PERIODIC DIELECTRIC STRUCTURE FOR PRODUCTION OF PHOTONIC BAND GAP AND DEVICES INCORPORATING THE SAME

Abstract: A method for fabricating a periodic dielectric structure which exhibits a photonic band gap. Alignment holes are formed in a wafer of dielectric material having a given crystal orientation. A planar layer of elongate rods is then formed in a section of the wafer. The formation of the rods includes the step of selectively removing the dielectric material of the wafer between the rods. The formation of alignment holes and layers of elongate rods and wafers is then repeated to form a plurality of patterned wafers. A stack of patterned wafers is then formed by rotating each successive wafer with respect to the next-previous wafer, and then placing the successive wafer on the stack. This stacking results in a stack of patterned wafers having a four-layer periodicity exhibiting a photonic band gap.

Description: PERIODIC DIELECTRIC STRUCTURE FOR PRODUCTION OF PHOTONIC BAND GAP AND DEVICES INCORPORATING THE SAME FIELD OF THE INVENTION This invention relates to periodic structures of dielectric material, and more particularly to such structures which produce a photonic band gap. GRANT REFERENCE This invention was made with Government support under Contract No. W-7405-Eng-82 (DOE-ISU) awarded by the Department of Energy. The U.S. Government has certain rights in the invention. BACKGROUND OF THE INVENTION A number of studies have been done regarding propagation of electromagnetic (EM) waves in periodic dielectric structures. It has been suggested that photons in such media can be described by a photonic band theory analogous to electronic band theory in crystals because of the wave nature of photons. One result of a photonic band theory is the possibility of the existence of photonic band gaps in periodic dielectric structures. The presence of a photonic band gap around a particular frequency would mean that propagation of EM waves would be forbidden for all wave vectors (i.e., in every direction) at frequencies within the gap. At least one experimenter has reported the existence of a photonic band gap in a structure where dielectric material was arranged in a face-centered-cubic (fee) lattice structure. That structure had spherical cavities at the lattice sites with another dielectric filling the gaps between the spheres. The filling ratio of the spheres was 86%, that is, slightly more than overlapped. The ratio of the dielectric constant of the filling dielectric to that of air in the spherical cavities was 3.5. The reported band gap only occurred in this particular structure, despite the fact that a wide variety of filling fractions and dielectric ratios were tried. It is now believed, however, that the results of that experiment were in error, and that a photonic band gap does indeed not exist in the lowest bands for dielectric spheres arranged in the fee structure. The present inventors have pointed out the error of that experiment and have proposed a diamond lattice crystal structure capable of achieving a true photonic band gap in a paper entitled "Existence Of A Photonic Gap In Periodic Dielectric Structures", by K. M. Ho et al., Physical Review Letters, Vol. 65, No. 25, pp. 3152-3155 (December 17, 1990) . The structures proposed in that paper have been further developed in a paper entitled "Photonic Band Gaps In Experimentally Realizable Periodic Dielectric Structures", by C. T. Chan et al., Europhvsics Letters, 16(6), pp. 563-568 (October 7, 1991). In all cases, however, the periodic dielectric structures which have been proposed are difficult to build in the micron or submicron length scales. Thus, while theory has proposed a number of dielectric structures capable of producing photonic band gaps, the actual experiments which have resulted from the papers have utilized crystal structures which are difficult to build with precision, because of the difficulty of positioning the dielectric materials in the desired orientations with respect to each other. Moreover, while devices which may benefit from use of material exhibiting a photonic band gap exist in theory, the realization of such devices has been delayed due to the difficulties encountered in building the photonic band gap material. SUMMARY OF THE INVENTION Accordingly, it is a general aim of the present invention to provide a periodic dielectric structure capable of producing a photonic band gap and which is readily buildable in a practical sense. In achieving that aim, it is an object of the present invention to produce a layered structure, in which elements of the periodic structure can be arranged with respect to each other in layers, with the layers stacked one on the other to produce a three-dimensional periodic structure capable of achieving a true photonic band gap. In that respect, it is an object to use elements to form the respective layers which can be readily and easily fabricated, such as cylinders or rods which are primarily one-dimensional in nature, and which can be arranged with respect to each other in a layer and fixed in that layer, with additional layers stacked one on the other to form the three-dimensional structure. Thus, it is an object to produce a periodic dielectric structure comprised of elongate rods or cylinders arranged in layers, with the layers stacked one on the other, and the respective dimensions of the rods, layers and interspersed material being such as to produce a photonic band gap at a desired frequency. A related object is to provide a method whereby layers including the elongate elements and a supporting structure can be easily formed, such that the resulting layers can be stacked to form the three-dimensional structure. A further object of the invention is to provide a three-dimensional structure capable of achieving a photonic band gap in which the mechanical configuration of the structure is readily tunable to achieve a desired mid-gap frequency and gap width. A still further object is to provide a structure exhibiting the photonic band gap which can be easily modified for use in microelectronic devices. It is a feature of the present invention that the photonic band gaps can be achieved in a periodic dielectric structure with a variety of filling ratios. It is a further feature of the invention that photonic band gaps can be achieved in the periodic dielectric structure comprised of material which has a variety of indices of refraction among the constituent dielectrics. In accordance with the invention, there is provided a periodic dielectric structure which exhibits a photonic band gap. A plurality of dielectric rods are arranged in layers, and the layers stacked to provide a matrix. The rods are interspersed with a material of a contrasting dielectric index. Each of the layers which form the three- dimensional structure has a plurality of rods arranged in parallel and at a given spacing. The axes of the rods in adjacent layers are rotated at an angle with respect to the neighbor layer. In alternating layers (i.e., successive layers having their axes in the same direction) , the rods in one layer are