Flash Lamp Annealing and Photoluminescence Imaging of Thin Film Silicon Solar Cells on Glass

The University of New South Wales,

School of Photovoltaics and Renewable Energy Engineering

A Thesis Submitted for the degree of Doctor of Philosophy

Anthony Teal

March 2013

Supervisors: Dr. Sergey Varlamov & Dr. Henner Kampwerth THE UNIVERSITY OF NEW SOUTH WALES Thesis/Dissertation Sheet Surname or Family name: Teal

First name: Anthony Other name/s: Shane

Abbreviation for degree as given in the University calendar: PhD

School: SPREE Faculty: Engineering

Title: Flash Lamp Annealing and Photoluminescence Imaging of Thin Film Silicon Solar Cells on Glass

Abstract 350 words maximum: (PLEASE TYPE)

This thesis is divided into three main chapters, covering Flash Lamp Annealing (FLA) experiments in Chapter 1, FLA thermal and structural simulations in Chapter 2, and Photoluminescence (PL) Imaging in Chapter 3.

The first and second chapters aim to gauge the feasibility of replacing the existing belt furnace Rapid Thermal Process (RTP) with FLA for Silicon (Si) films on a glass substrate that have been crystallised by Solid Phase Crystallisation (SPC). The experimental work gives us insight into the maximum stress that the film can handle during the FLA process, as well as giving us a baseline for parameters to investigate in any future experiments. It is found that FLA with 3ms pulses and 20ms pulses are not suitable replacements for the current RTP setup because significant damage to the film is observed at lower pulse energy densities than that required to achieve an adequate level of annealing. The modelling in chapter 2 predicts that the magnitude of the stress will increase with increasing pulse duration, making successful annealing at longer pulse durations unlikely.

Equipment capable of producing pulse durations above 80 milliseconds, and capable of heating the Si film to temperatures between 1350°C to 1400°C does not currently exist. For this reason these pulse durations have not been investigated, but a basic design guide on how longer pulse durations could be produced is provided.

The third chapter concentrates on PL Imaging of thin film Silicon Solar cells on glass. PL Imaging allows a noncontact method of characterising the quality of the Silicon film at various stages of the production process. Through PL Imaging, it was discovered that there is a large variation in material quality from sample to sample, as well as within the same sample. It is also found that the PL signal is wavelength dependent, and through modelling of cell parameters in PC1D, we can use this wavelength dependence to infer a minority carrier lifetime on low quality Si material.

Declaration relating to disposition of project thesis/dissertation I hereby grant to the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all property rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstracts International (this is applicable to doctoral theses only).

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Originality Statement

I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged.

Signed: ...... Date: ...... Copyright Statement

I hereby grant the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation.

I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstract International

I have either used no substantial portions of copyright material in my thesis or I have obtained permission to use copyright material; where permission has not been granted I have applied/will apply for a partial restriction of the digital copy of my thesis or dissertation.

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Acknowledgements

First and foremost I would like to thank my wife Alex. As well as tolerating the late- night work sessions and whole weekends tied up with writing, she has been a source of constant support, encouragement and inspiration. I am very grateful to her for all that she has done and continues to do, and I love her with all my heart. I would also like to thank my Mum and Dad for all their support. They have always encouraged me with whatever endeavours I choose to pursue. Their financial support in the earlier years is also very much appreciated. More than a few dollars were ‘borrowed’ from them while I was a poor University Student in Melbourne and in Sydney, allowing me to follow my dreams.

The most influential person in my PhD was my supervisor, Dr Sergey Varlamov. Firstly, he took me on as a student when I was looking for a topic, and was able to draw on my previous work with lasers and flash lamps, while guiding me through the intricacies of thin film Si solar cells. I cannot show enough admiration for the efforts Dr Varlamov put in on my behalf. Without his support, my venture into the world of research would have been short-lived.

For the flash lamp annealing work, I would like to thank Prof. Skorupa of FZDR in Germany. When I contacted him with a request to use his Flash Lamp equipment, he was able to provide valuable reading material and guidance as to what processing parameters would be optimal for our samples. As the experiments continued, Prof. Skroupa was very gracious with allocating time for us on the flash lamp equipment, and seeing that our samples were processed. I would also like to thank Thomas Schumann of FZDR, who did the FLA processing of our samples. I was lucky enough to spend time with Thomas at the Sub-Therm Conference in 2011, and the informal discussions I had with him were invaluable in learning the actual process of Flash Lamp Annealing, which cannot be learnt from a book.

The Photoluminescence Imaging of thin film Si solar cells part of this thesis began as a way of characterising some of our more damaged FLA samples, as contacting densely cracked films is extremely difficult. Initial work had already begun by the time I started working on the topic, with much headway being made by Dr. Mark Keevers and Dr.

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Oliver Kunz. After a few failed attempts at making a PL excitation source suitable for thin film Si, design input from both Mark and Oliver was incorporated into a system that proved more than adequate for the application. Before I began work on PL Imaging, an introduction to PL imaging was given to me by Yael Augarten. Yael saw the potential for PL imaging on thin films long before I did, and provided the knowledge base to investigate it. PL imaging would definitely not be a part of my thesis had I not shared an office with Yael. Once the investigations were underway and SPREE had moved to the TETB building, I found my desk close to that of Mattias Juhl. Conversations with Mattias helped to develop my ideas and the PL work immensely, and I am grateful for his input.

I must also acknowledge the efforts of all the people at CSG solar, now SunTech R&D Australia. When I needed training on how to do various processing steps, Kyung Kim, Daniel Ong and Patrick Campbell were always available to assist. In the workshop, the assistance of Graham Lennon was very helpful in designing and manufacturing many of the custom parts needed for PL Imaging of thin films.

And to my fellow students: Bonne, Chaho, Jae, Jialiang, Jono, Mark, Miga and Wei. Getting to know you was an added bonus to studying thin film Si Solar Cells, and the help you all provided made the task of completing a PhD fun and interesting. I am privileged to be colleague and friend to you all.

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“Before coming here I was confused about this subject. Having listened to your lecture I am still confused. But on a higher level”

- Enrico Fermi

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Abstract

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Table of Contents

Table of Contents ...... - 8 -

Chapter 1 ...... - 12 -

1.1 Introduction ...... - 13 -

1.2 Samples Investigated ...... - 16 -

1.3 Optimal Annealing Time at Various Temperatures ...... - 18 -

1.4 FLA on Wafers ...... - 22 -

1.5 Flash Lamp Crystallisation of thin film Silicon on Glass ...... - 23 -

1.6 Experimental FLA Parameters ...... - 27 -

1.6.1 Preheat Temperature ...... - 27 -

1.6.2 Pulse Width ...... - 29 -

1.6.3 Pulse Shaping ...... - 30 -

1.6.4 Film Thickness ...... - 38 -

1.6.5 Multiple Pulse FLA ...... - 38 -

1.6.6 Glass Substrates ...... - 39 -

1.6.7 Glass Texturing ...... - 40 -

1.7 Equipment for FLA ...... - 41 -

1.7.1 Commercially Available FLA Equipment ...... - 41 -

1.7.2 Equipment Available for Preliminary Experiments ...... - 42 -

1.7.3 Equipment designed for FLA on Thin Film Silicon ...... - 43 -

1.8 Results of FLA experiments ...... - 52 -

1.8.1 Level of annealing achieved ...... - 53 -

1.8.2 Mattson Tech. Results ...... - 62 -

1.9 Damage to Silicon Films ...... - 65 -

1.10 Discussion of FLA Experiments ...... - 70 -

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Chapter 2 ...... - 72 -

2.1 Introduction and Overview ...... - 73 -

2.2 Relevant example of FEM modelling ...... - 74 -

2.2.1 Modelling in 1-D ...... - 74 -

2.2.2 Modelling in 2-D ...... - 74 -

2.2.3 Modelling in 3-D ...... - 75 -

2.3 Thermal Model ...... - 76 -

2.3.1 Model overview ...... - 76 -

2.3.2 Thermal Properties ...... - 78 -

2.3.3 Input Flash Lamp Thermal Profiles ...... - 82 -

2.4 Displacement, Strain and Stress ...... - 85 -

2.4.1 Model overview ...... - 85 -

2.4.2 Mechanical Properties ...... - 85 -

2.4.3 Displacement Calculation MATLAB Code ...... - 86 -

2.4.4 Constitutive equations ...... - 88 -

2.5 Mechanical Failure of Silicon ...... - 100 -

2.6 Model Assumptions and Simplifications ...... - 106 -

2.7 Results of Simulations ...... - 108 -

2.7.1 Thermal ...... - 108 -

2.7.2 Structural ...... - 112 -

2.7.3 Discussion of Structural Modelling Results...... - 128 -

2.7.4 Pulse Energy Density Damage Threshold ...... - 131 -

2.8 Implications for FLA on Thin Film Si on Glass and Discussion ...... - 133 -

Chapter 3 ...... - 134 -

3.1 Introduction ...... - 135 -

3.2 Samples Investigated ...... - 136 -

3.3 Key Differences between PL on wafers and PL on thin film Si on glass . - 137 -

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3.4 Solar Cell Specific Photoluminescence Theory ...... - 141 -

3.5 Physical Setup of PL Imaging System ...... - 145 -

3.6 PL modelling in PC1D ...... - 153 -

3.6.1 Process Overview ...... - 153 -

3.6.2 Model Input Parameters ...... - 154 -

3.7 Results of Simulations ...... - 158 -

3.7.1 Diffused Junction vs. No Junction ...... - 158 -

3.7.2 Surface passivation...... - 160 -

3.8 Discussion of Simulation ...... - 163 -

3.9 Practical Considerations for PL Images of Thin Film Si on Glass ...... - 165 -

3.10 PL Imaging Equipment ...... - 167 -

3.11 Surface passivation ...... - 168 -

3.12 PL Intensity at the various stages of production ...... - 169 -

3.13 PL Imaging Results ...... - 170 -

3.13.1 Minority Carrier Lifetime from multi-wavelength PL Excitation ratio...... - 170 -

3.13.2 PL intensity variation within a sample ...... - 174 -

3.13.3 PL Intensity vs. Voltage ...... - 177 -

3.14 Further PL imaging investigation ...... - 180 -

3.15 PL Imaging Conclusions ...... - 181 -

Appendix A- Thermal Simulation Code ...... - 183 -

Appendix B – Stress Simulation Code ...... - 187 -

Bibliography ...... - 193 -

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Chapter 1

Flash Lamp Annealing of Thin Film Silicon on Glass Solar Cells

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1.1 Introduction Flash Lamp Annealing (FLA) is one of the many possible methods of Rapid Thermal Annealing (RTA). FLA uses a flash lamp is used to rapidly heat a semiconductor film or wafer, to remove electrically active defects. The process of Thermal Annealing improves electrical properties such as carrier lifetime, and carrier diffusion length by removing defects and activating dopants within the cell. The prefix term ‘Rapid’ refers to any thermal annealing process of the order of seconds and below. Heat sources previously investigated for RTA include high power lasers, microwaves, and electron beam, with each source having various levels of success. The most commercially viable method of defect annealing of thin film Si on glass has historically been achieved by passing the sample through a belt furnace, resulting in a heating cycle lasting minutes, not seconds. Belt furnace annealing serves the purpose of defect removal just like an RTA step, and so it is still loosely referred to as RTA even though it technically is not. In contrast to belt furnace annealing, FLA is typically achieved over the time scale of 0.1 to 10’s of milliseconds, and is thus described as a subcategory of RTA, called millisecond annealing (MSA).

There are many potential benefits to millisecond annealing methods over belt furnace annealing. These include a higher throughput capability and lower energy consumption, because of the shorter time spent at elevated temperatures. Millisecond annealing systems also are significantly smaller than a belt furnace, reducing the demands on cleanroom floor space. The capital cost and running cost of a flash lamp system is also less than that required for the belt furnace RTP system.

Perhaps the main advantage of millisecond annealing is that the very short heating time allows the Si film to reach temperatures near/above the melting point of the Si, without completely melting the glass. This may eventually enable the usage of soda-lime glass as a replacement substrate for Borosilicate glass, which will reduce the cost of the resultant solar cell significantly. This very short processing time also enables low dopant diffusion, with FLA on wafers being shown to produce the most abrupt dopant profiles of any annealing technique [Gebel, et al. - 2002, Zechner, et al. - 2008]. FLA has potential benefits over other millisecond scale RTA processes, because of the large area (potentially larger than 1m2) covered by a single flash lamp pulse. Comparing this

- 13 - to laser annealing for instance, where a beam around 1 cm wide must be raster scanned across the entire cell surface, taking significantly longer.

As stated earlier, annealing is the process of activating dopants and removing electrically active defects. FLA has successfully been used to activate ion implanted dopants in Si wafers, and remove the damage caused during the ion implanting process [Gebel.et .al - 2002]. However, modelling of FLA on Si wafers has shown that relatively large thermal gradients are generated during the flash lamp pulse. This thermal gradient in turn, produces large stresses and bending of the wafer, which is a potential source of cracking and other damage [Smith, et al. - 2006]. An overview of these stresses with be given in this chapter, while an in depth investigation into the thermal profile, and resultant stress involved in millisecond annealing is given in Chapter 2.

The main aim of this investigation into FLA, is to determine if the process is feasible as a replacement for RTA. To quantify the effectiveness of the defect removal process, the resultant open circuit voltage (Voc) after FLA and hydrogenation will be measured for each sample. The improved material quality is expected to increase the number of electrons reaching the junction which will also improve the short circuit current (Jsc) but measuring this would require more sample processing and add no deeper insight into the level of annealing achieved. For FLA to be a feasible replacement of the current belt furnace annealing step, the Voc of the FLA process must be equal to or better than the

Voc resulting from the current RTA process.

Previous to this investigation FLA had primarily focused on annealing the damage caused by Ion implantation of dopants into a Si wafer [Gelpey, et al. - 2008]. This process includes the re-crystallisation of a thin layer of amorphous Silicon (a-Si) on the wafer that had been amorphised to assist with the Ion implantation process. FLA has also been used to crystallise a-Si films by Ohdaira et al. [Ohdaira, et al. - 2007], but this is not considered defect annealing, so to differentiate this process from defect removal of already crystalline material, I will refer to the former as Flash Lamp Crystallisation (FLC). Another difference between the investigations into FLC and FLA is that a layer of Chromium is used to prevent the Si film from delaminating off the glass in the former. This approach cannot be used in our investigation as the glass is used in a superstate configuration, and the Chromium layer would prevent light reaching the Si. - 14 -

If FLA required the use of a non-transparent barrier layer, then FLA would not be a feasible replacement for the current belt furnace annealing step.

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1.2 Samples Investigated The samples on which FLA has been investigated, are thin film Si on glass produced by CSG Solar. The glass substrate in these samples is typically the borosilicate glass Borofloat supplied by Schott, but Soda-lime glass was also investigated as a substrate. The production process of thin film Si on glass has been well documented, and so only a summary of the sample properties is given here.

The starting point of the production process is to clean then texture the bare glass substrate, which is done by sandblasting, followed by a Hydrofluoric Acid (HF) dip [Young, 2009]. Texturing was not carried out on some samples Investigated, while others were not sandblasted, and are investigated as planar samples.

On the textured or planar glass substrate, a Silicon Nitride (SiN) intermediate layer is deposited. The SiN intermediate layer serves 3 main purposes. Firstly, to limit diffusion of impurities from the glass substrate to the Si film which would otherwise lower the material quality. Secondly the SiN serves as a surface passivation layer, reducing carrier recombination at the Si/glass interface. Thirdly, the SiN serves as an anti- reflection coating, as the glass is used in a superstrate configuration.

On the SiN intermediate layer, a 2µm layer of amorphous Silicon (a-Si) is deposited via PECVD or e-beam evaporation [Egan, et al. - 2009]. This a-Si film is subsequently crystallised via Solid Phase Crystallisation (SPC) at between 640°C to 680°C [Tao, et al. - 2010]. The n and p doping of the cell are performed during the deposition process, and the SPC process results in low dopant diffusion, so the dopant profiles remain almost unchanged.

It is at this stage of production that the Si films would undergo a Rapid Thermal Annealing (RTA) process, where they are passed through a belt furnace at between 900°C to 1050°C for a period of between 10 to 300 seconds. However, this study aims to replace RTA with FLA, so the samples do not undergo RTA.

