masters thesis: study of tin droplet impact on a substrate

Mechanical Engineering

CONFIDENTIAL

Study of tin droplet impact on asubstrate at low pressure usingParticle Tracking Velocimetry

Avinash Suresh Kumar

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Study of tin droplet impact on asubstrate at low pressure usingParticle Tracking Velocimetry

Master of Science Thesis

For the degree of Master of Science in Mechanical Engineering at DelftUniversity of Technology

Avinash Suresh Kumar

December 1st, 2016

Faculty of Process and EnergyDelft University of TechnologyReport Number P&E #2801

The work in this project was supported by ASML. Their cooperation is hereby gratefullyacknowledged.

Copyright © 3mEAll rights reserved.

Delft University of TechnologyFaculty of

3mEDepartment of

Process and Energy

The undersigned hereby certify that they have read and recommend to the Faculty of3mE for acceptance a thesis entitled

Study of Tin Droplet Impact on a Substrate at Low Pressure UsingParticle Tracking Velocimetry

byAvinash Suresh Kumar

in partial fulfillment of the requirements for the degree ofMaster of Science Mechanical Engineering

Dated: December 1st, 2016

Supervisor(s):Dr.ir. Christian Poelma

Prof.Dr.ir. Jerry Westerweel

Dr.ir. Volkert van Steijn

Abstract

Particle contamination is one of the serious issues concerning ASML in their lithographymachine designs. The new lithography machines make use of extreme ultra violet (EUV) forprinting at nano-scales. High powered EUV is achieved by plasma generation using a CO2laser light on hot tin droplets. The plasma generation results in excessive debris formation,which contain sub-micron tin droplets, flying with very high energy inside the system. It is ofcritical importance that even the smallest scale of debris are trapped before they contaminatethe machine. Trapping of sub-micron droplets was found to be difficult without the knowledgeof behaviour of the droplets. In this study, experiments were performed to understand andquantify the behaviour of sub-micron tin droplets, as they move inside the system, scatteringand splashing from the walls of the vessel. Deep understanding of fluid dynamic behaviourof these droplets impacting on materials similar to the walls of the vessel is required.The aim of the project was to perform controlled particle tracking experiments to study theimpact dynamics of sub micron tin droplets on substrates (target plates). The substrates werechosen with material properties identical to the walls of the EUV machines. Two conditionsof impact were studied, namely normal incidence and grazing incidence on sample substrateswith varying temperature properties. Based on the results obtained from the impact assess-ment, solutions were proposed to trap the debris from splashing or scattering.A brief outline of the project is:

• Selecting and developing the test setup to perform experiments

• Testing on different sample materials with varying temperatures

• Analysis of data using a newly developed PTV algorithm.

• Draw conclusions on impact behaviour of tin droplets on substrates at varying temper-atures.

Master of Science Thesis CONFIDENTIAL Avinash Suresh Kumar

ii Abstract

Avinash Suresh Kumar CONFIDENTIAL Master of Science Thesis

Table of Contents

Abstract i

Acknowledgement viii

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Previous work vs current work . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Source characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.2 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.3 Particle tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Theory 5

2.1 Particle tracking velocimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 High speed cameras for PTV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Types of imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Light scattering theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Scattering from a particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4.1 Rayleigh scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4.2 Geometric scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4.3 Mie scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4.4 Effect of numerical aperture . . . . . . . . . . . . . . . . . . . . . . . . 10

2.5 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10


iv Table of Contents

2.6 Droplet impact dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.6.1 Properties of drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.6.2 Droplet impact on solid surfaces . . . . . . . . . . . . . . . . . . . . . . 132.6.3 Droplet impact on liquid surfaces . . . . . . . . . . . . . . . . . . . . . . 142.6.4 Droplet impact on solid surfaces with liquid film . . . . . . . . . . . . . . 15

3 Experimental Description 17

3.1 Overview of the experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Vacuum chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3 Source region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4 Double pulsed laser - sheet of light . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4.1 Laser sheet modification . . . . . . . . . . . . . . . . . . . . . . . . . . 203.5 sCMOS Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.5.1 Time of flight and inter-frame time . . . . . . . . . . . . . . . . . . . . . 223.6 Setup geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.6.1 Normal incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.6.2 Grazing incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.7 Target samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.7.1 Thickness of tin deposited on plate . . . . . . . . . . . . . . . . . . . . . 24

4 PTV Measurements and Data analysis 25

4.1 Measurement details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2.1 Reference scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.3 Procedure for PTV measurements . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3.1 Laser and camera alignment . . . . . . . . . . . . . . . . . . . . . . . . 274.3.2 Checking window conditions . . . . . . . . . . . . . . . . . . . . . . . . 274.3.3 Installing target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3.4 Setting temperature conditions . . . . . . . . . . . . . . . . . . . . . . . 274.3.5 Performing PTV measurements . . . . . . . . . . . . . . . . . . . . . . . 27

4.4 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.4.1 Image processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.4.2 Particle detection and properties . . . . . . . . . . . . . . . . . . . . . . 294.4.3 Particle pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30


Table of Contents v

4.4.4 Choose best pairing configuration . . . . . . . . . . . . . . . . . . . . . 32

4.4.5 Determine velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.4.6 Determine impact time and position . . . . . . . . . . . . . . . . . . . . 35

4.4.7 Statistical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.4.8 Analysis schemes for normal and grazing incidence . . . . . . . . . . . . 38

5 Preliminary Tests 39

5.1 Particle source characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.1.1 SEM analysis of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2 Heat transfer from droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.2.1 Heat transfer to surrounding atmosphere . . . . . . . . . . . . . . . . . . 42

5.2.2 Solidifying upon impact on the plate . . . . . . . . . . . . . . . . . . . . 44

6 Results and discussion 46

6.1 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.1.1 Uncorrected scattered data . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.2.1 Cold clean Molybdenum plate - Normal Incidence . . . . . . . . . . . . . 49

6.2.2 Hot clean Molybdenum plate - Normal Incidence . . . . . . . . . . . . . 51

6.2.3 Cold Tin coated Molybdenum plate - Normal Incidence . . . . . . . . . . 52

6.2.4 Hot Tin coated Molybdenum plate - Normal Incidence . . . . . . . . . . 53

6.2.5 Cold Molybdenum plate - Grazing Incidence . . . . . . . . . . . . . . . . 55

6.2.6 Hot Molybdenum plate - Grazing Incidence . . . . . . . . . . . . . . . . 56

6.2.7 Cold Tin coated Molybdenum plate - Grazing Incidence . . . . . . . . . . 57

6.2.8 Hot Tin coated Molybdenum plate - Grazing Incidence . . . . . . . . . . 60

6.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.3.1 Normal incidence - Impact on solid surface . . . . . . . . . . . . . . . . . 62

6.3.2 Normal incidence - Impact on liquid surface . . . . . . . . . . . . . . . . 63

6.3.3 Grazing incidence of impact - Solid surface . . . . . . . . . . . . . . . . 64

6.3.4 Grazing incidence of impact - Liquid surface . . . . . . . . . . . . . . . . 65

7 Conclusion and recommendations 66

7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

7.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67


vi Table of Contents

A PTV Algorithm developed for the Thesis work 70


List of Tables

1.1 Results for normal incidence [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.1 Properties of tin used in this thesis work . . . . . . . . . . . . . . . . . . . . . . 203.2 Camera Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.1 Parameter space for experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.1 Assumptions considered for calculation of radiative cooling using properties of liquidtin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.1 Summary of results for Cold clean Molybdenum plate - Normal Incidence . . . . 506.2 Summary of results for Hot clean Molybdenum plate - Normal Incidence . . . . 516.3 Summary of results for Cold Tin coated Molybdenum plate - Normal Incidence . 526.4 Summary of results for Hot Tin coated Molybdenum plate - Normal Incidence . . 556.5 Summary of results for Cold Molybdenum plate - Grazing Incidence . . . . . . . 566.6 Summary of results for Hot Molybdenum plate - Grazing Incidence . . . . . . . . 576.7 Summary of results for Cold Tin coated Molybdenum plate - Grazing Incidence . 596.8 Summary of results for Hot Tin coated Molybdenum plate - Grazing Incidence . . 606.9 Summary of the results obtained in the experiments . . . . . . . . . . . . . . . . 616.10 Weber’s and Reynolds numbers found in experiments . . . . . . . . . . . . . . . 63


Acknowledgement

This project has consumed huge amount of work, research and dedication. I am personallyindebted to a number of people that a complete acknowledgement would be encyclopaedic.Firstly, I would like to convey my deep sense of gratitude to Dr. Christian Poelma for allowingme to perform my master thesis under his esteemed supervision. His ideas and his motivationto work harder, has always helped me to perform better during my thesis. His excellentguidance and his keen observations has given way for this project to be successful.Next, I thank Dr. Victoria Voronina sincerely for her constant support and supervisionthroughout this period. Her skills for technicality and critical analysis with respect to thisproject are greatly appreciated.I would like to thank Maarten van Kampen, for his wonderful suggestions, ideas and technicalsupport with regards to this project.I also thank Theo Driessen and Herve Allain, for extending their kind help with their techni-calities in all my experiments.I would like to warmly thank my best friend Srinidhi Desikan, for her amazing formattingand editing skills that has given this thesis a professional outlook.Finally, my deepest and my most sincere gratitude and respect to my parents Mrs. & Mr.Suresh Kumar, for their constant trust, love and care throughout my years of study.


Chapter 1

Introduction

This chapter describes the process involved in generation of extreme ultraviolet light and thesplashing/scattering problem associated with tin micro-droplets leading to contamination ofthe machine. To overcome the problems associated with splashing and scattering, better un-derstanding of the fluid dynamics associated with impact behaviour of the droplets is required.Some basic principles required to understand the work carried out are outlined.

1.1 Motivation

ASML is one of the leading companies in the manufacturing and development of highlyadvanced lithography machines for microprocessors printing. These machines utilize extremeultra violet (EUV) light which have extremely small wavelengths. Development of EUV hasproved to be of very high significance. As of 2011, the lowest wavelength achieved is 13.5 nm.EUV generation is achieved by impact of high powered CO2 laser light on liquid tin (Sn)droplets, jetted at high velocities. These droplets are ionized by the laser irradiation in avacuum environment. Interaction of the beam with droplets results in evaporation of Sn andsubsequent formation of EUV-emitting plasma. In the EUV source chamber, an elliptical col-lector captures the EUV and focuses it towards the scanner section, where the actual printingtakes place. This collector is located few centimeters away from the plasma. The ionisation ofthe Sn droplet by the laser results in large amount of debris formation as shown in figure 1.1.The debris contains a burst of sub-micro droplets of tin, flying with very high energy inside thesystem. The debris from the plasma must never accumulate on the collector for more than fewmicrometers. However, there are some problems with this arrangement, mainly spitting andsplashing/scattering behaviour. Spitting occurs due to presence of hydrogen in the vacuumvessel. The atomic hydrogen dissolves in liquid tin and forms bubbles. These bubbles canreach the collector surface and produce a jet of droplets. Splashing/scattering occurs whenhigh speed flying droplets impact on the collector vanes, breaking up and injecting furtherdebris into the scanner section of the machine with high velocities. Currently a mathematicalmodel is being developed by ASML to simulate Sn particle contamination behaviour from


2 Introduction

walls of the lithography machine to understand and quantify the contamination. To developa mathematical model the properties of particle, during splashing and scattering from thewalls, are required.

Figure 1.1: Scattering debris associated with plasma contamination

In this study, splashing/scattering is studied in detail. Droplet impact on solid and liquidsurfaces is crucial in understanding the droplet splashing and scattering properties whichcause contamination inside the EUV vessel. Suitable metal vanes are introduced inside theEUV machine to effectively trap these droplets from splashing and bouncing around insidethe vessel, but the fluid dynamic aspect of droplet impact was unclear.The first aim of the project is to advance the level of fundamental understanding of fluiddynamic issues which can be used to characterize the impact behaviour of tin droplet onsubstrates having similar material property as that of the vanes. The second aim is topropose a solution to prevent/trap the droplets from splashing, bouncing or jetting fromsurface based on the findings. Particle Tracking Velocimetry (PTV) experiments are used tostudy and understand the impact dynamics of tin micro droplet on substrates at low pressure.A robust PTV algorithm is constructed using Matlab, which is utilized for analysing particletrajectory, impact dynamics, and quantify the effect of splashing/scattering from differentsubstrates. The results obtained from the PTV experiments are used in the mathematicalmodel to simulate Sn particle contamination.After sufficient running of the EUV lithography machine, it was observed that the vane walls ofthe vessel have different properties at different sections inside the machine. Hence, substratesare chosen in such a way that the surface topology of the substrate plates are similar tothe vanes of the EUV vessel when in operation. In this study two types of plates made ofmolybdenum (Mo) and tin-coated molybdenum are selected based on their surface roughness.Both plates are subjected to high temperature (above 300◦C ) to analyse the impact in hotconditions which simulate the ideal working inside an operating EUV machine. At theseshigh temperatures, the surface topology of the tin-coated molybdenum plates changes toliquid form as the temperature is above the melting point of Sn. As the surface becomesliquid, splashing and jetting can occur.As the droplets move in multiple directions (figure 1.1) inside the EUV vessel, two differenttypes of impact configuration for droplets on target substrate are studied.

• Normal Incidence - Droplets impact perpendicular to target substrates.

• Grazing Incidence of impact - droplets impact at a grazing angle on the substrates.


1.2 Previous work vs current work 3

1.2 Previous work vs current work

M.Van Kampen [1] focused on particle tracking for droplet impact at normal incidence on adifferent set of samples. Table 1.1 shows the conclusions that were drawn from the previousexperiments. It was observed that hot tin coated molybdenum plates above 300◦C werebest suited to trap the droplets for normal incidence which can be seen from the fraction ofparticles scattered or splashed from surface. Some changes were incorporated into the presentwork as suggested by ASML.

Table 1.1: Results for normal incidence [1].

