Abstract:
A method is disclosed for forming a photonic crystal in a homogeneous layer of material. The method enables the fabrication of 1D, 2D, or 3D photonic crystals. Photonic crystals in accordance with embodiments of the present invention exhibit low temperature sensitivity and low device curvature. In some embodiments, photonic crystals in accordance with embodiments of the present invention are integrated with mechanical elements, such as micromechanical, nanomechanical, microelectronic, and microfluidics devices and systems.

Description:
STATEMENT OF RELATED CASES 
     This application claims priority of provisional patent application U.S. Ser. No. 60/978,941, filed 10 Oct. 2007, the entire contents of which are herein incorporated by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to photonic band gap devices in general, and, more particularly, to photonic crystals. 
     BACKGROUND OF THE INVENTION 
     A photonic crystal is a periodic lattice of medium that prohibits light waves of certain wavelengths from propagating in certain directions. The prohibited range of wavelengths (in certain directions) is referred to as a photonic band gap, and is a defining characteristic for the photonic crystal. A photonic band gap is analogous to an electronic band gap found in semiconductors wherein electrons are forbidden at certain energy levels. The photonic band gap is determined by the refractive index of the medium, the size of the features that compose the periodic lattice, and the periodicity of these features. 
     Another defining characteristic of a photonic crystal is the presence of certain allowed electromagnetic states (i.e., optical modes) in the photonic crystal. In other words, light waves of certain wavelengths are allowed to propagate in certain directions. These allowed electromagnetic states are commonly referred to as the “guided resonances” of the photonic crystal. 
     A photonic crystal can be formed as one-dimensional (1D), two-dimensional (2D), or three-dimensional (3D) structures. One-dimensional photonic crystal exhibit periodicity in only one dimension. For example, a dielectric mirror that comprises interleaving layers of thin-films is a 1D photonic crystal. A 2D photonic crystal exhibits periodicity in two dimensions, and therefore suppresses or guides light within a plane of material. Examples of 2D photonic crystals include integrated waveguides and planar mirrors. In similar fashion, 3D photonic crystals exhibit periodicity in three dimensions and can suppress or guide light within a volume. 
     Although 1D photonic crystals are widely used in many applications, 2D and 3D photonic crystals have not met with the same success as yet. One reason for the lack of success for 2D and 3D photonic crystals is the difficulty of their fabrication. Since the wavelength of light on which they operate is typically on the order of 1 micron, the size of the features that compose these structures is typically on the tens to hundreds of nanometer scale. In addition, 2D and 3D photonic crystals typically employ multiple layers of disparate materials. As a result, fabrication is complicated and the use of disparate materials leads to internal stress and thermal expansion coefficient (TEC) mismatch. Internal stress and TEC mismatch leads to device curvature and temperature sensitivity. 
     SUMMARY OF THE INVENTION 
     The present invention provides a photonic crystal formed in a homogeneous layer of material. For example, the present invention provides photonic crystals formed in a single layer of single-crystal silicon, such as a conventional silicon substrate. In addition, the present invention provides photonics crystals that are one-dimensional, two-dimensional, or three-dimensional. Embodiments of the present invention are particularly well-suited for use as mirrors, wavelength filters, tunable optical elements, integrated waveguides, and sensors. In addition embodiments of the present invention are integrated with mechanical components, such as micromechanical actuators or sensors, nanomechanical components, microfluidics systems, optical fibers, and microelectronic components. 
     The present invention comprises methods for fabricating photonic crystals. In some embodiments, a photonic crystal is formed by etching a first plurality of features into a surface of a substrate. This first plurality of features is then protected to enable it to act as a mask for a second etch that forms a second plurality of features in the substrate. This second plurality of features is self-aligned to and undercuts the first plurality of features. By virtue of the presence of the undercut below the first plurality of features, a vertical refractive index variation is introduced in the homogeneous substrate material. The refractive index of the substrate material, and the size and periodicity of the first plurality of features are selected to define the set of guided resonances of the photonic crystal. These guided resonances are defining characteristics of the photonic crystal. 