offset with respect to the other by about half the inter rod spacing. Thus, a four-layer periodicity is produced. The dimensions of the rods, the spacing between the rods (laterally and vertically) , and the dielectric constants of the materials are selected to produce a photonic band gap at a given wavelength. A method is also provided for simultaneously forming entire layers of dielectric rods along with a surrounding support structure. The method embraces both forming of a single layer of dielectric rods, and forming of two adjacent, relatively rotated layers. In either case, material is selectively removed from a section of a thin wafer of dielectric material to yield elongate rods of the dielectric material, separated by air gaps. The ends of the elongate rods thus formed extend from and are supported by the remaining, surrounding dielectric material. The orientation of the rods on the wafers is such that stacking of the wafers, with a rotation of each successive wafer before stacking, creates the periodic structure required for photonic band gaps. A further method is provided for forming individual layers of elongate rods. A first layer of rods is formed on a substrate using photolithographic techniques. A second wafer having a special layer structure is bonded to the first substrate. This second wafer includes a transfer layer, bonded to the first substrate, an etch-stop layer and a transfer substrate, with the transfer layer being of the same dielectric material as the first substrate. Using chemical etches, the transfer substrate and etch-stop layer are selectively removed. The remaining transfer layer is then patterned to yield rods rotated with respect to those of the first substrate. Repetition of this procedure allows layers to be built up to yield a well-supported periodic structure required for photonic band gaps. Other objects and advantages will become apparent from the following detailed description when taken in conjunction with the drawings, in which: BRIEF DESCRIPTION OF THE DRAWINGS FIGURE 1 is a perspective view of a dielectric structure exemplifying the present invention; FIG. la is a partial view taken along the line la-la of FIG. 1, showing certain geometric relationships for the periodic structure; FIG. 2 is a diagrammatic structure, intended to be similar to FIG. 1, but showing the use of circular rather than rectangular rods; FIG. 3 is a diagrammatic view showing the inverse of the system of FIG. 2 in which the cylinders are cylindrical holes formed in a dielectric material; FIG. 4 is a diagram similar to FIG. 3 but showing the use of elliptical cylinders; FIG. 5 is a graphical representation showing the dependence of the gap/mid-gap frequency ratio on the filling ratio for cylindrical holes in a dielectric material; FIG. 6 is a graphical representation showing the dependence of the gap/mid-gap frequency ratio on the filling ratio for a structure comprised of stacked layers of dielectric cylinders; FIG. 7 shows experimental results from a microwave model of a periodic dielectric structure of the type shown in FIG. 2; FIGS. 8(a) through 8(i) is a diagrammatic representation of the cross section of a dielectric wafer being processed according to one method of the present invention, at various stages of the processing; FIG. 9 is a perspective view of an alignment jig for use in a method according to the invention; FIGS. 10(a) through 10(f) is a diagrammatic representation of a cross section of a dielectric wafer being processed according to a method of the invention, shown at various stages of the processing; FIG. 11 is a diagram showing the relationship between the alignment posts of the alignment jig and an alignment hole in a wafer formed according to the double-etch method; FIG. 12 is a graphical representation showing the dependence of the normalized mid gap frequency on the over etch percentage for the double-etch structure; FIG. 13 is a diagrammatic representation of the cross section of a dielectric wafer being processed according to a further method of the invention, showing various stages of the processing; FIG. 14 is a diagrammatic representation of a photonic band gap crystal formed according to a further method of the invention; and FIG. 15 shows experimental results from a microwave model of a periodic dielectric structure formed according to the method and demonstrating a photonic band gap. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS While the invention will be described in connection with certain preferred embodiments, there is no intent to limit it to those embodiments. On the contrary, the intent is to cover all alternatives, modifications and equivalents included within the spirit and scope of the invention as defined by the appended claims. Turning now to the drawings, FIG. 1 shows a periodic dielectric structure 20 exemplifying the present invention. A group of four layers of the structure is bracketed at 21 and comprises separate layers 22, 23, 24, 25 stacked one ori the other in a configuration to be described below. Each of the layers is comprised of a plurality of rods 30 interspersed by segments 31 of a material having a contrasting dielectric constant. In the FIG. 1 embodiment, the rods 30 are dielectric material and are interspersed with material of a contrasting dielectric constant, such as air or water. In a modified embodiment, both the materials 30 and 31 can be solid, such as dielectric material within an insulating foam. The rods 30 which comprise the dielectric structure 20 of FIG. 1 are rectangular in cross section and are preferably all of the same cross sectional shape and size. The rods 30 are straight elongate members having axes which are arranged parallel with respect to each other to form a given layer, such as layer 22. The center-to-center spacing between the rods is defined as "a" (see FIG. la) . Adjacent layers of rods have their axes oriented at right angles with respect to the neighboring layer, and thus the layer 23, which has rods 30 of the same cross section as layer 22, and the axes of its rods oriented at right angles to the axes of the rods comprising layer 22. The next successive layer, such as layer 24, thereby has its axes parallel to the axis of the rods forming layer 22, and at the same center-to-center spacing "a". The terms "alternate layer" or "alternating layers" are sometimes used herein to refer to these layers which have their axes parallel to each other and are separated by a single layer with axes rotated by 90°. Thus, in the third layer, such as layer 24, the rods are offset with respect to the layer 22, such that the rods are displaced by about half the inter rod spacing. It will be seen in FIG. la that rod 30a is dimensioned to be at a distance a/2 with respect to the position of the rod 30b within the layer 22. Finally, the layer 25 has the axes of its rods oriented parallel to the axes of the rods 23, and the individual rods thereof displaced about centrally between the rods 23. It will be appreciated that the structure of FIG. 1 is relatively easy to build as compared to the structures proposed in the prior