Subsequent steps of the production process, such as contacting, are not performed prior to FLA, and if the samples investigated show improved material quality then the samples would continue through the production process.

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FLA was not investigated on LPCSG (Liquid Phase Crystalline Silicon on Glass) thin films, because RTA has been shown to not improve LPCSG material quality in a similar manor to SPC thin films. 10µm thick LPCSG films are the primary basis for the PL investigation done in Chapter 3, although some 2µm thick SPC films are investigated for comparison purposes.

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1.3 Optimal Annealing Time at Various Temperatures There are many complex and interacting phenomena occurring within the process of Thermal Annealing. These phenomena include dopant diffusion, dopant and impurity activation, junction smearing, as well as removal of intragrain defects within the crystal grains. There may also be a level of intergrain defect annealing resulting from adjustments to the misorientation of neighbouring grains. The defects at grain boundaries are not completely removed by RTA, which is why Hydrogenation is used to further passivate these inter-grain defects. Hydrogenation typically passivates grains by terminating dangling Silicon bonds and which would otherwise act as recombination centres for minority carriers.

A more in depth discussion on how reorientation of the grains, and migration of point defects within a crystal grain are removed during FLA is not given here, and there is little to be found in pervious journal papers. This thesis focuses on FLA as a method to remove electrically active defects and quantifies there removal by measuring the Open circuit Voltage. Quantifying the defects could be done in more detail by analysis of the films using Spectral Photoluminescence (PL), before and after FLA. However, because the level of annealing achieved is quite poor, further analysis on the technique detracts from the main aim of our research group which is to improve the efficiency of thin film Si solar cells on glass, while reducing the production cost. If the level of annealing achieved with FLA was higher, then more time would have been spent characterising and understanding the exact mechanisms by which this occurs.

In the case of polycrystalline Silicon (pc-Si) on glass, there are limitations to the temperatures and pulse durations that can be used for thermal annealing. On one hand, higher temperatures lead to better dopant activation, but dopant diffusion limits the time that the material can be at an elevated temperature without significant dopant smearing, and shunting. The problem of shunting is predominantly caused by increased dopant diffusion along grain boundaries, which is much higher than diffusion through a Si grain .It was shown in this paper by Terry et al., that an RTA process at 900°C for 420 seconds (7 minutes) can increase the Voc from around 135mV (pre-annealing) to 454mV after RTA. It is also noted in this paper that the time required for RTA reduced significantly from 420 sec @ 900°C to 90 sec @ 1000°C when the annealing temperature is increased. - 18 -

With the data from Terry et al. and other processing data at CSG solar, it can be shown that the level of annealing achieved, followed an Arrhenius type function shown in equation 1, below.

. 1

Where k is the rate constant which is equal to , t = time for process to occur. i.e. optimal annealing time, k = Boltzmann constant = 8.62E-0.5 ( ), A = pre- exponential factor = 1, E = activation energy, R = gas constant, and T = temperature.

The adherence of the data to the Arrhenius trend could be expected if we realise that the process of dopant activation and crystal defect removal are primarily solid state chemical processes. With some simple adjustment to equation 1, we can give the expression shown below;

This form reduces the complexity of the equation to a linear relationship between ln and with the gradient being equal to the activation energy. If we take the optimal thermal annealing times, for various annealing temperatures, given in Table 1, we can extrapolate an activation energy range that can be used to predict the possible annealing times required at temperatures close to the melting point of Si. The activation energy can be deduced from the gradient of a graph of log of inverse time versus inverse temperature, which can be seen in Figure 1. It should be noted that when calculating Eα, the temperature must be in Kelvin.

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Inverse Temperature vs. log of Inverse Time

ln(1/t) Time Data 1 0 Time Data 2 Extrapolatiion (Min) ‐2 Extrapolation (Max)

‐4 1/kBT

Figure 1, shows the log of inverse time vs. inverse temperature. From the gradient of this graph the maximum and minimum possible activation energies can be calculated.

Temperature 900°C 950°C 1000°C 1100°C Optimal Annealing 180 – 300 sec 80 sec 10 – 20 sec Times (CSG Solar) Optimal Annealing 420 sec 90 sec Times (2005 - Terry)

Table 1 shows the optimal annealing times for defect annealing at various temperatures.

From Figure 1 we can find the minimum and maximum possible activation energy for thermal annealing, by calculating the gradient of the two lines. These possible values are;

2.11 , and 3.28 .

With these minimum and maximum activation energies, we can estimate the optimal processing times for higher processing temperatures shown in Table 2.

Annealing 1200°C 1250°C 1300°C 1350°C 1400°C Temperature Minimum Time (ms) 2482 1360 559 284 150 Maximum Time (ms) 2871 1149 676 351 190 - 20 -

Table 2, shows the predicted optimal annealing times for our Si on glass samples. These values have been extrapolated from optimal annealing parameters at lower temperatures. As stated at the beginning of this section, thermal annealing is a product of multiple thermal processes, and the data fits well to the Arrhenius equation. However it is entirely possible that the results of thermal annealing at higher temperatures will show a deviation from this trend, as thermally active processes come into play closer to the silicon melting temperature. Thus, the predicted annealing times can only serves as a guide to the optimal FLA parameter space.

A significant limitation to the thorough investigation of FLA is the lack of equipment capable of achieving pulse duration of 50 ms or above. Of all research institutions and commercial organisations contacted, none has equipment capable of producing flash lamp pulses of 100 ms. The longest pulse duration available for this investigation was 40 ms from equipment at Helmholt Zentrum Dresden Rossendorf (HZDR). To explore the full parameter space available to us, 0.4, 3, 20, and 40 ms pulses were investigated.

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1.4 FLA on Wafers FLA has been developed primarily to anneal defects in Silicon wafers caused during ion implantation, for the electronics industry [Skorupa, et al. - 2005, Wundisch, et al. - 2008] [Gelpey.et .al - 2008]. The benefits of FLA over longer duration annealing methods, is a significantly reduced diffusion profile. This steep profile is capable of meeting the ever steeper dopant profiles required by the electronics industry, while activating a high proportion of dopant [Lee, et al. - 2010]. It has also been shown that a higher level of dopant activation is possible with millisecond time scale heating pulses, such as FLA, compared to longer timescale heating methods [Kato, et al. - 2009].

In the previous section, it was shown that the level of defect annealing in solid phase crystallised (SPC) thin film Si on glass will require pulse durations on the order of 10s to 100s of milliseconds. For the application of dopant activation, with low diffusion, a pulse duration of 2.5 milliseconds is considered long [Lee.et .al - 2010]. This means that although there is an overlap between FLA on wafers and thin films, but the required pulse durations do not necessarily overlap.

Perhaps the main difference between FLA on wafers and FLA on thin film Si, is the types of defects that are being removed. In wafers, FLA is used to remove the damaged caused by ion implantation, and amorphisation. This damage is localised within 10s of nm of the wafer surface, which is in contrast to SPC Si films, which have defects, throughout the thickness of the film (~ 2µm). Because FLA on wafers requires time scales of 0.1 to 2 milliseconds, and FLA of thin films is expected to require pulse durations of 10s to 100s of milliseconds, there are very few equipment manufacturers with adequate FLA equipment. An overview of equipment manufacturers is given at the beginning of section 1.7.

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1.5 Flash Lamp Crystallisation of thin film Silicon on Glass Flash Lamp Crystallisation (FLC) is the process of crystallising a thin film of a-Si, by heating the film for 5 – 20 milliseconds via intense light from a Xenon flash lamp. FLC is a similar application to FLA, in terms of the thicknesses of the Silicon films under investigation, the substrates used for the films, and the equipment required to perform both processes.

FLC was pioneered in work done by Ohdaira et al. [Ohdaira, et al. - 2008, Ohdaira.et .al - 2007, Ohdaira, et al. - 2009, Ohdaira, et al. - 2009, Ohdaira, et al. - 2007] [Ohdaira.et .al - 2009, Sugita, et al. - 2007], where it was first shown by Raman spectra, that the film had indeed changed from an a-Si state, to a crystalline state with a flash lamp pulse of under 10 milliseconds. Subsequent investigation showed that the crystallised film comprised of nanometres to micron scale crystal grains, and that there is periodic variation in grain size laterally across the film. It was shown that this periodic variation was a result of Explosive Crystallisation (EC) of the a-Si film, from the edge to the centre of the sample.

In FLC experiments performed by Ohdaira et al. crystal nucleation occured at the outer edge of the sample and propagated inward at speeds of the order of 17 m/s, which is faster than thermal diffusion of the material. This is typical of Explosive Crystallisation, as noted by Ohdaira [Ohdaira.et .al - 2009], and described by Geiler et al. in 1985. Explosive crystallisation is a process of a crystal boundary propagating laterally in an amorphous film, at a very high speed. The process of crystallisation at the amorphous boundary is driven by thermal energy from both the flash lamp, and from latent heat energy released during crystallisation. Thermal energy is released during crystallisation, because a-Si has a higher enthalpy than c-Si, and the process of a- Si to c-Si is exothermic. Geiler describes the process of explosive crystallisation, as consisting of 4 possible mechanisms [Geiler, et al. - 1986], which are;

 Solid Phase Crystallisation (SPC),  Solid Phase Epitaxy (SPE),  Liquid Phase Crystallisation (LPC), and  Liquid Phase Epitaxy (LPE). - 23 -

Solid or liquid phase nucleation is obviously the starting point of transformation from amorphous to a crystalline structure. The influence and prevalence of the following processes is still a point of debate, but there are some clues within Ohdaira’s work, that give us insight into the process in the case of FLC. Firstly, the a-Si film was doped before crystallisation, and the dopant profile was found to be predominantly unaltered after the crystallisation process. This tells us that if the Silicon is liquid at any point, then it is for a fleetingly short time. As well as this, we know that the resulting crystal structure is made up of small grains, which means that the process of nucleation is occurring constantly at the crystalline/amorphous boundary.

In TEM images of the film after FLC, a periodic structure is evident (Figure 2). The periodic change in crystal grains over a range of approximately 500nm shows that the dominance of process such as SPE, which results in larger grains, also leads to increased crystal nucleation, which drives the resultant material to consist of smaller crystal grain sizes. More detail on the material characterisation, can be found in the referenced papers, by Ohdaira.

pc-Si formed by Flash Lamp Crystallisation

Figure 2, shows a TEM image of pc-Si film after FLA [Ohdaira.et .al - 2009]

FLC is commercially interesting because the speed with which it occurs would be easy to incorporate into an industrial process, and is many orders of magnitude faster than SPC performed in a furnace, at temperatures between 600°C, as is the process at CSG solar [Keevers, et al. - 2005].

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Disadvantages of the material include very small nano-scale grains, which reduces the electron mobility significantly from that seen in single crystal silicon. This electron mobility can be increased dramatically in the material by passivating the grain boundaries with hydrogen, as is done in other SPC pc-Si. It has also been shown that grain size is proportional to the lamp irradiance energy [Ohdaira.et .al - 2008]. It is reasonable to assume that the grain size is thus dependent on the temperature of the material at the crystallisation boundary, which changes throughout the crystallisation process, as the thermal energy from the initial flash lamp pulse dissipates into the surroundings. This issue has party been overcome by pulsing the flash lamp at a high frequency, rather than one large pulse, which provides enough heat to maintain the explosive crystalline boundary propagation. This technique has been shown to result in an additional periodic structure in the material, which can be seen in [Ohdaira, et al. - 2011]. This structure can be used to accurately measure the speed of explosive crystallisation front. It was shown that cat-CVD deposited a-Si and sputtered a-Si results in a crystal propagation speed of 4 m/s. It was also shown that a-Si films deposited via e-beam, had a crystal propagation speed of 14m/s, which is significantly faster than that of a-Si films deposited via other methods. It is likely that this difference also means that there is a change in the mechanisms governing explosive crystallisation in the film. It is supposed by Ohdaira that LPN and LPE may be playing a more significant role in e-beam deposited a-Si films.

The resulting grains from FLC have a high density of electrical defects, which leads to inefficient solar cells. In fact the best solar cell made via this process has a Voc of 210mV, and an overall efficiency of 0.606%. So there is a considerable amount of work needs to be carried out to optimise the FLC process, and subsequent defect passivation and annealing.

The most significant drawback of the process, preventing FLC from being adopted by CSG, is that a Chromium layer (~200nm) must be deposited on the substrate before the a-Si precursor film is deposited, to prevent delamination of film. The Chromium layer is not transparent, which means that any resulting solar cell must work in a substrate configuration, as opposed to a superstrate configuration, which is one of the main advantages of creating a solar cell directly on glass. In recent experiments, the use of a

- 25 - chromium layer is not required on e-beam deposited a-Si films to prevent delamination, although further work must be done to further explore this [Ohdaira.et .al - 2011].

- 26 -

1.6 Experimental FLA Parameters In previous sections, the Arrhenius equation has been shown to be a suitable theoretical approach that indicates FLA is a feasible method for thermal defect annealing in Silicon. Examples of successful defect annealing and dopant activation in wafers, and Flash Lamp Crystallisation has also been demonstrated. However, before the capital outlay required to buy or build FLA equipment can be justified, it had to be shown that FLA could be successfully used to anneal the defects found in our thin film Si solar cells. This meant carrying out experiments in collaboration with an external third party. There were only a limited number of possible collaborators on this project, who had flash lamp equipment capable of pulse intensities and durations capable of FLA. A list of equipment manufacturers and research institutions working with Xenon flash lamp equipment is given in section 1.7.1.

At this stage, the investigation into FLA focused on the feasibility of FLA as an annealing technique capable of replacing the RTA process. Optimisation of the FLA process can be done at a later stage when the possible range of parameters has been narrowed.

1.6.1 Preheat Temperature Early experiments showed that Flash lamp heating from room temperature resulted in significant damage, and made FLA non-feasible without first preheating the sample above the glass transition temperature (Tg). Below Tg the glass primarily used in these investigations (Borofloat 33) has a coefficient of thermal expansion (CTE) similar to Silicon. However the CTE of Borofloat 33, as with all glasses, increases at temperatures above Tg, leading to a CTE mismatch between the Silicon and glass substrate. Because of the difference between the CTE of glass and Silicon above Tg, there is thermally induced stress which leads to cracking and crazing of the Si film.

The preheat temperature is an important factor in FLA processing of Si thin film on glass. Three preheat temperatures were investigated, 600°C 700°C, and 800°C. The samples were brought from room temperature, to these temperatures within 20 seconds, thus giving a minimum heating rate of 34°C per second. Although heating to 600°C and 700°C causes stress within the Si film, due to a difference in the coefficient of thermal expansion (CTE), our experiments have shown that this does not result in any

- 27 - cracking or crazing of the film. The CTE of Borosilicate glass and Silicon is actually very close below the glass transition temperature (Tg), as shown in Figure 3. Whatever stress is accumulated in the preheating stage, around 80% of this stress is dissipated by plastic deformation of the glass within 20 seconds of sample reaching 600°C [Brazil - 2009]. The time for 80% of the stress to be dissipated by plastic deformation, for a preheat temperature of 700°C is at least 2 second, which is an order of magnitude higher than at 600°C.

Relative Elongation – Silicon – Borofloat Glass - Pyrex

Figure 3, shows the relative elongation of Borofloat 33 glass from Schott, vs. the elongation of Silicon. We can see that there is only a very minor difference in thermal elongation between the two materials over the give temperature range.

Immediately after the flash lamp pulse, the temperature of the film and substrate quickly (10’s of milliseconds) reaches a stable temperature of a few 100°C lower than the peak temperature. At this point the power to the preheat lamps is turned off, and the sample cools to room temperature in a little over 5 minute. This means that the Si film cools through the glass transition temperature very fast. This rate of cooling is much faster than that used by Schott in the manufacturing of Borofloat 33, which is a slow as 14°C/minute. The implication of this fast cooling rate is that the glass does not cool uniformly, or at the same rate as it had during the manufacturing process. From glass forming theory, the density of the resultant glass is dependent on the rate at which it - 28 - cools through the glass transition temperature. The result is that the volume of the glass could increase during the process, leaving a stress in the Silicon film that will be ‘frozen in’ as the sample drops below the glass transition temperature (Tg). No measureable effect was seen in the experiments, from altering the rate of cooling from the preheat temperature. But in future experiments, where positive levels of annealing have been achieved, this phenomenon should be kept in mind.

