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Key Factors for Control of Micro Stereo Lithography System

Permanent Link: http://ufdc.ufl.edu/UFE0043078/00001

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Title: Key Factors for Control of Micro Stereo Lithography System
Physical Description: 1 online resource (47 p.)
Language: english
Creator: PANDEY,ABHINAV
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

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Subjects / Keywords: Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract: Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science KEY FACTORS FOR CONTROL OF MICRO STEREO LITHOGRAPHY SYSTEM By Abhinav Pandey May 2011 Chair: Toshikazu Nishida Cochair: David Arnold Major: Electrical and Computer Engineering Micro stereo lithography (?SL) process is gaining a lot of popularity due to its ability to fabricate complex and intricate 3D structure over a wide variety of materials. In order to build a ?SL system several parameters need to be known. Some of the most important parametrs are the curing depth and divergence of light produced by light source. Curing depth is calculated as a function of initiator and absorber concentration. An extensive mathematical model is derived taking into account the initiator concentration, absorber concentration and temperature effects. Solutions with different absorber and initiator concentration are used to show the monotonic dependence of initiator and absorber on curing depth. The exponential dependence of temperature is also demonstrated. Divergence study is performed to understand the effects of interference of light along the edges. As maintaining a closed gap between mask and monomer solution is a challenge, divergence study is used to derive the maximum allowed separation between mask and monomer solution.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by ABHINAV PANDEY.
Thesis: Thesis (M.S.)--University of Florida, 2011.
Local: Adviser: Nishida, Toshikazu.
Local: Co-adviser: Arnold, David.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2012-04-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043078:00001

Permanent Link: http://ufdc.ufl.edu/UFE0043078/00001

Material Information

Title: Key Factors for Control of Micro Stereo Lithography System
Physical Description: 1 online resource (47 p.)
Language: english
Creator: PANDEY,ABHINAV
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science KEY FACTORS FOR CONTROL OF MICRO STEREO LITHOGRAPHY SYSTEM By Abhinav Pandey May 2011 Chair: Toshikazu Nishida Cochair: David Arnold Major: Electrical and Computer Engineering Micro stereo lithography (?SL) process is gaining a lot of popularity due to its ability to fabricate complex and intricate 3D structure over a wide variety of materials. In order to build a ?SL system several parameters need to be known. Some of the most important parametrs are the curing depth and divergence of light produced by light source. Curing depth is calculated as a function of initiator and absorber concentration. An extensive mathematical model is derived taking into account the initiator concentration, absorber concentration and temperature effects. Solutions with different absorber and initiator concentration are used to show the monotonic dependence of initiator and absorber on curing depth. The exponential dependence of temperature is also demonstrated. Divergence study is performed to understand the effects of interference of light along the edges. As maintaining a closed gap between mask and monomer solution is a challenge, divergence study is used to derive the maximum allowed separation between mask and monomer solution.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by ABHINAV PANDEY.
Thesis: Thesis (M.S.)--University of Florida, 2011.
Local: Adviser: Nishida, Toshikazu.
Local: Co-adviser: Arnold, David.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2012-04-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043078:00001


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1 KEY FACTORS FOR CONTROL OF MICRO STEREO LITHOGRAPHY SYSTEM By ABHINAV PANDEY A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2011

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2 2011 Abhinav Pandey

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3 To my f amily

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4 ACKNOWLEDGMENTS I would like to thank my parents for their continued support and love. I am also truly grateful to my advisor Prof. Toshikazu Nishida for all his guidance. He supported me, encouraged me and guided me whenever needed. I feel really fortunate to hav e him as my advisor. I have learnt a lot of valuable lessons both academic and nonacademic, in the past tw o years while working with him I believe the experience I had with him was unique and it will truly help me in my future endeavors and for that I am really grateful to him. I would also like to thank my friend Raphael I used to have really long discussio ns with him and learnt a lot of valuable stuff. I really enjoyed working with him and I am thankful to him for all of his support.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 6 LIST OF FIGURES ................................ ................................ ................................ .......... 7 LIST OF ABBREV IATIONS ................................ ................................ ............................. 8 ABSTRACT ................................ ................................ ................................ ..................... 9 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 10 History ................................ ................................ ................................ ..................... 10 Working Principle ................................ ................................ ................................ .... 11 Issues ................................ ................................ ................................ ..................... 12 2 CURING DEPTH STUDY ................................ ................................ ....................... 16 Mathematical Model ................................ ................................ ................................ 17 Effect of Absorber Addition ................................ ................................ ..................... 20 Effect of Temperature ................................ ................................ ............................. 21 Experi ment Setup ................................ ................................ ................................ ... 23 3 DIVERGENCE STUDY ................................ ................................ ........................... 38 4 CONCLUSION ................................ ................................ ................................ ........ 43 LIST OF REFERENC ES ................................ ................................ ............................... 45 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 47

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6 LIST OF TABLES Table page 1 1 Comparison of different micromachining techniques ................................ .......... 15 3 1 Experimentally computed angle of convergence at different depth .................... 41