art. For example, an individual layer, such as layer 22, can be formed using a guide or template (or computer controlled formation devices) , to achieve the rod configuration and spacing desired for that particular application. The layer 23 can be separately formed or formed directly on the layer 22 after the layer 22 is in place. It may be preferable, for example, to form each of the layers 22, 23, 24, 25, etc. individually, then lay the layers up one on the other. In other cases, it may be preferable to build the structure starting with the lower layer and laying additional layers on top as the structure is completed. In any event, it will be appreciated that there is a relatively easy-to-construct structure having layers, such as layer 22, formed of materials 30 and 31 of substantial dielectric contrast and at a given spacing and configuration, with subsequent layers oriented at right angles with respect to each other, and alternating layers of the same orientation disposed with the rods of one spaced between the rods of the other, so as to form a sub-structure 21 of four-layer periodicity. The structures 21 are layered one on top of the other to form a larger three-dimensional structure which will be found to exhibit a photonic band gap. Referring again to FIG. la, parameters of the periodic structure will be pointed out, and will later be related to each other as they affect the ability of the structure to tune the wavelength of the forbidden gap. It will be seen that a four-layer composite is defined by the dimension "c", and the relationship between the depth (in the z dimension) and its relationship to the spacing between adjacent rods "a" will be discussed below. The aspect ratio of the rods will also be discussed. The aspect ratio is defined as the ratio between the height z of any given rod and its width x. Thus, for a rod which is shorter than it is wide (in the orientation shown in FIG. la) , the aspect ratio will be less than unity, and for a rod which is taller than it is wide, the aspect ratio will be greater than unity. The filling ratio is the ratio of the material of the rods to the material of the matrix which surrounds the rods. Taking the example of FIG. 1, the filling ratio will be the ratio of the volume of the rods 30 as compared to the volume of air (or other material 31) interposed between the rods. Similarly, when the rods are holes (low dielectric constant) in a high dielectric block, the filling ratio is the ratio of the volume of the holes (the rods) to the volume of the high dielectric matrix. While Figs. 1 and la show a relatively simple structure in which the layers touch but do not overlap, it is sometimes desirable to have overlapping layers. For example, as will be pointed out below, it is possible to form a dielectric structure according to the invention by drilling holes in a block of dielectric materials, with the rods being the holes in the material. In that structure it is relatively easy for the layers to overlap since the periphery of one hole can project into a layer defined by the periphery of another hole. Using solid rods, it is also possible to overlap the layers by appropriately notching the rods. It is also possible to interpose gaps of low dielectric constant material between layers. Performance-wise, that is not desirable, but when it is of constructional benefit, a relatively small space can be accommodated. As noted above, the materials which comprise the rods and the interstices should be of different dielectric constants or refractive indices. It will be appreciated that the dielectric constant is the square of the refractive index, and the terms are used somewhat interchangeably herein, except that where a numerical contrast is specified, the refractive index is always used. Examples of a choice of high refractive index (or high dielectric constant) material are alumina, silicon, GaAs, indium phosphide, titanium dioxide and diamond. Examples of the low refractive index material (or low dielectric constant material) are air, water and silicon dioxide. The ratio of the height of a group of layers (c) to the repeat distance (a) along a layer can be varied to optimize the band gap. Also, the aspect ratio has an impact on the band gap as does the fill ratio. The cross sectional shape of the rods can also be varied, and can comprise rectangular rods as illustrated in FIG. 1 (and the special case of square rods) , as well as rods of elliptical or circular cross section. Other shapes may also be useful. For example, when forming the rods by etching it may be difficult to form perfect rectangles, and the multi-sided shape or trapezoid which may result will also operate according to the invention. The stacked layers can be touching or they can overlap, or as noted above, they can be slightly separated. With proper choice of refractive index contrasts and fill ratios, as will be pointed out below, the above structures will exhibit photonic band gaps (that is, frequency regions in which no propagating electromagnetic wave modes can exist. These photonic band gap materials can be used in various applications which require the suppression of spontaneous emission of light inside the photonic gap. For example, they can be used in laser diodes to enhance efficiency. Turning to FIG. 2, there is illustrated a portion of a dielectric structure, like the structure of FIG. 1, but utilizing circular rods. A series of four layers 41-44 are illustrated to comprise a four-layer periodic structure 40 comprised of a plurality of rods 46 of circular cross section. The center-to-center distance "a" between the rods is utilized in the following expressions in the same fashion as the spacing in the rectangular case of FIG. 1. Similarly, the height and the z direction of a four-layer periodic structure is defined as "c", and the aspect ratio is defined in the same way as in the prior example. FIGS. 3 and 4 illustrate the converse structure where holes are formed in a block 50 or 51 of dielectric material. In the FIG. 3 embodiment, the holes 52 are circular, whereas in the FIG. 4 embodiment, the holes 53 are elliptical. The holes can be filled with air or other low dielectric index material. In both cases, the center- to-center spacing "a" is arranged as in the other embodiments. But in this case, the rod is of low dielectric material and the interstices of high dielectric material. The axes of the rods are parallel to each other, and in adjacent layers, the orientation is changed by 90° such that adjacent layers have mutually perpendicular axes. With respect to any two alternate layers (successive layers whose axes are in the same direction) , the rods of one layer are arranged at the mid-point between the rods of the other layer, to produce a structure of four-layer periodicity when the layers are stacked one on the other. It will be seen by a comparison of FIG. 3 and FIG. 4 that the same conditions apply to the elliptical embodiment. In the case of FIG. 4, the ellipses can be arranged with an aspect ratio greater than unity as illustrated, or the ellipses can be rotated 90° to produce an aspect