     An embodiment of the present invention comprises a method for forming a photonic crystal comprising: forming a first plurality of features in a substrate characterized by a refractive index, wherein the first plurality of features defines a pattern comprising a first periodicity in a first dimension, and wherein each of the first plurality of features comprises a first width that is substantially aligned to the first dimension; forming a second plurality of features in the substrate, wherein the second plurality of features are formed by operations comprising; (1) protecting each of the first plurality of features to form a first mask for a first etch; and (2) etching the substrate in the first etch; and selecting the refractive index, the first periodicity, and the first width to define a first photonic band gap and/or modes for light having a first wavelength. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  depicts a top view of a scanning mirror in accordance with an illustrative embodiment. 
         FIG. 2  depicts a method for fabricating a scanning mirror that comprises a photonic crystal in accordance with the illustrative embodiment of the present invention. 
         FIGS. 3A-3G  depict sequential cross-sectional views of scanning mirror  100  during fabrication in accordance with the method depicted in  FIG. 2 . 
         FIG. 4A  depicts a cross-sectional view of details of a scanning mirror in accordance with an alternative embodiment of the present invention. 
         FIG. 4B  depicts scanning mirror  400  after it has gone through a hydrogen anneal. 
         FIG. 5A  depicts a cross-section of a partially undercut photonic crystal. 
         FIG. 5B  depicts a reflection spectrum for photonic crystal  500 . 
         FIG. 6A  depicts a cross-section of a fully undercut photonic crystal. 
         FIG. 6B  depicts a reflection spectrum for a fully undercut photonic crystal. 
         FIG. 7  depicts a method for fabricating a photonic crystal in accordance with an alternative embodiment of the present invention. 
         FIGS. 8A-B  depict sequential cross-sections of photonic crystal  800  during fabrication in accordance with the alternative embodiment of the present invention. 
         FIG. 9  depicts a three-dimensional photonic crystal in accordance with an alternative embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     The following term is defined for use in this Specification, including the appended claims:
         Set of guided resonances means the electromagnetic modes of a photonic crystal.       

       FIG. 1  depicts a top view of a scanning mirror in accordance with an illustrative embodiment. Scanning mirror  100  comprises mechanical element  102 , and photonic crystal  110 . Photonic crystal  110  is formed in plate  106 . Mechanical element  102  is a torsional scanner that moves plate  106  relative to the underlying substrate (not shown). Specifically, mechanical element  102  rotates plate  106  about the x-axis by means of actuators  104 - 1  and  104 - 2  (referred to collectively as actuators  104 ). 
     Scanning mirror  100  is operable for light having a wavelength of approximately 1500 nanometers (nm). The optical characteristics of scanning mirror  100  are based upon the design parameters of photonic crystal  110 . These design parameters include the refractive index of the material of plate  106 , the size of features  108 , and the periodicity (i.e., pitch) of features  108 . In some embodiments, scanning mirror  100  is operable for electromagnetic waves having a wavelength other than 1500 nm, including any wavelength included in electromagnetic spectrum, and specifically light within the infrared, visible, and ultraviolet light spectra. 
     Actuators  104  are comb-drive actuators comprising comb finger electrodes  124 - 1  and  124 - 2  (referred to collectively as electrodes  124 ), which are rigidly attached to torsion beams  116 - 1  and  116 - 2 , respectively. Actuator  124 - 1  further comprises electrode  112 - 1  and  114 - 1 , which are positioned on either side of torsion beam  116 - 1 . Electrode  112 - 1  comprises stationary comb fingers  120 - 1 , which are interposed by half of comb fingers  120 - 1 . In similar fashion, electrode  114 - 1  comprises stationary comb fingers  122 - 1 , which are interposed by the other half of comb fingers  120 - 1 . 
     Actuator  124 - 2  further comprises electrode  112 - 2  and  114 - 2 , which are positioned on either side of torsion beam  116 - 2 . Electrode  112 - 2  comprises stationary comb fingers  120 - 2 , which are interposed by half of comb fingers  120 - 2 . In similar fashion, electrode  114 - 2  comprises stationary comb fingers  122 - 2 , which are interposed by the other half of comb fingers  120 - 2 . 
