<%BANNER%>

Fabrication and Testing of Dual-Wavelength Photon Sieves


PAGE 1

FABRICATION AND TESTING OF DUAL-WAVELENGTH PHOTON SIEVES By HSIU-HSIN CHUNG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

PAGE 2

Copyright 2005 by Hsiu-hsin Chung

PAGE 3

This document is dedicated to my parents and my loving husband.

PAGE 4

ACKNOWLEDGMENTS First of all I would like to thank my advisor, Dr. Paul Holloway, for his guidance, encouragement, and perseverance in seeing th is project to its completion. I would also like to thank Dr. Rolf Hummel, Dr. Wo lfgang Sigmund, Dr. Anthony Brenann and Dr. David Tanner for being my committee and for their valuable advice. I would like to thank Dr. Mark Davison for his technical guidance and Dr. O. Shenderova for simulation input. I would lik e to acknowledge the Major Analytical and Instrumentation Center (MAIC) staff for their training on in struments. A special thank you is due to Kwangje Woo, for his help in photon sieve property characterizations. I would like to thank all th e members of Dr. Holloway’s group for their help and kindness. Many thanks go to Narada Bradman for his great help, inspiring discussions, and mental support. All the work in process development presented in my dissertation is a result of the collaboration with Narada. I would also like to thank Philip Chung for his warm friendship and editorial comments during th e writing of this dissertation. Of course I could not forget Ludie, who always cheer s me up at the awful moments of my life during the past four years. I would like to thank my wonderful parent s, who love and support me without any condition my entire life. Finally I woul d like to thank my husband, Yusuf, for his tremendous support, encouragement, and ki ndness. Without him being on my side, I would not have made it to this point in my life.

PAGE 5

v TABLE OF CONTENTS page ACKNOWLEDGMENTS...................................................................................................4 LIST OF TABLES...........................................................................................................viii LIST OF FIGURES...........................................................................................................ix ABSTRACT.....................................................................................................................xi v CHAPTER 1 INTRODUCTION........................................................................................................1 2 LITERATURE REVIEW.............................................................................................3 2.1 Refraction vs. Diffraction.......................................................................................3 2.2 Diffraction Theories................................................................................................5 2.2.1 Huygens Principle, Huygens-Fresnel Principle, and Obliquity Factor........5 2.2.2 Fraunhofer Diffraction..................................................................................8 2.2.2.1 Single slit and double slit...................................................................8 2.2.2.2 Airy pattern – Fraunhofer diffr action from a circular aperture..........9 2.2.3 Fresnel Diffraction......................................................................................11 2.3 Frenel Zone Plate (FZP).......................................................................................14 2.3.1 Resolution of Image System and Zone Plates............................................16 2.3.2 Secondary Maxima for Fresnel Zone Plates...............................................17 2.3.3 Amplitude versus Phase Zone Plate...........................................................18 2.4 Photon Sieve.........................................................................................................21 2.4.1 Advantages of Photon Sieves over Fresnel Zone Plates............................23 2.4.1.1 Suppress higher diffraction order and improve focus......................23 2.4.1.2 Overcoming the limitation of the resolution of FZP........................25 2.4.2 Disadvantage of Photon Sieves over Fresnel Zone Plates..........................27 2.4.3 Apodization................................................................................................28 2.4.4 Applications of Photon Sieves....................................................................30 2.5 Chromatic Aberration...........................................................................................31 2.6 Justification of Research.......................................................................................32 3 PHOTON SIEVE FABRICATION............................................................................33 3.1 Introduction...........................................................................................................33

PAGE 6

vi 3.2 Process Development............................................................................................34 3.2.1 Substrate Preparation..................................................................................36 3.2.2 Film Deposition..........................................................................................37 3.2.2.1 E-beam evaporator: system and operation.......................................37 3.2.2.2 Deposition controller........................................................................42 3.2.3 Resist Coating.............................................................................................43 3.2.3.1 Electron-beam resists.......................................................................43 3.2.3.2 Spin-coating.....................................................................................44 3.2.4 Pattern Formation.......................................................................................48 3.2.5 Reactive Ion Etch (RIE).............................................................................50 3.2.6 Various Process Methods: Procedures and Results....................................51 3.2.6.1 Reversed image etching...................................................................51 3.2.6.2 Lift-off..............................................................................................58 3.2.6.3 Direct wet etching............................................................................61 3.2.6.4 Direct dry etching.............................................................................63 3.3 Discussions...........................................................................................................65 4 PHOTON SIEVE PROPERTIES...............................................................................69 4.1 Introduction...........................................................................................................69 4.2 Simulation of Photon Sieves Properties...............................................................70 4.2.1 Focal Length and Lens Diameter...............................................................70 4.2.2 K-factor.......................................................................................................71 4.2.3 Apodized vs. Unapodized Photon Sieves...................................................71 4.3 Photon Sieve Pattern Generation..........................................................................74 4.3.1 Single-wavelength Photon Sieve................................................................77 4.3.2 Dual-wavelength Photon Sieve..................................................................78 4.4 Characterizations..................................................................................................80 4.4.1 Perkin-Elmer 16U Grating Spectrometer...................................................80 4.4.2 Charge-Coupled Device (CCD) Camera....................................................83 4.4.3 Focal Length Characterization...................................................................86 4.4.4 Full Width Half Maximum (FWHM) Characterization.............................88 4.5 Results...................................................................................................................9 1 4.5.1 Focal Length Characterization...................................................................91 4.5.2 Full Width Half Maximum (FWHM) and Peak Intensity of PSFs.............93 4.6 Discussions.........................................................................................................102 4.7 Conclusions.........................................................................................................111 5 CONCLUSIONS......................................................................................................114 5.1 Photon Sieve Fabrication....................................................................................114 5.2 Photon Sieve (PS) Properties..............................................................................115 6 FUTURE WORKS...................................................................................................118

PAGE 7

vii LIST OF REFERENCES.................................................................................................120 BIOGRAPHICAL SKETCH...........................................................................................127

PAGE 8

viii LIST OF TABLES Table page 2-1 Step profiles and their calc ulated diffraction efficiency..........................................20 2-2 Equations of the apodization functions shown in Figure 2-25.................................29 3-1 Acronyms and abbreviations shown in Figure 3-2...................................................36 3-2 Densities and Z-ratios of mate rials used in the experiment.....................................43 3-3 Experiment parameters of plas ma-etching recipes for RIE process.........................51 4-1 Text file of the 6-sect or dual-wavelength photon sieve...........................................76 4-2 Number of holes and open hole area fo r the 4 single-wavelength photon sieves and 6-sector..............................................................................................................77 4-3 FWHM and peak intensity at Xand Yaxes for each PSF measured with each of the three light spectra – 500 nm 600 nm, and white lights......................................99

PAGE 9

ix LIST OF FIGURES Figure page 2-1 Schematic drawing of Snell’s law of refraction.........................................................4 2-2 Double-slit diffraction of light reflected from a doubl e wave pattern in water.........4 2-3 Illustration of Huygens’ pr inciple for spherical waves..............................................5 2-4 Diffraction at a small aperture....................................................................................6 2-5 The obliquity factor K( )...........................................................................................7 2-6 Fraunhofer diffraction through (a) single slit (b) double slit apertures......................8 2-7 Intensity pattern for diffraction from the double slit as shown in Figure 2-6(b)........9 2-8 An Airy pattern recorded on a slid e film and then digital-processed.......................10 2-9 Bessel function of the zero th, first, second, etc. kind...............................................11 2-10 Fresnel diffracti on by a single slit............................................................................12 2-11 Comparison between Fresnel and Fra unhofer diffraction through a single slit.......12 2-12 Cornu spiral.............................................................................................................. 14 2-13 Fresnel half period zone for plane wavefront...........................................................14 2-14 Dark center and bright ce nter Fresnel zone plates...................................................15 2-15 The Rayleigh and Sparrow criteria fo r resolving the overlapping point images from two distant point sources.................................................................................16 2-16 Secondary maxima from a zone plate......................................................................18 2-17 Kinoform Fresnel zone plates..................................................................................19 2-18 Three fabrication steps result an eight-phase-level Fresnel lens..............................20 2-19 Quaternary Fresnel zone plate design and SEM image of a fabricated PZP............21

PAGE 10

x 2-20 Schematic drawing of a photon sieve.......................................................................21 2-21 Diagram showing point-to-poin t imaging with a photon sieve................................22 2-22 A photon sieve and a FZP together with experimental and calculated results.........24 2-23 The relation between the contribution of focal amplitude and the ratio of the pinhole diameter over unde rlying zone width ( d / w ratio)........................................26 2-24 Some commonly used apodizati on functions in linear scale....................................29 2-25 Maskless, zone-plate-array lithography...................................................................30 2-26 Chromatic aberration of a refractive lens.................................................................31 3-1 Schematic drawing of a cross-sectioned photon sieve.............................................33 3-2 Flowchart of various processing methods................................................................35 3-3 Three-state cascade DI water rinse bath with N2 bubblers on the wet bench..........36 3-4 Schematic drawing of e-beam evaporator system....................................................37 3-5 Photograph of electron-beam de position chamber and control rack........................38 3-6 Detailed structures inside be ll jar of an e-beam evaporator.....................................38 3-7 Silver spitting...........................................................................................................4 1 3-8 Standard deposition monitor (a) an d quartz crystal oscillator (b)............................43 3-9 P6700 series spin coater...........................................................................................45 3-10 Relationship between the spin speed and thickness.................................................46 3-11 Optical photographs of spin coating defects............................................................47 3-12 Photograph of the PlasmaTherm SLR770................................................................50 3-13 Optical micrograph of an apodized photon sieve manufact ured by reversed image etching method..............................................................................................52 3-14 Process flow of the “rev ersed image etching” method.............................................53 3-15 SEM micrograph of residual dots within th e pinholes after plasma etching of Ag and Ni.......................................................................................................................54 3-16 Schematic drawing of interaction volume for various electron-specimen interactions...............................................................................................................55

PAGE 11

xi 3-17 Residual dots (a) SE image (b) BSE image..............................................................56 3-18 Indication of investigated area for Auger spectrum.................................................57 3-19 Auger spectra from a gene ral area with residual dots..............................................57 3-20 Argon sputtering depth profile fr om the area with residual dots.............................58 3-21 Process flow of the “lift-off” method.......................................................................59 3-22 Optical micrograph of a photon siev e manufactured by the lift-off method............60 3-23 Schematic drawing of sidewall residue....................................................................61 3-24 Process flow of the “direct wet etching” method.....................................................62 3-25 Optical micrographs of the photon siev e manufactured by direct wet etching........63 3-26 SEM micrographs of the veil-l ike matter at the edge of holes.................................63 3-27 A photon sieves with clean edge manuf actured by direct dry etching method........64 3-28 Process flow of the “d irect dry etching” method.....................................................65 4-1 Simulation result of the optimum K value...............................................................71 4-2 Simulated one-dimensional PSFs for apodized and unapodized photon sieves.......72 4-3 A simulation of the PSF (a) peak intens ity and (b) FWHM as a function of a and b.............................................................................................................................. ..73 4-4 The DesignCAD pattern of the 6-se ctor dual-wavelength photon sieve..................75 4-5 Schematic drawing of singlewavelength photon si eve patterns..............................77 4-6 Optical micrograph for the 605 single wavelength photon sieve.............................78 4-7 Schematic drawing of dual-wa velength photon sieve patterns................................79 4-8 Optical micrographs of dual-wavelength photon sieves (a) 6-s ector (b) 5in6-70%.80 4-9 Schematic drawing of the modified Perkin-Elmer 16U grating spectrometer.........81 4-10 The measurement result of intensity versus wavelength for the tungsten lamp used in the optical bench..........................................................................................82 4-11 Gratings (a) transmission amplitude grating (b) blazed reflection grating..............82 4-12 An illustration of the CCD read-out mechanism......................................................84

PAGE 12

xii 4-13 Saturated PSF...........................................................................................................85 4-14 A sample of PSF measuremen t taken by WinCamD CCD camera..........................86 4-15 Schematic drawing of the relationship between object distance (S), image distance (S’), and focal length (F)............................................................................87 4-16 A sample PSF (lens 610) to show the definition of FWHM....................................88 4-17 PSF of the refractive lens.........................................................................................90 4-18 Peak intensity of PSFs from 510 with 500 nm light obtained at various image distances...................................................................................................................91 4-19 Focal length characterization for si ngle-wavelength photon sieves under 500 nm and 600 nm lights.....................................................................................................92 4-20 PSFs at focal point....................................................................................................93 4-21 Top view of PSF for photon sieves under monochromatic 600 nm light................94 4-22 Top view of PSF for photon sieves under polychromatic white light......................95 4-23 PSFs under 600 nm light for all 13 photon sieves....................................................96 4-24 PSFs under 500 nm light for all 13 photon sieves....................................................97 4-25 PSFs under white light for all 13 photon sieves.......................................................97 4-26 FWHM and maximum intensity fo r photon sieves under 600 nm light.................100 4-27 FWHM and maximum intensity fo r photon sieves under 500 nm light.................100 4-28 FWHM and maximum intensity fo r photon sieves under white light....................101 4-29 Shape of focal spots................................................................................................102 4-30 Characteristic light rays of 600 nm light passed through (a) 6in5-50% and (b) 6in5-75%................................................................................................................104 4-31 Characteristic light rays of 600 nm light passed through PS 5in6-50%.................105 4-32 Characteristic light rays of polychrom atic white light which have passed through a PS lens of (a) 610 and (b) 510.............................................................................106 4-33 Realistic sketch of the image forma tion for a dual-wavelength photon sieve with white light illumination..........................................................................................107

PAGE 13

xiii 4-34 Comparison of FWHMs and intensities between 6in5-50% (red center PS) and 5in6-50% (blue center PS) under 50 0 nm and 600 nm light sources.....................109 4-35 The performance of photon sieves when switching the light sources from 500 nm to 600 nm..........................................................................................................110

PAGE 14

xiv Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy FABRICATION AND TESTING OF DUAL-WAVELENGTH PHOTON SIEVES By Hsiu-hsin Chung May 2006 Chair: Paul H. Holloway Major Department: Materials Science and Engineering A photon sieve (PS) is a diffr active lens composed of pinholes distributed in a similar way to the Fresnel zones in a Fresnel zone plate lens. In this research, multiple dual-wavelength PSs are designed, fabricated an d tested to determine the advantages and disadvantages of combining the diffractive elements into a single lens from two photon sieves which were designed for different wavelengths. Both singleand dual-wavelength PSs we re fabricated by first electron beam depositing a 3 nm adhesion layer of nickel, followed by a 100 nm layer of silver on a glass substrate. In the optimi zed procedure, the metallized substrate was then coated both with PMMA and ZEP7000, a positive electron -beam lithography resist with excellent resistance to dry-etching. After patterning of the underlying polymer and metal films, the ZEP7000 and polymer were removed to result in the pattern of pinholes in the metal layer on the substrate that constituted the photon sieve. Multiple singleand dual-wavelength PS designs were tested using a modified Perkin-Elmer 16U grating spectrometer wi th a WinCamD charge-coupled device (CCD)

PAGE 15

xv camera. The photon sieves were apodized and we re designed to have a focal length of 50 mm, lens diameter of 3 mm, and a K-factor (ratio of hol e spacing to diameter) of 1.2. The distributions of the two groups of pinholes for dual wavelength PSs were categorized as concentric and sectional designs. Th e point spread function (PSF) of each photon sieve was obtained using the CCD camera. The peak intensity and the full width half maximum (FWHM) of each PSF were used to evaluate the focusing ability of each photon sieve. The measured focal lengths were in th e range between 50.9 to 51.7 mm, i.e., very close to the nominal focal length of 50 mm The FWHMs and peak intensities data demonstrated that the focusing ability of a dual-wavelength PS was degraded by about 10% and 50%, respectively, as compared to a single-wavelength PS using either polychromatic or monochromatic light. When switching between two monochromatic (500 or 600 nm) light sources, dual-wavele ngth PSs focused both wavelengths with limited performance, while the ability of a si ngle-wavelength PSs to focus at the designed focal length was severely degraded at a wa velengths 100 nm or more away from the designed value (500 or 600 nm). The fact th at PSs are highly disp ersive for non-designed wavelengths would make them good candidate s for a simple focusing filter lens for polychromatic light. Dual-wavelength PSs can be used for an imaging device that does not require the filtering of polychromatic light, but at the cost of intensity. The results from concentric dual-wavelength photon siev es also demonstrated that the pinholes located in the center zone of a photon sieve dominated the lens properties.

PAGE 16

1 CHAPTER 1 INTRODUCTION Refractive optics has long been used for imaging, especially for visible light. However, high absorption coefficients for refr active lens materials limit their use at short wavelengths. Diffractive optics, such as Fr esnel zone plates, provides an effective solution for focusing short wavelength electroma gnetic radiation, such as X-rays [1, 2]. In addition to the ability to focus the s hort wavelength light, diffractive optics also exhibits potential advantages over refractive op tics such as significantly less weight and less volume. A photon sieve is a diffractive lens composed of pinholes distributed in a similar way to the Fresnel zones. Recently, it has been shown that photon sieves can achieve a sharper focus by suppressing the secondary ma xima and higher order diffraction effects [3], as compared to a Fresnel zone plate. However, the lens properties of diffractive optics are wavelength-depende nt. If a photon with a wavelength different from the designated value passes through a diffractive lens, chromatic aberration will be observed. Researchers [4-6] have discussed multiple solutions to correct this chromatic aberration. Since all of the experimental corrections involve multiple lenses, no single diffraction lens is free of chromatic aberration. The goal for this project is to study the pr operties of a photon sieve that is designed to focus two wavelengths simultaneously. In this research, multiple dual-wavelength photon sieves are designed, fabricated and tested to determine the advantages and disadvantages of combining the diffractive elements from two photon sieves (designed

PAGE 17

2 for different wavelengths) into a single lens. A dual-wavelength photon sieve would offer significant advantages in many applicatio ns. Considering the small size and light weight, the multi-wavelength photon sieve woul d be ideal for unmanned aerial vehicles (UAVs), smart missiles, and construction of a fly’s eye. A background and literature review of the diffraction theory of light and a review of photon sieve and Fresnel zone plate diffractiv e lenses is presented in Chapter 2. In Chapter 3, the process development and four different process methods to fabricate photon sieves are outlined. Some problems and issues encountered during the photon sieve fabrication are discussed in Chapter 3 as well. The optical bench set-up, photon sieves testing and the testing results are desc ribed in Chapter 4. Finally, the conclusions and future works are presented in Chapter 5 and Chapter 6, respectively.

PAGE 18

3 CHAPTER 2 LITERATURE REVIEW Due to strong absorption of high-energy radiation, refractive lenses have been replaced by diffractive lenses for focusing X-ra ys. The properties of diffractive lenses are wavelength dependent. There have been many efforts [4-6] to create achromatic diffractive lens systems. However, a true single achromatic diffractive lens has not yet been achieved, including the designs in this rese arch. The purpose of this research is to study the lens properties and to develop an understanding of the advantages and limitations of dual-wavelength photon sieves. Photon sieves, proposed by Kipp et al in 2001 [3], are a relatively new type of diffractive lens. Since a photon sieve is a co llection of pinholes distributed in Fresnel zone regions, there is an opportunity to al ter the pinhole distribution patterns and to combine two groups of pinholes that can be us ed to focus two different wavelengths. In this review of the literature, the diffractiv e lens properties already explored will be reviewed and related to photon si eves. This review of the lit erature covers the following topics: (a) diffraction theories (b) Fresnel zone plate, (c ) photon sieve, and (d) dualwavelength photon sieves. It is important to note that only the pertinent diffraction theories are discussed in this review, and the reader is encouraged to consult other bibliographic references in optics for more detailed studies [7-9]. 2.1 Refraction vs. Diffraction Refraction occurs when waves travel from a medium with a given refractive index into a medium with another index. The wave changes direction at the boundary between

PAGE 19

4 the two media. The “point of incidence” is the point where the light ray intersects the surface. The line constructed at this point wh ich is perpendicular to the surface is called the “surface normal.” The angle of incidence (1) and angle of refraction (2) are shown in Figure 2-1. According to Fermat’s principle – light travels with the shortest path – the laws of refraction can be de rived, such as Snell’s law ( n1 sin1 = n2 sin2) [7]. Figure 2-1. Schematic drawing of Snell’s law of refraction. However, diffraction is the bending and sp reading of waves when they meet an array of obstacles and then undergo interferen ce. The obstacles can be either opaque or transparent since the wavefront is changed in amplitude and/or phase when diffraction occurs. A very common example would be water waves causing diffraction of reflected light by a double-slit in a rippletank, as shown in Figure 2-2. Figure 2-2. Double-slit diffraction of light reflected from a d ouble wave pattern in water [10].

PAGE 20

5 2.2 Diffraction Theories To understand diffraction, it is first helpfu l to recall Huygens’ principle, which explains how wave propagates, and the Huygens-Fresnel prin ciple that explains why no back wave is formed during the wave propaga tion. After a brief introduction of how light propagates based on these principles, the diffraction phenomenon is then discussed. There are two types of diffraction: Fraunhofer and Fresnel. When the light source and the observation screen are far ap art and light is essentially parallel, the conditions are met for Fraunhofer diffraction, also known as far-fie ld diffraction. If the observation screen or light source is moved close to the apertu re (less than a few wavelengths), Fresnel diffraction occurs. 2.2.1 Huygens Principle, Huygens-Fresnel Principle, and Obliquity Factor In 1678, a Dutch physicist named Christian Huygens, presented the concept of wave propagation which is known as Huygens’ prin ciple [8]. This principle states that every point on a primary wavefr ont serves as the source of spherical secondary wavelets such that the primary wavefront at some late r time is the envelope of these wavelets [7, 11]. When a light wave propagates through free space at the speed of light, the light rays associated with this wavefront propagate in straight lines, as shown in Figure 2-3. Huygen’s principle provides the insight into the nature of wave propagation necessary to explain how wave theory can account for the laws of geometric optics. Figure 2-3. Illustration of Huygens’ pr inciple for spherical waves [11].

PAGE 21

6 However, Huygens’ principle does not indicate the direction of the wave propagation in time. Why does a spherical wa ve continue to expand outward from its source, but not re-converge inward back to the source? Augustin Jean Fresnel, a French physicist, resolved this problem in 1816 by slig htly modifying the Huygens’ principle [8]. The corresponding Huygens-Fresnel principle st ates that every unobstructed point of a wavefront serves as a source of spherical secondary wavelets, and the amplitude of the optical field at any point be yond the obstruction is the superp osition of all these wavelets [9]. This principle is illustrated in Figur e 2-4. Each small arrow shown in Figure 2-4 represents a phasor, which indicates the amplitude and phase of a wavelet. The amplitude observed at any point in the optical field, such as Po, P1, and P2, is the algebraic sum of the individual phasors. Each of the unobstructed poi nts (black dots within the single slit width AB in Figure 2-4) on th e incoming plane wave acts as a coherent secondary source. When the wavelength of th e source is larger th an the aperture, the coherent waves interfere constructively and result in the bright spots at Po, P1, P2, etc. The larger the wavelength, the wider the wave spread out. That means if a photon counter is placed at Po, it will see lots of light. When th e aperture is decreased in size or larger wavelength light is used, th e number of photons counted at P1 and P2 increases even as the counts at Po decreases. Figure 2-4. Diffraction at a sma ll aperture. The amplitude obs erved at any point in the optical field is the algebraic su m of the individual phasors [9].

PAGE 22

7 In 1883, Gustav Kirchhoff, a Russian th eoretical physicist [12], developed a rigorous theory based on the solution of the Kirchholff’s scalar diffe rential wave equation [9] and introduced the obliquity factor K ( ) as shown below: K ( ) = (1+ cos ) (2-1) where is the angle made with the normal to the primary wavefront vector k A schematic drawing of the secondary wavelets af fected by the obliquity factor is shown in Figure 2-5. At point P, the wave amplitude A becomes [8] A = K( )Ao (2-2) where Ao is the amplitude of the light source. K ( ) introduces an angular dependence for the vector k At = 0, the forward direction, the obliquity factor K (0) = 1. At = 90o, the amplitude falls off to of the original value. At = 180o, the backward direction, K ( ) = 0. This factor expresses theoretically that no back wave is formed during the wave propagation. Figure 2-5. The obliquity factor K( ), the gray area, makes the amplitude of the vector k vary as a function of the angle K( ) = 0 when = thus no wave travels backward during the wave propagation [9].

PAGE 23

8 2.2.2 Fraunhofer Diffraction 2.2.2.1 Single slit and double slit Fraunhofer diffraction was first propos ed by Joseph Fraunhofer in 1823 [9]. Consider a point source very far from a single slit aperture; thus the incident wavefront is planar. The slit width is d, and the observation screen is also far from the aperture with a distance D, shown in Figure 2-6(a) [13]. Figure 2-6. Fraunhofer diffrac tion through (a) single slit (b ) double slit apertures [13]. Imagine that three light rays pass through th e top, middle, and bo ttom of the slit in Figure 2-6 (a). If the paths of the top and middle rays differ by (wavelength), they will interfere destructively and cancel each ot her at point y. The middle and bottom rays will cancel each other because of the same condition. C onsequently, if the path difference between the top and bottom rays is an integral multiple of zero irradiance will be expected at point y of the observation plane. The equation for minima in Fraunhofer diffraction with a single slit can be written as [13] d sin = m m = 1, 2, 3……. (2-3) When is zero, the light wave passes through the slit without been diffracted and forms the maximum of the intensity peak which is referred to as zeroth-order maximum (see

PAGE 24

9 Figure 2-6(a)). This “undiffracted li ght” may cause the background noise and is discussed in Chapter 4. However, for a double slit aperture, a path length difference between the path lengths of the two slits produces constructive interference; thus maximum intensities will be observed as predicted by equation (2-3) (F igure 2-6(b)). Comb ining the single slit diffraction and double slit interf erence, the final pattern fo r Fraunhofer diffraction on a double slit aperture is shown in Figure 2-7. Figure 2-7. Intensity pattern fo r diffraction from the double slit as shown in Figure 2-6(b) [13]. 2.2.2.2 Airy pattern – Fraunhofer diffrac tion from a circular aperture When the slit aperture of Figure 2-6 is repl aced by a circular aperture in Fraunhofer diffraction as mentioned in last section, an Ai ry pattern, named after George B. Airy [9], will form as a result of the diffraction phenomenon. An Airy pattern, shown in Figure 28, consists of a circular spot, the Airy disk, surrounded by much fainter concentric circular rings. The Airy disk or the bright center spot is called “primary maximum” and the rest of surrounded rings are called “secondary maxima” [9].

PAGE 25

10 Figure 2-8. An Airy pattern reco rded on a slide film and then digital-processed. The grid lines are the result of digitization [14]. The intensity distribution, I(x ), of the Airy pattern is written as below [9]: I(x) = I(0) [ 2J1(x)/x ]2 (2-4) where I(0) is the intensity at the center of Airy disk, i.e., the intensity in the zeroth-order maximum, and J1(x) is the Bessel functi on of the first kind, show n in Figure 2-9. The x variable in J1(x) is written as [9] x = k dq /R (2-5) where k is the wave vector, d is the radius of the circular aperture, q is the radius of the Airy disk and R is the distance between the aperture and observation screen. The Bessel function attenuates slowly with os cillations as x increases. J1(0) = 0 and J1(x)/x approaches when x approaches 0 [9]. Since sin = q/R, the larger the diffraction angle ( ), i.e., the higher diffraction or der (m), the higher the q/R, thus the larger the x value. From equation (2-4), the larger x value results in a smaller I(x), i.e., the lower intensity. From equations (2-3) to (2-5), the diffrac tion intensity diminishes when the diffraction order is high.

PAGE 26

11 Figure 2-9. Bessel function of th e zeroth, first, second, etc. kind [15]. Only the Bessel function of the first kind (J1 (x), red so lid curve) is used to calculate the intensity of the Airy pattern. From Figures 2-8 and 2-9, the first dark ring corresponds to the first zero of the Bessel function, i.e., J1(x) = 0 when x = 3.83. The radius q of the first dark ring can be equated to the boundary of the Airy disk [9]: q = 1.22 R /2 d (2-6) where R is the distance between ap erture and observation screen, is wavelength, and d is the radius of the circular aperture. For a lens focused on the observation screen, R can be replaced with the focal length, f of the lens. The Airy pattern causes blur ring of images from a point source. For a refractive optical system with an aperture, if the blurri ng is larger than that produced by aberrations (spherical, chromatic, astigmatism, etc.) of the system, the imaging process is said to be diffraction-limited and the image is the best that can be obtained with that aperture. 2.2.3 Fresnel Diffraction Though the diffraction for the research of dual-wavelength photon sieves is catagorized as Fraunhofer (fa r-field) diffration, it is helpfu l to understand the difference between Fraunhofer and Fresnel diffractions and to distinguish the two diffractions.

PAGE 27

12 Fresnel diffraction is also called near-field diffraction. It occurs when either the source or the observation screen is close to the aperture (the distance is in the range of few wavelengths) and the wavefr ont is essentially spherical. A schematic drawing in Figure 2-10 indicates the Fresne l diffraction geometry for a single slit aperture. The appearance of the diffraction patte rn is similar to that from a Fraunhofer single slit except that the intensities at the minima are not zero. A comparison between Fresnel and Fraunhofer diffraction patterns is shown in Figure 2-11. Figure 2-10. Fresnel diffract ion by a single slit [8]. Figure 2-11. Comparison between Fresnel and Fraunhofer diffraction through a single slit. The minima in Fresnel diffraction pattern is not zero in contrast to minima in Fraunhofer diffraction [16].

PAGE 28

13 The intensity, I, of Fresnel diffraction at a single slit can be written as [8] I = [ ab / ( a + b )] [( cos 2 d )2 + [( sin 2 d )2] (2-7) where is the variable of a function related to the phase difference between rays, which can be written as [8] = h 2( a + b )/ ab (2-8) where is the wavelength, a and b (Figure 2-10) are the distances of the source to aperture and aperture to observation sc reen, respectively. If we assume [8] x = cos 2 d (2-9) y = sin 2 d (2-10) equation (2-7) can be rewritten as I = [ ab / ( a + b )] (x2 + y2) (2-11) where x and y are known as Fresnel’s integrals. When plotting x versus y, a spiral curve known as the Cornu spiral shown in Figure 212 can be obtained. The two eyes of the spirals located at (0.5, 0.5) and (-0.5, -0.5) represent image plane points at infinity. Depending on the Fresnel diffraction ge ometry, values of a, b, h, and will decide the value of At specific the corresponding x, y values can be found from the Cornu spiral and then the relative intensity of th e Fresnel diffraction pattern can be calculated. A dimensionless parameter, the Fresnel num ber (F), can be used to categorize the diffraction types. As men tioned in Figure 2-10, F = 4 h2/ b where h is half of the aperture width, is the wavelength, and b is the distance between observation plane and aperture. When F << 1, diffraction is of the Fraunhofer type; when F 1, the diffraction regime becomes Fresnel [17].

PAGE 29

14 Figure 2-12. Cornu spiral. The coordinates x and y are the Fresnel’s integrals [8]. 2.3 Frenel Zone Plate (FZP) Consider a light source incident upon a circ ular aperture from infinity; i.e., the incident waves are planar and not spherical. After passing through the aperture (Figure 2.13), the light will reach point Po at a distance b, from the aperture. This circular aperture can be divided into half-period zones, where each zone is a multiple of a half wavelength away from Po, as shown in Figure 2-13. Figure 2-13. Fresnel half period zone for plane wavefront. Each zone is a half wavelength away from Po [8]. Thus b + b + 2 ( ), and b + 3 ( ) represent the boundaries of the first, second, and third zone, respectively. The radius of the mth boundary (Rm) can be written as [9]

PAGE 30

15 Rm 2 = (b + m )2 – b2 (2-12) The area of each zone is approximately b However, the width of each zone ( w ) varies according to the radis of the zone. The intensity observed at Po is the sum of the contribution of the wavelets originating from each zone. Because each zone is away, the contribution from the adjacent zone is opposite in phase (i.e., a phase shift of ). The light diffraction from adjacent zones will th erefore cancel each other and the overall contribution at Po is null. By elimina ting the contribution from all odd or even zones, a dark or bright center Fresnel zone plate (F ZP) will be obtained, respectively (see Figure 2-14). The overall intensity at Po will be brighter as the number of zones is increased. Figure 2-14. Dark center and bright center Fresnel zone plates. The dark areas are opaque to the wavelength of the light [9]. Because the incident light is from infi nity, b is actually the focal length ( f )and Po is the focal point of this Fresnel le ns. The primary focal length, f is therefore [9]: f = b = Rm 2/m (2-13) It is apparent that the focal length depends strongly on the wavelength. For example, for a 500 nm designed FZP with a nominal focal length of 50 mm under 500 nm light, the focal length is shifted to 41.7 mm when the incident wavele ngth is changed to 600 nm. This focal length shifting is verified with the testing results presented in Chapter 4.

PAGE 31

16 2.3.1 Resolution of Image System and Zone Plates The resolution of a lens is the minimum distance between two objects that can be distinguished. Considering two equal-irradi ant and distant point sources passing through an aperture of an optical system, the Airy patterns formed from these two point sources are either overlapped or clearly resolve d. Depending on the degr ee of pattern overlap, two resolution limits, Rayleigh and Sparrow crite ria, can be applied, as shown in Figure 2-15. The Rayleigh criterion is applied when the center of one Airy disk falls on the first minimum of the Airy disk of another point image. When the distance between the two point sources further decreases, the central dip that appears in the Rayleigh criterion will finally disappear which is defined as the Sparrow criterion. The spatial resolution, m, based on the Rayleigh criterion is then written as [9] m = 1.22 f /D (2-14) where f is the focal length, is the wavelength of light, and D is the diameter of the aperture. Figure 2-15. The Rayleigh and Sparrow crite ria for resolving the overlapping point images from two distant poi nt sources. The gray ci rcles represent the Airy disks of the two point sources [9].

PAGE 32

17 However, for a FZP, the resolution is c ontrolled by the outermost zone width [3, 18, 29]. The optical resolution of a zone plate is given by [18] m = 1.22 rN/m (2-15) where N is the outermost zone index, rN is the outermost zone width and m is the diffraction order [18]. Due to the testing set-up in this research (described in section 4-4), the resolution of the photon sieves was not determined and is di scussed in Chapter 4. In this research, FWHM and intensity were used to characterize the measured point spread function (PSF) and the image quality instead of determ ining the resolution of the photon sieves. 2.3.2 Secondary Maxima for Fresnel Zone Plates As described above, an Airy disk is obs erved from Fraunhofer diffraction from a circular aperture. The intensity attenuates as predicted by the Besse l function of the first kind when light passes through a circular apertu re, where the transmission abruptly becomes zero at the edge of the aperture. For a Fresnel zone plate, the amplitude contribution of each ring is equal at the focus. When this contribution drops abruptly to zero beyond the outermost ring, an oscillation of light intensity occurs just as shown in the Airy pattern (Figure 2-8). Secondary ma xima is the collection of first, second, and higher order bright rings in th e Airy pattern resulting from diffractions from the many concentric circular zones of a FZP. The secondary maxima will cause blurring of the image. It also increases the level of b ackground noise and reduce the contrast of the image. The suppression of secondary maxi ma can be achieved by applying apodization technique which is discussed in sections 2-4-1-1 and 2-4-3. A schematic drawing of secondary maxima is shown in Figure 2-16.

