Raul Broto Master Thesis

DESIGN AND FABRICATION

OF INTEGRATED INDIUM

MICROMIRRORS

Raul Broto Cervera

Master Thesis (Projecte Final de Carrera)

September 2012

New Jersey Institute of Technology, Dr. Pérez-‐Castillejos

Universitat Politècnica de Catalunya, ETSETB

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INDEX CHAPTER 1 – INTRODUCTION ………………………………………………………………………..….. 5 CHAPTER 2 – MIRRORS, THEORETICAL DESCRIPTION …………………………………….... 21 CHAPTER 3 – DESIGN OF THE MIRROR, SIMULATION …………………………………….... 40 CHAPTER 4 – FABRICATION DESIGN ……………………………………………………………..… 58 CHAPTER 5 – FABRICATION TECHNOLOGY …………………………………………………..… 73 CHAPTER 6 – RESULTS ……………………………...……………………………………………………. 84 CONCLUSIONS ……………………..………………………………………………………………….……… 106 REFERENCES ………………………………………………………………………………………………… 108 ACKNOWLEDGEMENTS ……..………………………………………….………………………………. 111

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CHAPTER 1: INTRODUCTION 1.1 Analytical Lab-‐on-‐a-‐chip In the 20th century there has been a trending into the miniaturization in all electronic components and electronic integrated systems. All these advances in microfabrication technologies had soon started being applied to other fields, such as pressure sensors and accelerometers, enabling development of complex Micro Electro Mechanical Systems (MEMS), and at the end of the century, microfabricated devices for chemical or biological analysis and synthesis, that are called labs-‐on-‐chips (LOCs).

Figure 1.1: Lab-‐on-‐a-‐chip made of glass Source: http://www.gizmag.com/music-‐lab-‐on-‐a-‐chip-‐device/12402/

Microelectromechanical systems (MEMS) is the technology of very small mechanical devices driven by electricity. MEMS are separate and distinct from the old vision of molecular nanotechnology or molecular electronics, they are made of components between 1 to 100 micrometres in size and the devices generally range in size from 20 micrometres to a millimetre. They usually consist of a central unit that processes data, the microprocessor and several components that interact with the outside such as microsensors. At these size scales, the standard constructs of classical physics are not always useful. Because of the large surface area to volume ratio of MEMS, surface effects such as electrostatics and wetting dominate volume effects such as inertia or thermal mass. More specifically, Bio-‐MEMS refers to a special class of MEMS where biological matter is manipulated to analyze and measure its activity under any class of scientific study. This class of devices belongs to one of the areas of development based on microtechnology. Some of the applications based in Bio-‐MEMS are: biological and biomedical analysis and measurements, and micro total analysis systems (μTAS). Lab-‐on-‐a-‐chip devices are a subset of MEMS devices and often indicated by "Micro Total Analysis Systems" (µTAS) as well. The term "Lab-‐on-‐a-‐Chip" was introduced later on when it turned out that µTAS technologies were more widely applicable than only for analysis purposes. Lab-‐on-‐a-‐Chip indicates generally the scaling of

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single or multiple lab processes down to chip-‐format, whereas "µTAS" is dedicated to the integration of the total sequence of lab processes to perform chemical analysis. But before entering completely to our main topic (LOCs) it is necessary to make a brief introduction on Microfluidics. 1.1.1 Microfluidics

Microfluidics is a broader term that describes also mechanical flow control devices like pumps and valves, or sensors like flowmeters and viscometers. Microfluidics deals with the behavior, precise control and manipulation of fluids that are geometrically limited to a small scale (typically sub-‐millimeter). The behavior of fluids at the microscale can differ from 'macrofluidic' behavior in that factors such as surface tension, energy dissipation, and fluidic resistance start to dominate the system. Microfluidics studies how these behaviors change, and how they can be worked around, or exploited for new uses. High specificity of chemical and physical properties (concentration, pH, temperature, shear force, etc.) can also be ensured resulting in more uniform reaction conditions and higher grade products in single and multi-‐step reactions.

Figure 1.2: Microfluidic System Source: http://medgadget.com/2009/04/separating_chirality_with_microfluidics.html

Microfluidics is a multidisciplinary field intersecting engineering, physics, chemistry, microtechnology and biotechnology, with practical applications to the design of systems in which such small volumes of fluids will be used. Microfluidics emerged in the beginning of the 1980s and is used in the development of inkjet printheads, DNA chips, lab-‐on-‐a-‐chip technology, micro-‐propulsion, and micro-‐thermal technologies. One of the most important key application area is continuous-‐flow microfluidics. These technologies are based on the manipulation of continuous liquid flow through microfabricated channels. Actuation of liquid flow is implemented either by external

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pressure sources, external mechanical pumps, integrated mechanical micropumps, or by combinations of capillary forces and electrokinetic mechanisms. Continuous-‐flow microfluidic operation is the mainstream approach because it is easy to implement and less sensitive to protein fouling problems. Continuous-‐flow devices are adequate for many well-‐defined and simple biochemical applications, and for certain tasks such as chemical separation, but they are less suitable for tasks requiring a high degree of flexibility or ineffect fluid manipulations. These closed-‐channel systems are inherently difficult to integrate and scale because the parameters that govern flow field vary along the flow path making the fluid flow at any one location dependent on the properties of the entire system. An extense variety of microfluidics applications can be found1, such as flow control methods, DNA analysis systems or biosensors, with the corresponding information about all the theoretical aspects. 1.1.2 Lab-‐on-‐a-‐Chip A lab-‐on-‐a-‐chip (LOC) is a device that integrates one or several laboratory functions on a single chip of only millimeters to a few square centimeters in size. LOCs deal with the handling of extremely small fluid volumes down to less than pico liters.

Figure 1.3: Lab-‐on-‐a-‐Chip Source: http://www.directindustry.com/prod/agilent-‐technologies-‐life-‐sciences-‐and-‐chemical/labs-‐

on-‐a-‐chips-‐loc-‐32598-‐243049.html A big stimulation in research and commercial interest came in the 1990’s, when µTAS technologies turned out to provide interesting tooling for genomics applications, like capillary electrophoresis and DNA microarrays. The main point was the integration of lab processes for analysis, but also there was the additional value of the individual components and their application to other non-‐analysis lab processes. Hence, the term "Lab-‐on-‐a-‐Chip" was introduced.

1 Bingcheng Lin, Microfluidics: Technologies and Applications, 2011

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Even nowadays, there is still an increasing need for sensitive high-‐throughput analysis. Lab-‐on-‐a-‐chip devices can considerably improve the speed and scale at which chemical and biological analyses are performed. Such a microfluidics system exhibits the ability to reduce conventional analytical systems and bring advantages of high-‐throughput, low cost, low sample consumption and portability. The major challenge in the field of analytical Lab-‐on-‐a-‐chip devices is to provide sensitive detector for minute amount of samples (typically less than few nanolitres), which can be miniaturized in order not to compromise the portability of the Lab-‐on-‐a-‐chip device. The driving force behind the miniaturization is the aspiration to increase the processing power, while reducing the economic cost (and, only recently, environmental impact). Two important consequences appear from these important premises:

-‐ The increase in processing power brings new possibilities such as numerical modeling of complex systems, minimally invasive surgeries, and high throughput biochemical screening, to name a few current examples.

-‐ The decrease in production cost generally makes these capabilities more accessible to the general public, as it happened in the past with personal computers, glucose monitors or pregnancy tests.

Lab-‐on-‐chips generally speed up the reaction times, allow for massively parallel design, and are field deployable. Moreover, reagent and energy consumption are dramatically reduced, and so is the amount of waste produced. It should be noted, however, that the massive fabrication of inexpensive and disposable LOCs may pose an environmental problem simply due to the sheer volume of production -‐ a problem already faced with many other miniaturized technologies: nickel-‐cadmium batteries or mobile phones. The range of applications can suitably be divided into three major categories:

1) Micro total-‐analysis systems (µTAS), for analysis identification or quantification purposes. This concept was the main premise of microfluidic systems in the early 199Os, and has since emerged into a variety of diagnostic, environmental and military applications.

2) Microreactors for chemical synthesis or energy production. This field started in the late 199Os, and uses methods to synthesize unstable, precious or dangerous materials on demand, tailored nanoparticles and patterned surfaces or to develop micropower sources.

3) Microfluidic tools for purposes ranging from screening for protein

crystallization conditions to interacting with single cells. These strategies take the advantage of physical and chemical properties that are unique to microfluidic systems (laminar flow, high surface-‐to-‐volume ratio, or feature sizes comparable to the size of cells), enabling experiments that would be very hard or even impossible to realize in the conventional format.

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Large-‐scale integration and batch fabrication have led to commercial release of several LOCs, used mostly in the pharmaceutical and biotechnology markets. An extensive list of principal and optional modules of an analytical LOC, for instance, would include sample preparation and enrichment, pumping/manipulation, separation, detection, signal conditioning, temperature control, and power. More detailed information can be found in this reference2, where also can be found a deeply analysis of magnetic tools in lab-‐on-‐a-‐chip technologies. 1.1.3 Advantages and Disadvantages of LOCs As every new technology, with lab-‐on-‐a-‐chip we have to take into consideration the viability of its implementation. Here there is a list of some advantages, which are specific to their application:

-‐ Low fluid volumes consumption (less waste, lower reagents costs and less required sample volumes for diagnostics).

-‐ Faster analysis and response times due to short diffusion distances, fast heating, high surface to volume ratios, small heat capacities.

-‐ Compactness of the systems due to integration of much functionality and small volumes. Massive parallelization due to compactness, which allows high-‐throughput analysis.

-‐ Lower fabrication costs, allowing cost-‐effective disposable chips, fabricated in mass production.

-‐ Safer platform for chemical, radioactive or biological studies because of integration of functionality, smaller fluid volumes and stored energies.

There are also some aspects that need to be solved or minimized in the future. Some of the disadvantages of LOCs are:

-‐ Novel technology and therefore not yet fully developed. -‐ Physical and chemical effects (like capillary forces, surface roughness)

become more dominant on small-‐scale. This can sometimes make processes in LOCs more complex than in conventional lab equipment.

-‐ Detection principles may not always scale down in a positive way, leading to low signal-‐to-‐noise ratios.

-‐ Although the absolute geometric accuracies and precision in microfabrication are high, they are often rather poor in a relative way, compared to precision engineering for instance.

1.1.4 Present and Future For all the reasons that we have seen, it seems highly probable that lab-‐on-‐a-‐chip technology will be a powerful industry in the next decades. According to the experts, in next years will appear new discoveries in physics, micro-‐scale dynamics, and nanotechnology that will act as enabling technologies, solving dilemmas for LOC developers one step at a time.

2 Nikola Slobodan Pekas, Magnetic tools for Lab-‐on-‐a-‐chip Technologies, 2006

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Two major developments have occurred in the LOC landscape, opening doors for innovators while creating new standards. The first is the use of microarrays, where these tiny wafers are now standard laboratory equipment for almost any type of high-‐throughput analysis. The second is LOCs integration into market-‐ready products by several laboratories. Complete chemical LOCs will have the greatest direct impact on two markets: medical diagnostics and laboratory instrumentation. Chemical sensing markets and chemical synthesis will also be affected. LOCs will most likely not be used for uncomplicated "yes" or "no" tests, as simple, reliable, inexpensive solutions are already on the market. LOCs will be used to replace some functions of instruments in situations where concentrations of more than one analyte needs to be determined, or where a complex separation must precede analysis. While several groups are working on the realization of a complete LOC, some others are working on what will eventually become components of future LOCs: microfluidics, sample handling systems, analyzers and detection schemes, signal processors, control software, and chemical sensors for analytical LOCs. Finally, it is necessary to remark one important and hopeful idea related with the future of LOCs. This technology may soon become an important part of efforts to improve global health, particularly through the development of point-‐of-‐care testing devices. In countries with few healthcare resources, infectious diseases that would be treatable in a developed nation are often deadly. Many researchers believe that LOC technology may be the key to powerful new diagnostic instruments. The goal of these researchers is to create microfluidic chips that will allow healthcare providers in poorly equipped clinics to perform diagnostic tests such as immunoassays and nucleic acid assays with no laboratory support. These information can be extended in this source3.

3 http://en.wikipedia.org/wiki/Lab_on_a_chip#LOCs_and_Global_Health

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1.2 Optical Lab-‐on-‐a-‐chip Taking the next step from individual functional components to higher integrated devices, lab-‐on-‐a-‐chip systems are usually monolithically integrated on one substrate with other components. These components belong to the three main domains of microchip technology: optics, fluidics and electronics. In monolithic integration all the fabrication process steps are integrated on a single substrate, so it gives the benefit that no assembly of the components is required. The advantage of this technique is that the geometric measurements are no longer of primary importance for achieving functionality of nanosystem or control of the fabrication process. In essence, when we talk about Optical Lab-‐on-‐a-‐chip, it refers to integrate some high performance optics onto a chip that contains microfluidics as well. This allows us to be able to parallelize the optics in the same way that a microfluidic device parallelizes sample manipulation and delivery. Unlike a typical optical detection system that uses a microscope objective lens to scan a single laser spot over a microfluidic channel, the optical LOCs can be designed to detect light from multiple channels simultaneously. In several cases LOCs are interfaced with a detector, configuring the new LOC system, and due to its high sensitivity laser-‐induced fluorescence detection is very often the method of choice. For efficient measurements the exciting light has to be focused into the channel and the intensity of the excited fluorescence has to be collected and focused onto a photodetector. This requires a considerable amount of optical components, such as lenses, collimators, mirrors, pinholes and filters that need to be aligned very carefully. In relation to the microfluidic device this assembly becomes fairly bulky. This stands in contrast to the incentive of microfabrication and miniaturization.

Figure 1.4: Integrating optical sensing into Lab-‐on-‐a-‐Chip devices Source: http://spie.org/x35060.xml

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The tackling of this drawback goes together with poly(dimethylsiloxane) (PDMS) finding its way into microfabrication. For example, some researchers reported on integrating optical fibres and lenses for fluorescence detection by taking advantage of the elastomer’s extraordinary properties concerning the ability to form complex structures from a given mold4. Also, they found an improvement of laser-‐induced fluorescence and absorbance measurements by integrating arrangements of collector and collimator lenses. In one case collimation was achieved by combining a lens with channels made in PDMS that can be filled with black ink5. However, one problem that remains is the integration of filters. They are used to separate the wavelength of the exciting light from the one of the emitted fluorescence. This is essential when the output signal is generated by a photodetector. So far, filters are incorporated by either using conventional optical components or complex and expensive technological steps. 1.2.1 Optical Detection Detection is clearly one of the key features in analytical LOC platforms, but also plays a potentially important role as a part of process control in microdevices. A variety of detection strategies have been deployed in the LOC field, with different levels of integration and portability. Conventional microscopy abolishes the portability and low-‐cost advantages of such LOCs, and a number of groups have been working on integrating optical excitation sources and detectors into LOCs. Electrochemical methods usually rely on microfabricated, integrated electrodes and therefore promise a higher level of portability. Conventional optical detection methods, including absorbance, fluorescence, chemiluminescence, interferometry, and surface plasmon resonance, have all been applied in microfluidic biosensors. However, optical detection generally requires expensive hardware which is difficult to miniaturize, and it suffers at lower length scales. The shorter optical path lengths through the sample reduce sensitivity and higher surface-‐to-‐volume ratios lead to increased noise from non-‐specific adsorption to chamber walls. To address these issues, many integrated optical systems are being explored in which waveguides, filters, and even optoelectronic elements are integrated onto the microfluidic device to improve sensitivity while reducing cost. In conjunction with these on-‐chip integrated components, many groups are incorporating low-‐cost optics, laser diodes, LEDs, CCD cameras, and photodiodes into portable diagnostic platforms. It’s also worth noting that optical systems can not only be used for detection but also for actuation through various optical forces. Furthermore, through microscale manipulation of fluids one can achieve tunable and reconfigurable on-‐chip optical systems. These fascinating techniques have given rise to the new field of optofluidics.