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7 LIST OF FIGURES Figure page 1 1 Micro Stereo Lithography system setup ................................ ............................. 15 2 1 Curing Depth as a function of both initiator and energy dose. ............................ 28 2 2 Curing Depth as a function of time and area of exposure. ................................ .. 29 2 3 Temperature as a function of time and area of exposure. ................................ .. 30 2 4 Chemical structure. ................................ ................................ ............................. 31 2 5 Experimental setup used for curing depth study. ................................ ................ 31 2 6 Curing depth as a function of time for constant intensity exposure and absorber concentration of 1%.. ................................ ................................ ........... 32 2 7 Curing depth as a function of time for constant intensity exposure and absorber concentration of 3%.. ................................ ................................ ........... 33 2 8 Curing depth as a function of time for constant intensity exposure and initiator concentration of 2%.. ................................ ................................ ............. 34 2 9 Curing depth as a function of time for constant intensity exposure and initiator concentration of 4%.. ................................ ................................ ............. 35 2 10 Curing depth as a function of time for constant intensity exposure. .................... 36 2 11 Result for constant exposure time of 100 sec.. ................................ ................... 37 2 12 Result for constant curing depth of 100 m.. ................................ ...................... 37 3 1 Profile of mask having walls between holes as opaque to UV. ........................... 41 3 2 Diameter of Hole as a function of Depth. ................................ ............................ 41 3 3 Chemical St ructure of SU 8 Photoresist ................................ ............................ 41 3 4 Structure developed on SU 8 coated wafer as a function of distance. ............... 42

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8 LIST OF ABBREVIATION S CAD Computer Aided Design HDDA Hexanediol Diacrylate LIGA German acronym for Lithography, Electroplating and Molding MEMS Micro Electro Mechanical System SL Micro Stereo Lithography ODE Ordinary Differential Equation Si Silicon 3D Three Dimensional Ec Threshold Exposure UV Ultra Violet 3D LCVD 3 Dimensional Laser Chemical Vapor Deposition

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9 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science KEY FACTORS FOR CONTROL OF MICRO STEREO LITHOGRAPHY SYSTEM By Abhinav Pandey May 2011 Chair: Toshikazu Nishida Cochair: David Arnold Major: Electrical and Computer Engineering Micro s tereo lithography ( SL) process is gaining a lot of popularity due to its ability to fabricate complex and intricate 3D structure over a wide variety of materials. In order to build a SL system several parameters need to be known. Some of the most importa nt parametrs are the curing depth and divergence of light produced by light source. Curing depth is calculated as a function of initiator and absorber concentration. An extensive mathematical model is derived taking into account the initiator concentration, absorber concentration and temperature effects. Solutions with different absorber and initiator concentration are used to show the monotonic dependence of initiator and absorber on curing depth. The exponential dependence of temperature is a lso demonstrated. Divergence study is performed to understand the effects of interference of light along the edges. As maintaining a closed gap between mask and monomer solution is a challenge, divergence study is used to derive the maximum allowed separa tio n between mask and monomer solution

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10 CHAPTER 1 INTRODUCTION History A tremendous growth has been observed in the field of micro electro mechanical system (MEMS) during the past 20 years. Aside from laying planar 2D structure on the semiconductor substr ate, MEMS technologies require micro fabrication of complex 3D structures. The most typical silicon micro machining technologies, anisotropic etching and surface micromachining are used in past to produce 3D structures. However more complex structures cannot be fabricated using above mentioned techniques. Another limitation is due to the fact that these processes only apply to a handful of common semiconductors, metals and dielectrics [1]. In order to have complex 3D structures on a wide variety of materials, Becker et al. proposed LIGA process in 1986[2]. LIGA is a German word and it stands for Lithography, Electroplating and Molding. Primary template is formed using lithography and then its filled by metal using electro deposit ion. However very complex structures cannot be formed using this technique. 3D Laser Chemical Vapor Deposition is presented by Williams and Maxwell [3]. They demonstrated this technology for manufacturing of helical microstructures. 3D LCVD uses a scanni ng laser beam to deposit solid materials. The shape of the fabricated part is controlled by focusing the scanning laser beam. Another method is proposed by Cohen et al [4]. They demonstrated electrochemical fabrication process as an extension of LIGA pro cess to produce complex 3D structures. Metals are deposited in a layer by layer fashion which acts as electrode masks. The thickness of the layer is controlled by a planarizing procedure.

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11 However all of the above mentioned techniques suffer from high equ ipment cost and a very low throughput. The shortcomings of the above mentioned techniques are addressed by a new technique termed stereo lithography. This technique was invented by Chuck Hull in 1986 [5]. This technique forms the basis of micro stereo lit hography process. Micro stereo lithography process is same as stereo lithography process except for the fact that it is used to make much smaller parts. Working Principle The basic idea behind the micro stereo lithography process is the layer by layer for mation of a UV curable resin. Exposing the resin to UV hardens a small layer. This layer is then moved down and fresh layer of resin covers the hardened surface. Exposing it again makes the second layer stacked on top of the first one. A schematic of such a process is shown in Fig ure 1 1 Using such a technique lateral resolution of as low as 600nm is achieved using a two photon polymerization process [6]. Another important benefit of using micro stereo lithography is freedom to fabricate on a vast variety of materials. It is not just limited to UV curable resins. Complex 3D shapes in ceramics and metals also are demonstrated by mixing fine powder with UV curable resin [7]. Micro stereo lithography can be subdivided into two main sub processes namely vector by vector micro stereo lithography and integral micro stereo lithography. In vector by vector approach a focused light beam is scanned on the surface of monomer [8]. It provides a very high level of resolution. It does not require any mask or any specific tool. A complex 3D structure with very high aspect ratio can be fabricated by slicing a