Type of substrate Flux in % Scattered % Vin (m/s) Vsct (m/s) AngleHot Mo 100 31 98 13 50Cold Mo 44 14 98 12 50Hot Mo, Tin 48 3 100 13 60Cold Mo, Tin 39 45 99 14 25

1.2.1 Source characterization

The experimental setup used by M.Van Kampen [1] has a different method of producing tinparticles. A high powered 1 µm, CO2 laser was used, which was made to focus on a rotatingmolybdenum wheel coated with solid tin. The solid tin on the wheel is forced to break upinto small particles by ablation, caused due to the laser irradiation. The high powered laserproduced 400 mJ of energy in a single pulse. The double pulse configuration was adoptedto produce maximum flux of particles when observed through the PIV camera. A particleflux of 6000 particles/s/m2 was captured and recorded using the PIV camera. The high fluxrate produced statistical results with higher certainty when compared to the present setupwhich utilizes a lower flux rate (3000 particles/s/m2). The present configuration is explainedin detail in the experimental description section.M.Van Kampen [1] pointed out that accurate sizing of the particles through image processingand PTV algorithms were not possible due to restriction of the laser sheet and the cameraused. The laser sheet produced by the PIV laser, had a Gaussian distribution of energyacross its width. The Gaussian distribution created further ambiguity in determining theparticle sizes using the method of light intensities. In this study, an effort was made toremove the Gaussian distribution of energy across the width of the laser sheet by making theenergy constant through out its width span. This would then remove the difference in lightintensities when observing particle sizes. The sheet was modified to have constant energyalong its width by cutting the beam on either side and allowing only a tiny portion in themiddle to be expanded and used for the sheet. As a result, the observable region by thecamera was reduced.The current experimental setup involved developing a new PTV algorithm and performingexperiments of droplet impact on substrates at normal and grazing incidence. The completedescription of the PTV algorithm developed for this study is given in chapter 4. Since a newset of laser was incorporated in the source section, the first set of experiments were carriedout to quantify the sizes and velocities of the droplets produced by the new source. The


4 Introduction

substrates used were the same materials as in the previous study but a different set of plates.Hence, the normal incidence experiments were repeated not only to quantify the source butalso to tune the new PTV algorithm to capture and track particles efficiently. Once the resultswere acceptable or similar to previous experiments, grazing incidence of particles onto thesubstrate were carried out. The second part comprises of modifying the experimental setupto perform grazing incidence of particles onto the substrates. The scattering and splashingproperties are obtained for theses configurations

1.2.2 Data acquisition

Data acquisition in the previous experiments conducted by M.Van Kampen [1] was done byusing script ’LogIT’, developed within ASML. It is used to capture images effectively bysyncing camera and laser systems. The script also enables to vary the delay times of the laserflashes and choose different time of flight (TOF) to observe wide range of velocities. Time offlight is defined as the time taken by the tin particle to reach the observable region from thesource. The information on the time of flight was later used in particle tracking to steer theanalysis process and filter particles based on the time of flight values.The same methodology is used in the present experimental setup to capture images. Usingscript ’LogIT’ images were recorded with specified time interval and time of flight values.

1.2.3 Particle tracking

Particle tracking for the previous experiments were done using script developed by M.Vankampen and A.De Jong. The algorithm used statistical validation by grouping particles basedon their time of flight. In the current experiments, efforts are made to improve the accuracyof the obtained results and to see the proximity of results to the ones obtained in the previouswork.


Chapter 2

Theory

This chapter presents the theoretical and pre-requisite knowledge required before starting theexperiments related to Particle Tracking Velocimetry and droplet impact.

2.1 Particle tracking velocimetry

Particle Tracking Velocimetry (PTV) is one of the oldest flow measurement technique in thefield of fluid mechanics. PTV involves recording the position of small particles following afluid flow illuminated by a laser light sheet [2] at different instant of time. It aims to recognizethe position of each particle consisting of multiple spots to determine the trajectory of particleand its velocity vector. It is similar to Particle Imaging Velocimetry (PIV), but is based ona Lagrangian view, where individual particles are followed as they move through space andtime. It is sometimes also called as low density PIV [2] [3] [4].

Figure 2.1: Seeding density (N) for different imaging techniques.


6 Theory

Seeding density, characterized by the number of particles present per image, determines thetype of imaging technique to be adopted as shown in figure 2.1. Particle identification anddetermination of position is a very important step in PTV. It only works when the seedingdensity is low. Since individual particles are tracked, no overlap of particles is permitted andalso high spatial resolution is required for effective and accurate analysis.A typical PTV system consists of the following components as shown in figure 2.2 and arelisted below.

• High speed camera.

• Laser system to generate sheet of light.

• Particles following fluid flow(tracer particles).

• PTV algorithm to identify and analyze the particle behaviour with respect to fluiddynamic issues.

Figure 2.2: Components of PTV [5]

2.2 High speed cameras for PTV

Two basic types of high speed cameras are widely used for imaging in PTV. The choice ofthe camera depends on the other components used and also the individual needs of eachapplication.

• Charged coupled device (CCD) cameras - They are most widely used in PTVexperiments and are made using a special manufacturing process that allows the con-version to take place in the chip without distortion. This creates high quality sensorsthat produce excellent images. They are more expensive owing to the special manufac-turing process.

• Complementary Metal oxide semiconductor cameras (CMOS) - In these chips,transistors are used at each pixel to move the charge through traditional wires. Thisoffers flexibility because each pixel is treated individually. It is similar to creating amicrochip thereby making it easier to manufacture, and cheaper than CCD chips.


2.2 High speed cameras for PTV 7

The biggest difference is that CCD sensors create high quality images with low noise (grain)while CMOS images tend to contain higher noise. CCD sensors are more sensitive to lightwhile CMOS sensors need more light to create a low noise image at proper exposure.sCMOS are a new generation of scientific CMOS(sCMOS) sensors that are developed by LaV-ision. It has both the advantages of CCD and CMOS technologies. It provides exceptionalimage quality and system performance. The sCMOS camera has high resolution with ex-tremely low readout noise and high transfer rates. It offers excellent imaging performance.Due to the advantages of the sCMOS over the CCD and CMOS cameras, it was used in thePTV experiments.

2.2.1 Types of imaging

There are different modes of capturing images using the high speed cameras. The two widelyused settings are single exposure and double exposure imaging technique.Single exposure imaging technique using high speed camera captures the particle moving inthe sheet of light with a single exposure having a low shutter speed. As a result, streaksappear on the image indicating the particle trajectory as shown in figure 2.3. It is mainlylimited by the temporal resolution (frequency) of the camera and the dimensions of the lightsheet. Long streaks are required for an effective Lagrangian analysis [3]. This means that aparticle must be present inside the sheet of light for a sufficiently long time to obtain longstreaks.

Figure 2.3: Single Exposure

Figure 2.4: Double frame/Double exposure


8 Theory

Double exposure imaging technique using high speed camera makes two snapshots of the flowfield containing particles, denoted as Frame A and Frame B and separated by a small timeinterval (∆t) as shown in figure 2.4. By determining their locations in respective frames,the displacement and consecutively the velocity vector is obtained. This method is possiblewith high speed motion cameras (sCMOS and CCD) as they provide high resolution and fasttransfer rates of images captured. It is highly useful for fast moving particles when comparedto single exposure imaging technique. This technique is used in this thesis work.

2.3 Light scattering theory

Particles present in the sheet of light are observable by the camera as they scatter incidentlight. From the information of the scattered light captured in the image, it is possible toextract data regarding individual particle size, as they scatter light differently. Based on thediameter of the particle, three general scattering theories are applicable [6], namely:

• Rayleigh scattering

• Mie scattering

• Geometrical scattering

2.4 Scattering from a particle

Assume a laser light travel along x-axis and incident on a particle at (0,0,0) making an angle θwith x axis and φ with the yz plane as shown in figure 2.5. In order to calculate the scatteringcoefficients, the scattered angle θ and φ are required.

Figure 2.5: Coordinate system for scattering coefficients.

Particle sits at (0,0,0) and laser beam travels in the +x direction. θ is the scattering angle.

For PTV experiments the most common situation is θ = 90◦ scattering angle and out of planepolarization, φ = 0◦. The intensity or scattering cross-section is given by S190◦ m2/sterad.All the experiments in this thesis work was carried out in an vacuum chamber. The refractiveindex considered in the study, n =1 (vacuum).


2.4 Scattering from a particle 9

2.4.1 Rayleigh scattering

Rayleigh scattering is elastic scattering of light or other electromagnetic radiation by particlesmuch smaller than the wavelength of the radiation. It applies to cases when the scatteringparticle is very small and the whole surface re-radiates with the same phase. The polarization-averaged scattering cross-section for one small sphere is given by:

(S190◦)2 = 2.d6.π5

3.λ4 .

∣∣∣∣∣n2 − 1n2 + 1

∣∣∣∣∣Where,

D = Diameter,n = Refractive index,

S190◦ = Scattering coefficient,λ = Wavelength of light

The dependency on wavelength means shorter wavelength are scattered more strongly thanlonger wavelengths.

2.4.2 Geometric scattering

Scattering of light from objects that are large with respect to wavelength of light can beaddressed using geometric scattering theory. For opaque spheres with diameter (d), thepolarization-averaged scattering cross-section is found to be isotropic and proportional tosquare of the diameter. The geometry of particle considered for geometric scattering asshown in figure 2.6

Figure 2.6: Geometry of sphere used for scattering.


10 Theory

(S190◦) =R2φout

2 .d2

16Where,

Rφout = Fresnel reflection coefficient for s-polarised light,(S190◦) = Scattering cross-section.

The total intensity is proportional to the diameter S190◦ ∝ d2

2.4.3 Mie scattering

The Mie scattering equation is valid for particle sizes equal to the wavelength of light. TheMie solution takes the form of analytical infinite series that need to be computed numerically.Mie solutions are complex functions which must be solved analytically to obtain the scatter-ing cross sections S190◦. From the obtained scattering cross-sections, the particle sizes aredetermined based on Bessel functions. Mie solutions are too complex to calculate due to thenon-monotonous relation between scattered intensity and particle size.

2.4.4 Effect of numerical aperture

In an actual experiment the scattered intensity is measured that is collected by the lenshaving a finite numerical aperture(NA). The scattering cross-sections can be computed asshown below [4][1].

σ = (S190◦).2π(1− cos(arcsin(NA)))

Where,

σ = Intensity measured,S190◦ = Scattering cross-section,NA = Numerical apreture,

2π = Solid angle captured by imaging lens.

2.5 Methodology

The PTV algorithm utilizing double exposure imaging technique consists of seven majorsegments as shown in figure 2.7. The first step involves capturing images of the flow field con-taining particles. This is followed by pre processing and particle detection which differentiatesparticle from background and noise, while also locating particle centroids. Particle couplingidentifies and pairs particles in consecutive frames which is then used to obtain respectiveparticle properties (velocities and sizes). The final step involves post processing the obtainedproperties corresponding to fluid dynamics using statistical validations.In general, the image obtained from the camera after image processing, represents a set ofcoordinates and their corresponding velocity values at microscopic scales. The goal is thento learn how particles move through space, and quantify their impact dynamics.


2.6 Droplet impact dynamics 11

Figure 2.7: Methodology - PTV Algorithm

2.6 Droplet impact dynamics

Droplet impact on solid and liquid surfaces are key elements [7] in large technical publi-cations such as ink-jet printing, IC engines, plasma spraying etc. It is also of interest innon-engineering fields like agriculture, to prevent soil erosion.A droplet may be spherical or elliptical at the moment of impact. It may impact on a solidsurface [9] with varying roughness, deep liquid pools or thin liquid film on a dry surface. Theimpact may be normal or oblique, in air or vacuum. The liquid considered may be Newtonianor non-Newtonian. The surface of impact may be hot, at a temperature above or belowmelting point of the droplet, or also a cold surface. The fluid flow associated with impingingdroplet onto a surface is complex and involves large number of parameters as shown in figure2.8.

2.6.1 Properties of drop

Following the π theorem, the independent parameters can be deduced by the fundamentaldimensions of droplet that are present. A complete set of non-dimensional numbers can beused to describe various droplet impact dynamics that are shown in figure 2.8 [8] [10].The set of non-dimensional numbers governing droplet impact dynamics in the experimentalanalysis performed in this study are:

We = ρDV 2o

σ , Re = ρDVo

µ , Oh = We0.5

Re


12 Theory

Figure 2.8: Parameters governing impact of droplet [8]

Where,

ρ = Density,µ = Viscosityσ = Surface tensionD = Droplet diameterV0 = Impact velocityWe = Weber numberRe = Reynolds numberOh = Ohnesorge number

Most of the theoretical and numerical calculations are based on the assumption that thedrops are spherical. This is because of the phenomenon of surface tension inside the drop. Inreality the shape of the droplet [8], moving in a fluid will become slightly ellipsoidal due to



aerodynamic forces.The influence of pressure and density of the surrounding environment needs proper attentionin order to understand impact dynamics of the droplets. In experiments by Engel, reduction inpressure resulted in greater impact velocities which further bolster the importance of pressureon quantifying impact dynamics [11]. In the first quantitative approach adopted by Schotland,experiments were performed in de-pressurized chamber which provided substantial proof thatdensity of the fluid influenced impact behaviour [12].In this study, impact dynamics is studied in vacuum. This implies that aerodynamic forcessuch as drag and lift are zero due to non-existent frictional forces in vacuum. Based ontheses conditions, it is convenient to assume that the droplets are spherical when they travelin vacuum because of surface tension inside the droplet[13]. The generated droplets in thisstudy may be non-spherical at launch conditions, but due to absence of forces such as drag,lift or gravity, surface tension dominates, which forces the droplet to be spherical.

2.6.2 Droplet impact on solid surfaces

Droplets impacting on solid surfaces can result in three different behaviours, namely bounc-ing, splashing and spreading as shown in figure 2.9. These are governed by conventionaldimensionless parameters Weber number (We) and Reynolds numbers (Re) [14].

Figure 2.9: Droplet impact on solid surface exhibiting 3 basic phenomena [8].

When a droplet impacts on a solid surface, different outcomes may arise depending on thedynamics of interactions occurring at the liquid-solid interface. For impact onto cold, rigid,and dry surface, the expected behaviours are sticking, spreading or bouncing. Surface bound-ary conditions also alter the physics of the problem but cannot accurately be included in thedimensionless parameters. Their effects are usually roughness and wettability of surface andare accounted by topography of surface. Range and Feuillebois speculate the effects of theseproperties [15]. It is also studied in several practical situations e.g. Shen et al, 2016.Wettability is a thermodynamic property of the interface liquid-vapour meeting a solid surface,defined by the equilibrium contact angle θ , given by Young’s equation :

σlv.cosθ + σls = σsv


14 Theory

Where,

σlv = Interfacial tensions at the boundaries liquid-vapour,σls = Interfacial tensions at the boundaries liquid-solidσsv = Interfacial tensions at the boundaries solid-vapour

For low wetting surface, contact angle varies in range 90◦ < θ < 180◦. Impact behaviourcomprises of four stages: kinematic phase, spreading phase, recoil phase and equilibriumphase [16]. Inertial forces dominate initial kinetic phase [17]. Using energy conservation,energy balance is defined by :

EKi+ ESi

= EKf+ ESf

+ Ediss

Where,

EKi = Initial kinetic energy,ESi = Initial surface energyEKf

= Final kinetic energyESf

= Final surface energyEdiss = Enegy dissipated by viscous forces

2.6.3 Droplet impact on liquid surfaces

Droplets impacting on liquid surfaces have complex and interesting behaviour. The thicknessof the liquid layer is of importance as they influence the scattering or splashing properties. Incase of deep thickness, where the bottom does not affect the impact process, several regimesof splashing are observed [8].The collision of droplet with liquid surface may result in bouncing, splashing, jetting, orcoalescence as shown in figure 2.10 [18][10]. Sometime, after impact, liquid drops floats onsurface e.g. super phobic surfaces, observed by Reynold (1881).

• Bouncing - Upon collision, the droplets bounces from surface. The reflected drop maybe smaller than incident one. Very small Weber and Reynolds number can lead tobouncing of droplets [19].

• Splashing - In case of splashing the liquid surface is distributed evenly. The formationof liquid column that rises out of center of the crater formed upon impact is termedsplashing [18]. Splashing is further divided into jet formation, crown formation andbubble formation.

• Coalescence - The droplet upon impact, quickly disappears into the target liquid.Practically no secondary droplets are produced.

Complex nature of splashing was studied in detail by R.D.Deegan et al (2007). Using thedimensionless numbers (Re and We), the type of splashing can be quantified and predictedusing the figure 2.11.