In regard to the level of annealing achieved during the FLA process. Virtually the only factor that could clearly be linked to an improvement in the Voc, was the preheat temperature. It was found that only samples with a preheat temperature of 700°C or 800°C achieved a detectable level of annealing. Samples annealed with a preheat temperature of 700°C, showed a an increase in Voc, and samples annealed with a preheat temperature of 800°C showed a significantly higher PL signal regardless of the pulse duration (See section 1.8.1.5 below). The Voc of samples preheated to 600°C or not preheated at all showed no increase in Voc. Samples processed with a pulse energy theoretically high enough to achieve annealing were so badly cracked and delaminated, that a Voc measurement was not possible.

1.6.2 Pulse Width Four variations of pulse width were investigated in this set of experiments, 3 millisecond Gaussian pulse, 20 millisecond Gaussian pulses, 20 millisecond structured pulse, and a 40 millisecond pulse. The Gaussian shaped pulse is the pulse produced with a simple forming network, when discharged through a flash lamp. The structured pulse is produced using a more complex pulse forming network, and is intended to hold the peak temperature for a longer period of time.

The 0.4 millisecond pulse was investigated in collaboration with Matson Tech, while all other pulse durations were investigated with HZDR. The short pulse duration was expected to not be sufficient to anneal the defect in the material completely, but the results of the few tests conducted with Matson Tech were interesting. The details of the experiments and the results are discussed in section 1.8.

The 3 millisecond pulses have the advantage of being over a relatively short timescale, which reduces the pulse energy required to achieve the desired annealing temperature, there is also less thermal energy in the glass substrate once the pulse energy has diffused

- 29 - from the Si Film. This leads to an overall reduction in the thermally induced volumetric expansion of the glass relative to longer pulse durations. However, the 3 millisecond pulse has the downside of creating a larger thermal gradient through the depth of the glass, which may add to stress. Also, the amount of annealing achieved is proportional to the temperature achieved, and the duration of the heating. The 3 millisecond pulse may not have an adequate duration to achieve the desired level of annealing.

The 40 millisecond pulse is the maximum pulse duration achievable with the FLA system used in this set of experiments. The intent of using this pulse duration was to see if there was any benefit achieved in the level of defect annealing achieved, or a reduction in damage, from increasing the duration of the heating pulse. The energy density available from the 40 millisecond pulse configuration was barely enough to cause damage in the Si film, and as expected that the level of annealing observed from the 40 millisecond pulse experiments was not high.

The 20 millisecond pulse is approximately half way between the 40 millisecond pulse and the 3 millisecond pulse. This duration was investigated to see if a trend in the level of annealing could be observed. The results are discussed in detail in section 1.8, but no trend relating to pulse duration was observed.

The structured pulse was only achievable over a 20 millisecond duration, thus there was no comparison between two different duration structured pulses. However, we can compare the effects of annealing with a 20 millisecond structured, and 20 millisecond non-structured pulse. The structured pulse is closer to a heating profile that would lead to a constant peak temperature for the duration of the pulse. A more adequate pulse structuring may be investigated in the future if available.

1.6.3 Pulse Shaping

1.6.3.1 Temporal Pulse Shaping The 20 millisecond structured pulse is an example of temporal pulse shaping, aimed at altering the heating and cooling profile of the sample to reduce stress leading to cracking. No effect of altering the shape of the 20 millisecond pulse was observed, and this is most likely due to the fact that the heating cooling rates were still far outside the optimal pulse duration required to eliminate damage in the Si. Some work on altering the temporal flash lamp characteristics has been investigated for annealing Si wafers by - 30 -

Aoyama et al. with favourable results being obtained. These FLA pulses were used to anneal defects in ion implanted Si wafers [Aoyama, et al. - 2009], but the same techniques could be applied to Si thin films, once a suitable pulse duration has been found.

One possible way of reducing the thermal gradient is to have a preheated substrate, however the sudden rise in temperature that results from the flash lamp pulse is still present. A more appropriate way to control the thermal gradient during flash lamp annealing is to control the temporal light intensity coming from the Xenon flash lamps. It is possible that a combination of preheating and temporal pulse shaping is required to achieve a sufficient level of defect annealing from FLA.

Above the glass transition temperature, glass is especially sensitive to the rate of heating and cooling. This is due in part to the viscoelastic nature of the material, and the cooling rate dependent structural relaxation of the material. The viscoelasticity of glass is temperature dependent, with a higher rate of stress relaxation occurring at higher temperatures. A simple qualitative understanding of this increased viscosity with temperature, allows us to theorise that a slow heating/cooling rate is required at lower temperatures. The ideal pulse shape would take this into account by inducing a lower heating/cooling rate at lower temperatures, and a higher rate at higher temperatures. The influence of altering the pulse duration and intensity and shape on the stress induced in the film and substrate is covered in Chapter 2. Unfortunately, experimental verification of altering the heating rate over this time scale is not possible with currently available equipment.

Because this equipment is not available, the equipment required to generate the pulses was designed. The details of the design are covered in section 1.7, but a short discussion on the pulse shaping component of the design is given here. Controlling the pulse shape of a single lamp, via the electrical power dissipated across an arc can be achieved with a Pulse Forming Network (PFN). After a lamp is triggered, the fill gas on the lamp is ionised, and the resistance of the lamp drops from almost infinity to almost zero, in a few microseconds. After the gas is ionised, electricity will flow through the lamp as fast as the power supply, or charged capacitors will release the energy. It is shown later that with appropriate choices of capacitors and inductors in the PFN, a broad range of pulse durations can be achieved. - 31 -

A practical method to control the temporal pulse shape of the intensity falling on the substrate is to have control over the triggering time of a bank of lamps. In this way, one lamp can be fired at a different time to the other lamps in the system. With independent triggering of each lamp, then the time scale of the pulse can also be altered to multiples of the pulse duration of a single lamp. Figure 4 (a) and Figure 4(c) shows how short/long pulse widths may be achieved by simultaneously/independently triggering the lamps. Figure 4 (b) shows how the thermal gradient may be altered by triggering individual lamps, before/after the main heating pulse.

Possible Temporal Pulse Profiles

Figure 4 shows the possible temporal pulse changes that could be made with independently triggered lamps. (a) shows how the overall pulse duration may be extended, (b) shows how a reduction in the thermal gradient may be achieved by triggering lamps before and after the main energy dissipation, and (c) shows how each pulse may be triggered simultaneously, which is the shortest pulse duration that may be achieved. The above graph assumes that the pulse duration of a single pulse is 5 ms.

Temporal pulse shaping could also include a succession of multiple pulses which was investigated by Ohdaira for flash lamp crystallisation [Ohdaira.et .al - 2011]. This technique pulses the lamp at frequencies of 1 – 10 kHz over a millisecond duration. This technique allows a more uniform heating profile than one continuous 20 millisecond pulse, and makes the crystal growth more uniform over the whole film area.

1.6.3.2 Spatial Pulse shaping Spatial pulse shaping is simply varying the light intensity across the surface of the sample. This can be achieved by focusing light on certain areas of the sample, or by physically shading certain areas of the films.

- 32 -

This modulation could be altering the intensity profile from uniform, to periodic in one dimension, or periodic in two dimensions. See Figure 5. These intensity profiles are easily be achieved with series of apertures close to the substrate surface. A simple aperture system allows uniform illumination over an exposed area, while completely blocking direct heating of the rest of the sample. These apertures could consist of straight lines to achieve 1D shaping, or an arrangement of small squares to achieve a 2D shaping (See Figure 5). Once an area of the film has been irradiated and annealing achieved, the aperture could be relocated to shade the previously exposed area and allow heating of the previously shaded area. Thus, the entire sample would still receive direct thermal heating.

Spatial Modulation of Light

Figure 5, shows the possible spatial light modulation that may be done to a Flash lamp pulse with simple lenses. The advantages of spatial pulse shaping would include, limiting the build-up of thermal stress across the entire sample, and it would reduce the out of plane deflection of the sample induced discussed by Smith et al. [Smith.et .al - 2006]. For FLA on wafers periodic shading of the wafer during FLA would significantly reduce the wafer curvature cause by FLA processing, which has been shown to result in cracking [Smith, et al. - 2006].

2D pulse shaping was achieved in our investigation by using 10 x 10 mm, and 20 x 20 mm sections of films to physically block light from hitting the target sample. The masking was arranged in a similar fashion to that shown in the ‘2D modulation’ of Figure 5. This left areas of 10 x 10 mm and 20 x 20 mm exposed to flash lamp irradiation. The results of this masking are discussed further in section 1.8, but

- 33 - qualitatively we can say that periodic masking of flash lamp light did not serve to increase the flash lamp pulse energy density able to be deposited on the Si film before damage occurred.

Masking of the sample outlined in Figure 6 where the edges and centre of the sample were shaded was attempted as part of the spatial light modulation investigation. It was found that the cracks resulting from this masking pattern run radially from the centre of the film, as can be seen in Figure 7 and Figure 8.

Shading of Samples Used in Experiment

Figure 6, (a) shows the shading used in the experiment that caused the damage shown in Figure 7, and (b) shows the shading that caused the damage in Figure 8. The dotted line shows the edge of a 5cm x 5cm sample, with a 0.5 cm edge shading. The centre shading in (a) is 2cm x 2cm, and the centre shading in (b) is a 1cm x 1cm square.

- 34 -

Damage in FLA Samples with Shading on Edge and Centre of film

Figure 7 shows the damage resulting in the thin film Si by irradiating the sample with the mask shown in Figure 6 (a). The cracks predominantly occurred radially from the centre of the sample in each direction. The method by which the cracks were imaged makes the cracks at the top and bottom of the sample show up poorly in this image.

Damage in FLA Samples with Shading on Edge and Centre of film

Figure 8 shows the damage resulting in the thin film Si by irradiating the sample with the mask shown in Figure 6 (b). The irradiated area is larger than that in the above image, and although a significant number of the cracks have the same radial direction, there are more cracks in other directions too.

- 35 -

1.6.3.3 Edge Shading Edge shading of the samples is covered here because it is a form of spatial light modulation, or shaping. Also, the change in cracking observed when edge shading is implemented is shown here.

Early experiments into FLA showed that the first stages of damage to the films were cracks originating from the edge of the sample (See Figure 9). To overcome this problem, physical breaks were laser scribed into the film, but instead of limiting the propagation of the cracks, it simply acted as a source for new cracks (See Figure 10). The most effective way to prevent these cracks from originating was to physically block the FLA pulse light from reaching that area of the film. This is a form of spatial light shaping, and completely eliminated cracks from occurring at the edge of the sample. This simple technique increased the energy with which our samples could be irradiated before damage would occur. The cracks observed in samples with edge shading were still prominent at the edge of the irradiated area, where a large thermal gradient in the film exists. In contrast to the cracks induced with laser scribing, these cracks run parallel to the shading region, which can be seen in Figure 11.

FLA induced Cracks originating at Edge of sample

Figure 9 shows cracks that originated from the edge of the sample during FLA processing

- 36 -

FLA Induced Cracks originating from laser scribed lines

Figure 10 shows cracks originating from the laser scribed line intended to prevent their propagation. The crasks can be seen propagating from the laser scribed line on the left and from the line at the top.

Cracking Parallel to shaded edge – Dense Cracking in Centre of Film

Figure 11, shows cracks running parallel to the edge of the shaded edge region. The cracking in the bulk of the sample is still very dense, but no cracks originated at the edge of the sample. Only after cracks form in the centre of the film do cracks around the edge of the shaded area begin to form, suggesting that cracks no longer originate at the edge.

- 37 -

1.6.4 Film Thickness Varying film thicknesses of 0.5 µm, 2 µm, and 6 µm were investigated to deduce any trend in the level of annealing or of level of damage to the film. It was assumed that an increased film thickness would give added strength to the film increasing the energy density that could be deposited on the film before damage occurred.

The experiments showed that a 0.5 µm film did not absorb enough light to reach a high enough temperature for annealing (or damage) to occur. The 2 µm films are the standard thickness for CSG samples, and constituted to majority of the samples investigated. The 6 µm films showed no increase in the level of annealing, or any increase in the energy density that could be irradiated on the sample before the onset of damage. Films thicker than 6 µm were not investigated as there is no practical use for low lifetime pc-Si films of this thickness, and the results would have no real application.

1.6.5 Multiple Pulse FLA Multiple FLA pulses were pursued to investigate whether or not the annealing achieved by a single FLA pulse was cumulative. Multiple pulse experiments were first conducted at different energy densities, with the main focus being to find the damage threshold for each set of parameters. Analysis of these samples showed that some had an increase in the Voc similar to those processed with a single FLA pulse but the density of cracking was reduced. The main purpose of these samples was to investigate damage, and so all samples in this category had a significant amount of damage.

Subsequent investigation showed that multiple pulses below the damage threshold failed to show any increase in the level of annealing. It was then theorised that the increasing series of pulses served to create stress release points in the film at the exact points where it was require, thus allowing higher energy pulses to cause less damage. Although this technique allowed us to achieve annealing on samples with a cracking density low enough for us to be able to measure the voltage, the technique is not feasible in a production setting. The actual Voltages measured from multiple pulse FLA are clearly marked as such in the results section.

- 38 -

1.6.6 Glass Substrates Borofloat 33 (Borosilicate) glass from Schott is the glass substrate used predominantly in these experiments. This is the most common glass used for Si on glass experiments because of the similar coefficient of thermal expansion (CTE) between the glass and Si below temperatures of about 550°C. Our experiments showed that FLA induces damage to the Si film, but no damage to the borosilicate substrate was observed.

Soda-lime glass was also investigated as a substrate, as this is a significantly cheaper option than borosilicate glass. The reason it is not used as a standard in Si on glass applications is because the CTE is much higher than in borosilicate glass, and results in stresses in the film. Our investigation showed that a lower level of annealing was achieved on soda-lime glass relative to borosilicate glass. The soda-lime glass also showed a high degree of sensitivity to the thermal processing it experienced, with brittle fracture occurring with very little pressure after the FLA process.

Phase Separation in Soda-Lime glass

Figure 12 shows evidence of phase separation within the soda-lime glass. This image is approximately 240 µm high by 350µm Another negative impact of using soda-lime glass is evidence of phase separation, (see Figure 12). Phase separation is the when the calcium rich and silicate rich components of the glass clump together. This phase separation adds non-uniformity to the mechanical properties of the glass, which is most likely a contributing factor to the increased fragility. Modelling of the FLA process is also made inaccurate with soda- lime glass as phase separation makes the material properties deviate from those predicted in glass theory, such as Thermo-Rheological Simplicity (TRS). Modelling of - 39 - the FLA process is more realistic on borosilicate glass as no phase separation was observed in this glass. The details of the modelling are covered in Chapter 2.

1.6.7 Glass Texturing The first round of experiments also investigated the effect of a textured glass substrate. The glass substrate was abraded prior to deposition of the thin film silicon, which results in a microstructure at the glass-Si interface, and at the Si-Air interface. Other methods of light trapping, such as micro beads were not investigated here.

Glass texturing is employed in thin film solar cells as a method of light trapping, to increase the path length of the light inside the film, thus increasing light absorption. However, topographical variation of the silicon surface, has an effect on the mechanical properties of the Si film, and is a source of stress concentration points [Brazil - 2009].

So in theory, stress in a textured film may be concentrated at a point, and cause failure, where an equivalent amount of stress on a planar Si film would remain below the damage threshold. The experiments did reveal that textured films were damaged at a lower flash lamp energy density than a planar Si film under the same conditions. Voltage measurements could be taken on planar Si films which had a pulse energy density up to 58 J/cm2 (20 ms), while textured samples could only be flashed with a pulse energy density of 42 J/cm2 (20 ms) before dense cracking prevented voltage measurements being taken.

On first inspection this observation is consistent with the theory of stress concentration points in the silicon for the glass texturing. However, the method of heating the films is by absorption of visible and IR light, which is higher in textured films, compared to planar films. So although we did see an increase in the damage threshold of planar Si films compared to textured Si films, this could be accounted for by the increased absorption of the film, not by stress concentration points caused by the texturing itself.