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12 3D CAD file. However the process takes a lot of time and thus not suitable for batch production of micro structures. On the other hand, in the integral micro stereo l ithography a complete layer of monomer is exposed by projecting the image on it. In order to generate complex structure a digital micro mirror or an L iquid C rystal D isplay device can be used to project the image of cross section [9, 10]. To fabricate simpl e structure with high aspect ratio a fixed mask can also be used. The bitmap image is used to pattern light (typically UV ) which is then focused onto the surface of a light curable resin to form a layer. Subsequent layers are built on top of previous laye rs to form a 3 D structure. Because the light is focused, the realizable cross sectional is restricted. This limitation to mask projection micro stereo lithography can be overcome by "stitching" multiple segments of the total desired cross section together using a stage that can articulate in the X, Y axes. Multiple overlapping exposures are made at each level thus quilting together the total desired cross sectional area [11] A comparison of different micro stereo lithography technique is shown in Table 1 1 Issues One of the main challenges in micro stereo lithography fabrication is to accurately quantify the curing depth. When a monomer solution is exposed to light the extent of polymerization gradually decreases with an increase in depth from the surfa ce. Curing depth is defined as the depth inside the monomer solution up to which a critical polymerization is occurred on UV exposure. It is usually a complex function of exposure dose, reactivity of monomer solution and temperature of the monomer solution Curing depth dictates the thickness of layer to be formed. If a particular thickness is required the amount of exposure dose needed is also governed by curing depth Another

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13 important issue is the viscosity of the UV curable resin. In layer by layer for mation method after each step a fresh layer of monomer is required on top of polymerized surface. Also this small layer needs to be flat to ensure uniform polymerization across the entire cross section. After each step some time is required for fresh monom er layer to level across the surface. A more viscous liquid will require a longer leveling time and it may also happen that it will not level at all. In such a case platform should be dipped inside and then lifted back up [12]. Some other factors that lim it the resolution of the micro stereo lithography process are bleaching and print through. At high exposure doses, stereo lithography monomers undergo bleaching as the polymerization reactions precede. As a consequence of bleaching, radiation penetrates th e monomer more easily, thus causing polymerization at greater depths. Increased polymerization depths result in lower Z resolution. This phenomenon is known as bleaching effect [13]. Another challenge is the print through error [14]. When a layer is polyme rized, the layer thickness is set to the depth where the exposure falls to the threshold exposure Ec The monomer below this cured layer does not experience an exposure equal to Ec. However, it receives some exposure. As subsequent layers are polymerized, this point in the monomer receives incremental exposure until finally reaching Ec causing polymerization. The result is unwanted curing and the error introduced is called the print through error. This work deals with the issues mentioned above. An in dep th study of curing depth is performed and presented in Chapter 2. The effect of absorber concentration, initiator concentration, light intensity and temperature is taken into account. The mathematical model is also supported by the experimental results.

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14 The lateral resolution can also be limited by the divergence of collimated light source. A diverging light would set a maximum allowable separation between light source and monomer layer. Chapter 3 addresses the issue of divergence of collimated light sour ce. Experimental results are shown to quantify the effect upon lateral resolution as a function of separation between a light source and monomer layer. Chapter 4 summarizes the results of curing depth study and divergence study.

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15 Table 1 1 Comparison of different micromachining techniques Method Pros Cons LIGA High resolution High aspect ratio Used for simpler structure 3D Laser CVD Free standing helical structure Fast Limited material process Expensive EFab True 3D geometry Fast For metals only Expensive 2 Photon SL Submicron resolution Layer by layer is not needed Fast build time Very expensive Limited area of exposure Slow over large area Vector by Vector SL High Resolution Fast build time Complex free standing structure Limited area of exposure Slow over large area Expensive Integral SL Fast over large area High resolution Complex Structure High cost of equipment Limited area of exposure Figure 1 1 Micro Stereo Lithography system setup

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16 CHAPTER 2 CURING DEPTH STUDY Curing depth is defined as the depth up to which 3 dimensional gel networks is formed when monomer solution is irradiated with light. The critical conversion point of gel network known as gelation decides the level of polymerization. This conversion point is a function of both reaction rate and amount of photons present. Active research has been going on to study the reaction kinetics of these systems [15, 16]. Numerous parameters influence the polymerization reaction rate. Some of the most influential par ameters are temperature, concentration of absorber and initiator and light intensity. The effect of these parameters on overall bond conversion is well known however an in depth study for the roles of these parameter on cure depth has not been done. The typical reactants in photo polymerization reaction are initiator, and monomer molecule. The reaction mainly consists of three steps. The first step is initiation of free radical by photo radiation. The reaction involved is as follow The initiator molecule is split to generate free radicals when UV light shines upon it and is denoted by These free radicals combine with monomer molecules to generate longer chain radicals or oligomers. This process step is known as propag ation and the reactions involved are as follows The last step is the termination. Free radicals can combine with it or can combine with a chain to terminate the reaction. The reactions involved are as follows [ 2 1] [2 2] [2 3]

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17 Mathematical Model A model for curing dept h is derived using the kinetic e quation for photoinitiated polymerization [17]. where is given by is the rate of polymerization and is the rate of initiation of free radical by UV light exposure. is the concentration of monomer and is the concentration of radical chain. is the reaction rate constant of propagation. During steady state initiation of radicals due to light impingement is balanced by termination. Hence using the steady state approximation can be expressed [17]. where is the rate of initiat ion of polymer and is the reaction rate constant of termination. The initiation rate is a function of intensity of incident light. Its value is given by is the intensity of light at a depth z in the monomer solution. is the concentration of initiator, is the quantum yield of photo initiator and is the molar [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]