4 S. Camou, H. Fujita and T. Fujii, Lab Chip, 2003, 3, 40-‐45 5 K.W. Ro, B.C. Shim, K. Lim and J.H. Hahn, Micro Total Analysis Systems, 2001, 274-‐276

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In our project, our work will be centered exclusively in the absorbance detection, but more information and applications of optical lab-‐on-‐a-‐chip can be found in this review6. 1.2.1.1 Absorbance Detection The absorbance of an object quantifies how much of the incident light is absorbed by it (not all photons get absorbed, some are reflected or refracted instead). Precise measurements of the absorbance at many wavelengths allow the identification of a substance via absorption spectroscopy, where a sample is illuminated from one side, and the intensity of the light that exits from the sample in every direction is measured. The term absorption refers to the physical process of absorbing light, while absorbance refers to the mathematical quantity. Also, absorbance does not always measure absorption: if a given sample is, for example, a dispersion, part of the incident light will in fact be scattered by the dispersed particles, and not really absorbed. Absorbance is a quantitative measure expressed as a logarithmic ratio between the radiation falling upon a material and the radiation transmitted through a material: where Aλ is the absorbance, I1 is the intensity of the radiation (light) that has passed through the material (transmitted radiation), and I0 is the intensity of the radiation before it passes through the material (incident radiation).

Figure 1.5: Measuring Absorbance Source: http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Reaction_Rates/

Experimental_Determination_of_Kinetcs/Spectrophotometry

6 Frank B. Myers and Luke P. Lee, Innovations in optical microfluidic technologies for point-‐of-‐care diagnostics, Lab Chip, 2008, 8, 2015-‐2031

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Any real measuring instrument has a limited range over which it can accurately measure absorbance. An instrument must be calibrated and checked against known standards if the readings are to be trusted. Many instruments will become non-‐linear (fail to follow the Beer-‐Lambert law) starting at approximately ~1% transmission. It is also difficult to accurately measure very small absorbance values with commercially available instruments for chemical analysis. In such cases, laser-‐based absorption techniques can be used, since they have demonstrated detection limits that supersede those obtained by conventional non-‐laser-‐based instruments by many orders of magnitude.

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1.3 Materials, Structures and Fabrication The basis for most LOC fabrication processes is photolithography. Initially most processes were in silicon, as these well-‐developed technologies were directly derived from semiconductor fabrication. Because of demands (for example specific optical characteristics, bio or chemical compatibility, lower production costs and faster prototyping), new processes have been developed such as glass, ceramics and metal etching, deposition and bonding, polydimethylsiloxane (PDMS) processing (soft lithography), as well as fast replication methods via electroplating, injection molding and embossing. More specifically, soft lithography refers to a family of techniques for fabricating or replicating structures using "elastomeric stamps, molds, and conformable photomasks". It is called "soft" because it uses elastomeric materials, most notably PDMS. 1.3.1 PDMS Polydimethylsiloxane (PDMS) belongs to a group of polymeric organosilicon compounds that are commonly referred to as silicones. PDMS is the most widely used silicon-‐based organic polymer, and is particularly known for its unusual rheological (or flow) properties. PDMS is optically clear, and in general, is considered to be inert, non-‐toxic and non-‐flammable. PDMS is viscoelastic, meaning that at long flow times (or high temperatures), it acts like a viscous liquid, similar to honey. However, at short flow times (or low temperatures), it acts like an elastic solid, similar to rubber. In other words, if some PDMS is left on a surface overnight (long flow time), it will flow to cover the surface and mold to any surface imperfections. PDMS is commonly used as a stamp resin in the procedure of soft lithography, making it one of the most common materials used in microfluidics chips. The process of soft lithography consists of creating an elastic stamp, which enables the transfer of patterns of only a few nanometers in size onto glass, silicon or polymer surfaces. With this type of technique, it is possible to produce devices that can be used in the areas of optic telecommunications or biomedical research. The resolution depends on the mask used and can reach 6 nm. In Bio-‐MEMS, soft lithography is used extensively for microfluidics in both organic and inorganic contexts. Silicon wafers are used to design channels, and PDMS is then poured over these wafers and left to harden. When removed, even the smallest of details is left imprinted in the PDMS. With this particular PDMS block, hydrophilic surface modification is conducted using RF Plasma techniques. Once surface bonds are disrupted, usually a piece of glass slide is placed on the activated side of the PDMS (the side with imprints). Once the bonds relax to their normal state, the glass is permanently sealed to the PDMS, thus creating a waterproof channel. With these devices, researchers can utilize various surface chemistry techniques for different functions creating unique lab-‐on-‐a-‐chip devices for rapid parallel testing.

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1.4 Limitations due to optical path length The path that light takes in traversing an optical system is often called the optical path. In optics, optical path length (OPL) or optical distance is the product of the geometric length of the path light follows through the system, and the index of refraction of the medium through which it propagates. Optical path length is important because it determines the phase of the light and governs interference and diffraction of light as it propagates. In our case, optical path length is very important because it results in some limitations that we have to take into consideration. For example, the most important case is when we have a very low quantity of substance to measure the absorbance, when it is necessary to extend the optical path length to obtain a better result. On the other hand, we have other limitations such as the optical path can not be unlimited, there are some restrictions. That is why we need to enter deeply in the Beer-‐Lambert Law.

Figure 1.6: Beer-‐Lambert Law scheme Source: http://en.wikipedia.org/wiki/Absorbance

The law states that there is a logarithmic dependence between the transmission (or transmissivity), T, of light through a substance and the product of the absorption coefficient of the substance, α, and the distance the light travels through the material, ℓ. The absorption coefficient can, in turn, be written as a product of either a molar absorptivity (extinction coefficient) of the absorber, ε, and the molar concentration c of absorbing species in the material. For liquids, these relations are usually written as: And remembering the definition of the absorbance of a material, Beer-‐Lambert law implies that the absorbance becomes linear with the concentration according to: Hence, if the path length and the molar absorptivity are known and the absorbance is measured, the concentration of the substance can be deduced.

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More information about the law and the limitations that implies can be found at this source7 . In this introduction chapter, we do not want to extend the topics excessively, so now we will present briefly some other important aspects related to the optical path length such as refractive index, lower limit of detection and sensitivity. 1.4.1 Refractive Index In optics the refractive index of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium. This can be written mathematically as:

n = speed of light in a vacuum / speed of light in medium.

As light moves from a medium, such as air, water, or glass, into another it may change its propagation direction in proportion to the change in refractive index. This refraction is governed by Snell's law, and is illustrated in this figure:

Figure 1.7: Visualization for Snell’s Law Source: http://phelafel.technion.ac.il/~lk/

Another common definition of the refractive index comes from the refraction of a light ray entering a medium. The refractive index is the ratio of the sines of the angles of incidence θ1 and refraction θ2 as light passes into the medium: The wavelength λ of light in a material is determined by the refractive index according to λ = λ0 / n , where λ0 is the wavelength of the light in vacuum. The refractive index of materials varies with the wavelength (and frequency) of light. This is called dispersion and causes prisms to divide white light into its constituent spectral colors, and explains how rainbows are formed. So it’s obvious that the refractive index is a extremely important value in all the ray tracing theory. For example, concepts such as dispersion, Snell’s law, Brewster's angle, the critical angle for total internal reflection, and the reflectivity of a surface are also affected by the refractive index. All of these topics, as well as the Fresnel equations, will be expanded in Chapter 2 (Mirrors, Theoretical Description). 7 http://www.chemguide.co.uk/analysis/uvvisible/beerlambert.html

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1.4.2 Limit of Detection and Sensitivity These two concepts, Limit of Detection (LOD) and Sensitivity, are the key of our project and all the efforts will be directed to improve these two measures. We do not only want to design a system that helps us calculating the absorbance of a concentration, the main objective is to have the most accurate measure (sensitivity) and if even if the concentration is very low we can have a correct measure (LOD). As we have seen in this chapter, to improve both of them it is necessary to increase the optical path length, so finally everything is linked. In analytical chemistry, the detection limit, lower limit of detection, or LOD (limit of detection), is the lowest quantity of a substance that can be distinguished from the absence of that substance (a blank value) within a stated confidence limit (generally 1%). In our case, the LOD will be the lowest concentration of analyte detectable by the method. On the other hand, we have sensitivity that is the smallest concentration change that the method is capable of detecting. As we can read in this document8, it is very important to not confuse and take it as a synonim of LOD, the concepts are totally different. The best way to see these concepts is through the absorbance calibration curve (image below). LOD it is usually determined by extrapolating a plot of concentration (x) vs absorbance (y) to the x-‐axis. The intercept is the lower limit of detection. On the same plot we also can find sensitivity that it is determined from the slope of the plot of the LOD.

Figure 1.8: Example of an absorbance calibration curve Source: http://terpconnect.umd.edu/~toh/models/BeersLaw.html

8 http://www.clinchem.org/content/35/3/509.1.full.pdf+html

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1.5 Perspectives of the Project As we have seen in the previous chapters, our objective is to create a system that allows us to calculate the absorbance of a determined concentration. Using this result and Beer-‐Lambert Law, we will try to improve the system in order to obtain the minimum LOD as possible and the best sensitivity. On the way of conquering these goals we have seen clearly that there is key point: extend the optical path length as much as possible (always taking into consideration the superior limits). To achieve it, there are several methods but we have chosen following the work of the researcher A. Llobera. In the documentation that I could access9, the evolution of his systems can be summarized in 3 steps, (that we will analyze deeply in Chapter 2, Mirrors, Theoretical Description). But briefly we can state them:

1) Abbe Prism10: This system has two important targets. First as we said before, extend the optical path length with the reflection on the prism walls. Secondly, the collocation of the optical fibers, lenses and angles of the prisms allow only one wavelength to be collected by the photodetector.

2) Air Mirror11: This improvement was directed to solve the biggest problem of

the previous system. Due to the low difference between the index of refraction ‘n’ of the concentration and the PDMS, nearly all the light was escaping instead of being reflected. With the air mirror, this light that was escaping is now reflected again to the system so the reflectivity increase is huge.

3) Multiple Air Mirror12: In that case, they took the last system and they tried to

extend the optical path as much as possible with some extra reflections in other air mirrors. The results were also better than in the previous cases, and even there are some updates (like reducing the fluidic path or circular system), that even increase the system throughput.

In our project we will try to follow the work from this point on, but instead of using Air Mirrors we will try to substitute it with Indium Mirrors. Obviously, at first sight we can see that we are adding an extra fabrication step, but we think that this drawback will be exceeded by the benefits that the Indium Mirror will give us. The refraction index coefficient ‘n’ is even lower than air coefficient and therefore also the Reflectivity will be much better, so we expect to obtain a much better results than the previous works.

9 http://pubs.rsc.org/en/results/searchbyauthor?selectedAuthors=A.:Llobera 10 A. Llobera, R. Wilke and S. Büttgenbach, Lab Chip, 2004, 4, 24-‐27 11 A. Llobera, R. Wilke and S. Büttgenbach, Talanta, 2008, 75, 473-‐479 12 A. Llobera, S. Demming, R. Wilke and S. Büttgenbach, Lab Chip, 2007, 7, 1560-‐1566

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CHAPTER 2: MIRRORS, THEORETICAL DESCRIPTION

2.1 Theoretical Concepts During the realization of our project, we have to make a brief study in optics for a better understanding of the system and specifically about the working principles of mirrors. Optics is a branch of physics, which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Reflection, transmission and absorption and their relations to optical constants are matters of interest for experimental and theoretical investigations. The optical parameters like absorption coefficient, optical band gap and refractive index can be determined from transmittance as well as absorbance measurements. Another optical issue of high importance is ray tracing. Ray tracing is used to describe the propagation of light rays through a lens system or optical instrument, with regions of different propagation speed, absorption characteristics, and reflecting surfaces. The most important thing that we use from it is that allows the image-‐forming properties of the system to be modeled. The optical properties mainly depend on the refractive index of the material and thickness of the film. In this chapter will be presented several concepts that affect directly to the future design of the optical system such as Snell’s Law, Total Internal Reflection and Fresnel Equations. 2.1.1 Index of Refraction (‘n’) More fundamentally, ‘n’ is defined as the factor by which the wavelength and the velocity of the radiation are reduced with respect to their vacuum values: The speed of light in a medium is v = c/n, where c is the speed in vacuum. Similarly, for a given vacuum wavelength λ0, the wavelength in the medium is λ=λ0/n. This implies that vacuum has a refractive index of 1. Refractive index of materials varies with the wavelength. This is called dispersion and it causes the splitting of white light in prisms and rainbows. A widespread misconception is that according to the theory of relativity, nothing can travel faster than the speed of light in vacuum, the refractive index cannot be lower than 1. This is erroneous since the refractive index measures the phase velocity of light, which does not carry energy or information, the two things limited in propagation speed. The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, and thereby give a refractive index below 1.

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When light passes through a medium, some part of it will always be absorbed. This can be conveniently taken into account by defining a complex index of refraction: Here, the real part of the refractive index ‘n’ indicates the phase speed, while the imaginary part ‘k’ indicates the amount of absorption loss when the electromagnetic wave propagates through the material. The physical significance of k is that on traversing a distance equal to one vacuum wavelength, the amplitude of the wave decreases by the factor exp(-‐2πik). That effect can be seen by inserting ‘n’ into the expression for electric field of a plane electromagnetic wave traveling in the z-‐direction. We can do this by relating the wave number to the refractive index through this equation (k=2πn/λ0), with λ0 being the vacuum wavelength:

Here we see that ‘k’ gives an exponential decay, as expected from the Beer–Lambert law. Both n and k are dependent on the frequency. In most circumstances k>0 (light is absorbed) or k=0 (light travels forever without loss). 2.1.2 Snell’s Law Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled n1 and n2, are used to represent the factor by which a light ray speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum. As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the normal line, represented perpendicular to the boundary. Refraction between two surfaces is also referred to as reversible because if all conditions were identical, the angles would be the same for light propagating in the opposite direction. 2.1.3 Total Internal Reflection (TIR) and Critical Angle Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle. This can only occur where light travels from a medium with a higher refractive index to one with a lower refractive index. If the angle of incidence is greater than the critical angle, then the light will stop crossing the boundary altogether and instead be totally reflected back. The most known application of TIR is the principle of propagation of the light inside the optical fibers.