ratio which is less than unity. We have developed a calculation method which can be used to determine the band structure of periodic materials, and thus the presence of the photonic band gap. The calculation method takes into account the vector nature of the electromagnetic field present within the structure. While it is of general applicability, we have used it for the layered structures constructed in accordance with the present invention and have determined the presence, absence and quality of a band gap produced by such structures. We have furthermore determined the effect on the gap (or on the gap/mid-gap ratio) of different parameters of the structure, such as filling ratio, aspect ratio, c/a ratio, rod shape, refractive index contrast, and the like. We will first present the calculation method (and a portion of its derivation) and will thereafter illustrate the manner in which the periodic structures according to the present invention will provide the gap/mid-gap ratio. In such a periodic structure, the dielectric constant is position dependent, which allows Maxwell's equations to be written as: vx__ = i(-ω %)i f.-, V x H = -i (—ω )€(?)£, c c (1) which can be further simplified to; v x (—^— v x H) = H (2) e(r) c 2 The periodic dielectric function can then be expanded using Bloch's theorem to expand the H field in plane waves, substitution of equation 3 into the simplified Maxwell equation 2 results in the matrix equations: λ, λ < ω < > (4) G' . X' G, G' hp.. . ι.=— h G-, λ where: H Gi , G' (5) '/ It should be noted that the periodic dielectric structure €(r) only enters in the calculation through the position-dependent dielectric function which was evaluated on a fine grid in the real space unit cell and Fourier transformed into reciprocal space. This allows use of this calculation to calculate the photonic bands for any periodic arrangement of objects, including allowing them to have arbitrary shapes, filling ratios, and various index of refraction contrasts. The index of refraction contrasts refers to the ratio of the indices between the material filling the gaps between the dielectric spheres, and that of the dielectric spheres themselves. Utilizing the foregoing relationships, we have determined optimum characteristics for structures in accordance with the present invention, and those will be described in connection with FIGS. 5 and 6. FIG. 5 relates to periodic dielectric structure such as that shown in FIG. 3 which has cylindrical holes formed in a dielectric block. The refractive index contrast, that is, the ratio between the indices of the high and low index material, is taken to be 3.6 for the example of FIG. 5. It will be appreciated that a minimum refractive index contrast of about 2.0 is necessary to produce a photonic band gap in such structures. In the structure of FIG. 5, the individual rods can overlap one another, that is, the cylindrical holes in one layer can project into the succeeding layers. The ratio of the repeat distance in the z direction (identified as "c" in FIG. 1) to the repeat distance in the x and y direction "a", is taken to be 1.414 for the structure of FIG. 5. The figure illustrates the photonic band gap (normalized to the frequency at the center of the gap) , in other words, the gap/mid-gap frequency ratio as a function of filling ratio. It will be seen that the maximum gap/mid-gap ratio of about 0.26 is achieved for a filling ratio of about .81. The wavelength of the forbidden light is proportional to and of the same magnitude as the repeat distance of the structure. Thus, the dimensions of the rods themselves can be selected to meet this criteria, with the spacing and dielectric constants selected to meet the desired gap/mid-gap ratio. FIG. 6 illustrates the case such as shown in FIG. 2 for dielectric cylinders separated by material of lower dielectric constant. The c/a ratio for the structure of FIG. 6 is also taken to be 1.414, and the diagram of FIG. 6 illustrates two cases for a refractive index contrast of 3.6 and a refractive index contrast of 2.33. For the former, it will be seen that the optimum filling ratio is about 0.25 and achieves a maximum gap/mid-gap ratio of about 0.175. For the lower contrast material, the optimum filling ratio is about 0.38, but a gap/mid-gap ratio of only 0.04 is achievable in that configuration. As in the case of FIG. 5, the structure of FIG. 6 contemplates the condition where the rods can overlap one another. In order to physically demonstrate the results achievable with periodic structures according to the invention, a microwave-size model was constructed and tested. A microwave-size model is one which is scaled up in size from a photonic model, and which will operate at microwave frequencies, in the same way that a photonic model will operate at visible lightwave frequencies. The model was constructed based on the structure of FIG. 2, that is, the use of circular rods arranged in layers with the layers having their rods in contact. The model contained layers of parallel cylindrical alumina rods which were 0.08" in diameter. The center-to-center spacing between rods was 0.28". The model was built of 40 layers, one layer touching the next. There were ten rods per layer arranged on the 0.28" centers. Measurements for the transmission of microwaves through the model in the frequency range of 12 to 24 GHz. demonstrated the presence of a gap in the electromagnetic wave propagation in the "crystal" along the x and z directions for both polarizations. This is illustrated in FIG. 7 which represents the experimental data from the model operated at 12 to 24 GHz with propagation along the x axis and polarization along the z axis. While the preceding description has dealt primarily with the elongate rods as discrete building blocks which are arranged to form the photonic band gap material, entire layers of elongate rods could also be considered as the building blocks of photonic band gap material. In accordance with this implementation, the invention also includes methods for building photonic band gap structures wherein entire layers of elongate rods are formed, and then the layers are stacked together to yield the four-layer periodic structure required to produce a photonic band gap. Common to these methods is the use of certain photolithographic and material etching techniques, commonly used in semiconductor fabrication, to form the various layers required for a photonic band gap structure. Further, the methods include steps for properly orienting successive layers to form the photonic band gap structure. In the first of these techniques, semiconductor fabrication methods are used to form layers of spaced elongate rods in a wafer of a dielectric material. The term "wafer," as used herein, is intended to broadly refer to a relatively thin, planar sample of a given material and is not intended to be limited to any specific size, thickness or crystal orientation of the material. These elongate rods are formed by etching a portion of a wafer comprised of dielectric material such that air gaps are formed between the elongate rods. Once a number of