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18 extinction coefficient. Intensity of incident light at depth z can be given by Beer Lambert law. As the monomer solution is homogenous and scattering of light is negligible, Beer Lambert law can be applied. According to this, intensity of light in a medium at a depth z is given by [18, 19] where is the intensity of light at the surface. Hence Equation 2 10 can be written as Substituting the value of in the Equation 2 12 Assuming the terms on right hand side are time independent, separation o f variable can be used to obtain a closed for m solution of the differential e quation. However if the temperature dependence of reaction rate constant and are taken into account no closed form solution can be obtained. Thus the temperature depen dence is handled later in this chapter and numerical solutions are generated using M ATLAB Bringing on the left hand side and integrating with respect to time yields The de gree of polymerization is defined as [2 11] [2 12] [2 13] [2 14] [2 15]

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19 The relationship between degree of polymerization and extent of polymerization p can be given as Substituting this and squaring both sides yield Curing depth is defined as the depth at which the extent of polymerization reaches a threshold known as gel point [20, 21]. At this threshold transition from polymer to monomer takes place and it limits the cur ing depth. Substituting this and taking natural log on both sides Equation 2 18 reveals the dependence of curing depth on exposure time t and initiator concentration As initiator concentration is increased the rate of reaction increases, however the increase in initiator concentration decreases the amount of photon reached at depth z. These two conflicting behaviors give rise to an optimal value of initiator conce ntration beyond which curing depth starts to decrease. Differentiating with respect to yields Equating it to zero yields the optimal value of as Putting the value of in the Equation 2 18 yields [2 16] [2 17] [2 18] [2 19] [2 20]

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20 Fig ure 2 1 shows a plot of curing depth as a function of both initiator concentration and energy dose. Curing depth increases with an increase in energy dose. However for increasing initiator concentration it first increase, attains a maximum value and then rol ls off. As predicted by Equation 2 20 the optimum value of initiator is a function of energy dose also. Due to this the maximum value of curing depth in Fig ure 2 1 is obtained at different values of for different values of energy dose. Effect of Absorber Addition Sometimes it is required to have a small curing depth. For instance in micro stereo lithography, if curing depth is too high then the step size needs to be high too which in turn reduces the lateral resolution [22]. In order to reduce the curing depth certain absorbers may be added to the monomer solution. The role of the absorber is to absorb the incoming photon thereby decreasing the reaction rate. Since absorber only affects the incoming photon and does not have an y influence on generation of radical, In presence of absorber the rate of initiation of polymerization process can be written as where is the concentration of absorber in the monomer solution. Substitution of Equation 2 22 in to Equation 2 9 yields Assuming absorber absorbs bulk of the light and contribution of initiator in light absorption is negligible as compared to absorber Equation 2 23 can be simplified to [2 21] [2 22] [2 23]

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21 Looking at Equation 2 24 it can be observed that curing depth is now a monotonic ally increasing function of initiator concentration. Hence by using an absorber curing depth can be controlled more accurately Differentiating Equation 2 24 with respect to yields the maximum value of up to which monotonicity is insured. The maximum value of is thus given by Equation 2 25 predicts that by addition of absorber, the optimum value of can be increased substantially and thus curing depth can be controlled more precisely by changing the initiator concentration. Effect of Temperature Temperature plays a major role in the polymerization reaction rate. Reaction rate can be increased exponentially by increasing the temperature. Since polymerization reactions are usually exothermic, the temperature of monomer solution increases as reaction proceeds further. This increased temperature can drastically change the curing depth. T hus it is necessary to model the effect of temperature on curing depth model derived in previous section. W hile deriving the curing depth e quation it was assumed that except for every other parameter is temperature independent. However this is no t qui te the case. Both initiation rate and termination rate of radicals are altered by changing the temperature of the monomer solution. The reaction rate constants of radical initiation and termination are strong function of temperature. Their value can be given by Arrhenius relationship [2 24]

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22 If the temperature of system changes with time, value of and also changes with time. As the reaction proceeds the temperature of the system increases due to heat released by enthalpy of reaction. As the temperature increases, the reaction rate increases and polymerization goes on deeper and deeper. By including the temperature effect it is expected to have a larg er value of curing depth as compared to the case without temperature consideration. The rate of increase of temperature can be computed by the total heat generated by the polymerization reaction. If be the amount of heat generated per mole of the poly mer then Inclusion of temperature d ependence prohibits t he derivation of a closed form e quation for curing depth. In order to compute curing depth as a function of time Equation s 2 28 and 2 29 needs to be solved numerically. However the curing depth is not an independent variable, ro utine methods of solving ODE does not work here. In order to obtain curing depth as function of time, curing depth is set to a particular fixed value and then Equation s 2 28 and 2 29 are iterated to obtain the time required to reach the gel point. This met hod is then iterated for different values of curing [2 26] [2 27] [2 29]