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The critical angle of incidence is measured respect to the normal at the refractive boundary. When the incident angle is increased sufficiently, the transmitted angle reaches 90 degrees. The critical angle θc, is given by Snell's law: To find the critical angle, we find the value for θi when θt=90° and thus sin(θt)=1. If the incident ray is precisely at the critical angle, the refracted ray is tangent to the boundary at the point of incidence. Now, we can solve for θi, and we get the equation for the critical angle: If the fraction n2/n1 is greater than 1, then arcsin is not defined, meaning that total internal reflection does not occur even at very shallow or grazing incident angles. So the critical angle is only defined when n2/n1 is less than 1. 2.1.4 Fresnel Equations The Fresnel equations describe the behavior of light when moving between media of different refractive index. Snell’s Law is one of the Fresnel Equations, but these also contain some extra equations that state the behavior of the power in the media change. They describe what fraction of the light is reflected and what fraction is transmitted. The equations assume the interface is flat, planar and homogeneous, and that the light is a plane wave. Law of Reflection and Snell’s Law give the relation between these two angles: Also the equations state that the fraction of the incident power that is reflected from the interface, is given by the reflectance R and the fraction that is refracted is given by the transmittance T. Due to it is an important aspect in our work, it is necessary to enter deeply to Reflectivity and how to calculate it with the Fresnel equations. 2.1.4.1 Reflectivity Reflectivity and reflectance generally refer to the fraction of incident electromagnetic power that is reflected at an interface, while the term "reflection coefficient" is used for the fraction of electric field reflected. The reflectivity is thus the square of the magnitude of the reflection coefficient. According to the CIE (the International Commission on Illumination), reflectivity is distinguished from reflectance by the fact that reflectivity is a value that applies to thick reflecting objects13. When reflection occurs from thin layers of material, internal reflection effects can cause the reflectance to vary with surface thickness.

13 http://www.cie.co.at/index.php/index.php?i_ca_id=306

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Reflectivity is the limit value of reflectance as the surface becomes thick; it is the intrinsic reflectance of the surface. The calculations of R depend on polarization of the incident ray. If the light is polarized with the electric field of the light perpendicular to the plane of the diagram above (s-‐polarized), the reflection coefficient is given by this equation, where the second form is derived from the first by eliminating θt using Snell's law and trigonometric identities. The first one refers to s-‐polarized and the second one p-‐polarized

Finally, an important conclusion that we can take from these last plots, is that when TIR occurs, the reflectivity is equal to 1, so that is why we will try to be in the TIR angle zone as much as it is possible.

Figure 2.1: Reflectivity in different situations

Source: http://en.wikipedia.org/wiki/Fresnel_equations

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2.2 Previous Research (Other research groups) Now that we have seen the optical principles, it is time to take a look on other previous works that will be the basis for this project. It is strictly necessary to understand every of this references because it shows the evolution of the idea. Every time they are adding more improvements, which is basically what we want to do now. In this chapter will be taken into consideration the optical aspects, and in the next ones will be entered deeply in the fabrication methods and results. 2.2.1 Abbe Prism

The first reference taken into consideration14 is a hollow prism called Abbe prism. From all the prisms available, they have chosen this one because it is simple and allows the filling of the fluid under investigation through two inlets. As we said before, it is very important the monolithic integration. This device accomplishes it with the integration of several components on it, such as optical fiber positioners. If we enter deeply on the prism structure, we can see that is a combination of three prisms (ADE, AEB and BEC). One of the most important variables is ‘δ’, which is considerate the total deviation of a light ray propagating through the system. This total deviation can be easily calculated with ray tracing theory that results in 60°.

Figure 2.2: Abbe Prism, Working Principle Source: A. Llobera, R. Wilke and S. Büttgenbach, Lab Chip, 2004, 4, 24-‐27

Any other wavelength propagating through the prism does not fulfill the minimum deviation condition and emerges at a higher angle, being not collected by the output fiber optics. If we rotate the prism, the mentioned λ1 will not be collected for the output fiber because of the reason that we have just said. In that case, another λ2 will be collected on it.

14 A. Llobera, R. Wilke and S. Büttgenbach, Lab Chip, 2004, 4, 24-‐27

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From these theoretical concepts, a new optical detector was designed. On the next picture we can see the prim filled with the fluid under investigation through two fluidic reservoirs. Also we can see the inclusion of the optical fiber positioners, which allow a correct insertion of the fiber and together with the biconvex lenses produce parallel light beams on the prism entrance. In that case, the position of the fibers it is designed in order to have maximum intensity for λ =460nm.

Figure 2.3: Optical Detector System

Source: A. Llobera, R. Wilke and S. Büttgenbach, Lab Chip, 2004, 4, 24-‐27 2.2.2 Air Mirror Even tough the previous system had a good response for the designed purposes, some changes can be applied to obtain a better throughput. The first improvement that this research group made was the definition of an air mirror15, in order to improve the reflectivity of the Abbe prism. An air mirror can be seen as an air entrapment with a concrete shape and position that modifies the light path. The main objective is that the input ray strikes the mirror in the conditions of Total Internal Reflection (TIR). Even though we have seen that the Abbe prism is a good microfluidic system, we can confirm that this is not true in terms of reflectivity. The small difference between the index of refraction of the fluid and the PDMS (1.33 and 1.41 respectively) makes that only a tiny portion of the light is coupled back on the prism wall. With the Fresnell Equations we can exactly calculate that, and the results are 0.029 for s-‐polarized and 0.062 for p-‐polarized, which confirms that long integration times will be required and because of that the throughput obtained will be low.

15 A. Llobera, R. Wilke and S. Büttgenbach, Talanta, 2008, 75, 473-‐479

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Figure 2.4: Optical Detector System with Air Mirror Source: A. Llobera, R. Wilke and S. Büttgenbach, Talanta, 2008, 75, 473-‐479

A ray tracing simulation on the boundary region is presented in the picture below, with a special consideration of the angles that match the TIR-‐conditions.

Figure 2.5: Detailed Boundary Region

Source: A. Llobera, R. Wilke and S. Büttgenbach, Talanta, 2008, 75, 473-‐479

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As we can see at the first boundary region, the small step between the refraction coefficient of PDMS and the buffer, has the consequence that most of the light is not reflected back to the output fiber. Then, when the air mirror is included, this light that escapes can enter the TIR zone, resulting in a complete reflection towards the system. Using the Snell’s Law, we can find that the critical angle is θc PDMS–air= 45.17°. All the propagation angles with θ > θc PDMS–air (marked in dark grey in the figure) accomplish the TIR conditions, so we can assure that the reflectivity in that cases will be equal to 1, and the light will reach again the hollow prism. Apart from this TIR zone, we can see in the picture that there is another one when the light ray strikes back from the PDMS to the buffer. Using the Snell’s Law, we can find that this critical angle is θc PDMS–PBS= 70.60° (the angles where TIR regime happens are also marked in dark grey). Here enters one design condition, because in the way that the system is designed light matches the TIR at the PDMS-‐air region, but it is really difficult that at the same time it does it on the PDMS-‐fluid region. In case that this undesired happens, the light will remain confined at the PDMS like in a waveguide, which is totally the opposite that we want. Experimental results have shown that the use of air mirrors enhances the sensing properties of the hollow prisms due to several reasons:

-‐ The integration time is strongly reduced. -‐ The signal-‐to-‐noise ratio (SNR) is increased. -‐ An important improvement of the LOD has been experimentally measured. -‐ The sensitivity is increased (the factor depends on the geometry used).

2.2.3 Multiple air mirrors The next step on the evolution of the system was the positioning of multiple air mirrors (MIR systems16) at both sides of the sensing region. The reason behind this action is that it is possible to increase the optical path length and simultaneously reduce the fluidic path, which allows obtaining more compact and miniaturized lab-‐on-‐a-‐chip systems. After this increase of the path, the throughput will be increased also due to the higher absorption of light. It is easy to see that MIR systems have a lot of advantages compared to the previous systems (Abbe Prism and Air Mirror). But there are some problems that need to be addressed before the realization, because if not they may cause some problems. Firstly, light diverges since it is out of the source, and a larger optical path results in more divergence in all the process. Secondly, with each additional reflection in a mirror the intensity of the light decreases, which means that the power collected on the output fiber also decreases.

16 A. Llobera, S. Demming, R. Wilke and S. Büttgenbach, Lab Chip, 2007, 7, 1560-‐1566

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The solution to address these drawbacks was a change in the mirrors shape. Basically focused on avoiding the beam broadening, these curved mirrors were implemented (instead of the flat mirror previously seen). We can see on the next picture that a correct curvature of the mirror makes the light converge in a point inside the system, and even it is possible to choose this point depending on the curvature that we apply.

Figure 2.6: Ray tracing simulation in different situations Source: A. Llobera, S. Demming, R. Wilke and S. Büttgenbach, IEEE, 2009, (978-‐1-‐4244-‐4210-‐2)

After designing the air mirrors, two different configurations were presented. The first one consisted in an extra mirror placed on the position where the detection optical fiber was before (PMIR System). As in the previous system, the light strikes on the first mirror, but then light reaches the second mirror before being collected by the fiber. We can see that light propagates with a zigzag shape. As we said, every additional mirror supposes an increase on the whole systems dimensions. To tackle this situation, another system was designed following a ring configuration (RMIR). In this system, we can achieve a bigger number of reflections but without enlarging the fluidic volume.

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Figure 2.7 / Figure 2.8: Representation of the systems PMIR (left) and RMIR (right)

Source: A. Llobera, S. Demming, R. Wilke and S. Büttgenbach, Lab Chip, 2007, 7, 1560-‐1566 The predictions were confirmed after the experimental results, and different goals were achieved. The reduction of the integration time results in a reduction of the LOD (nearly 45 times smaller). Also, the RMIR configuration has the highest sensitivity, which matches exactly with the largest optical path.

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2.3 Other components of the System The most crucial step of the design of the system is the adequate positioning of the optical fibers in relation to the biconvex lens and the prism. Now, we will make a brief overview on how the previous papers tried to solve the issue. The results presented there, are referred to a single wavelength and a concrete buffer solution, but we can take the main idea and adapt it to our project. 2.3.1 Collimation Lenses Collimation lenses are necessary to achieve reasonable optical path lengths because light diverges from the source. In the optimal situation, light emerging from the microlens will have parallel beams and will not diverge. Obviously this behavior will only be obtained with perfect spherical microlenses, which are technologically difficult to obtain. For ease of fabrication, cylindrical lenses, which only vary the light direction in one axis (that is, instead of having a focal point, they have a focal plane), are more commonly used. The result is that light emerges from the lenses with parallel beams in the horizontal direction while it broadens in the vertical axis, which is exactly what we expect in our case. 2.3.2 Alignment of Optical Fibers This group is required to implement a system not only able to position the fiber optics but also to assure that the optimal condition is reached. Both issues are obtained by defining a microchannel slightly thinner than the diameter of the optical fiber. Optical fibers are stopped at a distance S0 that, considering the RI of PDMS and air, together with the curvature of the lens (R1 and R2), allows having parallel beams at the biconvex lens output. Lens and channel are tilted an angle θ to have the deserved propagation angle through the prism. For example, in the case that we want a 60° input light beam, applying the Snell’s Law we can find that the angle will be θ=54.8°. An air gap, with a minimum distance d, separates the PDMS bulk region from the PDMS lens. No variation of the ray tilt is produced at the air–PDMS interface due to the 90° incidence.

Figure 2.9: Scheme of the optical fiber channel and the lenses Source: A. Llobera, R. Wilke and S. Büttgenbach, Lab Chip, 2004, 4, 24-‐27

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2.4 Pure Indium Mirror Although silicon or metal-‐coated mirrors can be easily defined, this would lead to a more complex fabrication process and an increase of the cost of the device. The ideal solution would be to obtain a mirror without any additional process steps. This is the main reason why we have chosen to use a pure indium mirror in our project. As we have seen in previous chapters, a very important issue in lab-‐on-‐a-‐chip, is the monolithic integration, and with the indium mirror we keep the high rate of integration that the other groups have obtained. Also, as we will see in the next sections, with indium we can even obtain better conditions for the TIR and Reflectivity, so the situation is at first, highly favorable. 2.4.1 Material Characteristics Indium is a chemical element with the symbol ‘In’ and atomic number 49. Indium is a soft, ductile and malleable metal. It is liquid over a wide range of temperatures, like gallium that belongs to its same group. Indium has a low melting point, compared to those of most other metals, 156.60 °C (313.88 °F). Indium is stable in air and in water but dissolves in acids. Some other Indium chemical characteristics can be found here17. Normally, mirrors which need superior reflectivity for visible light are made with silver as the reflecting material in a process called silvering, though common mirrors are backed with aluminum. But we have found that Indium can be put on to metal or evaporated onto glass to form a good mirror. For example, an indium mirror is more resistant to corrosion. Also Indium can be used to make mirrors that are as reflective as silver mirrors but do not tarnish as quickly. So at this point, we arrive to the conclusion that Indium can be a good material for our purpose, but we need to enter deeply in a very important fact, the refractive index.

2.4.1.1 Refractive index of Pure Indium When we think about the mirror characteristics, two main parameters take high importance to have a successful result. These parameters are the critical angle and the reflectivity, and they depend directly from the value of the refractive index. We have seen that the air has a refractive index equal to 1, so we expect that indium will have a n<1, because it means that the critical angle will be lower (more incident angles are in TIR situation) and the reflectivity will be higher. It was very difficult to find this data, because pure indium is not one of the typical materials used for these purposes. In addition, as we can see in the next graph, it was difficult to find accurate values for the range of wavelength that we expect to be working. For example, in the next graph we can see the evolution of ‘n’ and ‘k’ in the whole spectrum, but in our region (300nm – 700nm) the graph is not clear, even though we can expect good results for the future.