such wafers have been formed, these wafers can be stacked up together to form the photonic band gap structure having a four-layer periodicity. In one embodiment of the present method, a single layer of parallel, spaced elongate dielectric rods is formed in a wafer of dielectric material. Formation of this single layer may be carried out by using the anisotropic etch properties of various crystal planes of the dielectric. In some dielectric materials, crystalline silicon (Si) being an example, different symmetry planes are etched at different rates. As an example, the {110} crystal plane of silicon etches at a rate between 500 - 2,000 times faster than the etch rate of the {111} crystal plane. By using the preferential etch rate of a given crystal plane according to the method of this invention, a single layer of elongate rods having straight side walls can be formed. One way to form the single layer of parallel, spaced elongate rods is to orient the desired rods parallel to the {111} crystal plane in {110} oriented wafers. That is, the wafers are patterned such that a portion of the wafers corresponding to the elongate rods are coated such that an etch solution will not contact that portion of the wafer. The wafers are then placed in the etch solution such that the {110} oriented material between the elongate rods, which etches at a significantly faster rate than the {111} material under the protected areas, are etched through. No significant under etch of the covered areas occurs since the material beneath these covered areas is parallel to the {111} plane, which plane etches at the slower rate. Thus, the result of etching through of the {110} wafer that is patterned in this manner is spaced, parallel elongate rods of essentially rectangular cross section. The preparation of a dielectric wafer for this etch to form the elongate rods begins by coating the entire wafer with an oxide. As is well known in the art, aqueous solutions of KOH etch silicon dioxide layers at a very slow rate as compared to the etching of the {110} or {100} crystal plane. Once the wafer is coated with the oxide, the oxide will be removed from the areas corresponding to the air gaps between rods. Placing the thus patterned wafer in the KOH will cause the air gaps to be etched through. For the purposes of carrying out this fabrication method, a 1 micron silicon dioxide layer (Si0 2 ) is thick enough to protect the regions of the silicon wafer which are not to be etched, for a wafer as thick as 500 microns. A cross- sectional view of a dielectric wafer with the oxide grown on is shown in FIG. 8a. Indeed, cross-sectional views of the wafer during various stages of this fabrication method are shown in FIGS. 8a-8h. FIGS. 8a-8h are included for the purpose of illustrating the process steps of this method, and do not necessarily accurately characterize the structure that results from this process. The oxide layers 101 (top) and 102 (bottom) are shown grown on the silicon substrate 100 in FIG. 8a. After the oxidation, one side of the wafer is patterned by conventional lithography. The purpose of this patterning is to selectively remove the Si0 2 from the areas of the wafer which will correspond to the gaps between the elongate rods. A mask is used for this patterning of the wafers. The mask consists of stripes which will define the dielectric rods in individual layers of the photonic band gap crystal and also includes four rectangular structures, which are used as pin holes during the alignment process (and will be referred to herein as alignment holes) where the wafers are optionally stacked on an alignment jig. Since the success of patterning the wafer depends on the elongate rods being parallel to the {111} crystal plane of the wafer, the mask is aligned to the crystal such that the elongate stripes are parallel to the {111} plane. A conventional photolithography technique is used to expose and develop a layer of resist 105 which is spun on the top surface of the wafer as shown in 8b. The mask is then aligned as explained above, and results in the arrangement shown in FIG. 8c where the lines of the mask are shown as 107. A dark mask and positive resist are used. Because of this, exposure and development of the resist removes the resist 105 that was in the area of the wafer not covered by the mask. The result of resist exposure and development is shown in FIG. 8d. Following this step, the resist on the front of the wafer is hardened by a 120C° bake. Following that bake, a thick layer of resist is spun onto the backside of the wafer and another 120C° post-bake is performed in order to protect the oxide on the backside of the wafer. A wafer including this backside resist 110 is shown in FIG. 8e. With the portions of the Si0 2 corresponding to the gaps between the rods now being exposed, the wafers are dipped into a buffer oxide etch solution to remove the Si0 2 between the rods. The wafer with the S i 0 2 thus removed is shown in FIG. 8f. Once the removal of the oxide between the rods is finished, the resist is washed away, and the oxide layer has the desired pattern. The wafer in this configuration is shown in FIG. 8g. The wafer is now prepared for the final KOH etch. As noted above, KOH solution preferentially etches the regions that are not covered by the oxide, while the regions that have the oxide are protected. Furthermore, since the rods are oriented parallel to the {111} plane, there is no significant under etch and an almost vertical wall is generated during the etching process. A variety of concentrations and temperatures of KOH solution may be used depending on the required etching speed. A typical concentration and temperature would be 40% KOH (by weight when mixed with water) with an etch temperature of 85C°. The wafer remains in the KOH solution until it is etched through, it being periodically removed to check on the etch progress. A wafer that is completely etched through is shown in FIG. 8h. Following etch through, the wafers are rinsed with deionized water and placed in the buffer oxide etch solution to remove the oxide. A properly patterned finished wafer is shown in FIG. 8i. Once a plurality of single layer wafers have been formed in this fashion, they are then stacked together to form the photonic band gap crystal. In the case of single- layer wafers, a 90° rotation between each successive wafer in the stack ensures that the required four-layer periodicity is achieved. As discussed above, it is preferable for the rods of alternating layers to be offset from one another by approximately one-half the repeat distance. This is achieved according to the present method by properly selecting the orientation of the alignment holes and the elongate rods in a given wafer. A typical jig that may be used to facilitate the stacking process is shown in FIG. 9. The jig is simply a circular piece of plexiglass 170 including a central opening 171. Four circular alignment posts 175-178 are mounted in the base 170. The jig may include a complemental cover having holes for receiving the posts. The posts 175-178 are received in complemental alignment