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23 depth to plot curing depth as a function of time. The dif ferential e quations are solved in M ATLAB using ode45 solver. Figure 2 2 shows the curing depth as a function of time for different areas of expo sure. As the area of exposure is increased, curing depth increases drastically. As the cuing depth is a strong function of temperature, if a smaller area is exposed the rise in temperature is insignificant. For smaller area the curing depth is similar to a s predicted by Equation 2 8. For large area of exposure curing depth increases significantly initially and then rolls off. The same behavior can be observed in temperatu re profile also as shown in Figure 2 3. Fig ure 2 3 shows the change in temperature as a function of time, it is interesting to note that temperature starts to increase rapidly but then rolls off. The primary reason behind such a behavior is the fact that as time passes by, more and more reaction goes to completion and thus the heat generated rolls off as time passes by. The strong temperature dependence can be observed by looking at T = 200 sec. Even for a temperature difference of 15 0 C the change in curing depth is more than 40%. Also the % change in curing depth is at its maximum at start and then it keeps a constant value. Both of these factors points to the fact that temperature plays a major role in curing depth. Experiment Setup In order to verify the validity of curing depth model proposed, exper imental study of curing depth is performed. The monomer used for the curing depth study is HDDA ( Hexanediol Diacrylate ) HDDA own in Figure 2 4. The photo initiator used is 2 hydroxy 2 methylpropiophenone and photo absorber used i s 2 hydroxy 4 (octyloxy)benzophenone The che mical structure of photo initiator and

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24 absorber is shown in Figure 2 4 A and 2 4 B The concentration of photo initiator is taken as 2% and 4% and concentration of absorber is taken as 1% and 3%. Mercury lamp is used to produce illumination. The UV lamp produces monochromatic light of wavelength 365nm with divergence less than 2.5 0 The experimental setup for curing depth study is shown in Fig ure 2 5. A clear glass plate is used as mask and is kept in contact wit h the monomer solution. The top surface of the glass mask is covered with a UV blocking layer. A small square opening of 1mm 2 is cut at the center. The reason behind exposing a small area is to minimize the temperature effects. The UV light intensity is k ept at its maximum value of 13.1mW/cm 2 Exposure dose is varied by opening the shutter for a variable time. Shutter is opened from 10s to 200s in the step of 10s. The resulting structure formed is then rinsed with methanol and dried off by blowing nitrogen to remove any un polymerized monomer. After rinsing the thickness of polymer is measured using a screw gauge. The curing depth is then plotted as a function of time and is shown in Fig ure 2 6 to Figure 2 9 Fig ure 2 6 and Figure 2 7 shows the curing depth as a function of time for different initiator and absorber concentrations. It is readily visible that with an increase in initiator concentration curing depth increases. The dependence of initiator concentration on curing depth can be computed as follows. Equation 2 6 can be simplified as follows. [2 30] [2 31]

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25 For absorber = 1%, (B1/A1) (B2/A2) yields 0.53 whereas log( ) has a value equals 0.35 For absorber = 3%, (B1/A1) (B2/A2) yields 0.45 whereas log( ) has a value equals 0.35. The slight dis crepancy is due to the fact that curing depth is computed using steady state assumption which gives rise to square root dependence. When steady state is not obtained initiator will have dependence which is greater than square root as rate of initiation is higher than rate of termination. Fig ure 2 9 shows the curing depth as a function of time for different absorber concentration. It is readily visible that with an increase in a bsorber concentration curing depth decreases. In order to understand the significance of curing depth, another experiment for constant curing depth is performed. If two different solutions have same curing depth then the resulting polymerized structure wo uld be the same. The overall process does not depend on the individual absorber and initiator concentration but depends upon the curing depth. In order to validate this hypothesis Two monomer solutions, one having 1% initiator and 2% initiator and other ha ving 3% absorber and 2% initiator are taken. Their curing depth curve is shown in Fig ure 2 10 These two solutions are irradiated to the UV light of intensity 13.1mW/cm 2 with an area of exposure of 1mm 2 The mask contains two types of pattern which results in holes of 82 m and 164 m diameter with 100 m and 200 m of pitch and posts of the same dimensions as holes. [2 32]

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26 The two monomer solution were irradiated for same amount of time = 100s. Solution of low absorber has a very high curing depth and thus results in loss of features. The results are shown in Fig ure 2 1 1 Also the loss of feature is more pronounced in the structure with lower feature size. Solution having 3% absorber and 4% initiator is abbreviated as Solution 1 and Solution having 1% absorber and 2% i nitiator is abbreviated as Solution 2 The case for constant curing depth is shown in Fig ure 2 12 The solution with lower absorber concentration is irradiated for a smaller period of time. Looking at the Fig2 9 for a constant curing depth of 100m Solu tion 1 is exposed for 20sec and solution 2 is exposed for 100 sec. The resulting structure is shown in Fig ure 2 1 2 By observing Figure 2 1 2 it can be said that both the solutions resulted in similar looking structures. However the exposure time is greatly reduced for solution with low absorber concentration. It is evident from Figure 2 1 1 and Figure 2 1 2 that curing depth is among the most important parameter for polymerization process. If two monomer solutions have same curing depth then they will result in similar looking structures despite having entirely different absorber and Initiator concentrations. Curing depth can be tuned by varying initiator and absorber concentrations, however addition of absorber makes the tuning easy. An increase in absorber concentration will decrease the curing depth and increase in initiator concentration will increase the curing depth. Their dependence is derived analytically in Equation 2 24. Another important parameter is the temperature of monomer solution. It has expo nential dependence on rate of reaction and thus it can change the curing depth substantially. The situation is exacerbated by the fact that temperature provides a

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27 positive feedback and thus a large increase in curing depth is observed at the start of the r eaction. This behavior result in print through error if a large area is exposed and temperature consideration is not taken into account.