17 http://www.lenntech.com/periodic/elements/in.htm

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Figure 2.10: ‘n’ and ‘k’ in the whole spectrum Source: http://www.angstec.com/nkPlots2.jsp

After a deep investigation and sending several mails to expert companies, one of the workers that nicely replied me, recommend me the book ‘Palik, Handbook of Optical Constants, Vol. 3’18. This book is the reference on the field, and it is commonly used to obtain the value of optical constants. The results obtained are presented in the next table:

λ (nm) n k 310 0,38 3 355 0,4 3,4 380 0,45 3,7 410 0,5 4 450 0,6 4,3 460 0,75 4,4 495 0,75 4,8 550 0,7 4,7 555 0,85 5,5 600 0,8 5 620 1,05 6 650 0,9 5,42

Figure 2.11: ‘n’ and ‘k’ values for the range (300nm – 700nm)

Source: Palik, Handbook of Optical Constants, Vol.3 (AP, 1998)(ISBN 0125444230) 18 Palik, Handbook of Optical Constants, Vol.3 (AP, 1998)(ISBN 0125444230)

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The results of the table are also presented in these graphics, to a better understanding of their evolution: As we can see, our expectation has been accomplished, and for the range between 300nm and 600nm the value of the refractive index is below 1. 2.4.1.2 Relation between ‘nindium’ , TIR and Reflectivity Now that we have the values of the refractive index, we are going to see the benefit that this supposes to the reflectivity and the critical angle. A comparison between the indium values and the air value will be made, to ensure and compare that the results are the expected. First, we can see that the values for the critical angle are much better than the air one. That implies that a higher number of light beams will be in the total internal reflection zone.

nAir θc (o) 1 45,17

0

0,2

0,4

0,6

0,8

1

1,2

310 355 380 410 450 460 495 550 555 600 620 650

n

λ (nm)

0

1

2

3

4

5

6

7

310 355 380 410 450 460 495 550 555 600 620 650

k

λ (nm)

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But the big improvement can be seen with the reflectivity values. There are two different situations, in one hand we can see that the TIR zone is larger, which implies that reflectivity will be equal to one in a higher range. On the other hand, we can also see that for the different angles of incidence we obtain much higher reflectivity values in the indium case. Reflectivity-‐TE (angle of incidence respect of the normal)

nAir 45 40 35 30 25 20 15 10 5 1 0,73 0,19 0,10 0,07 0,05 0,04 0,03 0,03 0,02

Reflectivity-‐TE (angle of incidence respect of the normal)

λ (nm) nindium 30 25 20 15 10 5 310 0,38 TIR(1) TIR(1) TIR(1) 0,73 0,43 0,35 355 0,4 TIR(1) TIR(1) TIR(1) 0,62 0,40 0,33 380 0,45 TIR(1) TIR(1) TIR(1) 0,46 0,33 0,28 410 0,5 TIR(1) TIR(1) 0,67 0,36 0,27 0,24 450 0,6 TIR(1) 0,80 0,33 0,23 0,19 0,17 460 0,75 0,43 0,23 0,16 0,12 0,11 0,10 495 0,75 0,43 0,23 0,16 0,12 0,11 0,10 550 0,7 TIR(1) 0,31 0,20 0,15 0,13 0,12 555 0,85 0,19 0,13 0,10 0,08 0,07 0,06 600 0,8 0,28 0,17 0,12 0,10 0,09 0,08 620 1,05 0,05 0,04 0,03 0,03 0,02 0,02 650 0,9 0,14 0,10 0,07 0,06 0,05 0,05

λ (nm) nindium θc (o) 310 0,38 15,63 355 0,4 16,48 380 0,45 18,61 410 0,5 20,77 450 0,6 25,18 460 0,75 32,13 495 0,75 32,13 550 0,7 29,76 555 0,85 37,07 600 0,8 34,56 620 1,05 48,13 650 0,9 39,66

0 10 20 30 40 50 60 70 80 90

310 355 380 410 450 460 495 550 555 600 620 650 θ c

(o)

λ (nm)

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For example, in the next graph we can see the evolution of the reflectivity for each wavelength. We can see that the lower wavelengths in our range have better results, but at the same time we have to be careful to do not enter to the infrared zone, so we will take a compromise between these two ideas and the best range for our purpose will be 400nm -‐ 550nm.

Finally, the next graph shows the difference between air and indium for a determined wavelength in that range (λ=460nm). As we can see the improvement is substantial, and our expectations are that the results will be positive.

All the graphics and calculations are presented in the attached Excel file ‘Calculations of R and Ocrit’. 2.4.2 Position Another important theoretical fact of the mirror is the place where it will be positioned. When we talk about this, we refer about two facts: the position of the mirrors in the whole system and the position of the fiber to obtain the desired angle at the entrance of the system.

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

310 355 380 410 450 460 495 550 555 600 620 650

R

λ (nm)

30º

15º

5º

0

0,2

0,4

0,6

0,8

1

45 40 35 30 25 20 15 10 5

R

Incidence Angle (º)

AIR

λ=460 nm

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For example, if we want that light starts propagating through the fluidic channel with an angle of 60°, it is required to study the relative position between the channel, the lenses and the prism wall. Considering that the prism is filled with buffer, we need to apply the Snell’s Law and we obtain that we need to position the lens-‐channel system with an angle of θ=52,98°, (buffer solution with n=1,3) or θ=54,8°, (buffer solution with n=1,334), just to put two examples of the situation. On the other hand, the position of the mirrors in the system have to be selected to have the previously mentioned TIR conditions of the incident light and hence assure the most of the light is reflected back. The first mirror has to be positioned on the way of the source light beam, which will be easy taking into consideration that we decide the angle of this light. Further mirrors will be positioned according to the results of the Matlab simulations of the next chapter, because due to the broadening, the light could not follow the desired path. 2.4.3 Shape As we have previously seen, light inherently diverges. As the optical path increases there is an enlargement of the diameter beam that causes a degradation of the properties of the system, due to a fraction of light is not collected by the photodetectors, causing a decrease of the SNR. The shape of the air mirror can modify the behavior of the optical beam, allowing the light focusing at concrete places. From the initial parallel beams, an adequate curvature of the air mirror make the light converge inside the system, as is also shown in the ray tracing of the next picture. With this simple structure, the two most significant problems (reflection and beam broadening) can be addressed and solved. So this shape change allows multiple reflections without causing a decrease of the SNR.

Figure 2.12: Ray tracing simulation on the mirror vicinity Source: A. Llobera, S. Demming, R. Wilke and S. Büttgenbach, Lab Chip, 2007, 7, 1560-‐1566

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2.4.4 Thickness Obviously thickness is a key aspect in the mirror design. Directly depending on the thick of the mirror we have the transmittance. The transmittance is the fraction of the power that trespass the mirror, so ideally, we want that this equals zero. With the indium thin films, transmittance is relatively high but asking experts on the field, with a thick higher than 20μm this totally disappears. The most important design condition related with this aspect is that we always have to maintain at least a relation 1:1 between the indium channel height and width. That means that we can have some indium parts wider than higher, but never on the opposite way. The consequences of this fact are that due to the microchannel designed to align the optical fiber, which has to be at least 250μm to contain it (the optical fiber diameter is around 230μm), we have a minimum width for our indium channels. That matches exactly with our purpose, because it is higher than 20μm, so our mirror thickness will be around these value, which means that no light will be transmitted from the mirror on. 2.4.5 Conclusions and Expectative Finally, summarizing all that we have seen during this chapter, it is necessary to list all the advantages that theoretically our system has:

-‐ The indium mirror does not affect the monolithic integration. We continue having the same level of it, because the mirror will be made in the same fabrication step of the rest of the system

-‐ We can easily obtain a better refractive index (compared with air mirrors) in a huge range of wavelength. This directly implies a lower critical angle (more beams in TIR conditions) and a higher reflectivity.

-‐ With the proposed shape, the light will converge in some point that we will

try to make coincidence with the next mirror. This will allow the system to have multiple reflections without a big decrease of the SNR.

-‐ With the thickness of our indium mirror we will not have any transmittance

of power. At the same time this obviously improves the reflection of our mirror.

So the conclusion that we can obtain is that at least our results will be better than the obtained with the air mirror. As we can see there are some advantages and none disadvantage, because the use of indium for the mirror is not adding any difficulty to the system realization. Our expectation is to obtain a better result, but as we have seen, one of the most important parts is the design of the mirror. In the next chapter, we will choose the best design to obtain the best response of the mirror with a Matlab simulation.

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CHAPTER 3: DESIGN OF THE MIRROR, SIMULATION

3.1 Previous considerations On the previous chapter we have seen the general aspects that we have to take into consideration when we are designing our system, but now that we are entering deeply on the simulation, we need to introduce some topics, more specifically, mirrors ray tracing. In optics, ray-‐tracing can be used to model how light interacts with optical components such as mirrors and lenses where the EM wave is approximated by a large number of narrow beams or rays that are traced throughout the optical system. The surface is treated as locally smooth so that each scattering event on the surface is treated as a specular reflection (Fresnel approximation). 3.1.1 Concave Mirror (Spherical/Parabolic) A curved mirror is a mirror with a curved reflective surface, which may be either convex or concave. As we have seen in the previous chapter, in our case, we will use a concave mirror. A concave mirror has a reflecting surface that curves away from the incident light. They reflect light inward to one focal point and are also called converging mirrors because they are used to focus light. For our purpose, the most important thing is that they refocus parallel incoming beams to a focus, which matches exactly with our expectations. On the previous theoretical investigation all the surfaces presented where flat, and now we are facing a curved mirror. It changes the way to calculate the rebounded ray, because in that case is it necessary to calculate the tangent of the parabola to apply the previously seen Law of Reflection. Normally, concave mirrors are shaped like part of a sphere, but other shapes are sometimes used in optical devices. The most common non-‐spherical types are parabolic reflectors, since spherical mirror systems suffer from spherical aberration. Spherical aberration occurs due to the reflection of light rays when they strike a mirror near its edge, in comparison with those that strike nearer the center. It results in an imperfection of the produced image. Parabolic mirrors and spherical mirrors have a lot of similarities. In our case these similarities are even more, due to we will have a large radius of curvature that makes the difference between the shapes nearly imperceptible. But the parabolic mirrors have some special characteristics that we will use for other purposes, such as to ensure that the simulation is working correctly.

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A parabolic mirror is normally used to collect or project energy from a distant source and bring it to a common focal point. Since the principles of reflection are reversible, parabolic reflectors can also be used to project energy of a source at its focus outward in a parallel beam. In this simulation, to ensure the proper operation, we will use that any incoming ray that is parallel to the axis of the mirror is reflected to the focus. If the rays are not accomplishing that, we can state that the simulation is not working properly.

Figure 3.1: Parabolic Mirror Ray Tracing

Source: http://www.slideshare.net/solartime/espejos-‐esfricos-‐cncavos 3.1.2 Focal point As we have seen, these mirrors are called "converging" because they tend to collect light that falls on them, refocusing parallel incoming rays toward a focus. This is because the light is reflected at different angles, since the normal to the surface differs in each spot of the mirror. For a spherical or parabolic mirror, a focal point it is a point onto which collimated light parallel to the axis is focused. The distance in air from the mirror's principal plane to the focus is called the focal length (F). It is very important to notice that this length is exactly the half of the center of curvature (2F).

Figure 3.2: Focus Point on the Mirror Source: http://en.wikipedia.org/wiki/Concave_mirror#Concave_mirrors

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As we can see in the next table, the focal point is very important because its relation with the convergence point. In our case, the situation it is not exactly like these, because we do not have a single object, we have parallel light beams. But we can take the general idea from the table and apply it to our purpose. As we can see, the most favorable case is the one where the object is between F and 2F. In that case the convergence point will be even more fare than the center of curvature, so it means that our fluidic channel can be enlarged (which means a larger optical path), but without affecting the SNR because the light can converge near the second mirror. The conclusion that we have to take from here is that for our purposes we need a high focal point compared to the measures of the system, which will allow a more distant convergence point. We will confirm these suppositions on the simulation. Object Position vs Focal Point Diagram

Object < F

2F < Object < F

Object > 2F

Figure 3.3: Different Situations Depending on the Object Position Source: http://en.wikipedia.org/wiki/Concave_mirror#Concave_mirrors

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3.2 Simulation Parameters Just before starting the simulation, it is necessary to declare the parameters that we are going to use for it. The main idea consist in having several inputs referred to the mirror characteristics, and changing these inputs will give as some degrees of freedom to obtain the optimum desired design. These inputs are:

-‐ Center of curvature (or focal length, R=2F). -‐ Angle of aperture (controlled by the variable size). -‐ Width.

Figure 3.4: Simulation Parameters The center of curvature is directly related to the shape of the sphere/parabola. If the center value is high the mirror will be more ‘opened’ (considering the same size value). The angle of aperture is related with the size of the mirror, a higher angle will make a bigger mirror. Finally, the width has not any effect on the simulation (always remembering that this has to be higher than 20 μm), but we also add it to the simulation to obtain a better visual result. Another simulation parameter that we have to take into consideration is that the values that we obtain during the simulation are referred in ‘pixels’. We have to realize one way to transform these pixels to real values such as micrometers. The way to make this conversion will be deeply explained in the following sections.

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3.3 Simulation Program At this point, the Matlab simulation program was designed. This simulation consists on reflections at a parabolic or spherical mirror and a light beam that reflects on it. All the code is inspired in versions found in MathWorks19, a free database from Matlab users, and also some others Internet sources 20,21. These programs were adapted to obtain our desired purpose and the result is presented here. 3.3.1 Program Structure

The program is divided in 6 modules, where each of them has a concrete purpose. In the next figure we can see the performance of the program. It starts with the execution of mirror.m, which calls mirr_draw.m to draw the initial mirror. From that point on, the Control Window is created (mirr_cntr.m) and all the changes applied to it involve the execution of the required module to make the change on the simulation.

19 http://www.mathworks.com/ 20 http://www.mysimlabs.com/ray-‐tracing.html 21 http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=48

MIRROR.m

Initialization

MIRR_DRAW.m

First Image

MIRR_BEAM.m

First Beam

MIRR_CNTR.m

Control Window

MIRR_CB.m

Execute Commands

MIRR_DRAW.m

Draw New Mirror

MIRR_BEAM.m

Draw New Beam

MIRR_MOVE.m

Pointer Position

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3.3.2 Matrix MC [6][5] One of the most important parts of the program is the Matrix MC[6][5], which is a global variable used in every module of the program. In this matrix all the values related to the working of the program are saved. In every module the values of the matrix are changed, so the objective is to obtain an overall pattern and avoid the overwriting between the different parts. For example, the variables MirrFig and MirrAxe contain the information related with the simulation figure that we could see on the users interface. All the other variables can be easily understood in the code context (also with the help of the comments available on the code).