holes in the patterned wafers. This method, by which individual layers of photonic band gap are easily formed, by existing fabrication techniques, and then stacked may be scaled down for the purpose of increasing the frequency range of the photonic band gap material. Using the reference letters of FIG. la, the "a" dimension and the "x" dimension may be modified by changing the dimensions of the dark and light portions of the mask used for the photolithography process. Furthermore, dimensions "c" and "z" may be modified by using thinner wafers. Use of this fabrication method results in photonic band gaps of around 100 GH-a for rods having a width of 340 microns formed on 380 micron thick dielectric material, the rods being separated by 1275 microns. Measurements for the transmission of microwaves through a photonic band gap structure meeting these specifications, and formed according to this method, were performed. These measurements demonstrated the presence of a gap in the electromagnetic wave propagation about a mid- gap frequency of approximately 100 GH-B, as depicted in FIG. 15. Of course, the values will vary with dielectric constant, filling ratio, etc. , as previously discussed. It may also be desirable to form a single layer of elongate rods in a dielectric wafer that does not exhibit the anisotropic etch properties of other dielectric materials. An example of a dielectric not exhibiting the advantageous anisotropic etch properties is alumina. When it is desired to use such dielectric material for forming photonic band gap structures, laser machining of the wafers, as opposed to chemical etching of the wafers, may be used to form the elongate rods. A similar method of 1) forming layers in a dielectric wafer and 2) stacking the wafers, is also used wherein two layers of elongate rods are formed in a single wafer. That is, one layer of elongate rods is formed on the frontside of the wafer, and a second layer of elongate rods, rotated relative to the first, is formed on the backside of the wafer. Since the dimensions of the elongate rods must be reduced to increase the frequency of the band gap, this method of producing the elongate rods is advantageous as each layer is half the height of a layer that would be formed according to the single layer method, for a given wafer thickness. Like the single layer method described above, the present method, referred to herein as the "double-etch" method, uses the anisotropic etch properties of a crystalline dielectric to form the desired layers. However, the preferential etch rate of a first plane (illustratively the {110} plane of Si) is used, as compared to three different {111} planes, which are angularly offset from each other. In the present embodiment, the two {111} planes are offset from each other by 70.2°. The rods of the first or top layer of the two layer wafer are parallel to a first {111} crystal plane, while the rods of the bottom layer are parallel to the other {111} plane, and are thus rotated with respect to the top layer by the 70.2° angle between the two crystal planes. Proper orientation and alignment of these two layers and the alignment holes according to the method of the invention allows a four- layer periodic material exhibiting a photonic band gap to be formed by stacking successive two-layer wafers and including a 180° rotation between successive wafers. Since the orientation of the top layer and bottom layer of elongate rods is different in a wafer formed according to this method, two different masks must be used to properly pattern the wafer. In order to properly align the masks to the front and back of the wafer, the wafer must include a common reference point visible both from the front and the back of the wafer. To provide for such a reference, the first step in this double-etch method of forming photonic band gap material is to etch the alignment holes through the wafer. The same photolithography techniques described above in relation to forming of the single layer rods is used. That is, an oxide layer is grown over the entire wafer. For the double-etch procedure, an oxide layer of 2.0 microns is sufficient for a 250 micron thick wafer. Lithography is then used to pattern photoresist such that the oxide areas above the alignment holes are exposed. The oxide in those exposed areas is then removed by an oxide etch. Finally, the wafer is dipped in a KOH solution which etches away the wafer in the alignment hole area only. To ensure that the alignment holes have straight sidewalls (so that their position on either surface of the wafer is the same) , they are formed as trapezoids, with each set of parallel sides being parallel to one of the nonpreferentially etched {111} crystal planes. Once the alignment holes are thus formed, the patterning of the oxide layers to allow etching of the two layers of elongate rods can be carried out. The method by which this is achieved is pictorially represented in FIG. 10 which shows cross-sectional views of the wafer during various processing stages. FIGS. lOa-lOf are limited, however, in that they do not accurately depict the 70.2° angle between the rods on the top surface of the wafer, and those on the bottom. Rather, these figures merely illustrate the processing steps of the double-etch wafer while not accurately depicting the resulting structure. Oxide layers 111 and 112 are formed on substrate 110. Photoresist 115 is added to the top layer of the wafer (10a) , and is exposed and developed so that the region of the oxide above the gaps between the elongate rods is exposed (10b) . After a hard-bake of the resist at 120 C° for 30 minutes, resist 116 is spun onto the backside (10c) , and is pre-baked at 90C° for 25 minutes. The backside of the wafer is then patterned with elongate rods at a 70.2° angle with respect to the top layer of rods. At this point, both the top and bottom of the wafer are patterned such that the oxide is exposed in the regions between the elongate rods in the respective layers (lOd) . Following a hard bake of the backside resist, the wafers are dipped in a buffer oxide etch solution to remove the exposed oxide (lOe) . The wafers are then dipped in a solvent to remove the resist from front and back (lOf) . The wafers are now ready for etch-through in the KOH solution. Again, a concentration of 40% KOH (by weight in water) is used at a temperature of 75°C. The wafers are periodically removed from the etch solution to check on their progress. Once the wafers are etched all the way through, the etching is stopped and the wafers are rinsed. A photonic band gap structure is then formed by stacking of a plurality of wafers formed in this manner. A similar stacking jig to that shown in FIG. 9, and having four milled circular posts, is used for alignment and stacking of the wafers. Unlike the single layer method, however, the wafers in this double-etch method are rotated 180° between successive wafers. This stacking method provides the necessary four-layer periodicity for achieving photonic band gaps. As in the single-layer stacking, the rods of alternating layers are offset from each other by