Figure 2.10: Impact of droplet on liquid surface [8].

Figure 2.11: Phase diagram indicating the quantitatively different regimes of drop impact [20].

2.6.4 Droplet impact on solid surfaces with liquid film

The presence of a liquid film over the solid surface alters the boundary conditions, as theimpact event now involves liquid/liquid interactions depending on the thickness of the film[21]. Using roughness and film thickness, two dimensionless parameters (Rdl and δ) areestablished which help predict the influence of the liquid film on impacting droplets.

Rdl = Ra

D0and δ = h

D0

Where,


16 Theory

Rdl = Dimensionless roughness,D0 = Diameter of dropleth = Thickness of liquid filmRa = Roughness of surface with thin film

The values of Rdl and δ can be used to establish the influence of the liquid film on the impactbehaviour.

• Thin film (3Rdl0.16 < δ < 1.5) : Dependency on surface topology is weak

• Thick film (1.5 < δ < 4) : droplet impact depends on film thickness and not surfacetopology

• Deep pool (δ > 4) : Droplet does not depend on neither surface topology nor filmthickness


Chapter 3

Experimental Description

In this chapter a detailed description of the experimental setup, used to perform PTV for thedroplet impact experiments, is given. All the hardware used and their specific details are alsomentioned. All the experiments were carried out at ASML research Lab at Veldhoven, TheNetherlands.

3.1 Overview of the experimental setup

Ideally to understand the behaviour of droplets in the lithography machines, a similar con-dition or environment must be adopted. The setup used to perform the PTV experiments isshown in figure 3.1. It has the following components and hardware.

• Vacuum Chamber

• Source Chamber - Particle/droplet generation.

• High Speed Complementary Metal Oxide Silicon Camera.

• Target samples and target holder

• Double pulsed PIV Laser

The setup geometry was modified in between to incorporate two types of droplet impactexperiments :

• Normal incidence of impact.

• Grazing incidence of impact.


18 Experimental Description

Figure 3.1: Schematic diagram of the experimental setup

3.2 Vacuum chamber

A vacuum chamber is used to create a similar low pressure environment as inside the lithogra-phy machines. The chamber consists of two regions, the source and the experimental region,separated by a distance of 40 cm as shown in figure 3.1 and 3.2. The source region consistsof an arrangement to generate particle source of fast moving tin droplets. It has a smallaperture opening, through which the droplets fly into the experiment region.

Figure 3.2: Vacuum chamber used in experiments

The experiment region has a small holder at the center facing the aperture. The holder consistsof a heating element, clamps to fix the samples plates and a thermocouple to measure thetemperature of the holder. This region has several glass openings which are used to fix thecamera, focus onto the holder and to illuminate the chamber by passing light through thewindows. The vacuum pump connected to the chamber is capable of reducing the pressureinside the chamber upto 2*10−4 mbar.


3.3 Source region 19

3.3 Source region

Source chamber is the region of the setup where fast moving droplets are produced. It consistsof:

• Tin bath containing tin

• Solid Molybdenum wheel

• High powered Nd-Yag Laser

The tin bath is a metal cup containing sufficient amount of tin as shown in figure 3.3. It isconnected to a heater which is used to heat the bath in order to have molten liquid tin. Thebath is heated and maintained at 300◦C degrees to have sufficient molten liquid tin (Note :Tin has a melting point at 233◦C ).

Figure 3.3: Tin bath with liquid tin

Figure 3.4: Molybdenum wheel coated with tin after exposure in hot tin bath

A solid Mo wheel is made to rotate inside the hot tin bath for sufficiently long duration oftime until it starts wetting the surface as shown in figure 3.4. Since, the experiments areperformed in a very low pressure environment, effect of oxidation on the wetted region of



wheel is neglected. When the wheel is wetted, a nice thin coating of liquid tin is achievedon the wheel. A high powered, pulsed PIV Nd-yag laser is focused on a small spot of thewetted region of the rotating Mo wheel. This generates large amount of debris of particulatedroplets of various sizes and velocities. The Mo wheel is oriented in such a way that thedroplets generated are directed towards the target sample in the adjacent section of the sourcechamber through the aperture. It must be noted that the particle generation is non-uniformand non-continuous. This results in variation in particle flux during running the experiment.For initial set of experiments, droplets impacting at normal incidence to the sample is studied.A 1µm wavelength pulsed laser having an energy of 100 mJ/pulse is used. It is focussed on therotating Mo wheel. For the second stage of experiments, droplet impact at grazing incidenceon sample, a double pulsed Nd-Yag laser with 532 nm wavelength is used. The improvedlaser has an energy of 200 mJ/pulse. Due to the changes in the source, massflux of dropletscaptured in the experiments per µm is higher as more particles were generated with the highpowered laser. The properties of tin (Sn) considered in this thesis work is given in table 3.1.

Table 3.1: Properties of tin used in this thesis work

Properties ValuesDensity 7310 Kg/m3

Kinematic viscosity 1.89 * 10−7

Melting point 233◦C

Frensel coefficient 0.8759Refractive index 1.6 + 4.3iSurface tension 0.54 N/m

3.4 Double pulsed laser - sheet of light

A double pulsed Nd-Yag laser (PIV) is used to produce a sheet of light inside the vacuumchamber wherein droplets impacting the target would be observed as shown in figure 3.5. Itproduces 2 pulses of 532 nm wavelength, which are focused using a combination of sphericaland cylindrical lenses to form a sheet of light with uniform thickness and sufficient length tocapture fast moving droplets. The 2 pulses are separated by a known time interval whichdetermines the time difference between the double frames captured.

3.4.1 Laser sheet modification

The light intensity of the laser beam produced by the Nd-Yag laser has a Gaussian distributionalong its length span. The Gaussian distribution affects the particle size determination. Apart of the light sheet is cut on either side using two black metal plates, allowing only apart of it to be used. The light sheet extracted has an even distribution of light intensitysince the large gradients were removed. It is then focused inside the vacuum chamber via thewindows. The sheet forming optics configuration is fixed for the experiments. The sheet oflight observable by the camera has dimensions 0.05 m × 0.08 m × 0.02 m (length × breadth× thickness).


3.5 sCMOS Camera 21

Figure 3.5: 532nm double pulsed Nd-Yag Laser Hardware [22]

3.5 sCMOS Camera

In this experiment, a single PIV camera is used, as shown in figure 3.6, which would provideinformation of particles in a 2-D plane. The camera used in the PTV experiments has asCMOS sensor that is capable of high speed imaging with a good resolution. The camerais focused on the region of target illuminated by a sheet of light (laser), to capture particlesmoving within the sheet of light. The camera is set to make ’double frame/double exposure’images with each camera trigger synchronized to the flashes of the laser light.

Figure 3.6: sCMOS PIV camera

The properties of the camera and sensor used are specified below:



Table 3.2: Camera Specifications

Type No. of pixels Double shutter Pixel sizeImager sCMOS 2560 x 2160 2 images with 120 ns interframe time 6.5µm × 6.5µm

3.5.1 Time of flight and inter-frame time

Time of flight (TOF) is a parameter, incorporated in the laser pulse trigger timing settings,adopted to capture droplets of various velocities moving towards the sample. TOF is a delayvalue, set to the trigger timing of the first laser pulse as shown in figure 3.7. The value ofTOF is equal to the time taken by droplets to reach the area of laser sheet, from the pointof generation in the source region. The laser sheet is located at a distance approximately 40cm from the Mo wheel. By setting a specific value of TOF, all droplets corresponding to thespecified TOF to reach the target are captured. It enables to capture and group particlesbased on velocities and TOF values. Inter-frame time (dt) is defined as the time intervalbetween 2 consecutive laser pulse flashes. Each pulse is set to fall in respective frames andthereby producing two illuminated images.

Figure 3.7: Camera trigger timing chart - TOF , dt

3.6 Setup geometry

3.6.1 Normal incidence

The focus in the first set of experiments were for droplets impacting at normal incidenceto the sample. The target plate was oriented at 90◦ to the incoming beam of particles. Aschematic diagram of the orientation is shown in the figure 3.8. The incoming droplets travelfrom left to right, whereas the scattered droplets fly from right to left (away from the sample).The region of the laser sheet visible on the camera is indicated as observable region. Anyparticle/droplet flying outside this region were not detected/captured by the camera.


3.6 Setup geometry 23

Figure 3.8: Schematic representation of orientation hardware - Normal Incidence

3.6.2 Grazing incidence

After assessing the results from the normal incidence, the next set of experiments were fordroplets impacting at a grazing incidence to the sample. The schematic orientation is shownin figure 3.9. The target plate was oriented at 15◦ to the incoming beam of particles. Inthis case, the incoming particles travel from left to right and the scattered particles travelis all possible directions, depending on how and where they impact. Particle tracking iscomplex when compared to normal incidence as no particular direction is known regardingthe scattered particles. Due to the restrictions of the vacuum chamber, only one grazingincident angle is possible for the incoming particles. In this study, the angle of incidence wasset to 15◦.

Figure 3.9: Schematic representation of orientation - Grazing Incidence



3.7 Target samples

In order to study the impact dynamics of tin droplets inside the EUV machine, sample plateshaving similar material and properties to that of the walls of the vanes, are used as substrates.Mainly two conditions are observed in the EUV machines, plain vanes and tin coated vanesafter collection of tin debris during the lithography process. Plain molybdenum plate andtin coated molybdenum plate having a dimension of 50 mm x 50 mm were used for theexperiments and are shown in figure 3.10a and 3.10b respectively. Using the heater, impactbehavior on the plate at high temperature was also studied. When the tin coated Mo plate isheated to high temperature (300◦C), above the melting point of tin, the surface of the platebecame liquid.

(a) Molybdenum plate used (b) Tin coated molybdenum plate.

Figure 3.10: Two target samples used in this study.

3.7.1 Thickness of tin deposited on plate

The plate coated with tin, was observed in scanning electron microscope (SEM). The approx-imate thickness of tin deposited is observed by the cross-section images shown in figure 3.11.It was observed that a tin coating of approximate thickness 10µm was deposited onto theplate.

Figure 3.11: SEM image of cross-section of Tin coated plate (50x magnification).


Chapter 4

PTV Measurements and Data analysis

A detailed description of the PTV algorithm used in the experiments and the experimentalprocedure followed is described in this chapter. A complete data analysis scheme from particledetection to data validation is also presented.

4.1 Measurement details

The main goal of the test series was to obtain information on scattering/splashing propertiesof tin droplets for normal and grazing incidence. Table 4.1 shown below describes the typeof plates, orientation and the temperature set in the experiments performed.

Table 4.1: Parameter space for experiments

Material Type Temperature (Celcius) Angle of incidencePlain Molybdenum 22 ◦C 90Plain Molybdenum 300 ◦C 90Molybdenum- coated with tin 22 ◦C 90Molybdenum- coated with tin 300 ◦C 90Plain Molybdenum 22 ◦C 15Plain Molybdenum 300 ◦C 15Molybdenum- coated with tin 22 ◦C 15Molybdenum- coated with tin 300 ◦C 15

4.2 Calibrations

Camera calibration is a very important step in Particle Tracking Velocimetry. All informationand values obtained from the captured images (in pixels) are scaled to actual length values(meters). The scaling factor is the magnification of the lens used to capture the images.


26 PTV Measurements and Data analysis

Magnification is defined as the ratio of height of the image to the height of the object. Thecamera is re-calibrated after successful running of each experiment to avoid errors and bias.

4.2.1 Reference scale

Before the calibration is done, the focal length and the working distance of the lens used iscalculated. This is done by imaging an object and identifying the minimum and maximumfocusing distances of the lens and depth of field. Now, using the focal distance found, anobject of known dimensions is placed in the focal plane. In this experiment a ruler was usedas shown in figure 4.1. An image of the visible region of the ruler was taken in which twopoints were drawn with a known separation. Ratio of the distance between the points (inpixels) to the actual distance in micro-meters determined the magnification (unit: µm/pixel).

Figure 4.1: Caliberation with a ruler

4.3 Procedure for PTV measurements

The following procedure is followed for every test described in table 4.1:

• Laser sheet and camera alignment

• Checking window conditions

• Installing the target

• Setting temperature conditions

• Determining background

• Performing PTV measurements


4.4 Data analysis 27

4.3.1 Laser and camera alignment

The laser sheet and the target holder were held parallel to each other and were aligned asclose as possible in order to optimize particle detection. Precautions were taken to avoidreflection from the holder or target plate which might damage the sensor of the camera. Asuitable beam dump was used to avoid further reflections from the surrounding walls of thevacuum chamber.

4.3.2 Checking window conditions

The windows in vacuum chamber were often contaminated after long test runs. Therefore,window conditions were checked before every experiment to avoid contamination. The win-dows, where the camera was mounted, were cleaned thoroughly in order to have clear images.

4.3.3 Installing target

The required target material of interest was placed on the holder using small clamps. It wasimportant to make sure that the laser sheet does not hit the plate but rather stays just infront of plate to view splashing or bouncing.

4.3.4 Setting temperature conditions

The required temperature of the target plate was set using the heater attached to the holder.Sufficient time was given for the plates to reach the desired temperature. The plates weremonitored continuously with the help of a thermocouple attached to it.

4.3.5 Performing PTV measurements

Initially the Mo wheel was made to rotate in an hot tin bath. The source laser for theparticle generation, was started. The beam of the laser was focussed onto the Mo wheel. Assoon as the beam hits the wheel wetted by tin, particles are generated. These particles flyto the experimental region and were visible through the data acquisition software ’LoGIT’.Using the software, the images were captured for varying time interval (dt) and time of flightvalues(TOF). Sufficient data was acquired by running the system approximately for 1 hour.

4.4 Data analysis

In the experimental setup, particles were generated at time t=0 by the source laser. At t = tAand t = tB, the PIV laser and the double frame camera fire respectively and take images ofthe particle flow field inside the chamber.The matlab analysis script consisted of the following steps:

• Image processing



• Particle detection

• Particle pairing

• Determine velocity, position of impact and time of impact

• Statistical analysis to compute velocity distribution, particle sizing

Extensive information on particle tracking algorithms are available in literature. In the analy-sis considered here, knowledge of particle trajectories were available. Incoming particles weregenerated from the source section while the scattered or splashed particles originate from thetarget plate. The data acquisition software was also tuned to capture images with specifiedTOF values which is used to group incoming and scattering particles. The complete analysisprocedure is described in the following sections.

4.4.1 Image processing

Particle detection was based on thresholding of the image data. Suitable and efficient imageprocessing was adopted to remove image noise and background. The average noise leveldepends on the camera properties.Normally in an experiment, significant noise arises due to varying stray light and laser lightscattered from walls and windows [1]. The High speed sCMOS camera used has uniqueread out unit for each pixel. The readout noise can be quantified by taking large data ofthe background without particle flow. Then, the average image background and standarddeviation for each pixel was obtained. Using this value, a suitable threshold limit was chosenfor the detection. The following steps were followed:

• Images were taken of the flow field without particles (particle source switched off).

• Calculate the average and standard deviation for the images captured to quantify back-ground noise.

• Begin particle generation.

• Eliminate the noise by subtracting background data (average) from every image cap-tured (with particles).