     Torsion beams  116 - 1  and  116 - 2  are attached to anchors  118 , which are fixed to the underlying substrate. Torsion beams  116 - 1  and  116 - 2  support plate  106  above the substrate, thereby enabling motion of plate  106  relative to the substrate. 
     In order to rotate plate  106  in one direction about the x-axis, a voltage is applied between electrodes  112 - 1  and  112 - 2  and comb finger electrodes  116 - 1  and  116 - 2 , respectively. In order to rotate plate  106  in the other direction about the x-axis, a voltage is applied between electrodes  114 - 1  and  114 - 2  and comb finger electrodes  116 - 1  and  116 - 2 , respectively. 
       FIG. 2  depicts a method for fabricating a scanning mirror that comprises a photonic crystal in accordance with the illustrative embodiment of the present invention. Method  200  is described with reference to  FIGS. 3A-3G  and with continuing reference to  FIG. 1 . 
       FIGS. 3A-3G  depict sequential cross-sectional views of scanning mirror  100  during fabrication in accordance with the method depicted in  FIG. 2 . 
     Method  200  begins with operation  201 , wherein mask layer  312  is formed on surface  310  of active layer  302  off substrate  308 . 
     Substrate  308  is a conventional semiconductor-on-insulator substrate comprising a single-crystal semiconductor layer that is disposed on a buried dielectric layer that is disposed on a bulk semiconductor handle wafer. In some embodiments, substrate  308  is a bulk material substrate, such as a semiconductor wafer, ceramic substrate, and the like. 
     Active layer  302  is a homogeneous layer of single-crystal silicon having a thickness of approximately 25 microns. In some embodiments, the thickness of active layer  302  is within the range of approximately 1 micron to approximately 100 microns. In some embodiments, active layer  302  is a homogeneous layer of a different material. Suitable materials for use in active layer  302  include, without limitation, silicon-carbide, III-V semiconductors, II-VI semiconductors, ceramics, glasses, oxides, nitrides, oxynitrides, composite materials, polymers, organo-metallics, and the like. It should be noted that the homogeneous nature of the material used in active layer  302  can mitigate or eliminate deleterious effects, such as deformation, warping, or bending of plate  106 , due to internal stress and stress gradients. 
     Mask layer  312  is a layer of material for protecting, in well-known fashion, regions of active layer  302  during subsequent patterning and/or etching operations. Mask layer  312  is a layer of thermally grown silicon dioxide having a thickness of approximately 460 nm. In some embodiments, mask layer  312  is a layer of material other than silicon dioxide. Suitable materials for use in mask layer  312  include, without limitation, silicon monoxide, silicon nitride, metals, polymers, silicon oxynitrides, and the like. In some embodiments, mask layer  312  has a thickness that is within the range of approximately 0.1 micron to approximately 1 micron, and is typically approximately 0.2 mm. It will be clear to one skilled in the art how to make and use mask layer  312 . 
     Mask layer  312  is patterned with openings  314  using conventional photolithography and etching. Openings  314  define pattern  316 . As depicted in  FIG. 1 , in the x-direction, pattern  316  has periodicity Px and width wx. In the y-direction, pattern  316  has periodicity Py and width wy. In the illustrative embodiment, the value of each of Px and Py is approximately 820 nm and the value of each of wx and wy is approximately 790 nm. Pattern  316  dictates the optical characteristics of photonic crystal  110 . In some alternative embodiments, pattern  316  comprises:
         i. openings  314  that are non-circular; or   ii. different periodicities along different direction; or   iii. a plurality of regions of openings  314 , wherein at least one region has a different periodicity than another region; or   iv. a plurality of regions of openings  314 , wherein at least one region has openings having a different width than openings in another region; or   v. a region having a periodicity that is unaligned with either the x-direction or the y-direction; or   vi. any combination of i, ii, iii, iv, and v.       