PAGE 33

18 Figure 2-16. Secondary maxima from a zone pl ate. The vertical scale is a logarithm of intensity and the horizontal axis is the displacement from the focal point [20]. 2.3.3 Amplitude versus Phase Zone Plate The zone plate described above is called an amplitude zone plate. The light passing through all odd or even zones are blocked, which means half of the light is not transmitted. To increase transmission, Kirz et al [21] proposed a method to shift the phase of the light transmitted through the opa que regions of the FZP by using the proper thickness of a transparent material. This pa rticular design is calle d a phase zone plate (PZP). Researches [22-24] combined the c oncepts of a phase-shift zone plate and a kinoform grating [25, 26] to cr eate a kinoform zone plate wher e the original light with destructive phases were shifted by ( ) and resulted in a totally constructive Fresnel zone plate, as shown in Figure 2-17. The conve x kinoform zone plate is equivalent to the concave type, which is the most common type.

PAGE 34

19 Figure 2-17. Kinoform Fresnel zone plates. The convex Fresnel lens is equivalent to the concave lens in properties. They all shift the light phase by between the regions [22, 27]. Also in 1999, Fabrizio et al [20] uti lized the same approximation of Schelokov’s ideal continuous phase-shifting pr ofile (ideal kinoform) but m odified the materials of the zone plate to make it totally transmitting rather than reflecting. In order to approach the ideal kinoform profile, a stepwise function was created in the profile for each zone (see Figure 2-18, 19). The efficiency ( m of the mth diffraction order) of the Fresnel zone plate was shown to be equal to [18] m = A2/C2 (2-16) where A is the observed amplitude and C is the intensity of the incoming field. This equation can be furthe r expressed as [18] m = 2 [1-cos(2 m /L)](L/ m )2 (2-17) where L is the number of profile steps. Table 2-1 shows the calculated diffraction efficiency with the various step-profiles of th e lens. Diffraction efficiency is determined by the ratio of the power of the diffracted light beam to the incident power of the beam while the transmittance is the fraction of light at a specific wavelength that passes through a Fresnel zone plate.

PAGE 35

20 Table 2-1. Step profiles and their calc ulated diffraction efficiency [27]. Step profile Efficiency (%) Theoretical (kinoform) 100 Linear 99 16-level 98.7 8-level 95 4-level 81.1 2-level 41 Amplitude 10 The diffraction efficiency of an amplitude zone plate is only 10%. If we make the originally opaque zone transparent but with a phase shifting, the diffraction efficiency can be increased to 41% (a binary phase zone plate). The profile steps are proportional to the number of fabrication steps with the following relationship [27]: # of profile steps = 2n (2-18) where n is the number of masks or fabricati on steps. Figure 2-18 shows that three masks (or fabrication steps) could re sult an eight-phase-level PZP. The profile of a PZP is closer to the ideal kinoform when the number of steps is increased. Figure 2-18. Three fabrication steps result an eight-phase -level Fresnel lens [27].

PAGE 36

21 A schematic drawing of working princi ple and a scanning electron microscope image for a quaternary Fresnel zone plate ar e shown in Figure 2-19. In a quaternary phase zone plate, each level in a single zone makes incident light phase shift by and results in total constructive interference and a higher efficiency ( 81% from Table 2-1). Figure 2-19. Quaternary Fresne l zone plate design and SEM image of a fabricated PZP [18]. 2.4 Photon Sieve As described above, a photon sieve is a diffractive lens composed of pinholes distributed in the Fresnel zones, as shown in Figure 2-20. Kipp et al proposed this concept in 2001 [3]. However, the phot on sieve pattern shown by Kipp et al was consisted of 5646 randomly distributed holes and was very complicated. The detail design rules of the complicated photon siev e were not described in their paper. Figure 2-20. Schematic drawing of a photon sieve. Each blue spot is a hole through an opaque film.

PAGE 37

22 Analogous to the concept of a Fresnel z one plate, the pinholes have to be positioned properly to fulfill the criterion for cons tructive interference. That requires that the optical path length (OPL) from the source via the center of the holes to the focal point be an integral number of wavelength, This criterion can be expressed as the equation shown below [3]: where p is the distance between th e source and the photon sieve, q is the distance between the photon sieve and the focal point, and rn is the distance be tween the center of the holes and the optical axis. A schematic drawing of the relationship between source, photon sieve, and focal plan e is shown in Figure 2-21. Figure 2-21. Diagram showing point-to-po int imaging with a photon sieve [3]. The theoretical analysis of focusing for photon sieves in the far-field [28] and nonparaxial modes [29] were published by Qing Cao et al in 2002 and 2003, respectively. Nonparaxial mode refers to the angle be tween light rays and the optical axis, being large. The paraxial approximation (sin( ) tan( ) when is small ) [30] is no longer valid for the calculation of the OPL. n q p q r p rn n 2 2 2 2 ( 2-19 )

PAGE 38

23 2.4.1 Advantages of Photon Sieves over Fresnel Zone Plates Fresnel zone plates have been used to focus X-ray radiation for many years [1, 2, 31, 32]. However, ring-shaped secondary maxi ma are usually observed at the focal plane and cause blurring of the images from the z one plates. In addition, the resolution of Fresnel zone plates is controlled by the width of the outermost zone. Processing limitation may exist when approaching high -resolution zone plates. Photon sieves provide an opportunity to suppress the seconda ry maxima for sharper focusing of images and also overcome the process limitation of th e resolution of Fresnel zone plates [3]. These two advantages are review ed in the following sections. 2.4.1.1 Suppress higher diffraction order and improve focus It is well known that side bands or s econdary maxima are produced if the light passes through a rectangular type transmission window [3, 14, 20]. In a binary amplitude zone plate, the transmitted zones stopping ab ruptly at the outermost zone represents a rectangular transmission window. Ring shaped secondary maxima are formed and cause blurring of images. Blurring is defined by the standard deviation of the intensity distribution. For example, if the type of di stribution is Gaussian, the degree of blur is then determined by the standard deviation ( ) of the Gaussian distribution (normal distribution) known as Gaussian blur [33, 34]. The greater the standard deviation, the higher the degree of blur and the greater the loss of resolution. In this research, the degree of blur was not characterized. Photon sieves, proposed by Kipp et al [3], suppress the secondary maxima and higher diffraction orders by modulating the pinhole density on each ring of the photon sieve to implement a smooth transmission window. This technique is called “apodizati on” and is reviewed in sect ion 2-4-3. Figure 2-22 shows a photon sieve and a zone pl ate together with the experiment al and calculated intensities at

PAGE 39

24 the focal plane [3]. Comparing the intensi ties measured at focal plane, the secondary maxima (concentric ring patterns shown in Figure 2-22 f ) observed in the zone plates were suppressed by two orders of magnitude (calculated result) when using photon sieves as the focusing element. This property wa s not examined in the research of dualwavelength photon sieves; however it was verified by the simulation result demonstrated in section 4-2-3. Figure 2-22. A photon sieve and a FZP together w ith experimental and calculated results. (a) photon sieve (b) FZP (c) smooth tr ansmission window (d) rectangular transmission window (e) intensity at fo cal plane for photon sieve (f) intensity at focal plane for FZP (g ) calculated intensity for photon sieve (h) calculated intensity for FZP. The secondary maxima shown in FZP was suppressed when changing the focus element from FZP to photon sieve [3]. The same phenomenon is observed from the simulation result demonstrated in section 42-3.

PAGE 40

25 2.4.1.2 Overcoming the limitation of the resolution of FZP In addition to suppressing the secondary maxima, photon sieves also provide an opportunity to overcome the limited zone plate resolution. The intensity at the observation plane is determined by the net cont ribution of interference. Kipp et al [3] produced the first photon sieve in 2001 and proposed the theo ry of the relation between the diffraction amplitude and the d / w ratio (i.e., the K factor in Chapter 4), where d is the pinhole diameter and w is the zone width of an underlyi ng zone plate. This relation is shown in Figure 2-23 In the inset of Figure 2-23, the black and white strips represent the zones with destructive and cons tructive interferen ces, respectively. Four pinholes, A, B, C and D, with various diameters are drawn and the d / w ratios for the 4 pinholes are 1, 1.5, 4 and 4, respectively. The calculated curves of constructive (so lid gray line) and destructive (dashed gray line) interferen ces and the total cont ribution of the two interferences (solid black cu rve) are shown in Figure 2-23. Both pinholes C and D have the same pinhole diameter and d / w ratio, however, the pinhole C is centered on a white zone thus the black area within the pinhole is greater than th e white area which results in a net destructive inte rference therefore a negative inte nsity. Once the center of the pinhole shifts to a black zone (pinhole D) the white area within the pinhole dominates the interference and a net positive intensity will be observed at the focal plane. The spatial resolution ( m) of a traditional zone plate is decided by the outermost zone width ( w ). However, for a photon sieve, the spatial resolution is limited by the smallest effective width ( weff min), which is determined by the maximum d / w ratio [3]: m = weff min = dmin / ( d / w )max (2-20)

PAGE 41

26 This equation implies that at a d / w ratio designed to be 1.5, a photon sieve with a smallest pinhole diameter of 45 nm has the same spa tial resolution as a FZP with the outermost zone width of 30 nm. As the d / w ratio increases, the diameter of the smallest pinholes of a photon sieve can also be incr eased while still maintaining the same spatial resolution. Figure 2-23. The relation between the contributio n of focal amplitude and the ratio of the pinhole diameter over unde rlying zone width ( d / w ratio). As long as the white area within a pinhole is larger than the black area, the net intensity at focal plane will be positive [3]. Menon et al [35] reported that when using a photon sieve in a maskless photonsieve-array lithographic system the size of the single-exposure focal spot was controlled by the K factor (d/w ratio) when the smallest pinhole diameter was fixed. The larger the K factor, the smaller the focal spot, which is consistent with the theory proposed by Kipp et al [3]. Neither Kipp et al [3] nor Menon et al [35] mentioned the limit of K factor. From the simulation result shown in secti on 4-2-3, the focal spot (FWHM) becomes

PAGE 42

27 smaller when the K factor becomes larger; however, the intensity of the focal spot diminishes dramatically when K factor increas es from 1.5 to 2. This implies that when K factor is large enough that the focal spot w ill not be formed since the intensity of the focal spot is too low to be observed. 2.4.2 Disadvantage of Photon Siev es over Fresnel Zone Plates As outlined above, photon sieves have seve ral advantages over zone plates. However, lower transmission is a very criti cal limitation of photon sieves. An amplitude zone plate typically has a transmission of 50% while a photo n sieve only has a transmission of 15 to 20% [3]. The tran smission difference between zone plates and photon sieves is proportional to the opening ar ea of the zones and th e pinholes. The low transmission does not prevent photon sieves from applications using high intensity sources, such as in synchrotrons used for X-ray microscopy [3]. For common applications where the light source is le ss intense, low transmittance may limit the applications of photon sieves. Low transm ission reduces the signal intensities and contrast between signals and background, causing poor image quality. The contrast of a image is defined as [9] contrast = (Imax – Imin)/(Imax + Imin) (2-21) where Imax and Imin are the maximum and minimum intensities of the image, respectively. The photon sieves produced in this research consisted of a glass substrate coated with opaque metals having pinholes where lig ht can pass through and diffract to form images. Antireflection coatings on both sides of the glass substrate can only enhance the transmission of the photon sieves by 8% at most (4% from each side) [8]. Menon et al in 2005 [35] suggested a phase-shift photon sieve, which works in the same fashion as the

PAGE 43

28 phase zone plate described in section 2-3-3. In a phase-s hift photon sieve, the entire photon sieve is transparent to the light sour ce and the pinholes have a phase shift of with respect to the rest of the photon sieve therefore the transmission can be enhanced significantly. However, neither the detailed design nor the actual device was reported in their paper. 2.4.3 Apodization The term “apodization” is derived from Gr eek which means “take away-foot” [9]. Apodization is the process of modulating the pinhole density on each ring of the photon sieve to implement a smooth transmissi on window and thus further suppress the secondary maxima of a diffraction patter n. It is possible to smooth the sharp discontinuity of the transmission window by adding another function onto the existing window function. The added function is ca lled an apodization function. Apodization technique also can be applied to FZP; how ever, it requires very complicated equations and computer calculations to apodize the zone plate [36]. Apodization techniques are util ized in many areas, such as searching for earth-like planets in astronomy [37], microscopy, medi cal imaging and optical storage [38]. Apodization can be achieved by changing the ap erture shapes [39] or alternating the transmission characteristics [37, 38, 40, 41]. Some of the most common apodization functions are plotted in Figure 2-24 [42]. The corresponding f unctions are listed in Table 2-2. For the designs of photon sieves used in this research, Ga ussian apodization functions were chosen and modified to fit the various photon sieve designs through a series of simulations, which were completed by Shenderova [43-45]. The details of the simulations are describe d below in section 4-2.

PAGE 44

29 Figure 2-24. Some commonly used apodization functions in linea r scale [42]. X-axis is value of x/L where x is optical path difference out to a maximum value of L (also shown in Table 2-2). Y-axis is the amplitude of the function. Table 2-2. Equations of the apodization functi ons shown in Figure 2-25 [42]. x is the optical path difference and L is the maximum value of x variable.

PAGE 45

30 2.4.4 Applications of Photon Sieves Photon sieves are made from a metal thin film on a thin substrate or from a free standing opaque film. In addition to their tr aditional use for focusing x-rays, they can be used in any application that requires small and light weight lenses Since photon sieves are a relatively new type of diffractive lens [3], reported applications of this device are limited. Gil and Menon in 2003 and 2005 [2, 35] reported using photon sieves to replace the zone plates in their “scanning-optical-beamlithography” system, which was based on the technique of maskless, z one-plate-array lithography (Z PAL) invented by Smith in 1996 [46]. Schematic drawings of a ZP AL system are shown in Figure 2-25. Figure 2-25. Maskless, zone-plate-array lithography (a) arra y membrane on the supporting joists (b) individual micromech anical shutter within each unit cell (c) pattern writing by scanning the sa mple in X and Y directions [46]. In the ZPAL system, thousands of 10 m-size zone plates were set in an array, where each zone plate was isolated in its unit cell that was supported on a thin carbonaceous membrane with vertical, anisot ropically etched Si (111) joists for

PAGE 46

31 mechanical support, as shown in Figure 2-25 (a ). Each zone plat e was responsible for exposure in its own unit cell. The exposure was controlled by a micromechanical shutter located within the individual uni t cells, as shown in Figure 2-25 (b). The stage that held the sample was scanned in the X and Y directio ns to get a full pattern, as shown in Figure 2-25 (c). 2.5 Chromatic Aberration Chromatic aberration of a refractive le ns results from the dispersion of the refractive index of the lens material with wavelength. For different wavelengths, the same materials will have different refractive in dices, thus cause diffe rent degrees of light bending. For example, in the range of visible wavelengths, blue rays bend more than red ones. For a polychromatic light source, the multi-wavelength rays will not focus at one single spot on the optical axial as shown in Figure 2-26, resulting in chromatic aberration. Figure 2-26 Chromatic aberration of a refractive lens [47]. For a diffractive lens, incide nt light rays bend when skimming the edge of an obstacle and then interfering with each othe r and finally focus on the observation screen. As reviewed in section 2-3, the focal length of diffractive lens is wavelength dependent. A very large longitudinal chromatic aberration is estimated by using equation (2-13). In

PAGE 47

32 the visible range, red rays bend more than blue one. The light bending mechanisms for refractive and diffractive lenses are differe nt, but both exhibit chromatic aberration. 2.6 Justification of Research There is no true single achromatic diffractiv e lens to date. In reported research of diffractive lenses, no single lens was designe d to have two diffraction elements. The purpose of this research is to study how lens properties changed when multiple diffraction elements with differe nt distributions were incorp orated in a single lens. A dual-wavelength photon sieve cons isting of two groups of pinholes, designed to focus two wavelengths of light, is the simplest system to investigate. As reported below, such a dual-wavelength diffractive lens exhibits signi ficant chromatic aberration. This is consistent with the diffraction theories (section 2-3) reviewed above. A number of different designs for the distri bution of the two groups of pinhol es were tested. The focal spot size obtained from a dual-wavelength photon sieve was same to the one obtained from a single-wavelength photon sieve but with equal or lower intensity under both monochromatic and polychromatic illuminati ons. The significant chromatic aberration observed in a single-wavelength photon sieve makes it a good candidate for a focusing filter lens for polychromatic light. Dual-wav elength photon sieves could be used for an imaging device that does not require complete f iltering of polychromatic light at the cost of intensity. The details of testing set-up and results are shown and discussed in Chapter 4.

PAGE 48

33 CHAPTER 3 PHOTON SIEVE FABRICATION 3.1 Introduction As discussed in chapter 2, a photon sieve ( PS) is a diffractive lens composed of pinholes distributed similar to the Fresnel z ones. The PS, shown in Figure 3.1, consist of a glass substrate (transparent to the waveleng th of interest) coated with opaque metals having a pattern of holes where light can pa ss through and diffract to form an image. Figure 3-1. Schematic drawing of a cross-s ectioned photon sieve. The size of pinhole various from 80 to 10 m depending on the location of pinhole for a PS designed for 500 nm light. To make this device, lith ographic techniques were used to transfer geometric patterns from software or masks to the me tal film on the substrate. Depending on the type of radiation, lithography can be divided into three cat egories: optical, x-ray, and electrons/ion beams. Though op tical lithography is widely used in the semiconductor industry, it reaches its limitations when the resolution requirements shift to submicron levels. Electron and ion beams possess high en ergies and therefore offer extremely small wavelengths which gives better resolution as comp ared to even deep or near ultra-violet

PAGE 49

34 (UV) light. In addition to th e better resolution, electron and ion beams can be focused to produce patterns on the resist directly without any mask. The minimum feature size of the photon siev e designs used in this study was in the micrometer range. Either traditional photolithography or electron beam (e-beam) lithography can therefore be use for this patterning process [ 48]. Due to the instrument accessibility and ease of use without a mask, e-beam lithography was chosen for process development. In the following sections, de tails and problems that encountered in each process step are illustrated. Background knowledge of some techniques including processing and analytical instru ments are introduced as well. 3.2 Process Development Photon sieves were fabricated by first de positing by electron beam evaporation [48] a thin adhesion layer of nickel (3 nm), fo llowed by deposition of a 150 nm silver layer on a glass substrate. The metallized substrate was then coated with electron beam (e-beam) resist, patterned using e-beam lithography and then developed. The patterned e-beam resist was used as a mask to protect the unde rlying metal films duri ng etching, either dry or wet etching depending on different pro cess method. The e-beam resist was then stripped, resulting in a photon si eve. A flow-chart of gene ral processing steps is shown in Figure 3-2. Four different process methods, which will be named (1) reversed image etching, (2) direct wet etching, (3) direct dry etching, and (4 ) lift-off, are described in Figure 3-2. The acronyms and abbreviations us ed in Figure 3-2 are listed in Table 3-1. The procedures of substrate cleaning, meta l deposition, and e-beam pattern writing were identical for these four procedures. The e-b eam resists, developers etching methods, and resist strippers were differe nt depending on the process method Complete descriptions of each method are given below in sections 3.2.6.1 to 3.2.6.4.

PAGE 50

35 Figure 3-2. Flowchart of vari ous processing methods (a) to (d). The whole development is divided into five big steps, substr ate preparation, film deposition, resist coating (flow charts within the top blue-double-line box), e-beam lithograph, and four process methods (flow char ts within the bottom blue-double-line box). Equipments, operation details, and problems of each step is discussed in the following corresponded section.

PAGE 51

36 Table 3-1. Acronyms and abbreviations shown in Figure 3-2. Acronym and Abbreviation Full Name PMMA Polymethylmethacrylate FOx-14 Liquid solution of hydr ogen silsesquioxane (HSQ) ZEP-7000 Proprietary positive e-beam resist MF-322 Proprietary developer for FOx-14 RIE Reactive Ion Etching MIBK Methyl isobutyl ketone IPA Isopropyl alcohol ZED-750 Proprietary developer for ZEP-7000 NPGS Nanometer Pattern Generation System 3.2.1 Substrate Preparation All PSs were fabricated on pre-cleaned gl ass microscope slides purchased from Fisher Scientific (Cat. No. 12544). The glass slides were 3 x 1 x 1/16 inch but were cut into 1 x 1 x 1/16 inch substrates followed by scrubbing for 5 min. in an Alconox (powder detergent from Fisher) DI water solution. Afte r rinsing-off the detergent, the substrates were submerged into a three-stage ca scade DI water rinse bath with N2 bubblers, as shown in Figure 3-3 (Bold Technologies Inc. Model 625T wet bench), for over 20 minutes. Substrates were always placed in the lowest (dirtiest) tank for 5 minutes, then the middle tank for another 5 minutes, and fi nally the highest (cleanest) tank for 10 minutes. The substrates were then blow dried with dry N2. Figure 3-3. Three-state cascade DI water rinse bath with N2 bubblers on the wet bench.

PAGE 52

37 3.2.2 Film Deposition Metal films were deposited by electron beam evaporation. The details of film deposition and the illustration of e-beam eva porator are given in the following sections. 3.2.2.1 Electron-beam evaporator: system and operation Figures 3-4 and 3-5 show a schematic drawing and a photograph of the e-beam evaporator, respectively. The detailed struct ure inside the proce ssing chamber is shown in Figure 3-6. The diffusion pump is used as an example when describing the process steps. Before starting to pump the chamber to lower pressure, the mechanical pump (Leybold Dryvac 100P) and diffusion pump need to be turned on for at least 30 minutes to allow the pumps to stabilize or re ach the operation temperature (about 250oC for diffusion pump oil). Stable operation and at tainment of the prope r vacuum should be verified by pressure gauge rea douts. Liquid nitrogen was added into the cold trap before pumpdown. The cold trap is used to condense the oil vapor into its solid phase to prevent the pump oil from backstreaming and contaminating the work chamber. Figure 3-4. Schematic drawing of e-beam evaporator system.

PAGE 53

38 Figure 3-5. Photograph of electron-beam deposition chamber and control rack. Figure 3-6. Detailed struct ures inside bell jar of an e-beam evaporator.

PAGE 54

39 After placing two substrates in the proce ss chamber, the bell jar was closed and the roughing line valve was opened to rough the ch amber down to a crossover pressure of 150 milliTorr. The roughing line valve was then closed and the foreline and high vacuum valves then opened. If the pressure in the foreline is pumped too low (<150mTorr), the mechanical pump oil will backstream and c ontaminate the chamber [49]. Conversely, if the crossover pressure is t oo high, backstreaming of the di ffusion pump oil to the process chamber will occur due to the collapse of vapor jets in the diffusion pump. Once the foreline and high vacuum valves were opene d, the diffusion pump could pump down the chamber to very high vacuum (10-6 Torr). The mechanical pump was left on to serve as a backing pump for the diffusion pump. An i on gauge was used to monitor the chamber pressure. Metal deposition was carried out at an operating pressure of 3 ~ 5 x 10-6 Torr. The water-cooled copper hearth can hold up to 5 different sources and the source in use was controlled by a small rotary motor. The ability to rotate a different hearth into the source position allows deposition of multi-layer thin f ilms of various materi als without breaking the vacuum. Each source material (e.g., Ni or Ag) was placed in a graphite crucible (1 inch in diameter, 0.75 inch in depth, Kurt J. Lesker EVCEB-11) in sufficient quantities to cover the whole base but no more than 2/3 of the depth of the crucible to avoid overflowing of the source material. Electrons are thermionically emitted from a hot filament then accelerated by a high voltage (30 kV). The electron beam is deflected by a magnetic field, focused by an electrostatic lens, and heats the source materials to a temperature where the sublimation or evapora tion rates are sufficientl y high to deposit a

PAGE 55

40 thin film at an acceptable rate. The electr on beam is controlled by an electron beam power supply (Airco Te mescal model ES-6). The cleaned, bare 1 x 1 inch substrates were placed on a sample holder which allowed a nearly normal-incidence of th e evaporative flux in order to minimize shadowing effects [48, 50]. The s ubstrates were heated to above 200oC by heating lamps (Globe D, 50V, 200W) to eliminate adsorbed water moisture. The heating lamps were then turned off and the substrates allowed to cool for about 15 minutes. Metal deposition was then initiated by heating the source metal with the electron beam An adhesion layer of nickel with a thickness of 30 was deposit ed at a rate of about 5 /s and a substrate temperature between 50-70oC controlled by the heat lamps. The elevated temperature provides a good film quality. The deposition ra te and thickness were controlled by an INFICON deposition controller XTC/2 which is described in sect ion 3.2.2.2. After the deposition of nickel, the copper hearth was rota ted to the silver sour ce and a 1500 silver film was deposited at a rate of 20 /s, with the substrate temperature again controlled between 50-70oC. The metal-film-coated substrate was left in the vacuum chamber for over 15 minutes to cool down close to room temperature before venting the chamber and removing the substrates. For silver deposition, when the bottom of th e crucible was not completely covered by the source metal, tiny silver balls (< 10 m) were observed on the silver film, as shown in Figure 3-7. Cotronakis et al [51] reported that carbon contamination was the cause of gold spitting. The gold spitting was reduced by removing the carbon residual from the gold source. It is speculated that when the electron beam hits the bottom of the graphite crucible, carbon contamination incr eased and caused the si lver spitting. This

PAGE 56

41 problem was avoided when the silver metal s ource was in sufficient quantity to cover the whole base. Figure 3-7. Silver spitting. Sm all spherical silver balls sp itted from the molten silver source. The size of the larg est silver balls is about 10 m. At the beginning of process development, a diffusion pump was used as the high vacuum pump in the e-beam deposition sy stem, but was replaced by a cryogenic pump for the last half of the research. This cha nge did not disrupt the re search results reported below for photon sieves. The most significan t difference between a diffusion pump and a cryogenic pump is that no pu mp fluid or lubricant is used in cryopumps; thus backstreaming of oil from the pump to th e processing chamber does not occur. The cryopump is continually running until regenera tion is needed to remove the captured gases and restore its pumping capacity. The mechanical pump can be turned off after opening the high vacuum valve since there is no need of a backing pump for the cryopump. The rest of the details of a cr yogenic pump can be found in the following references [49, 52, 53]. The change from diffusion pump to cryopump for the-beam evaporator reduced the processing time and also resulted in a better film quality.

PAGE 57

42 3.2.2.2 Deposition controller By setting multiple parameters of the source materials in the deposition controller (INFICON XTC/2), the controller can control the shutter to open and close automatically according to the preset film thickness. The deposition monitor is a quartz crystal with special piezoelectric sensitivity. The piezoelectric crystal changes its shape when a RF voltage is applied and mechanical oscillations result. The fr equency of the oscillation is a function of the thickness of the crystal. During the deposition, the added mass reduces the frequency of this oscillation. Before deposition, the density and the Z-ratio of the depositing film are entered into the micropr ocessor within the deposition controller to correctly convert frequency ch ange to film thickness. The Z-ratio is equal to [54] ( q uq / f uf)1/2 (3-1) where q, f are the densities of quartz and th e deposited film, respectively, and uq and uf are the shear moduli of the quartz and the f ilm, respectively. The derivation of equation (3-1) can be found in references [54-57]. Table 3-2 shows densities and Z-ratios of mate rials used in the project. If multiple layers were deposited, the Z-ratio used fo r the second layer is decided by the relative thickness of the two layers. When one layer is thick compare to another, the Z-ratio of the thick film is used for both layers regard less of the sequence of deposition. When the thickness of both layers is similar, a weighted average of the two Z-rati os is used [54]. A picture of a deposition monitor and a schematic drawing of a quartz cr ystal oscillator are shown in Figure 3-8 (a) and (b), respectively [57, 58].

PAGE 58

43 Table 3-2. Densities and Z-ratios of materials used in the experiment. Formula Density Z-ratio Material Name Ag 10.500 0.529 Silver Cr 7.200 0.305 Chromium Ni 8.910 0.331 Nickel MgF2 3.180 0.637 Magnesium Fluoride Figure 3-8. Standard deposition monitor (a) an d quartz crystal osc illator (b) [57, 58]. 3.2.3 Resist Coating 3.2.3.1 Electron-beam resists Depending on the processing methods, three different e-beam resists were used: PMMA, FOx-14, and ZEP-7000. PMMA is an ultra-high resoluti on positive e-beam resist [59]. Positive resist means that the exposed areas are removed during development, leaving a positive image in the resist. On th e other hand, the negative resist is the resist where the exposed areas are retained while th e unexposed areas are removed, resulting in a negative image in the resist [48]. The PMMA used in the experiment was 950 PMMA C4 obtained from Mirochem, Inc. Microchem offers a variety of molecular weights and solvent systems for PMMA. The “950” re sist has a molecular weight of 950,000 and “C4” represents a 4% PMMA c oncentration in chlorobenzene.

PAGE 59

44 FOx-14 is a liquid solution of hydrogen sils esquioxane (HSQ) in a solvent obtained from Dow Corning. First generation FOx (refe rred as FOx-1x) uses MIBK as the solvent while second generation resist (referred as FOx-2x) uses a volatile methyl siloxane (VMS) as the solvent [60]. FOx-14 is a flowable, inorganic polymer which forms a micro-porous amorphous (SiO2-like) film after the e-beam exposure. It is a high resolution negative e-beam resist. ZEP7000 is a high resolution positive e-beam resist with excellent dry-etching resistance obtained from Zeon Chemicals L. P ., a Japanese company. It is a polymer of an unspecified type with a molecular wei ght of 340, 000 and was dissolved in dietylene glycol dimethyl ether [61]. For positive resist, such as PMMA and ZEP7000, the energy provided by the electrons breaks bonds in the polymer chains an d results in a local reduction of molecular weight. As a result, the exposed area is mo re chemically active a nd can be dissolved by the developer. For negative resist, the elec trons provide energy for molecular chain to cross-link so that the exposure areas are retained while the unexposed areas are dissolved by the developer. The doses, energies a nd developers required for PMMA, FOx-14, and ZEP700 are described in section 3.2.4 on pattern formation. 3.2.3.2 Spin-coating and prebake The spin coater used in the experiment was a P6700 by Specialty Coating System, Inc. It has an 8-inch polytetrafluoroet hylene (PTFE) coated bowl with a programmable three-stage spin controller. The speed range of the spin coater is from 100 to 8000 rpm with hold times of 0 to 999 seconds. Figure 39 shows a picture of the P6700 spin coater.

PAGE 60

45 Figure 3-9. P6700 series spin coater by Specialty Coating System, Inc. The spin coating process can be separated into four stag es [62-64]. The first stage is dispensing the e-beam resist onto the subs trate by using a disposab le pipet. The second stage is the acceleration of the turntable to the desired spee d. In the third stage, the substrate is spinning in a cons tant speed and the viscosity force of the resist dominates the film thinning process. The fourth stage is similar to the third stage that the substrate spins at constant speed. However, the co ating thinning process is dominated by the solvent evaporation instead of fluid viscos ity. The coating thickness is essentially determined by the balance between forces that shear the resist toward the edge, and the drying rate that affects th e viscosity of the resist. Generally, for a known resist, higher spin speed and longer spin time result in thinner coatings. When the spin speed increa ses, the centrifugal fo rce increases and less fluid can be held on the substr ate; thus, the thickness of th e fluid decreases. Data from the manufacturer on the relations hip between the spin speed and thickness is shown in Figure 3-10 for ZEP resists [61]. For ZEP 7000, the film thickness was about 1800 for the spin speed of 3000 rpm used in this study.

PAGE 61

46 Figure 3-10. Relationship between th e spin speed and thickness [61]. The substrate with deposited films was first loaded onto the vacuum chuck and cleaned by spin-rinsing first with isopropyl al cohol (IPA) then methanol. The substrate was spun at 200 rpm for 10 seconds. E-beam re sist was then dispensed onto the rotating substrate and allowed to spread over the substr ate. This method conserved resist material since it was only necessary to cover the center of the substr ate. After this dispensing step, the spin speed was increased to 3000 rpm and held at that speed for 35 seconds. PMMA, FOx-14, or ZEP7000 were spun coated onto the substrates with the same recipe and the thicknesses of the coatings were 5000, 3000, and 1800, respectively. Spin coating defects, report ed in the literature and s hown in Figure 3-14 [64], were observed on the present samples. Come ts, Figure 3-11 (a), are caused by large contaminated particles on the substrate, and can be reduced by working in a particle-free environment. Uncoated areas, Figure 3-11 (b), are caused by dispensing insufficient amounts of resist, and can be corrected by simply increasing the amount of dispensed resist.

PAGE 62

47 Figure 3-11. Optical photographs of spin co ating defects: (a) comet, and (b) uncoated area [64]. After spin coating, the substrates were pr ebaked (soft baked) to remove solvents from the resist. The hot plate used in the experiment was a Cole Parmer DATAPLATE 720 Series Digital Hot Plate. It had a ceramic plate surface and is capable of temperatures in excess of 370oC. The film thickness of the re sists shrank to about 85% of its initial value during prebaking [61, 65]. The prebake temperature and time are different depending on type of resist. Depending on the heat transfer mode, either conduction (hot plate) or convection (oven), the time required for prebake is differe nt. It requires a l onger time, generally 20 to 30 minutes, to bake the substrate in a c onvection oven and it only needs 1 or 2 minutes to bake the substrate on a hot plate. In addition to the slower heat transfer mode (convection), a skin forms on th e top of the resist during th e solvent drying and further hinders the rapid evaporation of the volatile component within the resist [66] when baking the substrate in a conv ection oven. In this researc h, the temperature of the hot plate was set to be 180oC. The time of prebake for PMMA, FOx-14, and ZEP7000 were 15 minutes, 2 minutes, and 2 minutes, respectivel y. After spin coating and prebaking, the substrates were ready for writing of the patterns.

PAGE 63

48 3.2.4 Pattern Formation The photon sieve patterns were written w ith a Pillips XL 40 scanning electron microscope (SEM) controlled by the nanomet er pattern generation system (NPGS). NPGS is software and hardware that gene rated steering voltages to control the beam location and dwell time from an input data file (DesignCAD files in this research) describing the pattern to be written. The resist-coated substrate was loaded onto a multi-sample translatable stage along with a gold standard and a Faraday cup. The acceleration voltage wa s set to be 30kV and spot size of the electron beam is size 4, i. e., a diameter of a few nanometers. The gold standard was used to focus the electron b eam with a working distance of 12.8 to 13.2 mm depending on the minimum magnification re quired by the pattern design. Astigmatism and beam alignment (controlled by lens m odulator) were adjusted to resolve surface features at high magnification of 60,000 ~ 125,000X After these initial adjustments, no further changes in focus and astigmatism were made. By moving the stage to the Faraday cup and increasing the magnification, the electron beam current was measured and recorded. Due to the absence of a beam bla nker, the stage was then moved to place the beam on the edge of the substrate at a magni fication of 400X or gr eater to minimize the e-beam exposure in the area to be patterned. The stage rota tion was then adjusted by the Stage/x-align command for sample alignment. The height of the substrate was adjusted till the resist surface was in focused. Writi ng of the desired photon sieve pattern was controlled by the run file and the NPGS soft ware. The number and type of patterns, the locations of the patterns on the substrates, th e e-beam dose, the center-to-center distance and the line spacing of electron beam writing were all specified in the run file. The center-to-center distance is the distance between two e-beam exposed areas (area mode)

PAGE 64

49 and line spacing is the distance between two e-beam exposed lines (line mode). The beam current was between 1680 and 1720 pA for a beam spot size of 4. The e-beam dosage of PMMA, FOx-14, and ZEP7000 were set to an “area dose” of 130 C/cm2, 45 C/cm2, and 45 C/cm2, respectively. The line spacing a nd the center-to-center distance were both set to 100 nm. If the line spacing or the center-to-center dist ance is too small, over-exposure problems may occur. The “nonstop writing” mode was selected for all pattern writing processes. After entering al l the parameters, the NPGS calculated the exposure time automatically and controlled th e beam movement accord ing to the pattern design. The e-beam was turned off immediatel y after the pattern writ ing was finished to prevent unnecessary exposure to the resist. Depending on the pattern designs, the writing time of a single photon sieve was about 20 to 40 minutes. The chamber was then vented and the sample was unloaded for development of the resist pattern (see Figure 3-2 for process flow chart). The developer used for PMMA resist consists of MIBK with IPA in a ratio of 1 to 3. The developing time was 70 seconds in a be aker at room temperat ure without stirring. After development, the substrate was rinsed with IPA then blow dried with pure N2. The developer for FOx-14 was Microposit MF322 obtained from Shipley Company and consists of 2.44% tetramethylammonium hydroxi de (TMAH), less than 1% of surfactant [67] and water. The substrate was develope d in MF-322 for 90 seconds and rinsed by deionized (DI) water, th en dried with pure N2. For ZEP7000, the proprietary developer is ZED-750 obtained from the Zeon Chemicals L. P. The substrate was developed in ZED750 for 2.5 minutes, then rinsed in IPA and dried with N2.