MirrFig MirrAxe PonterX PointerY Empty HandleMirror HandleFocus Focus <1/2>

Parabolic/Sphere Empty

HandleMag X0 Y0 Rotation ScaleFactor HanldeBeam NofBeam ScatterAngle Empty InfDummy MirrBase MirrorXMax MirrorXMin MirrorYMax Empty ControlFig ControlAxe Empty Empty Empty

3.3.3 Modules Functions In this section we are going to see each module separately and a briefly summary of their functions. 3.3.3.1 Mirror.m Mirror.m is the central part of the program. It initializes the variable MC[6][5], and also the rest of the user interface parameters. At the end, it draws the first mirror and beam, and finally it opens a Control Window to start with the changes on the simulation. 3.3.3.2 Mirror_cntr.m In this part the Control Window is created. This window allows the user to control the parameters of the mirror and the light. The way that the Control Window works basically consists on different matrix 4x4 where each position of the matrix is related to the same position of the Control Window as seen on the screen. We can see an example here, with the matrix ‘tt’ that controls the editing types of each position of the matrix:

tt 1 1 NaN NaN 3 2 2 2 2 2 2 2 NaN 2 2 NaN

Types 1-‐Text 2-‐Edit 3-‐Popup

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There are different arrays that control different parameters, but the most important are MCii and MCjj, because they are related with the matrix MC[6][5]. In each position of MCii, for example, we have the row of MC[6][5] that correspond to the Control Window position, (and in MCjj the column). As an example, MCii(2,1) has the value 2, and MCjj(2,1) the value 4. So following what we have said, this refers to the value of MC(2,4) that is: ‘Parabolic/Sphere’. As we can easily see the position (2,1) in the Control Window is exactly the popup where we can choose between a parabolic or spherical shape. The module also defines all the style and graphical issues of the control window, and the relation between every button and its action. Finally, depending on the action taken it makes a callback that is received by the module mirror_cb.m. 3.3.3.3 Mirror_cb.m This module takes the different actions that are made in the Control Window and applies the next step to perform it; we have named these actions as Callbacks. Depending if it is an edit/slider/popup action, the parameter changes applied are different. In each of the three actions, the orders taken are very intuitive. The module it is required by mirror_cntr.m that is the want that creates the callbacks, and then mirror_cb starts mirr_draw.m with the parameters changed. 3.3.3.4 Mirror_draw.m Mirr_draw.m takes the orders from mirror_cb.m and execute them. Here is where the mirror, the light beams and the mag light are drawn. It needs mirror_beam.m for the calculation of the beam path. It differences between several situations: if the action involves the mirror, the light beams or the mag light (and therefore also the light beam in that case). Also there is a different protocol for the initialization of the simulation, where everything is drawn for the first time.

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3.3.3.5 Mirror_beam.m Mirror_beam.m is the part of the code where the mathematical calculations for the beam paths are made. The module receives 3 parameters: xx0 and yy0 are two vectors with the position of the points of the incoming light beam. The third parameter, beam0, is also a vector that contains the direction of those beams. The first action taken is the calculation of the equation of the line for all the incoming beams. After that, taking into consideration that the mirror equation is y=x2+p*x+q, the intersection points are found. There is a special attention on the special cases such as the horizontal or vertical beams, or the ones that cannot be exact points. As we have seen before, in the case of curved mirrors, the reflected beams are calculated with the law of reflection but it is necessary to calculate the tangent slope for the intersection points. So the next step made is to calculate that slope, and with it, calculate the angle of the reflected beam. Finally the module returns also three vectors, which are exactly the same as the parameters received but for the reflected beam (xx1, yy1 and beam1). 3.3.3.6 Mirror_move.m This module basically stores the mouse position, in MC[1][3] and MC[1][4]. The pointer position it is showed on the Control Window and every change it is displayed instantly. It will be used to know the position of the convergence point and therefore, calculate the width of the fluidic channel.

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3.4 Results

Once the simulation was programmed, it is time to ensure the correct performance and obtain the results from it. To make it we have performed some theoretical verifications such as the parallel beams on a parabolic mirror, or some tests based on the theory previously seen.

3.4.1 Verification As we have seen on the previous sections, when parallel light beams are reflected on a parabolic mirror on the direction of the x-‐axis, the convergence point is exactly the focus point. We thought about using this to ensure the correct performance of our simulation program. As we can see in the first figure, this is totally accomplished for a parabolic mirror and not accomplished for a spherical mirror (second image), so we can confirm that our simulation principles are working in the way that we desire.

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3.4.2 General simulation In this section we are going to study how the changes on the different parameters affect on the simulation result. Also we will try to obtain the best range of the parameter to obtain the optimum result. In this part we are going to explain the parameters that have a direct impact on the mirror (even the system) design. Parameters like number of beams, scattering or size of the light source do not affect to it, they only have the purpose of make the simulation more visual. 3.4.2.1 Focus The focus parameter is clearly the most important of all the control parameters. Is directly related with the radium (2F=R), so it controls basically the shape of the mirror making it more ‘opened’ (higher focus) or ‘closed’ (smaller focus), considering that we have the same size for each focus value. Also, as we have previously seen, the focus point has a huge importance on ray tracing. In our case, that we want to design a device as small as possible but with the longer optical path, we have to take special attention on it to decide the width of the fluidic channel. As an example, we can see here some pictures of the simulation with different focus values. From left to the right and up and down, the values are 25px, 75px, 125px and 200px:

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We can see that for small focus values the light beams converge really close from the mirror, so we can say that our goal (avoid beam broadening) is not achieved. On the other hand, for higher focus values the convergence point is more far from the mirror, and also the rays are not broadening so fast, which will give a degree of freedom when the system is designed (is not necessary to position exactly the mirror on the convergence point, it can be on the vicinity). The conclusion that we can take from it is that for our purpose a higher focus is more convenient. Even though, the difference of changing the focus from 100px on, is not so big, so considering other factors we have decided that the best range to choose our focus is around 150px-‐200px. 3.4.2.2 Size As we can see in the simulation, the size parameter has no effect on the light beams always that they can reach the mirror. So taking it into consideration, we need to take a compromise between two opposite factors:

-‐ A bigger size will lead to a bigger system that attempts directly to our idea of having a smaller system as possible.

-‐ Considering that the simulation is not an exactly reproduction of the reality (maybe in the real fabricated device the light beams can broaden more), a bigger mirror will allow to reflect more light beams.

Here there are two examples with different size (3px and 15px), remembering that size value is referred to the width of the mirror in the X-‐axis. Our idea is to have a mirror that improves that system considering these two factors, but at the moment it is no possible to say a value range, due to the hole size of the mirror is also depending on the focus value.

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3.4.2.3 Width We saw in the previous chapter that the width value is not related with the ray tracing or the reflection always that it is higher that 20μm. So in our simulation this is also accomplished, here we can see two different pictures with two different widths (3px and 10px) and the result is exactly the same.

3.4.2.4 Parabolic/Spherical Obviously there is a big difference between using a spherical or parabolic mirror in most of the cases. As we could see before, with a parabolic mirror and parallel beams, the reflected beams converge into the focal point, and with a spherical mirror not. Also there are little differences on the reflected beams depending on the shape. But in our case, considering that our focus point will be as high as possible, this difference is inexistent or so reduced that is nearly inappreciable. As we can see in the next figures, when the focal point is high enough (and considering also a little size compared with the focus) there are only small differences in the extremes of the mirror. In that case, and taking into consideration that our purpose is that the rays strike nearly the center as possible, there are no effects on the change between parabolic (left image) and spherical (right image). With this information, our decision is to use the spherical because it is easier to obtain all the parameters.

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3.4.2.5 Rotation

The rotation of the incoming beam it is not a parameter itself of the design of the mirror, but it has to be taken into consideration because it will determine other values such as the convergence point, that results directly in the value of the width of the fluidic channel or the position of the second mirror. The first factor to look at is that due to the better refractive index of the indium we can operate in a higher range of incoming angles. As we have seen before, the indium critical angle is around 30° or less, which allows us to have more degrees of freedom compared with the air mirror (critical angle equals 45°). It can be easily seen that a low entrance angle has the consequence of a wider fluidic channel (and the possibility that in the next reflections the light beam does not strike on the TIR zone), and a high angle gives as a result a long fluidic channel (with the consequent enlargement of all the system). That is the reason why we have chosen an intermediate point, so in our opinion the best entrance angle is 45° (right figure). Also at the same time we will make some tests with the value of 60° (left figure) because it is the value used in the previous papers, so a quick comparison can be made to ensure our hypothesis of the advantages of our system.

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3.5 Conclusions During the realization of this chapter some theoretical concepts were presented and then applied to the design of a Matlab simulation (with the corresponding verification of the correct working). After seeing how the different parameters of the simulation affect to the result, it is time to choose the optimum design for the mirror. Apart from the mirror design, the simulation will have a direct effect to other parameters such as the fluidic channel width or the position of the second mirror. 3.5.1 Searching of the Optimum Result As we have seen during the entire chapter, the design of the mirror has quite a lot of freedom degrees, so it is difficult to say exactly which one is the optimum result. Even though, we will try to focus on these ranges that are better for our purposes and then decide one value from it. Basically, the three parameters that we have to choose are focus, size and width:

-‐ On the previous section, it was said that the best range for the focus value is between 150px and 200px. The focus is directly related with the distance where we can find the convergence point, so we want it as far as possible, but avoiding the light divergence. These are the reasons why we have chosen to use 200px as focus.

-‐ Related with the size, the main objective is that the mirror can collect all the incoming beams, that is the reason why we have chosen a size of 2px, that maybe at first sight seems little, but due to the huge focus supposes a sufficiently big mirror for our system.

-‐ The width parameter as a result of the simulation and remembering that

when is greater than 20μm the transmittance equals zero, has no direct relation with this simulation, so the way that we will choose it is more related with fabrication parameters as we will see in the next chapter.

Apart from these parameters, the simulation also gives us another important information, that is the convergence point. The convergence point will help us to adjust the fluidic channel width and the position of the second mirror (we want it as close as possible from that point). Obviously, to know the position of the convergence point we have to decide the rotation of the incoming light. We will split it in two cases, 60° and 45°:

-‐ The first case with 60 degrees is basically oriented to directly compare our indium system with the paper proposed air mirror system. This income rotation is the one that they use, so the comparison between our system and there is direct and will allow us to see the impact of using an indium mirror. In that case, we can see that the convergence point is X=65px and Y=100px.

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-‐ The second case (45 degrees) is based on the better properties of the indium. As we have seen in previous chapters, the critical angle is lower so we have a higher range of entrance angles. This lower angle directly matches with our purpose of a more compact system, so theoretically is the angle of our final system. In that case, we can see that the convergence point is X=110px and Y=110px.

We can see all these results in the next figures (first 60° and second 45°):

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3.5.2 Conversion to Real Units Finally, the last step regarding to our simulation is the conversion from that pixel values to the real units. It is quite difficult to adjust exactly this conversion factor, and at the same time it is a crucial step because all the system measures will depend from it. A lot of ways to make this conversion are possible, but our decision finally has been to relate that conversion with the fluidic channel width. This width has to been planned beforehand, (it has a minimum value and also some optimum values), so our plan is to decide first the fluidic channel width and then relate it to the X value of the convergence point plus the PDMS gaps between the mirror and the fluidic channel. Once we have this value, we will obtain the desired conversion factor that will be used to multiply all the other pixel values and obtain the real measures. As an example, we can see here the values of all the parameters for a fluidic channel width equals to 900μm. We have also to consider that the width that light will travel it is not only the fluidic channel width, we have to add the PDMS gap between the channel and the mirror (900+250*2 = 1400 μm). Once we have this value we can obtain the conversion factor just dividing it by the pixel value and the result is a conversion factor of 21.5 for the 60 degrees case (and 12.7 for the 45 degrees). Here in the next tables we can see the values applying this factor:

Px Value Input 60° Fluidic Channel

Width 65 900 μm

Position of the second mirror 110 2365 μm

Mirror Focus 200 4300 μm Mirror Size 2 43 μm


Width 110 900 μm



Finally, only emphasize on the point that these calculations has been made for some specific values, but during the realization of the next chapter we will see that it is easy to change these parameters only taking into consideration the change on the conversion factor.

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CHAPTER 4: FABRICATION DESIGN 4.1 Introduction In this chapter we are going to enter deeply on the fabrication design of the master of our devices. We need to see how will be each one of the devices and calculate the exact dimensions of every part of it. It is a crucial part, because we are working on the micro scale, which means that every error in our calculations can carry a fatal error on the experimental results. The master is designed with Autocad software and sent to a specialized printer company. Basically, our idea is to create a master with 8 different devices, each one of them with a specific purpose. That is not a final design, we are going to check different values for different aspects so then we can decided which one is the best for our purposes. As we have been doing during the entire project, we will continue the work of the previous papers, so the idea is to start with the same design there (not 100% exactly but similar), and then add some modifications that we think that will improve the system. The different devices with their modifications are listed here (all the explanations are extended in the next sections):

1) PMIR inspired in the previous paper22. (REF) 2) Reduced gap between PDMS and fluidic channel to 100μm. 3) Input light angle changed to 45°. 4) Same case as 3 but with a wider fluidic channel. 5) Same case as 1 but adding a 3rd mirror. 6) Same case as 3 but adding a 3rd mirror. 7) Input light angle changed to 35°. 8) Final design with 4 mirrors and two different input light angles.

4.1.1 Master Design Before starting with the description of the designing reasons of the 8 devices, it is necessary to explain some generalities about the master design. The masters that we are going to use have 3 inches of diameter (7.6cm), but it is necessary to leave 1cm at the end of it, so finally we have a circle of 5.6 cm to fit as much devices as we can or want. Our initial idea was to fit as many devices as we can, but with a minimum dimensions that allow a correct working of the system. After trying some designs, the two options were 6 and 8 devices per master and we decided that the optimum

22 A. Llobera, S. Demming, R. Wilke and S. Büttgenbach, Lab Chip, 2007, 7, 1560-‐1566

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is with the design containing 8. The space is enough to fit our designs and there is enough space to work properly with it. Each device is contained in a rectangle with the following dimensions: 2.2 cm on the long side and 1.7 on the short side. Some parts of the square are outside the inner circle, but not the important parts, that are the ones that contain the device. We can see a sample of how is the master design:

Figure 4.1: AutoCad Mask Design

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4.2 Mirrors Design In this section, a complete characterization of the mirrors design will be made. Is the continuation of the last section of Chapter 3, but in this part we will add new design values such as height and also some changes will be applied from the theoretical design to the real world. As we have previously seen, the mirror design basically depends on the simulation values that we have obtained on the Matlab Simulation. After obtaining the values there is a conversion from the pixel values to the real values. We have to take special attention in this point because depending on the angle of the input fiber, these factors are different, which directly implies different values for the mirror. Another facts that can change the mirror design are the fluidic channel width, the gap length between the fluidic channel and the mirror, etc., but in this section we will focus on the general parameters and then on every specific case we will calculate specifically if there is some change to apply. The theoretical values for the two general cases are:

Px Value Input 60° Input 45° Mirror Focus 200 4300 μm 2540 μm Mirror Size 2 43 μm 25 μm

And the values for the real design are: We can see on the previous table that the radium value is exactly the double of the theoretical focus value. The size of the 60° input case has been round up to 50 μm, but the most important thing that we have to see in this table is the size value for the 45° input. With the theoretical value of 25 μm, the mirror height was too low, and the direct consequence of this is that maybe not all the light beams will be reflected. Remembering the conclusions that we extract on last chapter, the size value is only determined with the objective of reflect as much light as possible, and also doesn’t affect to the position of the convergence point, so we decided to enlarge it until 50 μm. The value of the mirror height has been calculated with the circumference equation (x2+y2=R2, considering x=R-‐Size). Finally, the mirror width has been decided to be 250 μm, because as we previously said, that is the minimum value to follow the relation 1:1 between width and height (due to the optical fiber diameter).

