The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

Modern cryptography relies on algorithmic one-way functions—numerical functions which are easy to compute but very difficult to invert. This dissertation introduces physical one-way functions and physical one-way hash functions as primitives for physical analogs of cryptosystems. 
Physical one-way functions are defined with respect to a physical probe and physical system in some unknown state. A function is called a physical one-way function if (a) there exists a deterministic physical interaction between the probe and the system which produces an output in constant time; (b) inverting the function using either computational or physical means is difficult; (c) simulating the physical interaction is computationally demanding and (d) the physical system is easy to make but difficult to clone. 
Physical one-way hash functions produce fixed-length output regardless of the size of the input. These hash functions can be obtained by sampling the output of physical one-way functions. For the system described below, it is shown that there is a strong correspondence between the properties of physical one-way hash functions and their algorithmic counterparts. In particular, it is demonstrated that they are collision-resistant and that they exhibit the avalanche effect, i.e., a small change in the physical system causes a large change in the hash value. 
An inexpensive prototype authentication system based on physical one-way hash functions is designed, implemented, and analyzed. The prototype uses a disordered three-dimensional microstructure as the underlying physical system and coherent radiation as the probe. It is shown that the output of the interaction between the physical system and the probe can be used to robustly derive a unique tamper-resistant identifier at a very low cost per bit. The explicit use of three-dimensional structures marks a departure from prior efforts. Two protocols, including a one-time pad protocol, that illustrate the utility of these hash functions are presented and potential attacks on the authentication system are considered. 
Finally, the concept of fabrication complexity is introduced as a way of quantifying the difficulty of materially cloning physical systems with arbitrary internal states. Fabrication complexity is discussed in the context of an idealized machine—a Universal Turing Machine augmented with a fabrication head—which transforms algorithmically minimal descriptions of physical systems into the systems themselves. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

/pdf/physical-one-way-functions-3b8omsfwkl.pdf

Physical one-way functions

Photonic bandgap crystals can reflect light for any direction of propagation in specific wavelength ranges1,2,3. This property, which can be used to confine, manipulate and guide photons, should allow the creation of all-optical integrated circuits. To achieve this goal, conventional semiconductor nanofabrication techniques have been adapted to make photonic crystals4,5,6,7,8,9. A potentially simpler and cheaper approach for creating three-dimensional periodic structures is the natural assembly of colloidal microspheres10,11,12,13,14,15. However, this approach yields irregular, polycrystalline photonic crystals that are difficult to incorporate into a device. More importantly, it leads to many structural defects that can destroy the photonic bandgap16,17. Here we show that by assembling a thin layer of colloidal spheres on a silicon substrate, we can obtain planar, single-crystalline silicon photonic crystals that have defect densities sufficiently low that the bandgap survives. As expected from theory, we observe unity reflectance in two crystalline directions of our photonic crystals around a wavelength of 1.3 micrometres. We also show that additional fabrication steps, intentional doping and patterning, can be performed, so demonstrating the potential for specific device applications.

On-chip natural assembly of silicon photonic bandgap crystals

The ability to pattern materials in three dimensions is critical for several technological applications, including composites, microfluidics, photonics, and tissue engineering. Direct-write assembly allows one to design and rapidly fabricate materials in complex 3D shapes without the need for expensive tooling, dies, or lithographic masks. Here, recent advances in direct ink writing are reviewed with an emphasis on the push towards finer feature sizes. Opportunities and challenges associated with direct ink writing are also highlighted.

/pdf/direct-ink-writing-of-3d-functional-materials-3agrqrwm1s.pdf

Direct ink writing of 3D functional materials

The past decade has witnessed intensive research efforts related to the design and fabrication of photonic crystals1,2. These periodically structured dielectric materials can represent the optical analogue of semiconductor crystals, and provide a novel platform for the realization of integrated photonics. Despite intensive efforts, inexpensive fabrication techniques for large-scale three-dimensional photonic crystals of high enough quality, with photonic bandgaps at near-infrared frequencies, and built-in functional elements for telecommunication applications, have been elusive. Direct laser writing by multiphoton polymerization3 of a photoresist has emerged as a technique for the rapid, cheap and flexible fabrication of nanostructures for photonics. In 1999, so-called layer-by-layer4 or woodpile photonic crystals were fabricated with a fundamental stop band at 3.9 μm wavelength5. In 2002, a corresponding 1.9 μm was achieved6, but the important face-centred-cubic (f.c.c.) symmetry was abandoned. Importantly, fundamental stop bands or photonic bandgaps at telecommunication wavelengths have not been demonstrated. In this letter, we report the fabrication—through direct laser writing—and detailed characterization of high-quality large-scale f.c.c. layer-by-layer structures, with fundamental stop bands ranging from 1.3 to 1.7 μm.