In fact the results of the FLA experiments showed a higher level of annealing present in the textured samples compared to planar samples. This may suggest that higher temperatures were reached in the textured samples, implying that they are better able to resist cracking induced by FLA relative the planar samples. More experiments will need to be conducted before a conclusion can be drawn on whether textured or planar samples are more appropriate for FLA. - 40 -

1.7 Equipment for FLA

1.7.1 Commercially Available FLA Equipment One of the first steps in investigating FLA is finding out what equipment is commercially available for the application. A summary of these equipment manufacturers and research institutions is given in Figure 3 below.

Company Pulse Duration (milliseconds) Pulse Area (cm x cm) Xenon Corp. 0.2 – 2 2 x 30 Mattson Tech. 0.1 – 2.5 30 x 30 DTF Technology 1 – 20 15 x 15 Ushio 5 – 20 2 x 2

Table 3, shows the organisations manufacturing pulsed flash lamp systems. The table also shows the range of pulse durations, pulse energies, and irradiation area typical of equipment from these organisations. There are two notable absentees from the above list, which are Perkin Elmer and Heraeus Noblelight. These have been omitted because they are manufacturers of flash lamps, but not of turnkey systems for FLA applications. Also, the pulse energy density capable from each organisation’s equipment is not listed, as this parameter is strongly dependent on the pulse duration, and cannot be compared simply. As the typical application of flash lamps with pulses of the millisecond scale is semiconductor processing, the pulse energy density of each organisation’s equipment is typically high enough to perform FLA on wafers. This energy density requirement for FLA on wafers is typically or the same order, or higher than the damage threshold of the thin film Silicon under consideration.

The first thing to note, is that the maximum possible pulse duration of any commercially available equipment is 20 milliseconds. This is significantly less than the heating duration predicted by the Arrhenius plot given in section 0 of this Chapter. It was apparent at this early stage, that if FLA experiments of pulse durations longer than 20 milliseconds were successful in annealing the electrical defect within the Silicon film, then the entire FLA system would have to be built in-house, or as a custom job in collaboration with one of the manufacturers listed above. The design of FLA equipment for the purpose of defect annealing in Si thin film on glass is given in section 1.7.3.

- 41 -

1.7.2 Equipment Available for Preliminary Experiments The FLA equipment at JAIST is manufactured by Ushio, and is used primarily by Ohdaira to investigate Flash Lamp Crystallisation. Unfortunately, JAIST did not show much interest in collaborating with UNSW in the investigation of defect annealing. This was probably due in part, to an exclusivity agreement between JAIST and Ushio, who were co-developing the FLA equipment.

Research Organisations Pulse Duration Pulse Area (milliseconds) (cm x cm) Japan Advanced Institute of Science and Technology 5 – 20 2 x 2 (JAIST) Helmholtz-Zentrum Dresden-Rossendorf (HZDR) 0.8 – 80 10 x 10

Table 4, shows the two main research organisations of interest in FLA. HZDR are a research institution based in Dresden Germany, and have FLA equipment that was built in-house. The group there, headed by Prof. Skorupa were willing to participate in FLA experiments with UNSW. When the preliminary FLA experiments began, HZDR were only capable of a maximum pulse durations of 20 milliseconds. For this reason, the first and second round of experiments, were conducted with a maximum pulse duration of 20 milliseconds. At this stage, there was no evidence to suggest that 20 milliseconds would result in a higher level of annealing than other pulse durations. Although we believed that loner pulse durations would result in a higher level of annealing, it was decided that we should take advantage of the shorter pulse durations offered by HZDR to see if a trend toward longer pulse durations could be attained. Although initial planning aimed at a pulse duration of 5 milliseconds, 3 millisecond experiments were possible with the HZDR equipment, and so this pulse duration was pursued. By investigating shorter pulse durations we could also eliminate short pulse durations from future experiments, or refocus our attention to this parameter space.

The process of organising, performing and analysing results of the preliminary FLA experiments with HZDR was a lengthy one. In preparation of positive preliminary results, and anticipation of wanting to investigate longer pulse durations further, FLA equipment for defect annealing in thin film Si on glass was designed.

- 42 -

1.7.3 Equipment designed for FLA on Thin Film Silicon Third party equipment showed some level of annealing, but at the cost of a high level of damage. For FLA parameter space to be investigated further as a feasible replacement for belt furnace annealing, customised equipment must be designed and built.

1.7.3.1 FLA Lamp Characteristics Designing flash lamp equipment was done primarily under the guidelines, and specifications given in the document ‘High Performance Flash and Arc Lamps’ from Perkin Elmer, and ‘The Lamp Book’ from Heraeus Noblelight. These two books contain all the standard equations for determining lamp parameters, such as lamp impedance (K0), voltage and current characteristics/requirements, and basic guidelines for designing appropriate pulse forming networks (PFNs). The motivation for commercial organisations to release this information, is in part to promote their own range of flash lamps, and make potential users more competent and comfortable with the technology. For a more complete overview, and equipment specific information, then the reader should refer to the above mentioned texts, as only the relevant equations and information pertaining to FLA are given here.

Equipment Minimum Maximum Units Parameter Area 5 x 5 cm Pulse Energy Density 20 400 J/cm2 Pulse Duration 5 100 Milliseconds Uniformity >95 %

Table 5 shows the minimum and maximum parameter space required to investigate FLA on equipment built in-house. Before designing FLA equipment, we must first establish the requirements of a system for this application. From the four basic requirements given in Table 5, and a few assumptions, a number of equipment parameters can be deduced. These quantities, and assumptions made are given in the table below.

- 43 -

Equipment Equation Value Assumptions Parameter ρ Current 650 Assuming lamps with an inner bore (Amps), (per diameter of 0.7 cm. Also assuming lamp) that the most efficient current density from the lamp is 2300 A/cm2 [Goncz, et al. - 1966]. At higher current densities the absorption coefficient of Xenon increases and reduces the efficiency [Oliver, et al. - 1971]

Lamp K 9.1 Assuming a lamp diameter of 0.7 cm, Impedance P a lamp length of 5 cm, and a lamp fill 1.28 .. 1/2 450 (K0)( ) pressure of 450 Torr. Lamp Voltage 272 This value relies only on assumptions K.I made above. Required 200 This value uses the values given in Energy Storage Table 5, and assumes that the in Capacitors conversion of electrical energy to (kJ) light is 50 %, and that 50 % of that light is absorbed by the Silicon film.

Capacitance 1 1.6 This is the capacitance required to Required 2 pulse all lamps in the illumination (Farads) area. We will see later from simulations, that the voltage drop across the lamp is much lower than that across the capacitors. (Assume initial

500 )

Table 6, covers the assumptions, equations and calculated values needed to estimate FLA equipment parameter values. The choice to use Xenon flash lamps with an inner bore diameter of 0.7 cm was made for a number of reasons. Firstly, using a number of lamps over the area would result in

- 44 - a higher uniformity in illumination. Secondly, multiple lamps could be switched on sequentially to increase the possible pulse length of the system.

One of the main assumptions made is that the optimal current density of the lamp is 2300 Amps per cm2. This recommendation can be found in posts and blogs by Don Klipstein (donklipstein.com), and Wikipedia (wikipedia.org/wiki/Flashtube). This current density is optimal because the plasma created inside the lamp is considered ‘grey body’. This means that the plasma emitting the light is also transparent to that light, giving the greatest possible conversion efficiency from electrical energy to light.

1.7.3.2 Physical and Optical Setup. With the lamp characteristics determines, this section focuses on the physical and optical setup. The preliminary experiments showed that preheating of the samples to a temperature of at least 600°C would be required for FLA to be possible on our samples. For this reason, the samples will sit on a heater at the bottom of the setup. The side of the setup will be made of aluminium with a mirror finish, to make a light integration box. Aluminium will be used because it can be made optically flat to reduce light loss, can be machined easily, and can withstand the temperatures that are experienced inside FLA setup. This would effectively redistribute the light to make it uniform at the sample surface, and is more efficient that using a diffuser to the scatter the incoming light. The lamps will be separated by only 1 mm so that there is no contact between them while pulsing, preventing damage, while allowing the maximum amount of light to be generated. The light emitted above the lamps will be reflected downwards by a large plane reflector. Although early design versions had a structured rear reflector to focus light through larger gaps between the lamps, this is unnecessary because the lamps and fill gas is transparent to the light. A simplified diagram of the FLA setup can be seen in Figure 13 below.

- 45 -

End on view of lamps Side view of lamps

Figure 13, shows the physical setup of the FLA test setup. 1 = Bottom row of Lamps The lamps are end on in the top image, and side on in the bottom image. The images are a large simplification of the 2 = Top row of Lamps FLA equipment, but convey all the necessary features of the proposed equipment. 3 = Reflective Surface 4 = Si on Glass Sample 5 = Preheat Stage

1.7.3.3 Pulse Forming Network (PFN) To achieve the required pulse duration and pulse shape, a pulse forming network (PFN) had to be designed. The features of 14 PFN’s shown in the work of Rim [Rim, et al. - 2003], are potential candidates for FLA. A review of these PFNs for the application of thermal flash processes was done by Barak [Barak - 2004]. This review covered the optimal design of the PFN, as well as some of the inefficiencies encountered during implementation.

Barak uses a SPICE program to simulate various PFN and obtain traces of the temporal pulse shape coming from the lamp. The PFN considered optimal in Barak’s review results in a pulse duration of approximately 1 millisecond, which is significantly less than that required for FLA. Simulations of the PFN considered for our application we run in Simulink, MATLAB. Within Simulink the current dependent resistance of the lamp can be modelled directly, which is more accurate than the approach used by Barak [Barak - 2004].

- 46 -

Type E Pulse Forming Network with N sections

Figure 14, shows a simple PFN that is most appropriate for the application of FLA. It consists of a number (N) of capacitors in parallel with the Xenon flash lamp, and N number or inductors in series, between the capacitors.

The PFN considered most appropriate for our application is shown in Figure 14. This PFN is one of the most simple found in the work of Rim [Rim.et .al - 2003], but has the advantage of easily being rearranged so that the pulse duration can be altered over a large range. Simulations of the lamp outputs under various operating conditions show that required range of pulse durations outlined in Table 5 is achieved with this PFN configuration. The simulation parameters, PFN configuration, and the results of the simulations are shown in figures Figure 15 and Figure 16.

The number of LC segments in the PFN () is linearly proportional to the pulse width (in milliseconds) by equation 3;

. 3

- 47 -

Lamp Pulse Output – 1 to 5 PFN Sections

50000 45000 40000 35000 1 Segment 30000 2 Segments (Watts) 25000 20000 3 Segments

Power 15000 4 Segments 10000 5 Segments 5000 0 024681012 Time (milliseconds)

Figure 15, shows the output of a lamp, with 1 to 5 LC segments.

Lamp Pulse Output – 5 to 40 PFN Sections

50000 45000 40000 35000 5 Segments 30000 10 Segments (Watts) 25000 20 Segments 20000 30 Segments Power 15000 10000 40 Segments 5000 0 0 20406080 Time (milliseconds)

Figure 16, shows the output of a lamp, with 5 to 40 LC segments.

- 48 -

Pulse Width vs. No. of LC Segments

90 80 70 60 50

(milliseconds) 40 30 20 Width 10 0

Pulse 0 5 10 15 20 25 30 35 40 No. of LC Segments

Figure 17, shows the relationship between number of LC segments with the pulse width from the lamp

With this simple design feature a system capable of delivering constant pulse energy density over a large pulse width range is easily achievable.

Adjusting the intensity of the flash lamp pulse is achieved by altering the initial voltage on the capacitors, when the lamp is triggered. Figure 18 to Figure 20 show the power, voltage and current variation, when the initial voltage of the capacitors is changed from 300 to 500 V.

- 49 -

Lamp output power during pulse

50000 V = 300 V 40000 V = 400 V

30000 V = 500 V

20000 (Watts)

10000 Power 0 0 5 10 15 20 Time (ms) Figure 18 shows the power output of the lamp, given a PFN shown in Figure 14 with 10 segments, and an initial Voltage across the capacitors from 300 V to 500 V.

Voltage Across Lamp during pulse

180 160 V = 300 V 140 V = 400 V

120 V = 500 V 100 80 Voltage 60 40 20 0 0 5 10 15 20 Time (ms) Figure 19 shows the Voltage drop across the lamp, given a PFN shown in Figure 14 with 10 segments, and an initial Voltage across the capacitors from 300 V to 500 V.

Current Across Lamp during pulse

350 300 V = 300 V 250 V = 400 V

200 V = 500 V 150 (Amps) 100 50

Current 0 0 5 10 15 20 Time (ms) Figure 20, shows the current through the lamp, given a PFN shown in Figure 14 with 10 segments, and an initial Voltage across the capacitors from 300 V to 500 V.

- 50 -

It should be notes that if the initial voltage across the capacitors is 500 V, the voltage across the flash lamp never exceeds 160 V. This is due simply to the dynamics of the PFN, and should be taken into consideration in calculations of the maximum voltages across the lamp.

The currents and voltages of the lamps given above are appropriate for small bore diameter lamps. They are significantly less than those used in other flash lamp annealing equipment, which is designed for larger area irradiation and thus uses larger bore diameter lamps.

Building the flash lamp equipment designed above was not achieved in the time available for this investigation. However, to explore the FLA parameter space further, building equipment for the above design principles will be the first step. This is the reason why a section on design was included in this thesis.

- 51 -

1.8 Results of FLA experiments Section 0 showed that the pulse duration theoretically required to achieve the desired level of defect annealing is of the order of several 10s to 100s of milliseconds. The available pulse durations for experimentation cover the 0.4 to 40 millisecond range, and the results of these experiments are covered here. The results are divided into two sections covering the level of annealing achieved, quantified by the Open Circuit voltage (Voc) and the level of damage resulting from the FLA process.

The primary aim of the first round of experiments was to find a set of processing parameters that reduced or eliminated cracking and crazing of the Si film during FLA. To this end, each sample type and processing parameter combination was first flashed with gradually increasing pulse energies to find a pulse energy density where damage occurred. From a maximum pulse energy, the lamp voltage was reduced 100 V and then the same combination of parameters was used on another set of samples. 100 V difference in the lamp voltage equates to approximately 5 J/cm2 difference in pulse energy for the 20 ms pulse, and 2 J/cm2 difference for the 3 ms pulse. By investigating the FLA process in this way, we ensured that Voc and Sheet Resistance data was obtainable from most samples.

As well as removing defects, FLA is expected to increase dopant activation which will also result in increased Voc. The increase in dopant activation could be characterised separately by observing a reduction in sheet resistance, measured by a 4 point probe. However after FLA, no reduction in sheet resistance was observed in samples that could be measured. Samples that would be more likely to have shown a reduction in sheet resistance were too badly cracked to fit the 4 point probe on any one section of film.

To be able to relate all the various pulse durations the peak temperature attained during the FLA pulse was used. In the following graphs the temperature is an estimate of the actual peak temperature achieved, calculated using a formula supplied by HZDR who carried out the experiments. The formula used is that used to predict the peak temperature of thick Si wafers undergoing FLA in this particular setup and is as accurate estimation as could be sourced. Firstly, the pulse energy density is calculated from the Flash lamp voltage, using the below formula;

/ . 4 - 52 -

2 where E/A = pulse energy density in Joules/cm , C1 is a constant which equals 12 for a 20sm pulse and 4.43 for a 3ms pulse, and U is the Voltage set across the lamp. If we consider that the energy stored on a capacitor proportional to the square of the Voltage across the capacitor, then the energy density given by the above equation is a good approximation.

With this pulse energy density we can then predict the peak temperature of the sample from the equation;

5 where Tpeak is the peak temperature reached during the FLA pulse, C2 is a constant equal to 20.76 for a 3ms pulse and 8.68 for a 20ms pulse. These values were derived from Simulations presented in Chapter 2, where parameters such as reflection, film thickness and glass properties were taken into consideration. It can be seen in Figure 44 that the peak temperature is indeed linearly proportional to the input pulse energy density for a wide range of pulse durations.

The temperature reached in the 0.5 µm film would not absorb as much of the pulse energy as the 2 µm films, and similarly, the textured samples would trap more of the pulse energy than the planar samples. The enhanced light trapping ability would lead to an increased peak temperature reached, and potentially a higher degree of defect annealing achieved. Thus the plotted temperature for each type of sample can only be taken as a guide. Similarly the pulse energy density for the 3 ms pulse and the 20 ms pulse are different, but because of the varying time scale over which the energy is deposited, the peak temperature achieved may be the same. This makes it hard to compare 3 millisecond pulses with 20 millisecond pulses. This temperature estimation problem also exists when comparing structured pulses with standard pulse shaped.