Input 60° Input 45° Mirror Radium 8600 μm 5080 μm Mirror Size 50 μm 50 μm Mirror Height 926 μm 711 μm Mirror Width 250 μm 250 μm

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4.3 Design of the General Aspects Before entering deeply to each particular case, there are some issues that are exactly the same in each device, so we can make a brief study before entering the different cases. First of all, as it was commented before, the group lenses-‐fiber has been inspired from the design of the previous papers. As it was mentioned in chapter 2, the design is exactly the same (maintaining the distance L=140μm between the corner of the lens and the fluidic channel) and the only thing that will change is the tilted angle depending on each case. Continuing with that issue, the position of the output fiber is exactly the same than the input, only considering that this time our reference is the second (or third) mirror instead of the first. The vertical position respect the fluidic channel length also varies depending of the number of mirrors. Secondly, if we talk about the fluidic channel measures, we can see that the width it is set by us in each case, but the channel length has a degree of freedom. Finally we fixed it at 1.2cm that will allow us to contain there the designs with 3 mirrors without any problem. The drawback is that for the designs with 2 mirrors there will be too much fluid without use, but we have preferred to have a standard fluidic channel for all the cases instead of one different for each one. Thirdly, and maybe one of the most important facts, is that the real measures between the mirrors does not exactly coincide with the theoretical results obtained with the Matlab simulation in Chapter 3 (even though the results are very approximate). The main reason is that in our simulation the little PDMS gap between the mirror and the fluidic channel is not taken into consideration. As we have said before, the convergence point is an approximate measure, so the most important aspect with it is to be on the vicinity, it is not necessary an exactly coincidence. That is why we use the simulation as a reference. Also related with the mirrors, we determine the position of the first mirror, and the main objective is to have the light beam striking on the center of it. So it is directly depending on the input light angle. Finally, there is two last aspects determined by us that we designed following our judgments: the indium mirror reservoirs and the fluidic reservoirs. On the indium one, we made a circle to put the indium into the channels, and the distance between it and the mirrors is the same as other designs available on the lab, to ensure that will be enough space to have a correct working. On the fluidic case, the shape and length is oriented to have the optimum result and avoid some problems that can be presented with more complex designs.

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4.4 Design of the Specific Cases In this section the different cases will be reviewed. It is necessary to remember that there is a main case (Case 1) and then all the others are the same pattern with some specific change or some mixture between two different cases, that is the reason why only the changes applied to every case will be commented. We can also see in the pictures a theoretical ray-‐tracing, that simulates the light path. 4.4.1 Case 1 (PMIR inspired on the paper, Gap=250 μm)

Figure 4.2: Case 1 This case is made following similar measures and similar aims as the device that we have on the previous paper. The reason for making it is that we will obtain a direct comparison between the air mirror and the benefit of using indium mirrors. It is necessary to point that is not an exactly copy, (we don’t have the exact measures, so it was not possible) it is only a source of inspiration and the easiest way to compare with our system. It is also very important to point the fact that this device will be the pattern from where all the other cases will be inspired. The reason is that with the same system but with a small change applied, it is possible to notice quickly where are the points where we can improve the device. This will allow the future designs to include these improvements. Entering deeply to the device measures, first we can see that the position and angle of the group fiber-‐lenses is exactly the same that we stated in the Chapter 3, (that

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also coincides with the paper value). The entrance angle value is 54.8°, to obtain the desired 60° inside the fluidic channel. Also the mirror measures are the ones that we have seen before on the previous section. On the next table we can see the measures for the distances on the device. As it was said before, the real value is a bit different due to the change of surface (not included on the simulation).

Simulation Value Distance between Mirrors

Distance between Mirrors and Lenses

Case 1 2365 μm 2409.4 μm 2559.5 μm One of the differences between our design and the one in the paper is the mirror gap (PDMS distance between the fluidic channel and the mirror). Following a recommendation of the professor, we put it on 250um, just to be sure that no problems will appear because of not following the law 1:1. This point will be reviewed with Case 2, because the law 1:1 refers to the indium parts but we wanted to be completely sure in this pattern case. Also another difference is the reservoir shape and measures, but we concluded that these facts would not have a big importance on the result, always remembering that our objective is to see that if the difference of these two similar devices is huge due to the indium mirror. 4.4.2 Case 2 (Reduced Gap=100 μm)

Figure 4.3: Case 2

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As we have just seen, the objective of this case is to confirm if it is possible to use in our device a mirror gap under 250 μm. The design is exactly the same as the case 1, only changing the gap distance between the mirror and the fluidic channel from 250 μm to 100 μm. This distance change causes that the whole system is slightly changed. If we remember the way that we calculated all the parameters, it was supposing a total distance of 1400 μm (900 μm + 250 μm *2), so now the new value should be 1100 μm (900 μm + 100 μm *2). This makes changes on the distance between the two mirrors, and the distance between the mirrors and the fiber-‐lenses, the new distances are:



Case 2 -‐ 1984.1 μm 2346.9 μm If we compare it with case 1, the distances are shorter (which totally makes sense). After that, considering the new mirrors values, we noticed that the values were extremely similar. Remembering the purpose of the mirror, and more exactly the convergence point, the most important thing is to stay on the vicinity of it. That is the reason why this system also incorporates the same mirror than in Case 1. 4.4.3 Case 3 (Input light 45°)

Figure 4.4: Case 3

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With this system our goal is to try to take advantage of the indium properties, such as the lower critical angle. We can have a lower input angle and still be in TIR zone, which means that we are reducing the volume of our system. The only drawback is that the optical path is reduced, so it will be worse for the lower concentrations. This fact will be treated in case 4. Comparing with Case 1, the change on the input fiber angle (42°) to obtain the desired 45° inside the fluidic channel, makes a positional change in the entire device. The values of the mirror measures have been presented before, and the distance between the lenses-‐fiber group and the mirrors change to these new values:



Case 3 1400 μm 1440.2 μm 1492.2 μm 4.4.4 Case 4 (Input light 45° with wider fluidic channel)

Figure 4.5: Case 4 In Case 3 it was mentioned that the optical path was strongly reduced, producing a undesired effect for the lower concentrations. In Case 4, our objective is to compare if with a wider fluidic channel we can also have good results for the 45° input. The enlargement of the fluidic channel to 1900 μm (2400 μm if we count the gaps) produces a change in the whole system because the fluidic channel width was the

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base for all the transformation between the simulation and the real world. With the new values, the new conversion factor is 17.2, which gives us these values:


Width 110 1900 μm



Exactly as in the previous cases, these values correspond to the simulation and when they are transformed into the real world, the results are:

Simulation Value Distance

between Mirrors Distance between Mirrors and Lenses

Case 4 2400 μm 2442.4 μm 2492.2 μm 4.4.5 Case 5 (Original + 3rd mirror)

Figure 4.6: Case 5

Input 45° Mirror Radium 6680 μm Mirror Size 50 μm Mirror Height 815.8 μm Mirror Width 250 μm

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Case 5 is exactly the same than the case 1, but adding a third mirror. Our goal behind that is that an enlargement of the optical path can bring us more sensitivity and LOD. An extra reflection always involves some dangers (lose of SNR or beam broadening) so we will compare if the three mirrors present advantages respect the one with only two. The most important design fact is that the vertical distance between the second and the third mirror is the same as the distance between the first and the second, (maybe we can not ensure this, but is the idea that seems more reasonable). Another option it can be thought is that the distance should be the same as it was with the output fiber before (replace the output fiber in case 1 for the third mirror), but with ray-‐tracing this theory is down, mostly because the horizontal distance are not the same in both cases. The distance between the 3rd mirror and the output fiber is the same as with the first mirror and the input fiber.



Case 5 2365 μm 2409.4 μm 2559.5 μm Finally, it is necessary to ensure two facts: the first one is to look at the values of the previous table. They totally coincide with the ones in Case 1. The second fact is that there is not an enlargement of the channel length. The only change is related with the distance between the fluidic reservoir and the lenses-‐fiber group, that it is strongly reduced. 4.4.6 Case 6 (Input light 45° + 3rd mirror)

Figure 4.7: Case 6

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In that case, as in the previous one, is exactly the same than Case 3 but adding a third mirror. Our objective is to try the enlargement of the optical path with the 45 input. This case is also very important compared to Case 4, because it will show us if there is a bigger improvement with a third mirror or with a wider fluidic channel. As in Case 5, the most important design fact is that the vertical distance between the second and the third mirror is the same as the distance between the first and the second, (maybe we can not ensure this, but is the idea that seems more reasonable).



Case 6 1400 μm 1440.2 μm 1492.2 μm Finally, it is necessary to point that in this case there is no change on the position of the input fiber-‐lenses group (in Case 5 it was different). 4.4.7 Case 7 (Input light 35°)

Figure 4.8: Case 7 As in Case 3, we will try to take advantage of the indium properties, and in that case we will try to go even further, with a 35° input angle. Theoretically we will still be in TIR zone with most of the angles, but we have chosen 35° just to be sure that we will not reach the critical angle. The change in the input fiber angle (32,9°) to obtain the desired 35° inside the fluidic channel, makes a positional change in the entire device. The values of the

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mirror and the distance between the lenses-‐fiber group and the mirrors change to these new values (considering also a change in the Conversion Factor = 9.93):


Width 141 900 μm



Exactly as in the previous cases, these values correspond to the simulation and when they are transformed into the real world, the results are:



Case 7 963 μm 1018.3 μm 1029.2 μm

Input 30° Mirror Radium 3972 μm Mirror Size 50 μm Mirror Height 628.3 μm Mirror Width 250 μm

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4.5 Case 8 (Final Design)

Figure 4.9: Case 8 As we can see in the picture, this case is a mixture between case 1 and case 3. Our main objective here is to have in the same device two ways of calculating different concentrations. The first way is related with the 3 mirrors path, which means a longer optical path that allows a better calculation for lower concentrations. At the same time with the second way we can calculate better the result for higher concentrations (shorter path). As a specific design characteristics, we only have to state that the design values are exactly the same than in the previous cases, except that due to a possible blocking of the light between the 45° input/output fiber and the second mirror, we cut a little bit of the mirrors edge (it is a little part that will not affect to the reflection on it).

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Finally, we can see the final design of the mask that was sent to the printer company:

Figure 4.10: Mask Design sent to the Printer Company

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CHAPTER 5: FABRICATION TECHNOLOGY 5.1 Master Fabrication In the previous chapter, the devices were designed and now we are going to describe the fabrication process. The process consists in three different main steps: first the fabrication of the SU-‐8 100 master (which contains the 8 different devices), the replication of the devices in different PDMS stamps and finally the filling of melted indium inside the microchannels. In this section we will take special attention on the master fabrication process, and the other two other main steps will be deeply commented in following sections. 5.1.1 Fabrication Process The master fabrication process is based on conventional photolithography. In our case it is not necessary to use a cleanroom, because we will not be working with an extremely small scale or an extremely accurate precision (even though, we will try to avoid dust entrapment as much as possible). There are several reasons why we have chosen soft lithography: is inexpensive, easy to learn, and accessible to a wide range of users. The master is a silicon substrate with microscopic reliefs, which in our case are made of a negative photoresist called SU-‐8. A negative photoresist is a light sensitive polymer that cures when exposed to UV radiation. The pattern of photoresist is the negative replica of our devices on the silicon substrate. In the picture below, we can see a simple case of a photolithography master with some microstructures on it:

Figure 5.1: Master for soft lithography Source: Anil B. Shrirao et al. (manuscript in preparation)

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The design of our photolithography mask was discussed in the last chapter, and the real mask is showed in the next picture. The Autocad file was sent to an outside vendor, who printed the mask on a flexible transparent film using a high-‐resolution laser printer.

Figure 5.2: Photolitography Mask The process starts with the cleaning of the silicon wafer on the Plasma Cleaner. After that, the negative photoresist SU-‐8 100 is deposited on the top of it, approximately 1 mL per inch (in our case we have a 3 inches wafer, so 3 mL). The next step is the Pre-‐exposure baking, used to evaporate the unnecessary solvent in the photoresist. Then, the wafer is exposed to a 365 nm UV light through the photolithography mask, which will ‘print’ our draw in the photoresist. The working principle is to cross-‐link the photoresist through the transparent region of the mask. The exposure intensity is 5 mW/cm2 (we will need this data on further calculations). After this step, a Post-‐exposure baking is made for a better adhesion between the cross-‐linked photoresist and the silicon wafer. With a developing in a solvent (PGMEA), the non cross-‐linked photoresist is eliminated, and we obtain our desired draw (the negative replica of the microchannels). Finally, a process called silanization is performed, in order to avoid the sticking of the PDMS stamps on the master during the next process of replication. This process is performed in a vacuum chamber with a product called Tridecafluoro-‐1,1,2,2-‐Tetrahydrooctyl-‐1-‐Trichlorosilane, for at least 4 hours (usually we leave it there during approximately half a day).

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Here we can see a schematic that summarizes all the process:

Figure 5.3: Schematic of photolithography process used to fabricate the SU-‐8 100 master for soft lithography

Source: Anil B. Shrirao et al. (manuscript in preparation) All the values used in the different process parts, can be found at the datasheet of photoresist SU-‐8 100 according to our desired thickness23 (250μm). On that datasheet is also where we can see why we have chosen the SU-‐8 100 instead of the SU-‐8 50. The reason is that with SU-‐8 50 it is not possible to achieve the desired 250 μm of height. All the values found there are direct numbers, except for the UV exposure time, where we have to make an easy calculation:

23 http://mems.mirc.gatech.edu/msmawebsite/members/processes/processes_files/SU8/ Data%20Sheet%2050-‐100.pdf

2

2

8 50 ( / ) ( / )

dosetocurethedesigned thicknessofUVE T SU mJ cmxposureUV Intensityof exposuretoo

imel mW cm

=−

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The most tricky part on this step is to obtain the desired height, because a height below the desired won’t be able to contain the optical fiber, and a height above it will make the optical fiber not being constrain and this means that light can diverge on the vertical direction. The value of this desired height is 250 μm, and the theoretical datasheet values to obtain it are:

Datasheet Values Spin Speed 1000 rpm

Pre-‐Bake/Soft-‐Bake 30 min / 90 min UV Exposition 75 sec Post-‐Bake 1 min / 20 min Develop 20 min

The values on this table are used only as a reference. We will see with the real experimentation that the height obtained using these values does not match our desired, and then a little adjustment will be necessary. The same problem applies to the UV exposure time, because with 75 sec some devices are not printed perfectly. All the master fabrication process is fully explained in the Dr. Shrirao Protocol24, taking special attention at the equipment necessary, precautions, calculations and equipment preparation, as well as obviously, all the procedure explained in great detail. The final result of one of the masters fabricated:

Figure 5.4: Master Fabricated by us

24 Fabrication of SU-‐8 Master for Soft Lithography: Standard Operating Protocol, Dr. Anil Shrirao

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5.2 PDMS Stamp Fabrication The second step in the soft-‐lithography fabrication process is the replication of the master by using PDMS in order to obtain the PDMS stamp. After obtaining it, it is sealed to a glass substrate, to prepare the device for the indium filling. In this section we will explain all the steps involved in this fabrication. 5.2.1 Fabrication Process The process starts with the mixture of the PDMS elastomer and its curing agent, in a proportion 10:1 by weight (that is 2g of curing agent and 20g of elastomer, for example). After this, it is necessary to remove all the bubbles from the PDMS (in order to avoid future problems and also to enhance mechanical force). So first we have to degas the mixture alone and after pouring it over the master, we degas it again. The master covered with PDMS and conveniently degassed, is then cured in an oven at 65˚C for 60 minutes, which accelerates the cross-‐linking rate of the PDMS. After that, the PDMS is peeled off the master and we obtain a PDMS stamp as we can see on the next picture:

Figure 5.5: PDMS Stamp Once we have the PDMS Stamp, it is very important to take special attention during the perforation of the indium filling holes. Sometimes, the hole can not match exactly with the indium microchannel or some PDMS can remain inside the hole, which causes a failure on the next step. Finally, the patterned side of the PDMS Stamp and the glass substrate are oxidized on the Plasma Cleaner and irreversibly sealed together. In order to have a stronger seal, they are kept in an oven at 65˚C for 10 min.

