing one or more of the feature parameters will produce a different simulated intensity distribution.  
         [0078]      FIG. 5B  is an image of a measured intensity distribution  820  of an actual microstructure on a workpiece. The measured intensity distribution  820  includes a corresponding first interference pattern  822 , a second interference pattern  824 , and a third interference pattern  826 . In operation, the computer  800  ascertains the parameters of the microstructure by selecting and/or determining a simulated intensity distribution  810  that best fits the measured intensity distribution  820 .  
         [0079]      FIG. 6  illustrates one embodiment for ascertaining the feature parameters of the microstructure. In this embodiment, the computer  800  includes a database  830  including a large number of predetermined simulated reference intensity distributions  832  corresponding to different sets of feature parameters. The computer  800  further includes a computer-operable medium  840  that contains instructions that cause the computer  800  to select a simulated intensity distribution  832  from the database  830  that adequately fits a measured intensity distribution  850  within a desired tolerance. The computer-operable medium  840  can be software and/or hardware that evaluates the fit between the stored simulated intensity distributions  832  and the measured intensity distribution  850  in a manner that quickly selects the simulated intensity distribution  832  having the best fit with the measured intensity distribution  850  or at least having an adequate fit within a predetermined tolerance. In the case where a plurality of the simulated intensity distributions  832  have an adequate fit with the measured intensity distribution  850 , the computer  800  can extrapolate or interpolate between the simulated distributions. Once the computer has selected a simulated intensity distribution with an adequate fit or the best fit, the computer selects the feature parameters associated with the selected simulated distribution.  
         [0080]     In an alternative embodiment, the computer calculates a simulated intensity distribution and performs a regression optimization to best fit the measured intensity distribution with the simulated intensity distribution in real time. Although such regressions are widely used, they are time consuming and they may not reach a desired result because the regression may not converge to within a desired tolerance.  
         [0081]     In still other embodiments, the computer  800  may perform further processing or different processing such as finite element models for evaluating non-periodic or pseudo-periodic structures. The computer  800  may also be able to solve for the refraction index and reflectivity index of the particular materials by determining the film thickness. Therefore, the enhanced data in the measured intensity distribution enables the computer  800  to more accurately determine the feature parameters of the microstructure and may enable more feature structures to be monitored (e.g., line edge roughness, refraction index, reflectivity index, etc.).  
         [0082]     In a surprising discovery, it has been found that scatterometry is also useful for measuring dimensions or angles of optical devices, and lighting devices, such as light emitting diodes (LEDs), lasers and optical waveguides having periodic or patterned features like photonic crystal structures.  
         [0083]     Relative to optical devices, it is significant that scatterometry is an optical metrology or measuring technique based on the analysis of light scattered from an array of features. When an array of features is illuminated with a light source, the reflectance properties of the scattered and/or diffracted light varies with the structure and composition of the scattering features themselves. Consequently, by analyzing the light scattered from the features, various precise non-destructive and rapid measurements of the features can be obtained. Although commonly referred to as scatterometry, the so-called scatter of the light generally results from diffraction, in contrast to random scattering.  
         [0084]     The present systems and methods can also be used not only for measuring, but also for designing more optimized optical or lighting devices, such as LEDs. By essentially reversing the light measurement and analysis process through simulations, the light output characteristics of devices such as PC-LEDs may be analytically predicted. The use of specific beam profile models may be integrated with the scattering simulations to simulate highly specific device conditions. Consequently, the geometry and/or dimensions of highly efficient light emitting devices can be calculated. This helps to reduce or avoid the slow, time consuming and costly trial and error development steps of device manufacturing.  
         [0085]     While LED&#39;s now in use are low power devices (about 5 watts maximum) and are costly in comparison to conventional lighting sources, they have several important advantages. LEDs consume far less power than equivalent lighting sources, such as incandescent, or even fluorescent bulbs. They also last far longer, and are much more durable, than virtually any conventional bulbs. It is generally presumed that LED&#39;s will eventually replace conventional lighting all together. This would allow for massive conservation of electricity and materials on a global scale, and a corresponding reduction in use of combustion fuels. Generation of exhaust and greenhouse gases would also be greatly reduced. So-called solid state lighting could also be created in various ways, and in various places not conceivable with conventional bulbs.  
         [0086]     LEDs create visible light by forcing together positive and negative electric charge carriers in a region where two different types of semiconductor material meet. Voltage drives the electrons and holes to an active layer at the boundary between the n- and p-type materials. When an electron and a hole meet, they release energy in the form of a photon. A photon is the smallest particle of light.  
         [0087]     However, not all photons escape from the LED device to provide useful visible light. Impurities and defects or dislocations in the crystal structure of the LED materials absorb photons. A large fraction, or even a majority of the light generated by an LED, is absorbed and not emitted from the LED. LEDs must be able to provide significantly more light before they can replace incandescent and fluorescent lighting.  