PAGE 65

50 3.2.5 Reactive Ion Etch (RIE) The RIE system used for the experiment is a PlasmaTherm SLR770 series reactive ion etcher with a turbopump (Leybold Turbovac 1000) and two mechanical pumps (Leybold Trivac BCS) used for backing th e turbopump and roughing the loadlock, respectively. The system includes a loadlock chamber with an automatic arm to move the sample into the etching chamber. The lo ading platform was able to handle different sample sizes from small to a 4-inch wafer. The PlasmaTherm SLR770 has an ECR plasma source produced by a 1000W microwave power supply and is combined with a 13.56MHz 500W RF power supply. The E CR source operated at 2.45GHz [65]. Reactive ion etching is discusse d in detail in reference [ 48]. Figure 3-12 is a photograph of the PlasmaTherm SLR770. Figure 3-12. Photograph of the PlasmaTherm SLR770. During the process development, etch ing recipes with oxygen, argon, or a proprietary H2/Ar/CH4 etching recipe [68], were used to etch PMMA and silver. Oxygen plasma was used to etch the PMMA layer a nd the argon plasma was used to sputter etch

PAGE 66

51 the silver metal. The proprietary etching re cipe (patent pending) was used to etch the silver metal with excellent selectivity betw een chromium and silver. Selectivity in plasma etching is defined as the ratio of the etching rates of two different materials when exposed to the same plasma environment [48]. When the etch rate of the mask is low and the etch rate of the underlying material is high, the selectivity is good. The actual reason for the excellent selectivity is not clear The detailed compositions and operation parameters for the recipes are shown in Table 3-3. Table 3-3. Experiment parameters of pl asma-etching recipes for RIE process. Oxygen plasma Proprietary recipe (Patent pending) Argon plasma Etched material PMMA Ag Ag or Ni Mask FOx-14 Cr ZEP-7000 Pressure 10 mtorr proprietary recipe 1 mtorr Temperature Room temp. Room temp Room temp RF power (W) 100 proprietary recipe 100 ECR power (W) 0 proprietary recipe 900 Gas / Flow rate O2 / 20 sccm H2 / proprietary recipeAr / 10 sccm Ar / proprietary recipe CH4 / proprietary recipe 3.2.6 Various Process Methods: Procedures and Results Photon sieve patterns were created by f our different processes (reversed image etching, lift-off, direct wet etch ing, and direct dry etching) as described in the flow chart in Figure 3-2. They are de scribed in detail below. 3.2.6.1 Reversed image etching process Photon sieves were fabricated by first depositing by electron beam evaporation a thin adhesion layer of nickel of 30 , followe d by deposition of a layer of silver (1500 )

PAGE 67

52 on a cleaned glass substrate. In the reve rsed image etching process, the metallized substrate was coated, first with PMMA with a prebake at 180oC for 15 minutes, and subsequently with FOx-14 with a prebake at 180oC for 2 minutes. The FOx-14 was patterned using electron beam lithogra phy and then developed by MF-322 for 90 seconds. The unexposed FOx-14 was dissolved in the developer a nd then the exposed PMMA was removed by oxygen plasma etching. The oxygen plasma recipe and detailed operation procedures for RIE and etching reci pes were described above. After etching the PMMA, a 250-thick chromium (Cr) layer, used as a hard mask for RIE, was deposited by e-beam evaporation. The sample was then rinsed by ultrasonication in an acetone bath (Fisher Scientific ultrasonic FS-28) to lift off the Cr/FOx-14/PMMA masked areas, exposing the silver layer. After lift off, the sample was dried and the silver and nickel was etched using RIE with the pr oprietary recipe [68] (see Table 3-3) to produce the transparent PS holes Figure 3-13 shows an op tical micrograph of a photon sieve manufactured by this method. The pr ocess steps in this method are shown schematically in Figure 3-14. Figure 3-13. Optical micrograph of an apodi zed photon sieve manufa ctured by reversed image etching method.

PAGE 68

53 Figure 3-14. Process flow of the “reversed im age etching” method. Th e direction of flow is from left to right, top to bottom.

PAGE 69

54 This process method required a chromium film deposition and over 40 minutes of high-power reactive ion etchi ng of silver. The whole process took about a half day longer than the other methods. In addition to the complicated process, residual dots of material, shown in Figure 3-15, observed after th e etching of silver with the proprietary recipe [68] are described as below. The sizes of the residual dots were on the order of a micrometer and the dots were only distributed within the large pinholes near the center of a photon sieve. After 20 minutes of etching, the residual dots were already formed and they became bigger as etching continued. The SEM micrograph shown in Figure 3-15 was taken after 40 minutes of etching. Figure 3-15. SEM micrograph of residual dots within the pinhol es after plasma etching of Ag and Ni. The composition of the residual dots wa s analyzed by Auger spectroscopy and evaluated by secondary and backscattered elect ron images in the SEM. Figure 3-16 [69] shows a schematic drawing of the interac tion volume for various electron-specimen interactions. Auger emission is preferred fo r detection of low atomic number elements, while X-ray emission is preferred for high at omic number elements [70]. Only Auger electrons generated closed to the specimen surface can escape with their characteristic

PAGE 70

55 energies and be used to identify the atom s in the specimen (10 from the surface in Figure 3-16). Figure 3-16. Schematic drawing of interac tion volume for various electron-specimen interactions [69]. The micrographs of secondary and backsc attered electron images of the residual dots are shown in Figure 3-17 (a ) and (b) respectively. Both micrographs were taken at the same location with the sa me magnification for comparis on. Secondary electron yield does not change systematically with the atom ic number, Z, of the element being imaged, whereas the backscatte red electron yield increases w ith increasing Z. Secondary electrons provide a better topographical contra st while backscattere d electrons provide some information about the specimen elements [70]. From the backscattered electron micrograph, shown in Figure 3-17 (b), the re sidual dots appear to be hemispherical bodies with dark strips, and th eir appearance is very simila r to those in the secondary electron micrograph, shown in Figure 3-17 (a ). The information provided by the BSE micrograph confirmed that the dark strips on th e residual dot consists of relatively low Z elements as compared to the rest (w hite part) of the hemispherical bodies.

PAGE 71

56 Figure 3-17. Residual dots (a) SE image (b ) BSE image. SE yield does not change systematically with the atomic numb er, Z, of the element being imaged, whereas backscattered electron yield incr eases with increasing Z. BSE image confirmed the dark strips on residual dot consisted of relatively low Z element compared to the rest of hemispherical body. The same specimen was analyzed by A uger electron spectroscopy. The Auger spectra were taken in an area with residual do ts instead of from a single dot. Charging artifacts occurred when the primary beam wa s focused onto a single dot due to the nonconductive glass substrate undern eath. Generally, the charging problem can be improved by lowering the energy of incident beam or tilting the sample. Both actions had been taken and charging still occurred, so the area of analysis was expande d to include an area of residual dots, as shown in Figure 318. Auger spectra before and after argonsputtering are shown in Figure 3-19 (a) and (b ), respectively. The depth profile from argon sputtering on the residual dot s is shown in Figure 3-20.

PAGE 72

57 Figure 3-18. Indication of inves tigated area for Auger spectrum. (a) (b) Figure 3-19. Auger spectra from a genera l area with residual dots (a) before argon sputter, and (b) af ter argon sputter.

PAGE 73

58 Figure 3-20. Argon sputtering depth profile from the area with residual dots. Before argon sputtering, chromium (Cr), nickel (Ni), oxygen (O), carbon (C), and silicon (Si) peaks were found in the area with residual dots. After sputtering, Si, calcium (Ca), and O peaks were found in the same ar ea whereas Cr, Ni, and C peaks disappeared and so did the residual dots. The strong Si and O (from SiO2) and weak Ca peak after sputtering came from the glass substrate. The Cr, Ni, C and part of the O peaks found before sputtering are from either the residual dots or surface contaminations. To avoid the long process time (chrom ium deposition and 40 minutes of RIE etching) and the possibility of residual dots formation, the lift-off process was developed. 3.2.6.2 Lift-off process The lift-off method to fabricate PS was deve loped consisting of first evaporating a 30 adhesion layer of nickel, which also se rved as a charge di ssipation layer during ebeam lithography. The substrate was then coat ed, first with PMMA with a prebake at 180oC for 15 minutes, and subsequently with FOx-14 with a prebake at 180oC for 2 minutes. The FOx-14 was patterned using electron beam lithography and developed by MF-322 for 90 seconds. The unexposed FOx-14 was dissolved and the unmasked PMMA

PAGE 74

59 was removed by RIE. After the etching of the PMMA, a 1000-thick silver (Ag) layer was deposited on the substrate by e-beam evaporation. The sample was rinsed by ultrasonication in an acetone bath (Fisher Sc ientific ultrasonic FS-28) to lift off the Ag/FOx-14/PMMA layers. The sample was s ubjected to RIE for 10 seconds to remove the thin nickel layer by argon sputtering. A schematic process flow of this method is shown in Figure 3-21. Figure 3-21. Process flow of the “lift-off” met hod. The direction of flow is from left to right, top to bottom.

PAGE 75

60 This process method shortened the proce ssing time by eliminating the steps of Cr deposition and 40 minutes of silver etching. However, it required a short etching of nickel by argon sputtering, which bombarded the silver surface simultaneously and caused roughening. No residual dots were obs erved in this process method. Figure 3-22 shows an optical micrograph of a photon siev e manufactured by the lift-off method. The sidewall residue, shown in Figure 3-23, limited the deposited thickness of silver. If the silver was too thick, it prevented the PMMA layer from being dissolved in acetone during the lift-off process. In addition, the oxygen plasma was not stable (with unknown contamination) over the time pe riod of the process developmen t. In order to avoid the problem of sidewall residues and the use of oxygen plasma, the process of direct wet etching was studied. Figure 3-22. Optical micrograph of a photon si eve manufactured by the lift-off method.

PAGE 76

61 Figure 3-23. Schematic drawing of sidewall re sidue. Some of the deposited silver atoms stuck on the sidewall of the patterned resist and prevented the PMMA layer from being dissolved in acetone during the lift-off process. 3.2.6.3 Direct wet etching process In the direct wet etching method, photon si eves were fabricated by first depositing by electron beam evaporation a 30 adhesion la yer of nickel, followed by deposition of a layer of silver (1500 ) on a cl eaned glass substrate. The me tallized substrate was then coated with PMMA w ith a prebake at 180oC for 15 minutes. The PMMA was patterned using electron beam lithography and developed by MIBK:IPA (1:3) for 70 seconds. The exposed silver was etched using 12M nitric acid (HNO3) in 1 second. The sample was rinsed with DI water twice. The PMMA wa s removed by rinsing w ith ultrasonication in an acetone bath. A schematic process flow of this method is shown in Figure 3-24. This method was the simplest compared to other three process methods because it required neither Cr deposition nor long time RI E, and only required one spin coating of PMMA, which was used as a mask for direct wet etching. However, the quality of etching was poor. The uniformity of wet et ching over different feature sizes was a

PAGE 77

62 problem. Figure 3-25 shows th at the large pinholes (80 m in diameter) located in the center of the photon sieve were etched clearly while the small pinholes (10 m in diameter) located at the outer area of photon si eve were not etched completely. In order to avoid this problem, the process of direct dry etching was studied. Figure 3-24. Process flow of the “direct wet et ching” method. The direction of flow is from left to right, top to bottom.

PAGE 78

63 (a) (b) Figure 3-25. Optical micrographs of the phot on sieve manufactured by direct wet etching (a) completely etched large center pinholes (80 m in diameter), and (b) incompletely etched small outer pinholes (10 m in diameter.) 3.2.6.4 Direct dry etching process In the direct dry etching process, the me tallized substrate (3 nm of Ni and 150 nm of Ag) was coated with PMMA and prebaked at 180oC for 15 minutes. The PMMA was patterned using electron beam lithography and developed by MIBK:IPA (1:3) for 70 seconds. PMMA was used as a mask for the RIE argon etching. The PMMA demonstrated a poor resistance to dry etching and veil-like material accumulated at the edge of each pinhole which caused the e dge roughening, as shown in Figure 3-26. Figure 3-26. SEM micrographs of the veil-like matte r at the edge of holes after argon sputtering using only PMMA for an etch mask.

PAGE 79

64 Thus another positive e-beam resist ZEP7000, was added on the top of PMMA during the coating stage. The ZEP7000 was patterned using e-beam lithography with an “area dose” of 45 C/cm2 and developed using ZED750 for 2.5 minutes followed by a rinse in IPA. The ZEP7000 with e-beam exposure was dissolved in ZED750. The sample was subjected to argon plasma etchi ng inside a RIE system to etch away the exposed PMMA, silver, and nickel layers. The PMMA and ZEP7000 coatings were then removed by ultrasonicating in acetone. Use of th is procedure resulted in clean edges as shown in Figure 3-27. A schematic process fl ow of this method is shown in Figures 328. The direct dry etch process using P MMA plus ZEP7000 was selected to be the standard process to make singleor dual-w avelength photon sieves. No chrome coating and oxygen plasma etching were needed and the silver-etching st ep took only 30 second rather than 40 minutes as in the reverse image method. Figure 3-27. A photon sieves with clean edge manufactured by direct dry etching method.

PAGE 80

65 Figure 3-28. Process flow of the “direct dry et ching” method. The direction of flow is from left to right, top to bottom. 3.3 Discussions In the reversed image etching process (section 3.2.6.1), the reason for the excellent selectivity of Cr over Ag with the proprietary H2/Ar/CH4 RIE recipe [68] is still not clear. It is speculated that the silver atoms a nd the hydrogen or hydrocarbon molecules form organometallic complexes. Hydrogen atom s and linear or cyclic hydrocarbon groups with -bond systems, such as ethylene (H2C=CH2), acetylene (HC CH), -allyl (C3H5),

PAGE 81

66 cyclopentadienyl (Cp, C5H5) and benzene (Ph, C6H6) are very common ligands in organometallic complexes [71] and are possibl e to form during the plasma discharge. Because the bonding between silver and carbon or hydrogen is thermodynamically weak [72], the organometallic complexes tend to undergo homolytic dissociation [73], which results in metal and hydrocarbon radicals and been removed by turbopump. The purpose of adding argon atoms in the proprietary reci pe [68] is to stimulate the gas-solid reactions, i.e., to remove deposited polymer and increas e the etching rate [48]. It is reasonable to speculate that the mo st probable mechanism of formation of the residual dots formation during RIE of PSs is primary particle agglomeration during plasma etching. This mechanism is consiste nt with the results s hown in section 3.2.6.1. These particles stick onto the substrate surface after the plasma is turned off. Particles can be produced in many ways, such as flak ing from substrate or chamber walls, metal clustering and polymerization of the gases or substrate materials, condensation of sputtered material, and aerosols from gase s [74-77]. Yellow colored polyimide was found to built-up on the sidewall of the reaction chamber as a result of contamination from other users of the RIE system. This polyimide may flake and become contaminate particles. In addition to c ontamination from chamber built-u p, re-deposited metal atoms, such as Cr and Ni, and polymers formed from CH4/H2 radicals and atoms are all possible sources of primary particles. The mechanism of particle growth du ring RIE has been investigated by many researchers [74-77]. It is believed that the nanometer size crystallites can be formed and may coalesce into particles when the concentratio n of crystallites reaches a critical value. The particles further grow by molecular bonding with surface atoms and radicals from

PAGE 82

67 the plasma and formed primary spherical particles about 0.2 m in size [76]. These primary particles undergo clustering or agglom eration and form large particles about 2~5 m [76]. From the Auger spectra (Figure 3-22), Cr, Ni, and C peaks were found before sputtering and the peaks and residual dots were absent after sputtering. This suggests that the residual dots contained these three elements. In the reversed image etching process, the final layers exposed to plasma etching we re the Cr hard mask and the Ni adhesion layer. It is speculated that these tw o metal atoms combined with the C from contamination and polymerization were bonded onto the nanoparticles that underwent agglomeration and formed the residual dots. From the Auger data (Figure 3-22), no silv er peak was found in the residual dots. A possible reason is that th e silver atoms and the hydroge n or hydrocarbon molecules within the etch gases formed the organomet allic complexes that were removed by the vacuum system. It is also possible that some of the silver atoms re-deposited back onto the substrate and were covered by the molecu lar bonded Cr, Ni, and C elements. As long as the coating of Cr, Ni, and C was thicke r than 30 , Auger el ectrons from the inner portion of the residual do ts would not be detected in the Auger spectra. 3.4 Conclusions Four process methods for photon sieve fabr ication were developed and tested. The advantages and disadvantages of each method were described and compared. First, the reversed image etching method was successful but complicated. It was accomplished by reactive ion etching with a patent ed RIE recipe to pattern Cr hard masks [68]. The reverse image etching method requi red deposition of a chromium film over the

PAGE 83

68 Ag film and more than 40 minutes of highpower reactive ion etch ing (RIE) of silver, which makes this process longer than the other methods. The photon sieves obtained from this method were good, but residual dot s within the open hol es of photon sieves were observed. It is speculated that the residual dots were formed by primary nanoparticles agglomerating during the plasma etching. To simplify the process flow and avoid th e possibility of residual dots formation, the lift-off method was developed. Good phot on sieves were produced by using this method. However, sidewall resi due of silver atoms stuck on the patterned resist limited the deposited thic kness of silver. To avoid the problem of sidewall residue and the use of unstable oxygen plasma in the RIE system, the direct wet etching me thod was studied. The direct wet etching method was simple and fast. However, th e manufacturing result was not promising due to the non-uniform etching rate for different sizes of mask openings. The direct dry etching method was devel oped to solve the non-uniform etching problems of wet etching. P MMA was shown to be a poor mask for argon sputtering due to residual deposits at the edge of holes. A positive e-beam resist, ZEP700, was used on top of the PMMA because of its excellent dry etching resistance. The direct dry etching method combined with ZEP7000 resulted in th e most successful process method in terms of simplicity and repeatability for production of photon sieves.

PAGE 84

69 CHAPTER 4 PHOTON SIEVE PROPERTIES 4.1 Introduction Refractive optics have long been used for imaging, especially for visible light. However, high absorption coefficients for lens materials limit the use of refractive optics for short wavelengths. Diffrac tive lenses, for instance Fresnel zone plates (FZP) and photon sieves (PS), are attractive not only because they can be used to focus high or low energy radiation but also because of their small size and weight. A photon sieve is a diffractive lens compos ed of many pinholes distributed in the all-even or all-odd Fresnel zones. The lens properties of diffraction optics are wavelength-dependent. If photons with wave lengths different from the designed value pass through a diffractive lens, aberration will occur. In this research, multiple patterns of dual-wavelength photon si eves were designed, fabricated and tested to charac terize the lens properties. The fabrication process of direct dry etching with ZEP7000 e-beam resist, desc ribed in Chapter 3, was used. The purpose of this research was to evaluate the advant ages and disadvantages of dual-wavelength PS lenses and to verify the feasibility of comb ining the two diffractive elements for different wavelengths into a single lens. It will be concluded that a si ngle-wavelength PS would be a good focusing filter for polychromatic light since it only focuses the designed wavelength and disperses the rest of the wave lengths. In addition, a dual-wavelength PS is inferior to the single-wavelength PS under monochromatic and polychromatic light sources. However, the dual-wavelength PS is able to focus the image with limited

PAGE 85

70 performance when switching between different light sources and can be used for the imaging device that does not requ ire the filtering of polychrom atic light at the cost of intensity. 4.2 Simulation of Photon Sieves Properties The fundamental theories of Fresnel z one plates and photon sieves have been reviewed in Chapter 2. The photon sieves used in this research were all designed to have a focal length of 50 mm, a lens diameter of 3 mm, a K-factor of 1.2 (the ratio of pinhole diameter over the zone width, i.e., the d / w ratio in section 2.4.1.2), and they were all apodized as discussed below. These fact ors were determined by simulated results reported by O. Shenderova [43-45]. The simulations were performed using MATLABbased software [78]. Fresnel-Kirchhoff diff raction theory [9] was used for the large pinholes, while the analytical far-field based expression [28] was used for small pinholes [45]. The point spread function (PSF) on the image plane of a point source was computed to optimize the lens properties. A small full width half maximum (FWHM) and large intensity of the PSF at the focal point were the characteristics used to determine the quality of the design. 4.2.1 Focal Length and Lens Diameter The two wavelengths that were chosen for the dual-wavelength design were 500 nm and 600 nm. The difference between these two wavelengths is big enough to minimize the influence of each other but is within the visible spectrum for regular photography. Equations 2-12 and 2-13 in Ch apter 2 show that once the wavelength and focal length were determined, the lens diam eter and the resolution (outermost zone width) were dependent on each other. Th e bigger the lens diameter, the narrower the outer-most zone width, the better the resolu tion. One of the simulation results [43]

PAGE 86

71 showed that a photon sieve with a 3 mm diam eter had a smaller PSF FWHM than a 1 mm diameter with the same focal length. A sm aller FWHM represents a better optical resolution as defined by the Rayl eigh Criterion [9] in section 2.3.1. 4.2.2 K-factor The K-factor is the d / w ratio described in Figure 223 and equation (2-20), where d is the pinhole diameter and w is the zone width. According to the simulation results shown in Figure 4-1, 1.2 is a reasonable K valu e where the peak intensity of the PSF is a maximum while the FWHM is acceptably small. Figure 4-1. Simulation result of the optimum K va lue. The horizontal axis is the K value, the vertical axis at left is the FWHM in micrometers, and the vertical axis at right is the intensity in arbitrary units [44]. 4.2.3 Apodized vs. Unapodized Photon Sieves As reviewed in section 2. 4.3, apodization is the proce ss of modulating the pinhole density on each ring of a photon sieve to create a smooth transmission window and thereby suppress the secondary maxima in the diffraction pattern. The simulated PSFs for apodized (modified Gaussian function; s ee below) and unapodized photon sieves are shown in Figure 4-2. The apodized photon si eve exhibited better contrast (Equation 2-

PAGE 87

72 21) despite the fact that the absolute transm ission (not shown) was about one half of the unapodized lens. The low transmission of an apodized photon sieve was mainly due to fewer holes (2722 pinholes for the unapodized photon sieve and only 818 pinholes for the apodized lens). Figure 4-2. Simulated one-dimensional PSFs for apodized and unapodized photon sieves. The light intensity at the vertical axis is in arbitrary units. The absolute intensity for apodized ph oton sieve is lower than the unapodized one [45]. Figure 4-2 also showed that the seconda ry maxima in the PSF of an unapodized photon sieve was suppressed by the apodizati on. The apodization function used for simulation was a modified one-d imensional (1D) Gaussian di stribution function, equal to exp(-axb) [44]. The appropriate valu es of the Gaussian parameters a and b were chosen to reduce the FWHM and increase the intensity for a lens with specific geometric parameters. A typical simulation of the FW HM as functions of a and b is shown in Figure 4-3. It is an example to illustrate that apodization is a compromise between resolution and transmittance. The smallest FWHM was obtained when a = 15 and b = 3.6 while the peak intensity (Imax) was low with the same a and b parameters.

PAGE 88

73 (a) (b) Figure 4-3. A simulation of the PSF (a) peak intensity and (b) FWHM as a function of a and b, the coefficients of a modified Gaussian distribution function, exp(-axb). In this example, the smallest FWHM was obtained when a equaled to 15 and b equaled to 3.6. However with a = 15 and b = 3.6, the intensity became low. This demonstrated that apodization is a compromise between resolution and transmittance [44].

PAGE 89

74 4.3 Photon Sieve Pattern Generation The patterned photon sieves were genera ted by the direct dry etching process described in section 3.2.6.4. The positions of the holes in the PS were generated by entering the desired wavelength, focal length, and lens diameter in to the MATLAB-based software. This software generated the hole pattern of single-wave length photon sieves in a text format containing the X, Y coordinate s of the center of each hole and its radius ( m). The text file was inputted into De signCAD which generated a file for electron beam patterning, that was then loaded in to the NPGS for electron-beam lithography. An example of the text file for a 6-sector dual-wavelength photon sieve (see below) is shown in Table 4-1. Only the fi rst 9 and last 9 pinholes of each wavelength (500 nm or 600 nm) are shown in the table. The pinhole sequence numbers show that pinholes from 1 to 5280 are for 500 nm li ght, and pinholes from 5281 to 8973 (3693) are for 600 nm light. The smallest pinhole diameters for 500 nm and 600 nm wavelengths are 10.14 m and 12.66 m, respectively. The pinhole pattern of a 6-sector dualwavelength photon sieve is show n in Figure 4-4. If only th e 500 nm pinholes or 600 nm pinholes are used individuall y, two 3-sector single-wavel ength photon sieves, shown as 505 and 605 in Figure 4-5, were formed, with th e other 3 sectors remaining unpatterned. There were a total of thirteen (13) desi gns of photon sieves patterns used in this research. These patterns are shown in Figures 4-5 and 4-6 and their designated names are shown in bold-faced when used in the text throughout this chapter. The nomenclature used in the names is that the first number (5 or 6) designates the wavelengths of 500 nm and 600 nm. For single-wavelength photon siev e patterns, the second and third numbers indicated the pattern is a complete photon siev e (10) or a half one (05, 3-sectors). For

PAGE 90

75 dual-wavelength photon sieve patte rns, the sectional designs were named directly with the number of sectors and the concentric desi gns were named with the ratios of open hole area of the two wavelengths. For example, 5in6-75% means that the blue (500 nm) holes are in the center of the c oncentric designed dual-wavelengt h PS with nominally 75% hole area and red holes (600 nm) are in th e outer zone with 25% hole area. Figure 4-4. The DesignCAD pattern of the 6-sector dual-wavelength p hoton sieve. Blue and red pinholes are designed to focus 500 nm and 600 nm wavelengths, respectively.

PAGE 91

76 Table 4-1. Text file of the 6-sector dual-wavelength photon sieve. Only the first 9 and last 9 pinholes designed for 500 nm and 600 nm wavelengths are shown in the table. Pinhole Sequence X (um) Y(um) Radius (um) Wavelength (nm) 1 189.27 40.93 39.3 500 2 143.45 130.09 39.3 500 3 294.51 27.68 25.42 500 4 282.32 88.31 25.42 500 5 257.79 145.07 25.42 500 6 221.99 195.5 25.42 500 7 176.49 237.38 25.42 500 8 370.23 20.74 20.25 500 9 365.32 63.58 20.25 500 ~ ~ ~ ~ ~ 500 ~ ~ ~ ~ ~ 500 5272 195.54 -1414.1 5.26 500 5273 438.12 -1358.66 5.26 500 5274 667.39 -1261.94 5.26 500 5275 -352.06 -1401.42 5.19 500 5276 148.49 -1437.32 5.19 500 5277 631.13 -1299.85 5.19 500 5278 -370.33 -1414.5 5.13 500 5279 386.54 -1410.16 5.13 500 5280 718.71 -1292.84 5.07 500 5281 63.56 202.39 43.05 600 5282 -46.15 207.05 43.05 600 5283 129.41 297.07 27.85 600 5284 64.82 317.49 27.85 600 5285 -2.61 324.03 27.85 600 5286 -69.92 316.41 27.85 600 5287 -134.17 294.95 27.85 600 5288 181.64 363.33 22.18 600 5289 138.23 381.96 22.18 600 ~ ~ ~ ~ ~ 600 ~ ~ ~ ~ ~ 600 8965 1011.03 -1001.61 6.33 600 8966 1169.6 -810.83 6.33 600 8967 1292.63 -595.41 6.33 600 8968 1376.39 -361.9 6.33 600 8969 1418.32 -117.4 6.33 600 8970 971.07 -1068.86 6.23 600 8971 1278.08 -672.27 6.23 600 8972 1430.93 -194.6 6.23 600 8973 738.09 -1265.18 6.15 600

PAGE 92

77 4.3.1 Single-wavelength Photon Sieve Figure 4-5 shows four schematic patterns of single-wavelength photon sieves. The red pinholes represent those designed to focus 600 nm light, while the blue ones are designed to focus 500 nm light. Table 4-2 shows the number of holes and the open hole area for the four single-wavelength photon siev es and one of the dual-wavelength photon sieve, 6-sector. Figure 4-5. Schematic drawing of single-wave length photon sieve pattern s. Red and blue pinholes are the pinholes designed to focus 600 nm and 500 nm wavelength, respectively. Combining 605 and 505 can result the pattern of 6-sector as shown in Figure 4-6. Table 4-2. Number of holes and open hole ar ea for the 4 single-wavelength photon sieves and 6-sector (the combination of 605 and 505 ). The percentage of open hole area are the ratio of open hole area of a specific PS over the one of 610 ( 610 was set to be 100%). 610 510 605 505 6-sector number of holes 10653 7478 5280 3693 8973 open hole area ( m2) 2228306 2219339 1106907 1102851 2209758 % of open hole area 100 99.6 49.7 49.5 99.2 Though the number of holes for 610 and 510 are quite different (7478 in 610 and 10653 in 510 ), the open hole area for the two comple te PS are very close to each other (only 0.4 % difference). Lenses 605 and 505 (3-sector) are half of the complete singlewavelength photon sieves (percent age of open hole area is greate r than 49.5%). The open hole area of the 6-sector is 0.8% smaller than that of 610 due to the sectional boundaries,

PAGE 93

78 where no open holes are placed. The open hole area for the photon si eves is slightly different, but the difference is less than 1% An optical micrograph of a 605 lens is shown in Figure 4-6. Combining the designs of lenses 605 and 505 results in the 6-sector dual-wavelength photon sieve patte rn, as discussed above and shown in Figures 4-4 and 4-7. Figure 4-6. Optical micrograph for the 605 single wavelength photon sieve. 4.3.2 Dual-wavelength Photon Sieve Dual-wavelength patterns were generated with either a sectional or concentric designs. They are shown schematically in Fi gure 4-7. As before, red and blue pinholes are designed to focus 600 nm and 500 nm light, respectively. The dual-wavelength photon sieve patterns were generated by comb ining the hole pattern of the two singlewavelength patterns, 610 and 510 in Figure 4-5, with differe nt sector numbers for the sectional designs or area ratios for the con centric designs. Optical micrographs of the 6-

PAGE 94

79 sector and 5in6-70% lenses are shown in Figure 4-8. The area ratios shown in the concentric dual-wavelength PSs are rounded pe rcentages based on the radii of the areas containing holes for either 500 nm or 600 nm light. The actual ratios of the open hole areas for the 500 nm and 600 nm pinholes are 51.1% for 6in5-50% for 500 nm designed pinholes (48.9% for 600 nm designed pinholes). Figure 4-7. Schematic drawing of dual-wavele ngth photon sieve patterns. Red and blue pinholes are designed to focus 600 nm and 500 nm light, re spectively. The percentage shown in the concentricpattern name i ndicated the area occupied by holes with the wavelength design fo r the center zone. For example, 5in670% means that the blue (500 nm) holes are in the center of the concentric designed dual-wavelength PS with no minally 70% hole area and red holes (600 nm) are in the outer zone with 30% hole area. The actual percent of open area of holes are very close to these nominal values.

PAGE 95

80 Figure 4-8. Optical micrographs of dual-wavelength photon sieves (a) 6-sector (b) 5in670% The red arrows indicate the bo undaries between 500 nm and 600 nm pinholes. 4.4 Characterizations The two primary characteristics used to ev aluate the quality of a photon sieve were the FWHM and peak intensity of the corres ponding point spread function (PSF). The PSF of each photon sieves was measured with a modified Perkin-Elmer 16U grating spectrometer with a charge -coupled device (CCD) camera. The Perkin-Elmer 16U grating spectrometer, the CCD camera, and the measurements of focal length and PSF are explained in the next three sections below. 4.4.1 Perkin-Elmer 16U Gr ating Spectrometer A schematic drawing of the modified Pe rkin-Elmer 16U grating spectrometer is shown in Figure 4-9. It was capable of measur ements in the near-infrared (NIR), visible, and ultraviolet (UV) regions from wavelengths of 2600 nm to 220 nm (3800 cm-1 ~ 45000 cm-1; 0.5 ~ 5.8 eV). The system consists of multiple light sources, a grating monochromator, and a series of mirrors allowi ng collection of transm ission data with two photon detectors or measurement of the PSF w ith a CCD camera. The transmission and the PSF arrangements are shown as (A) and (B), respectively, in Figure 4-9.

PAGE 96

81 Figure 4-9. Schematic drawing of the modified Perkin-Elmer 16U grating spectrometer. Part (A) and (B) are used to measur e transmission and PSF, respectively. The light sources used for NIR to visi ble, and UV regions were a tungsten (W) lamp or a deuterium (D2) lamp, respectively.The tungsten lamp was used to characterize PS lenses designed for 500 nm and 600 nm. The illuminatioin spectra from 496 nm and 773 nm for a W lamp was measured and shown in Figure 4-10. The intensity of light from the W lamp at 600 nm was about 4.6 times stronger than that at 500 nm. The dispersion element inside the monochromator is a blazed reflection grating, and is shown schematically in Figure 4-11. Th e grating equation is expressed as [9]: d (sin m – sin i) = m (4-1) where d is the groove spacing, m is the diffraction angle at mth order, i is the incident angle and is the wavelength. The diffraction a ngles are dependent on the wavelength

PAGE 97

82 resulting in dispersion of th e light. Mirrors increase the path length of the light and therefore the divergence prior to the light reaching the exit slit. Figure 4-10. The measurement result of in tensity versus wavelength for the tungsten lamp used in the optical bench (scan m ode). The relative intensity at 600 nm is about 4.6 times higher than at 500 nm. Figure 4-11. Gratings (a) transmission amplit ude grating (b) blazed reflection grating [9]. The wavelength resolution of the monochrom ator is controlled by the entrance and exit slits. The entrance slit controls the in cident beam size which only allows a very small portion of light to enter the monochromator to ensure that the light rays that strike

PAGE 98

83 the grating are parallel. A stepping motor controls the grating rotation and allows a certain portion of the light spectrum to pass thro ugh the exit slit. Two filters, a highand a low-pass filter, are placed in the optical pathway to create a band-pass filter for the wavelength range of interest, wh ich eliminates spurious signa ls from higher orders of diffraction. The transmission pathway (part (A) in Figur e 4-9) contains a series of mirror and two light detectors (a lead sulfide (PbS) a nd a silicon (Si) dete ctor) but only the Si detector was used for visibl e light in this study. The PSF pathway (part (B)) in Figure 49) consists of a point source aperture of 100 m, a 3 mm aperture, and a CCD camera. The point source aperture defines the point source for measurement of the PSF. The 3 mm aperture restricts the measurement to th e area of a photon sieve. The CCD camera provides a read-out of intensity versus x a nd y coordinates for generation of the PSF as described below. 4.4.2 Charge-Coupled Device (CCD) Camera A CCD is a sensor that consists of grid -like array of coupled capacitors, which can store electric charges after e xposure to light. A schematic dr awing of a CCD is shown in Figure 4-12 [79]. The electric charge gene rated on each capacitor, or pixel, is proportional to the light intens ity impinging on that location. After capturing an image, the first row of capacitors tr ansfer the amount of charge on each pixel to a readout register, which converts the charges to voltage s. The charges are de leted after reading, and the charges from the next row are moved to the readout register. The process is repeated until the charges of th e last row of array been read. The voltages from the array form the two dimensional image.