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28 Figure 2 1 Curing Depth as a function of both initiator and energy dose. The parameters used to generate this image are taken from [12] 0 0.001 0.002 0.003 0.004 0.005 1,000 6,000 11,000 16,000 21,000 26,000 31,000 36,000 41,000 46,000 Initiator Conc. in mol/L Energy in J/m 2 10 1 10 2 10 3 10 4

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29 Figure 2 2 Curing Depth as a function of time and area of exposure. The red curve shows the curing depth for an exposed area o f 1mm 2 the blue curve shows the curing depth for an exposed area of 10mm 2 and the green line shows the curing depth for an exposed area of 1cm 2 0 20 40 60 80 100 120 140 160 180 200 0 200 400 600 800 1000 Curing Depth in m Time in Sec

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30 Figure 2 3 Temperature as a function of time and area of exposure. The red curve shows the curing depth for an exposed area of 1mm 2 the blue curve shows the curing depth for an exposed area of 10mm 2 and the green line shows the curing depth for an exposed area of 1 cm 2 295 300 305 310 315 320 325 330 335 0 200 400 600 800 1000 Temperature in K Time in Sec

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31 Figure 2 4 Chemical structure of A) cis 7,cis 11 Hexadecadienyl acetate B) 2 hydroxy 2 methylpropiophenone and C) 2 hydroxy 4 (octyloxy) benzophenone [23] Figure 2 5 Experimental setup used for curing depth study. A B C

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32 Figure 2 6 Curing depth as a function of time for constant intensity exposure and absorber concentration of 1%. The black line shows the logarithmic fit and its Equation is shown next to the curve. y = 77.047ln(x) 139.08 y = 85.712ln(x) 109.57 0 50 100 150 200 250 300 350 400 0 50 100 150 200 Curing Depth in m Time in Sec A = 1%, I = 2% A = 1%, I = 4%

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33 Figure 2 7 Curing depth as a function of time for con stant intensity exposure and absorber concentration of 3%. The black line shows the logarithmic fit and its Equation is shown next to the curve. y = 32.779ln(x) 71.037 y = 34.896ln(x) 59.415 0 20 40 60 80 100 120 140 0 50 100 150 200 250 300 Curing Depth in m Time in Sec A = 3%, I = 2% A = 3%, I = 4%

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34 Figure 2 8 Curing depth as a function of time for constant intensity exposure and initiator concentration of 2%. The black line shows the logarithmic fit and its Equation is shown next to the curve. y = 77.047ln(x) 139.08 y = 32.779ln(x) 71.037 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Curing Depth in m Time in Sec A = 1%, I = 2% A = 3%, I = 2%

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35 Figure 2 9 Curing depth as a function of time for constant intensity exposure and initiator concentration of 4%. The black line shows the logarithmic fit and its Equation is shown next to the curve. y = 85.712ln(x) 109.57 y = 34.896ln(x) 59.415 0 50 100 150 200 250 300 350 400 0 50 100 150 200 Curing Depth in m Time in Sec A = 1%, I = 4% A = 3%, I = 4%

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36 Figure 2 10 Curing depth as a function of time for constant intensity exposure. The two solutions have both different initiator and absorber concentration. y = 77.047ln(x) 139.08 y = 34.896ln(x) 59.415 0 50 100 150 200 250 300 0 50 100 150 200 Curing Depth in m Time in Sec A = 1%, I = 2% A = 3%, I = 4%

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37 Figure 2 11 Result for constant exposure time of 100 sec. A1: Posts of 164m diameter at 20X mag. for Solution 1. A2: Posts of 164m diameter at 20X mag. for Solution 2. B1: Holes of 82m diameter at 20X mag. for Solution 1. B2: Holes of 82m diameter at 20X mag. for Solution 2. C1: Posts of 82m diameter at 20X mag. for Solution 1. C2: Posts of 82m diameter at 20X mag. for Solution 2. D1: Holes of 164m diameter at 20X mag. for Solution 1. D2: Holes of 164m diameter at 20X mag. for Solution 2. Figure 2 12 Result for constant curing depth of 100 m. A1: Posts of 164m diameter at 20X mag. for Solution 1. A2: Posts of 164m diameter at 20X mag. for Solution 2. B1: Holes of 82m diameter at 20X mag. for Solution 1. B2: Holes of 82m diameter at 20X mag. fo r Solution 2. C1: Posts of 82m diameter at 20X mag. for Solution 1. C2: Posts of 82m diameter at 20X mag. for Solution 2. D1: Holes of 164m diameter at 20X mag. for Solution 1. D2: Holes of 164m diameter at 20X mag. for Solution 2. A1 A2 B1 B2 C1 C2 D1 D2 A1 B1 C1 D1 D2 C2 B2 A2

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38 CHAPTER 3 DIVE RGENCE STUDY In proximity micro stereo lithography it is required to maintain the monomer top layer and mask in close proximity (~50 100 m) to overcome the divergence of collimated light source. However maintaining such a small gap during a polymerizati on run is troublesome. A number of factors can disturb the top layer of monomer and cause the monomer and mask surface to be in contact. Some of the factors are vibration due to stepper motor and curling due to stress in the polymer structure. These factor s further reduce the gap as the polymerization reaction proceeds making it more susceptible to unwanted contact. The value of divergence angle of light source sets up a maximum value of the separation between mask and monomer layer. If monomer is beyond t hat limit, spatial resolution of resulting structure will be distorted or in a worst scenario everything will be exposed uniformly. To understand it more clearly consider the case shown in Fig ure 3 2. The mask consists of UV blocking holes as shown in Fig u re 3 1. The UV light is convergent with an angle of The diameter of resulting holes is shown as a function of depth. It is interesting to note that diameter of holes first increases and then starts decreasing. Also when it obtains its maximum value the light can also start making diffraction patterns which will result in distorted shape. Experimental Setup In order to quantify the result, a divergence study is performed. Si wa fers are coated with SU 8 photoresist. It is a negative photo resist used to m ake high aspect ratio structures. SU 8 has a maximum absorption at 365 nm which coincides with the