1.8.1 Level of annealing achieved To quantify the level of annealing achieved during the FLA process, each sample was hydrogenated, and the Open Circuit Voltage (Voc) was measured. The measured data is presented in this section.

- 53 -

1.8.1.1 Borosilicate Glass ‐ Planar

Below are graphs showing the Voc vs. flash lamp pulse energy density, for the Planar Si film on BSG. We can see that only one sample achieved an increase in Voc over that of the un-annealed samples.

Voc vs. Pulse Energy

420 BSG‐P‐3ms ‐600°C BSG‐P‐3ms ‐700°C 410 BSG‐P‐20ms gaussian‐600°C 400 BSG‐P‐20ms gaussian‐700°C (mV) BSG‐P‐20ms struc‐600°C 390 BSG‐P‐20ms struc‐700°C 380 Planar‐BSG‐no FLA Voltage

370 Circuit

360

350 Open 18 23 28 33 38 43 48 53 58

2 Pulse Energy Density (J/cm ) Figure 21, shows the Open Circuit Voltage achieved after Flash Lamp Annealing and Hydrogen Passivation vs. the Pulse Energy Density used. Each parameter combination used has a unique marker

Voc vs. Temperature 410 BSG‐P‐3ms ‐600°C BSG‐P‐3ms ‐700°C BSG‐P‐20ms gaussian‐600°C 400 BSG‐P‐20ms gaussian‐700°C BSG‐P‐20ms struc‐600°C (mV)

BSG‐P‐20ms struc‐700°C 390 Planar‐BSG‐no FLA Multi‐pulse Struct‐600 Multi‐pulse 20ms‐600 Voltage

380

Circuit 370

Open 360

350 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 Peak Temperature(°C)

Figure 22, shows the Open Circuit Voltage achieved after Flash Lamp Annealing and Hydrogen Passivation vs. The estimated peak temperature achieved during FLA. Each parameter combination used has a unique marker. The markers with Red outlines have undergone multiple FLA pulses at different pulse energies. The peak temperature shown is that of the highest peak temperature achieved on that sample.

- 54 -

We can see in the above graphs that the 3 millisecond pulses resulted in the superior defect annealing on the BSG-Planar samples. Figure 21 shows that the pulse energy required to achieve this level of annealing was lower than that for the 20 millisecond pulses. However to be able to compare the 3 millisecond pulses with the 20 millisecond pulses, the peak temperature achieved in the cell must be estimated, and this is shown in Figure 22. We can see from this graph, as was expected, the higher defect annealing was achieved at the highest peak temperature achieved.

There is another small peak between 1050°C and 1100°C where the longer pulse durations showed an increase in Voc. This is most likely due to the longer annealing time of the experienced by the sample, even though it was at a much lower temperature.

The decease of the Voc at higher temperatures from this peak is due to the increase in damage to the sample. The measurement of the Voc in these samples became less accurate and increasingly difficult as the density of cracks increased. The damage to the films is covered in section 1.9.

Not included in the above graphs are the results of samples annealed in the final round of experiments. The final round of experiments consisted of only 3 µm planar silicon films on Borosilicate glass, and the aim of the tests was to determine if edge shading and periodic shading of the sample could raise the damage threshold sufficiently to achieve annealing without destroying the Si film. In the final round of experiments, the samples were flashed with a lower pulse energy density than in previous experiments in order to stay below the damage threshold. The results of the experiments showed no significant increase in the Voc of the samples, and were low compared to those shown in the above graphs. The Voc of the samples in the final round of testing was in the range of 280 mV to 320 mV, with no observable trend in pulse energy density or pulse duration. Only preheat temperature showed to be an experimental parameter that altered the level on annealing in the samples from other parameters investigated.

The pulse duration of 40 ms investigated in the last round of experiments showed no significant increase in Voc. However the pulse energy density attainable with the FLA system was not enough to reach the damage threshold of the samples, and thus was not enough to reach the maximum possible level of annealing with a 40 ms pulse. Further investigation into longer pulse durations was not possible because the pulse energy density was also no high enough to achieve annealing in our samples. - 55 -

1.8.1.2 Borosilicate Glass – Textured

The following graphs show the Voc of the FLA experiments conducted on textured Borosilicate Glass (BSG) substrates.

Voc vs. Pulse Energy 450 440 BSG‐T‐3ms ‐600°C 430 BSG‐T‐3ms ‐700°C (mV)

BSG‐T‐20ms gaussian‐600°C 420 BSG‐T‐20ms gaussian‐700°C 410 BSG‐T‐20ms struc‐600°C 400 BSG‐T‐20ms struc‐700°C Voltage 390 Text‐BSG‐no FLA 380 Circuit

370 360

Open 350 340 0 102030405060 2 Pulse Energy Density(J/cm ) Figure 23, shows the Open circuit voltage achieved after FLA and hydrogen passivation vs. The pulse energy density of the flash lamp used to irradiate the sample.

Voc vs. Peak Temperature 450 BSG‐T‐3ms ‐600°C 440 BSG‐T‐3ms ‐700°C

430 BSG‐T‐20ms gaussian‐ (mV) 420 600°C BSG‐T‐20ms gaussian‐ 410 700°C 400 BSG‐T‐20ms struc‐600°C Voltage

390 380 Circuit 370 360 Open 350 340 800 900 1000 1100 1200 1300 Temperature (°C) Figure 24, shows the Open circuit voltage achieved after FLA and hydrogen passivation vs. estimated peak temperature achieved during the flash lamp pulse. It is important to note that this temperature is only an estimation, which is generally lower than those achieved on BSG-Planar samples. However, the greater light trapping ability of the textured cells, means that the actual temperature is most likely higher than that estimated here.

- 56 -

In the above graphs it can be seen that the Voc achieved on textured BSG is higher than that on planar BSG. It is important to note that the approximated temperature shown on the x axis is most likely an under estimation of the actual peak temperature reached during the FLA pulse. This higher temperature would contribute the higher level of annealing achieved, and thus the higher Voc on average. However, this trend is definitely not seen in the above graph (Figure 24). This trend may be explained by considering how the damage to the sample may reduce the Voc or impede the measurement of it.

In contrast to the experiments on planar BSG, a significant increase in the Voc was achieved with the 20 millisecond Gaussian and 20 millisecond structured pulse, not the 3 millisecond pulse. There was also a less clear trends in the data compared to the planar BSG case. The data appears more random, although on the whole a higher level of annealing was achieved with a broader range of experimental parameters.

1.8.1.3 Soda lime Glass – Planar

Voc vs. Pulse Energy

410 SLG‐P‐3ms ‐600°C 400 SLG‐P‐3ms ‐700°C 390 (mV)

SLG‐P‐20ms gaussian‐600°C 380 SLG‐P‐20ms gaussian‐700°C 370 Planar‐SLG‐no FLA 360 Voltage

"Multip‐Pulse 700" 350 340 Circuit

330 320

Open 310 300 10 20 30 40 50 60 70 2 Pulse Energy (J/cm ) Figure 25, this graph shows the open circuit voltage vs. The pulse energy of the flash lamp pulse, for Soda-lime glass.

- 57 -

Voc vs. Estimated Temperature

410 SLG‐P‐3ms ‐600°C 400 SLG‐P‐3ms ‐700°C 390 SLG‐P‐20ms gaussian‐600°C (mV) 380 SLG‐P‐20ms gaussian‐700°C 370 Planar‐SLG‐no FLA Multi‐Pulse‐700 360 Voltage 350 340 Circuit

330 320

Open 310 300 750 850 950 1050 1150 1250 Temperature (°C)

Figure 26, this graph shows the open circuit voltage vs. Peak temperature during the FLA pulse, for Soda-lime glass.

In the above results we can see that the Voc for SLG samples that the level of annealing is lower than both the textured and planar BSG samples. We can also see that the Voc of the samples was lower than that of the BSG samples even before FLA was attempted. The experiments showed that there is little effect of the various processing parameters on increasing the Voc, apart from one sample which showed an increase in Voc of 56 mV, which is higher than any Voc in the Planar BSG samples, and equivalent to the best

Voc increase achieved in the textured BSG samples. This particular sample underwent multiple pulses at different pulse energy densities, and it is possible that the first pulses, which were of lower energy density, created cracks which served as stress release points for the later/higher energy density pulses. It is also possible that each pulse enhanced the amount of defect annealing in the cell. This will be covered in more detail in the discussion section.

1.8.1.4 Samples with no Damage

The below graph shows the Voc vs. Temperature for all the undamaged samples tested. We can see that there were many parameter combinations that didn’t result in any samples that didn’t show any signs of damage. There are many samples that did show no sign of damage, and did receive some level of annealing. The level of defect annealing is less than that of damaged samples that received higher energy density pulses, however this graph best illustrates the fact that only moderate annealing can be achieved in samples with FLA pulses without physically damage the sample.

- 58 -

Voc vs. Temperature (Samples with No Damage)

390 BSG‐P‐3ms ‐600°C BSG‐P‐3ms ‐700°C 380 BSG‐P‐20ms gaussian‐600°C BSG‐P‐20ms gaussian‐700°C BSG‐P‐20ms struc‐600°C 370 BSG‐P‐20ms struc‐700°C BSG‐T‐3ms ‐600°C BSG‐T‐3ms ‐700°C (mV) 360 BSG‐T‐20ms gaussian‐600°C BSG‐T‐20ms gaussian‐700°C BSG‐T‐20ms struc‐600°C Voltage 350 BSG‐T‐20ms struc‐700°C SLG‐P‐3ms ‐600°C SLG‐P‐3ms ‐700°C Circuit

340 SLG‐P‐20ms gaussian‐600°C SLG‐P‐20ms gaussian‐700°C Open Planar‐BSG‐no FLA 330 Text‐BSG‐no FLA Planar‐SLG‐no FLA

320 Red Text = No Samples 800 900 1000 1100 were undamaged Temperature (°C) Figure 27, shows the Open Circuit Voltage vs. Temperature for all samples tested that did not show any visible signs of damage.

Measurement of the Voc is achieved by etching away the emitter of the film in a small section of the sample, and contacting the p and n type material while illuminating with 1 sun. If the cracking in the film is too dense then the cell cannot be contacted, and a Voc measurement cannot be taken. While higher pulse intensity FLA pulses were investigated, the voltage could not be measured on these samples. The trend toward higher Voc with an increase in FLA pulse intensity seen in the results would most likely continue, it measurements were possible.

1.8.1.5 Photoluminescence of FLA and RTA experiments

As well as measuring Voltage (Voc) as a means of determining the effectiveness of FLA as a method of annealing, Photoluminescence (PL) imaging was also measured on some samples. PL imaging is a well-established way of measuring the quality of solar cell wafers, but is relatively new as a technique for measuring the quality of thin films. The use of PL imaging on thin films is covered in more detail in Chapter 3. For the purposes of this section it is sufficient to say that the intensity of the PL signal is proportional to the Voc, minority carrier lifetime and the quality of the Si film.

- 59 -

Although it should be noted, an exact relationship between PL and Voc, has not yet been experimentally shown in these samples.

Photoluminescence imaging has advantages over measuring the Voc of the samples for two reasons. Firstly, PL is non-contact and requires less processing to obtain a measurement. Secondly, the FLA samples were very badly damaged, and finding an area to contact where no crack interrupts the measurement was quite difficult.

PL Signal from samples after RTA & FLA

170 Single Pulse (Below 150 Damage Threshold) multiple pulses 130 multiple pulse ‐ Surface 110 Damage (counts/sec) RTA‐ No FLA 90 No RTA ‐ No FLA 70 Intensity Filter Noise* 50 PL 30 0 102030405060 Pulse Width (ms)

Figure 28 shows the PL signal measured on samples after RTA and FLA and Hydrogenation. The sample that has a high PL signal at 3 ms, has a high amount of surface damage, and hazing, which may explain the high PL signal without an associated high Open Circuit Voltage.

In Figure 28, It can be clearly seen that samples which underwent a standard RTA anneal, and a subsequent FLA anneal did not result in a level of annealing as good as that achieved with just an RTA anneal. The standard RTA process is a belt furnace anneal of the samples at 870°C for over 1 minute, on a belt furnace. It can also be seen that there was some level of annealing achieved with just the FLA step, over that of samples which had neither the FLA nor RTA anneal. The data points in Figure 28 represent all the samples investigated with both FLA and RTA. The reason these samples and the E-beam samples below were analysed with Photoluminescence while earlier samples were not, is because the PL system was not available until very near the end of the FLA investigation. Shortly after the PL imaging system was operational and fully characterised, the camera which records the PL

- 60 - intensity malfunctioned and was not repaired or replaced before the completion of this thesis. This is why PL analysis of earlier FLA investigations was not done.

PL from E-Beam samples after FLA

60 preheat = 800 °C 55 preheat = 700 °C 50 Multiple Pulses Filter Noise * (counts/sec)

40 Intensity 35 PL 30 0 1020304050 Pulse Width (ms) Figure 29, shows PL from samples that have undergone only FLA and Hydrogenation. The Results are separated by pulse duration. E-beam samples are samples where the Si film was deposited via e-beam evaporation. Figure 29 shows the PL intensity from a number of samples separated by preheat temperature and FLA pulse duration. Most e-beam deposited samples were annealed with a FLA preheat temperature of 700°C which is denoted by blue squares in Figure 29. It can be seen that there is only a small deviation of the PL intensity depending on pulse duration, and all other experimental parameters investigated, compared to the difference recorded for samples with a higher preheat temperature. The Green circles in Figure 29 which denote a preheat temperature of 800°C, show a relatively large increase in PL from these samples compared to lower preheat temperatures.

Given that preheat temperature is the only parameter that resulted in a clear increase in the level of annealing, and that the Voc is still quite low, it is possible that the time spent at an elevated temperature during the preheat stage, and not the flash lamp pulse itself is responsible for the increase in Voc and PL intensity.

- 61 -

Voc vs. PL Intensity

1000 FLA Annealed (E‐Beam samples) Belt Furnace Annealed LPCSG Filter Noise *

100 Counts

10 250 300 350 400 450 500 550 Open Circuit Voltage (mV)

Figure 30, shows the PL intensity measured of a number of samples, and is plotted against the measured Voc. It can be seen that there is good qualitative agreement with the Voltage and the PL intensity of the various films investigated. The blue data points represent FLA samples, the red data points represent RTA annealed samples, and the green represent a broad range of processing parameters investigated in relation to LPCSG material. The LPCSG results shown above are to give the reader a sense of PL intensities from other thin film Si, and give some perspective. FLA was not performed on LPCSG material.

Figure 30 shows the qualitative agreement of PL intensity measurements with the measured Voc data. There are other factors, not taken into account, that may explain the spread of data points in each cluster, but the details of the parameters investigated on LPCSG material is not the main focus here. The purpose of including the above graph is to show that there is indeed a relationship between the Voc measured on our films and the PL intensity. This relationship between Voc, material quality, and PL intensity is explained in depth in Chapter 3.

1.8.2 Mattson Tech. Results The results of FLA experiments carried out at Mattson Tech are covered in this section. There were only a preliminary run of 4 samples processed at Mattson, to evaluate the likelihood of successful annealing being achieved with their equipment. These four samples alone are not enough to draw conclusive data from, but interesting trends can be seen in the Voc data of these samples.

There is one advantage of the equipment at Mattson Tech, for our experiments and one disadvantage. The advantage is that Mattson Tech had the ability to preheat samples to 1100°C before applying the FLA pulse. The disadvantage is that the pulse width was - 62 - limited to 0.3 to 0.4 milliseconds. This pulse duration is considerably less than that theoretically required from extrapolation from RTP annealing data at lower temperatures (See section 0).

Heat Profile of FLA at Mattson Tech Heating pulse of FLA at HZDR

Figure 31, shows the difference in the heating profile of the Mattson FLA process (left), vs. the heating process of the HZDR process (right).

The thermal cycle of FLA with the Mattson Tech equipment differed from that at HZDR in that an additional heating step is used between the preheating stage and the FLA pulse. This intermediate heating process occurs over a time span of a few seconds, rather than the millisecond scale of the FLA pulse itself. This is shown in Figure 31 below.