PAGE 99

84 Figure 4-12. An illustration of the CCD readout mechanism. The white squares are the readout register and are connected to an output amplifier. Charges generated in each row are moved down to the r eadout register and transformed to voltages for display purposes [79]. The CCD camera used in the experime nt is a WinCamD camera with a Sony progressive scan inch CCD th at contains 1360 (H) x 1024 (V) 4.65 m square pixels. It also has a 14-bit (16384 level) analog to digital converter (ADC) which provides better resolution for the input signals. The electronic shutter contro ls the exposure time from 16 to 1048 ms in a 16 ms step. It has two capture modes: full and fast. The full mode gives a pixel size of 4.65 x 4.65 m while the fast mode gives a larger pixel of 9.3 x 9.3 m but takes less time to capture imag es. Only the fast mode (9.3 m pixel size) was used for the measurement in this research. The CCD inside the WinCamD exhibits a saturation irradiance of 0.15 mW/cm2 under a monochromatic light with wavelength of 630 nm and exposure time of 25 ms [80]. Saturation of a CCD is the highest possible number of electrons that a pixel can cont ained and is generally referred to as the “full well” capacity

PAGE 100

85 [81]. Saturation irradiance is the power of incident light per unit area that causes the saturation of a CCD. If the incident intensit y is higher than the sa turation irradiance, a flat-top (saturated intensity) PSF will form as shown in Figure 4-13. The damage threshold of the CCD is a few mW/cm2. Damage threshold is the highest irradiance that a CCD can tolerate without causing permanen t damage [82]. Satu ration irradiance and the damage threshold need to be noted in order to prevent artifact or damage, respectively, to the CCD camera. In this research, all the PSFs we re measured under the normal condition of the CCD camera without saturation. Figure 4-13. Saturated PSF. The flat-top of the PSF indicated the saturation of the CCD camera. The saturated intensity of this 14-bit WinCamD CCD camera was found to be around 15000 (15163 in this example). A sample screen of a PSF measurement ta ken by WinCamD CCD camera is shown in Figure 4-14. The two one dimensional (1-D ) PSFs shown at the bottom represent the intensity profiles across the focused point al ong the X and Y axes, which are shown as a 90o crosshair in the image. The image at the right shows the th ree dimensional (3-D) PSF. The color column at the right side of the 3-D PSF shows the intensity scale from high to low intensity as white pink, red, yellow, to blue.

PAGE 101

86 Figure 4-14. A sample of PSF measurement taken by WinCamD CCD camera. The two one dimensional (1-D) PSFs shown at the bottom represent the intensity profiles across the focused spot along the X and Y axes, which are shown as a 90o crosshair in the image. 4.4.3 Focal Length Characterization As described above, the arrangement shown in part (B) in Figure 4-9 was used to measure the focal length and PSF of photon siev es. Before attaching the photon sieve onto the sample holder, the alignment of the elements was checked by using the 3 mm aperture attached onto a refr active optic lens and focuse d under white (polychromatic) light from the tungsten lamp. This step en sured that the point source image was captured by the approximately 6 x 4 mm CCD chi p. Once the alignment was verified, no transaxial movement (i.e. in the plane of th e PS) was allowed for any optical element. The single-wavelength photon sieve, 610 shown in Figure 4-5, was placed on the 3 mm aperture then attached onto the sample hol der. The placement of the photon sieve onto

PAGE 102

87 the aperture was carried out under an optical microscope to ensure placement in the center of the aperture and that no pi nholes were blocked by the aperture. Since the lens properties of a singlewavelength photon sieves is wavelength dependent, the light source was changed from the polychromatic white light to the monochromatic 600 nm light for measurement of the focal length. As shown in Figure 49 part (B) and the enlarged diagram in Figur e 4-15, the distance between the point source aperture and the photon sieve (object distance, S) was fixed while the distance between the photon sieve and the CCD camera (image distance, S’) was changed for measurement of the focal length. Figure 4-15. Schematic drawing of the relatio nship between object di stance (S), image distance (S’), and focal length (F). h a nd h’ are the heights of the object and the image, respectively. The PSF was measured at each S’ position, then the peak intensity of each PSF was recorded to identify the best focal poin t. After finding the image distance S’ corresponding to the maximum intensity, the fo cal length (F) was obtained by the simple equation [9]: 1/S + 1/S’ = 1/F (4-2)

PAGE 103

88 The PS (e.g. 610 ) was then retested under both monochromatic 500 nm light and white light to characterize the focusing abil ity at different wave lengths. The same procedures were repeated for all of the PS patterns (Figure 4-5 and 4-7) in a similar fashion. For example, for lens 510 the light source was changed from 500 nm to 600 nm and white light accordingly to characterize the focusing ability. 4.4.4 Full Width Half Maximum (FWHM) Characterization The FWHM of the PSF was measured usi ng three light sources (500 nm, 600 nm, and polychromatic white light). The PSF for each photon sieve under each of the three light spectra were obtained at the character istic focal length. This tested the image quality (in terms of FWHM and intensity) of each photon sieves when a single detector (CCD camera in this case) was set to the designed, fixed focal plane. This allowed a direct comparison between the singleand dual-wavelength photon sieves. The PSF from lens 610 tested with monochromatic 600nm light illustrates the principle of obtaining the FW HM, as shown in Figure 4-16. Figure 4-16. A sample PSF (lens 610 ) to show the definition of FWHM. The signal is counted from the noise level (0%) to the peak intensity (100%). The FWHM of the PSF was the width across the signal peak at half of its maximum value.

PAGE 104

89 The PSF consisted of an intensity signal and a background noise. The first 200 data points within the noise level we re averaged to determine the intensity of noise level and was set to be 0% The FWHM of the PSF was the width across the signal peak at half of its maximum value corrected for the noise level. For the FWHM characterizati on, experiences showed that the peak intensity and the FWHM of a PSF were very sensitive to the op tical bench setup and the parameters set in the CCD software, as described below. The first issue was the magnification effect for the PSFs obtained at different object and image distances. The image obtained with the CCD camera located at the focal plane is the image of the point s ource with an aperture of 100 m. As shown by the equation (4-2), a focal length can be obtained by many sets of object and image distances. However, the size of the image is magnified or reduced dependent on the ratio of S’/S, as shown in Figure 4-15. For example, when tw o sets of distances (S’/S), 100 mm/100 mm and 106 mm/95 mm, are used to measure a PSF of a photon sieve, the focal length for both cases is 50 mm; however, the FWHMs obtained from the se t of 106 mm/95 mm is 12% larger than the one from 100 mm/ 100 mm (magnification = 1). To minimize random-error, all photon sieves were tested in the same optical setup and finished in one day. The magnification factor of the FWHMs fo r all the photon sieves was kept constant without any correction. In this research, the trend instead of absolute values of FWHM and intensity was studied. As long as the ma gnification factor remained constant for all measurements, it is not critical to correct it for the data presented below. The second issue was the parameters fo r image capture by the CCD. If the detection system is not saturated, the signa l intensity and the noise level should double

PAGE 105

90 when the exposure time is doubled, and the FWHM of the two PSFs remain unchanged. However, the FWHM increased about the size of 1 pixel (9.3 m in fast-scan mode) when the exposure time was changed from 400 ms to 600 ms. Due to this problem, all the photon sieves were tested with the same exposure time of 800 ms. The characterization of FWHM was repeated the next day with the same optical bench set up and same exposure time to vali date the trend in the experiment results. For the reference purpose, the PSF measured by using a refractive lens with focal length of 50 mm is shown in Figure 4-17 (measur ed in different day). The transmission of refractive lenses is much higher than diffractive lenses. To avoid the saturation problem, only 600 nm light was used for PSF me asurement and the exposure time was set as 200 ms. The calculated FWHM of this measurement is 70 m. Figure 4-17. PSF of the refractive lens with a focal length of 50 mm measured under 600 nm light with a exposure time of 200 ms.

PAGE 106

91 4.5 Results 4.5.1 Focal Length Characterization A typical plot of intensity versus CCD de tector distance from the PS (lens 510 with monochromatic 500 nm light) is shown in Figur e 4-18. As discussed above, the position of maximum intensity was associated with the best focus, which in this case is 106 mm (with the object distance fixe d at 101 mm). By applying the simple equation (4-2), the focal length for 510 under 500 nm light is characterized as 51.7 mm, which is 3.4% larger than the designed focal length of 50 mm. Figure 4-18. Peak intensity of PSFs from 510 with 500 nm light obtained at various image distances. The highest intensity was obtained when the image distance was 106 mm when the object distance was 101 mm, resulting in a focal distance of 51.7 mm. The focal lengths for the two single-wavelength photon sieves ( 510 and 610 ) using 500 nm and 600 nm light are summarized in Figure 4-19. When the 600 nm light passed through lens 610 or the 500 nm light passed through lens 510 the focal length was 51.7mm. The corresponding PSFs are shown in Figure 4-20. When 500 nm light passed

PAGE 107

92 through lens 610 (shown as blue line in Figure 4-19 (a)), the light was focused at a distance greater than 59.5 mm, which is the farthest distan ce the CCD camera can be moved along the optical axis. When 600 nm light passed through lens 510 (shown as red line in Figure 4-19 (b)), the light was focused with a focal length of 42.4 mm. From the simple Fraunhofer diffraction equation (2-3), the longer the wavelength, the larger the diffraction angle. This is true for all diffraction lenses and can be seen clearly in Figure 4-19. The comparisons between the experiment results and the theoretical values for the diffraction angle and focal length are discusse d in section 4-6. The same focal length characteristics were observed for the 3sector single-wavelength photon sieves, 605 and 505 The differences between the complete and half (3-sector) photon sieves were the intensity and FWHM of the PSFs. Figure 4-19. Focal length characterizati on for single-wavelength photon sieves under 500 nm and 600 nm lights. (a) PS 610 (b) PS 510 The red and blue lines indicated the stronger 600 nm and the weaker 500 nm lights, respectively.

PAGE 108

93 Figure 4-20. PSFs at focal point. (a) top view (b) 3-D tilted view for 600 nm light passed through PS 610 ; (c) top view (b) 3-D tilted view for 500 nm light passed through PS 510 The rainbow column in the 3-D tilted view indicates the magnitude of intensity (red to blue: high to low). 4.5.2 Full Width Half Maximum (FWHM) and Peak Intensity of PSFs The trend obtained from the repeated measurement of the FWHM versus wavelength and lens designs were identical. A typical set of data are shown below. The CCD camera was always placed at the measured focal length, which is 50.9 mm for these data. Figures 4-21 shows the top view of the PSFs for each photon sieve under 600 nm light source. In Figure 4-21, no focal spot is detected from single-wavelength photon sieves 505 and 510 This is because of the pinholes in these two photon siev es were not designed to focus the 600 nm light. From the focal le ngth characterization, wh en the 600 nm light passed through pinholes designed for 500 nm, it was focused at a focal length of 42.4 mm, which was 9.3 mm in front of the CCD camera. Thus no focused image was observed on the CCD camera.

PAGE 109

94 Figure 4-21. Top view of PSF for photon si eves under monochromatic 600 nm light.

PAGE 110

95 In Figure 4-21, the PSFs of PS 605 and PS 610 show clear focal spots and the focal spot of 610 is brighter than that from 605 because of the greater pinhole open area of PS 610. The PSFs of the balance of the dual-wavelength photon sieves show focal spots with different side patterns, which were i ndicated with red arrows in Figure 4-21. For example, 2-fold, 3-fold, and 6-fold side pa tterns are found in the PSFs of 4-sector, 6sector, and 12-sector photon sieves, respect ively. For the PSFs of 5in6-50%, 5in6-70%, 6in5-25%, 6in5-50% and 6in5-70% the side patterns become ring-shape due to the concentric designs of photon sieves. The PSFs for photon sieves under 500 nm light are not shown due to the low intensity of the s ource at this wavele ngth (see Figure 4-10). Figures 4-22 shows the top view of the PSFs for each photon sieve under polychromatic white light source. In Figure 4-22, a focal spot and a bright side pattern was observed for every photon sieve, includi ng all singleand dualwavelength designs. Figure 4-22. Top view of PSF for photon si eves under polychromatic white light.

PAGE 111

96 The side patterns were the bright area outsi de the focal spots and were dependent on the distribution of pinholes and the design for two wavelengths. The side patterns of 505 and 605 show the design of the photon sieves (3-s ector) clearly. In addition, the boundaries of each sector of the sectional designed photon sieves are clearly observed for the 4sector 6-sector and 12-sector lenses. It is difficult to dis tinguish the side patterns of concentric designed dual-wavelength photon sieves ( 5in6-50% 5in6-70% 6in5-25% 6in5-50% and 6in5-70% ) from the single-wavelength photo n sieves (510 and 610), since all the side patterns appear to be similar – a bright focal spot with ring-shape side patterns. The PSF of each photon sieve measured under 600 nm, 500 nm, and white lights with intensity scales of 7000, 1800, and 14000 are shown in Figure 4-23, 4-24, and 4-25, respectively. Figure 4-23 PSFs under 600 nm light for all 13 photon sieves.

PAGE 112

97 Figure 4-24 PSFs under 500 nm light for all 13 photon sieves. Figure 4-25 PSFs under white light for all 13 photon sieves.

PAGE 113

98 Only the PSFs along the X-axis are show n and the intensities are on a relative scale, which means that an intensity count of 14000 is two times brighter than 7000. PS 610 has the highest signal intensity unde r 600 nm light (Figure 4-23) while PS 510 has the highest signal intensity under 500 nm light (Figure 4-24). When tested under white light, 610 6in5-70% 6in5-50% and 6in5-25% have almost equal highest intensities, as shown in Figure 4-25. In addition, th e background noise found in Figure 4-25 (polychromatic white light) is much higher (~ 1000 in relative intensity) than the noise in Figures 4-23 (monochromatic 600 nm light, ~ 100 in relative intensity) and Figure 4-24 (monochromatic 500 nm light, ~ several tens in relative intensity ). The FWHMs and peak intensities of each PSF in both X and Y-axes measured with each of the three light spectra were calculated and are summarized in Table 4-3. The FWHMs and intensities from Table 4-3 for all photon sieves under 600 nm, 500 nm, and white light are plotted in Fi gures 4-26, 4-27, and 428, respectively. The FWHMs in Xand Y-axes (FWHM x and FWHM y, respectively), the average (Ave), and the (X x Y)/Ave are shown in the figures (see legend of the figure). The average (Ave) is equal to (FWHM x + FWHM y)/2 while (X x Y)/Ave is equal to (FWHM x x FWHM y)/Ave. The error bar for a ll points are in the range of 10 m, which is nearly twice the single pixel size (fast mode, pixel size is 9.3 m) in WinCamD CCD camera. The PS with cross mark indicates a focal spot was not detected for that PS under the measurement condition. This conditi on can be seen in photon sieves 505 and 510 in Figure 4-26 and 605 610 and 6in5-70% in Figure 4-27. An in tensity curve corrected with the open hole area scale (pink dash line with white dots) for all the PSs under white light is shown in Figure 4-28.

PAGE 114

99 Table 4-3. FWHM and peak intensity at Xand Y-axes for each PSF measured with each of the three light spectra – 500 nm, 6 00 nm, and white lights. “N/A” means that no focused image was formed with the photon sieve under the specific light spectrum. Light Source PS type FWHM ( m) Peak Intensity (nm) X-axis Y-axis Ave X-axis Y-axis Ave 500 505 154 122 138 358 356 357 500 510 123 80 102 1596 1600 1598 500 605 N /A N /A N /A N /A N /A N /A 500 610 N /A N /A N /A N /A N /A N /A 500 4-sector 87 104 96 568 652 610 500 6-sector 87 97 92 603 589 596 500 12-sector 117 98 108 358 299 328.5 500 random 133 77 105 98 120 109 500 5in6-50% 129 95 112 1057 1057 1057 500 5in6-70% 116 82 99 1386 1401 1394 500 6in5-25% 140 89 115 1071 1047 1059 500 6in5-50% 119 162 141 272 286 279 500 6in5-70% N /A N /A N /A N /A N /A N /A 600 505 N /A N /A N /A N /A N /A N /A 600 510 N /A N /A N /A N /A N /A N /A 600 605 122 112 117 1943 1875 1909 600 610 109 93 101 6058 6058 6058 600 4-sector 113 88 101 2502 2502 2502 600 6-sector 99 103 101 2218 2218 2218 600 12-sector 116 123 120 1230 1230 1230 600 random 120 92 106 1591 1591 1591 600 5in6-50% 189 138 164 1038 1038 1038 600 5in6-70% 213 123 168 363 391 377 600 6in5-25% 85 82 84 772 978 875 600 6in5-50% 118 97 108 3631 3631 3631 600 6in5-70% 118 84 101 4437 4437 4437 White 505 176 165 171 3526 3526 3526 White 510 149 119 134 9547 9547 9547 White 605 226 263 245 3492 3432 3462 White 610 141 127 134 12604 12604 12604 White 4-sector 180 157 169 7183 7183 7183 White 6-sector 191 199 195 6807 6783 6795 White 12-sector 211 180 196 4454 4301 4378 White random 161 126 144 3763 3763 3763 White 5in6-50% 149 141 145 9766 9766 9766 White 5in6-70% 155 128 142 9597 9597 9597 White 6in5-25% 158 132 145 12409 12409 12409 White 6in5-50% 148 142 145 12295 12295 12295 White 6in5-70% 139 124 132 12547 12547 12547

PAGE 115

100 Figure 4-26. FWHM and maximum intensit y for photon sieves under 600 nm light. FWHM is the left vertical axis and relative intensity is the right vertical axis. The peak intensity trend line is shown as a green dash line with white dots. Figure 4-27. FWHM and maximum intensit y for photon sieves under 500 nm light. FWHM is the left vertical axis and relative intensity is the right vertical axis. The peak intensity trend line is shown as a green dash line with white dots.

PAGE 116

101 Figure 4-28. FWHM and maximum intensit y for photon sieves under white light. FWHM is the left vertical axis and relative intensity is the right vertical axis. The measured and corrected (by open hol e area) peak intensity trend lines are shown as a green and pink dash lin e with white dots, respectively. Sometimes the focused image of the point source aperture was not round (see Figure 4-29). If only the data in one axis is taken into account, the result may not reflect the real trend in the perfor mance of photon sieves. The se paration between the average and (X x Y)/Ave indicates the difference of the FWHMs obtained from Xand Y-axes. If the focal spot is close to a circle, the FWHM along the X-axis will be close to the one along the Y-axis and the (X x Y)/Ave data points will fall close to the average data points, as shown in Figure 4-29 (a). On the ot her hand, if the focal s pot is not in a round shape, the FWHM in Xand Y-axes will be very different and the (X x Y)/Ave data points will be farther from the Ave data points, as shown in Figure 4-29 (b).

PAGE 117

102 Figure 4-29. Shape of focal spots. (a) focal s pot is close to round sh ape (b) focal spot is not round shape. 4.6 Discussions From the focal length data, the change of focal length is close to 10 mm (20% of nominal focal length) when switching the monochromatic light source from 500 nm to 600 nm or vice versa for a 3 mm single-wavele ngth PS with the nominal focal length of 50 mm. This result indicates that for a dual-wavelength photon si eve tested with a polychromatic light source that contained both 500 nm and 600 nm wavelengths would form only the designed wavelength at the 51.7 mm focal plane. The lens properties of diffractive lenses are known to be waveleng th dependent. For example, for a pinhole located at the edge of a 500 nm designed FZ P (1.5 mm in radius) with a nominal focal length of 50 mm under 500 nm light, the diffraction angle is 1.72o. The theoretical calculation of diffraction angle (E quation 2-3) will change to 2.06o and the focal length (Equation 2-13) will shift to 41.7 mm when th e incident wavelength is changed to 600 nm. From the experiment data, th e diffraction angle changed from 1.66o to 2.03o and the focal length shifted from 51.7 mm to 42.4 mm when the incident wavelength changed from 500 nm to 600 nm. This comparison i ndicates that the measured results are consistent with the theoretical calculati ons. The very large focal length difference

PAGE 118

103 resulted in a large chromatic aberration. From the result of focal length characterization, the longitudinal chromatic aberration was 9.3 mm for 100 nm wavelength differences. The measured focal length, 51.7 mm, was sli ghtly different from the designed focal length, 50 mm, by a 3% variation. This variat ion may come from two sources, different wavefront shapes and substrate refraction, as described below. First, in the simulation, the wavefront of incident light was assumed to be planar. However, the wavefront of the incident light in the optical be nch was slightly spherical (fro m a point source with finite distance) with a half angle about 1o of the maximum cone of light picked up by a photon sieve. Second, the refraction of glass substr ate was ignored in the simulation; however, the glass substrate was about 1 mm thick with a refractive index of 1.5 in the real sample. The diffracted light may not focus on the desi gned focus point after being refracted by the glass substrate. It is possible that the 3% variation in the focal length measurement is caused either by the slightly different wave front shapes or by the inconsistency of substrate refraction between simulation and measurement. The focal length characterization also help ed to understand the formation of image patterns for the photon sieves. For instance, pl otting the characteristic light rays of 600 nm light passed through the 500 nm and 600 nm designed pinholes for dual-wavelength photon sieves 6in5-50% (Figure 4-30 (a)), a ring pattern around the focal spot is formed which matches the image observed during the testing. For PS 6in5-70% since the ratio of 500 nm designed pinholes is small (25%), th e intensity of this portion of light rays is weak, thus the ring pattern becomes faint and not visible in the image observed during the testing, as shown in Figure 4-30 (b).

PAGE 119

104 (a) (b) Figure 4-30. Characteristic light rays of 600 nm light passed through (a) 6in5-50% and (b) 6in5-75% and explained the formation of ring pattern observed in the images. Thin lines represent weak in tensity. Red and blue sections in PS represent the pinholes designed to focus 600 nm and 500 nm light, respectively. When plotting the same characteristic light rays for PS 5in6-50% as shown in Figure 4-31, a smaller ring pattern is formed and matches the image observed for that photon sieve. For PS 5in6-50% the pinholes designed for 500 nm are located at the center of the PS. The geometric relation of the undesigned pinholes (designed for 500 nm) makes the unfocused 600 nm light form a smaller ring pattern when comparing to the PS with 500 nm designed pinholes located at the outer area (i.e., 6in5-50% Figure 430 (a)). The same analyzing technique can be applied to all the photon sieves and explains the PS images obtained for 600 nm monochromatic light shown in Figure 4-21.

PAGE 120

105 From the examples in Figures 4-30 and 4-31, the side patterns (ring shape), were mainly caused by the 600 nm light passed through the 500 nm designed pinholes and focused at the different focal spot as described in above. Figure 4-31. Characteristic light rays of 600 nm light passed through PS 5in6-50% and formed a smaller ring pattern compared to the photon sieves with 600 nm designed pinholes at the central zone. For the images in Figure 4-22 from all PS designs with white light, the rule is similar but more complicated since the lig ht source is polychromatic and the light intensity is much stronger than the monoc hromatic light. When white light passed through the PS 610 the stronger light rays (red line s, 600 nm in wavelength) were focused at the focal plane (51.7 mm, Figure 4-32 (a)). However, when white light passed through the PS 510 the stronger light rays were focuse d at a spot in front of the focal plane (42.4 mm) and the weak light rays (blu e lines, 500 nm in wavelength) were focused at the CCD detector plane which resulted in a less bright focal spot, as shown in Figure 432 (b). Though this analysis gives a simple pred iction of the image formation, it did not explain all the sources that caused the hi gh background noise and side patterns of the images.

PAGE 121

106 (a) (b) Figure 4-32. Characteristic light rays of polychromatic wh ite light which have passed through a PS lens of (a) 610 and (b) 510 Red and blue lines represent light rays with intense 600 nm and weak en intensity 500 nm wavelengths, respectively. Green lines represent the light rays with wavelength in-between 600 and 500 nm. The peak intensity obtained from 610 is higher (red center, 12604 in intensity) than the one obtained from 510 (yellow center, 9547 in intensity). The undiffracted light (zerothorder intensity) for the pinholes located far from the optical axis were projected on the focal plane instead of focused at the focal point (see Chapter 2) which contributed to the high b ackground noise. In addi tion, the light rays from higher order diffraction do not focus at th e focal spot which also give rise to high background noise. A more realistic plot of the characteristic light rays is shown in the Figure 4-33. The image background noise show n in the Figure 4-22 consists of light from undiffracted light rays, higher orders of diffraction, an d light rays passing through

PAGE 122

107 PS pinholes which were not desi gned for that specific wave length. The contribution of each source to background noise is not quantifie d in this research. However, from the results shown in Figure 4-21, if the intensit y of light source is low (monochromatic 600 nm), the effect of undiffracted light rays a nd higher order diffraction is weak since the background intensity is low (~ 100 in relative intensity). Figure 4-33. Realistic sketch of the image formation for a dual-wavelength photon sieve with white light illumination. Undiffract ed light rays, the higher orders of diffraction, and the light rays passed through the pinholes which were not designed for that specific wavelengt h are the sources of high background noise of the image. From data in Figures 4-26 to 4-28, in general, larger FWH Ms correspond to lower focal spot intensities. This is because the source light intensity is spread out over a large area at the focal spot. In Figure 4-26, the average FWHMs of most of the photon sieves illuminated by 600 nm light are ~100 m, except for 5in6-50% and 5in6-70% which are

PAGE 123

108 ~150 m. PS 505 and PS 510 did not focus 600 nm light at a ll. This indicates that the focusing ability and image quality of most of the photon sieves is very similar at the design wavelength. However, the highe st intensity is observed for PS 610 which makes it the better diffractive lens under 600 nm light. In Figure 4-27, the average FWHMs of mo st of the photon sieves illuminated by 500 nm light are again ~100 m except for PS 505 and PS 6in5-50% which are ~140 m (PSs 605 610 and 6in5-75% did not focus 500 nm light). The highest intensity has observed for PS 510 which makes it the better diffractive lens under 500 nm light. From the data shown in Figures 4-26 and 4-27, a couple of conclusions can be drawn. The first conclusion is that the pinholes located at the center zone of the concentric dual-wavelength PSs dominate the performance of these photon sieves. Figure 4-34 shows a comparison of the FWH Ms and focal spot intensities of PSs 6in550% and 5in6-50% under 500 nm and 600 nm illumination. Both photon sieves have equal open area for 500 nm and 600 nm de signed pinholes. When illuminating the photon sieves with 600 nm light, a smaller FWHM and higher intensity were obtained from the PS with the 600 nm designed pinholes located in the center zone ( 6in5-50% ) versus PS 5in6-50% For 500 nm illumination, smaller FWHM and higher intensity were obtained from the PS 5in6-50% (500 nm designed pinholes in the center). Since the central zone is close to the optical axis, the light rays that are diffracted and focused by the pinholes closer to the center are mainly from low or der diffraction, which exhibit stronger intensity than the higher order diffraction (see Ch apter 2 Literature Review). The light rays diffracted and focused by the pinh oles located far from the optical axis are from higher order diffraction, wh ich contribute lower intensity to the focal point intensity

PAGE 124

109 (equations 2-3 to 2-5). Thus the pinholes located in th e central zone dominate the performance of photon sieves. Figure 4-34. Comparison of FW HMs and intensities between 6in5-50% (red center PS) and 5in6-50% (blue center PS) under 500 nm and 600 nm light sources. The pinholes located in the central zone do minate the performance of the photon sieves. The second, under monochromatic light, th e intensity of a single-wavelength photon sieve is better than the dual-wavele ngth photon sieves, while the FWHMs are similar. However, the single-wavelength photon sieves do not func tion at wavelengths 100 nm from the design wavelength. Due to the existence of the two diffraction elements, the dual-wavelength photon sieves ar e capable of focusing two wavelengths of light but at lower intensity (tra nsmission), as shown in Figure 4-35. In Figure 4-28, the result showed that th e concentric dual-wavelength PSs had the same FWHMs and intensities as the singlewavelength PSs under polychromatic white light. However, the sect or designed photon sieves ( 505 605 4-sector 6-sector and 12sector) exhibit larger FWHMs and lower inte nsities as compared to the singlewavelength or concentric dualwavelength designed photon sieves. It is not clear why the sectional designed dual-wavelengt h PS have worse performance.

PAGE 125

110 Figure 4-35. The performance of photon siev es when switching the light sources from 500 nm to 600 nm. X-axis is position in m and Y-axis is relative intensity in arbitrary units. The intensity sc ales are 1800 and 7000 under 500 nm and 600 nm light, respectively. Single-wavelength PSs, 510 and 610 cannot focus the light other than the designed wa velength. Dual-wavelength PS, 6in5-25% can focus two light sources simultaneous ly (focal spots were found in both images) but with limited performance. From the literature review (Chapter 2) the resolution of a photon sieve is controlled by the K factor and the diameter of the pinholes located at the outermost zone. The smallest pinholes for the PS designs in this research have ~10 m in diameter with a K factor of 1.2 which implies that the resolution of the PSs is ~10 m. However, this

PAGE 126

111 resolution effect was not observed in this research. A possible reason is that the PSF measured by the CCD camera is essential a im age of the point source. Since the point source aperture in the optical bench is 100 m in diameter with a finite distance, the FWHM of the PSF measured by the CCD camera will be ~100 m. In addition, the pixel size of the CCD used in this research is 9.3 m, which is close to the theoretical resolution of the PS. Thus the FWHMs obtaine d in this research are indications of the image quality of the point s ource rather than the reso lution of the photon sieves. The overall result shows that a singl e-wavelength PS would be a good focusing filter for polychromatic light since it only focuses the designed wavelength and disperses the rest of the wavelengths. The result al so indicates that the dual-wavelength PS exhibits lower intensity but equal FW HM to the single-wavelength PS under monochromatic and polychromatic light sources The dual-wavelength PS is able to focus the image with reduced intensity when switc hing between different light sources. Dualwavelength PSs can be used for the imag ing device that requ ires filtering of polychromatic light at two wavele ngths at the cost of intensity. 4.7 Conclusions Singleand dual-wavelength phot on sieves (PSs) were design ed and tested in this research project. Based on simulations of the PS properties, the lens di ameter was fixed at 3 mm, designed focal lengt h was 50 mm, K factor ( d / w ratio) was set to be 1.2, and all the photon sieves were apodized by a modifi ed Gaussian function. PS sieves were fabricated having hole sizes a nd spacing appropriate to focus either 500 or 600 nm light, and dual-wavelength PS were created by mi xing the holes for each wavelength in a

PAGE 127

112 sector, concentric or random pattern. The PS sieves were tested in a modified PerkinElmer 16U grating spectrometer with a WinCamD CCD camera. The PSs were tested for focal length, FW HM and maximum intensity of the image of a 100 m point source either monochromatic 500 or 600 nm light, or polychromatic white light from a tungsten halogen lamp. The focal length data show that a clear focal spot was formed with a focal length of 51.7 1 mm when monochromatic 500 or 600 nm light passed through the PSs with pinholes designed for 500 nm or 600 nm, respectively. The measured focal length has a 3% variation of the designed focal length (50 mm). This variation may be caused either by the slightly different wavefront sh apes (planar versus spherical) or by the inconsistency of the substrate refraction between simulation and measurement. When 600 nm light passed through the PS with pinholes designed for 500 nm, the best image of the point source was formed at a focal length of 42.4 1 mm. For 500 nm light through PS with pinholes designed for 600 nm, the focal length was greater than 59.5 mm. From the result of focal length characteriza tion, the longitudinal chromatic aberration was 9.3 mm for 100 nm wavelength differences, resulting in defocused images of the point source at a fo cal plane of 51.7 mm. The experiment data is consistent with the theoretical calc ulation for the focal length shifting. When the CCD camera was placed at the measured focal length of 51.7 mm, a 2-D image was formed of a center focu sed spot with a FWHM of 100-200 m, and intensity patterns over the balance of th e CCD area (6 x 4 mm) which we re termed side patterns. The side patterns were dependent on the PS design and the light spectrum. The side pattern formation can be explained and predic ted by plotting the charac teristic light rays through photon sieves. The hi gh background noise (b right side patter ns) observed under

PAGE 128

113 polychromatic white light was caused by the higher order diffraction, undiffracted light rays, and the light rays diffracted through the non-designed pinholes. For dual-wavelength PSs, the pinholes locate d near the central zone lead to higher intensity of the focal spot without degrading the FWHM. This was attributed to the fact that light rays diffracted a nd focused by the pinholes near the central zone are mainly from lower order diffraction, which exhibit st ronger intensity than those higher order diffraction from outlying pinholes. The FWHM measurements demonstrated that the dual-wavelength PSs focus a lower intensity as compared to single-wavele ngth PSs under either the monochromatic or polychromatic light spectra. However, the single-wavelength PSs were not able to focus the light rays at the non-designed wavelength, while the dual-wavelength PSs were able to focus both monochromatic wavelengths w ith low intensity. The property of high dispersion of a single-wavelength PS for non-designed wavelengths would make it a good candidate for a focusing filter for polychr omatic light. Dual-wavelength PSs can be used for the imaging device that requires filtering of polychromatic light at two wavelengths at the cost of lower intensity. The FWHM data also showed that the focu s of sectional designed PSs were broader and less intense than from concen tric designed dual-wavelength PSs.

PAGE 129

114 CHAPTER 5 CONCLUSIONS 5.1 Photon Sieve Fabrication Four process methods of photon sieve fabr ication were developed and tested as summarized below. The first method, reversed image etching, was successful but complicated. It required depos ition of a chromium film over the Ag film and more than 40 minutes of high-power reactiv e ion etching (RIE) of silver which makes this process more time consuming than the other methods In addition, formation of residual dots within the open holes of the photon sieves was observed. It is speculated that the residual dots were formed by the primary metals/ hydrocarbon particles agglomerating during plasma etching. Contamination from cham ber build-up, re-deposited metal atoms, and polymer formed from CH4/H2 radicals are possible sources of primary particles. More experiments are needed to verify this specu lation about the mechanism for residual dots formation during reversed image etching. To simplify the process flow and avoid the possibility of residual dots formation, a second method, the lift-off met hod, was developed. However, the deposited silver atoms stuck on the sidewalls of the patterned resi st and limited the deposition thickness of silver. To avoid the problem of sidewall depos its and the use of unstable oxygen plasmas in the reactive ion etching (RIE) system, a third method, the direct wet etching method, was studied. The direct wet etching method was simple and fast. However, non-uniform etching rates for different f eature sizes resulted in a poor quality of the photon sieves.