The images obtained were 16-bits with double precision and in gray scale. Due to largeamount of data acquired, the images were converted to 8-bit unsigned images. An array ofclass 8-bit has 256 intensity values with a value of 255 representing complete white while avalue 0 represents complete black on the image. Conversion to 8-bit image was advantageousbecause the program was able to distinguish easily between particle and noise. For effectivedetection and thresholding of the image, band pass filter functions were used.A band-pass filter is a combination of a low pass and a high pass filter which are based onFourier transform. It provides sharp peaks, where the particles were located. The brightestfeature in the image was determined. Using the standard deviation calculated (backgrounddata) and the brightest pixel value, the thresholding was set such that the threshold value



was greater than twice the standard deviation and less than 60 percent of the brightest valuein an image. The value 60 percent was obtained from literature.The threshold determines the smallest particle that can be detected in the image. It wasnot guaranteed that every particle that scattered light above the set threshold was detected.There were some particles flying outside the focal plane of the camera. They were imaged asweak blobs with very low intensity counts. Thus, they were not be picked up by the programas they could fall below the threshold limit.

4.4.2 Particle detection and properties

Particles were detected in the background subtracted images. When a pixel exceeds thethreshold value, it was considered a particle. After clear identification of the particle, positionand intensity were determined as follows:

• Weighed centroid - The location of weighed centroid is possibly the best method todetermine the peak location on the particle. The particle may or may not be spherical.Thus, using weighed centroid corrects for this condition. The output from the weighedcentroid calculation gives a string with the x and y coordinate of the particle centroid.

• Dialation - After background subtraction and thresholding, some area around theparticle is removed, keeping only the peak as shown in figure 4.2. This results in loss ofcounts in the total intensity which may give errors in sizing. The area of each particlewas expanded by 1 pixel in the neighboring region of the peak as shown in figure 4.3.Expanding the particle by a radius of 1 pixel was done using structuring element (strel)fucntion present in MATLAB.

Figure 4.2: Example of particle in image. It occupies 9 pixels, with peak at the center.

Figure 4.3: left : Shows particle after applying the threshold cut-off, with a thresholding of 0.5.Only the peak is maintained and rest all are set to zero. Right: shows the effect of ’strel’ function.Expands by 1 pixel in neighborhood of peak.



• Area of particle - The area occupied by the particle in the image (in pixels) wasobtained for each frame.

• Intensity counts - Intensity counts give the light intensity values for a particle foundon the image. To analyze the particle size, it was necessary to have the total intensitycounts on the particle.

Total intensity = Mean intensity of particle × Area occupied by the particle

• Eccentricity - Eccentricity is a parameter associated with every conic section. It isa measure of how much the conic section deviates from being a circle. A circle hasan eccentricity of zero. The eccentricity of every particle was also calculated. Thisinformation was used for statistics and comparing particle sizes.

The end result of particle detection is a list with particle index, x and y coordinates, area,intensity and eccentricity.

4.4.3 Particle pairing

Particle pairing is the most important and complex part in particle tracking. The high speedsCMOS makes two quick snapshots of the flow of particles. The particles in frame A must belinked to the same particle in frame B, if present in both frames.The interframe time (dt) and the time of flight (TOF) were varied while acquiring datathrough the high speed sCMOS camera. This enabled to capture particles with variousvelocities. Figure 4.4 shows an example of particles in frame A and B.

Figure 4.4: An example of particles in frame A and in Frame B. It results in 6 different possiblepairs.

The particle pairing consists of the following steps: nearest neighbour method, intensity ratioand area ratio.



Nearest neighbour methodNearest neighbor also known as proximity search is an optimization for finding the closestpair. This method was adopted to define a maximum distance a particle could travel in agiven pair of image.

di =√

(x1(i)− x1)2 + (y1(i)− y1)2

Figure 4.5: Example of particles in Frame A. Distances between particle A1-A2 d1 and A1-A3d2, respectively. Minimum distance, calculated from distance formula is d1.

From the figure 4.5, it can be seen that the minimum distance is d1. Using this value, themaximum distance a particle was allowed to travel was 50 percent of the minimum distancebetween its closest neighbour.

maximum distance = 0.5× d1

This criteria was checked for every particle found in the images.Intensity ratioParticles found in frame A and frame B are always present inside the sheet of light. If theparticle found in frame A are the same in frame B, it is assumed that they must scattersimilar light counts as they will be of similar size. Intensity ratio, between frame A and frameB, with values between 0.8 - 1.2, were chosen to be matching criteria. Figure 4.6 shows theintensity signal matching criteria. Ratio values close to 1 are found to be best pair.Area ratioFrom the assumption that the particle does not change shape between the two frames sepa-rated by a small inter frame time, the area occupied by particle must also be similar. Thearea ratio of particle, frame A to value in frame B, must be centered around 1. Hence a valuebetween 0.8 - 1.2 was chosen to be right match for particle coupling.



Figure 4.6: Figure shows intensity signal matching in frame A and Frame B as found in theexperiments. Values centered around 1 were best match for the experiments.

4.4.4 Choose best pairing configuration

The particle pairing procedure consists of two steps:

• Remove pairs with distance larger than set cut off.

• Scan all permutations to obtain best pair.

In the scattering experiments, the maximum particle velocity (Vmax) was given by the distanceL from the particle source to the sheet and the time of first flash of the PIV laser ta.

Vmax = L/ta

Therefore, the maximum possible distance (dmax) is given by,

dmax = (dt).L/ta

Particles separated by more than this distance cannot be pairs. Scanning all permutationswas numerically tedious. If an image pair has 10 particles in each frame, it gives 3.106

combinations. Using maximum distance value, as described above, particle pairs exceedingthe maximum distance are removed.An example of choosing the best pair is described in following sections. Figure 4.7 showsparticles in frame A and in frame B. Using the pairing criteria described earlier, the bestpossible pairing is obtained. Figure 4.8 shows the nearest neighbor search for every particlein frame A. Here the minimum distance to its closest neighbor is calculated. The nextstep involved determining the location of the couple particle in frame B, which can only beseparated by the maximum distance (50 % of distance from the nearest neighbor)



Figure 4.9 and 4.10 describes particle pairing based on intensity ratios and area ratios for thegiven example. The green boxes indicate best matching of particles. Particle pair satisfyingall three conditions were only allowed to exist as effective pairs.The result of particle pairing is a list with paired particles and their respective properties anda list with unpaired particles which helps identify the total number of particle arriving andleaving the target plate.

Figure 4.7: left: shows example of particles moving in space in Frame A. right: shows exampleof particles found in frame B. From the particles seen, 6 different pairs are possible.

Figure 4.8: Distances to the neighbor particles. Considering particle A1 ,d11 and d12 are thedistances to its neighbor. The minimum distance is indicated by the green box. The pair forparticle A1 in frame B cannot be located further than this distance , max.distance = 0.5 ∗ d11



Figure 4.9: Example of intensity matching based on the counts in frame A and Frame B. Thegreen box indicate best matching pairs. Ratio values between 0.8 - 1.2 are chosen as the matchingcriteria.

Figure 4.10: Area matching for all possible combinations for given example. Area ratio between0.8 - 1.2 are found as good match criteria. Green boxes indicate best matching ratio values andcorresponding best pairs. Particle A1 - B2 are a good pair and particle A2-B1 are a good pair.

4.4.5 Determine velocity

When the particle pairs are found, their velocity can simply be computed by:

V = B − Atb − ta

Where,

B =[xbyb

],Coordinates of particle position in frame B,

A =[xaya

],Coordinates of particle position in frame A,

tb − ta = Interframe time interval.



4.4.6 Determine impact time and position

For the analysis, particle impact position and time of impact on the target plate are important.From the images captured, the position of the target plate is specified on the images by theuser, which is constant for a set of experiments. From the direction and velocity of the particlepairs, the impact time and position of impact on the plate are calculated. Figure 4.11 showsthe schematics of the extrapolation procedure used to find the impact position and time.Using the method of line intersect, the point of impact on target plate is obtained. This isbased on assumption that, the particle travels a straight line between the position found onimages and the intersecting point on sample. This assumption was later checked by plottinga density graph of the incoming particle beam towards the sample.

Figure 4.11: Interpolation procedure for example pairs A1 - B1, going towards the sample andA2 - B2, flying away from sample. From the direction vectors, we can compute the angle betweenthem.

4.4.7 Statistical analysis

The goal of the scattering experiments was to determine the particle scattering properties of asurface for a range of incoming velocities and sizes. Scattering properties include percentage ofparticles stuck and scattered from the surface, the angular distribution of scattered particlesand potentially size comparison for incoming and scattered particles to understand break-upof particles.The particle source used in the experiments generate particles with a range of velocities andsizes. By selecting the time of flight (TOF), a limited velocity range of incoming particles wasselected. By comparing the incident and scattered particles within the same time interval,conclusions are drawn on the scattering properties of the surface. Particles are captured by



the camera only when they are present in the sheet. It is observed that, for a finite dimensionsof the sheet of light, only a part of incoming and scattered particles are captured.

Figure 4.12: Position x versus time t for PTV measurement. The red lines indicate time intervaland the blue line indicates position for a particles traveling at velocity Va and Vb.The shaded arearepresents the space for a time interval ptvdt1 and ptvdt2

It is clearly seen from figure 4.12, particles with a low velocity (Va) stay inside the sheetduring both flashes. Particles with higher velocity (Vb), will leave the sheet of light before thesecond flash of the laser. Thus, they escape the sheet and are not captured. The result of theanalysis then gives only the density of particles present inside the sheet at any given time.Slower particles reside inside the sheet for longer duration than fast moving particles. Theanalysis then pick up lots of scattered particles as they have lower velocity than the incomingparticles. In order to have an unbiased detection, particles are grouped using the TOF valuesof the images captured. For a TOF of 4 ms, incident particles hit the sample plate at 4.2 ms.All incident particle velocities are integrated between 4 ms and 4.5 ms TOF values, givingan average incident velocity of 100 m/s. All scattered particles that are captured betweenTOF values of 3.5 ms to 4.5 ms are selected. The impact time and position on the sampleplate for the scattered particles are extrapolated. Scattered particles with an impact time onthe plate between 3.5 ms - 4.5 ms are grouped together. Integrating the velocity distributionfor the scattered particles results in an average scatter velocity of 20 m/s. From the velocitydistribution obtained for the two groups, it is easier to calculate the mass flux of particles seenin the analysis. Mass flux through the finite observable region of the sheet (2D) is considered.It is defined as the rate of mass flow per unit area. Using vector definition, mass flux is equalto:

φm =∫ xmax

xmin

∫ l

0

∫ Vb

Va

ρ ∗ Vt.dV.dA



Where ρ is given by:

n∑i=0

t=t2∑t=t1

ρ

Where,

xmin − xmax = Dimensions of the sheet along x-axis,l = Length of sample,ρ = Number of particles,

t1 − t2 = Time of flight values (TOF) selected using script (ms),Va, Vb = Velocity groups,

n = Number of particles.

The filter criteria counts all detected particle within the specified TOF limit.

Defining the target area in 1D

From the captured images, the target plate is a 1D object. The position of the target plateis obtained from the raw images. The position is described as a linear target :

xt(l) = xt,0 + r.l

with xt,0 one end of line, r a unit length vector along line and l length of line.

Angular distribution

From the captured images, the coordinates of the target plate was easily identified by thealgorithm. Using line equation, the angle between the trajectory vector of particle and theline vector of the position of sample plate is calculated as shown in figure 4.13.

Figure 4.13: Angular distribution calculated from the position of sample plate and the locationof particles w.r.t the plate.



4.4.8 Analysis schemes for normal and grazing incidence

Normal incidence - scheme

For the normal incidence experiments, it is easier to differentiate between incoming and scat-tered particles by the their trajectories or direction. Any particle travelling away from sampleis considered as scattered particle 4.14. For normal incidence, the x-axis definition is usedto identify incoming and scattered particles. Particles travelling in positive x direction areincoming whereas, those travelling in negative x direction are scattered particles respectively.

Figure 4.14: Particle trajectories for normal incidence.

Grazing incidence - scheme

For grazing incidence, scattered particles travel in all possible direction from the sample asshown in figure 4.15a. Let us consider particle pair A1-B1. For the particle pair A1 - B1, thedistance of particle from the point of impact in frame A and frame B is given by d1.1 andd2.1 respectively as shown in figure 4.15b. If d1.1 − d2.1 > 0 , it is an incoming particle. Ifd1.1 − d2.1 < 0, then the particle is a scattered particle.

(a) Grazing incidence. (b) Grazing incidence.

Figure 4.15: Distance of impact position from position in frame A and Frame B, denoted by d1and d2.


Chapter 5

Preliminary Tests

Before the start of PTV experiments on the samples, it was necessary to characterize theparticle source used in the experiments. PTV measurements in the absence of target plateswere performed to study the particles being generated.

5.1 Particle source characterization

The particles produced by the pulsed source had a wide range of sizes and velocities. Sufficientdata of particle flow in the chamber was captured in the absence of the target plate, meaningthat there are no scattered particles. The TOF values and the inter-frame time interval dtwere varied in order to observe wide range of velocities. The TOF values were varied from 3ms to 6 ms and the dt values from 6µm to 15µm.

Figure 5.1: Graphs obtained for TOF vs velocity. Different TOF values were selected to capturedifferent velocity of particles.

Figures 5.1 shows the velocity distribution of particles produced by the source in the present


40 Preliminary Tests

experiments. For a range of TOF values, peaks of incoming velocities with respect to itscorresponding TOF value were identified as shown in figure 5.1. It can be seen that a velocityrange from 60− 140m/s were recorded. By selecting the TOF value, the observable particlevelocity can be fixed. Images were captured with varying inter-frame time (dt) also. It wasobserved that, the displacement of the particle varied between the two frames but the obtainedvelocity distribution remained the same for a fixed TOF. From the figure5.1, it can be seenthat for a TOF value of 3 ms, particles with velocity around 130 m/s and for a TOF valueof 4 ms, particle velocity of 100m/s are observed and captured by the sCMOS. In the actualexperiments, high speed particle are of interest. For the first set of experiments involvingnormal incidence, incoming particles were filtered between 3.5 ms - 4.5 ms, and for the secondset of experiments involving grazing incidence, incoming particles were filtered between 2.5ms - 3.5 ms.

Figure 5.2: Size distribution based on Intensity counts for incoming particles.

Initially, to quantify the size of the particles, method of diffraction limited imaging [4] wasused. However this method was found to be unsuitable because of large diffraction limitof 30µm present in the lens and windows of the vacuum chamber. This means that smallparticles show up as diffraction limited spot with a size of 30µm.Size distribution was then calculated based on the scattered intensity counts from the particle,as described in theory section. Based on the theory of geometric scattering, the scatteredintensity from a particle scales with the diameter square. Using this method, the diameterswere compared between the incoming and scattered particles. The information obtained,shown in figure 5.2, describes the scattered intensity pattern for incoming particle sizes.Effect of numerical aperture was also included in determining the scattering intensity/cross-sections for incoming particles. This information was used in the experiments to comparethe scattered intensity of the scattered particle from the target plate. This would thenprovide a quantitative size comparison between the particles. From the size comparison itwas analysed whether the incoming particle breakup upon impact (smaller than incomingparticles). Accurate sizing was not possible due to optic constraints.