The first thing that we noticed was that all samples showed a Voc much less than that typically achieved with the current RTP (belt furnace) annealing. However, it can also be seen that there is a clear trend to higher voltages with an increase in the peak temperature of the FLA pulse, which can be seen in Figure 32 below.

The experimental parameters investigated are outlined in Table 7 below, along with the measured Voc after FLA.

- 63 -

Experiment Intermediate Temperature Peak Temperature Voc After FLA (°C) (°C) (mV) 1 1100 1100 311

2 1100 1350 323.5

3 1100 1400 354.6

4 1050 1400 365

Table 7 shows the experimental parameters and the measured Voc of the Mattson experiments.

Voc After Mattson FLA

370 360 350 (mV)

340 Voc 330 320 Sample 310 300 1000 1100 1200 1300 1400 1500 Peak Temperature of FLA pulse (°C)

Figure 32, shows the trend of increased Voc with an increase in the peak FLA pulse temperature.

It is possible that the low Voc measured is a result of faults with the hydrogenation process, which was intermittently and unpredictably not working at that time. If this was the case, then the important information would be in the increase in Voc of the samples with increasing peak temperature, rather than the absolute Voc. The above figure shows us that an increase of as much as 55 mV was achieved with an FLA pulse of 0.4 ms, over that achieved with only an intermediate heating pulse.

Another benefit of heating the samples relatively slowly to a temperature of 1100°C before applying the FLA pulse, is that the samples underwent a significantly smaller thermal gradient, and any structural in the glass occurred over the time scale of the pulse. See chapter 2 for a discussion on structural relaxation and the viscoelastic nature of glass. - 64 -

1.9 Damage to Silicon Films FLA was attempted in 2006 before the current investigation commenced. The samples investigated at the time consisted of the same 2µm SPC films on a BSG substrate; however the films at that time had small quartz beads at the Si-glass interface. The effects of stress concentration in the film from the beads was investigated by Brazil in 2009 [Brazil - 2009], and the use of beads as an optical trapping method was discontinued shortly after. Despite not using quartz beads currently, the damage of the samples did give some insight into the failure mechanism we could expect to see in our experiments. Unfortunately, there was no information on the level of annealing that was achieved from FLA in the samples with quartz beads, as all samples were too badly damaged to be able to contact and part of the sample.

Various types of damage seen in thin films are covered by Hutchinson [Hutchinson - 1996]. According to this paper, the failure modes can be divided into two categories; those induced by tension and those induced by compression. Tension induced failure modes are summarised in Table 8, while failure induced by compression is typically limited to film debonding or delamination.

Failure modes induced by tension  Surface Crack,  Channelling,  Substrate Damage,  Spalling, and  Debonding. Table 8 is a list of failure modes observed in thin film materials as given by Hutchinson [Hutchinson - 1996]. Surface cracks are simply cracks in the film only, which do not propagate into the substrate. Channelling is where the cracks propagate laterally through the film, but again do not propagate into the substrate, which is also known as crazing. Substrate damage occurs when damage in the film does propagate into the substrate, and if the damage propagates laterally once in the substrate. Debonding simply describes the delamination of the film from the substrate, which can occur at an edge or near cracks, or in otherwise undamaged areas of the film forming a blister. Debonding and delamination are the two forms of damage that can occur under both tension and compression, according to Hutchinson [Hutchinson - 1996]. - 65 -

In addition to the above mentions modes of failure, FLA has been shown to induce pin holes in the Si film, melting and balling op of the silicon film and phase separation of the glass substrate. Below are normal and microscope images showing examples of the damage which has been observed after FLA processing.

The most common form of failure seen in our samples is cracking, and channelling. Examples of the many types of failure in Si films induced by FLA are shown in the below images.

Fine Surface Cracks Crazing / Dense Pin Holes in Si

Debonding/ Cracking Crazing/ Channelling

- 66 -

Channelling Channelling / Peeling

Rippleing Rippling

Melt Spot (SEM) Lines of dense phase separation in glass

- 67 -

Hazing Delamination / Crazing / Melted Si

The evolution of film damage with increasing FLA pulse energy can be observed in Figure 33. The cracks from low pulse energy densities can be seen to originate on the left most image, and channel progressively inward with increasing pulse energy density. At high pulse energy densities, the cracks become more and more dense, and less or a radial pattern in the cracks can be seen.

Run Glass Thickness Textured Preheat Pulse Width Pulse Shape No Type (µm) (°C) (milliseconds) 10 BSG 2 Textured 700 20 Structured 1 2 3 4

1.7kV≈30.2 J/cm2 1.8kV≈35.8 J/cm2 1.9kV≈41.4 J/cm2 1.6kV - 1.9kV ≈41.4 J/cm2

Figure 33, shows the evolution of the cracking of Si due to varying levels of pulse energy density during FLA. It can be seen that the higher the pulse energy the denser the cracks and the further they propagate toward the centre of the film.

- 68 -

All things being equal, a lower glass transition temperature (Tg) would be better for FLA as more relaxation of the stresses would occur. However soda-lime glass, which has a much lower Tg than borosilicate glass, has shown a higher level of damage in the film and a high level of residual stress in the glass, which shattered easily in handling. Soda-lime glass, as well as having a much lower melting temperature than Borosilicate glass, also has a much higher mismatch of CTE to Silicon compared to BSG. Although the stress of the FLA process may be dissipated much faster than BSG glass at a comparable temperature, the magnitude of the stress is significantly increased.

Also the mismatch in the CTE causes a build-up of stress in the Si film during the cool down phase that cannot be relaxed by viscoelastic glass flow because it is already below the glass transition temperature. Also the soda-lime glass has shown signs of phase separation from the thermal cycling of the SPC process and FLA process. This phase separation which can be seen in Figure 34 below, makes the glass less uniform and more prone to failure.

Phase separation in Soda-lime Glass Substrate

Figure 34 (a) shows a significant amount of phase separation in soda-lime glass (High FLA pulse intensity), and on the right (b) can be seen small areas of phase separation within soda-lime glass. (low FLA pulse intensity).

- 69 -

1.10 Discussion of FLA Experiments Experimentation in FLA as a replacement for the conventional Belt Furnace RTA process has given us greater insight into the millisecond scale dynamics of failure in Si films, and the dynamics of millisecond scale heating and cooling of glass. Unfortunately, experimentation has also shown that currently available FLA equipment is not a feasible replacement for the conventional belt furnace RTA process. The reason for this is primarily that the FLA pulse energy density damage threshold is lower than that required for a sufficient level of annealing to occur. The source of the stresses in the film is the mismatch of the coefficient of thermal expansion between the Si film and the glass.

Longer pulse durations raise a greater volume of the glass substrate to a higher temperature, which increases the stress in the Si film. However from the discussion in section 0 we can see that the Arrhenius like relationship of annealing temperature and duration suggests that a longer pulse duration is required for successful annealing. The longer pulse durations are not available for investigation at this time, so the relevant design principles required to make FLA equipment with an appropriate pulse duration was covered in section 1.7.3.

Of all the parameters investigated, the only parameter which clearly increased to Voc of our samples was the preheat temperature. With a higher preheat temperature, a higher

Voc was achieved, and a low preheat temperature (600°C or below resulted in very low to no annealing at all.

Methods of raising the damage threshold, other than periodic and edge shading, such as adding a SiN to the film were not investigated. Theory suggests that the thicker Si and SiN would be better able to resist cracking during the FLA pulse. Another benefit is that surface damage seen in the Si film may transfer to the SiN, which can be etched off after the FLA process, without adverse effects to the Si.

Early experiments showed that crack in the film originated on the edges of the film and propagated toward the centre via a mechanism called channelling. The initial failure point moved from the edge of the sample toward the centre by shading the FLA light from the Silicon. However this only marginally increased the pulse energy density

- 70 - damage threshold of the sample, and an adequate amount of annealing was still not achieved before the onset of cracking.

Although FLA presented many potential benefits over alternative annealing methods, there are drawbacks to FLA of thin film Si on glass, which have to be considered. The main drawback is that the rapid heating leads to rapid thermal expansion of both the Silicon film and the glass, and the mismatch of CTE between the Si and glass.

The thermal stress between the Silicon film and glass is dissipated by viscoelastic relaxation within the glass, with a higher rate of relaxation occurring when the glass has a higher temperature (lower viscosity). If the heating rate is higher than that which will allow structural relaxation in the glass, then stresses will accumulate within the film, the substrate, and at the interface. The damage threshold for various pulse durations and pulse intensities, the thermal profile within the sample, and stress minimisation is investigated further by simulations described in Chapter 2.

The next Chapter is dedicated to understanding the cause of the stress in the Si film, with the ultimate aim of finding a method to eliminate it altogether. By modelling the process we gain can predict the outcome of longer pulse duration experiments, and whether they are feasible as a replacement for RTA or not. The current round of FLA experiments has shown us the threshold of stress and strain that the film can take, and we can infer the likely hood of success of future experiments by combining this information with the computer model.

- 71 -

Chapter 2

Modelling of Thermally induced Stress/Strain during Sub-second Thermal Annealing

- 72 -

2.1 Introduction and Overview The primary aim of thermal and structural modelling of the Si film on glass is to gain insight into the source of damage to the Si film caused by Flash Lamp Annealing.

It was shown in Chapter 1 that 2 µm pc-Si film on a glass substrate will crack as a result of the FLA process before an appreciable level of electrically active defects are removed. In this chapter, details of a thermal model and a viscoelastic stress/strain modelling are given in this chapter. From these models, estimates of the stress/strain experienced by the Si film and the glass during and after the FLA pulse are given. Also, predictions are made of the stress and strain the would be experienced by the sample under pulse durations longer than those investigated experimentally. These predictions are then discussed in relation to the actual failure observed in the Si film. The actual mechanisms of plasticity within c-Si and pc-Si at elevated temperatures are also discussed, with a focus on how these mechanisms manifest during the FLA process. A discussion of the viscoelastic nature of glass is also given, as this plays a significant role in stress relaxation in our experiments.

- 73 -

2.2 Relevant example of FEM modelling

2.2.1 Modelling in 1-D The simplest of thermal models, is the 1D model, where thermal energy is simulated moving in only one dimension. This can be adequate for thermal modelling flash lamp heating as thermal diffusion occurs predominantly in only 1 dimension. This type of simulation can be achieved with a Crank-Nicholson, or Backward Euler method. This was the approach taken in simulating the thermal diffusion of in a thin a-Si film on glass substrate, by Smith et. al. [Smith.et .al - 2006]. No thermal results are presented in this paper, but the results must be adequate to input the thermal results into a stress model which is also presented in the paper.

2.2.2 Modelling in 2-D The Flash lamp crystallisation model discussed in section 2.2.1 [Smith.et .al - 2006], extrapolates the 1D thermal model to 2D and inputs the model into a finite element package called ABAQUS. From these simulations, deformations of the film are obtained for various size sample sizes, for 3 and 20 millisecond pulses. Although the thermal profile is not presented, the maximum stresses present in the film are. A maximum compressive stress of -285 MPa was predicted for the film, and no tensile stress was present. As the investigation is into flash lamp crystallisation, the temperatures involved must be of the same order as those of interest in our investigation.

Another investigation into the stress induced in thin film silicon on glass during the belt furnace RTA process, was conducted by Brazil [Brazil - 2009]. This investigation was not into Flash lamp heating, but the sample films and substrate are the same as those investigated here. This investigation included experimentation to measure the resultant strain of the Silicon film, as well as a 2D simulation of the RTA process carried out in COMSOL Multiphysics software and ANSYS. In this model the residual stress in the film was investigated, and along with experimentation the maximum stress was found to be -350 MPa. This investigation takes into account the structural relaxation and viscoelastic relaxation of the glass at and above the glass transition temperature (Tg). During the annealing process, the temperature of the sample reached 930°C, at which point the sample reaches a compressive stress of -777 MPa. The stress seems to relax - 74 - very little over the 4 minutes that the film is kept at the peak temperature. However, data supplied by Schott states that the viscosity of BSG glass at 930°C is 6.46 dPas, which equates to a relaxation time of 0.1 milliseconds. It is acknowledged by Brazil that the bonding of the Si and glass in the simulation is questionable, and no accurate simulation of the process trough time is given to compare with our investigation. Another drawback of the simulation is that size of the sample in the model is 40 µm by 3 µm, so features that occur over a larger scale may not be predicted by this model.

2.2.3 Modelling in 3-D An important simulation of flash lamp heating of silicon wafers was conducted by Smith [Smith.et .al - 2006], who is the same author of the model referenced in section 2.2.1. The simulation looks at the thermal profile within Si wafers of different thicknesses, the resulting stress profile, and the deflection of the wafer during the pulse. The wafer is found to initially deflect the same in each direction radially from the centre of the sample. This symmetry is broken during the pulse, where the deflection in one axis becomes significantly larger than that in the other, forming a saddle like pattern referred to bifurcation in the paper [Smith.et .al - 2006]. This non-uniformity in the strain of the wafer across the surface is not predicted by 2D simulations, presented earlier. The simulation shows that an increase in the thickness of the sample results in a decrease of the out of plane deflection. The deflection of a 1 mm wafer is 70% of that of a 0.5 mm thick wafer. Young’s modulus of the BSG glass used in our samples is approximately 1/6th that of Si, so the predicted deflection of our samples may be larger than that seen in the simulations of Smith et. al. even though the thickness is greater (3 mm). It should be noted that the model presented in this thesis is a 2D model, and bifurcation of the stress profile of the sample may occur in thin film on Si, as it does in wafers, even though it may not be predicted.

- 75 -

2.3 Thermal Model

2.3.1 Model overview The source of thermal energy in the FLA process is broadband light from a Xenon flash lamp. A significant amount of the light energy from a flash lamp is contained in the visible and near IR part of the spectrum, which can be seen in Figure 35. At room temperature the absorption of visible light is high, but the majority of IR energy would pass straight through our thin films (2 – 10 µm). However at elevated temperatures the absorptivity of Silicon increases significantly, allowing a larger proportion of the incident light to contribute to heating of the film. It is believed this increase in absorption is due to free carrier absoption.

Typical Xenon Flash Lamp Output

Figure 35 shows a typical spectrum of a Xenon flash lamp with a high current density (4000 A/cm2). Flash lamps with a current density of 1000 A/cm2 have significantly less energy in the visible part of the spectrum and more in the IR (800nm – 1000nm) [PerkinElmer - 2001]. [Goncz.et .al - 1966]

For reasons related to minimising stress in the Si film, it is assumed that the silicon film is already elevated to a temperature above the glass transition temperature. This also has the effect that the absorption of the silicon is high during FLA processing. For this reason it is assumed that light is absorbed in the Si film, and no light is absorbed by the glass substrate. This leads to the heat addition term in to model being exclusively in the Si film, with heating of the glass occurring only through diffusion between the two materials.

- 76 -

Normal Spectral Emissivity

Figure 36 shows the spectral emissivity of a lightly doped silicon wafer at various temperatures [Gruzdev, et al. - 2004]. The absorptivity is equal to the emissivity of a material via Kirchhoff’s law.

The absorption coefficient () is assumed to be 100 cm-1, which is a valid assumption for visible light, and IR light at elevated temperatures [Timans - 1996]. With this absorption coefficient such that light is almost completely absorbed in the silicon film of 2 µm. This absorption coefficient results in realistic values of heat addition () in the silicon film seen in experiment, and intrinsically accounts for higher absorption in thicker films and lower absorption in thinner films. Although in some cases light may penetrate the Si film, the absorption of glass is low, and only a negligible amount of thermal energy is absorbed directly by the glass substrate. The resulting equation for heat addition is given below;

. 4

. 5

Where is a measure of the incident light intensity, α is the absorption coefficient of silicon, y is the axis parallel to the depth which is outlined in Figure 37, t = total thickness of glass and Si, and = thickness of the glass substrate.

Another assumption made is that there is no thermal energy lost due to thermal emission. The amount of energy lost via thermal radiation is governed by the Stefan– Boltzmann law;

- 77 - where is area, is the Stefan-Boltzmann constant, is emissivity, and T = Temperature. It can be seen clearly that as the temperature increases further from the surrounding environment, the amount of energy lost due to thermal radiation becomes increasingly significant.

Diagram of Sample

Figure 37 shows a diagram of Si film on glass sample used in the FLA experiments and simulations.