PAGE 130

115 The fourth method, the direct dry etching method, was developed to solve the nonuniform aqueous etching problems. PMMA was shown to be a poor mask for argon sputter etching due to deposits of residual c ontaminants at the edge of holes. A positive electron beam resist, ZEP700, was used to cover the PMMA because of its excellent resistance to dry etching. The direct dry etching method using the ZEP7000 plus PMMA resulted in the most successful process method in terms of simplicity and repeatability for the production of photon sieves. 5.2 Photon Sieve (PS) Properties Singleand dual-wavelength phot on sieves (PSs) were design ed and tested in this research project. Based on simulations of the PS properties, the diam eter was fixed at 3 mm, designed focal length at 50 mm, K factor (the ratio of the hole separation to hole diameter) was set at 1.2, and all the photon si eves were apodized by a modified Gaussian function. PSs were fabricated having hole si zes and spacing appropria te to focus either 500 or 600 nm light, and dual wavelength PSs we re created by mixing the holes for each wavelength in a sector, concentric or random pattern. The PS sieves were tested in a modified Perkin-Elmer 16U grating sp ectrometer with a WinCamD CCD camera. The PSs were tested for focal length, FW HM and maximum intensity of the image of a 100 m point source either monochro matic 500 or 600 nm light, or polychromatic white light from a tungsten halogen lamp. The focal length data show that a clear focal spot was formed with a focal length of 51.7 1 mm when monochromatic 500 or 600 nm light passed through the PSs with pinholes designed for 500 nm or 600 nm, respectively. When 600 nm light passed through the PS w ith pinholes designed for 500 nm, the best image of the point source was formed at a focal length of 42.4 1 mm. For 500 nm light

PAGE 131

116 through PS with pinholes designed for 600 nm, the focal length was greater than 59.5 mm. The measured focal length has a 3% vari ation of the designed focal length (50 mm). This variation may be caused either by the slightly different wavefront shapes (planar versus spherical) or by the inconsistency of the s ubstrate refraction between simulation and measurement. From the re sult of focal length characterization, the longitudinal chromatic aberration was 9.3 mm for 100 nm wavelength differences, resulting in defocused images of the point source at a focal plane of 51.7 mm. The experiment data is consistant with the theo retical calculation for th e focal length shifting. When the CCD camera was placed at the measured focal length of 51.7 mm, a 2-D image was formed of a center focu sed spot with a FWHM of 100-200 m, and intensity patterns over the balance of th e CCD area (6 x 4 mm) which we re termed side patterns. The side patterns were dependent on the PS design and the light spectrum. The side pattern formation can be explained and predic ted by plotting the charac teristic light rays through photon sieves. The hi gh background noise (b right side patter ns) observed under polychromatic white light was caused by the higher order diffraction, undiffracted light, and the light rays diffracted through the non-designed pinholes. For dual-wavelength PSs, the pinholes locate d near the central zone lead to higher intensity of the focal spot without degrading the FWHM. This was attributed to the fact that light rays diffracted a nd focused by the pinholes near the central zone are mainly from lower order diffraction, which exhibit st ronger intensity than those higher order diffraction from outlying pinholes.

PAGE 132

117 The FWHM measurements demonstrated that the dual-wavelength PSs focus a lower intensity as compared to single-wavele ngth PSs under either the monochromatic or polychromatic light spectra. However, the single-wavelength PSs were not able to focus the light rays at the non-designed wavelength, while the dual-wavelength PSs were able to focus both monochromatic wavelengths w ith low intensity. The property of high dispersion of a single-wavelength PS for non-designed wavelengths would make it a good candidate for a focusing filter for polychr omatic light. Dual-wavelength PSs can be used for the imaging device that requires filtering of polychromatic light at two wavelengths at the cost of lower intensity. The FWHM data also showed that the focu s of sectional designed PSs were broader and less intense than from concen tric designed dual-wavelength PSs.

PAGE 133

118 CHAPTER 6 FUTURE WORKS There were some speculative explanations of some of the experiment results in this research that require further study. An exampl e is the mechanism of silver etching with the proprietary RIE recipe [68]. It was speculated that silver organometallic complexes were formed. This should be verified by in-sit u analysis with proper instruments, such as mass spectroscopy. Second, the charging problem in Auger analysis for the residual dots observed during the reversed image etching process can be solved by terminating the etching near the half way point, where the s ilver film is not completely etched. The remaining silver film on the top of glass s ubstrate would serve as a charge dissipation path, which should make the Auger analysis on the surface of a single dot more reliable. With respect to the properties of the 3% difference between the designed and measured focal length may be caused either by the slightly different wavefront shapes (planar versus spherical) or by the inconsistency of the substrate refraction between simulation and measurement. This could be verified by either modifying the simulation equations or adjusting the optical bench set up to create a plan ar wave source. The effect of the substrate refraction could be verified by testing the sample from both sides. It is also important to quantify the various source of the background noise (undiffracted light, higher order diffraction, etc.). This will a llow a better understanding of the complicated diffraction behavior s of photon sieves. The question of why sectional designed PSs are inferior to concentric designed dual-wavelength PSs remains unanswered. Th e major difference between the sectional

PAGE 134

119 and concentric designs is the symmetry of pi nholes distribution. This may be a hint to the answer of this question. In addition, in this research, the e ffect of theoretical resolution (10 m) of the photon sieves was not obse rved and probably was due to the large point source (100 m) with a finite distance and the large pixel (9.3 m) of the CCD camera. Further studies would be necessary to solve these questions It would be very useful to test the ph oton sieves with imaging. Comparing the PSFs with photographs taken with refractive lenses would help to understand the image formation by the photon sieves. It would be very interesting to fu rther investigate the performance of a single-wavelength photon siev e as a focusing filter in an imaging system.

PAGE 135

120 LIST OF REFERENCES 1. Chao, W., Anderson, E., Denbeaux, G. P., Ha rteneck, B., Kiddle, J. A., Olynick, D. L., Pearson, A. L., Salmassi, F., Song, C. Y., and Attwood, D. T. (2003). 20-nmresolution soft x-ray microscopy dem onstrated by use of multilayer test structures:erratum. Opt. Lett., 28 2530. 2. Gil, D., Menon R., and Smith, H. I. (2003). The case for diffractive optics in maskless lithography. J. Vac. Sci. Technol. B, 21 2810-2814. 3. Kipp, L., Skibowski, M., Johnson, R. L., Berndt, R., Adelung, R., Harm, S., and Seemann, R. (2001). Sharper images by fo cusing soft X-ray with photon sieves. Nature, 414 184-188. 4. Kato, M., Maeda, S., Yamagishi, F., Iked a, H., and Inagaki, T. (1989). Wavelength independent grating lens system. Applied Optics, 28 (4), 682-686. 5. Ferriere, R., and Goedgebuer, J. P. (1 983). Achromatic system for far-field diffraction with broadband illumination. Applied Optics, 22 (10), 1540-1545. 6. Bennett, S. J. (1976). Achromatic combin ations of hologram optical elements. Applied Optics, 15 (2), 542-545. 7. Pedrotti, F. L., and Pedrotti, L. S. (1992). Introduction to optics (pp. 30-36). Englewood Cliffs: Prentice-Hall. 8. Meyer-Arendt, J. R. (1989). Introduction to classi cal and modern optics (pp. 247269). Englewood Cliffs: Prentice-Hall. 9. Hecht, E. (2002). Optics (pp. 443-446). San Franci sco: Addison Wesley. 10. Wikipedia. (n.d.). Diffraction. Retrieve d October 19, 2005, from Wikipedia. Web site: http://en.wikipedia.org/wiki/Diffraction 11. MathPages. (n.d.). Huygens’ principle Retrieved October 10, 2005, from MathPages, Physics. Web site: http ://www.mathpages.com/home/iphysics.htm 12. O’Connor, J. J. and Robertson, E. F. (2002). Gustav Robert Kirchhoff biography. Retrived October 20, 2005, from TURNBU LL WWW server, U. of St. Andrew, UK. Web site: http://www-groups.dcs.st -and.ac.uk/~history/Mathematicians/ Kirchhoff.html

PAGE 136

121 13. Nave, C. R. (2005). Fraunhofer diffracti on geometry. Retrieved October 23, 2005, from HyperPhysics, Georgia State U. Web site: http://hyperphysics.phyastr.gsu.edu/hbase/ phyopt/sindoub.html#c1 14. Nave, C. R. (2005). Circular aperture diffraction. Retr ieved October 23, 2005, from HyperPhysics, Georgia State U. Web site: http://hyperphysics.phyastr.gsu.edu/hbase /phyopt/cirapp2.html 15. Weisstein, E. W. (1999). Bessel function of the first kind. Retrieved October 24, 2005, from MathWorld, A Wolfram web res ource. Web site: http://mathworld. wolfram.com/BesselFunctionoftheFirstKind.html 16. Nave, C. R. (2005). Comparison: Fraunhofer and Fresnel slit. Retrieved October 25, 2005, from HyperPhysics, Georgia State U. Web site: http://hyperphysics.phyastr.gsu.edu/hbase/ phyopt/fresli.html#c2 17. Weisstein, E. W. (1999). Fresnel numbe r. Retrieved November 1, 2005, from MathWorld, A Wolfram web resource. Web site: http://scienceworld.wolfram.com/ physics/FresnelNumber.html 18. Fabrizio, E., Romanato, F., Gentili, M., Ca brini, S., Kaulich, B., Susini, J., and Barrett, R. (1999). High-efficiency mu ltilevel zone plates for keV X-rays. Nature, 401 895-898. 19. Cao, Q., and Jahns, J. (2003). Modified Fr enel zone plates that produce sharp Gaussian focal spots. J. Opt. Soc. Am. A, 20 (8), 1576-1581. 20. Kipp, L. (2002). Focusing soft X-ray w ith photon sieves. Retrieved November 20, 2005, from U. of Kiel, Germany. Web site: http://www.photonsieve.de/home.htm 21. Kriz, J. (1974). Phase zone plat e for X-ray and the extreme UV. J. Opt. Soc. Amer. 64 301. 22. Schelokov, I. A., Roshchupkin, D. V., Kondakov, A. S., Irzhak, D. V., Brunel, M., and Tucoulou, R. (1999). Second generati on of grazing-incidence-phase Fresnel zone plates. Optics Communications, 159 278-284. 23. Morgan, B., Waits, C. M., Krizmanic, J., and Ghodssi, R. (2004). Development of a deep silicon phase Fresnel lens using gray -scale lithography and deep reactive ion etching. J. of MEMS, 13 (1), 113-120. 24. Yasumoto, M., Tamura, S., Kamijo, N., Su zuki, Y., Awaji, M., Takeuchi, A., and Takano, H. (2003). Sputtered-sliced fabrica tion of kinoform zone plate for hard Xray focusing. J. Phys. IV France, 104 189-192.

PAGE 137

122 25. Pelka, D. (2003, October). Kinoform-base d diffusers help lighting designers leverage unique LED advantages. Retr ieved December 2, 2005, from SPIE’s oe magazine database. Web site: http://o emagazine.com/fromTheMagazine/oct03/ kinoforms.html 26. Lesem, L. B., Hirsch, P. M., and Jord an, J. A. (1969). The kinoform: A new wavefront reconstruction device. IBM J. Res. Develop., 13 (2), 150-155. 27. Horan, P. (2005). T222/4 Applied optics, module 7: diffractive optical elements lenses. Retrived November 13, 2005, from Resources and downloads, DIT School of Physics, Ireland. Web site: http:/ /physics.dit.ie/resources/physicstech4/ optics/module%207%20B&W.ppt 28. Cao, Q., and Jahns, J. (2002). Focusing analysis of the pinhole photon sieve: Individual far-field model. J. Opt. Soc. Am. A, 19 (12). 2387-2393. 29. Cao, Q., and Jahns, J. (2003). Nonparaxial model for the focusing of highnumerical-aperture photon sieves. J. Opt. Soc. Am. A, 20 (6), 1005-1012. 30. Weisstein, E. W. (1999). Paraxial ap proximation. Retrieved November 25, 2005, from MathWorld, A Wolfram web resour ce. Web site: http://scienceworld. wolfram.com/physics/ParaxialApproximation.html 31. Pfeifer, D. C., and Ferris, L. D. (1973). Optical image formation with a Fresnel zone plate using vacuum -ultraviolet radiation. J. Opt. Soc. Amer., 63 91. 32. Niemann, B., Rudolfph, D., and Schmahl, G. (1974). Soft X-ray imaging zone plate with large zone numbers for micros copic and spectroscopic applications. Opt. Comm., 12 160. 33. Wikipedia. (n.d.). Gaussian blur. Retr ieved December 19, 2005, from Wikipedia. Web site: http://en.wikipedia.org/wiki/Gaussian_blur 34. Graham, D. T., and Cloke, P. (2003). Principles of radiological physics Churchill Livingstone: Elsevier. 35. Menon, R., Gil, D., Barbastathis, G., and Smith, H. I. (2005). Photon-sieve lithography. J. Opt. Soc. Am. A, 22 (2), 342-345. 36. Engel, A., and Herziger, G. (1973). Co mputer-drawn modulated zone plate. Applied Optics, 12 (3), 471-479. 37. Amie, C., Soummer, R., and Ferrari, A. (2001). Interferometric apodization of rectangular apertures – applic ation to stella r coronagraphy. A & A, 379 697-707. 38. Wang, H., and Gan, F. (2002). Phase-shifti ng apodizers for increasing focal length. Applied Optics, 41 (25), 5263-5266.

PAGE 138

123 39. Kasdin, N. J., Vanderbei, R. J., Littman, M. G., and Spergel, D. N. (2005). Optimal one-dimensional apodizations and shaped pupils for planet finding coronagraphy. Applied Optics, 44 (7), 1117-1128. 40. Gao, X., Fei, Z., Xu, W., and Gan, F. ( 2005). Tunable three-dimensional intensity distribution by a pure ph ase-shifting apodizer. Applied Optics, 44 (23), 4870-4873. 41. Ledesma, S., Campos, J., Escalera, J. C., and Yzuel, M. J. (2004). Symmetry properties with pupil phase-filters. Optics Express, 12 (11), 2548-2559. 42. Weisstein, E. W. (1996). Apodization. Retrieved November 11, 2005, from Eric Weisstein’s home page, Th esis: Millimeter/submillimeter fourier transform spectroscopy of jovian planet atomosphe res. Web site: http://www.ericweisstein. com/research/thesis/node37.html 43. Shenderova, O. (2005). Multicolor photon si eves: number of sect ors and symmetry of paraxial point spread function. Privat e project report. International Technology Center, N. Carolina. 44. Shenderova, O. (2004, October). Photon si eves simulation – I. Presentation for private internal project review. International Technology Center, N. Carolina. 45. Shenderova, O. (2004, February). Photon si eves simulation – II. Presentation for private internal project review. International Technology Center, N. Carolina. 46. Smith, H. I. (1996). A proposal for mask less, zone-plate-array nanolithography. J. Vac. Sci. Technol. B, 14 4318-4322. 47. Wikipedia. (n.d.). Chromatic aberration. Retrieved December 19, 2005, from Wikipedia. Web site: http://en.wikip edia.org/wiki/Chromatic_aberration 48. S. Mahajan and Sree Harsha, K. S. (1999). Principles of growth and processing of semiconductors (pp. 408-480). Singapore: McGraw-Hill. 49. O’Hanlon, J. F. (1989). A user’s guide to vacuum technology New York: JohnWiley & Sons. 50. DeVoe, D. (2002, spring). Thin film de position. Retrived November 21, 2005, from ENME 489F Course intruction, Dept. of Mech. Eng., U. of Maryland. Web site: http://www.glue.umd.edu/~ddev/ me489f/slides/2b_deposition_x6.pdf 51. Cotronakis, J., Clarke, M., Lawrence, R., Campbell, J., and Gaw, C. (2004). Continuous defectivity improvements and impact on high-density metal-insulatormetal (HDMIM) capacitor yields. Retrieved November 23, 2005, from International Conf. on Compound Semic onductor Technology, On-line digest, 2004. Web site: http://www.gaasmantec h.org/Digests/2004/2 004Papers/12.3.pdf

PAGE 139

124 52. Mattox, D. M. (2001). Educational guide to vacuum coating processing. Retrieved November 18, 2005, from SVC Educational Program. Web site: http://www.svc. org/EP/EP_FeatureGuide.html 53. Ash, G. (2005) Cryogenic high vacuum pu mp. Retrieved October 29, 2005, from Brookes Automation technology articles. Web site: http: //www.helixtechnology. com/technology/page81.html 54. Operation manual for Inficon deposition controller XTC/2. Inficon Corp. 55. Miller, J. G., and Bolef, D. I. (1968) Sensitivity enhancement by the use of acoustic resonators in cw ultrasonic spectroscopy. J. Appl. Phys., 39 4589-4593. 56. Miller, J. G., and Bolef, D. I. (1968). Ac oustic wave analysis of the operation of quartz-crystal film-thickness monitors. J. Appl. Phys., 39 5815-5816. 57. Lu, C. S., and Lewis, O. (1972). Investig ation of film-thickness determination by oscillating quartz resonators with large mass load. J. Appl. Phys., 43 4385-4390. 58. Inficon (2004). Thin film deposition contro llers and monitors. Retrieved November 16, 2005, from Inficon: product listing. Web site: http://www.inficon.com/ download/en/Thin%20Film%20F amily%20Brochure%2012-04.pdf 59. Conway, J. (2005). E-beam lithography resi st processing. Retrieved November 22, 2005, from Standford Nanofabrication Facil ities: Process, Stanford University. Web site: http://snf.stanford.edu/Process/Lithography/ebeamres.html 60. Dow Corning (2002). FOX (R)-14 flowable oxides. Retrieved: November 21, 2005, from Dow Corning: Product list. Web site: http://www.dowcorning.com/ applications/product_finder/pf_de tails.asp?l1=009&pg=00000037&prod=0233491 7&type=PROD 61. Zeon Chemicals. (n.d.). ZEP7000 technica l report and ZEP7000 info sheet. Retrieved November 20, 2005, from Ze on Chemicals: Products. Web site: http://www.zeonchemicals.com/productgrade.asp?id=234 62. Birnie, D. P. (1997). Combined flow a nd evaporation during spin coating of complex solutions. Journal of Non-Crystalline Solids, 218 174-178. 63. Haas, D. E., and Birnie, D. P. (2001) Real-time monito ring of striation development during spin-on-glass deposition. In X. Feng, L.C. Klein, E.J.A. Pope, and S. Komarneni (Ed.), Sol-Gel Commercializa tion and Applications (pp. 133138). Westerville: Amer Ceramic Society. 64. Birnie, D. P. (2000). Coating quality a nd spin coating. Retrieved December 1, 2005, from Dept. of MSE, U. of Ariz ona. Web site: http://www.mse.arizona. edu/faculty/birnie/Coatings/index.htm

PAGE 140

125 65. Ghandhi, S. K. (1994). VLSI fabrication principles – silicon and gallium arsenide New York: John Wiley & Sons. 66. Brubaker, C. (2004, November 11). Oven/ hot plate bake. mems-talk. Retrieved December 3, 2005, from memsnet.org. Massage posted to: http://mail.memsexchange.org/pipermail/mems-talk/2004-November/014370.html 67. Georgia Insititute of Technology. (n.d.). MSDS of Microposit MF-322 developer. Retrieved November 27, 2005, from Microe lectronics Research Center, Georgia Insititute of Technology. Web site: http://g roverc.mirc.gatech.edu/data/msds/ 273.html 68. VI Microsystem Inc. (2003). Proprietary etching recipe (patent pending) VI Microsystem Inc, Gainesville, FL. 69. Yacobi, B. G., and Holt, D. B. (1990). Cathodoluminescence microscopy of inorganic solids New York: Plenum Press. 70. Brundle, C. R., Evans, C. A., and Wilson, S. (1992). Encyclopedia of materials characterization Boston: Butterworth-Heinemann. 71. Miessler, G. L., and Tarr, D. A. (1990). Inorganic chemistry Englewood Cliffs: Prentice-Hall. 72. Denk, M. K. (2005). Polar organometallic compound Retrieved December 14, 2005, from Denk group: Lecture: Chem 462, University of Guelph, Canada. Web site: http://131.104.156.23/Lectures /CHEM_462/462_Alkali.html 73. Wang, K., Zhang, W., Xian, M., Hou, Y. C ., Chen, X. C., Cheng, J. P., and Wang, P. G. (2000). New chemical and biol ogical aspects of S-Nitrosothiols. Current Medicinal Chemistry, 7 (8), 821-834. 74. Yoo, W. J., and Steinbruchel C. (1992). Kinetics of particle formation in the sputtering and reac tive ion etching. J. Vac. Sci. Technol. A, 10 (4), 1041-1047. 75. Boufendi, L., Hermann, J., Bouchoule, A., Dubreuil, B., Stoffels, E., Stoffels, W. W., and de Giorgi, M. L. (1994). Study of initial dust formation in an Ar-SiH4 discharge by laser induced pa rticle explosive evaporation. J. Apl. Phys., 76 (1), 148153. 76. Setyawan, H., Shimada, M., Hayashi, Y., Okuyama, K., and Yokoyama, S. (2004). Particle formation and trapping behavior in a TEOS/O2 plasma and their effects on contamination of a Si wafer. Aerosol Science an d Technology, 38 120-127. 77. Moriya, T., Nakayama, H., Nagaike, H., Kobayashi, Y., Shimada, M., and Okuyama, K. (2005). Particle reduction and control in plasma etching equipment. IEEE Transactions on Semiconductor Manufacturing, 18 (4), 477-486.

PAGE 141

126 78. Stark, C. (1997). Matalab summary and tutorial. Retrieved December 5, 2005, from Dept. of Mathematics, University of Florida. Web site: http://www.math.ufl. edu/help/matlab-tutorial/ 79. Curtin, D. P. (2006). Image sensors. Retrieved November 18, 2005, from The Home of Short Courses P ublishing Company. Web site : http://www.shortcourses. com/choosing/sensors/05.htm#Types%20of%20image%20sensors 80. Data Ray Inc. (2002). User manual for WinCamD CCD beam imager Boulder Creek: DataRay Inc. 81. Cooper, A. (1996). CCD problems. Retrieved December 15, 2005, from Silicon Owl. Web site: http://www.siowl.com /index.html?CCDproblems/CCDProblems. html 82. Tucker, R. (2001). Damage threshold fo r over illumination. Retrieved December 18, 2005, from CCD-world. Web site: http ://www.ctio.noao.edu/pipermail/ccdworld/2001/000502.html

PAGE 142

127 BIOGRAPHICAL SKETCH Hsiu-hsin Chung was born in Taiwan. She obtained her BS degree in chemistry at National Tsing-Hua University, Hsinchu, Taiw an, in 1994. After worked as a packaging engineer for four years, she enrolled at Sa n Jose State University and received her MS degree in materials engineering in 2004. While she was studying at San Jose State University, she worked as a co-op in th e Packaging Technology Group in the National Semiconductor Corporation for over 2 years. She was admitted to the University of Florida, Department of Materials Scien ce and Engineering, in 2001 and obtained her Ph.D. in 2006. She is a recipient of three FLAVS student poster awards (2003-2005) and she holds two US patents (1998).


Permanent Link: http://ufdc.ufl.edu/UFE0013424/00001

Material Information

Title: Fabrication and Testing of Dual-Wavelength Photon Sieves
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0013424:00001

Permanent Link: http://ufdc.ufl.edu/UFE0013424/00001

Material Information

Title: Fabrication and Testing of Dual-Wavelength Photon Sieves
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0013424:00001


This item has the following downloads:


Full Text












FABRICATION AND TESTING OF DUAL-WAVELENGTH PHOTON SIEVES


By

HSIU-HSIN CHUNG


















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006





























Copyright 2005

by

Hsiu-hsin Chung

































This document is dedicated to my parents and my loving husband.















ACKNOWLEDGMENTS

First of all I would like to thank my advisor, Dr. Paul Holloway, for his guidance,

encouragement, and perseverance in seeing this project to its completion. I would also

like to thank Dr. Rolf Hummel, Dr. Wolfgang Sigmund, Dr. Anthony Brenann and Dr.

David Tanner for being my committee and for their valuable advice.

I would like to thank Dr. Mark Davison for his technical guidance and Dr. O.

Shenderova for simulation input. I would like to acknowledge the Major Analytical and

Instrumentation Center (MAIC) staff for their training on instruments. A special thank

you is due to Kwangje Woo, for his help in photon sieve property characterizations.

I would like to thank all the members of Dr. Holloway's group for their help and

kindness. Many thanks go to Narada Bradman for his great help, inspiring discussions,

and mental support. All the work in process development presented in my dissertation is

a result of the collaboration with Narada. I would also like to thank Philip Chung for his

warm friendship and editorial comments during the writing of this dissertation. Of course

I could not forget Ludie, who always cheers me up at the awful moments of my life

during the past four years.

I would like to thank my wonderful parents, who love and support me without any

condition my entire life. Finally I would like to thank my husband, Yusuf, for his

tremendous support, encouragement, and kindness. Without him being on my side, I

would not have made it to this point in my life.
















TABLE OF CONTENTS



A C K N O W L E D G M E N T S ........................................................................ .....................4

LIST OF TABLES ......... .. ...................................................... .......... viii

LIST OF FIGURES ......... ............................... ........ ............ ix

ABSTRACT ........ .............. ............. ...... ...................... xiv

CHAPTER

1 IN TRODU CTION ................................................. ...... .................

2 LITER A TU R E REV IEW ............................................................. ....................... 3

2 .1 R fraction v s. D iffraction .......................................................................... ...... 3
2.2 D iffraction Theories................... ....... ... .. ............. .. ........ ..... ............... 5
2.2.1 Huygens Principle, Huygens-Fresnel Principle, and Obliquity Factor ........5
2.2.2 Fraunhofer D iffraction ............................................... ........ ............... 8
2.2.2.1 Single slit and double slit ........................ ........ ...................... .8
2.2.2.2 Airy pattern Fraunhofer diffraction from a circular aperture..........9
2.2.3 Fresnel D iffraction........................... .... ........................... ........ ......11
2.3 Frenel Zone Plate (FZP) ............................................................................... 14
2.3.1 Resolution of Image System and Zone Plates.......................................16
2.3.2 Secondary Maxima for Fresnel Zone Plates.......................................17
2.3.3 Am plitude versus Phase Zone Plate ................................. ............... 18
2.4 Photon Sieve ................................................................................... .. .... ..... 21
2.4.1 Advantages of Photon Sieves over Fresnel Zone Plates ..........................23
2.4.1.1 Suppress higher diffraction order and improve focus ....................23
2.4.1.2 Overcoming the limitation of the resolution of FZP........................25
2.4.2 Disadvantage of Photon Sieves over Fresnel Zone Plates.......................27
2.4.3 A podization ........................ .................. .................. ........ 28
2.4.4 Applications of Photon Sieves......................................... ............... 30
2.5 Chrom atic Aberration ............. ..... ................. ... ........................ 31
2 .6 Ju stification of R research ............................................................ .....................32

3 PHOTON SIEVE FABRICATION ................................... ................. 33

3.1 Introduction ............................................. ............. 33









3.2 Process D evelopm ent...................... .... ................... ................... ............... 34
3.2.1 Substrate Preparation ............................................ ........... ............... 36
3.2.2 Film D position ........... ...... ................ .. .. .......... .......37
3.2.2.1 E-beam evaporator: system and operation ....................................37
3.2.2.2 D position controller.................................... ........................ 42
3.2.3 Resist Coating ............... ...... .......... ... ............ ... ............. 43
3.2.3.1 Electron-beam resists ............................................ ............... 43
3.2.3.2 Spin-coating ... ............................................. ........ .. .......... 44
3.2.4 Pattern Form ation ................. ........ .............. .............................. 48
3.2.5 R active Ion Etch (R IE) .............................................. ............... .... 50
3.2.6 Various Process Methods: Procedures and Results............................... 51
3.2.6.1 Reversed im age etching ....................................... ............... 51
3 .2 .6 .2 L ift-o ff ........................................................................................ 5 8
3.2.6.3 D irect w et etching ........................................ ........................ 61
3.2.6.4 Direct dry etching.................. ..... ......... ..................... 63
3 .3 D isc u ssio n s ..................................................................................................... 6 5

4 PHOTON SIEVE PROPERTIES ........................................ .......................... 69

4.1 Introduction ................. ... ................69
4.2 Simulation of Photon Sieves Properties .................................... ............... 70
4.2.1 Focal Length and Lens Diameter .................................... ............... 70
4 .2 .2 K -factor ............. ......... .. .. ................................... .............. ... ..... 7 1
4.2.3 Apodized vs. Unapodized Photon Sieves.............................. ..............71
4.3 Photon Sieve Pattern Generation................................................74
4.3.1 Single-wavelength Photon Sieve................................. .......................77
4.3.2 Dual-wavelength Photon Sieve ...................................... ............... 78
4.4 Characterizations ...................... .. ............... .................... 80
4.4.1 Perkin-Elmer 16U Grating Spectrometer ............................................80
4.4.2 Charge-Coupled Device (CCD) Camera..............................................83
4.4.3 Focal Length Characterization ..................................................................86
4.4.4 Full Width Half Maximum (FWHM) Characterization .............................88
4 .5 R e su lts ....................................................................... .. 9 1
4.5.1 Focal Length Characterization ......................................................... .... 91
4.5.2 Full Width Half Maximum (FWHM) and Peak Intensity of PSFs.............93
4 .6 D iscu ssions .......... ........ .............. .................... .................. 102
4.7 Conclusions .. ......... ......... ............. ............... ................... 111

5 C O N CLU SIO N S ............................................... ............ .............114

5.1 Photon Sieve Fabrication .............. ............ ............... 114
5.2 Photon Sieve (PS) Properties...................................... ........... ..... .......... 115

6 F U T U R E W O R K S ......................................................................... ......... ........... 118









L IST O F R E FE R E N C E S ......................................................................... ................... 120

BIOGRAPHICAL SKETCH ............................................................. ..................127
















LIST OF TABLES


Table p

2-1 Step profiles and their calculated diffraction efficiency .......................................20

2-2 Equations of the apodization functions shown in Figure 2-25..............................29

3-1 Acronyms and abbreviations shown in Figure 3-2.......................................... 36

3-2 Densities and Z-ratios of materials used in the experiment. ................................43

3-3 Experiment parameters of plasma-etching recipes for RIE process....................51

4-1 Text file of the 6-sector dual-wavelength photon sieve. ............... ..................76

4-2 Number of holes and open hole area for the 4 single-wavelength photon sieves
an d 6-sector. ....................................................... ................. 77

4-3 FWHM and peak intensity at X- and Y-axes for each PSF measured with each of
the three light spectra 500 nm, 600 nm, and white lights...................................99
















LIST OF FIGURES


Figure page

2-1 Schematic drawing of Snell's law of refraction. .......... ............ ......................4

2-2 Double-slit diffraction of light reflected from a double wave pattern in water .........4

2-3 Illustration of Huygens' principle for spherical waves........................ ...........

2-4 D iffraction at a sm all aperture......................................................... ............... 6

2-5 The obliquity factor K ( ) ........................................ ................................. 7

2-6 Fraunhofer diffraction through (a) single slit (b) double slit apertures....................8

2-7 Intensity pattern for diffraction from the double slit as shown in Figure 2-6(b)........9

2-8 An Airy pattern recorded on a slide film and then digital-processed.....................10

2-9 Bessel function of the zeroth, first, second, etc. kind ............................................11

2-10 Fresnel diffraction by a single slit........................................................ ... ........... 12

2-11 Comparison between Fresnel and Fraunhofer diffraction through a single slit.......12

2-12 Cornu spiral ............... ......... ...... ....... ........ ............... .......... 14

2-13 Fresnel half period zone for plane wavefront.............. .... .................14

2-14 Dark center and bright center Fresnel zone plates ............................................. 15

2-15 The Rayleigh and Sparrow criteria for resolving the overlapping point images
from tw o distant point sources ...................................................................... ..... 16

2-16 Secondary maxima from a zone plate ........................................... ............... 18

2-17 K inoform Fresnel zone plates ............................................................................ 19

2-18 Three fabrication steps result an eight-phase-level Fresnel lens..............................20

2-19 Quaternary Fresnel zone plate design and SEM image of a fabricated PZP............21









2-20 Schematic drawing of a photon sieve.................................................................... 21

2-21 Diagram showing point-to-point imaging with a photon sieve.............................22

2-22 A photon sieve and a FZP together with experimental and calculated results.........24

2-23 The relation between the contribution of focal amplitude and the ratio of the
pinhole diameter over underlying zone width (d/w ratio) .....................................26

2-24 Some commonly used apodization functions in linear scale.................................29

2-25 M askless, zone-plate-array lithography ....................................... ............... 30

2-26 Chromatic aberration of a refractive lens............... ........ .................... 31

3-1 Schematic drawing of a cross-sectioned photon sieve...........................................33

3-2 Flowchart of various processing methods............................................................35

3-3 Three-state cascade DI water rinse bath with N2 bubblers on the wet bench ..........36

3-4 Schematic drawing of e-beam evaporator system..............................................37

3-5 Photograph of electron-beam deposition chamber and control rack........................38

3-6 Detailed structures inside bell jar of an e-beam evaporator ...................................38

3 -7 S ilv er sp ittin g ...................................................................... 4 1

3-8 Standard deposition monitor (a) and quartz crystal oscillator (b)............................43

3-9 P6700 series spin coaster ....................................................................... 45

3-10 Relationship between the spin speed and thickness .......................................46

3-11 Optical photographs of spin coating defects ................................. ..................... 47

3-12 Photograph of the PlasmaTherm SLR770 ...................... ............................. 50

3-13 Optical micrograph of an apodized photon sieve manufactured by reversed
im age etching m ethod ...................... ...... ............ ................... .. ...... 52

3-14 Process flow of the "reversed image etching" method.......................................53

3-15 SEM micrograph of residual dots within the pinholes after plasma etching of Ag
a n d N i ............................................................................ 5 4

3-16 Schematic drawing of interaction volume for various electron-specimen
in te ra ctio n s ...............................................................................................................5 5









3-17 Residual dots (a) SE image (b) BSE image................................... ............... 56

3-18 Indication of investigated area for Auger spectrum ..............................................57

3-19 Auger spectra from a general area with residual dots ........................................... 57

3-20 Argon sputtering depth profile from the area with residual dots ...........................58

3-21 Process flow of the "lift-off' method................................................59

3-22 Optical micrograph of a photon sieve manufactured by the lift-off method............ 60

3-23 Schematic drawing of sidewall residue........... ................... ................... .............. 61

3-24 Process flow of the "direct wet etching" method ...... .... ..................................... 62

3-25 Optical micrographs of the photon sieve manufactured by direct wet etching........63

3-26 SEM micrographs of the veil-like matter at the edge of holes..............................63

3-27 A photon sieves with clean edge manufactured by direct dry etching method........64

3-28 Process flow of the "direct dry etching" method ................................ ............... 65

4-1 Simulation result of the optimum K value ...................................................71

4-2 Simulated one-dimensional PSFs for apodized and unapodized photon sieves.......72

4-3 A simulation of the PSF (a) peak intensity and (b) FWHM as a function of a and
b ......................................................... .............................. . 7 3

4-4 The DesignCAD pattern of the 6-sector dual-wavelength photon sieve..................75

4-5 Schematic drawing of single-wavelength photon sieve patterns............................77

4-6 Optical micrograph for the 605 single wavelength photon sieve..........................78

4-7 Schematic drawing of dual-wavelength photon sieve patterns .............................79

4-8 Optical micrographs of dual-wavelength photon sieves (a) 6-sector (b) 5in6-70%.80

4-9 Schematic drawing of the modified Perkin-Elmer 16U grating spectrometer .........81

4-10 The measurement result of intensity versus wavelength for the tungsten lamp
used in the optical bench ..............................................................................82

4-11 Gratings (a) transmission amplitude grating (b) blazed reflection grating .............82

4-12 An illustration of the CCD read-out mechanism..........................................84









4 -13 S atu rated P SF ...................................................... ................ 8 5

4-14 A sample of PSF measurement taken by WinCamD CCD camera ..........................86

4-15 Schematic drawing of the relationship between object distance (S), image
distance (S'), and focal length (F) ................................ ................... ...... ....... 87

4-16 A sample PSF (lens 610) to show the definition of FWHM ...................................88

4-17 P SF of the refractive lens .............................................................. .....................90

4-18 Peak intensity of PSFs from 510 with 500 nm light obtained at various image
d ista n c e s ........................................................................... 9 1

4-19 Focal length characterization for single-wavelength photon sieves under 500 nm
an d 6 0 0 n m lig hts ................................................................... 92

4-20 P SF s at focal point............. .... ........................................................ .......... ....... 93

4-21 Top view of PSF for photon sieves under monochromatic 600 nm light ................94

4-22 Top view of PSF for photon sieves under polychromatic white light....................95

4-23 PSFs under 600 nm light for all 13 photon sieves............................ .....................96

4-24 PSFs under 500 nm light for all 13 photon sieves............................ .....................97

4-25 PSFs under white light for all 13 photon sieves........................................... 97

4-26 FWHM and maximum intensity for photon sieves under 600 nm light................. 100

4-27 FWHM and maximum intensity for photon sieves under 500 nm light................. 100

4-28 FWHM and maximum intensity for photon sieves under white light....................101

4-29 Shape of focal spots....................................................................... ......................... 102

4-30 Characteristic light rays of 600 nm light passed through (a) 6in5-50% and (b)
6in5-75% ..................................... ................................. ......... 104

4-31 Characteristic light rays of 600 nm light passed through PS 5in6-50%.................105

4-32 Characteristic light rays of polychromatic white light which have passed through
a PS lens of(a) 610 and (b) 510 ................................. 106

4-33 Realistic sketch of the image formation for a dual-wavelength photon sieve with
w hite light illum nation .......................................................... ............... 107









4-34 Comparison of FWHMs and intensities between 6in5-50% (red center PS) and
5in6-50% (blue center PS) under 500 nm and 600 nm light sources.....................109

4-35 The performance of photon sieves when switching the light sources from 500
nm to 600 nm .................................... ............................... .......... 110















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

FABRICATION AND TESTING OF DUAL-WAVELENGTH PHOTON SIEVES

By

Hsiu-hsin Chung

May 2006

Chair: Paul H. Holloway
Major Department: Materials Science and Engineering

A photon sieve (PS) is a diffractive lens composed of pinholes distributed in a

similar way to the Fresnel zones in a Fresnel zone plate lens. In this research, multiple

dual-wavelength PSs are designed, fabricated and tested to determine the advantages and

disadvantages of combining the diffractive elements into a single lens from two photon

sieves which were designed for different wavelengths.