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39 UV lamp used in this study. When exposed to light, it becomes insoluble to the photo resist developers. The chemical structure of SU 8 is shown in Fig ure 3 3 The mask used to illuminate the wafer has a pattern as shown in Fig ure 3 1. The diameter of the hole is 41 m and the pitch is 50 m. The SU 8 coated Si wafer is put at a certain distance below the mask and then irradiated for 30 sec. The exposed wafer is t hen developed. The resulting pattern for different separation distance d sep is shown in Fig ure 3 4 A to Figure 3 4 E The diameters of the resulting holes on the Si wafer are tabulated in the table 3 1. The angle of divergence of light is calculated using the formula As noted from the table the angle of divergence of collimated light source is in the order of 1.3 0 Using this value the maximum value of can be computed by substituting Substituting this, yields a maximum value of 400 m on separation between mask surface and monomer layer. At separation of 400 m bet ween mask and monomer, all lateral features will be lost. This case is shown in Figure 3 4 D. At 400 m separation the definition of holes is completely lost and a strong interference pattern is observed. This interference pattern increases as separation b etween mask and monomer solution increases. Even at 200 m the edges of holes are not perfectly round and presence of interference pattern can be observed along the edges. When the separation is higher than maximum allowed value the entire substrate is exp osed. This can be seen in Figure 3 4 E where the separation is kept twice the maximum allowed value. In this case the entire SU 8 is exposed.

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40 Divergence study becomes extremely useful to set the gap between mask and monomer layer. Since this gap is constra ined by divergence of light source and also since the effect of interference increases with an increase in separation, a smaller value of gap is preferred. For typical cases the gap desired is usually tens to hundreds of micron. However maintaining such a small gap during the polymerization process is a big challenge. Numerous factors can change the gap between mask and monomer and may result in unintentional contact between the two. The surface roughness of substrate itself is usually few tens of microns. It results in a big challenge to obtain a gap which is of the same order. Meniscus effect on edges also poses a challenge to obtain such a small gap. Apart from these factors the gap between mask and monomer layer changes during the polymerization process also. A very small vibration can cause a contact between mask and monomer layer. Also as polymerization process happens a new monomer layer comes on top of polymerized structure which further reduces the gap. Also if during the polymerization process if p olymerized part is not fully cured and is under stress, it may bend and cause the monomer solution to contact the mask surface. Taking these factors into consideration, the gap between monomer and mask can not be fixed to an arbitrary small value. As seen from the results, the lateral feature size does not degrade if the gap is kept less than half the maximum allowed gap. The divergence study not only provides an upper bound on the gap between mask and monomer but also provides the range on which the latera l resolution is preserved.

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41 Table 3 1 Experimentally computed angle of convergence at different depth Separation in um Diameter of hole in um Angle of Divergence in 0 50 42 1.16 0 100 43.2 1.26 0 200 45.4 1.26 0 Figure 3 1 Profile of mask having walls between holes as opaque to UV. Figure 3 2 Diameter of Hole as a function of Depth. Figure 3 3 Chemical Structure of SU 8 Photoresist [24].

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42 Figure 3 4 Structure developed on SU 8 coated wafer as a function of distance. A: d sep = 50m, B: d sep = 100m, C: d sep = 200m, D: d sep = 400m, E: d sep = 800m, B A A D C E

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43 CHAPTER 4 CONCLUSION Among the various parameters to characterize and control a polymerization process, curing depth is one of the most important parameter. It is directly responsible for the minimum lateral feature size. Hence to obtain a particular cross section, curing depth needs to be controlled very precisely. Also to avoid excess polymerizati on via punch through error per step displacement and exposure dose is determined by curing depth and thus it has to be controlled accurately. An extensive mathematical model of curing depth is presented in this work The effect of initiator and energy dos e is derived and optimal curing depth is computed. As initiator has a complex dependence on curing depth controlling the curing depth by just varying initiator is difficult. The optimal curing depth is not only a function of initiator but also of energy d ose. In order to tune the curing depth more accurately absorber is added so that effect of initiator is simplified. With the addition of absorber curing depth can be increased or decreased more accurately by increasing or decreasing the concentration of i nitiator or absorber. The mathematical model incorporating all of these factors is derived and verified using experimental results. The strong dependence of curing depth on lateral resolution also suggests that two solutions with similar curing depths will produce similar structure. This property of curing depth is verified using experimental results. These results suggest that monomer solution behaves according to curing depth which is a combination of both initiator and absorber concentration rather than their individual concentrations. Another important parameter in characterizing micro stereo lithography is the divergence of collimated light source. This divergence sets the maximum allowable limit on the mask monomer separation without loss of latera l feature size. The effect of

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44 increasing separation on lateral feature size is demonstrated. This study not only provides an upper limit on allowable gap but also the safe region of operation to ensure lateral resolution is not distorted. These two paramet ers are two of the most parameters in a micro stereo lithohgraphy process. These parameters can be used to obtain the value of different variables such as initiator and absorber concentration, exposure dose, step size and gap between mask and monomer. Thes e are the main parameters in a lithography process. By performing a curing depth and divergence study, these parameters can be set accurately which will result in more accurate polymerization process.