approximately one half the separation distance between rods. To provide this offset, both of the elongate rod patterns are oriented with respect to their alignment holes in a similar manner as in the single layer method. Since a single wafer contains two separate planar layers of elongate rods, relative motion between successive wafers, allowable in the single layer wafer stacking, is not allowable in the stacking of the present method. The configuration of the alignment holes in the double-etch method prevents such relative movement. As mentioned previously, the alignment holes are trapezoidal and have straight sidewalls. A trapezoidal shape, with each set of parallel sides parallel to a {111} plane was chosen to ensure the straight sidewalls. The lengths of the sides of these trapezoids were also carefully chosen, to ensure that the alignment rods of the alignment jig exactly fit within the trapezoids, and to prevent any relative lateral movement of the stacked wafers. The orientation of one of the trapezoidal alignment holes and one of the alignment posts is shown in FIG. 11. It can be seen in that figure that the post contacts all four sides of the trapezoid, thus holding the wafer in position. In the present embodiment, posts having a diameter of .025" were used. The length of the sidewalls of the trapezoid were then chosen taking into account the 70.52° angle θ shown in Fig. 21. This is the angle between respective {111} planes referred to above. One advantage of the double-etch method is the possibility of tuning the mid-gap frequency of a given structure. As mentioned earlier, the mid-gap frequency of a photonic band gap crystal may be modified by changing the filling ratio as by notching of the rods at the point of contact with rods in the layer below. A similar "notching" can be obtained by overetching the double-etch wafers. Overetch is accomplished by simply exposing etched-through wafers to the KOH etch solution for longer periods of time. A theoretical graphical representation of the effect of overetch of the double-etch structure on mid-gap frequency is seen in FIG. 12. Since the method of the present invention provides for simple stacking and unstacking of wafers of a given crystal, wafers can be repeatedly overetched by incremental amounts and restacked until the resulting stack yields the desired mid-gap frequency. To provide for even further size reduction of the photonic band gap structure, and concomitant increase in mid-gap frequency, a further fabrication method is provided. According to this method, standard lithography techniques are applied to a single wafer to build up individual, properly-oriented layers of elongate rods of dielectric material which form a structure having the required four-layer periodicity. In this process, each layer is first bonded to a previous layer, and is then patterned using photolithographic techniques. Since lithography tools can achieve sub-micron alignment accuracy, and the thickness of each layer can be as small as 0.1 micron, this technique can be used to build photonic band gap crystals at optical wavelengths from 0.3 micron to 10 micron. The process starts with patterning of the original substrate, illustratively Si. A typical pattern consisting of parallel rods is etched on the substrate. An illustration of a cross-section of the wafer during the various steps of this process can be seen in FIG. 13. This layer, formed by standard photolithographic techniques, is seen in FIG. 13a. Next, another wafer 210 with a special epitaxial layer structure is brought in contact with the etched substrate 200 (13b) . The contact is principally made in the area of the etched substrate beyond the etched region, which ensures good contact between the substrates. This bonding itself may either be done by gluing, or by a special surface treatment of the mating surfaces, which allows for their bonding at the atomic level. The next step is the etch back of the two layers 211 and 212 overlying the transfer layer 213. As can be seen in FIG 13, the transfer layer 213 and the transfer substrate 211 are separated by a special etch-stop layer 212. The etch stop layer 212 is chosen such that when the transfer substrate is etched, the etch will stop at this layer. A number of options are available for forming such an etch- stop layer. For Silicon wafers, highly doped (p++) layers can be used. For GaAs wafers, an AlGaAs layer can be used. Once the whole transfer substrate 211 is etched (13c) , the wafer and its associated bonded structure are removed from the etch solution. This step is followed by another selective etch step which is designed to etch only the etch-stop layer 212 (13d) . This results in a structure where a very thin semiconductor transfer layer 213 is bonded on a patterned substrate 200. The thickness of the transfer layer 213 can be chosen during its epitaxial growth before bonding, and may be thinner than 0.1 micron. At this point in the process, the transfer layer 213 is patterned using photolithographic techniques. A layer of photoresist is applied, and then the mask for the next layer is aligned to the underlying pattern. Once the resist is patterned and baked, the transfer layer is etched chemically, or with a reactive ion etch, to result in rods that are perpendicular to the direction of the rods in the substrate 200. Once this etch is completed, two patterned layers that are bonded to each other result. The process can then be repeated again by bonding on another epitaxial structure, etching back the substrate and etch-stop layer and patterning the transfer layer. This process is repeated until the desired number of layers is reached, illustratively as in FIG. 14. The resulting structure will be very similar to those previously described in relation to other fabrication techniques for rod-based millimeter wavelength photonic band gap structures, but the dimensions will be 100-1000 times smaller. Thus, the invention provides a readily fabricatable structure exhibiting a photonic band gap. Elongate rods form each given layer with the rod axes parallel to one another and at a given spacing. A second layer can be formed in the same fashion, but with the axes at an angle to and preferably perpendicular to the rods of the first layer. The third layer has its axes parallel to the first, but has the rods in the mid-gap in the first layer. The fourth layer has its axes parallel to the second, but with the rods mid-gap of the second. Thus, a four-layer periodic structure is repeated until a three-dimensional structure of desired dimension is achieved. The practical advantage of the invention makes it possible to readily achieve the photonic band gap structure. The invention also provides a method for forming an entire layer or layers of elongate rods in dielectric wafers. The wafers thus formed are stacked together to achieve the photonic band gap structure. Another method provides for fabrication of successive individual layers on a single wafer, where the material to form a layer is bonded to the previous layer, then patterned to form properly oriented elongate rods.

