Large Uniform Arrays Research Articles

Diffractive lens design for optimized focusing.

We utilized nonlinear optimization to design phase-only diffractive lenses that focus light to a spot, whose width is smaller than that dictated by the far-field diffraction limit. Although scalar-diffraction theory was utilized for the design, careful comparisons against rigorous finite-difference time-domain simulations confirm the superfocusing effect. We were able to design a lens with a focal spot size that is 25% smaller than that formed by a conventional lens of the same numerical aperture. An optimization strategy that allows one to design such lenses is clearly explained. Furthermore, we performed careful simulations to elucidate the effects of fabrication errors and defocus on the performance of such optimized lenses. Since these lenses are thin, binary, and planar, large uniform arrays could be readily fabricated enabling important applications in microscopy and lithography.

Parylene peel-off arrays to probe the role of cell–cell interactions in tumour angiogenesis

Microenvironmental conditions impact tumour angiogenesis, but the role of cell-cell interactions in modulating the angiogenic capability of tumour cells is not well understood. We have microfabricated a peel-off cell-culture array (PeelArray) chip to spatiotemporally control interactions between tumour cells in a large array format and to analyse angiogenic factor secretion in response to these conditions. The PeelArray chip consists of a polyethylene glycol (PEG) treated glass coverslip coated with a parylene-C template that can be easily peeled off to selectively micropattern biomolecules and cells. We have designed the PeelArray chip to reproducibly deposit large uniform arrays of isolated single cells or isolated cell clusters on fibronectin features of defined surface areas. We have utilised this microfabricated culture system to study the secretion of angiogenic factors by tumour cells, in the presence or absence of cell-cell contact as controlled by micropatterning. Our results indicate that cell-cell interactions play a synergistic role in regulating the expression of angiogenic factors (i.e., vascular endothelial growth factor [VEGF] and interleukin-8 [IL-8]) in various cancer cell lines, independent of other more complex microenvironmental cues (e.g. hypoxia). Our PeelArray chip is a simple and adaptable micropatterning method that enables quantitative profiling of protein secretions and hence, a better understanding of the mechanisms by which cell-cell interactions regulate tumour cell behaviour and angiogenesis.

The Combined Effect of Pressure and Autofrettage on Uniform Arrays of Three-Dimensional Unequal-Depth Cracks in Gun Barrels

Due to the repeated firing of the gun, large uniform arrays of unequal-depth fatigue cracks develop from the inner surface of the barrel. The combined effect of pressure and autofrettage on the mode I stress intensity factor (SIF) distribution along the fronts of these three-dimensional, semi-elliptical, surface cracks is herein studied. Crack depth inequality is modeled using the “two-crack depth level model” previously proposed. The analysis is performed via the finite element (FE) method employing singular elements along the crack front. The autofrettage residual stress field is simulated using an equivalent thermal load. The distribution of the combined stress intensity factor due to pressurization and full autofrettage KIN=KIP+KIA, for numerous array configurations is evaluated for a barrel of outer to inner radii ratio of Ro/Ri=2. These configurations bear n=n1+n2=8 to 128 cracks, a wide range of crack depth to wall thickness ratios, a1/t=0.01 to 0.40, and various crack depth to half-length ratios (ellipticities) a1/c1=0.30 to 1.50. The results for KIN distributions clearly indicate that the level of effect of crack depth inequality depends on all three parameters: crack number in the array, crack depth and crack ellipticity. Furthermore, the results indicate that adjacent unequal-depth cracks influence each other only within a limited range of their depths, i.e., the “interaction range”. The range of influence between adjacent cracks on the maximal SIF KNmax depends on crack ellipticity and is found to be inversely proportional to the crack density of the array. The results re-emphasize the favorable effect the residual stress field has on the fracture endurance and the fatigue life of gun barrels bearing uniform arrays of three-dimensional unequal-depth cracks at their inner surface. This favorable effect is governed by the ratio of the gun’s material yield stress to its internal pressure—ψ=σ0/p. The higher ψ is, the more effective autofrettage becomes.

A homogenization model for laser beam-induced current imaging and detection of non-uniformities in semiconductor arrays

We present an approximate model for laser beam-induced current (LBIC) imaging of arrays of semiconductor devices based on homogenization. LBIC is a non-destructive technique useful for the characterization and quality control of semiconductor focal plane arrays, a key component in modern imaging systems. The model provides not only an efficient alternative for LBIC image simulation of large uniform arrays, but also an effective method for detection of non-uniformities among arrays. Numerical examples are presented to illustrate the effectiveness of this method in detecting array non-uniformities due to variations in dislocation/size or doping level among p–n junction diodes.

The Effect of Autofrettage on Uniform Arrays of Three-Dimensional Unequal-Depth Cracks in a Thick-Walled Cylindrical Vessel

The distribution of the mode I stress intensity factor (SIF), resulting from autofrettage, along the fronts of radial, semi-elliptical surface cracks pertaining to large uniform arrays of unequal-depth cracks emanating at the bore of an overstrained thick-walled cylinder is studied. The three-dimensional analysis is based on the “two-crack depth level model” previously proposed and is performed via the finite element method employing singular elements along the crack front. The autofrettage residual stress field is simulated using an equivalent thermal load. The distribution of KIA, the stress intensity factor due to autofrettage, for numerous uneven array configurations bearing n=n1+n2=8-128 cracks, a wide range of crack depth-to-wall thickness ratios, a1∕t=0.01-0.4, and various crack ellipticities, a1∕c1=0.3-1.5, are evaluated for a cylinder of radii ratio Ro∕Ri=2. The results clearly indicate that unevenness, as reflected in KIA distribution, depends on all three parameters (i.e., the number of cracks in the array, cracks’ depth, and cracks’ ellipticity). The “interaction range” for the different combinations of crack arrays and crack depths is then evaluated. The range of influence between adjacent cracks on the maximal SIF, KAmax, is found to be dependent on the density of the array, as reflected in the intercrack aspect ratio, as well as on the cracks’ ellipticity.