     Typically, openings  314  have a width within the range of approximately 200 nm to approximately 2000 nm and the periodicity of pattern  316 , in at least one dimension, is within the range of approximately 300 nm to approximately 2000 nm. It will be clear to one skilled in the art, however, that each of the width of openings  314  and the periodicity of pattern  316  can be any value suitable for the application for which photonic crystal  110  is intended. 
     At operation  202 , pattern  316  is transferred into active layer  302 , using a directional etch, to form features  108 . Features  108  are circular regions having a substantially uniform width of approximately 820 microns and a depth, d 1 , of approximately 1 micron. In some alternative embodiments, the depth of features  108  is within the range of approximately 0.2 micron to approximately 15 microns. The use of a directional etch results in features  108  that have substantially the same cross-sectional shape as openings  314 . After their formation, features  108  have substantially vertical sidewalls  318  and bottom surface  320 . Suitable directional etches include, without limitation, deep reactive ion etching (DRIE), ion milling, sand blasting, anisotropic wet etching, and the like. It will be clear to one skilled in the art, after reading this specification, how to transfer pattern  316  into active layer  302 . 
       FIG. 3A  depicts a cross-section of scanning mirror  100 , through line a-a, after operation  202 . 
     At operation  203 , mask layer  322  is formed. Mask layer  322  is a layer of thermally-grown silicon dioxide having a thickness within the range of approximately 100 nm to approximately 1 micron, and typically 150 nm. Mask layer  322  forms on mask layer  312 , sidewalls  318 , and bottom surface  320 . In order to enable the subsequent formation of features  324 , mask layer  322  is removed from bottom surface  320  using a directional etch. This etch leaves mask layer  322  on sidewalls  318 , however. 
       FIG. 3B  depicts a cross-section of scanning mirror  100 , through line a-a, after operation  203 . 
     At operation  204 , features  324  are formed by etching active layer  302  through features  108 . Mask layer  312 , features  108 , and layer  322  collectively define a mask for forming features  324  in operation  204 . Features  324  are formed by etching active layer  302  in a conventional directional silicon etch. In some embodiments, features  324  are formed using a non-directional etch, such as a conventional reactive ion etch using sulfur hexafluoride as the etch primary etch gas. In embodiments wherein a non-directional etch is used to form features  324 , the width of features  324  is greater than width wx 1 . It will be clear to one skilled in the art, after reading this specification, how to form features  324 . 
     At operation  205 , mask layer  326  is formed. Mask layer  326  is a layer of thermally-grown silicon dioxide having a thickness within the range of approximately 100 nm to approximately 1 micron, and typically 150 nm. Mask layer  326  forms on mask layer  322 , sidewalls  318 , and the bottom surface of features  324 . Mask layer  326  protects partially formed photonic crystal  110  during the subsequent formation of mechanical element  102 . 
       FIG. 3C  depicts a cross-section of scanning mirror  100 , through line a-a, after operation  205 . 
     At operation  206 , mechanical element  102  is formed. In operation  206 , suitable conventional photolithography and direction etching is used to pattern active layer  304 , thereby defining the structural material of plate  106 , actuators  104 - 1  and  104 - 2 , torsion beams  116 - 1  and  116 - 2 , and anchors  118 . It will be clear to one skilled in the art, after reading this specification, how to make and use alternative embodiments of the present invention wherein mechanical element  102  is a mechanical element other than a torsional scanner. 
       FIG. 3D  depicts a cross-section of scanning mirror  100 , through line a-a, after operation  206 . 
     At operation  207 , mask layer  328  is formed on all exposed surfaces of scanning mirror  100 , including the back surface of bulk layer  306 . 
     At operation  208 , mask layer  328  is patterned to open a region on the back surface of bulk layer  306 . 
     At operation  209 , bulk layer  306  is etched in conventional fashion to form cavity  330 , which exposes buried dielectric layer  304 . 
     At operation  210 , mask layer  328  is removed from the bottom surface of features  324 . 
       FIG. 3E  depicts a cross-section of scanning mirror  100 , through line a-a, after operation  210 . 