Both single- and dual-wavelength PSs were fabricated by first electron beam

depositing a 3 nm adhesion layer of nickel, followed by a 100 nm layer of silver on a

glass substrate. In the optimized procedure, the metallized substrate was then coated both

with PMMA and ZEP7000, a positive electron-beam lithography resist with excellent

resistance to dry-etching. After patterning of the underlying polymer and metal films, the

ZEP7000 and polymer were removed to result in the pattern of pinholes in the metal layer

on the substrate that constituted the photon sieve.

Multiple single- and dual-wavelength PS designs were tested using a modified

Perkin-Elmer 16U grating spectrometer with a WinCamD charge-coupled device (CCD)









camera. The photon sieves were apodized and were designed to have a focal length of 50

mm, lens diameter of 3 mm, and a K-factor (ratio of hole spacing to diameter) of 1.2.

The distributions of the two groups of pinholes for dual wavelength PSs were categorized

as concentric and sectional designs. The point spread function (PSF) of each photon

sieve was obtained using the CCD camera. The peak intensity and the full width half

maximum (FWHM) of each PSF were used to evaluate the focusing ability of each

photon sieve.

The measured focal lengths were in the range between 50.9 to 51.7 mm, i.e., very

close to the nominal focal length of 50 mm. The FWHMs and peak intensities data

demonstrated that the focusing ability of a dual-wavelength PS was degraded by about

10% and 50%, respectively, as compared to a single-wavelength PS using either

polychromatic or monochromatic light. When switching between two monochromatic

(500 or 600 nm) light sources, dual-wavelength PSs focused both wavelengths with

limited performance, while the ability of a single-wavelength PSs to focus at the designed

focal length was severely degraded at a wavelengths 100 nm or more away from the

designed value (500 or 600 nm). The fact that PSs are highly dispersive for non-designed

wavelengths would make them good candidates for a simple focusing filter lens for

polychromatic light. Dual-wavelength PSs can be used for an imaging device that does

not require the filtering of polychromatic light, but at the cost of intensity. The results

from concentric dual-wavelength photon sieves also demonstrated that the pinholes

located in the center zone of a photon sieve dominated the lens properties.














CHAPTER 1
INTRODUCTION

Refractive optics has long been used for imaging, especially for visible light.

However, high absorption coefficients for refractive lens materials limit their use at short

wavelengths. Diffractive optics, such as Fresnel zone plates, provides an effective

solution for focusing short wavelength electromagnetic radiation, such as X-rays [1, 2].

In addition to the ability to focus the short wavelength light, diffractive optics also

exhibits potential advantages over refractive optics such as significantly less weight and

less volume.

A photon sieve is a diffractive lens composed of pinholes distributed in a similar

way to the Fresnel zones. Recently, it has been shown that photon sieves can achieve a

sharper focus by suppressing the secondary maxima and higher order diffraction effects

[3], as compared to a Fresnel zone plate. However, the lens properties of diffractive

optics are wavelength-dependent. If a photon with a wavelength different from the

designated value passes through a diffractive lens, chromatic aberration will be observed.

Researchers [4-6] have discussed multiple solutions to correct this chromatic aberration.

Since all of the experimental corrections involve multiple lenses, no single diffraction

lens is free of chromatic aberration.

The goal for this project is to study the properties of a photon sieve that is designed

to focus two wavelengths simultaneously. In this research, multiple dual-wavelength

photon sieves are designed, fabricated and tested to determine the advantages and

disadvantages of combining the diffractive elements from two photon sieves (designed









for different wavelengths) into a single lens. A dual-wavelength photon sieve would

offer significant advantages in many applications. Considering the small size and light

weight, the multi-wavelength photon sieve would be ideal for unmanned aerial vehicles

(UAVs), smart missiles, and construction of a fly's eye.

A background and literature review of the diffraction theory of light and a review

of photon sieve and Fresnel zone plate diffractive lenses is presented in Chapter 2. In

Chapter 3, the process development and four different process methods to fabricate

photon sieves are outlined. Some problems and issues encountered during the photon

sieve fabrication are discussed in Chapter 3 as well. The optical bench set-up, photon

sieves testing and the testing results are described in Chapter 4. Finally, the conclusions

and future works are presented in Chapter 5 and Chapter 6, respectively.














CHAPTER 2
LITERATURE REVIEW

Due to strong absorption of high-energy radiation, refractive lenses have been

replaced by diffractive lenses for focusing X-rays. The properties of diffractive lenses

are wavelength dependent. There have been many efforts [4-6] to create achromatic

diffractive lens systems. However, a true single achromatic diffractive lens has not yet

been achieved, including the designs in this research. The purpose of this research is to

study the lens properties and to develop an understanding of the advantages and

limitations of dual-wavelength photon sieves.

Photon sieves, proposed by Kipp et al in 2001 [3], are a relatively new type of

diffractive lens. Since a photon sieve is a collection of pinholes distributed in Fresnel

zone regions, there is an opportunity to alter the pinhole distribution patterns and to

combine two groups of pinholes that can be used to focus two different wavelengths. In

this review of the literature, the diffractive lens properties already explored will be

reviewed and related to photon sieves. This review of the literature covers the following

topics: (a) diffraction theories, (b) Fresnel zone plate, (c) photon sieve, and (d) dual-

wavelength photon sieves. It is important to note that only the pertinent diffraction

theories are discussed in this review, and the reader is encouraged to consult other

bibliographic references in optics for more detailed studies [7-9].

2.1 Refraction vs. Diffraction

Refraction occurs when waves travel from a medium with a given refractive index

into a medium with another index. The wave changes direction at the boundary between









the two media. The "point of incidence" is the point where the light ray intersects the

surface. The line constructed at this point which is perpendicular to the surface is called

the "surface normal." The angle of incidence (01) and angle of refraction (02) are shown

in Figure 2-1. According to Fermat's principle light travels with the shortest path the

laws of refraction can be derived, such as Snell's law (nl sinO1 = n2 sinO2) [7].


Surface normal




Point of incidence





Figure 2-1. Schematic drawing of Snell's law of refraction.

However, diffraction is the bending and spreading of waves when they meet an

array of obstacles and then undergo interference. The obstacles can be either opaque or

transparent since the wavefront is changed in amplitude and/or phase when diffraction

occurs. A very common example would be water waves causing diffraction of reflected

light by a double-slit in a ripple-tank, as shown in Figure 2-2.












Figure 2-2. Double-slit diffraction of light reflected from a double wave pattern in water
[10].









2.2 Diffraction Theories

To understand diffraction, it is first helpful to recall Huygens' principle, which

explains how wave propagates, and the Huygens-Fresnel principle that explains why no

back wave is formed during the wave propagation. After a brief introduction of how light

propagates based on these principles, the diffraction phenomenon is then discussed.

There are two types of diffraction: Fraunhofer and Fresnel. When the light source and

the observation screen are far apart and light is essentially parallel, the conditions are met

for Fraunhofer diffraction, also known as far-field diffraction. If the observation screen

or light source is moved close to the aperture (less than a few wavelengths), Fresnel

diffraction occurs.

2.2.1 Huygens Principle, Huygens-Fresnel Principle, and Obliquity Factor

In 1678, a Dutch physicist named Christian Huygens, presented the concept of

wave propagation which is known as Huygens' principle [8]. This principle states that

every point on a primary wavefront serves as the source of spherical secondary wavelets

such that the primary wavefront at some later time is the envelope of these wavelets [7,

11]. When a light wave propagates through free space at the speed of light, the light rays

associated with this wavefront propagate in straight lines, as shown in Figure 2-3.

Huygen's principle provides the insight into the nature of wave propagation necessary to

explain how wave theory can account for the laws of geometric optics.

light rays


c wave front at time t+At


wave front at tim e t


Figure 2-3. Illustration of Huygens' principle for spherical waves [11].









However, Huygens' principle does not indicate the direction of the wave

propagation in time. Why does a spherical wave continue to expand outward from its

source, but not re-converge inward back to the source? Augustin Jean Fresnel, a French

physicist, resolved this problem in 1816 by slightly modifying the Huygens' principle [8].

The corresponding Huygens-Fresnel principle states that every unobstructed point of a

wavefront serves as a source of spherical secondary wavelets, and the amplitude of the

optical field at any point beyond the obstruction is the superposition of all these wavelets

[9]. This principle is illustrated in Figure 2-4. Each small arrow shown in Figure 2-4

represents a phasor, which indicates the amplitude and phase of a wavelet. The

amplitude observed at any point in the optical field, such as Po, Pi, and P2, is the algebraic

sum of the individual phasors. Each of the unobstructed points (black dots within the

single slit width AB in Figure 2-4) on the incoming plane wave acts as a coherent

secondary source. When the wavelength of the source is larger than the aperture, the

coherent waves interfere constructively and result in the bright spots at Po, Pi, P2, etc.

The larger the wavelength, the wider the wave spread out. That means if a photon

counter is placed at Po, it will see lots of light. When the aperture is decreased in size or

larger wavelength light is used, the number of photons counted at Pi and P2 increases

even as the counts at Po decreases.

-- Phasor









Figure 2-4. Diffraction at a small aperture. The amplitude observed at any point in the
optical field is the algebraic sum of the individual phasors [9].









In 1883, Gustav Kirchhoff, a Russian theoretical physicist [12], developed a

rigorous theory based on the solution of the Kirchholff s scalar differential wave equation

[9] and introduced the obliquity factor K(O) as shown below:

K(O) = /2 (1+ cos O) (2-1)

where 0 is the angle made with the normal to the primary wavefront vector k. A

schematic drawing of the secondary wavelets affected by the obliquity factor is shown in

Figure 2-5. At point P, the wave amplitude A becomes [8]

A = K(0)Ao (2-2)

where Ao is the amplitude of the light source. K(9) introduces an angular dependence for

the vector k. At 0 = 0, the forward direction, the obliquity factor K(0) = 1. At 0 = 90,

the amplitude falls off to 12 of the original value. At 0 = 180, the backward direction,

K(7n) = 0. This factor expresses theoretically that no back wave is formed during the

wave propagation.













Secondary wavelet

Primary wave


Figure 2-5. The obliquity factor K(0), the gray area, makes the amplitude of the vector k
vary as a function of the angle 0. K(0) = 0 when 0 = n, thus no wave travels
backward during the wave propagation [9].









2.2.2 Fraunhofer Diffraction

2.2.2.1 Single slit and double slit

Fraunhofer diffraction was first proposed by Joseph Fraunhofer in 1823 [9].

Consider a point source very far from a single slit aperture; thus the incident wavefront is

planar. The slit width is d, and the observation screen is also far from the aperture with a

distance D, shown in Figure 2-6(a) [13].




I I




d -" D .- d -... D--

(a) Single slit (b) Double slit

Figure 2-6. Fraunhofer diffraction through (a) single slit (b) double slit apertures [13].

Imagine that three light rays pass through the top, middle, and bottom of the slit in

Figure 2-6 (a). If the paths of the top and middle rays differ by 1/2 X (wavelength), they

will interfere destructively and cancel each other at point y. The middle and bottom rays

will cancel each other because of the same condition. Consequently, if the path

difference between the top and bottom rays is an integral multiple of k, zero irradiance

will be expected at point y of the observation plane. The equation for minima in

Fraunhofer diffraction with a single slit can be written as [13]

d sin 0 = m k m = 1, 2, 3....... (2-3)

When 0 is zero, the light wave passes through the slit without been diffracted and forms

the maximum of the intensity peak which is referred to as zeroth-order maximum (see









Figure 2-6(a)). This "undiffracted light" may cause the background noise and is

discussed in Chapter 4.

However, for a double slit aperture, a X path length difference between the path

lengths of the two slits produces constructive interference; thus maximum intensities will

be observed as predicted by equation (2-3) (Figure 2-6(b)). Combining the single slit

diffraction and double slit interference, the final pattern for Fraunhofer diffraction on a

double slit aperture is shown in Figure 2-7.



S-Single slit













Figure 2-7. Intensity pattern for diffraction from the double slit as shown in Figure 2-6(b)
[13].

2.2.2.2 Airy pattern Fraunhofer diffraction from a circular aperture

When the slit aperture of Figure 2-6 is replaced by a circular aperture in Fraunhofer

diffraction as mentioned in last section, an Airy pattern, named after George B. Airy [9],

will form as a result of the diffraction phenomenon. An Airy pattern, shown in Figure 2-

8, consists of a circular spot, the Airy disk, surrounded by much fainter concentric

circular rings. The Airy disk or the bright center spot is called "primary maximum" and

the rest of surrounded rings are called "secondary maxima" [9].










First dark ring

First bright ring
Second bright ring

Airy disk







Figure 2-8. An Airy pattern recorded on a slide film and then digital-processed. The grid
lines are the result of digitization [14].

The intensity distribution, I(x), of the Airy pattern is written as below [9]:

I(x) = I(0)[ 2Jl(x)/x ]2 (2-4)

where I(0) is the intensity at the center of Airy disk, i.e., the intensity in the zeroth-order

maximum, and Ji(x) is the Bessel function of the first kind, shown in Figure 2-9. The x

variable in Ji(x) is written as [9]

x = kdq/R (2-5)

where k is the wave vector, d is the radius of the circular aperture, q is the radius of the

Airy disk and R is the distance between the aperture and observation screen. The Bessel

function attenuates slowly with oscillations as x increases. Ji(0) = 0 and Ji(x)/x

approaches /2 when x approaches 0 [9]. Since sin 0 = q/R, the larger the diffraction angle

(0), i.e., the higher diffraction order (m), the higher the q/R, thus the larger the x value.

From equation (2-4), the larger x value results in a smaller I(x), i.e., the lower intensity.

From equations (2-3) to (2-5), the diffraction intensity diminishes when the diffraction

order is high.










dark ring


1>
0.8
0.6
0. 4
0.2: /


----- Second dark ring


-0.2"
4k~ I


Figure 2-9. Bessel function of the zeroth, first, second, etc. kind [15]. Only the Bessel
function of the first kind (J1 (x), red solid curve) is used to calculate the
intensity of the Airy pattern.

From Figures 2-8 and 2-9, the first dark ring corresponds to the first zero of the

Bessel function, i.e., Ji(x) = 0 when x = 3.83. The radius q of the first dark ring can be

equated to the boundary of the Airy disk [9]:

q = 1.22 RX/2d (2-6)

where R is the distance between aperture and observation screen, X is wavelength, and d

is the radius of the circular aperture. For a lens focused on the observation screen, R can

be replaced with the focal length,J of the lens.

The Airy pattern causes blurring of images from a point source. For a refractive

optical system with an aperture, if the blurring is larger than that produced by aberrations

(spherical, chromatic, astigmatism, etc.) of the system, the imaging process is said to be

diffraction-limited and the image is the best that can be obtained with that aperture.

2.2.3 Fresnel Diffraction

Though the diffraction for the research of dual-wavelength photon sieves is

categorized as Fraunhofer (far-field) diffration, it is helpful to understand the difference

between Fraunhofer and Fresnel diffractions and to distinguish the two diffractions.










Fresnel diffraction is also called near-field diffraction. It occurs when either the

source or the observation screen is close to the aperture (the distance is in the range of

few wavelengths) and the wavefront is essentially spherical. A schematic drawing in

Figure 2-10 indicates the Fresnel diffraction geometry for a single slit aperture. The

appearance of the diffraction pattern is similar to that from a Fraunhofer single slit except

that the intensities at the minima are not zero. A comparison between Fresnel and

Fraunhofer diffraction patterns is shown in Figure 2-11.


spherical I
wavefront




P.
Source

observation


------------------- ------------~-----------
I screen


a b
snge slit


Figure 2-10. Fresnel diffraction by a single slit [8].



5111 vidib




0,1
Fresnel Piaramers for cal tlaties
Calculation using
Cornu
O.0f Spiral"

Fraunhmoer Diffraction

Ab-l .84 mme o aIais or 500 am

Figure 2-11. Comparison between Fresnel and Fraunhofer diffraction through a single
slit. The minima in Fresnel diffraction pattern is not zero in contrast to
minima in Fraunhofer diffraction [16].









The intensity, I, of Fresnel diffraction at a single slit can be written as [8]

I = /2 [ab, / (a + b)] [( J cos /2 u 2 d u)2 + [( sin /2 ) 1 2 d u)2] (2-7)

where u is the variable of a function related to the phase difference between rays, which

can be written as [8]

v = h V 2(a + b)/ab, (2-8)

where X is the wavelength, a and b (Figure 2-10) are the distances of the source to

aperture and aperture to observation screen, respectively. If we assume [8]

x = J cos 1/2 7t 2 d u (2-9)

y = sin /2 7 U 2 d U (2-10)

equation (2-7) can be rewritten as

I = 1/2 [abk / (a + b)] (x2 + y2) (2-11)

where x and y are known as Fresnel's integrals. When plotting x versus y, a spiral curve

known as the Cornu spiral shown in Figure 2-12 can be obtained. The two eyes of the

spirals located at (0.5, 0.5) and (-0.5, -0.5) represent image plane points at infinity.

Depending on the Fresnel diffraction geometry, values of a, b, h, and X will decide the

value of u. At specific u, the corresponding x, y values can be found from the Cornu

spiral and then the relative intensity of the Fresnel diffraction pattern can be calculated.

A dimensionless parameter, the Fresnel number (F), can be used to categorize the

diffraction types. As mentioned in Figure 2-10, F = 4h2/b where h is half of the

aperture width, k is the wavelength, and b is the distance between observation plane and

aperture. When F << 1, diffraction is of the Fraunhofer type; when F > 1, the diffraction

regime becomes Fresnel [17].











.6
: : : : .t. : : 1..5.I -: :



----------- ----- ------ --- -- I ---------i ....--


T 6 5 4---- ----------- 2 0-----
i !.6 .5 !.4 i !
2 .4 5 .6
!. ..... .... ...... i .....I...






1: :




Figure 2-12. Cornu spiral. The coordinates x and y are the Fresnel's integrals [8].

2.3 Frenel Zone Plate (FZP)
-- -- ------ ------ ---- --- --- ...... ...... "-... -". -----














Consider a light source incident upon a circular aperture from infinity; i.e., the

incident waves are planar and not spherical. After passing through the aperture (Figure

2.13), the light will reach point Po at a distance b, from the aperture. This circular
----- L -j -- .... .... i---- -- -- --- -- .... ----- -------- -- .... ------.. -----















aperture can be divided into half-period zones, where each zone is a multiple of a half

wavelength away from Po, as shown in Figure 2-13.


b+3(' X)
b+ 2( X)
b+'X


Figure 2-13. Fresnel half period zone for plane wavefront. Each zone is a half
wavelength away from Po [8].

Thus b + 12 k, b + 2 (1/2 ), and b + 3 (1/2 ) represent the boundaries of the first, second,

and third zone, respectively. The radius of the mth boundary (Rm) can be written as [9]









Rm2 = (b + /2 mX)2 b2 (2-12)

The area of each zone is approximately 7rbk. However, the width of each zone (w) varies

according to the radis of the zone. The intensity observed at Po is the sum of the

contribution of the wavelets originating from each zone. Because each zone is 1/2 X away,

the contribution from the adjacent zone is opposite in phase (i.e., a phase shift of r). The

light diffraction from adjacent zones will therefore cancel each other and the overall

contribution at Po is null. By eliminating the contribution from all odd or even zones, a

dark or bright center Fresnel zone plate (FZP) will be obtained, respectively (see Figure

2-14). The overall intensity at Po will be brighter as the number of zones is increased.













Figure 2-14. Dark center and bright center Fresnel zone plates. The dark areas are
opaque to the wavelength of the light [9].

Because the incident light is from infinity, b is actually the focal length (f)and Po is the

focal point of this Fresnel lens. The primary focal length,J is therefore [9]:

f= b = Rm2/mX (2-13)

It is apparent that the focal length depends strongly on the wavelength. For example, for

a 500 nm designed FZP with a nominal focal length of 50 mm under 500 nm light, the

focal length is shifted to 41.7 mm when the incident wavelength is changed to 600 nm.

This focal length shifting is verified with the testing results presented in Chapter 4.








2.3.1 Resolution of Image System and Zone Plates

The resolution of a lens is the minimum distance between two objects that can be

distinguished. Considering two equal-irradiant and distant point sources passing through

an aperture of an optical system, the Airy patterns formed from these two point sources

are either overlapped or clearly resolved. Depending on the degree of pattern overlap,

two resolution limits, Rayleigh and Sparrow criteria, can be applied, as shown in Figure

2-15. The Rayleigh criterion is applied when the center of one Airy disk falls on the first

minimum of the Airy disk of another point image. When the distance between the two

point sources further decreases, the central dip that appears in the Rayleigh criterion will

finally disappear which is defined as the Sparrow criterion. The spatial resolution, 6m,

based on the Rayleigh criterion is then written as [9]

6m = 1.22 fA/D (2-14)

where f is the focal length, h is the wavelength of light, and D is the diameter of the

aperture.



00 ( O 0
a
FWHM




W FWHMHM


clearly Rayleigh Sparrow not
resolved Criterion Criterion resolved

Figure 2-15. The Rayleigh and Sparrow criteria for resolving the overlapping point
images from two distant point sources. The gray circles represent the Airy
disks of the two point sources [9].









However, for a FZP, the resolution is controlled by the outermost zone width [3,

18, 29]. The optical resolution of a zone plate is given by [18]

6m = 1.22 ArN/m (2-15)

where N is the outermost zone index, ArN is the outermost zone width and m is the

diffraction order [18].

Due to the testing set-up in this research (described in section 4-4), the resolution of

the photon sieves was not determined and is discussed in Chapter 4. In this research,

FWHM and intensity were used to characterize the measured point spread function (PSF)

and the image quality instead of determining the resolution of the photon sieves.

2.3.2 Secondary Maxima for Fresnel Zone Plates

As described above, an Airy disk is observed from Fraunhofer diffraction from a

circular aperture. The intensity attenuates as predicted by the Bessel function of the first

kind when light passes through a circular aperture, where the transmission abruptly

becomes zero at the edge of the aperture. For a Fresnel zone plate, the amplitude

contribution of each ring is equal at the focus. When this contribution drops abruptly to

zero beyond the outermost ring, an oscillation of light intensity occurs just as shown in

the Airy pattern (Figure 2-8). Secondary maxima is the collection of first, second, and

higher order bright rings in the Airy pattern resulting from diffractions from the many

concentric circular zones of a FZP. The secondary maxima will cause blurring of the

image. It also increases the level of background noise and reduce the contrast of the

image. The suppression of secondary maxima can be achieved by applying apodization

technique which is discussed in sections 2-4-1-1 and 2-4-3. A schematic drawing of

secondary maxima is shown in Figure 2-16.
































Figure 2-16. Secondary maxima from a zone plate. The vertical scale is a logarithm of
intensity and the horizontal axis is the displacement from the focal point [20].

2.3.3 Amplitude versus Phase Zone Plate

The zone plate described above is called an amplitude zone plate. The light passing

through all odd or even zones are blocked, which means half of the light is not

transmitted. To increase transmission, Kirz et al [21] proposed a method to shift the

phase of the light transmitted through the opaque regions of the FZP by using the proper

thickness of a transparent material. This particular design is called a phase zone plate

(PZP). Researches [22-24] combined the concepts of a phase-shift zone plate and a

kinoform grating [25, 26] to create a kinoform zone plate where the original light with

destructive phases were shifted by + 1/2 X (7r) and resulted in a totally constructive Fresnel

zone plate, as shown in Figure 2-17. The convex kinoform zone plate is equivalent to the

concave type, which is the most common type.













Transfer into
grating

Fresnel lens

/ 7



Figure 2-17. Kinoform Fresnel zone plates. The convex Fresnel lens is equivalent to the
concave lens in properties. They all shift the light phase by 7 between the
regions [22, 27].

Also in 1999, Fabrizio et al [20] utilized the same approximation of Schelokov's

ideal continuous phase-shifting profile (ideal kinoform) but modified the materials of the

zone plate to make it totally transmitting rather than reflecting. In order to approach the

ideal kinoform profile, a stepwise function was created in the profile for each zone (see

Figure 2-18, 19). The efficiency (rim of the mth diffraction order) of the Fresnel zone

plate was shown to be equal to [18]

= A2/C2 (2-16)

where A is the observed amplitude and C is the intensity of the incoming field. This

equation can be further expressed as [18]

Tri = 2 [1-cos(27rm/L)](L/m)2 (2-17)

where L is the number of profile steps. Table 2-1 shows the calculated diffraction

efficiency with the various step-profiles of the lens. Diffraction efficiency is determined

by the ratio of the power of the diffracted light beam to the incident power of the beam

while the transmittance is the fraction of light at a specific wavelength that passes

through a Fresnel zone plate.










Table 2-1. Step profiles and their calculated diffraction efficiency [27].
Step profile Efficiency (%)

Theoretical (kinoform) 100

Linear 99

16-level 98.7

8-level 95

4-level 81.1

2-level 41

Amplitude 10


The diffraction efficiency of an amplitude zone plate is only 10%. If we make the

originally opaque zone transparent but with a 7r phase shifting, the diffraction efficiency

can be increased to 41% (a binary phase zone plate). The profile steps are proportional to

the number of fabrication steps with the following relationship [27]:

# of profile steps = 2n (2-18)

where n is the number of masks or fabrication steps. Figure 2-18 shows that three masks

(or fabrication steps) could result an eight-phase-level PZP. The profile of a PZP is

closer to the ideal kinoform when the number of steps is increased.

2 PHASE LEVELS
MASK


PATTERN PR

ETG '

ALIGN MASK
PATTERN PR

ETCM

ALGN MASX
PATEF-N

ETCH


I PHASE LEVELS

.-------- -LE--.---


I PHASE LEVELS
-i"----...rl-,


Figure 2-18. Three fabrication steps result an eight-phase-level Fresnel lens [27].










A schematic drawing of working principle and a scanning electron microscope

image for a quaternary Fresnel zone plate are shown in Figure 2-19. In a quaternary

phase zone plate, each level in a single zone makes incident light phase shift by 1/4 X and

results in total constructive interference and a higher efficiency (81% from Table 2-1).

Wavelength X)



Incomingave

waA ..-- ...._ -J-------- -


NI phase shifter
Sia I4 membrane

Figure 2-19. Quaternary Fresnel zone plate design and SEM image of a fabricated PZP
[18].

2.4 Photon Sieve

As described above, a photon sieve is a diffractive lens composed of pinholes

distributed in the Fresnel zones, as shown in Figure 2-20. Kipp et al proposed this

concept in 2001 [3]. However, the photon sieve pattern shown by Kipp et al was

consisted of 5646 randomly distributed holes and was very complicated. The detail

design rules of the complicated photon sieve were not described in their paper.












Figure 2-20. Schematic drawing of a photon sieve. Each blue spot is a hole through an
opaque film.









Analogous to the concept of a Fresnel zone plate, the pinholes have to be

positioned properly to fulfill the criterion for constructive interference. That requires that

the optical path length (OPL) from the source via the center of the holes to the focal point

be an integral number of wavelength, k. This criterion can be expressed as the equation

shown below [3]:


r,2 + +P +q2 = p+q+nA (2-19)


where is the distance between the source and the photon sieve, q is the distance

between the photon sieve and the focal point, and rn is the distance between the center of

the holes and the optical axis. A schematic drawing of the relationship between source,

photon sieve, and focal plane is shown in Figure 2-21.




.,










Figure 2-21. Diagram showing point-to-point imaging with a photon sieve [3].

The theoretical analysis of focusing for photon sieves in the far-field [28] and

nonparaxial modes [29] were published by Qing Cao et al in 2002 and 2003, respectively.

Nonparaxial mode refers to the angle between light rays and the optical axis, 0, being

large. The paraxial approximation (sin(0) z tan(0) z 0 when 0 is small ) [30] is no longer

valid for the calculation of the OPL.









2.4.1 Advantages of Photon Sieves over Fresnel Zone Plates

Fresnel zone plates have been used to focus X-ray radiation for many years [1, 2,

31, 32]. However, ring-shaped secondary maxima are usually observed at the focal plane

and cause blurring of the images from the zone plates. In addition, the resolution of

Fresnel zone plates is controlled by the width of the outermost zone. Processing

limitation may exist when approaching high-resolution zone plates. Photon sieves

provide an opportunity to suppress the secondary maxima for sharper focusing of images

and also overcome the process limitation of the resolution of Fresnel zone plates [3].

These two advantages are reviewed in the following sections.

2.4.1.1 Suppress higher diffraction order and improve focus

It is well known that side bands or secondary maxima are produced if the light

passes through a rectangular type transmission window [3, 14, 20]. In a binary amplitude

zone plate, the transmitted zones stopping abruptly at the outermost zone represents a

rectangular transmission window. Ring shaped secondary maxima are formed and cause

blurring of images. Blurring is defined by the standard deviation of the intensity

distribution. For example, if the type of distribution is Gaussian, the degree of blur is

then determined by the standard deviation (c) of the Gaussian distribution (normal

distribution) known as Gaussian blur [33, 34]. The greater the standard deviation, the

higher the degree of blur and the greater the loss of resolution. In this research, the

degree of blur was not characterized. Photon sieves, proposed by Kipp et al [3], suppress

the secondary maxima and higher diffraction orders by modulating the pinhole density on

each ring of the photon sieve to implement a smooth transmission window. This

technique is called "apodization" and is reviewed in section 2-4-3. Figure 2-22 shows a

photon sieve and a zone plate together with the experimental and calculated intensities at










the focal plane [3]. Comparing the intensities measured at focal plane, the secondary

maxima (concentric ring patterns shown in Figure 2-22 f) observed in the zone plates

were suppressed by two orders of magnitude (calculated result) when using photon sieves

as the focusing element. This property was not examined in the research of dual-

wavelength photon sieves; however, it was verified by the simulation result demonstrated

in section 4-2-3.


(a) I (b)

























104' -- -- i -- -- 104" i -- -- i ---- -
-0.5 0 0.5 -0.5 0 0,5
x (mm) x (mm)

Figure 2-22. A photon sieve and a FZP together with experimental and calculated results.
(a) photon sieve (b) FZP (c) smooth transmission window (d) rectangular
transmission window (e) intensity at focal plane for photon sieve (f) intensity
at focal plane for FZP (g) calculated intensity for photon sieve (h) calculated
intensity for FZP. The secondary maxima shown in FZP was suppressed
when changing the focus element from FZP to photon sieve [3]. The same
phenomenon is observed from the simulation result demonstrated in section 4-
2-3.









2.4.1.2 Overcoming the limitation of the resolution of FZP

In addition to suppressing the secondary maxima, photon sieves also provide an

opportunity to overcome the limited zone plate resolution. The intensity at the

observation plane is determined by the net contribution of interference. Kipp et al [3]

produced the first photon sieve in 2001 and proposed the theory of the relation between

the diffraction amplitude and the dlw ratio (i.e., the K factor in Chapter 4), where d is the

pinhole diameter and w is the zone width of an underlying zone plate. This relation is

shown in Figure 2-23 In the inset of Figure 2-23, the black and white strips represent the

zones with destructive and constructive interference, respectively. Four pinholes, A, B,

C and D, with various diameters are drawn and the dlw ratios for the 4 pinholes are 1, 1.5,

4 and 4, respectively. The calculated curves of constructive (solid gray line) and

destructive (dashed gray line) interference and the total contribution of the two

interference (solid black curve) are shown in Figure 2-23. Both pinholes C and D have

the same pinhole diameter and dlw ratio, however, the pinhole C is centered on a white

zone thus the black area within the pinhole is greater than the white area which results in

a net destructive interference therefore a negative intensity. Once the center of the

pinhole shifts to a black zone (pinhole D), the white area within the pinhole dominates

the interference and a net positive intensity will be observed at the focal plane.

The spatial resolution (6m) of a traditional zone plate is decided by the outermost

zone width (w). However, for a photon sieve, the spatial resolution is limited by the

smallest effective width (wffmin), which is determined by the maximum d/w ratio [3]:

6m = effmin = dmin / (d/)max (2-20)









This equation implies that at a dlw ratio designed to be 1.5, a photon sieve with a smallest

pinhole diameter of 45 nm has the same spatial resolution as a FZP with the outermost

zone width of 30 nm. As the dlw ratio increases, the diameter of the smallest pinholes of

a photon sieve can also be increased while still maintaining the same spatial resolution.












i X
3 ~ x Constructive ---- ,r
Sn iDestuctive
ruc


0 2 4 6 B
d/w

Figure 2-23. The relation between the contribution of focal amplitude and the ratio of the
pinhole diameter over underlying zone width (d/w ratio). As long as the white
area within a pinhole is larger than the black area, the net intensity at focal
plane will be positive [3].

Menon et al [35] reported that when using a photon sieve in a maskless photon-

sieve-array lithographic system, the size of the single-exposure focal spot was controlled

by the K factor (d/w ratio) when the smallest pinhole diameter was fixed. The larger the

K factor, the smaller the focal spot, which is consistent with the theory proposed by Kipp

et al [3]. Neither Kipp et al [3] nor Menon et al [35] mentioned the limit of K factor.

From the simulation result shown in section 4-2-3, the focal spot (FWHM) becomes









smaller when the K factor becomes larger; however, the intensity of the focal spot

diminishes dramatically when K factor increases from 1.5 to 2. This implies that when K

factor is large enough that the focal spot will not be formed since the intensity of the

focal spot is too low to be observed.

2.4.2 Disadvantage of Photon Sieves over Fresnel Zone Plates

As outlined above, photon sieves have several advantages over zone plates.