5.1 Particle source characterization 41

5.1.1 SEM analysis of Particles

Since the size analysis had to further refined to explain the behaviour of particles, a SEManalysis was performed on the captured particles. To get an idea of the the sizes of particleproduced, clean silicon wafer plates were placed on the holder. The use of these wafer plateswere to capture the particles flying towards it. After sufficient exposure to the particle beam,the wafers were observed under a scanning electron microscope and the size of the particlestuck on the wafer were determined.

Figure 5.3: SEM images of particle spread out and stuck on wafer

Figure 5.4: Droplet morphology as observed by SEM on the wafer

Figure 5.3, 5.4 show images of droplets captured on the wafer plate. It can be seen that amaximum diameter of 10µm and a minimum of 750 nm was observed as shown in figure 5.5.It must be noted that the droplet seen in the images were only the ones that were stuck onwafer and spread out. Some particles may not stick to the surface and may bounce off. Thus,the above distribution only provides information on the probable particle sizes that couldoccur in the system. Using theses size ranges, the necessary scattering theory is selected.From the distribution obtained above geometric scattering theory was found suitable withparticle sizes (10µm to 750 nm) larger than the incident laser light (532 nm).



Figure 5.5: Size distribution from SEM analysis

5.2 Heat transfer from droplets

Initially the state of the particles during impact were unknown and required further clarifica-tion. The particles could be solid spheres or liquid droplets, flying towards the sample/targetplate. Hence, heat transfer from the particle to the surrounding atmosphere and to the targetplate upon impact was studied to identify the state of particle during impact. It must benoted that only radiation mode of heat transfer exists in vacuum.

5.2.1 Heat transfer to surrounding atmosphere

The atmosphere inside the chamber was a very low pressure of 2*10−4 mbar, thus radiationwas found to be the only possible mode of heat transfer. Newton’s radiative cooling equationswere solved for the droplets to calculate the freezing time.The Newton’s cooling equation used is given below:

t =[

ρ.V.Cp4.A.ε.σ.T 3

0

] lnT 2

0 − T 2f

T 20 − T 2

i

+ 2(arctan

TfT0− arctanTi

T0

)Avinash Suresh Kumar CONFIDENTIAL Master of Science Thesis

5.2 Heat transfer from droplets 43

Where,

ρ = Density,ε = Emissivity of tin,V = Volume of droplet,A = Area of droplet,Cp = Specific heat of tin,σ = Boltzmann’s constantT0 = Temperature of environment,Ti = Initial temperature of droplet,Tf = Final temperature of droplet,t = Time taken to cool (seconds)

Table 5.1: Assumptions considered for calculation of radiative cooling using properties of liquidtin

Density(kg/m3) T0 Ti Tf σ Specific heat (Cp)7310 20 ◦C 300◦C 233◦C 5.67*10−8 0.21 KJ/Kg.k

Figure 5.6: Solidification time vs diameter of droplet. The solidification time (>5 ms) is largerthan impact time (3.5 ms).



Figure 5.6 shows the cooling time as a function of diameter of particle. Table 5.1 showsassumptions considered in solving radiative cooling equation. The initial temperature of thedroplet was assumed to be equal to the temperature of the tin bath and Mo wheel, usedto generate the droplets as described in the theory section. The tin bath was maintainedat 300◦C during the experiments. The temperature of the environment, T0 was assumedto be equal to the room temperature approximately 20◦C. It can be seen that for dropletssizes greater than 1µm in diameter, the solidification time was higher than the time of flightto the target plate. Droplets travelling at 130m/s reach the sample at 3.5ms. Hence, itwas concluded that the particles recorded were indeed droplets. This was also verified andaccepted from the SEM images shown above.

5.2.2 Solidifying upon impact on the plate

Heat transfer to the target plate upon impact was studied. Since the contact time for theparticle with the target plate was very short, time scales of heat transfer were observed.Characteristic time scale for heat transfer is defined as:

τh = R2

α

Where,

τh = Characteristic time scale for heat transfer,R = Radius of particle,α = Thermal diffusivity.

The contact time τc, defined as the time for which the particle rests on the sample, must belarger than the time scale for heat transfer for solidification. The impact of droplet on targetplate is mainly inertial. τc is a function of only R, v, ρ and λ [23]. The contact time τc then ispropotional to the maximum deformation of droplet on impact δ and inversely to the velocityV of droplet.

τc ∝ δV

δ = R.ρ2.V 2

E2

Where,

τc = Time for which the particle rests on the sample,δ = Maximum deformation of droplet,V = Velocity of droplet.E = Youngs modulus


5.2 Heat transfer from droplets 45

Using the above equation, it was found that the contact time τc varies as V −1/5 and R7/5

[23]. Figure 5.7 shows that the time scale of heat transfer is much higher than the contacttime, hence it is concluded that the droplets do not lose temperature by conduction with thetarget plate.

Figure 5.7: Time scale for heat transfer vs Contact time on sample.


Chapter 6

Results and discussion

This sections presents the results obtained from all the experiments followed by discussion onthe extracted results.

6.1 Validation

The analysis procedure was validated by performing measurements on the tin droplets. Allthe graphs presented in the following sections follow the schematic configuration as shown infigure 6.1a for normal and figure 6.1b for grazing incidence.

(a)(b)

Figure 6.1: left : Schematic for normal incidence on target plate, right: Schematic for grazingincidence on target plate.

For first set of experiments, cold plain molybdenum plate was installed, and the PTV algo-rithm was validated. Since the tin particles are emitted continuously from the source, thePTV algorithm effectively measured the particle density. Density plots were plotted by takingthe sum of complete set of images from an experiment. A Gaussian low pass filter was usedto smoothen the image and produce a contour plot of the particle flow. A uniform density


6.1 Validation 47

plot was obtained as shown in figure 6.2. By reading the density plots, the region of interest(ROI) was selected manually. Figure 6.2 shows the ROI chosen to speed up the computationprocess. ROI must be chosen in such a way that it captures maximum incoming and scatteredparticles without losing information. Using the raw density images, the sample plate positionwas also defined as described in the data analysis section. The sample position are indicatedas red lines on the figures 6.3. After defining the sample position and ROI, the algorithmthen easily differentiates incoming and scattered particles. Figure 6.3 and 6.4 show incomingand scattered beam for normal and grazing incidence respectively.

Figure 6.2: left : density plots for Normal incidence, right: density plots for grazing incidence

Figure 6.3: Normal Incidence - left : density plots incoming beam, right: density plot scatteredbeam

From the figures, it can be seen that the incoming particle beam is narrow with a diameter of179 pixels. From the camera calibration and magnification, 1 pixel is equal to 35µm. Thus wehave a beam diameter of 6.5 mm approximately. The scattering particles have a wide angulardistribution in both cases, normal and grazing incidence of impact. The particle source usedin the experiments generate particles with a varying flux rate as mentioned earlier. Someparticle also fly out of the focal plane after scattering from the target plate. Theses particlesare not captured or imaged by the camera. Hence, the density plots obtained above for theincoming and scattered beam have weak diffracted limited spots.


48 Results and discussion

Figure 6.4: Grazing incidence - left : density plots incoming beam, right: density plot scatteredbeam

6.1.1 Uncorrected scattered data

After effectively choosing ROI and sample position, the velocity distribution was calculatedfor a set of data captured for impact on plain cold Mo plate at normal incidence. To applythe statistical corrections, a fixed TOF was chosen. For the normal incidence experiments,the source produced slower particles than in case of grazing incidence. Thus, a TOF of 4ms was fixed for normal incidence experiments. At this value of TOF, sufficient flux of fastparticles were achieved.The algorithm then measures incident particles with a TOF of 4 ms, travelling with a velocityof 100m/s. At this fixed TOF, incident particles hit the sample at t = 4.2ms and scatterparticles leave the sample at t = 3.5ms. The algorithm then extrapolates and calculates theimpact time and position of the scattered particles on the target plate. Scattered particleswith impact time between t = 3.5ms to t = 4.5ms are chosen and grouped together. Byintegrating the velocity distribution of both groups, it is found that about 3× more particlesare scattered from the surface as shown in figure 6.5a. This shows a scattering percentage of300%. The average incoming velocity is 100m/s and average scatter velocity is around 20m/s.The discrepancy in the high scattering percentage was initially thought to be due to break upof incident particles. However, after calculating the mass flux of the incoming and scatteredparticles, the scattering percentage significantly changes as shown in figure 6.5b. The totalparticle flux observed was then calculated from the area under the curves in figure 6.5b. Allparticles that arrived on sample between 3.5ms - 4.5ms time interval are considered and thevelocity distribution is obtained for the specified time interval. It was then observed that thescattering % reduced to about 40%. In a similar manner, for experiments involving grazingincidence, a TOF of 3 ms was fixed. The algorithm then captured particles with velocities of130 m/s. Particles were filtered betweem 2.5 ms - 3.5 ms time interval.

6.2 Results

This section provides the complete set of results obtained from the experiments. Impact atnormal incidence on target is presented first followed by grazing incidence on target plates.


6.2 Results 49

(a) (b)

Figure 6.5: left : uncorrected velocity for fixed Tof of 3ms, right: Corrected velocity for the fixedTof

All data were acquired by running the experiments for approximately 1 hour. About 200gbof data was captured for each run which was then analysed through the PTV algorithm.

6.2.1 Cold clean Molybdenum plate - Normal Incidence

From the data acquired, the density plots of incoming and scattered particles were observed.Figures 6.6 shows density plots of incoming and scattered particle to and from the samplerespectively. After running the PTV script, data set with linked particles, their positions,velocities, intensity counts and angular orientation from plate was extracted. Particles werethen filtered by their arrival time in order to effectively measure incoming and scatteredparticles within the same time interval. Statistics was then improved on the filtered data.

Figure 6.6: left : density plots for incoming beam, right: density plot for scattered beam

Figure 6.7 shows velocity vs mass flux graph obtained for particles impact on plain cold Moplate. It can be seen that the percentage of scattered particle flux was detected to be around35% of the incident particle flux. The average incoming velocity was around 100m/s and theaverage scatter velocity was reduced by 75% to 25m/s.The angular distribution for the scattered particles are shown in figure 6.8a. The scattering



Figure 6.7: Velocity distribution

(a) (b)

Figure 6.8: left : Angular distribution, right: Size distribution based on scattered intensity

particles have a wide angular distribution between 50◦-130◦ degrees, showing scattering angleof 80◦, whereas the incoming beam is strictly incident at 90◦ degrees. It was expected thatthose particles that scatter over large out-of-plane angles will leave the sheet and not showup in the algorithm. The size distribution was then observed for the incoming and scatteredparticles. Figure 6.8b shows size distribution of incoming and scattered particles based onscattered light intensities, plotted on each other. It was noticed that the distribution patternwas very much similar, that is the size of incoming and scattered particles were of the sameorder. From the histogram graph it was concluded that the particles do not break up as theyretain their size after impact.

Table 6.1: Summary of results for Cold clean Molybdenum plate - Normal Incidence

Incoming Velocity Scatter velocity Angle of incidence Scatter angle % of Scatter100m/s 25m/s 90◦ 80◦ 35 %


6.2 Results 51

Figure 6.9: left : density plots incoming beam, right: density plot scattered particles

6.2.2 Hot clean Molybdenum plate - Normal Incidence

To test the effect of temperature on the target plate, the plain Mo plate was heated to 300◦

C, very much above the melting point of tin (Sn). Figures 6.9 show density plots obtainedfrom this experiment. In a similar manner, the ROI was chosen and sample plate was defined.Particles were grouped based on TOF values as discussed in the previous result.


Figure 6.10 shows velocity distribution extracted from the data. It was observed that thescatter particle flux percentage did not significantly change due to the high temperature ofthe plate. The average incoming velocity was around 100m/s and the average scatter velocitywas found to be around 30m/s. The scatter particle flux was reduced to 25% of the incomingflux. The angular distribution, shown in figure 6.11a, was found to be a narrow distributionbetween 70◦-130◦ degrees for the scattered particles. It was observed that the scattering anglewas reduced for impact on hot plates. The size distribution of scatter particles were comparedto the distribution of incoming particles, as shown in figure 6.11b. The scatter distributionpattern match with the incoming particles distribution, hence, no break was recorded.

Table 6.2: Summary of results for Hot clean Molybdenum plate - Normal Incidence




(a) (b)


6.2.3 Cold Tin coated Molybdenum plate - Normal Incidence


To test the effect of surface property, tin coated molybdenum plates were used. Density mapsobtained for these experiments are shown in figure 6.12. Particle grouping was similar toprevious experiments.Figure 6.13 shows velocity distribution obtained from this experiment. It was observed that30% of incoming particle scatters back from the sample plate. The average incoming velocitywas at 100m/s and the average scatter velocity was found to be around 35m/s. Size validationwas done by comparing scatter light intensity counts of incident and scattered particles.Figure 6.14b shows that particles retain size after impact. No break up was recorded fromthis experiment. The angular distribution, shown in figure 6.14a pointed out that for incomingparticles at 90◦, scattering angle was between 50◦-120◦ degrees. It was observed that the wideangular distribution was due to impact on cold surface.

Table 6.3: Summary of results for Cold Tin coated Molybdenum plate - Normal Incidence



6.2 Results 53


(a)(b)


6.2.4 Hot Tin coated Molybdenum plate - Normal Incidence

The tin plates used in the previous experiment was heated to 300◦C. The experiment wasperformed after the desired temperature was reached, such that the surface of the plate hadliquid property due to molten tin (Sn).Figures 6.15 show density plots obtained for the experiments. An interesting point is tonote that the density for scattered particles are much lower. The velocity distribution wascalculated as shown in figure 6.16. The incoming velocity was at average of 100m/s and theaverage scatter velocity is reduced to 5m/s.The size and angular distribution for the incoming and scatter particles are given in figure6.17. It was observed that the scatter particle flux was very much lower than other impactconditions. Due to low scatter particles observed, the statistics to check the angular distri-bution was quite low. The incoming beam was incident at 90◦ and the scatter angles werearound 80◦ - 110◦ approximately. The size distribution, figure 6.17b, shows that the scatterparticles are of similar sizes than the incoming particles. The average scatter velocity was





(a) (b)


reduced to 5m/s, and the % of scatter flux was found to be around 10% of incoming particleflux. High probability of sticking was recorded for impact on hot Sn coated Mo plates.


6.2 Results 55

Table 6.4: Summary of results for Hot Tin coated Molybdenum plate - Normal Incidence


6.2.5 Cold Molybdenum plate - Grazing Incidence

The next set of experiments were performed for grazing incidence of impact on the targetplates. The experiment setup was modified for theses experiments as described in chapter 3.It must be noted that the particle source was also modified to improve particle flux observed,as discussed in the experimental description section. As a result, higher velocities of incidentparticles were observed. The schematic for grazing incidence is given in figure 6.1.



The plain cold Mo plate was fixed on the holder at 15◦ degrees to the incoming particlebeam. The statical analysis follows the same procedure as the previous experiments involvingnormal incidence. Since higher velocities were observed, the TOF was chosen as 3 ms. Thissetting captured particles with a velocity of 130 m/s, travelling towards the sample plate.Particles were filtered by their arrival time and only an interval between 3ms and 3.5mswas considered. The density plot obtained for incoming and scatter particles are shown infigures 6.18. The velocity distribution, calculated for the incoming and scattered particlesis shown in figure 6.19. It can be seen that the average incident velocity is around 130m/s



and the scatter velocity had a wide distribution between 20−80m/s, with an average around60m/s. The angular distribution is shown in figure 6.20a. Incoming particles are incident at

(a) (b)

(c)

Figure 6.20: left : Angular distribution, right: Average scatter velocity vs angle, bottom: Sizedistribution based on scattered intensity

an angle of 15◦ degrees and the scatter particles have a wider distribution between 80◦−130◦.Figure 6.20b shows scatter velocity plotted vs scatter angles. It was observed that there wasno strict relation between scatter angles and scatter velocities. Size distribution based onscattered light intensities for the particles are shown in figure 6.20c. It was noted that thesize distribution pattern for incoming and scattered were near identical. Thus, no break-upof particles were reported.