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The entire PDMS Stamp fabrication is fully explained in the Dr. Shrirao Protocol25. All the procedure explained in great detail. Here we can see a schematic that summarizes all the process, and the result of one PDMS Stamp fabricated sealed with the glass substrate:

Figure 5.6: Schematic of step-‐by-‐step process used to fabricate the PDMS Stamp Source: Source: Anil B. Shrirao et al. (manuscript in preparation)

Figure 5.7: PDMS Stamp sealed with a Glass Substrate

25 PDMS-‐Glass Bonding using air Plasma: Standard Operating Protocol, Dr. Anil Shrirao

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5.3 Filling molten indium using Vacuum The final step in the soft-‐lithography fabrication process is the filling of the molten indium in the microchannels through the single inlet, using vacuum. In this section we will examine all the process, as well as the physics involved in this special situation. 1.4.1 Physics involved in the Process If we take a look at the physics involved in the process, there are two characteristics that are clearly important: the surface tension and the gas permeability. Molten Indium has a high surface tension that implies that does not go into the microchannel on its own, it requires an external force to pull the indium inside it. The permeability of a material is defined as the ability of a material to allow the passage or diffusion of other materials through it. The PDMS blocks vapor and liquids, but allows the passing of gasses, which is the reason why it is called gas permeable. We use this characteristic together with the vacuum to solve the previous problem. Because of the gas permeability, the applied vacuum removes the air of the device in two different ways: the blue lines represent the air that flows through the inlet, and the red lines represent the air that is removed due to the gas permeability.

Figure 5.8: Air removed by the applied Vacuum Source: Anil B. Shrirao et al. (manuscript in preparation)

When inside the chamber we have the vacuum applied conditions, the pressure in both regions (microchannel and chamber) is the same. Then, when indium melts it seals the microchannel region completely and it stays isolated. The next step is releasing the vacuum, so the chamber recovers the atmospheric pressure (but we still keep the vacuum in the microchannel). The pressure gradient between the two regions causes the flow of molten indium from the inlet to the microchannel and the mirror. However, if we take into

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consideration the Ideal Gas Law (P*V=Constant), we can easily see that when the volume decreases the pressure raises and can turn equal to atmospheric pressure. But as we have previously seen, PDMS is a gas permeable material that implies that the vacuum it is also inside the walls of the PDMS. That is the reason why the Ideal Gas Law cannot be applied on it. This means that apart from the vacuum inside the channel pulling force, there is another pulling force due to the vacuum inside the PDMS walls. Therefore, the melted indium continues flowing until it reaches the end of the mirror (the indium cannot pass through the PDMS). When this happens, the device is cooled at room temperature, in order to solidify the indium Finally, just mention that we have chosen indium due to its low melting point (156˚C), which is much more below than the temperature when PDMS starts being unstable (343˚C). 1.4.2 Fabrication Process Before starting with the process, the device should be placed on the flat surface of a hot plate. Then we put two pieces of Indium exactly over the hole that we previously have made (large enough to cover the mirror and the microchannel). After that, we place the vacuum chamber over the hot plate and we turn on the vacuum.

Figure 5.9: Hot plate and conical Vacuum Chamber After 20 minutes applying the vacuum, we turn on the hot plate to a temperature of 205˚C (250˚C on the display) for 10 minutes more, without disconnecting the vacuum. 30 minutes after the start of the process, we have to turn off the vacuum but without taking out the vacuum valve. It is very important that the indium is melted (it only takes around 5 min), and some knocks on the hot plate are necessary to ensure that the indium covers the inlet hole.

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Finally, we open the valve and the vacuum is released to the normal atmospheric pressure. Then, we can see how the indium flows inside the microchannel until it arrives to the mirror (or mirrors in some cases). Sometimes we need a second round to achieve the complete filling, but normally it works at the first one. As soon as the mirror is completely filled, the device is removed from the hotplate to cool at room temperature to solidify the indium. If required, the excess of indium can be removed. The entire Indium filling process is fully explained in the Dr. Shrirao Protocol26. All the procedure is explained in great detail. Here we can see a schematic that summarizes all the process (note that our hot plate temperature is 205˚C (250˚C on the display)), and the result of one PDMS Stamp with indium filling:

Figure 5.10: Schematic of process used to fill the molten Indium using vacuum Source: Anil B. Shrirao et al. (manuscript in preparation)

26 PDMS-‐Glass Bonding using air Plasma: Standard Operating Protocol, Dr. Anil Shrirao

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Figure 5.11: PDMS Stamp with indium filling the mirrors and the microchannels In this chapter we have seen all the procedures and theory implied in our fabrication process. In the next one, we will present the results that we have obtained, as well as, the problems encountered during it.

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CHAPTER 6: RESULTS 6.1 Experimentation Results This chapter is oriented to present the results obtained from the fabrication of the masters and the stamps. We will show the evolution during the experimentation process, as well as the different problems that had appeared during the realization and the solutions that we have applied. The following sections will be focused on a general view of all the experiments, but a more detailed view of the progress of each day can be found on the attached Laboratory Notebook, that present the work done each day. Also, related with the microscope pictures, only the most significant will appear in this chapter but every picture that we made can be found on the attached Microscope Pictures (organized depending on the day it were taken). 6.1.1 Master Results In this section, the results obtained with the fabrication of the different masters are presented. As an overview, we can say that from the 7 attempts, 6 resulted in a master but only 4 of it were a master with our desired height (or with all the devices fully defined). The reason behind that is that the experimentation is a path where every day we were refining more the result obtained, depending on the result (satisfactory or not) obtained the day before. The first important thing that we noticed during the process is that the values presented on the datasheet (also presented in the last chapter), are not the correct values to obtain our perfect result. So our main objective was changing these values to arrive to the optimal point. The variables changed were:

-‐ Increase of the spin speed. -‐ Increase of the exposure time. -‐ All the other values were exactly the same as in the datasheet.

On the next table we can see a summary of the different masters that we have fabricated:

Spin Speed (rpm)

Exposure Time (sec)

Height (μm) Observations

Master #1 1100 75 380-‐395 Some devices are not perfectly defined. High height.

Master #2 1500 81 295-‐305 The wafer was used on the wrong side. Still high height.

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Master #3 1700 81 245-‐250 Nearly good, a little bit below the desired.

Master #4 1680 81 245-‐252 Good. We realized that it is not possible to accurate more.

Master #5 1690 81 -‐ Problem after developing. The master was ruined.

Master #6 1690 81 248-‐250 Perfect. Third master with the desired height.

Master #7 1690 81 255-‐260 A little bit high. It is not possible to accurate more.

From the seven experiments, we can see that 4 cases match nearly exactly with our desired height. We realized that it is not possible to accurate more because it depends on a huge variety of factors such as temperature, humidity and others; that can change the height a little around this value. Apart from the height, we also found that was necessary an increase of the exposure time, because some devices were not perfectly defined with 75 seconds. Finally, in all the fabricated masters, the general measures were the ones that we designed. If we talk about the problems, we can consider that the fabrication process is not really difficult, but it contains some steps where it is necessary to put a lot of attention. For example, master #2 was fabricated on the wrong side (the side that is not polished), resulting in a wrong master even though we use it for calculating the height. Also a problem happened during the realization of master #5, because during the drying after the develop some accident happened with an object wrongly fixed, that led into the explosion of the master (and of course, ruining it). This special attention is not only related with the fabrication process. For example, master #3 (a correct master), was broken during the cutting of the PDMS Stamp, which ruined the master completely. We conclude that even it is not a complicated process, there are several aspects that have to be into consideration, and always it is necessary to be very careful on it. Another difficulties that we found are mainly that is a long process in time. Considering only the fabrication time, it takes approximately 3 hours since we have the plain silicon wafer until we obtain the wafer with our design on it. After that it is necessary to add the silanization time, which is at least of four hours. Apart from this, the hot plate is not enough big to perform more than one master at each time. This is the reason why we can only fabricate one master per day. Finally, only comment that concerning on the accuracy of the different measurements, they are not highly precise mainly because one reason: the microscope measures are done manually, which means that some precision error can be made. The microscope is connected to a computer, which calculates the

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distance between two points that we select with the mouse (here is where the problem is located, the point where we click the mouse can not be 100% exact). Then, this distance is calculated with a conversion factor (it is necessary to consider the same optical lens in the computer and the microscope). Now we will show each of these characteristics more detailed, with the diverse problems and solutions that we have taken. 6.1.1.1 General measures First, it is necessary to take a look at the general measures of the devices, to ensure that the values that we designed are respected after all the fabrication process. The result is that all the measures are accomplished, considering as we said before that there are several reasons that may cause a little variation. As we can see on the next pictures, the different measures such as fluidic channel width, fiber-‐channel gap, mirror width and mirror-‐fluidic channel gap width, match nearly exactly with the ones that we designed.

§ Fiber-‐Channel Gap Length: 149 μm

Figure 6.1: #35 Fiber-‐Channel Gap Case 5 GAP LENGTH

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§ Fluidic Channel Width: 899 μm

Figure 6.2: #36 Fluidic Channel Case 5 WIDTH

§ Mirror Microchannel Width: 224 μm § Distance between Mirror and Fluidic Channel: 252 μm

Figure 6.3: #37 Mirror Measures Case 5

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§ Mirror width: 254 μm

Figure 6.4: #7 Mirror Case 2 WIDTH 6.1.1.2 Exposure time Another important point is the exposure time. At the beginning, our calculations of it where 75 sec, but some of the devices (Case 6, 7 and 8) had some of their parts not perfectly defined. That is the reason why we increase it until 81 sec, where all the devices and parts of it are perfectly defined. The reason behind these values is that if we take a look at the SU-‐8 datasheet, there is not an exact value for the exposure energy. The range goes from 400-‐650 (approximately), and that is why we have chosen 550 mJ/cm2 in first instance, because it was near the central point of the range. This value of 550 mJ/cm2, after applying the correspondent formula (explained in the last chapter) is what results in the 75 seconds.

Figure 6.5: Recommended exposure dose Process Source: http://mems.mirc.gatech.edu/msmawebsite/members/processes/processes_files/SU8/

Data%20Sheet%2050-‐100.pdf

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As we can see on the pictures at the end of this section, with this exposure time some of the devices were not totally defined. We can see that some parts of the device does not appear, for example the part for the optical fibers (Case 6, 7 and 8), and even in Case 7 one mirror does not exist. After examining these problems, we took the decision of increasing the exposure time. Instead of 550 mJ/cm2, we decided to choose 600 mJ/cm2, which results in 81 seconds of exposure time. After this change, all the devices were clearly defined and we decided that this is the exposure time we will be using in the following experiments. Here we can see some of the problems that appear with the Master #1 (exposure time 75 seconds): Figure 6.6: Case 6 not defined, Master #1 Figure 6.7: Case 7 not defined, Master #1

Figure 6.8: Case 8 not defined, Master #1

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6.1.1.3 Master Height Finally, the measure that was more difficult to achieve is the master height. As we said in numerous occasions before, it is important to achieve a value very close to the 250 μm because the optical fiber diameter is 230 μm, so a value under 250 μm will not allow the fiber to enter and a value above it will result in light divergence due to a bad position of it. The most important parameter related with the height is the Spin Speed. As we can see on the previous table, with the first master we used a low speed (1100 rpm although the recommended value in the datasheet was 1000 rpm, we supposed that a higher value was necessary) that gave us a high height (390 μm). From that point on, an increase of the Spin Speed resulted on a decrease of the height until the desired point, reached with the third master. In the next picture we can see the calculation of the height on the first master:

Figure 6.9: #1 Fluidic Channel Case 4 HEIGHT, Master #1 At this point it is necessary to explain a bit more how we calculate this height. Unlike the general measures, where the stamp was in the normal position at the microscope, with the height measures the procedure is completely different. First of all, we cut the stamp vertically, in order to obtain a thin portion of it. After that, we place it with the channel horizontally, in order to have a transversal view of the stamp. This method is what allows us to have a picture as the one presented above. After the fabrication of the first master, an increase of the spin speed was clearly necessary. There is no special reason why we have chosen 1500 rpm, the only reason was that a big increase was necessary to go from 390 μm to the desired 250

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μm. So we picked 1500 rpm as well as we could choose another value. The same happens with the change between the second and third master. But in that case the height change necessary was smaller, and that is why we changed from 1500 rpm to 1700 rpm. Here we can see a couple of pictures of the height on the second master (295 μm and 299 μm respectively):

Figure 6.10: #31 Fluidic Channel Case 4 HEIGHT, Master #2

Figure 6.11: #33 Mirror Case 4 HEIGHT, Master #2 Then, with the increase to 1700 rpm on the third master, we finally obtained our desired height. As we have said in multiple occasions, we considered this height accurate enough for our purpose. Here we can see some pictures from it:

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Figure 6.12: #51 Fluidic Channel Case 4 HEIGHT, Master #3

Figure 6.13: #53 Mirror Case 4 HEIGHT, Master #3 After that point, we tried to be more accurate refining the spin speed, but as can be seen on the results table that was not possible. We can state it because for slightly different speeds we keep obtaining the same result. Even with the masters #6 and #7 we can see that with the same speed results are a little different. Here we can see the pictures of the masters #4, #6 and #7:

Figure 6.14: #71 Fluidic Channel Case 4 HEIGHT, Master #4 (249μm)

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Figure 6.15: #73 Mirror Case 4 HEIGHT, Master #4 (247 μm)

Figure 6.16: #101 Fluidic Channel Case 4 HEIGHT, Master #6 (248 μm)

Figure 6.17: #102 Input fiber Case 4 HEIGHT, Master #6 (248 μm)

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Figure 6.18: #171 Fluidic Channel Case 4 HEIGHT, Master #7 (256 μm)

Figure 6.19: #172 Input fiber Case 4 HEIGHT, Master #7 (257 μm)

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6.1.2 PDMS Stamp with Indium Filling Results The process to fabricate the PDMS stamp with Indium filling was explained in the last chapter, but we will make a brief summary to remember it:

§ PDMS Stamps: 1) Mixture 1:10 between the PDMS elastomer and the curing agent

(normally, if we want to fill an entire master we need 20g:2g). 2) Degassing the mixture. 3) Put the mixture over the master and degassing again. 4) 1 hour into the 65ºC Oven.