         [0088]     Recent research in the LED field suggests that more light can be obtained from LED&#39;s by applying patterned scattering structures above the emission region of the LED. These scattering structures are generally known as photonic crystals (PCs) but are also known as photonic band gap crystals. Although PCs may come in various forms, a typical PC, as shown in  FIG. 7 , has a repeating pattern of features, such as holes or openings. The holes are typically e.g., about 200 or 300-600 nm in diameter, and with a pitch or spacing generally about 1.5-2.5 times the diameter. The performance of the PC depends on accurately holding various design parameters (such as dimensions and angles) within specified tolerances. As a result, these design parameters must be measured if PCs are to be successfully and economically manufactured on a large scale.  
         [0089]     The inventors have discovered that systems and methods described above in connection with  FIGS. 1-6  may be modified and used to perform scatterometry measurements on photonic crystals. This is a surprising result for several different reasons. Initially, scatterometry has been developed and used, in the semiconductor device industry, on silicon based devices. Silicon has relatively low light transmissivity. In contrast, LEDs and PCs are made of relatively transparent optical materials, such as gallium nitride and sapphire, having much higher transmissivity. In silicon devices, the substrate is virtually opaque, so that there is little, if any, substrate optical effect. On the other hand, with optical devices such as LEDs, the substrates are much more transparent. This creates significant substrate optical effects. Similarly, in silicon, multiple buried or underlying layers, even if present, have little effect on scatterometry. As shown in  FIG. 7 , LEDs however typically have large numbers of internal layers. The interface between each set of layers causes refraction and internal reflections. Hence the optical characteristics are entirely different from silicon.  
         [0090]     In addition, silicon has a cubic crystal structure, while the optical materials used in LEDs and PCs generally have hexagonal crystal structures. Silicon devices are largely made up of micro structures formed in straight lines. Optical structures typically involve curved or round structures (although some may also include straight lines or features). In silicon devices, the straight lines or features are generally used to interconnect areas or microelectronic components formed on the substrate. Optical structures tend to have periodic or repeating patterns, without extensive interconnect lines. For these reasons, use of scatterometry for measurement of PC features is more complicated.  
         [0091]     Referring to  FIGS. 8 and 9 , the target area having a periodic pattern is preferably about 50-70 or about 60 microns by about 70-100 or about 85 microns. With additional optics, the target area can be reduced to about 40-50 or about 45 microns by about 50-70 or about 60 microns. The periodic pattern need not fill the entire target area. Especially if the periodic pattern is surrounded by a uniform surface, the pattern itself may be much smaller that the target area. Of course, the pattern may also be larger than (or overfill) the target area as well. In general terms, 8-12 cycles of a repeating pattern are needed to obtain acceptable measurement results. However, the minimum number of cycles needed will vary based on several factors.  
         [0092]      FIG. 9  shows a basic doubly periodic structure similar to the photonic crystal shown in  FIG. 7 . The holes are round, and the holes are aligned in a square pattern. With a nominal hole diameter of e.g. 500 nm, and with the holes spaced apart at e.g., 750 nm centers, the target area shown in  FIG. 8  would overlay an array of holes having about 110 columns and about 80 rows. The array in  FIG. 9  is not drawn to scale relative to the target area shown in  FIG. 8 , as  FIG. 8  is described in micron units and  FIG. 9  is described in nanometers. With respect to a general minimum number of cycles of a pattern, for example, 10 of the rows or columns in  FIG. 9  would occupy only 7.5 microns.  
         [0093]      FIG. 10A  is a section view of a gallium nitride (GaN) LED with a photonic crystal. The photonic crystal  900  is formed as a layer on the LED  902 . The LED itself is based on a substrate  904 . Various known materials and techniques may be used to the form the PC  900  and the LED  902 .  FIG. 10B  shows actual simulated data from an intensity distribution of the structure shown in  FIG. 10A .  FIG. 10C  shows the same data when the critical dimension (i.e., the dimension of interest here, which is the spacing S between adjacent scattering features  910 ) is changed by 1% or 3 nm. Comparison of  FIGS. 10B and 10C  shows that measurement sensitivity for scatterometry on the PC/LED structure is resolvable.  
         [0094]      FIGS. 11A , B, and C are similar to  FIGS. 10 A , B and C, except that the dimension of interest is the sidewall angle A. The angle A is greatly exaggerated for purpose of illustration. A 0.5 degree change in the sidewall angle is resolvable.  
         [0095]      FIGS. 12 A , B, and C are similar to  FIGS. 10A , B and C, except that the dimension of interest is the height of the feature  910 . The plotted data shows that a 1% change (2.5 nm) in the height of the feature  910  is resolvable.  FIGS. 10A , B, and C,  FIGS. 11A , B and C, and  FIGS. 12A , B and C show that scatterometry systems and methods can be used to measure PC structures, notwithstanding the complexities of multiple layers and transmissive materials.  