To gauge the importance of neglecting this term, we will look at a simple illustrative example. If the preheat temperature were 600°C and the maximum temperature of the silicon before melting was reached (1400°C) and held for the duration of a typical pulse (20 ms), then the amount energy lost over 1cm2 would be approximately 3 Joules. From experiments we know that the energy required to reach 1400°C is above 70 Joules/cm2. This result confirms the assumption that neglecting thermal radiation from the Si film has a negligible effect on the thermal profile during a flash lamp pulse.

2.3.2 Thermal Properties With the heat addition part of the model accounted for, the next step is to account for thermal diffusion within each material, between the different materials. The thermal properties of Silicon and glass do change with temperature [Wu, et al. - 2010] [Shanks, et al. - 1963], however, in the model these properties are assumed constant and are given in Table 9. A discussion on these thermal properties is given below.

- 78 -

Property Units Silicon Glass Air Thermal Conductivity (k) W/(m.K) 30 1.3 6E-2

Specific Heat (cp) J/(kg.K) 1000 830 1050 Density(ρ) kg/m3 2329 2230 0.5

Table 9 shows the thermal material properties used in model. Another model of interest to the current investigation is that done on laser bending of Borosilicate glass [Wu.et .al - 2010]. In this paper, Experiments are conducted with Borosilicate glass being bent using a high power laser, and simulations presented show the mechanisms involved in the bending process. Also in this paper, material and thermal properties of Borosilicate glass over a temperature range 273 K to 1500 K.

Property Units Silicon to Glass Silicon to Air Glass to Air Convective heat 41,000 1,000 100 transfer coefficient (h) 2. [van der Tempel, et al. - 2000]

Table 10 shows the convective heat transfer coefficient used in model The data shows that the thermal conductivity, over the range of 873 K to 1500 K, varies from approximately 2 to 2.5 . Over the same range heat capacity varies from1000 . to 1100 , and the coefficient of thermal expansion changes from 4.5E6 to 3.6E6. . The change in value of these parameters over this temperature range is quite small, and justifies an assumption that the thermal properties of borosilicate glass are constant over this temperature range. The paper also gives Young’s modulus (E), which changes from 40 GPa at 873 K to approximately 3 GPa at 1500 K. The change in this material parameter is significant, and the assumption of a constant value for E may mean that the simulation deviates from reality. In the present simulation, the Young’s modulus value was chosen to be an average of the values over the temperature range of interest. Young’s modulus at room temperature, in the Schott Borofloat Brochure [Schott - 2010] is given as 64 GPa, which is similar to that in Wu’s paper. Therefor the decrease in Young’s modulus at elevated temperatures would be similar, so a value of 20 GPa was chosen as the constant value for this investigation.

A point of variation between the Borosilicate investigated by Wu [Wu.et .al - 2010], and Borofloat by Schott, is that the composition is different, as is shown in Table 11.

- 79 -

This difference in composition would result in a difference in material properties, but the extent of the difference cannot be quantified, due to the lack of supplied data by Schott of material properties at elevated temperatures. For this reason thermal properties similar to those presented in Wu are chosen, not the exact same values.

Chemical Borosilicate - Wu Borofloat - Schott

SiO2 74.8% 81%

B2O3 14.7% 13%

Na2O/ K2O 5.0% 4% BaO 2.0% 0% AlO 0.0% 2%

Table 11, shows the difference in the chemical composition of the Borosilicate glass used by Wu [Wu.et .al - 2010],, and the Borosilicate used in this investigation [Schott - 2010].

Another paper which had a significant influence on the selection of thermal expansion used in this model is that by Fluegel et. al. [Fluegel - 2007]. In this paper the density and thermal expansion of silicate glass melts at temperatures of 1000°C to 1400°C were investigated. Data from a large number of sources were used, to construct a model that would predict the material properties of variety of chemical compositions in silicate glasses. The paper is supplied with an Excel spread sheet, where the chemical composition of the glass of interest can be input and the predicted material properties can be calculated. The author states the predicted values and a confidence interval, which quantifies the level of certainty of the predicted value. A copy of the spread sheet, and data used, can be found at Fluegel’s website (http://glassproperties.com). When the chemical composition of Borofloat is put into the model, then a linear thermal expansion coefficient of 33 15 10 is predicted. This value is significantly larger than that given in Wu’s paper which is approximately 410 . So a compromised value of 10 10 was chosen to be on the lower end of the range predicted by Fluegel, and of the same order as that reported by Wu [Wu.et .al - 2010].

Initially it was thought that the relativistic heat equation may be required, as the timescales of interest are in the millisecond range, and spatial ranges of microns. The relativistic heat equation accounts for the finite propagation speed of heat from one point to another whereas the Fourier equation does not [Ali, et al. - 2005]. Although a model using the relativistic heat equation was developed, the difference in the resulting thermal profile was negligible (<1°C). Implementing the more complex simulation also - 80 - took a significantly longer computer simulation time. The Fourier (parabolic) heat equation used in the simulation is;

7 This is an example of a partial differential equation (PDE) where the solution u is dependent of the derivative of . Thermal diffusion in Silicon and glass, during FLA is predominately in the y direction (depth), with lateral diffusion occurring only at the edges of the irradiated area. The computation time, and memory demands of a 3D model make it implausible to implement on a standard PC, and are significantly larger than a 1D or 2D model of the thermal profile of the sample during FLA. However a 1D model would be insufficient for modelling the stress in the film and substrate during the FLA, process. For this reason a 2D model was developed, that would later give insight into the thermally induced stress of the film, and reduce the computation time to a reasonable duration. A discussion on previous models investigated, of various dimensionality is given in section 2.2.

As a starting point, some code used in the thermal model was obtained by exporting code generated by MATLAB’S PDETOOL. Information on the meshing, boundary conditions, and spatially varying heat addition could then be added. The code generated simultaneous equations that were then solved by a PDE solver, and could be plotted against time. This section is expected to give an overview of the thermal model, and justify some of the assumptions made, so the resulting thermal profiles are given in a later section.

The input parameters to the code are given in Table 9and Table 10, and the physical dimensions of the simulation are given in Figure 37. In addition to this an array of times at which the user wants the resultant thermal profile to be output, must be supplied. The MATLAB PDE solver requires the spatial information to be translated into a decomposed geometry, which boundary conditions are applied to, and which serves as a guide for generating a mesh. The mesh is calculated using a Delaunay triangulation algorithm, and is essentially the original surface, divided into a number of triangles. More information on the PDE tool and its component parts can be found in the MATLAB help menu. They are not covered here because the focus of this chapter

- 81 - is the resulting thermal and stress profiles generated during FLA, not the detailed working of the MATLAB solvers.

The output of the thermal solver is a thermal profile over a large number of points (up to 56,000) which are non-homogeneously spaced over the Si on glass sample. There are more points in the Si film, relative to the glass, to prevent spurious temperature spikes at points with larger thermal gradient. This thermal data is data is then homogenised over the sample and gives a thermal profile over an x axis 400 points wide, and a y axis 127 points deep. The thermal profile is found for each point at between 80 and 110 discrete times during and after the FLA pulse. The thermal profile array contains a temperature value for each x, y, and t value which can be as large as a 400 x 127x 100 array. This array is approximately 30MB in size with each point having double precision (64 bit) value.

2.3.3 Input Flash Lamp Thermal Profiles The thermal profile of the Si film and glass substrate determines the thermal strain, and subsequently the resultant damage. FLA experiments were carried out in collaboration with Helmholt Zentrum Dresden Rosendorf (HZDR), where pulse durations of 3, 20, and 40 milliseconds were available. The actual pulse shapes of the 3ms and 20 millisecond pulses used in experiments are shown in Figure 38, along with the fit used as in input for MATLAB. The pulse shape of a 40ms pulse was not available at the time of writing, so an estimation of the 40ms pulse was obtained from the model of a flash lamp and Pulse forming network outlined in Chapter 1.

A function of the pulse shapes was developed, so that it could be input into the thermal model. The closest agreement of the model to the pulse shape was obtained by using a sum of Gaussian functions of varying amplitude, and delayed in time. The pulse shapes used for the 3ms pulse and 20ms pulse are shown in Figure 38.

- 82 -

3ms Pulse Shape Input to MATLAB

1 0.8 0.6 0.4 (Arb) 0.2 0 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 Intensity Time (sec)

Actual Pulse Intensity Fit ‐ Input to MATLAB

20ms Pulse Shape Input to MATLAB

0.8

0.6

0.4 (Arb) 0.2

0 0 5 10 15 20 25 30 Intensity Time (sec) Actual Pulse Intensity Fit ‐ Input to MATLAB

40ms Pulse Shape Input to MATLAB

0.8

0.6

0.4 (Arb) 0.2

0 0.00E+00 5.00E‐03 1.00E‐02 1.50E‐02 2.00E‐02 2.50E‐02 3.00E‐02 3.50E‐02 4.00E‐02 Intensity Time (sec)

Simulated Pulse Intensity Fit ‐ Input to MATLAB

Figure 38, shows the pulse shape function used to input energy into the Si film. The dashed lines show the actual temporal pulse shapes of the flash lamps used in experiments at HZDR [Gebel, et al. - 2006].

- 83 -

As well as the above input pulses, a 100 ms pulse, and a 200 ms pulse were investigated. These pulses had a rise time of approximately 1 ms, were constant over the duration of the pulse, and has a fall time of approximately 1 ms. The simulation results of all pulse durations are presented together in section 2.7.

As well as Flash lamp pulses being investigated with the developed model, the thermal profile induced in the film during laser annealing was also simulated. The stress induced by the laser annealing was not completed in this thesis, but will be in future work. The illumination intensity of the laser is constant, but moves at a constant speed across the surface of the film. The equation governing the laser energy added to the film is;

. , , , 8 .

and 9 .√ . .

= laser power per unit area, = distance scan direction of the laser, = time, = laser scan speed, = laser start position. = Full Width at Half Maximum, = laser energy density profile. This equation described the energy deposition over the width of the laser, and beyond the width () of the laser the energy density is 0.

- 84 -

2.4 Displacement, Strain and Stress

2.4.1 Model overview The thermal simulation gives the distribution of temperatures through time, over a 2D cross section of a sample. These thermal profiles are used as an input to the displacement, strain, and stress simulation covered in this section. The assumptions made in using the thermal profile as an input, with no feedback from the displacement or annealing process, are covered in section 2.6.

Diagram showing outline of program

Figure 39 shows an outline of the Simulation process employed to calculate the displacement, strain, and stress. Firstly, the thermal profile is calculated for all times, and then at each time step, the elastic response of the system is calculated. After the elastic response is known, the viscoelastic relaxation is calculated at each time step, and used as an input for the displacement calculation of the following time step. This occurs until the final time step, where the simulation ends, and the results are presented. The process of calculating the viscoelastic stress in the glass can be better understood if the process is shown graphically. Figure 40 shows the process of obtaining the viscoelastic stress in the Si film from the thermal profile.

Process overview of modelling

Figure 40 shows graphically the modelling process used in this simulation. Firstly the temperature is calculated for each point in the Si film and glass substrate. Secondly, the strain is calculated for each point without viscosity of the glass being taken into consideration. Then the viscoelatic relaxation is taken into account using the equations outlined in section 2.4.4. 2.4.2 Mechanical Properties The mechanical properties of the silicon thin film and the glass substrate influence the resultant stress and stain profile greatly, and accurate values for these parameters are - 85 - important for an accurate model of the FLA process. The properties of the glass substrate and Si film are temperature dependent, but the model implemented does not allow for a temperature dependent material properties. As a result this simulation uses an average of the properties over the temperature range 600°C to 1400°C was used. The material properties vary by less than a factor of 2 over the investigated temperature range [Wu.et .al - 2010], so the effect on the simulation results is a small level of uncertainty. This uncertainty is discussed further in section 2.6.

For Silicon, the properties vary only marginally from room temperature to temperatures just below the melting temperature (1414°C), and because the film is composed of microcrystalline material there is no dominant crystal orientation and thus the material properties are isotropic. The Silicon properties used in the model are given in Table 12.

Property Silicon Boro-float Glass Units Young’s Modulus 130 20 GPa Poisson Ratio 0.2 0.2 - CTE 4E-6 9.7E-6 1/°C

Table 12, shows the material properties used in the simulation.

The properties of the Borosilicate Glass substrate do not change significantly from room temperature to temperatures around the glass transition temperature (Tg) [Schott - 2010]. Above the glass transition temperature however, the coefficient of thermal expansion (CTE) increases 3 to 4 times, which is typical of glasses. [Brazil - 2009]. Brazil also shoes that Young’s modulus of Borofloat glass decreases from its noted value below Tg. These two factors have been taken into consideration in the values given in Table 12. Below the glass transition temperature, the CTE of Borofloat glass is 3.26E-6 per °C, and Young’s modulus is 64 GPa [Schott - 2010].

2.4.3 Displacement Calculation MATLAB Code The resultant temperature profiles presented in section 2.7.1 are used as an input for calculation of the Stress in the film and glass substrate. The process of obtaining the stress in the sample at various times during the FLA pulse involves first obtaining the physical displacement field. The displacement fields are arrays of scalar values of the

- 86 - physical distance each point has moved from its original starting position at t = 0. There is one displacement array for the x displacement, and one for the y direction.

The source of displacement of each point is thermal strain, as no other forces are imposed on the body, or the boundaries of the sample. This is realistic in our case as there is no clamping of the sample during the FLA process.

The code which calculates the physical displacement of each point is based on freely available code written by Peter Krysl [Krysl - 2005]. The original code was designed to evaluate the stress imposed by uniformly heating two connected elastic materials with different coefficients of thermal expansion. The original code was altered in 2 significant ways;

 Allow non-uniform thermal profiles,  The sub-code ‘targe2.exe’ was rewritten to allow the boundaries of the materials to be altered to those of the Si and glass substrate.  The T3 meshing elements were changed to T6 elements to allow a greater level of convergence with fewer elements.

Non-uniform thermal profiles are already supported by the code, although mapping the output of thermal code, with that used by Krysl was not straightforward. The code targe2.exe creates a text file which contains information on the points, mesh triangles, and boundaries in the simulation, and for some reason that supplied by Krysl does not run correctly. Because it is a .exe file the code inside cannot be viewed and altered in MATLAB, so after analysing a sample output of the code, a MATLAB equivalent was developed. Perhaps the most significant alteration of the code was changing the T3 mesh to a T6 mesh. A T3 mesh element contains 3 nodes and 3 edges, while the T6 mesh element contains a node on each edge. This increases the degrees of freedom of the element, and allows the solution to converge with fewer node points [Krysl - 2005].

- 87 -

Mesh Objects in FAESOR

Figure 41 shows a 3 node triangle mesh element (T3) and a 6 node triangle mesh element (T6).

Early versions of the code imported the thermal profile data directly from the thermal code to the displacement code. Because of the non-uniformity of the mesh, very low angle triangular mesh elements generate stress ‘singularities’. Stress singularities are an artefact of a simulation whereby points are so close together that the distance between the points () is less than the accuracy limit of the data type. This inaccurate discretisation of a finite dx value to 0 results in a strain value of Infinity. This problem was removed by homogenising the points and mesh in the simulation, and altering T3 elements for T6 elements as described earlier.

2.4.4 Constitutive equations A background into the theory of viscoelastic relaxation in glass can be found in the Paper ‘Viscoelastic-Elastic Composites: I, General Theory’ and ‘Thermal Stresses, Relaxation, and Hysteresis in Glass’ by Scherer [Scherer, et al. - 1982] and Rekhson [Rekhson - 1993] respectively. Some of the constitutive equations and definitions of strain used in this thesis are the same as that used in the above mentioned papers. The constitutive equations covering viscoelastic relaxation in this model, have come mostly from a paper by Soules et. al. In this paper [Soules, et al. - 1987] the thermally induced strain is incrementally introduced in small discrete time steps, allowing an iterative solution to the viscoelastic relaxation in glass. According to Soules et. al. in viscoelastic materials the bulk Modulus () does not relax with time, and is thus constant. The Shear modulus () however does relax with time, and this how viscoelastic relaxation is factored into our simulation. The shear modulus relaxes according to an experimentally determined compliance function which is the same as that used by Brazil, in his investigation into stress induced by the current RTA process [Brazil - 2009]. In order to clearly understand the viscoelastic model, we will first describe the elastic equivalent.