However, lower transmission is a very critical limitation of photon sieves. An amplitude

zone plate typically has a transmission of 50% while a photon sieve only has a

transmission of 15 to 20% [3]. The transmission difference between zone plates and

photon sieves is proportional to the opening area of the zones and the pinholes. The low

transmission does not prevent photon sieves from applications using high intensity

sources, such as in synchrotrons used for X-ray microscopy [3]. For common

applications where the light source is less intense, low transmittance may limit the

applications of photon sieves. Low transmission reduces the signal intensities and

contrast between signals and background, causing poor image quality. The contrast of a

image is defined as [9]

contrast = (Imax Imin)/(Imax + Imin) (2-21)

where Imax and Imin are the maximum and minimum intensities of the image, respectively.

The photon sieves produced in this research consisted of a glass substrate coated

with opaque metals having pinholes where light can pass through and diffract to form

images. Antireflection coatings on both sides of the glass substrate can only enhance the

transmission of the photon sieves by -8% at most (4% from each side) [8]. Menon et al

in 2005 [35] suggested a phase-shift photon sieve, which works in the same fashion as the









phase zone plate described in section 2-3-3. In a phase-shift photon sieve, the entire

photon sieve is transparent to the light source and the pinholes have a phase shift of 7T

with respect to the rest of the photon sieve therefore the transmission can be enhanced

significantly. However, neither the detailed design nor the actual device was reported in

their paper.

2.4.3 Apodization

The term "apodization" is derived from Greek which means "take away-foot" [9].

Apodization is the process of modulating the pinhole density on each ring of the photon

sieve to implement a smooth transmission window and thus further suppress the

secondary maxima of a diffraction pattern. It is possible to smooth the sharp

discontinuity of the transmission window by adding another function onto the existing

window function. The added function is called an apodization function. Apodization

technique also can be applied to FZP; however, it requires very complicated equations

and computer calculations to apodize the zone plate [36].

Apodization techniques are utilized in many areas, such as searching for earth-like

planets in astronomy [37], microscopy, medical imaging and optical storage [38].

Apodization can be achieved by changing the aperture shapes [39] or alternating the

transmission characteristics [37, 38, 40, 41]. Some of the most common apodization

functions are plotted in Figure 2-24 [42]. The corresponding functions are listed in Table

2-2. For the designs of photon sieves used in this research, Gaussian apodization

functions were chosen and modified to fit the various photon sieve designs through a

series of simulations, which were completed by Shenderova [43-45]. The details of the

simulations are described below in section 4-2.















0d
0.4
0 21
-1 -o.s 0, 5

Bartlett

k- .





-L -0.5 .S 1

Cosine


0-1 -
-1 -o.5 O-s


ti
0
0 1

-1 -I0


Blackman


B.5 1


Connes


/.20.
1 --O.s O-S s I -1 -0,5 O' s I


Gaussian


Hamming


I~s

p.5


-1 -0 S 0 S L


-1 -. S


O.5 1


Hanning Uniform


Figure 2-24. Some commonly used apodization functions in linear scale [42]. X-axis is
value of x/L where x is optical path difference out to a maximum value of L
(also shown in Table 2-2). Y-axis is the amplitude of the function.


Table 2-2. Equations of the apodization functions shown in Figure 2-25 [42]. x is the
optical path difference and L is the maximum value ofx variable.

T', I Ar: I an:rit FI'jn r"i






(l1- ( )

E.I:a,,, L.4+o.so .( f)







'3aru ; il-,' e-zl / IL )


H w-rr, 0.54+0.46cos (Y)


H.,uuw t CS (Cf)


.1 Tru .rr,









2.4.4 Applications of Photon Sieves

Photon sieves are made from a metal thin film on a thin substrate or from a free

standing opaque film. In addition to their traditional use for focusing x-rays, they can be

used in any application that requires small and light weight lenses. Since photon sieves

are a relatively new type of diffractive lens [3], reported applications of this device are

limited. Gil and Menon in 2003 and 2005 [2, 35] reported using photon sieves to replace

the zone plates in their "scanning-optical-beam-lithography" system, which was based on

the technique of maskless, zone-plate-array lithography (ZPAL) invented by Smith in

1996 [46]. Schematic drawings of a ZPAL system are shown in Figure 2-25.





zone, phtay & y ,


b(a) ndcnn(b)








(c)
huetr open shutr open shutter closed

Figure 2-25. Maskless, zone-plate-array lithography (a) array membrane on the
supporting joists (b) individual micromechanical shutter within each unit cell
(c) pattern writing by scanning the sample in X and Y directions [46].

In the ZPAL system, thousands of 10jm-size zone plates were set in an array,

where each zone plate was isolated in its unit cell that was supported on a thin

carbonaceous membrane with vertical, anisotropically etched Si (111) joists for









mechanical support, as shown in Figure 2-25 (a). Each zone plate was responsible for

exposure in its own unit cell. The exposure was controlled by a micromechanical shutter

located within the individual unit cells, as shown in Figure 2-25 (b). The stage that held

the sample was scanned in the X and Y directions to get a full pattern, as shown in Figure

2-25 (c).

2.5 Chromatic Aberration

Chromatic aberration of a refractive lens results from the dispersion of the

refractive index of the lens material with wavelength. For different wavelengths, the

same materials will have different refractive indices, thus cause different degrees of light

bending. For example, in the range of visible wavelengths, blue rays bend more than red

ones. For a polychromatic light source, the multi-wavelength rays will not focus at one

single spot on the optical axial as shown in Figure 2-26, resulting in chromatic aberration.






--- - -



Chromatic aberration



Figure 2-26 Chromatic aberration of a refractive lens [47].

For a diffractive lens, incident light rays bend when skimming the edge of an

obstacle and then interfering with each other and finally focus on the observation screen.

As reviewed in section 2-3, the focal length of diffractive lens is wavelength dependent.

A very large longitudinal chromatic aberration is estimated by using equation (2-13). In









the visible range, red rays bend more than blue one. The light bending mechanisms for

refractive and diffractive lenses are different, but both exhibit chromatic aberration.

2.6 Justification of Research

There is no true single achromatic diffractive lens to date. In reported research of

diffractive lenses, no single lens was designed to have two diffraction elements. The

purpose of this research is to study how lens properties changed when multiple

diffraction elements with different distributions were incorporated in a single lens. A

dual-wavelength photon sieve consisting of two groups of pinholes, designed to focus

two wavelengths of light, is the simplest system to investigate. As reported below, such a

dual-wavelength diffractive lens exhibits significant chromatic aberration. This is

consistent with the diffraction theories (section 2-3) reviewed above. A number of

different designs for the distribution of the two groups of pinholes were tested. The focal

spot size obtained from a dual-wavelength photon sieve was same to the one obtained

from a single-wavelength photon sieve but with equal or lower intensity under both

monochromatic and polychromatic illuminations. The significant chromatic aberration

observed in a single-wavelength photon sieve makes it a good candidate for a focusing

filter lens for polychromatic light. Dual-wavelength photon sieves could be used for an

imaging device that does not require complete filtering of polychromatic light at the cost

of intensity. The details of testing set-up and results are shown and discussed in Chapter

4.













CHAPTER 3
PHOTON SIEVE FABRICATION

3.1 Introduction

As discussed in chapter 2, a photon sieve (PS) is a diffractive lens composed of

pinholes distributed similar to the Fresnel zones. The PS, shown in Figure 3.1, consist of

a glass substrate (transparent to the wavelength of interest) coated with opaque metals

having a pattern of holes where light can pass through and diffract to form an image.


Pinholes with various sizes
i

Opaque
metal film
Glass


Figure 3-1. Schematic drawing of a cross-sectioned photon sieve. The size of pinhole
various from 80 to 10 |tm depending on the location of pinhole for a PS
designed for 500 nm light.

To make this device, lithographic techniques were used to transfer geometric

patterns from software or masks to the metal film on the substrate. Depending on the

type of radiation, lithography can be divided into three categories: optical, x-ray, and

electrons/ion beams. Though optical lithography is widely used in the semiconductor

industry, it reaches its limitations when the resolution requirements shift to submicron

levels. Electron and ion beams possess high energies and therefore offer extremely small

wavelengths which gives better resolution as compared to even deep or near ultra-violet









(UV) light. In addition to the better resolution, electron and ion beams can be focused to

produce patterns on the resist directly without any mask.

The minimum feature size of the photon sieve designs used in this study was in the

micrometer range. Either traditional photolithography or electron beam (e-beam)

lithography can therefore be use for this patterning process [48]. Due to the instrument

accessibility and ease of use without a mask, e-beam lithography was chosen for process

development. In the following sections, details and problems that encountered in each

process step are illustrated. Background knowledge of some techniques including

processing and analytical instruments are introduced as well.

3.2 Process Development

Photon sieves were fabricated by first depositing by electron beam evaporation [48]

a thin adhesion layer of nickel (3 nm), followed by deposition of a 150 nm silver layer on

a glass substrate. The metallized substrate was then coated with electron beam (e-beam)

resist, patterned using e-beam lithography and then developed. The patterned e-beam

resist was used as a mask to protect the underlying metal films during etching, either dry

or wet etching depending on different process method. The e-beam resist was then

stripped, resulting in a photon sieve. A flow-chart of general processing steps is shown

in Figure 3-2. Four different process methods, which will be named (1) reversed image

etching, (2) direct wet etching, (3) direct dry etching, and (4) lift-off, are described in

Figure 3-2. The acronyms and abbreviations used in Figure 3-2 are listed in Table 3-1.

The procedures of substrate cleaning, metal deposition, and e-beam pattern writing were

identical for these four procedures. The e-beam resists, developers, etching methods, and

resist strippers were different depending on the process method Complete descriptions

of each method are given below in sections 3.2.6.1 to 3.2.6.4.


















































Figure 3-2. Flowchart of various processing methods (a) to (d). The whole development
is divided into five big steps, substrate preparation, film deposition, resist
coating (flow charts within the top blue-double-line box), e-beam lithograph,
and four process methods (flow charts within the bottom blue-double-line
box). Equipments, operation details, and problems of each step is discussed in
the following corresponded section.









Table 3-1. Acronyms and abbreviations shown in Figure 3-2.
Acronym and Abbreviation Full Name
PMMA Polymethylmethacrylate
FOx-14 Liquid solution of hydrogen silsesquioxane (HSQ)
ZEP-7000 Proprietary positive e-beam resist
MF-322 Proprietary developer for FOx-14
RIE Reactive Ion Etching
MIBK Methyl isobutyl ketone
IPA Isopropyl alcohol
ZED-750 Proprietary developer for ZEP-7000
NPGS Nanometer Pattern Generation System


3.2.1 Substrate Preparation

All PSs were fabricated on pre-cleaned glass microscope slides purchased from

Fisher Scientific (Cat. No. 12544). The glass slides were 3 x 1 x 1/16 inch but were cut

into 1 x 1 x 1/16 inch substrates followed by scrubbing for 5 min. in an Alconox (powder

detergent from Fisher) DI water solution. After rinsing-off the detergent, the substrates

were submerged into a three-stage cascade DI water rinse bath with N2 bubblers, as

shown in Figure 3-3 (Bold Technologies Inc. Model 625T wet bench), for over 20

minutes. Substrates were always placed in the lowest (dirtiest) tank for 5 minutes, then

the middle tank for another 5 minutes, and finally the highest (cleanest) tank for 10

minutes. The substrates were then blow dried with dry N2.











Figure 3-3. Three-state cascade DI water rinse bath with N2 bubblers on the wet bench.


Figure 3-3. Three-state cascade DI water rinse bath with N2 bubblers on the wet bench.










3.2.2 Film Deposition

Metal films were deposited by electron beam evaporation. The details of film

deposition and the illustration of e-beam evaporator are given in the following sections.

3.2.2.1 Electron-beam evaporator: system and operation

Figures 3-4 and 3-5 show a schematic drawing and a photograph of the e-beam

evaporator, respectively. The detailed structure inside the processing chamber is shown

in Figure 3-6. The diffusion pump is used as an example when describing the process

steps.

Before starting to pump the chamber to lower pressure, the mechanical pump

(Leybold Dryvac 100P) and diffusion pump need to be turned on for at least 30 minutes

to allow the pumps to stabilize or reach the operation temperature (about 250C for

diffusion pump oil). Stable operation and attainment of the proper vacuum should be

verified by pressure gauge readouts. Liquid nitrogen was added into the cold trap before

pumpdown. The cold trap is used to condense the oil vapor into its solid phase to prevent

the pump oil from backstreaming and contaminating the work chamber.




Processing
chamber


High-vacuum valve --

LiquidN, trap
Hh i ln'iifLr ion pw r-|-

SRoughing line valve
High-vacuum pump l Ru im alve
(Diffusion pump or
Cryogenic pump) Exh lin
-* Exhaust line

Foreline valve Roughing pump
(Machanical pump)


Figure 3-4. Schematic drawing of e-beam evaporator system.































Figure 3-5. Photograph of electron-beam deposition chamber and control rack.



Heating Bell jar
lamps ^ (process chamber)
iV --..


Crystal
monitor

Metal
sources


4r--


-- Substrate


- -- Shutter

..- Electron beam




.- Water-cooled
S Cu hearth


Figure 3-6. Detailed structures inside bell jar of an e-beam evaporator.


~II









After placing two substrates in the process chamber, the bell jar was closed and the

roughing line valve was opened to rough the chamber down to a crossover pressure of

150 milliTorr. The roughing line valve was then closed and the foreline and high vacuum

valves then opened. If the pressure in the foreline is pumped too low (<150mTorr), the

mechanical pump oil will backstream and contaminate the chamber [49]. Conversely, if

the crossover pressure is too high, backstreaming of the diffusion pump oil to the process

chamber will occur due to the collapse of vapor jets in the diffusion pump. Once the

foreline and high vacuum valves were opened, the diffusion pump could pump down the

chamber to very high vacuum (10-6 Torr). The mechanical pump was left on to serve as a

backing pump for the diffusion pump. An ion gauge was used to monitor the chamber

pressure.

Metal deposition was carried out at an operating pressure of 3 5 x 10-6 Torr. The

water-cooled copper hearth can hold up to 5 different sources and the source in use was

controlled by a small rotary motor. The ability to rotate a different hearth into the source

position allows deposition of multi-layer thin films of various materials without breaking

the vacuum. Each source material (e.g., Ni or Ag) was placed in a graphite crucible (1

inch in diameter, 0.75 inch in depth, Kurt J. Lesker EVCEB-11) in sufficient quantities to

cover the whole base but no more than 2/3 of the depth of the crucible to avoid

overflowing of the source material. Electrons are thermionically emitted from a hot

filament then accelerated by a high voltage (30 kV). The electron beam is deflected by a

magnetic field, focused by an electrostatic lens, and heats the source materials to a

temperature where the sublimation or evaporation rates are sufficiently high to deposit a









thin film at an acceptable rate. The electron beam is controlled by an electron beam

power supply (Airco Temescal model ES-6).

The cleaned, bare 1 x 1 inch substrates were placed on a sample holder which

allowed a nearly normal-incidence of the evaporative flux in order to minimize

shadowing effects [48, 50]. The substrates were heated to above 200C by heating lamps

(Globe D, 50V, 200W) to eliminate adsorbed water moisture. The heating lamps were

then turned off and the substrates allowed to cool for about 15 minutes. Metal deposition

was then initiated by heating the source metal with the electron beam. An adhesion layer

of nickel with a thickness of 30 A was deposited at a rate of about 5 A/s and a substrate

temperature between 50-70C controlled by the heat lamps. The elevated temperature

provides a good film quality. The deposition rate and thickness were controlled by an

INFICON deposition controller XTC/2 which is described in section 3.2.2.2. After the

deposition of nickel, the copper hearth was rotated to the silver source and a 1500A silver

film was deposited at a rate of 20 A/s, with the substrate temperature again controlled

between 50-70C. The metal-film-coated substrate was left in the vacuum chamber for

over 15 minutes to cool down close to room temperature before venting the chamber and

removing the substrates.

For silver deposition, when the bottom of the crucible was not completely covered

by the source metal, tiny silver balls (< 10 [tm) were observed on the silver film, as

shown in Figure 3-7. Cotronakis et al [51] reported that carbon contamination was the

cause of gold spitting. The gold spitting was reduced by removing the carbon residual

from the gold source. It is speculated that when the electron beam hits the bottom of the

graphite crucible, carbon contamination increased and caused the silver spitting. This









problem was avoided when the silver metal source was in sufficient quantity to cover the

whole base.






Silver balls










Figure 3-7. Silver spitting. Small spherical silver balls spitted from the molten silver
source. The size of the largest silver balls is about 10 |tm.

At the beginning of process development, a diffusion pump was used as the high

vacuum pump in the e-beam deposition system, but was replaced by a cryogenic pump

for the last half of the research. This change did not disrupt the research results reported

below for photon sieves. The most significant difference between a diffusion pump and a

cryogenic pump is that no pump fluid or lubricant is used in cryopumps; thus

backstreaming of oil from the pump to the processing chamber does not occur. The

cryopump is continually running until regeneration is needed to remove the captured

gases and restore its pumping capacity. The mechanical pump can be turned off after

opening the high vacuum valve since there is no need of a backing pump for the

cryopump. The rest of the details of a cryogenic pump can be found in the following

references [49, 52, 53]. The change from diffusion pump to cryopump for the-beam

evaporator reduced the processing time and also resulted in a better film quality.









3.2.2.2 Deposition controller

By setting multiple parameters of the source materials in the deposition controller

(INFICON XTC/2), the controller can control the shutter to open and close automatically

according to the preset film thickness. The deposition monitor is a quartz crystal with

special piezoelectric sensitivity. The piezoelectric crystal changes its shape when a RF

voltage is applied and mechanical oscillations result. The frequency of the oscillation is a

function of the thickness of the crystal. During the deposition, the added mass reduces

the frequency of this oscillation. Before deposition, the density and the Z-ratio of the

depositing film are entered into the microprocessor within the deposition controller to

correctly convert frequency change to film thickness. The Z-ratio is equal to [54]

(pqUq / pfUf)1/2 (3-1)

where pq, pf are the densities of quartz and the deposited film, respectively, and Uq and uf

are the shear moduli of the quartz and the film, respectively. The derivation of equation

(3-1) can be found in references [54-57].

Table 3-2 shows densities and Z-ratios of materials used in the project. If multiple

layers were deposited, the Z-ratio used for the second layer is decided by the relative

thickness of the two layers. When one layer is thick compare to another, the Z-ratio of

the thick film is used for both layers regardless of the sequence of deposition. When the

thickness of both layers is similar, a weighted average of the two Z-ratios is used [54]. A

picture of a deposition monitor and a schematic drawing of a quartz crystal oscillator are

shown in Figure 3-8 (a) and (b), respectively [57, 58].









Table 3-2. Densities and Z-ratios of materials used in the experiment.
Formula Density Z-ratio Material Name

Ag 10.500 0.529 Silver

Cr 7.200 0.305 Chromium

Ni 8.910 0.331 Nickel

MgF2 3.180 0.637 Magnesium Fluoride





L*Ac





(a) Top view Bottom view (b)

Figure 3-8. Standard deposition monitor (a) and quartz crystal oscillator (b) [57, 58].

3.2.3 Resist Coating

3.2.3.1 Electron-beam resists

Depending on the processing methods, three different e-beam resists were used:

PMMA, FOx-14, and ZEP-7000. PMMA is an ultra-high resolution positive e-beam

resist [59]. Positive resist means that the exposed areas are removed during development,

leaving a positive image in the resist. On the other hand, the negative resist is the resist

where the exposed areas are retained while the unexposed areas are removed, resulting in

a negative image in the resist [48]. The PMMA used in the experiment was 950 PMMA

C4 obtained from Mirochem, Inc. Microchem offers a variety of molecular weights and

solvent systems for PMMA. The "950" resist has a molecular weight of 950,000 and

"C4" represents a 4% PMMA concentration in chlorobenzene.









FOx-14 is a liquid solution of hydrogen silsesquioxane (HSQ) in a solvent obtained

from Dow Corning. First generation FOx (referred as FOx-lx) uses MIBK as the solvent

while second generation resist (referred as FOx-2x) uses a volatile methyl siloxane

(VMS) as the solvent [60]. FOx-14 is a flowable, inorganic polymer which forms a

micro-porous amorphous (SiO2-like) film after the e-beam exposure. It is a high

resolution negative e-beam resist.

ZEP7000 is a high resolution positive e-beam resist with excellent dry-etching

resistance obtained from Zeon Chemicals L. P., a Japanese company. It is a polymer of

an unspecified type with a molecular weight of 340, 000 and was dissolved in dietylene

glycol dimethyl ether [61].

For positive resist, such as PMMA and ZEP7000, the energy provided by the

electrons breaks bonds in the polymer chains and results in a local reduction of molecular

weight. As a result, the exposed area is more chemically active and can be dissolved by

the developer. For negative resist, the electrons provide energy for molecular chain to

cross-link so that the exposure areas are retained while the unexposed areas are dissolved

by the developer. The doses, energies and developers required for PMMA, FOx-14, and

ZEP700 are described in section 3.2.4 on pattern formation.

3.2.3.2 Spin-coating and prebake

The spin coater used in the experiment was a P6700 by Specialty Coating System,

Inc. It has an 8-inch polytetrafluoroethylene (PTFE) coated bowl with a programmable

three-stage spin controller. The speed range of the spin coater is from 100 to 8000 rpm

with hold times of 0 to 999 seconds. Figure 3-9 shows a picture of the P6700 spin coater.






















Figure 3-9. P6700 series spin coater by Specialty Coating System, Inc.

The spin coating process can be separated into four stages [62-64]. The first stage

is dispensing the e-beam resist onto the substrate by using a disposable pipet. The second

stage is the acceleration of the turntable to the desired speed. In the third stage, the

substrate is spinning in a constant speed and the viscosity force of the resist dominates

the film thinning process. The fourth stage is similar to the third stage that the substrate

spins at constant speed. However, the coating thinning process is dominated by the

solvent evaporation instead of fluid viscosity. The coating thickness is essentially

determined by the balance between forces that shear the resist toward the edge, and the

drying rate that affects the viscosity of the resist.

Generally, for a known resist, higher spin speed and longer spin time result in

thinner coatings. When the spin speed increases, the centrifugal force increases and less

fluid can be held on the substrate; thus, the thickness of the fluid decreases. Data from

the manufacturer on the relationship between the spin speed and thickness is shown in

Figure 3-10 for ZEP resists [61]. For ZEP7000, the film thickness was about 1800A for

the spin speed of 3000 rpm used in this study.


................. _^










500 EP7000
45. ZEP7O0B-32
ZEP70B-48B
40MD00Q
ZEP7000A
S3E5000P700l17


I --^ ---



aow

1000
0 1000 2D00 3000 4000 5COo
Spi speed ir p m)


Figure 3-10. Relationship between the spin speed and thickness [61].

The substrate with deposited films was first loaded onto the vacuum chuck and

cleaned by spin-rinsing first with isopropyl alcohol (IPA) then methanol. The substrate

was spun at 200 rpm for 10 seconds. E-beam resist was then dispensed onto the rotating

substrate and allowed to spread over the substrate. This method conserved resist material

since it was only necessary to cover the center of the substrate. After this dispensing

step, the spin speed was increased to 3000 rpm and held at that speed for 35 seconds.

PMMA, FOx-14, or ZEP7000 were spun coated onto the substrates with the same recipe

and the thicknesses of the coatings were 5000A, 3000A, and 1800A, respectively.

Spin coating defects, reported in the literature and shown in Figure 3-14 [64], were

observed on the present samples. Comets, Figure 3-11 (a), are caused by large

contaminated particles on the substrate, and can be reduced by working in a particle-free

environment. Uncoated areas, Figure 3-11 (b), are caused by dispensing insufficient

amounts of resist, and can be corrected by simply increasing the amount of dispensed

resist.






















Figure 3-11. Optical photographs of spin coating defects: (a) comet, and (b) uncoated
area [64].

After spin coating, the substrates were prebaked (soft baked) to remove solvents

from the resist. The hot plate used in the experiment was a Cole Parmer DATAPLATE

720 Series Digital Hot Plate. It had a ceramic plate surface and is capable of

temperatures in excess of 370C.

The film thickness of the resists shrank to about 85% of its initial value during

prebaking [61, 65]. The prebake temperature and time are different depending on type of

resist. Depending on the heat transfer mode, either conduction (hot plate) or convection

(oven), the time required for prebake is different. It requires a longer time, generally 20

to 30 minutes, to bake the substrate in a convection oven and it only needs 1 or 2 minutes

to bake the substrate on a hot plate. In addition to the slower heat transfer mode

(convection), a skin forms on the top of the resist during the solvent drying and further

hinders the rapid evaporation of the volatile component within the resist [66] when

baking the substrate in a convection oven. In this research, the temperature of the hot

plate was set to be 180C. The time of prebake for PMMA, FOx-14, and ZEP7000 were

15 minutes, 2 minutes, and 2 minutes, respectively. After spin coating and prebaking, the

substrates were ready for writing of the patterns.









3.2.4 Pattern Formation

The photon sieve patterns were written with a Pillips XL 40 scanning electron

microscope (SEM) controlled by the nanometer pattern generation system (NPGS).

NPGS is software and hardware that generated steering voltages to control the beam

location and dwell time from an input data file (DesignCAD files in this research)

describing the pattern to be written.

The resist-coated substrate was loaded onto a multi-sample translatable stage along

with a gold standard and a Faraday cup. The acceleration voltage was set to be 30kV and

spot size of the electron beam is size 4, i.e., a diameter of a few nanometers. The gold

standard was used to focus the electron beam with a working distance of 12.8 to 13.2 mm

depending on the minimum magnification required by the pattern design. Astigmatism

and beam alignment (controlled by lens modulator) were adjusted to resolve surface

features at high magnification of 60,000 125,000X. After these initial adjustments, no

further changes in focus and astigmatism were made. By moving the stage to the Faraday

cup and increasing the magnification, the electron beam current was measured and

recorded. Due to the absence of a beam blanker, the stage was then moved to place the

beam on the edge of the substrate at a magnification of 400X or greater to minimize the

e-beam exposure in the area to be patterned. The stage rotation was then adjusted by the

Stage/x-align command for sample alignment. The height of the substrate was adjusted

till the resist surface was in focused. Writing of the desired photon sieve pattern was

controlled by the run file and the NPGS software. The number and type of patterns, the

locations of the patterns on the substrates, the e-beam dose, the center-to-center distance

and the line spacing of electron beam writing were all specified in the run file. The

center-to-center distance is the distance between two e-beam exposed areas (area mode)









and line spacing is the distance between two e-beam exposed lines (line mode). The

beam current was between 1680 and 1720 pA for a beam spot size of 4. The e-beam

dosage of PMMA, FOx-14, and ZEP7000 were set to an "area dose" of 130 [tC/cm2, 45

[tC/cm2, and 45 [tC/cm2, respectively. The line spacing and the center-to-center distance

were both set to 100 nm. If the line spacing or the center-to-center distance is too small,

over-exposure problems may occur. The "non-stop writing" mode was selected for all

pattern writing processes. After entering all the parameters, the NPGS calculated the

exposure time automatically and controlled the beam movement according to the pattern

design. The e-beam was turned off immediately after the pattern writing was finished to

prevent unnecessary exposure to the resist. Depending on the pattern designs, the writing

time of a single photon sieve was about 20 to 40 minutes. The chamber was then vented

and the sample was unloaded for development of the resist pattern (see Figure 3-2 for

process flow chart).

The developer used for PMMA resist consists of MIBK with IPA in a ratio of 1 to

3. The developing time was 70 seconds in a beaker at room temperature without stirring.

After development, the substrate was rinsed with IPA then blow dried with pure N2. The

developer for FOx-14 was Microposit MF-322 obtained from Shipley Company and

consists of 2.44% tetramethylammonium hydroxide (TMAH), less than 1% of surfactant

[67] and water. The substrate was developed in MF-322 for 90 seconds and rinsed by de-

ionized (DI) water, then dried with pure N2. For ZEP7000, the proprietary developer is

ZED-750 obtained from the Zeon Chemicals L. P. The substrate was developed in ZED-

750 for 2.5 minutes, then rinsed in IPA and dried with N2.









3.2.5 Reactive Ion Etch (RIE)

The RIE system used for the experiment is a PlasmaTherm SLR770 series reactive

ion etcher with a turbopump (Leybold Turbovac 1000) and two mechanical pumps

(Leybold Trivac BCS) used for backing the turbopump and roughing the loadlock,

respectively. The system includes a loadlock chamber with an automatic arm to move

the sample into the etching chamber. The loading platform was able to handle different

sample sizes from small to a 4-inch wafer. The PlasmaTherm SLR770 has an ECR

plasma source produced by a 1000W microwave power supply and is combined with a

13.56MHz 500W RF power supply. The ECR source operated at 2.45GHz [65].

Reactive ion etching is discussed in detail in reference [48]. Figure 3-12 is a photograph

of the PlasmaTherm SLR770.




U




Loadlock
chamber


ciaml ei






Figure 3-12. Photograph of the PlasmaTherm SLR770.

During the process development, etching recipes with oxygen, argon, or a

proprietary H2/Ar/CH4 etching recipe [68], were used to etch PMMA and silver. Oxygen

plasma was used to etch the PMMA layer and the argon plasma was used to sputter etch









the silver metal. The proprietary etching recipe (patent pending) was used to etch the

silver metal with excellent selectivity between chromium and silver. Selectivity in

plasma etching is defined as the ratio of the etching rates of two different materials when

exposed to the same plasma environment [48]. When the etch rate of the mask is low and

the etch rate of the underlying material is high, the selectivity is good. The actual reason

for the excellent selectivity is not clear. The detailed compositions and operation

parameters for the recipes are shown in Table 3-3.

Table 3-3. Experiment parameters of plasma-etching recipes for RIE process.
Proprietary recipe
Oxygen plasma (Patent pending) Argon plasma
Etched material PMMA Ag Ag or Ni
Mask FOx-14 Cr ZEP-7000
Pressure 10 mtorr proprietary recipe 1 mtorr
Temperature Room temp. Room temp Room temp
RF power (W) 100 proprietary recipe 100
ECR power (W) 0 proprietary recipe 900
Gas / Flow rate 02 / 20 sccm H2 / proprietary recipe Ar / 10 sccm
Ar / proprietary recipe
CH4 / proprietary recipe


3.2.6 Various Process Methods: Procedures and Results

Photon sieve patterns were created by four different processes (reversed image

etching, lift-off, direct wet etching, and direct dry etching) as described in the flow chart

in Figure 3-2. They are described in detail below.

3.2.6.1 Reversed image etching process

Photon sieves were fabricated by first depositing by electron beam evaporation a

thin adhesion layer of nickel of 30 A, followed by deposition of a layer of silver (1500 A)









on a cleaned glass substrate. In the reversed image etching process, the metallized

substrate was coated, first with PMMA with a prebake at 1800C for 15 minutes, and

subsequently with FOx-14 with a prebake at 1800C for 2 minutes. The FOx-14 was

patterned using electron beam lithography and then developed by MF-322 for 90

seconds. The unexposed FOx-14 was dissolved in the developer and then the exposed

PMMA was removed by oxygen plasma etching. The oxygen plasma recipe and detailed

operation procedures for RIE and etching recipes were described above. After etching

the PMMA, a 250A-thick chromium (Cr) layer, used as a hard mask for RIE, was

deposited by e-beam evaporation. The sample was then rinsed by ultrasonication in an

acetone bath (Fisher Scientific ultrasonic FS-28) to lift off the Cr/FOx-14/PMMA

masked areas, exposing the silver layer. After lift off, the sample was dried and the silver

and nickel was etched using RIE with the proprietary recipe [68] (see Table 3-3) to

produce the transparent PS holes. Figure 3-13 shows an optical micrograph of a photon

sieve manufactured by this method. The process steps in this method are shown

schematically in Figure 3-14.

opaque
silver film








transmitted
pinholes



Figure 3-13. Optical micrograph of an apodized photon sieve manufactured by reversed
image etching method.













Silver film (150 nm)

G ass substrate

E-beam evaporatively deposit Ni
then Ag films on a glass substrate.
SE-beam


PMMA (-500nm)
Silver film (150 nm)
Glass substrate
Write a pattern using the e-
beam of a SEM controlled by
the NPGS.

** ocA pl prr s *
I 1 A4 (- 2 4 ml I
PMMA (-590nm)
Silver ilm (15D nm)

Gl Iass substrate

Etch the PMMA in RE with
O0 plasma.


Platnajpriprietary etpe)
... -l Aj.l raTWia259t0 .-I rl .
Silver film (15 nm)

Gl Iass substrate
Lift offthe Cr/FOx-14PMMA
masks with acetone. Etch the
Ag and Niin RIE.


PMMA (-~500nm)
Silver film (150 nm)
S>
SI ass substrate

Spin coat PMMA then prebake.
Spin coat FOx-14 then prebake.

I FIoE4 i~; nnri
PMMA (-500nm)
Silver film (150 nm)

SI ass substrate
Develop the pattern using MF-
322, rinse with DI water.



i io-l`4, ,, i i
PMMA (-D5Onm)
Lkf,. i CC.".', L t." CI L :-
S ilve r film (1 0 nm)

G I ass substrate

Deposit a 25nm-thick layer of Cr.




&Ct. f m~i'gftatit25 nl) fl C*
S ilver film (150 nm)
Gl ass substrate

A finished photon sieve.


Figure 3-14. Process flow of the "reversed image etching" method. The direction of flow
is from left to right, top to bottom.









This process method required a chromium film deposition and over 40 minutes of

high-power reactive ion etching of silver. The whole process took about a half day

longer than the other methods. In addition to the complicated process, residual dots of

material, shown in Figure 3-15, observed after the etching of silver with the proprietary

recipe [68] are described as below. The sizes of the residual dots were on the order of a

micrometer and the dots were only distributed within the large pinholes near the center of

a photon sieve. After 20 minutes of etching, the residual dots were already formed and

they became bigger as etching continued. The SEM micrograph shown in Figure 3-15

was taken after 40 minutes of etching.


No residual
dots inside
smaller pinholes
More residual
dots inside
bigger pinholes.
SResidual dot
Near the center
ora pinhole



Figure 3-15. SEM micrograph of residual dots within the pinholes after plasma etching of
Ag and Ni.

The composition of the residual dots was analyzed by Auger spectroscopy and

evaluated by secondary and backscattered electron images in the SEM. Figure 3-16 [69]

shows a schematic drawing of the interaction volume for various electron-specimen

interactions. Auger emission is preferred for detection of low atomic number elements,

while X-ray emission is preferred for high atomic number elements [70]. Only Auger

electrons generated closed to the specimen surface can escape with their characteristic










energies and be used to identify the atoms in the specimen (10A from the surface in

Figure 3-16).


Electron



urEloecro
-B- Sen Rdtry

EV Rklons
E E chmaractdatic









Figure 3-16. Schematic drawing of interaction volume for various electron-specimen
interactions [69].






The micrographs of secondary and backscattered electron images of the residual

dots are shown in Figure 3-17 (a) and (b) respectively. Both micrographs were taken at
II I
I :8.E Roadutwa rI



Figure 3-16. Schematic drawing of interaction volume for various electron-specimen
interactions [69].

The micrographs of secondary and backscattered electron images of the residual

dots are shown in Figure 3-17 (a) and (b) respectively. Both micrographs were taken at

the same location with the same magnification for comparison. Secondary electron yield

does not change systematically with the atomic number, Z, of the element being imaged,

whereas the backscattered electron yield increases with increasing Z. Secondary

electrons provide a better topographical contrast while backscattered electrons provide

some information about the specimen elements [70]. From the backscattered electron

micrograph, shown in Figure 3-17 (b), the residual dots appear to be hemispherical

bodies with dark strips, and their appearance is very similar to those in the secondary

electron micrograph, shown in Figure 3-17 (a). The information provided by the BSE

micrograph confirmed that the dark strips on the residual dot consists of relatively low Z

elements as compared to the rest (white part) of the hemispherical bodies.



