Analysis of Uniform Arrays of Three-Dimensional Unequal-Depth Cracks in a Thick-Walled Cylindrical Pressure Vessel

The effect of crack depth unevenness on the mode I stress intensity factor (SIF) distributions along the fronts of semi-elliptical surface cracks is studied. These three-dimensional radial cracks pertain to large uniform arrays of unequal-depth cracks emanating from the bore of a pressurized thick-walled cylinder. The analysis is based on the “two crack depth level model,” previously proposed, and is performed via the finite element (FE) method employing singular elements along the crack front. The distribution of KIP-the stress intensity factor due to pressurization, for numerous uneven array configurations bearing n=n1+n2=8 to 128 cracks, a wide range of crack depth to wall thickness ratios, a1/t=0.01 to 0.4, and various crack ellipticities, a1/c1=0.3 to 1.5, are evaluated for a cylinder of radii ratio Ro/Ri=2. To increase the accuracy of the evaluated SIFs an existing improved version of the displacement extrapolation method is used. The results clearly indicate that unevenness, as reflected in KIP distributions, depends on both the number of cracks in the array as well as on the cracks’ depths and ellipticities. The “interaction range” for the various configurations of uneven crack arrays is evaluated. The range of influence between adjacent cracks on the maximal SIF, KPmax, is found to be dependent on the density of the array, as reflected in the inter-crack aspect-ratio, as well as on the cracks’ elipticity.

Diamond emitter arrays with uniform self-aligned gate built from silicon-on-insulator wafer

A self-aligned gate fabrication technique utilizing silicon-on-insulator technology is developed for the fabrication of large uniform arrays of diamond field emitters with self-aligned gate and sharp tip cathode. A uniform array with millions of gated diamond microemitters was reproducibly achieved. The diamond field emitter array, tested in triode configuration with an external anode, has a low turn-on gate voltage of 26 V. A high emission current of 1 μA per tip was obtained at a gate voltage of approximately 60 V and an anode voltage of 200 V. The ability to modulate emission current at low gate voltage allows more practical usage of a diamond field emitter in vacuum microelectronics.

Methods for fabricating arrays of holes using interference lithography

Optical interference lithography provides a robust patterning technology capable of achieving deep submicron resolution over extremely large field sizes (∼1 m2). Here, we compare two approaches for fabricating arrays of holes using interferometric techniques. We first show that, by applying an image reversal process to standard two-beam interference lithography, arrays of high aspect ratio holes (2:1) can be generated. This process scales well to submicron periods and allows holes as small as 0.1 μm to be patterned. Next, we present an analysis of the multiple-beam approach for patterning holes. This technique offers a potentially higher throughput process compared to other techniques. We demonstrate that, while the formation of higher contrast intensity profiles is possible by interfering four or more beams, the shape and modulation depth of such profiles are sensitive to relative phase variations. This dependence complicates the application of multiple-beam techniques for patterning large uniform arrays of resist structures.

The Effect of Crack Length Unevenness on Stress Intensity Factors Due to Autofrettage in Thick-Walled Cylinders

The effect of crack length unevenness on the mode I stress intensity factors (SIFs) for large uniform arrays of radial cracks of unequal depth in fully or partially autofrettaged thick-walled cylinders is investigated. The analysis is based on the previously proposed “two-crack-length level model.” Values for KIA—the SIF due to the compressive residual stress field—for various crack arrays bearing n1 = n2 = 2−512 cracks, a wide range of nondimensional crack lengths l1/a=0.01−0.1, and numerous levels of autofrettage ε = 30−100 percent are evaluated by the finite element method for a cylinder of radii ratio of b/a = 2. The interaction range for different combinations of crack arrays and crack length is then determined. The obtained results show that the unevenness in the SIFs depends on all three parameters, i.e., the number of cracks in the array, the cracks’ lengths, and the level of autofrettage, while the interaction range between adjacent cracks is determined only by the relative length of the cracks and the density of the array.

Uniform Arrays of Unequal-Depth Cracks in Thick-Walled Cylindrical Pressure Vessels—Part I: Stress Intensity Factors Evaluation

The influence of the unevenness of crack lengths on the mode I stress intensity factors (SIF) for large uniform arrays of radial cracks of unequal depth in thick-walled pressurized cylinders is investigated applying the previously proposed “two-crack-length level model.” Using the finite element method, SIFs are evaluated for numerous configurations of crack arrays bearing a wide range of crack lengths. The interaction range for various combinations of crack arrays and crack lengths is then determined. The numerical results anticipate that any statistical unevenness of the initial crack lengths, prevailing in the pressurized cylinder, will be amplified during the process of fatigue crack growth. Thus, while the fatigue life of the vessel is determined by a large number of cracks, its final failure, which is governed by a small number of the largest cracks, is likely to be caused by one major crack, as is usually the case. This sequence of events results from the particular nature of the inter-crack stress field, which is analyzed and discussed in detail in Part II of the paper.