     At operation  211 , active layer  302  is etched in a non-directional etch. Active layer  302  is etched through features  108  and  324  to form features  332 . Features  108  are protected by the mask layer that still remains on sidewalls  318 . 
     At operation  212 , scanning mirror  100  is treated in a hydrogen anneal. During the hydrogen anneal, hydrogen absorbs on all exposed silicon surfaces. As a result, silicon atoms are dissociated from the exposed surfaces at a temperature much lower than the normal melting point of silicon. The dissociated silicon atoms reflow to reduce surface energy. By virtue of the hydrogen anneal, the surface roughness of exposed silicon surfaces is reduced. The smoothing of these surfaces, in turn, reduces optical scattering and other undesired optical effects and improves the optical performance of photonic crystal  110 . 
       FIG. 3F  depicts a cross-section of scanning mirror  100 , through line a-a, after operation  212 . 
     At operation  213 , mask layers  312 ,  326 ,  328 , and exposed regions of buried dielectric layer  304  are removed in a vapor hydrofluoric acid etch. As a result, scanning mirror  100  comprises only the material of active layer  302 . As discussed above, the use of a homogeneous material for active layer  302  affords several advantages for scanning mirror  100 . For example, a photonic crystal comprising a single material typically exhibits lower internal stress, little or no stress gradient, and little or no temperature sensitivity due to thermal expansion mismatches. Furthermore, a photonic crystal comprising a homogeneous material structure is less likely to encounter etch-selectivity problems when subjected to subsequent fabrication steps. As a result, such a photonic crystal is more easily integrated with other components, such as micromechanical devices, nanomechanical devices, photonic devices, microfluidics components, and the like. In some embodiments, however, mask layer  312  and layer  322  are not removed but, instead, form part of the structure of photonic crystal  110  and impact its optical characteristics. 
       FIG. 3G  depicts a cross-section of scanning mirror  100 , through line a-a, after operation  213 . 
       FIG. 4A  depicts a cross-sectional view of details of a scanning mirror in accordance with an alternative embodiment of the present invention. Scanning mirror  400  comprises mechanical element  102 , and photonic crystal  402 . Photonic crystal  402  is formed in plate  106 . 
     Photonic crystal  402  is analogous to photonic crystal  110  and scanning mirror  400  is formed using the operations of method  200 . In contrast to the illustrative embodiment, however, operation  211  continues until the width of features  324  is greater than one half the period of photonic crystal  110  (i.e., wx 2 &gt;Px/2 along the x direction and wy 2 &gt;Py/2 along the y direction [not shown]). This enables features  324  to merge together to form gap  406 . The formation of gap  406  completely undercuts membrane  404 , which comprises photonic crystal  402 . The removal of active layer material completely from the region beneath photonic crystal  402  enables optical characteristics of photonic crystal  402  to be substantially free of influence by the substrate. 
     In some embodiments, gap  406  is less than the remainder of the thickness of active layer  302 ; therefore, a sheet of active layer material remains below membrane  404 . In such embodiments, a micromechanical actuator (e.g., an electrostatic actuator, an electromagnetic actuator, a thermal actuator, a microfluidics actuator, etc.) can be added to change the thickness of gap  406 . Using such an actuator, gap  406  can be controlled to, for example, change the optical characteristics of photonic crystal  402  by variably introducing substrate effects or form an etalon. 
       FIG. 4B  depicts scanning mirror  400  after it has gone through a hydrogen anneal. By virtue of the reflow of the silicon atoms, the sharp edges and projections associated with the formation of photonic crystal  402  are smoothed and the overall surface roughness of all of the exposed silicon surfaces is reduced. 
       FIG. 5A  depicts a cross-section of a partially undercut photonic crystal. Photonic crystal  500  is analogous to photonic crystal  110 . Photonic crystal  500  comprises a 100×100 micron two-dimensional pattern of features  502 , which are 620 nm circular features. Features  502  are arrayed in a square lattice having a 1 micron periodicity in both the x and y dimensions. 