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45 LIST OF REFERENCES [1] S.M. Sze, Semiconductor Sensors, Wiley, New York, 1994. [2] E.W. Becker, W. Ehrfeld, P. Hagmann, A. Maner, D. Munchmeyer, Fabrication of microstructures with high aspect ratios and great structural heights by synchrotron radiation lithography, galvanof orming, and plastic moulding (LIGA process), Microelectronic Engineering, Volume 4, Issue 1, May 1986, Pages 35 56 [3] K. Williams, J. Maxwell, K. Larsson, M. Boman, Freeform fabrication of functional microsolenoids, electromagnets and helical springs usin g high pressure la ser chemical vapor deposition Micro Electro Mech anical Systems, 1999. MEMS '99. Twelfth IEEE International Conference on vol., no., pp.232 237, 17 21 Jan 1999 [4] A. Cohen, G. Zhang, F. G Tseng, U. Frodis, F. Mansfeld, P. Will EFAB: r apid, low cost desktop micromachining of high aspect ratio true 3 D M EMS, Micro Electro Mechanical Systems, 1999. MEMS '99. Twelfth IEEE International Conference on vol., no., pp.244 251, 17 21 Jan 1999 [5] Hull, C. (1986), Apparatus for Production of Th ree Dimensional Objects by Stereolithography, U.S. Pat. No. 4575330 [6] S. Maruo, K. Ikuta, Movable microstructures made by two photon thre e dimensional microfabrication, Micromechatronics and Human Science, 1999. MHS '99. Proceedings of 1999 International Symposium on vol., no., pp.173 178, 1999 [7] X. Zhang, X. N. Jiang, C. Sun, Micro stereolithography of polymeric and ceramic microstructures, Sensors and Actuators A: Physical, Volume 77, Issue 2, 12 October 1999, Pages 149 156 [8] A. Bertsch, S. Jig uet P. Bernhard, P. Renaud, Microstereolithography: a Review, Materials Research Society Symposium Proceedings, Volume 758, 2002 [9] A. Bertsch, S. Zissi, J. Y. Jzque l, S. Corbel, and J. C. Andr. Microstereophotolithography using a liquid crystal dis play as dynamic mask generator. Microsystem Technologies 3, no. 2 (February 25, 1997): 42 47. [10] Beluze, Laurence, Arnaud Bertsch, and Philippe Renaud. Microstereolithography: a new proce ss to build complex 3D objects. In Design, Test, and Microfabrication of MEMS and MOEMS, edited by Bernard Courtois, Selden B. Crary, Wolfgang Ehrfeld, Hiroyuki Fujita, Jean Michel Karam, and Karen W. Markus, 3680:808 817. Paris, France: SPIE, 1999. [11] M. Alonso, Optimization of a light emitting diode based projection stereolithograp hy system and its applications, Micro, 2010.

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46 [12] J.H. Lee, R.K. Prud'homme and I.A. Aksay, Cure depth in photopolymerization: experiments and theory, J Mater Res 16 (2001), pp. 3536 3544 [13] X. Zhang, X. N. Jiang, C. Sun, Micro stereolitho graphy of polymeric and ceramic microstructures, Sensors and Actuators A: Physical, Volume 77, Issue 2, 12 October 1999, Pages 149 156 [14] S. Maruo, K. Ikuta, Movable microstructures made by two photon thre e dimensional microfabrication, Micromechatronics and Human Science, 1999. MHS '99. Proceedings of 1999 International Symposium on vol., no., pp.173 178, 1999 [15] J.P. Fouassier, Photoinitiation, Photopolymerization, and Photocuring (Hanser, Cincinnati, OH, 1995). [16] J.P. Fouassier and J.F. Rabek, R adiation Curing in Polymer Science and Technology (Elsevier, New York, 1993). [17] G.G. Odian, Principles of Polymerization, 3rd ed. (Wiley, New York, 1991). [18] J.H. Lambert, Photometrie (Augsburg, Germany, 1760). [19] A. Beer, Ann. Physik Chem. 2, 78 (1 852). [20] S.P. Obukhov, M. Rubinstein an d R.H. Colby, Netw ork Modulus and Superelasticity Macromolecules, Volume 27, Issue 12, Pages 3191 3198, 1994 [21] Hale, Arturo, Macosko, Chri stopher W. and Bair, Harvey E, Glass transition temperature as a function of conversion in thermosetting polyme rs Macromolecules, Volume 24, Issue 9, Pages 2610 2621, 1991 [22] C. Sun, N. Fang, D.M. Wu, X. Zhang, Projection micro stereolithography using digital micro mirror dynamic mask, Sensors and Actuators A: Physical, Volume 121, Issue 1, 31 May 2005, Pages 113 120 [23] http://www.sigmaaldrich.com [24] http://www.microchem.com/products/su_eight.htm

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47 BIOGRAPHICAL SKETCH Abhinav Pandey is a graduate student at University of Florida in Electrical and Computer Engineering. He received his Master of Science degree from University of Florida in spring 2011. He received his Bachelor of Technology degree from Indian Institute of Technology, Kanpur in Electrical Engineering in 2009.