Claims: WHAT IS CLAIMED IS: 1. A periodic dielectric structure which exhibits a photonic band gap comprising, in combination: a plurality of dielectric rods arranged in a matrix of a material having a different and contrasting refractive index, a number of said rods being arranged to form a planar layer, and a plurality of layers being stacked one on the other to form a three-dimensional structure, each layer having a plurality of rods arranged with parallel axes at a given spacing, each layer having its axes oriented at an angle with respect to its adjacent layers, alternate layers having their axes parallel to each other with the rods of one layer in offset between the rods of the other, thereby to form a three-dimensional structure of stacked layers having a four-layer periodicity, the dimensions of the rods, and the spacing between the rods, being selected to produce a photonic band gap at a given wavelength. 2. The combination set forth in claim 1, wherein the angle is 90°. 3. The combination set forth in claim 2, wherein the refractive contrast of the materials is selected to produce a photonic band gap. 4. The combination as set forth in claim l, wherein the angle is other than 90°. 5. The combination as set forth in claim l wherein the alternate layers are arranged with the rods of one layer offset at about the midpoint between the rods of the other layer. 6. The combination as set forth in claim 5 wherein the layers are stacked such that the rods of successive layers overlap. 7. The combination as set forth in claim 5 wherein the material of the matrix is a dielectric material and the rods are elongate holes formed in the dielectric material. 8. A method of fabricating a periodic dielectric structure exhibiting a photonic band gap, comprising the steps of: (a) forming alignment holes in a wafer of dielectric material having a given crystal orientation; (b) forming at least one planar layer of elongate rods in a section of the wafer, including the step of selectively removing the dielectric material between the rods; (c) repeating steps (a) and (b) on a plurality of wafers to form a plurality of patterned wafers; and (d) forming a stack of patterned wafers having a four-layer periodicity by rotating each successive wafer with respect to the next-previous wafer, and then placing the successive wafer on the stack. 9. The method of claim 8, wherein the steps of forming alignment holes and selectively removing dielectric material between the rods are performed by laser machining the wafer. 10. The method of claim 8, wherein the steps of forming alignment holes and selectively removing dielectric material between the rods are performed by chemically etching the wafer. 11. The method of claim 10, wherein the step of removing dielectric material between the rods is achieved by using an etch solution with a significantly faster etch rate along the given crystal orientation of the wafer than along a first symmetry plane. 12. The method of claim 10, wherein forming the elongate rods includes the steps of forming a first layer of rods on a first surface of the wafer, and forming a second layer of rods on a second surface of the wafer. 13. The method of claim 12, wherein the steps of forming the first layer and second layer are achieved by using an etch solution with a significantly faster etch rate along the given crystal orientation of the wafer than along first and second symmetry planes. 14. A method of claim 8, wherein the stacking step includes placing each patterned wafer on an alignment jig including alignment posts adapted to be received in the alignment holes. 15. A method for fabricating a periodic dielectric structure exhibiting a photonic band gap, comprising the steps of: (a) patterning a portion of a substrate of given dielectric material to form a layer of parallel rods; (b) bonding an epitaxial layer structure to the substrate, the epitaxial layer including a transfer layer of the given dielectric material, an etch-stop layer and a substrate layer; (c) etching the substrate layer; (d) etching the etch-stop layer; (e) patterning the transfer layer to expose an area of the transfer layer corresponding to a pattern of parallel rods having an axis perpendicular to an axis of the rods of the previous layer; and (f) repeating steps (b)-(e) and successively adding layers of parallel rods until the desired number of layers is reached. 16. The method of claim 15, including offsetting the rods of alternate layers, such that the rods of one layer are at about the midpoint between the rods of the other layer.

Inventors: BISWAS RANA, CHAN CHE-TING, HO KAI-MING, MICHEL ERICK, OZBAY EKMEL, SOUKOULIS COSTAS, TUTTLE GARY, BISWAS, RANA, CHAN, CHE-TING, HO, KAI-MING, MICHEL, ERICK, OZBAY, EKMEL, SOUKOULIS, COSTAS, TUTTLE, GARY
Applicants: UNIV IOWA RES FOUND, IOWA STATE UNIVERSITY RESEARCH FOUNDATION, INC.
Application year: 1993
Main classification: H01S3
IPC codes: G02B6