§ Indium filling:

1) Plasma Cleaner: 3 min for the glass slides only. 2) Plasma Cleaner: 2 min for the PDMS stamp with the glass slides. 3) 10 minutes into the 65ºC Oven. 4) 20 Minutes over the hot plate with the vacuum activated but without the

hot plate. 5) 10 minutes at 250ºC with the vacuum still activated. 6) Turn off the vacuum and release the valve. 7) If the micro channels are correctly filled, let the device cool at room

temperature. After the step number 6, we were having some troubles because some micro channels were not completely filled. That is the reason why it is very important to comment the solution that we adopted (it is also presented at the protocol that we were using). If the micro channels and the mirrors were not completely filled after step 6, we try again the step 5 but only for two minutes (vacuum on and the hot plate at 250ºC). After this, we perform step 6 again and most of the times the micro channels are successfully filled. Sometimes it is necessary a third attempt. We are not able to find the reason why this extra step works, but experimentally we found that it is. Also, it is important to comment that in this section, the results are obtained through the microscope pictures, but due to the entire device is too big, we have to use the method ‘Scan Large Image’, where different pictures are captured as an Array. In our case, the best array that fits the devices is 9x10 images. 6.1.2.1 Problems encountered during the Process During the fabrication process (specially the first days of experimentation), we found a lot of problems that did not allow us to obtain a correct result. As in the master fabrication, the process is not particularly complicated, but it has a lot of tricks where it is necessary a lot of attention to avoid undesired mistakes.

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Some of the general problems that happened during the process are presented on the following list:

-‐ Mostly at the beginning, due to our inexperience we sealed some of the devices on the wrong side. This implied that the channel was on the upper side, so we were not able to perform the indium filling process.

-‐ Some of the inlet holes were too close to the end of the PDMS stamps. This made that when the inlet hole was performed the wall had broken. Also, sometimes the wall kept apparently fine but due to the proximity of the wall, some air was entering inside the channel, avoiding the indium filling process.

-‐ After re-‐using the masters, some of them had damaged devices. That is

mostly due to the cutting process, where a mistake can damage seriously one of the parts of the master.

-‐ Finally, without finding any reason, in some devices the indium was not able

to reach the mirror correctly. Also, during some days of the experimentation we were finding lots of problems basically focused on the cutting and the indium filling. After some investigation, we found that it was due to the excessive height of the PDMS stamp. Instead of 20:2, we were mixing 30:3 and that made a high stamp, which was difficult to cut, to perform the input hole and to be filled with indium (due to the vacuum force necessary to enter the micro channel needed was also higher). After locating the problem, we tried with some thin PDMS stamps, but we also found the problem that the sealing was not enough strong in some occasions, which made that some stamps were unsealed avoiding the indium filling. So we concluded that it is necessary to achieve a compromise between this two aspects, and our solution was the previously commented 20g:2g per master. Finally, the last trouble that we had is that after some days of fabrication, we realized that maybe it is necessary to cut the PDMS stamp just over the start of the input fiber channel. We think that maybe it is not possible to cut it after the sealing, so can be a huge problem that will disable all the stamps that does not accomplish that. Apart from these general problems, we can find also some problems in specific cases. Sometimes it can be due to a bad cleaning process, a damaged master or some indium filling imperfection. In the next pictures we can see some of it:

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-‐ Case 5 with an imperfection in front of the first mirror.

Figure 6.20: #91 Case 5 Ind Fill Input Entire Image

-‐ Case 1 with the input fiber wrong fabricated (the failure is on the master, so every stamp replicated has this error).

Figure 6.21: #104 Case 1 Ind Filll Entire Image

-‐ Case 2 with the second mirror not completely filled.


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-‐ Case 6 with the connection between the fluidic reservoir and the fluidic channel broken.


-‐ Case 6 with the fluidic channel bonded to the glass, probably due to an excessive pressure during the sealing step.

Figure 6.24: #137 Case 6-‐2 Ind Filll Entire Image

-‐ Case 5 with the fluidic channel damaged.


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6.1.2.2 Results Study In this section, we are going to present the final results obtained during the fabrication process. Before starting, it is necessary to note some considerations that will be present here:

-‐ A successful device is a device where the indium filled completely and any problem was detected.

-‐ A correct device is a device where the indium filled completely but some defect is present that probably will prevent the correct working.

-‐ A failure is a device where the indium was not correctly filled, (we don’t have

microscope pictures for these stamps). First of all, we want a present a table that shows the number of cases that where successful, correct or failure during every day of experimentation:

Day 9 Day 10 Day 13 Day 14 Day 15

TOTAL 8 8 16 8 12

Successful 0 2 8 6 10

Correct 1 2 3 1 1

Failure 7 4 5 1 1

And if we take a look at the successful percentages of the total, we can easily see our improvement during all the fabrication process.

Day 9 Day 10 Day 13 Day 14 Day 15

TOTAL 8 8 16 8 12

Successful 0 2 8 6 10

Percentage 0% 25% 50% 75% 83%

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Secondly, we will present a table with the successful and correct devices per case, to see if we can find a pattern of a wrong designed case or some other conclusion: Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8

TOTAL 4 4 4 2 6 7 3 4

Successful 2 3 4 1 4 5 3 4

Correct 2 1 0 1 2 2 0 0

We can extract several conclusions from the table:

-‐ The first and most important is that seeing that we have at least one successful device in every case, we can totally reject that the master is wrongly designed. At the same time, we should point that in the cases 1 and 4, the fact that they have less successful is due to a defective master (Case 1) or a damaged master (Case 4), not because of a design mistake.

-‐ Another very important conclusion, directly related with the design chapter, is the results of Case 2. It is necessary to remember that this case is the only one with a different gap width between the mirror and the fluidic channel. Our hypothesis was that maybe it would not work because the height is higher than the width. We can see that this is not accomplished; the devices were successful as much as the others.


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-‐ Finally, we can see that there is not any problem with the cases that contain 2 or 3 mirrors to be filled. They are successful as much as the others, and any problem was related with this fact. We can ensure that the design on this aspect has been perfect.



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Figure 6.29: #139 Case 8 Ind Filll Entire Image As we said before, a picture of every correct/successful device and the daily progress can be found in the Laboratory Notebook.

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6.2 Experimentation Conclusions After all the experimentation process, we can draw some conclusions extracted from our daily work. Related with the master fabrication, we have found the correct fabrication values that meet our purposes, (which are different from the datasheet ones): Datasheet Values Experimentation Values

Spin Speed 1000 rpm 1690 rpm Pre-‐Bake/Soft-‐Bake 30 min / 90 min 30 min / 90 min

UV Exposition 75 sec 81 sec Post-‐Bake 1 min / 20 min 1 min / 20 min Develop 20 min 20 min

Also, as we have seen on the previous section, we can conclude that the master is well designed, because we have at least one successful device from every case. The mistakes that appear on the devices were product of external conditions. Related with the PDMS stamps fabrication and the Indium filling process, the first comment is that we found that a lot of careful is needed to perform all the fabrication, and that is the reason why we were having some troubles at the beginning. But as we can see in the previous results, our progress has been totally satisfactory, with a bigger percentage of successful cases every day. The biggest problem that we found during the stamps fabrication was the excess of the PDMS stamp height. This allows us to conclude that in order to avoid the majority of the problems that we are having, it is extremely important that the height of the stamp is not very high (but avoiding also a very thin stamp). Our final decision has been to use a mixture of 20g:2g on every master. Another problem that we encountered at the beginning is related with the letters present in every device (explaining the particular characteristics). They were wrongly replied, and it may cause some problems to the device. That is the reason why we were thinking on erasing it from the fabrication mask. After some time, and due to our improvement in the fabrication process, this problem disappeared and we kept the letters on the design. If we talk about the improvements that can be made on future designs, in order to make easier the fabrication process, we found two:

-‐ As we said we had some problems because the inlet holes were two close to the PDMS wall. The solutions for that can be shorten the mirror micro channel or separate more the devices inside the master.

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-‐ Enlarge the fiber positioner, in order to avoid the mentioned cut. As we have seen, a diagonal cut was necessary because after the sealing maybe it was not possible to enter the fiber inside the micro channel.

Finally, talking more concretely about the cases, we can state that:

-‐ It is not necessary to have a gap of 250 μm between the mirror and the fluidic channel. We can see that in Case 2 (with only 100 μm) the device is fabricated correctly. This will imply a big improvement because this distance does not contain any fluid, so it is not useful for our purpose.

-‐ The second aspect is that even the cases with two and three mirrors are correctly filled, which means that our design has been perfect.

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CONCLUSIONS AND FUTURE WORK In conclusion, my work during these eight months has been focused on the design and fabrication of integrated Indium micromirrors. Starting from the investigation of all the information available about the topic and a deep study of some concrete papers about it, we realized that could be a good option to implement these mirrors with Indium. We went on with a simulation test to optimize the design, and finally the fabrication process, which has been successful. One of the most important things that I can conclude after the realization of the project, is that is really gratifying that from a topic where I did not had any knowledge, I have reached this learning level eight months later. During the research, we hypothesized that the Indium mirror will have better response than the previously studied air mirror. We found some theoretical material that support our idea, but unfortunately due to the lack of time, we were not able to test the devices to characterize the response. Also, another hypothesis was the inclusion of a third mirror with the purpose of enlarging the optical path. As we have said, we were not able to characterize it, but at least we can say that during our experimentation we have seen that there is not any problem about adding it, from the fabrication point of view. To support these hypotheses, we performed a Matlab simulation focused on the obtaining of the optimum design. Also, we used this simulation to confirm all the theoretical facts that we had previously found. The fabrication process is very novel, and basically permits the filling of a dead end micro channel with the vacuum force. We have dealt with some problems, but we have been able to find a solution for them. Finally, we obtained excellent results, with a total of 26 successful devices. In this way, the experimentation has demonstrated that our design was correct, even tough some improvements could be made in the future. The fact of positioning 4 mirrors in one device (actually in less than 2 cm2) and see that works correctly, confirms our statement.

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To fabricate the device, we had followed some protocols that we optimized for our purpose. For the master fabrication some adjustments were necessary, as well as for the PDMS stamp fabrication, where we improved our results every day of experimentation. The proposed fabrication method is simple, inexpensive, supports mass fabrication and is suitable to fabricate devices for Micro Total Analysis System (µTAS). It is important to remark that during the project, we have been working on a field that can turn out in a leading market in the future years. As we previously said, this technology has a lot of advantages and for sure will become very important in a near future. Finally, it is necessary to talk about the future work related concretely with this thesis. As I have said before, a lack of time has made that we were not able to characterize the devices. With this characterization, some important conclusions will appear, in order to improve a future design. We have to remember that the eight devices presented on every master, have different characteristics to accomplish this purpose, after testing each of them we will choose the most beneficial ones. Also this testing will serve to see if our hypothesis were correct or not. So after this characterization, a final device can appear with the best characteristics.

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REFERENCES

[1] Bingcheng Lin, Microfluidics: Technologies and Applications, 2011

[2] Nikola Slobodan Pekas, Magnetic tools for Lab-‐on-‐a-‐chip Technologies, 2006

[3] http://en.wikipedia.org/wiki/Lab_on_a_chip#LOCs_and_Global_Health

[4] S. Camou, H. Fujita and T. Fujii, Lab Chip, 2003, 3, 40-‐45

[5] K.W. Ro, B.C. Shim, K. Lim and J.H. Hahn, Micro Total Analysis Systems, 2001, 274-‐

276

[6] Frank B. Myers and Luke P. Lee, Innovations in optical microfluidic technologies

for point-‐of-‐care diagnostics, Lab Chip, 2008, 8, 2015-‐2031

[7] http://www.chemguide.co.uk/analysis/uvvisible/beerlambert.html

[8] http://www.clinchem.org/content/35/3/509.1.full.pdf+html

[9] http://pubs.rsc.org/en/results/searchbyauthor?selectedAuthors=A.:Llobera

[10] A. Llobera, R. Wilke and S. Büttgenbach, Lab Chip, 2004, 4, 24-‐27

[11] A. Llobera, R. Wilke and S. Büttgenbach, Talanta, 2008, 75, 473-‐479

[12] A. Llobera, S. Demming, R. Wilke and S. Büttgenbach, Lab Chip, 2007, 7, 1560-‐

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[13] http://www.cie.co.at/index.php/index.php?i_ca_id=306

[14] A. Llobera, R. Wilke and S. Büttgenbach, Lab Chip, 2004, 4, 24-‐27

[15] A. Llobera, R. Wilke and S. Büttgenbach, Talanta, 2008, 75, 473-‐479


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[17] http://www.lenntech.com/periodic/elements/in.htm

[18] Palik, Handbook of Optical Constants, Vol.3 (AP, 1998)(ISBN 0125444230)

[19] http://www.mathworks.com/

[20] http://www.mysimlabs.com/ray-‐tracing.html

[21] http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=48


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[23]http://mems.mirc.gatech.edu/msmawebsite/members/processes/processes_fil

es /SU8/Data%20Sheet%2050-‐100.pdf

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[24] Fabrication of SU-‐8 Master for Soft Lithography: Standard Operating Protocol,

Dr. Anil Shrirao

[25] PDMS-‐Glass Bonding using air Plasma: Standard Operating Protocol, Dr. Anil

Shrirao

[26] PDMS-‐Glass Bonding using air Plasma: Standard Operating Protocol, Dr. Anil

Shrirao

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ACKNOWLEDGEMENTS This Master Thesis would not have been possible without the help and support of

several persons who contributed in the realization of the Project.

First of all, I must present my gratitude to my advisor, Dr. Raquel Pérez-‐Castillejos.

Thanks for the opportunity given, and also for all the guidance, the advices and your

patience and time.

Also very important for the realization of the Thesis is my first laboratory mate, Anil

B. Shrirao. Thanks for all the help, tips and all the transferred knowledge.

I am also very thankful with my second laboratory mate, Jeremy Hsiao. It was a

pleasure working with you as a team in the realization of Chapter 4.

The same applies to my third and last laboratory mate, Rafa Gómez. Thanks for the

help and support during the fabrication progress. It was a pleasure working (and

even risking our lives) with you. Good luck with the future work that you have from

this point on.

Also thank to ETSETB-‐UPC and NJIT for the opportunity given.

And finally, the greatest gratitude goes to my family. The moral and economic

support has been really appreciated.

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Raul Broto Master Thesis