Table 6.5: Summary of results for Cold Molybdenum plate - Grazing Incidence


6.2.6 Hot Molybdenum plate - Grazing Incidence

The Mo plate was heated to 300◦C and the experiments were repeated for particles incident at15◦. The figure 6.21 shows density plots obtained from the experiment. The scatter particledensity was observed to be identical as in the cold impact condition. Figure 6.22 showsvelocity distribution. The incident particles have an average incoming velocity of 130m/sand the scatter velocity is reduced to 40m/s. Slower scatter velocities were also observed


6.2 Results 57


within the same time interval of 2.5 ms - 3.5 ms. The scatter particle flux was equal to 85%of incoming particle flux.


Figure 6.23 shows size distribution and angular distribution of the observed particles. Theincoming particles impact at 15◦ and the scatter particles have a wide distribution between90◦ − 130◦. Figure 6.23b shows velocity as a function of scatter angles. It can be seen thatthere is no dependency of angle and velocity. Size distribution based on scattered intensitieswere also observed as shown in figure 6.23c. It was noted that the distribution was identicalfor incoming and scattered particles. The identical distributions showed no variation in sizes.

Table 6.6: Summary of results for Hot Molybdenum plate - Grazing Incidence


6.2.7 Cold Tin coated Molybdenum plate - Grazing Incidence

Experiments were performed on Cold Tin coated Molybdenum plates as described in chapter3. The same impact angle of 15◦ was set and the following results were observed. Figure6.24 shows density plots obtained for incoming and scattered particles, with the position of



(a) (b)

(c)



the sample plate. The velocity distribution was calculated and is shown in figure 6.25. Itwas observed that the incoming particles had an average velocity of 130m/s and the averagescatter velocity was reduced to 80m/s. The % of scatter particle flux is equal to 90% of theincoming particle flux.The angular and size distribution were evaluated from the data acquired. Figure 6.26a showsangular distribution and size distribution for the incoming and the scattered particles. Theincoming beam was well defined at 15◦ and the scatter angles were between 80◦ − 130◦. Thescattering angles do not show any relation with scattering velocity as shown in figure 6.26b.The size distribution based on scattered intensities, shown in figure 6.26c, convey identical


6.2 Results 59


(a) (b)

(c)


distribution patterns. It was concluded that particle break up were unlikely to happen.

Table 6.7: Summary of results for Cold Tin coated Molybdenum plate - Grazing Incidence




6.2.8 Hot Tin coated Molybdenum plate - Grazing Incidence



The Sn coated Mo plate was heated to 300◦C and the experiments were carried out. Theplate was oriented at 15◦ to the incoming particle beam. The density plots are shown infigures 6.27. It was noted that, the scatter density dropped when compared to the previousexperiments. The velocity distribution is given in the figure 6.28. The average incomingvelocity was 130m/s and the average scatter velocity was reduced to 40m/s. The scatterparticle flux was reduced to 30% of the incoming flux. The angular distribution and sizedistribution were calculated. It can be seen in figure 6.29a, the scatter angle is 20◦ between110◦ - 130◦ for incoming beam at 15◦. The scattering angle is lower than in other grazingimpact experiments. The size distribution, evaluated with scattered light intensity, is shownin figure 6.29c. Identical distribution pattern was observed with very low scatter counts. Itwas concluded that most particles stick to the wet surface leading to low scattering probabilitythan other grazing experiments.

Table 6.8: Summary of results for Hot Tin coated Molybdenum plate - Grazing Incidence



6.3 Discussion 61

(a) (b)

(c)


6.3 Discussion

Two important aspects were studied namely, normal incidence of impact and grazing incidenceof impact of Sn particle on target plates with different surface topology and thermal properties.From the results obtained above, various conclusions were drawn on the behaviour of particleupon impact.Table 6.9 shows summary of all the results. Discussion is separated into two sections, normaland grazing incidence.

Table 6.9: Summary of the results obtained in the experiments

Type of sample Impact angle Vin Scatter angle Vsct Scatter %Cold plain Mo 90◦ 100m/s 80◦ 25m/s 35%

Hot plain Mo 90◦ 100m/s 60◦ 20m/s 25%Cold Sn coat Mo 90◦ 100m/s 70◦ 20m/s 30 %Hot Sn coat Mo 90◦ 100m/s 30◦ 5m/s 10%Cold plain Mo 15◦ 130m/s 50◦ 60m/s 90%Hot plain Mo 15◦ 130m/s 40◦ 40m/s 85%Cold Sn coat Mo 15◦ 130m/s 40◦ 60m/s 95%Hot Sn coat Mo 15◦ 130m/s 20◦ 40m/s 30%



6.3.1 Normal incidence - Impact on solid surface

Experiments performed with Cold plain Mo, Hot plain Mo and Cold Sn coated Mo wereconsidered as solid surfaces. The scatter percentage from the samples were 25%, 20%, 25%respectively. It was observed that the incoming Sn droplet losses approximately 75% of itsincident velocity upon impact with Cold plain Mo and Sn coated Mo and 80% upon impacton Hot plain Mo at 300◦C. The size distribution showed that the incoming and scatteredparticle were of the same size, that is break up droplet did not occur. To understand thescattering of droplets, the energy conservation was solved as described in the theory section.The equation used is given below :

EKi + ESi = EKf + ESf + Ediss

EK = (ρ.U2.π.D3)12

ES = π.D2.σ

Where,

Eki = Impact kinetic energy,Ekf = final kinetic energy,σ = Surface tension,U = Impact velocity m/s,

Ediss = Energy dissipated,V = Final velocity m/s.

The viscous dissipation is [24] given by

Ediss ∼ Eki × Ekf × tc

Where,

Eki = Impact kinetic energy,Ekf = final kinetic energy,tc = Contact time of droplet on target plate.

It was observed that the viscous dissipation was much smaller at low contact times. The finalkinetic energy Ekf is found to be 25% of impact kinetic energy EKi. The loss in energy isdue to viscous dissipation of droplet upon impact.The sizes of the incoming and scattered droplets were extracted from the results of SEManalysis. Using the equations above, the energy dissipated was found, which pointed outthe loss in velocity upon impact was acceptable. The size distribution shows no break up ofdroplets, which meant that the droplets bounce upon impact. The We and Re values used


6.3 Discussion 63

Table 6.10: Weber’s and Reynolds numbers found in experiments

Weber’s Number 130 - 550Reynolds number 700 - 1150

in this study are shown in table 6.10. From theory, we do not expect perfectly bouncingdroplet for the Re and We values in the study. Wettability of the surface also plays a role inbounce mechanism of droplets. Wettability can be defined using the contact angle of dropleton the target surface. For high contact angles 90◦ < θ < 180◦, wettability is low, meaningthat the droplet does not spread on the surface easily. For low wettability surfaces, bouncingis highly probable as droplet spreading is low. In the sample plate used the wettability wasfound to be 100◦, as measured and reported my ASML. This could influence the bouncemechanism observed in the experiments. Comparing the angular distribution of scatteredparticles, narrow scatter distribution was achieved from hot plates. The droplet loses energywhen impact on hot plate leading to narrow scattering angles.

6.3.2 Normal incidence - Impact on liquid surface

The Hot Sn coated Mo at 300◦C was considered as impact on liquid surface. It was observedthat the scatter mass flux was 10% of incoming mass flux and the average scatter velocity wasreduced to 10m/s. The liquid surface has high viscosity which traps the incoming droplets.Energy dissipation occurs at the underlying viscous fluid layer on the target plate. In a fluidfilm with thickness h ∼ R, the pressure induced by impact scales with ρ.U2 where ρ, V, Rare density, velocity and radius of droplet respectively. The pressure gradient is then givenby ρ×U2

R . The characteristic velocity (u) of droplet in the viscous sub layer is given by:

u ∼ [ρ.U2

R .h2

µf]

The energy dissipated by viscosity of the thin film on target plate is given by,

Ef = [h.R2.µf .uh2 .τc]

Where,

µf = Viscosity of the thin film layer,τc = Contact time of droplet on target plate,

The energy dissipated is compared to the kinetic energy during impact,

EfKi

= [h.R2.µf .

uh2 .τc

ρ.U2.R3 ]

It can then be observed that,

Ef ∼ hR.Ki



Viscous dissipation by the viscous layer scales with the roughness,

hR

For a tin layer with thickness h ∼ R, the viscous dissipation is very much equal to the impactkinetic energy. Thus, the thin film layers trap droplets efficiently. The results from theexperiment agrees with the above theory. Hot tin coated Mo plates trap maximum amountof droplets. From the dimensionless numbers, We and Re, shown in table 6.10, the phasediagram indicating different regimes of drop impact [8] was compared. Figure 6.30 indicatesthe regime (Blue circle) expected for the We and Re numbers found in the experiments. Itwas noted that no crown splashing or micro droplet splashing would occur. Figure 6.31 showsgraph obtained from simulation experiments performed at ASML for droplet jetting [22] uponimpact. It could be seen that no jetting would occur for the range of We and Re found in theexperiments. The size distribution showed that the scatter particles have similar distribution.pattern. This could mean that the scatter particles bounced from the surface. Bouncing ofdroplets is ideally not possible. The scatter droplets must have loss in size(mass) due toenergy loss in the viscous layer. The Sn coated Mo plate is non-uniformly coated as describedin the experimental section. The scatter fraction could then be of droplets bouncing fromun-patched or non-coated region on the plate where wettability is low. Comparing otherimpact conditions from the results, hot Sn coat Mo was best suited to trap droplets.

Figure 6.30: Splashing regime for We and Re. Blue shaded region indicates the regime presentin this study. No splashing is expected [20].

6.3.3 Grazing incidence of impact - Solid surface

Results on experiments involving grazing incidence of impact were considered here. As dis-cussed in previous section, Cold plain Mo, Hot plain Mo, and Cold Sn coated Mo wereconsidered as solid surfaces. It was observed that the particle scatter percentage were signifi-cantly higher than in cases of normal impact on target plates. Scatter flux percentage of 90%,85% and 95% were observed respectively. The contact time tc was found to be much smallerthan earlier experiments. This was because of higher impact velocity than in experiments


6.3 Discussion 65

Figure 6.31: Jetting regime for We and Re. Blue shaded area represent current regime fordroplet, no jetting expected in the blue area [22].

involving normal incidence. As a result of very low contact time, the effect of viscous dissi-pation was neglected. The average scatter particle velocity was around 60m/s, 55% of theincoming velocity of 130m/s. The high scatter velocity is due to the effect of roughness, hightangential impact velocity of 130 m/s and low dissipation of energy by viscous effects. Thesurface roughness has more irregularities for grazing impact on the plate, leading to higherscattering velocities. Droplet sticking probability was found to be low for grazing incidence.Particle size distribution were computed for every experiment. It was observed that the sizeof scatter particles were of the same order of the incoming particles. Hence, no break up wasfound. This means that droplets bounced from the surface upon impact. From theory, the sizesimilarities of incoming and scattered particles were not expected. Since the particle lossesenergy upon impact, the scatter particle size must be smaller than incoming. The angulardistribution clearly distinguishes incoming and scattered particles. The incoming particlesarrive at 15◦ and scatter particles have a distribution between 110◦ − 130◦.

6.3.4 Grazing incidence of impact - Liquid surface

The Sn coated Mo plate, oriented at 15◦ and heated to 300◦C was used. It was observed that30% of the incoming particle flux, scatter back from the sample. The average scatter velocitywas reduced to 40m/s. As discussed in previous section, no splashing or jetting were expectedfor the We and Re found in the experiments as shown in figures 6.30 and 6.31. Size distributionbased on scattered intensity was compared between incident and scattered particles, whichshowed no break up of droplets. A higher scatter percentage was observed than in case ofnormal incidence involving the same target plate, Hot Sn coated Molybdenum. For impactat grazing incidence the film thickness (h) is smaller when compared to the normal impactconditions. This means that the influence of surface topology is more significant, leading tohigh scattering percentage. The sticking probability is higher on liquid surface which couldbe explained by the effect of viscous dissipation on the droplet upon impact on hot liquidsurface. Ideally, due to energy loss, the scatter particle must be smaller than the incidentparticle (no bouncing). This was not observed when the size distribution was compared.Another external factor that could influence bouncing is uneven coating of the Mo plate withtin. This could lead to exposure of solid Mo surface during the experiment, thereby alteringthe scattering properties.


Chapter 7

Conclusion and recommendations

7.1 Conclusion

In order to understand tin droplet impact mechanism on substrates and to control the splash-ing and scattering of the drops, their impact behaviour was studied using PTV experiments.A robust PTV algorithm was built using MATLAB which was used to study the dropletsplashing and scattering properties of different materials selected. The results of the scat-tering and splashing properties for the different materials selected were discussed in detail inthe previous sections. Tin droplets of high velocities in the size range of 500 nm to 10µmwere generated which were directed towards the target plates. By analysing and quantifyingthe scattering and splashing properties of the different plates chosen, suitable conclusions arepresented to choose the best orientation and condition for trapping or reducing the effect ofthe splashing and scattering inside the EUV machines.

• Results from first set of experiments involving normal incidence was compared andvalidated using the results of the previous work done by M.Van Kampen [1]. It wasobserved that, hot tin coated Mo plates at 300◦C trapped maximum droplets in bothexperiments. By comparing the scatter flux percentage of particles between the currentwork and previous work, the results were accepted.

• The hot tin coated plates have a high viscous layer due to the molten tin on the surface.This viscous layer is suitable to trap nano and micro tin droplets from splashing andscattering from the surface as seen in the experiments. It must also be noted that thethickness of the molten tin layer on the plate must be either larger than the diameterof the incident droplet or of the same size range, refer to figure 3.11 in chapter 3.

• By comparing the normal and grazing impact experiments, the scatter flux percentage isfound to be much lower in case of normal impact. This is explained through the energybalance given in the discussion section. Droplets with normal impact to target plateslose higher kinetic energy by viscous dissipation than for impact at grazing incidence.


7.2 Recommendations 67

• For grazing incidence of impact, the incident angle was fixed in the present study. Theangular distribution showed a clear trend for incoming and scattering droplets. Thescattering angles did not change for different materials rather was fixed for a givenincident angle.

• It must also be noted that the performed PTV experiment is 2D. Hence, particles flyingout of plane after impact (along the 3rd axis) are not captured or recorded by thesCMOS camera. This could influence the scatter flux percentage.

• A high probability of droplet bouncing was witnessed in the grazing experiments in-volving solid surfaces. The influence of surface roughness for grazing impact reducesthe wettability of surface, which could explain the occurrence of bouncing.