       FIG. 5B  depicts a reflection spectrum for photonic crystal  500 . The influence of the photonic crystal structure on reflectivity spectrum  504  is evinced by the deviation of the spectrum from the reflectivity spectrum for bare silicon (approximately 31% across the wavelength range shown). In addition, the partially undercut structure of photonic crystal  500  results in the spectrum having regions that rapidly change from high reflectivity to very low reflectivity (i.e., high transmissivity) over only a few tens of nm. For example, the reflectivity of the photonics crystal is nearly 0% for light having a wavelength of approximately 1535 nm, yet is approximately 30-40% for light having a wavelength of 1520 or 1560 nm. As such, photonic crystal  500  could be used as an effective wavelength filter in some applications. 
     It should be noted that the amount of lateral undercut in photonic crystal  500  will affect the spectral characteristics of the device and, therefore, its suitability in some applications. 
       FIG. 6A  depicts a cross-section of a fully undercut photonic crystal. Photonic crystal  600  is analogous to photonic crystal  402 . Photonic crystal  600  comprises a 100×100 micron two-dimensional pattern of features  602 , which are 790 nm circular features. By virtue of the complete undercut beneath features  602 , membrane  604  is formed. Membrane  604  is separated from underlying layer  608  by gap  606 . In some embodiments, membrane  604  and underlying layer  608  collectively define an etalon. Features  602  are arrayed in a square lattice having a periodicity of 820 nm in both the x and y dimensions. 
       FIG. 6B  depicts a reflection spectrum for a fully undercut photonic crystal. Reflectivity spectrum  610  demonstrates a broadband reflectivity for photonic crystal  600  that is higher than that of bare silicon. Photonic crystal  600 , therefore, is suitable for use an effective mirror in many applications. 
     As mentioned briefly above, an actuator for controlling the separation between membrane  604  and an underlying layer (i.e., layer  608 ) can be formed. Such an actuator would enable the control of gap  606  and, therefore, the degree to which the underlying layer affects the spectral characteristics of photonic crystal  600 . Such a device, therefore, may be suitable for: (1) optical switching applications, wherein it is desired to alternate between a degree of reflectivity and a degree of transmissivity; or (2) tunable wavelength filter applications, wherein the wavelength at which the photonic crystal is transmissive (or reflective) is controllable. 
       FIG. 7  depicts a method for fabricating a photonic crystal in accordance with an alternative embodiment of the present invention. Method  700  comprises operations for forming features  804  below features  108 . In some embodiments, method  700  can be used instead of operation  204  in method  200 . The formation of features  804  is described below and with respect to  FIGS. 8A and 8B , with continuing reference to  FIG. 1 . 
       FIGS. 8A-B  depict sequential cross-sections of photonic crystal  800  during fabrication in accordance with the alternative embodiment of the present invention. 
     Method  700  begins with operation  701 , wherein features  802  are formed by etching active layer  302  through features  108 . As in operation  204 , features  108 , and mask layer  322  together define a mask for forming features  802  in operation  701 . Features  802  are formed by etching active layer  302  in a substantially directional etch. 
     At operation  702 , active layer  302  undergoes a hydrogen anneal. During this operation, dissociation and reflow of silicon atoms in the exposed sidewalls  804  and bottom  806  of feature  802  enables the silicon atoms to substantially minimize surface energy. As a result, exposed silicon surfaces become smoother and form substantially spherically shaped features  808 . 
       FIG. 9  depicts a three-dimensional photonic crystal in accordance with an alternative embodiment of the present invention. Photonic crystal  900  comprises a vertical repetitive pattern of features  108  and  332 . This pattern is duplicated in both x and y dimensions, thereby defining a three-dimensional photonic crystal. In some embodiments, at least some of features  108  are replaced by features  332 . 
     Photonic crystal  900  is formed by operations of method  200 , wherein any combination of some or all of its operations is repeated as many times as necessary to form the desired number of features in the vertical dimension. 
     It is to be understood that the disclosure teaches just one example of the illustrative embodiment and that many variations of the invention can easily be devised by those skilled in the art after reading this disclosure and that the scope of the present invention is to be determined by the following claims.