/pdf/direct-laser-writing-of-three-dimensional-photonic-crystal-4vf97ivkpd.pdf

Direct laser writing of three-dimensional photonic-crystal templates for telecommunications

The ability to confine and control light in three dimensions would have important implications for quantum optics and quantum-optical devices: the modification of black-body radiation, the localization of light to a fraction of a cubic wavelength, and thus the realization of single-mode light-emitting diodes, are but a few examples1,2,3. Photonic crystals — the optical analogues of electronic crystal — provide a means for achieving these goals. Combinations of metallic and dielectric materials can be used to obtain the required three-dimensional periodic variations in dielectric constant, but dissipation due to free carrier absorption will limit application of such structures at the technologically useful infrared wavelengths4. On the other hand, three-dimensional photonic crystals fabricated in low-loss gallium arsenide show only a weak ‘stop band’ (that is, range of frequencies at which propagation of light is forbidden) at the wavelengths of interest5. Here we report the construction of a three-dimensional infrared photonic crystal on a silicon wafer using relatively standard microelectronics fabrication technology. Our crystal shows a large stop band (10–14.5 μm), strong attenuation of light within this band (∼12 dB per unit cell) and a spectral response uniform to better than 1 per cent over the area of the 6-inch wafer.

A three-dimensional photonic crystal operating at infrared wavelengths

A method is disclosed for micromachining recessed layers (e.g. sacrificial layers) of a microelectromechanical system (MEMS) device formed in a cavity etched into a semiconductor substrate. The method uses chemical-mechanical polishing (CMP) with a resilient polishing pad to locally planarize one or more of the recessed layers within the substrate cavity. Such local planarization using the method of the present invention is advantageous for improving the patterning of subsequently deposited layers, for eliminating mechanical interferences between functional elements (e.g. linkages) of the MEMS device, and for eliminating the formation of stringers. After the local planarization of one or more of the recessed layers, another CMP step can be provided for globally planarizing the semiconductor substrate to form a recessed MEMS device which can be integrated with electronic circuitry (e.g. CMOS, BiCMOS or bipolar circuitry) formed on the surface of the substrate.

Chemical-mechanical polishing of recessed microelectromechanical devices

CMP planarization of oxide results in e xcellent long-range uniformity compared to other planarization techniques but remains hampered by systematic pattern sensiti vities. In the recent literature, se veral semi-empirical or physically-based models have been proposed to explain ILD thickness pattern sensiti vities in CMP, but all of these models either f ail to predict k ey empirical results, are not described fully , or do not present tractable closed form models. In this paper , we de velop and derive a closed form model for ILD thickness variation and v erify this model on datasets obtained o ver different polishing tools, consumable sets, and process conditions, and as a function of polishing time.

A closed-form analytic model for ild thickness variation in cmp processes

A method is disclosed for fabricating a two- or three-dimensional photonic bandgap structure (also termed a photonic crystal, photonic lattice, or photonic dielectric structure). The method uses microelectronic integrated circuit (IC) processes to fabricate the photonic bandgap structure directly upon a silicon substrate. One or more layers of arrayed elements used to form the structure are deposited and patterned, with chemical-mechanical polishing being used to planarize each layer for uniformity and a precise vertical tolerancing of the layer. The use of chemical-mechanical planarization allows the photonic bandgap structure to be formed over a large area with a layer uniformity of about two-percent. Air-gap photonic bandgap structures can also be formed by removing a spacer material separating the arrayed elements by selective etching. The method is useful for fabricating photonic bandgap structures including Fabry-Perot resonators and optical filters for use at wavelengths in the range of about 0.2-20 μm.

Use of chemical-mechanical polishing for fabricating photonic bandgap structures

Optical interferometry was used to quantitatively characterize the surface of chemical-mechanical polishing (CMP) pads used to polish oxide films. We discuss the optical interferometry technique, including a description of the parameters necessary to compare pad samples. Flat, mesa-like structures formed on the pad during the first 5 min polish when conditioning was not used. The data from the optical interferometer indicated that the surface topography did not change with subsequent polishing, even though the thermal oxide removal rate continued to decrease. We found conditioning roughened the pad surface. Rougher pad surfaces removed more oxide during a single 5 min polish than comparatively smooth pad surfaces. Data indicates that conditioning increases and stabilizes pad surface roughness.

Dale L. Hetherington

Papers

A three-dimensional photonic crystal operating at infrared wavelengths

Chemical-mechanical polishing of recessed microelectromechanical devices

A closed-form analytic model for ild thickness variation in cmp processes

Use of chemical-mechanical polishing for fabricating photonic bandgap structures

Optical interferometry for surface measurements of CMP pads