• Droplet bouncing was the only scatter mechanism observed in this study. Since, accuratedroplet sizing was not possible, scattered light intensity matching was performed tocompare sizes for incoming and scattered particles. All results pointed out that thesizes of incoming and scattered droplets do not change. From the Weber and Reynoldsnumber for the generated droplets, bouncing was not expected rather some loss of sizewas predicted. Accurate sizing must be adopted to be certain of bouncing droplets.

• It was also observed that the tin coated Mo plate was sparsely coated after sufficientrunning of the experiment(2hrs of exposure @ 300◦C ). It can then be that the dropletsbounce off from non-coated/sparsely coated region on the plate, leading to higher scatterflux percentage.

• From the results and conclusion discussed above, metal vanes coated with tin having athickness(h) ∼ radius of incident droplet(R), and heated above the Sn melting point,are best suited to trap the droplets inside the EUV machine.

7.2 Recommendations

Several recommendations and future work prospects include:.

• Sn droplet impact on liquid surface with varying thickness could be studied to under-stand the effect of layer thickness on splashing/scattering properties.

• Accurate particle sizing with high resolution cameras with high magnification lens couldbe adopted to measure size directly using PTV algorithms and laser diffraction methods.

• Droplet impact for various grazing angles could be studied to understand the effect ofimpact angles on splashing/scattering behaviour.

• The overall particle flux recorded in the experiments were quite low. Producing higherflux with a better particle source could improve statistics of the results.

• To avoid loss of data in capturing particles, a 3D ptv or stereo PTV could be adoptedto capture the out of plane particles. This would then provide more accuracy on theresults obtained.


References

[1] Maarten van kampen. Partcile scattering experiments. 2014.

[2] Ronald J Adrian. Particle-imaging techniques for experimental fluid mechanics. Annualreview of fluid mechanics, 23(1):261–304, 1991.

[3] AA Adamczyk and L Rimai. 2-dimensional particle tracking velocimetry (ptv): techniqueand image processing algorithms. Experiments in fluids, 6(6):373–380, 1988.

[4] Markus Raffel, Christian E Willert, Jürgen Kompenhans, et al. Particle image velocime-try: a practical guide. Springer, 2013.

[5] J.Westerweel and C.Poelma. Introduction to particle image velocimetry. Power PointSlides, http://www2.cscamm.umd.edu/programs/trb10/presentations/PIV.pdf, 2010.

[6] David W Hahn. Light scattering theory. Department of Mechanical and AerospaceEngineering, Florida, 2006.

[7] Brian Derby. Inkjet printing of functional and structural materials: fluid propertyrequirements, feature stability, and resolution. Annual Review of Materials Research,40:395–414, 2010.

[8] Martin Rein. Phenomena of liquid drop impact on solid and liquid surfaces. FluidDynamics Research, 12(2):61, 1993.

[9] Daozhi Shen, Guisheng Zou, Lei Liu, Walter W Duley, and Y Norman Zhou. Investigationof splashing phenomena during the impact of molten sub-micron gold droplets on solidsurfaces. Soft matter, 12(1):295–301, 2016.

[10] YK Cai. Phenomena of a liquid drop falling to a liquid surface. Experiments in fluids,7(6):388–394, 1989.

[11] Olive G Engel. Crater depth in fluid impacts. Journal of Applied Physics, 37(4):1798–1808, 1966.


REFERENCES 69

[12] RM Schotland. Experimental results relating to the coalescence of water drops withwater surfaces. Discussions of the Faraday Society, 30:72–77, 1960.

[13] Keeney Willis and Melissa Orme. Binary droplet collisions in a vacuum environment:an experimental investigation of the role of viscosity. Experiments in fluids, 34(1):28–41,2003.

[14] Ted Mao, David Kuhn, and Honghi Tran. Spread and rebound of liquid droplets uponimpact on flat surfaces. AIChE Journal, 43(9):2169–2179, 1997.

[15] Kai Range and François Feuillebois. Influence of surface roughness on liquid drop impact.Journal of Colloid and Interface Science, 203(1):16–30, 1998.

[16] Romain Rioboo, Cameron Tropea, and Marco Marengo. Outcomes from a drop impacton solid surfaces. Atomization and Sprays, 11(2), 2001.

[17] António L. N. Moreira, A. S. Moita, and S. Chandra. Handbook of Atomization andSprays: Theory and Applications, chapter Droplet Impact on a Solid Surface. 2011.

[18] AL Yarin. Drop impact dynamics: splashing, spreading, receding, bouncingâĂę. Annu.Rev. Fluid Mech., 38:159–192, 2006.

[19] Francisco Rodriguez and Russell Mesler. Some drops don’t splash. Journal of colloidand interface science, 106(2):347–352, 1985.

[20] RD Deegan, P Brunet, and J Eggers. Complexities of splashing. Nonlinearity, 21(1):C1,2007.

[21] Nasser Ashgriz. Handbook of atomization and sprays: theory and applications. SpringerScience & Business Media, 2011.

[22] ASML. Investigation of impact of 300nm droplet onto liquid and dry surface. 2014.

[23] Denis Richard, Christophe Clanet, and David Quéré. Surface phenomena: Contact timeof a bouncing drop. Nature, 417(6891):811–811, 2002.

[24] Paul R Chiarot and TB Jones. Grazing impact of continuous droplet streams with asuperhydrophobic surface. Experiments in fluids, 49(5):1109–1119, 2010.


Appendix A

PTV Algorithm developed for theThesis work

1 % The algorithm developed for particle tracking is given in this section.Itshows every command used to obtain the necessary results shown in the resultssection.

23 %STEPS followed:4 %1. Load images5 %2. subtract background and stray noise/light6 %3. Apply suitable image filters7 %4. Identify the particles/couple them8 %5. Obtain information on size, velocity and impact time from the particle9 %flow

10 %6. Post process data wrt fluid dynamic issues - graph plots and data11 %analysis.12131415161718 %1. Load Images1920 %Initially run the raw data to extract TOF and dt for every frame21 % captured.2223 ic = UT_IcabReader('F:\Msc.Thesis backup-24-8\Grazing experiments\

Hot_Mo_grazing_set1 - PCO.icab');24 % Figure out tof and dt data25 t_tof = zeros(ic.NoImages, 1);26 t_dt = zeros(ic.NoImages, 1);27 for i=1:ic.NoImages28 fh = ic.ReadFrameHeader(i-1);29 [ t_tof(i) t_dt(i) ] = ic.ExtraToFloat(fh.Extra);


71

30 i31 end32 % Close ic33 delete(ic);34 fh3536 %2.3738 %Find the background - quantify noise and remove. Standard deviation of each

pixel.39 %include file without particles. I.e. only background4041 ic = UT_IcabReader('F:\Msc.Thesis backup-24-8\Grazing experiments\

Hot_Mo_grazing_set1_bcgkd - PCO.icab');4243 avg = zeros(ic.Height, ic.Width);44 sd = zeros(ic.Height, ic.Width);4546 for i=1:15047 img = ic.ReadImage(i-1);4849 avg = avg + img;50 sd = sd + img.^2;51 i52 end;5354 avg = avg / ic.NoImages;55 sd = sqrt(sd ./ ic.NoImages - avg.^2);56 figure;plot(avg(:), sd(:),'.');57 figure;imagesc(avg, [0 1500]); axis image;58 ic.Close();596061 %define variables to store values62 velArrayx = []; %velocity distribution x direction63 velArrayy = []; %velocity distribution y direction64 particlearray = [];65 countsarray_f1 = []; %Scatter intensity of particles in A66 countsarray_f2 = []; %Scatter intensity of particles in B67 x_positions_A = []; % A position of particles,x.68 x_positions_B = []; % B position of particles,x.69 y_positions_A = []; % A position of particles,y.70 y_positions_B = []; % B position of particles,y.71 p_velocity = []; %Particle velocity array72 blockyImageSDold = []; % USE THIS VARIABLE FOR DENSITY PLOTS73 Eccentricity1 = []; %Eccentricity in both frames for the particles observed74 Eccentricity2 = [];7576 ic = UT_IcabReader('F:\Msc.Thesis backup-24-8\Grazing experiments\

Hot_Mo_grazing_set1 - PCO.icab'); % Read the raw data7778 for j = 1:ic.NoImages % cycle through the images7980 Image= ic.ReadImage(j-1); %Read Image8182 z = uint8(Image/3180*256);c%convert to 8bit83


72 PTV Algorithm developed for the Thesis work

84 avg_1 = uint8(avg/3180*256); %get average of background8586 v = (z-avg_1);87888990 v(v<0)=0;91 %imshow(v);92 % important step : What i do?93 % I subtract raw image with zero particles and with only the laser94 % sheet95 % This gives me a very good particle detection. No dead pixels and96 % errors979899 t_dt(j) ; %Time interval between frames in micro seconds.

100 t_tof(j) ;%TOF values101102103 %split the image in half. 1st half frame A and the scond Frame B104105106 nCols = length(v(1,:)); % or a = size(v) ; ncols = a(2);107 vR = v(:,1:(nCols/2));108 vL = v(:,(nCols/2+1):end);109 vR_x = avg_1(:,1:(nCols/2));110111112 % 3.113114 % The image is too big. And lot of ambiguities at the edges due to115 % excessive reflection.116 %Hence, i define a ROI to discard unwanted portion of image.117 %ROI crops the image with the respective coordinates.118 % must be very careful in selecting the ROI.119120 img1 = vR;121 img2 = vL;122 if j==1123 imagesc(vR_x); % ROI chosen by the user124 h = impoly;125 position = wait(h);126 boundbox = [min(position(:,1)), ....127 min(position(:,2)), ....128 max(position(:,1))-min(position(:,1)), ....129 max(position(:,2))-min(position(:,2))];130 BW = createMask(h);131132 end133134 v_crR =uint8(BW).*img1; %Identify the blobs in A & B135 v_crL = uint8(BW).*img2;136137138 v_crR1=bpass(v_crR, 1, 5);139 v_crL1=bpass(v_crL, 1, 5);140


73

141 % R IS FIRST FRAME ; L IS 2ND FRAME142143 %used bandpass filter144145 %bpass is a spatial bandpass filter which smooths the image and subtracts the

background off. The two numbers are the spatial wavelength cutoffs inpixels. The first one is almost always '1'.

146 %The second number should be something like the diameter of the 'blob's youwant to find in pixels.

147 %Try a few values and use the one that gives you nice, sharply peakedcircular blobs where your particles were; remember the numbers you usedfor bpass.

148149 % I found median for the images. median was around 40. Anything above 80 is a

particle because they150 % have sharp peaks. This is the THRESHOLD. (80-120) no changes but good151 % detection152 %the maximum after bpass filter gives around 130.Thus, 75% of that153 %value must be a particle.154155 max_bpass = max(max(v_crR1));156 if max_bpass < 25157 threshold = 14;158 else159 threshold = 0.40*max_bpass;160 end161 vRbw = v_crR1>threshold;162 vLbw = v_crL1>threshold;163 %imshow(vRbw);164165 ee1=0.95*bwmorph(vRbw,'dilate',3);166 ee2=0.35*bwmorph(vLbw,'dilate',30);167 totBW = ee1+ee2 ;168169 % new trick, found a way to merge 2frames with particles.170 %gives both in A and in B. Useful for visualisation.171 %using regionprops I find all required parameters172173174 blobsRA = regionprops(vRbw,'Centroid');175 blobsLA = regionprops(vLbw,'Centroid');176177 pixel_list1 = regionprops(vRbw, 'PixelIdxList'); % obtain total counts in

the particle178 pixel_list2 = regionprops(vLbw, 'PixelIdxList');179180 %calculating the position of the particle181 %i dilate the particle to occupy few more pixel in surrounding. Since i182 %cut most of the value using threshold.183 %i dilate only by 0.5 pixel in neighbourhood184185 SE = strel('disk', 1) ;186187 %strel function coupled with imdilate is used to expand the particle.188 %This is done to correct for the loss of values through thresholding.189 %thresholding not only removeds noise, but also removes some intensity190 %values from the particle.



191192193 vRRbw = imdilate(vRbw,SE);194 vLLbw = imdilate(vLbw,SE);195196 %after dilate , labeling the connected regions.197198 [position1,N1] = bwlabel(vRRbw);199 [position2,N2] = bwlabel(vLLbw);200201 %find all necessary parameter for the connected blobs.202203204 parameter1_ca=regionprops(position1,'Centroid','Area');205 parameter2_ca=regionprops(position2,'Centroid','Area');206207208 dia_f1 = regionprops(position1,'EquivDiameter');209 dia_f2 = regionprops(position2,'EquivDiameter');210211 Ecc_f1 = regionprops(position1,'Eccentricity');212 Ecc_f2 = regionprops(position2,'Eccentricity');213214215216 parameter1_wm=regionprops(position1,v_crR,'weightedcentroid','meanintensity')

;217 parameter2_wm=regionprops(position2,v_crL,'weightedcentroid','meanintensity')

;218219 %4.220221 %to find mean intensity always use raw image to find mean. It only give222 %accurate values223224 x1=zeros(N1,1);225 y1=zeros(N1,1);226 A1=zeros(N1,1);227 P1=zeros(N1,1);228 D1=zeros(N1,1);229 Ec1 = zeros(N1,1);230 pi=3.14159292;231232 %due to computation limit, I process images only with particles. If no233 %particle in either of frame, I omit.234235 if(N1 > 0 && N2 > 0)236237238 %calculate the x and y coordinate particles in for frameA239240 for l = 1:N1241 x1(l) = parameter1_wm(l).WeightedCentroid(1);242 y1(l) = parameter1_wm(l).WeightedCentroid(2);243 A1(l) = parameter1_ca(l).Area;244 P1(l) = A1(l).*parameter1_wm(l).MeanIntensity; %to find total intensity

from particle, multiply with the area of particle


75

245 D1(l) = dia_f1(l).EquivDiameter ;246 Ec1(l) = Ecc_f1(l).Eccentricity;247 end;248249 x2=zeros(N2,1);250 y2=zeros(N2,1);251 A2=zeros(N2,1);252 P2=zeros(N2,1);253 D2=zeros(N2,1);254 Ec2 = zeros(N1,1);255256 %calculate the x and y coordinate particles in for frameB257258 for l = 1:N2259 x2(l) = parameter2_wm(l).WeightedCentroid(1);260 y2(l) = parameter2_wm(l).WeightedCentroid(2);261 A2(l) = parameter2_ca(l).Area;262 P2(l) = A2(l).*parameter2_wm(l).MeanIntensity;263 D2(l) = dia_f2(l).EquivDiameter;264 Ec2(l) = Ecc_f2(l).Eccentricity;265266 end;267268269270271 %linking of particles - We found the coordinates, now link them with272 %accuracy.273274 linkp12 = zeros(N1:1);275 dist_neighbours = zeros(N1);276 for i=1:N1277278 dist_neighbours = ((x1(i)-x1).^2 + (y1(i)-y1).^2).^(0.5) ;279 if N1 >1280 dist_neighbours(dist_neighbours==0) = inf;281 end282283 dist_neighbours_min = min(dist_neighbours);284285 if min(dist_neighbours)==0286287 maxdist_p = 20*D1(N1);288289 else290291 %nearest neighbour method292 %this is to tell that a particle can only travel some distance.293 % This is calculated from the nearest neighbour294 maxdist_p = 0.5* dist_neighbours_min ;295296 end297298 Aratio=A1(i)./A2;299300 Pratio=P1(i)./P2;301 %the filter i placed - which depends on the intensity count ratio.