Figure 3-17. Residual dots (a) SE image (b) BSE image. SE yield does not change
systematically with the atomic number, Z, of the element being imaged,
whereas backscattered electron yield increases with increasing Z. BSE image
confirmed the dark strips on residual dot consisted of relatively low Z element
compared to the rest of hemispherical body.

The same specimen was analyzed by Auger electron spectroscopy. The Auger

spectra were taken in an area with residual dots instead of from a single dot. Charging

artifacts occurred when the primary beam was focused onto a single dot due to the non-

conductive glass substrate underneath. Generally, the charging problem can be improved

by lowering the energy of incident beam or tilting the sample. Both actions had been

taken and charging still occurred, so the area of analysis was expanded to include an area

of residual dots, as shown in Figure 3-18. Auger spectra before and after argon-

sputtering are shown in Figure 3-19 (a) and (b), respectively. The depth profile from

argon sputtering on the residual dots is shown in Figure 3-20.

















Auger spectrum
investigated area







Figure 3-18. Indication of investigated area for Auger spectrum.


dN(E)








50











dN(E)


Mm -1971 Max 1567


0N
01


C'


250 450 650 850 1050 1250
Kinetic Energy (eV)


1450 1850 1850 2050


Kinelle Energy (V)


Figure 3-19. Auger spectra from a general area with residual dots (a) before argon
sputter, and (b) after argon sputter.


I


00*Ojp 1044 1














I







Sil
0 1 2
Time (mins)

Figure 3-20. Argon sputtering depth profile from the area with residual dots.

Before argon sputtering, chromium (Cr), nickel (Ni), oxygen (0), carbon (C), and

silicon (Si) peaks were found in the area with residual dots. After sputtering, Si, calcium

(Ca), and O peaks were found in the same area whereas Cr, Ni, and C peaks disappeared

and so did the residual dots. The strong Si and O (from SiO2) and weak Ca peak after

sputtering came from the glass substrate. The Cr, Ni, C and part of the O peaks found

before sputtering are from either the residual dots or surface contaminations.

To avoid the long process time (chromium deposition and 40 minutes of RIE

etching) and the possibility of residual dots formation, the lift-off process was developed.

3.2.6.2 Lift-off process

The lift-off method to fabricate PS was developed consisting of first evaporating a

30A adhesion layer of nickel, which also served as a charge dissipation layer during e-

beam lithography. The substrate was then coated, first with PMMA with a prebake at

180C for 15 minutes, and subsequently with FOx-14 with a prebake at 1800C for 2

minutes. The FOx-14 was patterned using electron beam lithography and developed by

MF-322 for 90 seconds. The unexposed FOx-14 was dissolved and the unmasked PMMA










was removed by RIE. After the etching of the PMMA, a 1000A-thick silver (Ag) layer

was deposited on the substrate by e-beam evaporation. The sample was rinsed by

ultrasonication in an acetone bath (Fisher Scientific ultrasonic FS-28) to lift off the

Ag/FOx-14/PMMA layers. The sample was subjected to RIE for 10 seconds to remove

the thin nickel layer by argon sputtering. A schematic process flow of this method is

shown in Figure 3-21.


*
0
S 0

Glass substrate
E-beam evaporatively deposit Ni
film on a glass substrate.

jE-beam


PMMA (-500nm)

Glass substrate
Write apattem using the e-
beam of aSEM controlled by
the NPGS.


1 O1 p0lt irrI 1

PMMA (-500nm)

Glass substrate
Etch the PMMA in RIE with
0, plasma.

Argon Plasma


Glass substrate
Lift off the Ag/FOx-14/PMMA
masks with acetone. Etch the
Ni with RIE.


6

PMMA (-500nm)

Glass substrate
Spin coat PMMA then prebake.
Spin coat FOx-14 then prebake.


I 1o0 4 (- rl I
PMMA (-500nm)
: Glass substrate
Develop the p attem using MF-
322, rinse with DI water.




I lo1 4 ( I-2 I
Silver film (1o00nm)
Glass subsr'ate
Deposit a 100nm-thick layer
of Ag.



Silver film (1i inm
S-I U 1itJqc I-
Glass substrate
A finished photon sieve.


Figure 3-21. Process flow of the "lift-off' method. The direction of flow is from left to
right, top to bottom.









This process method shortened the processing time by eliminating the steps of Cr

deposition and 40 minutes of silver etching. However, it required a short etching of

nickel by argon sputtering, which bombarded the silver surface simultaneously and

caused roughening. No residual dots were observed in this process method. Figure 3-22

shows an optical micrograph of a photon sieve manufactured by the lift-off method. The

sidewall residue, shown in Figure 3-23, limited the deposited thickness of silver. If the

silver was too thick, it prevented the PMMA layer from being dissolved in acetone during

the lift-off process. In addition, the oxygen plasma was not stable (with unknown

contamination) over the time period of the process development. In order to avoid the

problem of sidewall residues and the use of oxygen plasma, the process of direct wet

etching was studied.


S- O b -


Figure 3-22. Optical micrograph of a photon sieve manufactured by the lift-off method.










Side-wall residue




FOx-14 FO:,-14 FOX FX-14 z-14
PMMVIA PM NIA PM12A P1 PMMA



Glass Substrate





Figure 3-23. Schematic drawing of sidewall residue. Some of the deposited silver atoms
stuck on the sidewall of the patterned resist and prevented the PMMA layer
from being dissolved in acetone during the lift-off process.

3.2.6.3 Direct wet etching process

In the direct wet etching method, photon sieves were fabricated by first depositing

by electron beam evaporation a 30A adhesion layer of nickel, followed by deposition of a

layer of silver (1500 A) on a cleaned glass substrate. The metallized substrate was then

coated with PMMA with a prebake at 1800C for 15 minutes. The PMMA was patterned

using electron beam lithography and developed by MIBK:IPA (1:3) for 70 seconds. The

exposed silver was etched using 12M nitric acid (HNO3) in 1 second. The sample was

rinsed with DI water twice. The PMMA was removed by rinsing with ultrasonication in

an acetone bath. A schematic process flow of this method is shown in Figure 3-24.

This method was the simplest compared to other three process methods because it

required neither Cr deposition nor long time RIE, and only required one spin coating of

PMMA, which was used as a mask for direct wet etching. However, the quality of

etching was poor. The uniformity of wet etching over different feature sizes was a









problem. Figure 3-25 shows that the large pinholes (80 jtm in diameter) located in the

center of the photon sieve were etched clearly while the small pinholes (10 jtm in

diameter) located at the outer area of photon sieve were not etched completely. In order

to avoid this problem, the process of direct dry etching was studied.


Silver film (150nm)

Glass substrate

E-beam evaporatively deposit Ni
then Ag films on a glass substrate.

VE-beam

PMMA (-500nm)
Silver film (150nm)

Glass substrate
Write a pattern using the e-
beam of a SEM controlled by
the NPGS.



FMMA (-500nrm)
Silver film (150nm)

Glass substrate

Etch the Ag with cone. HNO3


PMMA. (-500nm)
Silver film (150nm)

Glass substrate

Spin coat PMMA then prebake.




PMMA (-500nmi
Silver film (150nm)

Glass substrate
Develop the pattern using
MIBK:IPA 1:3 and rinse with
IPA.




Silver film (150nm)
m mick 3nrM
I Glass substrate

Dissovie PMMA in acetone.
A finished photon sieve.


Figure 3-24. Process flow of the "direct wet etching" method. The direction of flow is
from left to right, top to bottom.



















S ((a) (b)

Figure 3-25. Optical micrographs of the photon sieve manufactured by direct wet etching
(a) completely etched large center pinholes (80 |tm in diameter), and (b)
incompletely etched small outer pinholes (10 |tm in diameter.)

3.2.6.4 Direct dry etching process

In the direct dry etching process, the metallized substrate (3 nm of Ni and 150 nm

of Ag) was coated with PMMA and prebaked at 1800C for 15 minutes. The PMMA was

patterned using electron beam lithography and developed by MIBK:IPA (1:3) for 70

seconds. PMMA was used as a mask for the RIE argon etching. The PMMA

demonstrated a poor resistance to dry etching and veil-like material accumulated at the

edge of each pinhole which caused the edge roughening, as shown in Figure 3-26.















Figure 3-26. SEM micrographs of the veil-like matter at the edge of holes after argon
sputtering using only PMMA for an etch mask.









Thus another positive e-beam resist, ZEP7000, was added on the top of PMMA

during the coating stage. The ZEP7000 was patterned using e-beam lithography with an

"area dose" of 45 [tC/cm2 and developed using ZED750 for 2.5 minutes followed by a

rinse in IPA. The ZEP7000 with e-beam exposure was dissolved in ZED750. The

sample was subjected to argon plasma etching inside a RIE system to etch away the

exposed PMMA, silver, and nickel layers. The PMMA and ZEP7000 coatings were then

removed by ultrasonicating in acetone. Use of this procedure resulted in clean edges as

shown in Figure 3-27. A schematic process flow of this method is shown in Figures 3-

28. The direct dry etch process using PMMA plus ZEP7000 was selected to be the

standard process to make single- or dual-wavelength photon sieves. No chrome coating

and oxygen plasma etching were needed and the silver-etching step took only 30 second

rather than 40 minutes as in the reverse image method.


Figure 3-27. A photon sieves with clean edge manufactured by direct dry etching method.














Silver film (150nm)

Glass substrate

E-beam evaporatively deposit Ni
then Ag films on a glass substrate.


E-beam


PMM NiA (-.5i0r.,m i
Silver film (150nrm)
Glass substrate
Write a pattern using the e-
beam of a SEM controlled by
the NPGS.


Argon plasma
*I EFUno (-InBI)I
PMMA (-1i:rnmr I
SSilver film (150r m) i
rMI film IImn) m
Glass substrate

Etch the PMMA/Ag/Ni in RIE
with argon plasma.


4


Pfr11-4 1 -500rn)
Siler film (160nm)

Glass substrate

Spin coat PMMA then prebake.
Spin coat ZEP7000 then prebake.




| EF3'30 ID n[) I
P f.-Ir-lA 1.-5 l001nm:i
Silver film TT5Onm)

Glass substrate
Develop the pattern using
ZED750, rinse with IPA.







Silver film (15-:nnm
[ m m a mlicks lnWl a m-
Glass substrate
Remove ZEP and PMMA
with acetone.


Figure 3-28. Process flow of the "direct dry etching" method. The direction of flow is
from left to right, top to bottom.

3.3 Discussions

In the reversed image etching process (section 3.2.6.1), the reason for the excellent

selectivity of Cr over Ag with the proprietary H2/Ar/CH4 RIE recipe [68] is still not clear.

It is speculated that the silver atoms and the hydrogen or hydrocarbon molecules form

organometallic complexes. Hydrogen atoms and linear or cyclic hydrocarbon groups

with 7t-bond systems, such as ethylene (H2C=CH2), acetylene (HC-CH), 7t-allyl (C3H5),









cyclopentadienyl (Cp, C5H5) and benzene (Ph, C6H6) are very common ligands in

organometallic complexes [71] and are possible to form during the plasma discharge.

Because the bonding between silver and carbon or hydrogen is thermodynamically weak

[72], the organometallic complexes tend to undergo homolytic dissociation [73], which

results in metal and hydrocarbon radicals and been removed by turbopump. The purpose

of adding argon atoms in the proprietary recipe [68] is to stimulate the gas-solid

reactions, i.e., to remove deposited polymer and increase the etching rate [48].

It is reasonable to speculate that the most probable mechanism of formation of the

residual dots formation during RIE of PSs is primary particle agglomeration during

plasma etching. This mechanism is consistent with the results shown in section 3.2.6.1.

These particles stick onto the substrate surface after the plasma is turned off. Particles

can be produced in many ways, such as flaking from substrate or chamber walls, metal

clustering and polymerization of the gases or substrate materials, condensation of

sputtered material, and aerosols from gases [74-77]. Yellow colored polyimide was

found to built-up on the sidewall of the reaction chamber as a result of contamination

from other users of the RIE system. This polyimide may flake and become contaminate

particles. In addition to contamination from chamber built-up, re-deposited metal atoms,

such as Cr and Ni, and polymers formed from CH4/H2 radicals and atoms are all possible

sources of primary particles.

The mechanism of particle growth during RIE has been investigated by many

researchers [74-77]. It is believed that the nanometer size crystallites can be formed and

may coalesce into particles when the concentration of crystallites reaches a critical value.

The particles further grow by molecular bonding with surface atoms and radicals from









the plasma and formed primary spherical particles about 0.2 rtm in size [76]. These

primary particles undergo clustering or agglomeration and form large particles about 2-5

|tm [76].

From the Auger spectra (Figure 3-22), Cr, Ni, and C peaks were found before

sputtering and the peaks and residual dots were absent after sputtering. This suggests that

the residual dots contained these three elements. In the reversed image etching process,

the final layers exposed to plasma etching were the Cr hard mask and the Ni adhesion

layer. It is speculated that these two metal atoms combined with the C from

contamination and polymerization were bonded onto the nanoparticles that underwent

agglomeration and formed the residual dots.

From the Auger data (Figure 3-22), no silver peak was found in the residual dots.

A possible reason is that the silver atoms and the hydrogen or hydrocarbon molecules

within the etch gases formed the organometallic complexes that were removed by the

vacuum system. It is also possible that some of the silver atoms re-deposited back onto

the substrate and were covered by the molecular bonded Cr, Ni, and C elements. As long

as the coating of Cr, Ni, and C was thicker than 30 A, Auger electrons from the inner

portion of the residual dots would not be detected in the Auger spectra.

3.4 Conclusions

Four process methods for photon sieve fabrication were developed and tested. The

advantages and disadvantages of each method were described and compared.

First, the reversed image etching method was successful but complicated. It was

accomplished by reactive ion etching with a patented RIE recipe to pattern Cr hard masks

[68]. The reverse image etching method required deposition of a chromium film over the









Ag film and more than 40 minutes of high-power reactive ion etching (RIE) of silver,

which makes this process longer than the other methods. The photon sieves obtained

from this method were good, but residual dots within the open holes of photon sieves

were observed. It is speculated that the residual dots were formed by primary

nanoparticles agglomerating during the plasma etching.

To simplify the process flow and avoid the possibility of residual dots formation,

the lift-off method was developed. Good photon sieves were produced by using this

method. However, sidewall residue of silver atoms stuck on the patterned resist limited

the deposited thickness of silver.

To avoid the problem of sidewall residue and the use of unstable oxygen plasma in

the RIE system, the direct wet etching method was studied. The direct wet etching

method was simple and fast. However, the manufacturing result was not promising due

to the non-uniform etching rate for different sizes of mask openings.

The direct dry etching method was developed to solve the non-uniform etching

problems of wet etching. PMMA was shown to be a poor mask for argon sputtering due

to residual deposits at the edge of holes. A positive e-beam resist, ZEP700, was used on

top of the PMMA because of its excellent dry etching resistance. The direct dry etching

method combined with ZEP7000 resulted in the most successful process method in terms

of simplicity and repeatability for production of photon sieves.














CHAPTER 4
PHOTON SIEVE PROPERTIES

4.1 Introduction

Refractive optics have long been used for imaging, especially for visible light.

However, high absorption coefficients for lens materials limit the use of refractive optics

for short wavelengths. Diffractive lenses, for instance Fresnel zone plates (FZP) and

photon sieves (PS), are attractive not only because they can be used to focus high or low

energy radiation but also because of their small size and weight.

A photon sieve is a diffractive lens composed of many pinholes distributed in the

all-even or all-odd Fresnel zones. The lens properties of diffraction optics are

wavelength-dependent. If photons with wavelengths different from the designed value

pass through a diffractive lens, aberration will occur.

In this research, multiple patterns of dual-wavelength photon sieves were designed,

fabricated and tested to characterize the lens properties. The fabrication process of direct

dry etching with ZEP7000 e-beam resist, described in Chapter 3, was used. The purpose

of this research was to evaluate the advantages and disadvantages of dual-wavelength PS

lenses and to verify the feasibility of combining the two diffractive elements for different

wavelengths into a single lens. It will be concluded that a single-wavelength PS would

be a good focusing filter for polychromatic light since it only focuses the designed

wavelength and disperses the rest of the wavelengths. In addition, a dual-wavelength PS

is inferior to the single-wavelength PS under monochromatic and polychromatic light

sources. However, the dual-wavelength PS is able to focus the image with limited









performance when switching between different light sources and can be used for the

imaging device that does not require the filtering of polychromatic light at the cost of

intensity.

4.2 Simulation of Photon Sieves Properties

The fundamental theories of Fresnel zone plates and photon sieves have been

reviewed in Chapter 2. The photon sieves used in this research were all designed to have

a focal length of 50 mm, a lens diameter of 3 mm, a K-factor of 1.2 (the ratio of pinhole

diameter over the zone width, i.e., the dlw ratio in section 2.4.1.2), and they were all

apodized as discussed below. These factors were determined by simulated results

reported by O. Shenderova [43-45]. The simulations were performed using MATLAB-

based software [78]. Fresnel-Kirchhoff diffraction theory [9] was used for the large

pinholes, while the analytical far-field based expression [28] was used for small pinholes

[45]. The point spread function (PSF) on the image plane of a point source was

computed to optimize the lens properties. A small full width half maximum (FWHM)

and large intensity of the PSF at the focal point were the characteristics used to determine

the quality of the design.

4.2.1 Focal Length and Lens Diameter

The two wavelengths that were chosen for the dual-wavelength design were 500

nm and 600 nm. The difference between these two wavelengths is big enough to

minimize the influence of each other but is within the visible spectrum for regular

photography. Equations 2-12 and 2-13 in Chapter 2 show that once the wavelength and

focal length were determined, the lens diameter and the resolution (outermost zone

width) were dependent on each other. The bigger the lens diameter, the narrower the

outer-most zone width, the better the resolution. One of the simulation results [43]







71


showed that a photon sieve with a 3 mm diameter had a smaller PSF FWHM than a 1 mm

diameter with the same focal length. A smaller FWHM represents a better optical

resolution as defined by the Rayleigh Criterion [9] in section 2.3.1.

4.2.2 K-factor

The K-factor is the dlw ratio described in Figure 2-23 and equation (2-20), where d

is the pinhole diameter and w is the zone width. According to the simulation results

shown in Figure 4-1, 1.2 is a reasonable K value where the peak intensity of the PSF is a

maximum while the FWHM is acceptably small.


7.24 6000
+ -FWHM
7.23 --*--max y 5500
7.22 % 5000
7.214500
4500
7.2
4000
7.19
3500
7.17

7. 2500
7.16
7.15 4 2000
7.14 1500
7.13 1000
0 0.5 1 1.5 2 2.5
K


Figure 4-1. Simulation result of the optimum K value. The horizontal axis is the K value,
the vertical axis at left is the FWHM in micrometers, and the vertical axis at
right is the intensity in arbitrary units [44].

4.2.3 Apodized vs. Unapodized Photon Sieves

As reviewed in section 2.4.3, apodization is the process of modulating the pinhole

density on each ring of a photon sieve to create a smooth transmission window and

thereby suppress the secondary maxima in the diffraction pattern. The simulated PSFs

for apodized (modified Gaussian function; see below) and unapodized photon sieves are

shown in Figure 4-2. The apodized photon sieve exhibited better contrast (Equation 2-









21) despite the fact that the absolute transmission (not shown) was about one half of the

unapodized lens. The low transmission of an apodized photon sieve was mainly due to

fewer holes (2722 pinholes for the unapodized photon sieve and only 818 pinholes for the

apodized lens).


11000
I0oU apodized



Unapodized:
2,722 pinholes, transmission 55.8% w.


unapodized



Aapodized: o 5 10o
818 pinholes, transmission 28.3% Distance from optical axis (am)


Figure 4-2. Simulated one-dimensional PSFs for apodized and unapodized photon sieves.
The light intensity at the vertical axis is in arbitrary units. The absolute
intensity for apodized photon sieve is lower than the unapodized one [45].

Figure 4-2 also showed that the secondary maxima in the PSF of an unapodized

photon sieve was suppressed by the apodization. The apodization function used for

simulation was a modified one-dimensional (ID) Gaussian distribution function, equal to

exp(-axb) [44]. The appropriate values of the Gaussian parameters a and b were chosen

to reduce the FWHM and increase the intensity for a lens with specific geometric

parameters. A typical simulation of the FWHM as functions of a and b is shown in

Figure 4-3. It is an example to illustrate that apodization is a compromise between

resolution and transmittance. The smallest FWHM was obtained when a = 15 and b = 3.6

while the peak intensity (Imax) was low with the same a and b parameters.







73








Moo-
1800-

400.





8X 1225
1OO-







11 7





b (a)







1007
27.5












5.25
&5 1125
11 75
15 15 a



























b
(a)




























Figure 4-3. A simulation of the PSF (a) peak intensity and (b) FWHM as a function of a
too












and b, the coefficients of a modified Gaussian distribution function, exp(-ax
11.75
15 45 a
b
(b)

Figure 4-3. A simulation of the PSF (a) peak intensity and (b) FWHM as a function of a
and b, the coefficients of a modified Gaussian distribution function, exp(-axb).
In this example, the smallest FWHM was obtained when a equaled to 15 and b
equaled to 3.6. However with a = 15 and b = 3.6, the intensity became low.
This demonstrated that apodization is a compromise between resolution and
transmittance [44].









4.3 Photon Sieve Pattern Generation

The patterned photon sieves were generated by the direct dry etching process

described in section 3.2.6.4. The positions of the holes in the PS were generated by

entering the desired wavelength, focal length, and lens diameter into the MATLAB-based

software. This software generated the hole pattern of single-wavelength photon sieves in

a text format containing the X, Y coordinates of the center of each hole and its radius

([tm). The text file was inputted into DesignCAD which generated a file for electron

beam patterning, that was then loaded into the NPGS for electron-beam lithography.

An example of the text file for a 6-sector dual-wavelength photon sieve (see

below) is shown in Table 4-1. Only the first 9 and last 9 pinholes of each wavelength

(500 nm or 600 nm) are shown in the table. The pinhole sequence numbers show that

pinholes from 1 to 5280 are for 500 nm light, and pinholes from 5281 to 8973 (3693) are

for 600 nm light. The smallest pinhole diameters for 500 nm and 600 nm wavelengths

are 10.14 |tm and 12.66 |tm, respectively. The pinhole pattern of a 6-sector dual-

wavelength photon sieve is shown in Figure 4-4. If only the 500 nm pinholes or 600 nm

pinholes are used individually, two 3-sector single-wavelength photon sieves, shown as

505 and 605 in Figure 4-5, were formed, with the other 3 sectors remaining unpatterned.

There were a total of thirteen (13) designs of photon sieves patterns used in this

research. These patterns are shown in Figures 4-5 and 4-6 and their designated names are

shown in bold-faced when used in the text throughout this chapter. The nomenclature

used in the names is that the first number (5 or 6) designates the wavelengths of 500 nm

and 600 nm. For single-wavelength photon sieve patterns, the second and third numbers

indicated the pattern is a complete photon sieve (10) or a half one (05, 3-sectors). For









dual-wavelength photon sieve patterns, the sectional designs were named directly with

the number of sectors and the concentric designs were named with the ratios of open hole

area of the two wavelengths. For example, 5in6-75% means that the blue (500 nm) holes

are in the center of the concentric designed dual-wavelength PS with nominally 75% hole

area and red holes (600 nm) are in the outer zone with 25% hole area.


Figure 4-4. The DesignCAD pattern of the 6-sector dual-wavelength photon sieve. Blue
and red pinholes are designed to focus 500 nm and 600 nm wavelengths,
respectively.










Table 4-1. Text file of the 6-sector dual-wavelength photon sieve. Only the first 9 and
last 9 pinholes designed for 500 nm and 600 nm wavelengths are shown in the
table.
Pinhole Sequence X (um) Y(um) Radius (um) Wavelength (nm)
1 189.27 40.93 39.3 500
2 143.45 130.09 39.3 500
3 294.51 27.68 25.42 500
4 282.32 88.31 25.42 500
5 257.79 145.07 25.42 500
6 221.99 195.5 25.42 500
7 176.49 237.38 25.42 500
8 370.23 20.74 20.25 500
9 365.32 63.58 20.25 500
.- -500
...- -500
5272 195.54 -1414.1 5.26 500
5273 438.12 -1358.66 5.26 500
5274 667.39 -1261.94 5.26 500
5275 -352.06 -1401.42 5.19 500
5276 148.49 -1437.32 5.19 500
5277 631.13 -1299.85 5.19 500
5278 -370.33 -1414.5 5.13 500
5279 386.54 -1410.16 5.13 500
5280 718.71 -1292.84 5.07 500
5281 63.56 202.39 43.05 600
5282 -46.15 207.05 43.05 600
5283 129.41 297.07 27.85 600
5284 64.82 317.49 27.85 600
5285 -2.61 324.03 27.85 600
5286 -69.92 316.41 27.85 600
5287 -134.17 294.95 27.85 600
5288 181.64 363.33 22.18 600
5289 138.23 381.96 22.18 600
S. -600
...- -600
8965 1011.03 -1001.61 6.33 600
8966 1169.6 -810.83 6.33 600
8967 1292.63 -595.41 6.33 600
8968 1376.39 -361.9 6.33 600
8969 1418.32 -117.4 6.33 600
8970 971.07 -1068.86 6.23 600
8971 1278.08 -672.27 6.23 600
8972 1430.93 -194.6 6.23 600
8973 738.09 -1265.18 6.15 600









4.3.1 Single-wavelength Photon Sieve

Figure 4-5 shows four schematic patterns of single-wavelength photon sieves. The

red pinholes represent those designed to focus 600 nm light, while the blue ones are

designed to focus 500 nm light. Table 4-2 shows the number of holes and the open hole

area for the four single-wavelength photon sieves and one of the dual-wavelength photon

sieve, 6-sector.



.: .i:...


1 ... . .... .....


610 510 605 505

Figure 4-5. Schematic drawing of single-wavelength photon sieve patterns. Red and blue
pinholes are the pinholes designed to focus 600 nm and 500 nm wavelength,
respectively. Combining 605 and 505 can result the pattern of 6-sector, as
shown in Figure 4-6.

Table 4-2. Number of holes and open hole area for the 4 single-wavelength photon sieves
and 6-sector (the combination of 605 and 505). The percentage of open hole
area are the ratio of open hole area of a specific PS over the one of 610 (610
was set to be 100%).
610 510 605 505 6-sector
number of holes 10653 7478 5280 3693 8973
open hole area (tm2) 2228306 2219339 1106907 1102851 2209758
% of open hole area 100 99.6 49.7 49.5 99.2


Though the number of holes for 610 and 510 are quite different (7478 in 610 and

10653 in 510), the open hole area for the two complete PS are very close to each other

(only 0.4 % difference). Lenses 605 and 505 (3-sector) are half of the complete single-

wavelength photon sieves (percentage of open hole area is greater than 49.5%). The open

hole area of the 6-sector is 0.8% smaller than that of 610 due to the sectional boundaries,









where no open holes are placed. The open hole area for the photon sieves is slightly

different, but the difference is less than 1%. An optical micrograph of a 605 lens is

shown in Figure 4-6. Combining the designs of lenses 605 and 505 results in the 6-sector

dual-wavelength photon sieve pattern, as discussed above and shown in Figures 4-4 and

4-7.
























Figure 4-6. Optical micrograph for the 605 single wavelength photon sieve.

4.3.2 Dual-wavelength Photon Sieve

Dual-wavelength patterns were generated with either a sectional or concentric

designs. They are shown schematically in Figure 4-7. As before, red and blue pinholes

are designed to focus 600 nm and 500 nm light, respectively. The dual-wavelength

photon sieve patterns were generated by combining the hole pattern of the two single-

wavelength patterns, 610 and 510 in Figure 4-5, with different sector numbers for the

sectional designs or area ratios for the concentric designs. Optical micrographs of the 6-









sector and 5in6-70% lenses are shown in Figure 4-8. The area ratios shown in the

concentric dual-wavelength PSs are rounded percentages based on the radii of the areas

containing holes for either 500 nm or 600 nm light. The actual ratios of the open hole

areas for the 500 nm and 600 nm pinholes are 51.1% for 6in5-50% for 500 nm designed

pinholes (48.9% for 600 nm designed pinholes).






























Figure 4-7. Schematic drawing of dual-wavelength photon sieve patterns. Red and blue
pinholes are designed to focus 600 nm and 500 nm light, respectively. The
percentage shown in the concentricpattem name indicated the area occupied
by holes with the wavelength design for the center zone. For example, 5in6-
70% means that the blue (500 nm) holes are in the center of the concentric
designed dual-wavelength PS with nominally 70% hole area and red holes
(600 nm) are in the outer zone with 30% hole area. The actual percent of
open area of holes are very close to these nominal values.

























Figure 4-8. Optical micrographs of dual-wavelength photon sieves (a) 6-sector (b) 5in6-
70%. The red arrows indicate the boundaries between 500 nm and 600 nm
pinholes.

4.4 Characterizations

The two primary characteristics used to evaluate the quality of a photon sieve were

the FWHM and peak intensity of the corresponding point spread function (PSF). The

PSF of each photon sieves was measured with a modified Perkin-Elmer 16U grating

spectrometer with a charge-coupled device (CCD) camera. The Perkin-Elmer 16U

grating spectrometer, the CCD camera, and the measurements of focal length and PSF are

explained in the next three sections below.

4.4.1 Perkin-Elmer 16U Grating Spectrometer

A schematic drawing of the modified Perkin-Elmer 16U grating spectrometer is

shown in Figure 4-9. It was capable of measurements in the near-infrared (NIR), visible,

and ultraviolet (UV) regions from wavelengths of 2600 nm to 220 nm (3800 cm-1

45000 cm-1; 0.5 5.8 eV). The system consists of multiple light sources, a grating

monochromator, and a series of mirrors allowing collection of transmission data with two

photon detectors or measurement of the PSF with a CCD camera. The transmission and

the PSF arrangements are shown as (A) and (B), respectively, in Figure 4-9.


:,Cr
"'' I,
+,r +r
...;, ~lllk-
::

;.~~



































Figure 4-9. Schematic drawing of the modified Perkin-Elmer 16U grating spectrometer.
Part (A) and (B) are used to measure transmission and PSF, respectively.

The light sources used for NIR to visible, and UV regions were a tungsten (W)

lamp or a deuterium (D2) lamp, respectively.The tungsten lamp was used to characterize

PS lenses designed for 500 nm and 600 nm. The illumination spectra from 496 nm and

773 nm for a W lamp was measured and shown in Figure 4-10. The intensity of light

from the W lamp at 600 nm was about 4.6 times stronger than that at 500 nm.

The dispersion element inside the monochromator is a blazed reflection grating,

and is shown schematically in Figure 4-11. The grating equation is expressed as [9]:

d (sinOm sinOi) = mX (4-1)

where d is the groove spacing, 0m is the diffraction angle at mth order, Oi is the incident

angle and X is the wavelength. The diffraction angles are dependent on the wavelength










resulting in dispersion of the light. Mirrors increase the path length of the light and

therefore the divergence prior to the light reaching the exit slit.




Intensity of Tungsten Lamp at Various Wavelength

90000
80000
70000
.g 60000


W 40000
30000
20000



450 500 550 600 650 700 750 800

Wavelength (nm)


Figure 4-10. The measurement result of intensity versus wavelength for the tungsten
lamp used in the optical bench (scan mode). The relative intensity at 600 nm
is about 4.6 times higher than at 500 nm.


Figure 4-11. Gratings (a) transmission amplitude grating (b) blazed reflection grating [9].

The wavelength resolution of the monochromator is controlled by the entrance and

exit slits. The entrance slit controls the incident beam size which only allows a very

small portion of light to enter the monochromator to ensure that the light rays that strike









the grating are parallel. A stepping motor controls the grating rotation and allows a

certain portion of the light spectrum to pass through the exit slit. Two filters, a high- and

a low-pass filter, are placed in the optical pathway to create a band-pass filter for the

wavelength range of interest, which eliminates spurious signals from higher orders of

diffraction.

The transmission pathway (part (A) in Figure 4-9) contains a series of mirror and

two light detectors (a lead sulfide (PbS) and a silicon (Si) detector) but only the Si

detector was used for visible light in this study. The PSF pathway (part (B)) in Figure 4-

9) consists of a point source aperture of 100 |tm, a 3 mm aperture, and a CCD camera.

The point source aperture defines the point source for measurement of the PSF. The 3

mm aperture restricts the measurement to the area of a photon sieve. The CCD camera

provides a read-out of intensity versus x and y coordinates for generation of the PSF as

described below.

4.4.2 Charge-Coupled Device (CCD) Camera

A CCD is a sensor that consists of grid-like array of coupled capacitors, which can

store electric charges after exposure to light. A schematic drawing of a CCD is shown in

Figure 4-12 [79]. The electric charge generated on each capacitor, or pixel, is

proportional to the light intensity impinging on that location. After capturing an image,

the first row of capacitors transfer the amount of charge on each pixel to a readout

register, which converts the charges to voltages. The charges are deleted after reading,

and the charges from the next row are moved to the readout register. The process is

repeated until the charges of the last row of array been read. The voltages from the array

form the two dimensional image.









Last raw
Spread










read
o.to output amplifier

Figure 4-12. An illustration of the CCD read-out mechanism. The white squares are the
readout register and are connected to an output amplifier. Charges generated
in each row are moved down to the readout register and transformed to
voltages for display purposes [79].
The CCD camera used in the experiment is a WinCamD camera with a Sony

progressive scan /2 inch CCD that contains 1360 (H) x 1024 (V) 4.65 |tm square pixels.

It also has a 14-bit (16384 level) analog to digital converter (ADC) which provides better

resolution for the input signals. The electronic shutter controls the exposure time from 16

to 1048 ms in a 16 ms step. It has two capture modes: full and fast. The full mode gives

a pixel size of 4.65 x 4.65 |tm while the fast mode gives a larger pixel of 9.3 x 9.3 |tm but

takes less time to capture images. Only the fast mode (9.3 |tm pixel size) was used for

the measurement in this research. The CCD inside the WinCamD exhibits a saturation

irradiance of 0.15 mW/cm2 under a monochromatic light with wavelength of 630 nm and

exposure time of 25 ms [80]. Saturation of a CCD is the highest possible number of

electrons that a pixel can contained and is generally referred to as the "full well" capacity









[81]. Saturation irradiance is the power of incident light per unit area that causes the

saturation of a CCD. If the incident intensity is higher than the saturation irradiance, a

flat-top (saturated intensity) PSF will form, as shown in Figure 4-13. The damage

threshold of the CCD is a few mW/cm2. Damage threshold is the highest irradiance that

a CCD can tolerate without causing permanent damage [82]. Saturation irradiance and

the damage threshold need to be noted in order to prevent artifact or damage,

respectively, to the CCD camera. In this research, all the PSFs were measured under the

normal condition of the CCD camera without saturation.


PSF of Refractive Lens under Polychromatic White light



S12000


0 V 3
5000
-m






0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
x(um)


Figure 4-13. Saturated PSF. The flat-top of the PSF indicated the saturation of the CCD
camera. The saturated intensity of this 14-bit WinCamD CCD camera was
found to be around 15000 (15163 in this example).

A sample screen of a PSF measurement taken by WinCamD CCD camera is shown

in Figure 4-14. The two one dimensional (1-D) PSFs shown at the bottom represent the

intensity profiles across the focused point along the X and Y axes, which are shown as a

900 crosshair in the image. The image at the right shows the three dimensional (3-D)

PSF. The color column at the right side of the 3-D PSF shows the intensity scale from

high to low intensity as white, pink, red, yellow, to blue.