         [0096]     In these Figures, the data shows extreme spikes at certain angles of incidence, which is unknown in silicon scatterometry. These spikes have been found to be characteristic of scatterometry of optical materials, such as the PC/LED combination shown in  FIG. 10A . As a result, smaller increments in change of incident angle are used to avoid loss of detail. For example, rather than using 1 or 2 degree increments (as is typical for silicon), the increment is reduced to 0.5, 0.4, 0.3, 0.2 or 0.1 degree, in regions having spikes. These regions can be determined from the database of simulated intensity distributions. To avoid slowing excessively slowing down the measuring process, larger 1 or 2 degree increments may be used at flatter areas of the intensity plots, and much finer increments may be used at the spiked regions.  
         [0097]     While the results from  FIGS. 10-12  were obtained using a database of intensity distributions, the regression optimization methods discussed above may alternatively be used in performing scatterometry on optical devices, such as PC/LED devices. In addition, although the results here relate to light intensity distributions, these same techniques may be performed by detecting or measuring phase or polarization of light, within the scope of the invention. It is also not necessary to change the angle of incidence of the light. If a multiple wavelength (e.g. spectral or white light) source is used, the angle of incidence may remain fixed, and measurements made using color intensity distributions, instead of a single wavelength intensity distribution.  
         [0098]     The relatively simple photonic crystal structure shown in  FIG. 7  has a regular doubly periodic array of round holes. A more optimized scattering structure can offer even further enhancements to the output efficiency of LEDs.  
         [0099]     Various geometric designs can help optimize performance of the scattering PC structure. As shown in  FIGS. 9, 13A , B and C, a square or other non-triangular array layout, or a hexagon array layout, as shown in  FIGS. 16A, 16B  and  16 C, may be used. As used here, the word scattering feature or scattering structure means a structure or condition where there is a localized difference in refractive index relative to the host medium (with the host medium being air in the examples shown). Accordingly, while scattering features are generally described here as solid surfaces, scattering features may also take other forms.  
         [0100]     As shown in  FIGS. 14A, 14B  or  14 C, a rectangular or non-symmetric array layout, and oval or elliptically shaped scattering features, as shown in  FIGS. 13B, 14B ,  15 B or  16 B may be used. Similarly, as shown in  FIGS. 13C, 14C ,  15 C or  16 C, the scattering features may be square or rectangular, or have other non-circular shapes. The scattering feature may also be flared or tapered, with a sidewall of the structure intentionally not vertical, as shown in  FIG. 19A . Multiple tapers along the profile of the scattering feature may also be used, as shown in  FIG. 19B . As shown in  FIGS. 19C  and D, the corners on the scattering feature can be radiused or rounded or chamfered (at either end of the feature).  
         [0101]     The scattering feature of the PC may be made of different materials. PCs typically use air as the scattering feature, as shown in  FIGS. 21 and 22 . In these designs, the holes are surrounded by a filler material. In the design shown in  FIGS. 21 and 22 , the filler material is GaN. The filler material may also be a metal, or an oxide, such as silicon oxide, silicon oxy-nitride, or silicon nitride. The filler material may also have a non-uniform index of refraction, such as a material with a graded index of refraction. The holes may also be replaced with (or filled with) a material, including any of the materials listed above, so long as the filler material and the hole material have sufficiently different indices of refraction. In these designs, where the scattering element and the surrounding or filler area are solid materials, there are no holes per se. Rather, the PC is formed with the scattering features (formed as rods, bars, etc.) surrounded by the filler material, as shown in  FIGS. 23 and 24 . In addition to GaN, other materials such as AlInGaP, AlInGaN, or GaAs may be used.  
         [0102]     The geometries of the scattering features may vary across the array. For example, one application for optimal light extraction might require circular features near the center of the PC, with elliptical features near the edge, e.g., as shown in  FIG. 17 . Alternatively, patterns made via combinations of compact features (round, elliptical, square, rectangular, etc.), and elongated features (such as lines), as shown in  FIG. 18 , may be used. In some designs, the use of combined doubly-periodic (holes or posts) and singly-periodic (lines or spaces) as the scattering features, in the same array, may be advantageous.  
         [0103]     These description above may also apply to other optical devices and synthetic optical structures, as well as to for example semiconductor laser diodes, holograms, synthetic lenses, optical filters, optical switches, waveguides and other devices. Similarly, the systems and methods described may be used with flat wafers, structured wafers, LED chips, photonic crystal chips, LED devices with photonic crystals on top, and fully packaged devices. The methods may also be used in optical modeling to simulate emission behaviors of an LED and photonic crystal combination.  
         [0104]     From the foregoing, it will be appreciated that specific embodiments of the invention have been described herein for purposes of illustration, but that various modifications may be made without deviating from the spirit and scope of the invention. Accordingly, the invention is not limited except by the following claims and their equivalents.