302303304 goodparticles = (Pratio > 0.8 & Pratio < 1.35 & Aratio > 0.8 & Aratio < 1

.35); % i also added area filter. This means a particle is a coupled(linked) only if all the conditions are satisfied. Hence, a suitablewide range could be given.

305 goodparticles_loc = find(goodparticles);306307 %once found the goodparticles, find the distance between them wrt308 %to one particle in frame A.309310 if any (goodparticles);311 dist1 = ((x1(i)-x2(goodparticles_loc)).^2 + (y1(i)-y2(

goodparticles_loc)).^2).^(0.5) ;312 dist1(dist1==0) = max(dist1) +100000 ; %If particle doesnt move313314315 [mindist index] = min(dist1);316317 % now link particles - with min distance.318319 if (mindist)<maxdist_p ;320 linkp12(i) = goodparticles_loc(index);321 end322 end323324 if any(goodparticles)==0 || (mindist) >=maxdist_p % no droplet of similar

size, or no droplet close enough: omit droplet.325 linkp12(i)=0;326 end327328 end329330 %Now store all data in struct for easy readability.331 couples1 = find(linkp12 > 0);332 couples2 = linkp12(couples1);333334 %5.335336337 frameparticles = zeros(length(couples1),17);338339340 if (length(couples1)==0)341342 x1p = 0;343 y1p = 0;344 A1p = 0;345 P1p = 0;346 x2p = 0;347 y2p = 0;348 A2p = 0;349 P2p = 0;350 uxp = 0; % speed in x direction. The 2e-05 is the size of 1 pixel. Thus,

i multiply with the dx351 uyp = 0;352 D1t = 0;


77

353 D2t = 0;354 umag = 0;355 Ecc1 = 0;356 Ecc2 = 0;357 %Iox = 0;358 %Ioy = 0;359 frameparticles(l,1)=0; % x1 particles in frame 1360 frameparticles(l,2)=0; % y1 particles in frame 1361 frameparticles(l,3)=0; % A1 particles in frame 1362 frameparticles(l,4)=0; % P1 particles in frame 1363 frameparticles(l,5)=0; % x2 particles in frame 2364 frameparticles(l,6)=0; % y2 particles in frame 2365 frameparticles(l,7)=0; % A2 particles in frame 2366 frameparticles(l,8)=0; % P2 particles in frame 2367368 frameparticles(l,9)=0; % velocity in x direction369 frameparticles(l,10)=0;370 frameparticles(l,11)=0;371 frameparticles(l,12)=0;372 frameparticles(l,13)=0;373 frameparticles(l,14)=0;374 frameparticles(l,15)=0;375 frameparticles(l,16)=0;376 frameparticles(l,17)=0;377 else378379380 for l = 1:length(couples1);381 x1p = x1(couples1(l));382 y1p = y1(couples1(l));383 A1p = A1(couples1(l));384 P1p = P1(couples1(l));385 x2p = x2(couples2(l));386 y2p = y2(couples2(l));387 A2p = A2(couples2(l));388 P2p = P2(couples2(l));389 D1t = D1(couples1(l));390 D2t = D2(couples2(l));391 Ecc1 = Ec1(couples1(l));392 Ecc2 = Ec2(couples2(l));393 dxp = (x2p)-(x1p); % displacement in x direction394 dyp = y2p-y1p; % displacement in y direction395 uxp = (dxp*3.5e-05)/t_dt(j); % speed in x direction. The 3.5e-05 is the

size of 1 pixel. Thus, i multiply with the dxp396 uyp = (dyp*3.5e-05)/t_dt(j); % speed in y direction. The 3.5e-05 is the

size of 1 pixel. Thus, i multiply with the dyp397 umag = sqrt(uxp^2+uyp^2); % speed of particle398 %dx_base = dxp/dyp*(ybase-y1p); % dx of particle at the base399 %xbase = x1p+dx_base; % location where particle left the base.400401402403 format short404405 frameparticles(l,1)=x1p; % x1 particles in frame 1406 frameparticles(l,2)=y1p; % y1 particles in frame 1407 frameparticles(l,3)=A1p; % A1 particles in frame 1



408 frameparticles(l,4)=P1p; % P1 particles in frame 1409 frameparticles(l,5)=x2p; % x2 particles in frame 2410 frameparticles(l,6)=y2p; % y2 particles in frame 2411 frameparticles(l,7)=A2p; % A2 particles in frame 2412 frameparticles(l,8)=P2p; % P2 particles in frame 2413414 frameparticles(l,9)=uxp; % velocity in x direction415 frameparticles(l,10)=uyp;% velocity in y direction416 frameparticles(l,11)=D1t;417 frameparticles(l,12)=D2t;418419420 frameparticles(l,13)= t_tof(j);421 frameparticles(l,14)= t_dt(j);422 frameparticles(l,15)= Ecc1;423 frameparticles(l,16)=Ecc2;424 frameparticles(l,17)=umag;425426 %frameparticles(l,11)=umag; % velocity magnitude427 %frameparticles(l,12)=xbase; % x xbasein of the particle (assuming

straight path).428 end429430 %particle size determination431432 % For the first analysis I consider that the particles have a size433 % bigger than the wavelengh of the laser pulse(532nm).434 %This means we can use geometric scattering theory which relates the435 %dia of particle to intensity count, which we already know.436 % If this assumption is false, we have to go for mie scattering or437 % rayleigh scattering.438439440441 end442443 all_linked_particles(j).frameparticles = frameparticles;444 all_linked_particles(j).N1 = N1;445 all_linked_particles(j).N2 = N2;446 all_linked_particles(j).Nlinked = length(frameparticles(:,1));447 % all_linked_particles(i).mask1BW_label448 all_linked_particles(j).SumA1 = N1;449450 all_linked_particles(j).x1p = frameparticles(:,1)';451 all_linked_particles(j).y1p= frameparticles(:,2)';452 all_linked_particles(j).x2p = frameparticles(:,5)';453 all_linked_particles(j).y2p= frameparticles(:,6)';454 all_linked_particles(j).A1p = frameparticles(:,3)';455 all_linked_particles(j).A2p = frameparticles(:,7)';456 all_linked_particles(j).uxp = frameparticles(:,9)';457 all_linked_particles(j).uyp = frameparticles(:,10)';458 all_linked_particles(j).P1p = frameparticles(:,4)';459 all_linked_particles(j).P2p = frameparticles(:,8)';460 all_linked_particles(j).D1t = frameparticles(:,11)';461 all_linked_particles(j).D2t = frameparticles(:,12)';462 all_linked_particles(j).tof = frameparticles(:,13)';463 all_linked_particles(j).dt = frameparticles(:,14)';


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464 all_linked_particles(j).Ecc1 = frameparticles(:,15)';465 all_linked_particles(j).Ecc2 = frameparticles(:,16)';466 all_linked_particles(j).umag = frameparticles(:,17)';467468469 %all_linked_particles(j).Iox = frameparticles(:,13)';470 %all_linked_particles(j).Ioy = frameparticles(:,14)';471 %%472 %velocity distribution473 uxp = all_linked_particles(j).uxp;474 uyp = all_linked_particles(j).uyp;475 velArrayx = [velArrayx;ones(size(uxp'))*j,uxp'];476 velArrayy = [velArrayy;ones(size(uyp'))*j,uyp'];477 umag = all_linked_particles(j).umag;478 p_velocity = [p_velocity;ones(size(umag'))*j,umag'];479 Ecc1 = all_linked_particles(j).Ecc1;480 Ecc2 = all_linked_particles(j).Ecc2;481 Eccentricity1 = [Eccentricity1;ones(size(Ecc1'))*j,Ecc1'];482 Eccentricity2 = [Eccentricity2;ones(size(Ecc2'))*j,Ecc2'];483484 %i group all diameters of particles. this is only image diameter not485 %the actual diameter.486487 %i calculate diameter from arear. I could also use equi-diamter from488 %regionprops and see if there is change.489490 D1p = all_linked_particles(j).D1t;491 particlearray = [particlearray;ones(size(D1p'))*j,D1p'];492 P1p = all_linked_particles(j).P1p;493 countsarray_f1 = [countsarray_f1;ones(size(P1p'))*j,P1p'];494 P2p = all_linked_particles(j).P2p;495 countsarray_f2 = [countsarray_f2;ones(size(P2p'))*j,P2p'];496497498 % To get all the x & y coordinates in frame A and B.499 x1p = all_linked_particles(j).x1p;500 x_positions_A = [x_positions_A;ones(size(x1p'))*j,x1p'];501 x2p = all_linked_particles(j).x2p;502 x_positions_B = [x_positions_B;ones(size(x2p'))*j,x2p'];503 y1p = all_linked_particles(j).y1p;504 y_positions_A = [y_positions_A;ones(size(y1p'))*j,y1p'];505 y2p = all_linked_particles(j).y2p;506 y_positions_B = [y_positions_B;ones(size(y2p'))*j,y2p'];507508509510511512 end513 j514515 end516517518 %6.519520 % particle linking is done. We also found the velocity of particles.



521522 % Now I build an array with all linked particles.523 dat.x_positions_A = x_positions_A(p_velocity(:,2)~=0,2);524 dat.x_positions_B = x_positions_B(p_velocity(:,2)~=0,2);525 dat.y_positions_A = y_positions_A(p_velocity(:,2)~=0,2);526 dat.y_positions_B = y_positions_B(p_velocity(:,2)~=0,2);527 dat.tof = t_tof(p_velocity(p_velocity(:,2)~=0,1));528 dat.dt = t_dt(p_velocity(p_velocity(:,2)~=0,1));529 dat.intensity = countsarray_f2(p_velocity(:,2)~=0,2);530 dat.velocity = p_velocity(p_velocity(:,2)~=0,2);531 dat.eccentricity2 = Eccentricity2(p_velocity(:,2)~=0,2);532 plot(t_tof(p_velocity(p_velocity(:,2)~=0,1)),p_velocity(p_velocity(:,2)~=0,2),'.'

); %to see if tof and velocity match - yes - then good coupling.533 scatter(countsarray_f1(:,2),countsarray_f2(:,2),'b','o'); %for matching accuracy534535 % The above groups will be for incoming particles. Similiarly find for536 % outgoing/scattering particles and compare.537538 %Find point of interection on sample for every pair.539 %From that fget distance between point in frame A and point in Frame B. %540 %Depending on the distance values, we can differentiate incoming and541 %scattering particles542543 x_interesect = ones(size(dat.x_positions_A));544 y_interesect = ones(size(dat.x_positions_A));545546 for i = 1:size(dat.x_positions_A)547548 %line1549 x1 = [dat.x_positions_A(i) dat.y_positions_A(i)];550 y1 = [dat.x_positions_B(i) dat.y_positions_B(i)];551552 if i==1553 figure, imagesc(vR) %define sample position BY USER554 q=imline;555 pos_line = getPosition(q);556 end557558559 %line2560 x2 = [pos_line(1) pos_line(2)];561 y2 = [pos_line(3) pos_line(4)];562 %fit linear polynomial563 p1 = polyfit(x1,y1,1);564 p2 = polyfit(x2,y2,1);565 %calculate intersection566 x_intersect(i) = fzero(@(x) polyval(p1-p2,x),3);567 y_intersect(i) = polyval(p1,x_intersect(i));568 % line(x1,y1);569 hold on;570 line(x2,y2);571 plot(x_intersect(i),y_intersect(i),'r*')572573574575 end576


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577 dat.x_intersect = x_intersect'; %contains impact positions578 dat.y_intersect = y_intersect'; % contains impact positions579 dat.d1 = sqrt((dat.x_intersect - dat.x_positions_A).^2 + (dat.y_intersect -

dat.y_positions_A).^2);580 dat.d1 = sqrt((dat.x_intersect - dat.x_positions_A).^2 + (dat.y_intersect -

dat.y_positions_A).^2);581 dat.d2 = sqrt((dat.x_intersect - dat.x_positions_B).^2 + (dat.y_intersect -

dat.y_positions_B).^2);582 dat.d = (dat.d1 - dat.d2) ; %d positive is incoming particles and d negative

value is scattered particles583 dat.xi = dat.xA(dat.d > 0);584 dat.yi = dat.yA(dat.d > 0);585 dat.xs = dat.xA(dat.d < 0);586 dat.ys = dat.yA(dat.d < 0);587 dat.in_tof = dat.tof(dat.d > 0);588 dat.sct_tof = dat.tof(dat.d < 0);589 dat.in_vel = (dat.velocity(dat.d > 0));590 dat.sct_vel = (dat.velocity(dat.d < 0));591 dat.intensity_out = dat.intensity(dat.d < 0) ;592 dat.intensity_in = dat.intensity(dat.d > 0) ;593 dat.intensity_out = dat.intensity() ;594 dat.eccentricity_out = dat.eccentricity(dat.d < 0) ;595 dat.eccentricity_in = dat.eccentricity(dat.d > 0) ;596597598 % Show image599 handles.vars.image = imagesc(CreateDensityPlot(handles, 10, ':'));600 uistack(handles.vars.image, 'bottom');601602 % Make density plot603 img = zeros([handles.vars.icab.Height/2 handles.vars.icab.Width]);604 xi = round(handles.vars.dat.xa(2,filter));605 yi = round(handles.vars.lstat.ya(1,filter));606 ind = sub2ind(size(img), xi, yi);607 smoothing = 300;608 histo = hist(ind, 1:numel(img));609 img(1:numel(img)) = histo;610 filter = fspecial('gaussian', [smoothing smoothing], smoothing/3);611 img = imfilter(img, filter, 'replicate');612613614 %Now we can group as per tof to match incoming and outgoing particles.615 m=unique(dat.tof);616 %m(1).....m(6) all tofs arranged.617 %mention which tof need to filter, specify the m value.618619 dat.p_in_fast = dat.in_vel(dat.in_tof < m(3) & dat.in_tof > m(2));620 dat.p_in_fast = dat.in_vel(dat.in_tof < m(2)) ;621 dat.p_sct_fast = dat.sct_vel(dat.sct_tof < m(2));622 group1 = histogram(dat.p_in_fast);623 mass_flux_in = (group1.Values).* (group1.BinEdges(1:8));624 q=group1.BinEdges(1:8);625 group2 = histogram(dat.p_sct_fast);626 mass_flux_out = (group2.Values).* (group2.BinEdges(1:4));627 p = group2.BinEdges;628629 plot(q , mass_flux_in,'r')



630 hold on631 plot(p , mass_flux_out,'b')632633 imax = max(dat.intensity_out(dat.sct_tof < m(2)));634 histogram(dat.intensity_in(dat.in_tof < m(2)))635 hold on636 histogram(dat.intensity_out(dat.sct_tof < m(2)))637 histogram(dat.eccentricity_in(dat.in_tof < m(2)))638 hold on639 histogram(dat.eccentricity_out(dat.sct_tof < m(2)))640 dat.ri = sqrt(dat.xi + dat.yi);641 dat.thetai = atan(dat.yi ./ dat.xi);642 dat.rs = sqrt(dat.xs + dat.ys);643 dat.thetas = atan(dat.ys ./ dat.xs);644 polar(dat.thetai,dat.ri,'.')645 hold on646 polar(dat.thetas,dat.rs,'.')


masters thesis: study of tin droplet impact on a substrate

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