- 88 -

Then analogies will be drawn between the elastic models and its viscoelastic equivalents. If a viscoelastic material is subjected to an instantaneous strain, and no time is allowed for relaxation, then elastic equations govern the materials behaviour.

Firstly we define the stress (), and the strain () is the sum of its 3D components;

11 The above equations describe the dilatational, (volume changing) properties of the material. As well as dilatational stress and strain, deviatoric (shear, shape changing) stress (), and deviatoric strain () are present in the Si film on glass, where , , . The deviatoric properties are related to the dilatational properties by;

, 12

, 13 The stress and strain can also be given as arrays containing the dilatational and deviatoric components;

,,,,, 14

,,,,, 15

The stress and strain is related in elastic materials by the bulk modulus (K) and the shear modulus (G). The bulk modulus related the dilatational stress and strain of the material and the shear modulus relates the deviatoric stress and strain of the material, and is given by;

where E is Young’s modulus, and is Poisson’s ratio. The exact form of the relationship between stress and strain is given by;

- 89 -

Where is a 6x6 matrix for stress and strain described in 3 dimensions, and is given by;

All of the above equations describe the interaction of stress and strain in elastic materials. The difference between elastic and viscoelastic materials arises once time is taken into consideration. The equations governing viscoelastic materials are given in the same paper as those where the above equations describing elastic materials is given [Scherer.et .al - 1982]. The deviatoric stress and strain are governed by viscoelastic relaxation given by the following equations;

, , . , , 20

, , . , , 21 where x, and y denote position, G and J are the shear and compliance modulus respectively, and ξ is the reduced time. Similarly, G and J are the bulk and compliance modulus for dilatation in the following equations.

, , . , , ′ , , ′ 22

, , ′ , , ′ . , , 23 The reduced time ξ is a measure of time that is independent of the relaxation time of the glass, thus it is independent of temperature. The reduced time is applicable to glasses which display thermo-rheological simplicity (TRS), which means that the relaxation behaviour of the glass at any given temperature can be expressed as a function of the relaxation at some Reference temperature (τ . According to

- 90 -

Narayanaswamy, [Narayanaswamy - 1988] the concept of TRS originated with the experimental work of Leaderman on textile fibers. Thermo-rheological Simplicity in the Glass Transition More on thermo-rheological simplicity is given by Scherer [Scherer.et .al - 1982], including more on the definition of the reduced time;

24 Brazil stated that Schott Borosilicate glass follows thermo-rheological simplicity [Brazil - 2009], however phase separation was observed in the other glass investigated, which was soda-lime glass. TRS does not hold for glasses that experience phase-separation [Scherer.et .al - 1982], so modelling of FLA on this substrate would be considerably more difficult.

The compliance functions in the above equations are functions that are determined by experiment for each glass, but an approximation to the function has already been established by Brazil [Brazil - 2009]. This approximation is taken from analysis of many other types of glasses, and the reader is referred to Brazil’s PhD thesis for a more in depth background. The approximation to the compliance function that describes viscoelastic relaxation in Borosilicate glass is given by:

, 25

where is time and is the viscoelastic relaxation time, which is given by:

26 where is the temperature dependant viscosity of the glass and is the shear modulus [Brazil - 2009]. This expression also describes the structural relaxation of the glass given later.

The above equations are recast in a form which can be more easily implemented in the incremental stress relaxation model implemented here. Here, is where the method employed by Soules [Soules.et .al - 1987] is followed. Firstly, equation 18 must be recast in its viscoelastic analogue.

. .′ 27

- 91 -

Where Dt t’ has the same definition as in equation 19, only with the shear modulus replaced with its viscoelastic time dependent analogue;

. 28

With these simple equations and a few assumptions we can now derive the specific equations used in the viscoelastic model. As the model is two dimensional, only the x, y and one shear component of the stress and strain are considered.

. . .′ 29 .

The above matrix equation gives rise to three constitutive equations.

. . ′ 30

∆ ∆ ′ ∆ ∆ ′ 31 It can be shown that;

. . 32

Thus equation 32 becomes:

∆ ∆ . . ∆ ∆ 33

Similarly for the y stress component;

∆ ∆ . . ∆ ∆ 34

And the shear component of stress can be calculated to be:

- 92 -

. . ∆ 35

With these basic equations, we can now define the various strains in the sample.

Physical Strain (ε)

 Physical strain is the gradient of the actual displacement experienced by the sample from its original point where T T0. Where at , , . The physical strain is calculated from the altered MATLAB code of Krysl discussed in section 2.4.3. At each time step, the physical displacement is calculated, then the viscoelastic relaxation of the glass is calculated, and so becomes the initial stress into the calculation of the physical strain at the next time step.

Free Strain (ε)

 The free strain is the strain in the material that would result, if each point in the material were free to thermally expand and contract. The free strain at a point p(x,y) is given by;

, , 36

 where is the coefficient of thermal expansion. It is assumed that the input thermal profile produces only dilatational strains and does not induce any shear strains.

Thermal Strain (ε)

 The thermal strain is the difference between the physical strain and the free strain of the material.

, , , . 37

 The thermal strain can also be described as the physically induced strain minus the thermally induced strain. The thermal stress and strain is that which is

- 93 -

considered to result in failure of the sample. This strain is the most important strain to consider when modelling a thermal process.

Viscoelastic Strain (ε)

 The viscoelastic strain is the strain relaxation that occurs in viscoelastic materials over time. The viscoelastic strain is the plastic deformation of the material cause by the thermal stress in the sample. The stress relaxed in viscoelastic materials is only deviatoric (shear). Logically we do not expect that the dilatational (volume changing) strain does not dissipate over time, or we would see a change in the volume of the glass, simply by applying a uniform pressure over its surface.  The Stress of a Viscoelastic material is given by [Scherer.et .al - 1982]:

∆ 38 which becomes:

. 39

if we assume that the change is strain over the time → is linear. This change in strain is the thermal strain that would occur if no time were allowed for relaxation (i.e. elastic strain). From this point we can derive an analytical expression for the integrand in the above equation to obtain an analytical expression for the viscoelastic stress from the following set of equations.

τ, and 2τ

. 41

Then using integration by parts;

42 - 94 -

where, , , , 1.

. – . .

. 43

where C is a constant

Remember , and calculating Φtdt 0, at 0, means C = -1.

. 44

This leads to an expression for stress,

. 45

With this equation the stress can be calculated over small time steps as an elastic material in MATLAB, and the viscoelastic nature of the material can be taken into account in subsequent code.

Structural Relaxation (ε)

Another important relaxation in glass is structural relaxation. Structural relaxation is the reorientation of atoms and molecules within the glass due to temperature change, and is strongly dependent on the rate of change of temperature. The structural relaxation is important in modelling of glass around the glass transition temperature. As the thermal model does not include a transition across the glass transition temperature, then the influence of the structural relaxation function is limited, and is omitted from this model. Structural relaxation describes the change of a glass property, such as volume, as the temperature is changed through the glass transition region. The best explanation of structural relaxation can be found in a paper by Rhijnsburger [Rhijnsburger - 1998], and Figure 42 is transcribed from this paper. In Figure 42 we can see the case where an instantaneous temperature change results in an instantaneous change in the volume. However, as this temperature change was through the glass transition region, the change in volume is governed by the - 95 -

properties of both the liquid and glass properties of the material. As time passes after the instantaneous volume change, the volume relaxes further to a steady state. The rate at which this relaxation evolves is governed by the structural relaxation function. For many glasses, the structural relaxation function is given as;

, 46

where is the structural relaxation time of the glass, which is dependent on temperature. More information on the structural relaxation function can be found in Brazil’s Thesis [Brazil - 2009], and the above mentioned papers [Rhijnsburger - 1998], [Scherer.et .al - 1982], and [Rekhson - 1993].

Glass Property vs. Temperature

Figure 42 shows a property of glass (such as Volume) changing with temperature

Structural relaxation is important to take into consideration around the glass transition region, but as our experiments, and model are well above this region, the effect on the result in minimal, and is not included in the calculation. This means that the model is limited to considering the case of stress induced during the FLA cycle, and not able to simulate the slower cooling process back to room temperature. Simulation of this range of the cooling cycle has already been completed by Brazil [Brazil - 2009]. The viscosity of borosilicate glass is covered well by Brazil in his thesis, however, many of the assumption made in his thesis, are now available in the Borofloat brochure from Schott, confirming many of the viscosity calculations used. It is important to note that

- 96 - the structural, and viscoelastic, relaxation time is dependent on the viscosity of the material as stated in

Where = the shear modulus of the material. The viscosity of the glass is in turn dependent on the temperature, which can be described by the Vogel- Fulcher- Tammann (VFT) equation

48 In the case of Borofloat glass from Schott, the coefficients describing the viscosity of the material are A = 0, B = -4200, T0 = 250, and T = Temperature.

Taking the above relationship between temperature, viscosity and structural relaxation time, we can see that the stress in the glass will relax at a faster rate as the temperature of the sample increases. The structural relaxation constant (τ) is a measure of how long the stress in the material takes to relax to 1/e (or 36.7%) of its original value. It is noted by Brazil that the viscoelastic relaxation time is between 4 and 20times the structural relaxation time, so in this thesis it is assumed that the viscoelastic relaxation time is 10 times longer than the structural relaxation time.

Temperature Viscosity Tau (Structural) Tau (Viscoelastic) (°C) (dpas) (seconds) (seconds) 400 28 3.9E+17 3.90E+18 500 16.8 2.5E+06 2.50E+07 600 12 39.68 3.97E+02 700 9.33 8.55E-02 8.55E-01 800 7.63 1.72E-03 1.72E-02 900 6.46 1.15E-04 1.15E-03 1000 5.6 1.58E-05 1.58E-04 1100 4.94 3.46E-06 3.46E-05 1200 4.42 1.04E-06 1.04E-05 1300 4 3.97E-07 3.97E-06 1400 3.65 1.78E-07 1.78E-06

Table 13 shows the structural and viscoelastic relaxation time predicted from the viscosity data supplied by Schott [Schott - 2010]. - 97 -

The FLA simulations carried out in this thesis deal with time scales on the millisecond, to tens of milliseconds range. It is clear from a simple analysis of the relaxation times that the viscoelastic nature of the glass will not affect the stress in the film or glass blow approximately 600°C. Even at 700°C the structural relaxation time of the glass is at least double the FLA pulse duration times investigated. However, during the FLA pulse, the film and glass immediately below it does reach temperatures exceeding 900°C where the relaxation time is of the same order as or shorter than the pulse under investigation. For longer pulse durations, more of the glass is at a higher temperature, and more time is spent at the higher temperatures allowing more relaxation to occur. This is shown to occur in the results section of this Chapter.

Once the elastic stress and strain within the glass and Si film have been simulated, and the viscoelastic relaxation of the glass has been calculated, then the stress within the Si film is then recalculated to take account of the reduced stress in the glass. This calculation is done with the following equations. Firstly from Rekhson [Rekhson - 1993], we can get an expression for the relationship between the various strains within the glass and the resulting stress. The stresses and strained are defined earlier in this subsection.

49 Similarly for the elastic materials (Silicon);

50 For viscoelastic material that has undergone viscoelastic relaxation. The strain of the Si film is governed by the physical and viscous strain of the substrate;

_ 51 If we substitute equation 51 into equation 50, when we can see how the stress in the Si film is governed by the physical and viscoelastic relaxation of the glass substrate, immediately below the film.

52 If we rearrange equations 51 and 52 we get

- 98 -

53 From here we can get an expression for the thermal stress in the Silicon film, directly from the stress in the glass substrate immediately below the film.

_ 54

Where is the free strain in the glass immediately below the Si film and is the free thermal strain in the Si film immediately above the Si/Glass interface. could be replaced with ∆ ∆, where ∆ is not necessarily equal to

∆. If the temperature in the Si film is the same as that in the glass then can be calculated as ∆.

With equation 55 we are able to calculate the stress within the film from only the stress in the glass immediately below the Si film, and physical constants of the two materials. This method of calculating the stress in the Si film from stress in the glass, was tested using the elastic stress data from the simulation outlined in section 2.4, and the results were found to be consistent.

- 99 -

2.5 Mechanical Failure of Silicon Up until this point the focus of this chapter has been to quantify the stress and strain experienced by the Silicon film, and glass substrate due to the FLA process. By obtaining estimates of the stress and strain experienced during FLA, then previously investigated mechanical failure of Silicon information can be directly compared to our findings.

The samples which have undergone FLA in this thesis are Solid Phase Crystallised (SPC) Silicon thin films on Glass. The films investigated are 0.5µm, 2µm, and 6µm thick. The resulting grain structure from the Solid Phase Crystallisation (SPC) process has been investigated previously, showing the films under investigation to have a grain size of around 1 micron. The effect of the Si grains on stress and failure of the Si film is discussed further in this section. Should the reader require additional information on the properties of the SPC Si film, the paper by Tao [Tao.et .al - 2010] has information on the grain size and shape and is a very good starting point.

Investigation into elasticity, the onset of plasticity, and ultimate failure of both single crystal silicon and nano-scale polycrystalline silicon has been investigated previously by many authors [Krus - 1991], [Pope - 2001], [Chasiotis, et al. - 2003], [Kahn, et al. - 2004]. It is stated by Krus, that the yield stress of a thin film is dependent on the inverse square root of the grain size in pc-Si films , where d is the grain size. This √ increase in yield stress with decreasing grain size can be attributed to a higher number of dislocation glide planes between grains. The number of glide planes through the thickness of the film is limited by the size of the individual grains and the thickness of the film. It is estimated that the Si grain sizes in our samples is from 0.9 to1.5 µm depending on the solid phase crystallisation parameters [UNSW - 2011]. Given that our films are only 2 to 3 µm thick, the number of inter granular glide planes is low, and decreases the yield strength of the film for an applied stress.

Experiments are carried out predominantly by applying a well controlled mechanical force to a bulk piece, or thin film, to obtain a relationship between the applied stress and induced strain. Similarly a well controlled strain can be induced in the material, and the resulting stress is measured, to obtain basic material properties such as Young’s modulus, and Poisson ratio and Fracture Strength. By performing these experiments at

- 100 - elevated temperatures, information on change in mechanical behaviour with relation to temperature can be obtained. This temperature dependent information is especially valuable for analysis of our experiments, as the temperatures are typically at or above the Brittle to Ductile Transition Temperature (BDTT) of Silicon. The BDTT is the temperature above which plastic deformation occurs due to an induced stress, rather than brittle (catastrophic) failure which occurs at temperatures below BDTT.

Through Monte Carlo simulation and experiments at elevated temperature, Pope showed that there is a strain rate dependence on the BDTT, and that some level of plastic deformation occurs up to 100°C below the BDTT [Pope - 2001]. This finding is significant for FLA because the rate at which strain is introduced into the Silicon film is significantly higher than the belt furnace annealing, which is the standard defect annealing method.

Pope also showed that there is a significant difference between the onset of plastic failure in single crystal Silicon compared to polycrystalline Silicon in a three point bend test. In a single crystal sample, plastic failure is localised around the centre contact point of the strain inducing apparatus, and plastic failure in polycrystalline silicon is distributed more uniformly throughout the whole sample. The reason for this difference between c-Si and pc-Si is the higher level of pre-existing dislocations in the polycrystalline material.

The onset of plastic deformation in silicon is shown to depend on 3 populations of dislocations;

 pre-existing dislocations,  thermally nucleated dislocations, and  atomic size dislocation loops.

As stated above there is a higher level of pre-existing dislocation loops in pc-Si relative to c-Si, which leads to plastic deformation at points away from the contact loading point in the former. Thermally nucleated dislocations are generated more readily at higher temperatures, which allow a higher degree of plasticity (ductility) as the temperature increases. Thermally nucleated dislocations play a role, but atomic scale dislocation loops being able to expand without any energy barrier [Pope - 2001] is the predominate reason for Silicon’s plastic deformation above the BDTT. - 101 -

Theoretical values and experimental values of the BDTT are given by Pope [Pope - 2001] for strain rates from 10 – 200 µm per minute, and a general trend toward an increase in BDTT can be seen for an increasing strain rate. The strain rate associated with FLA is or the order of 100’s of micrometers per millisecond, which is many orders of magnitude higher than that investigated by Pope. If this relation holds for the strain rates involved in FLA, then the predicted BDTT would increase significantly, or not occur at any point below the melting point. The reason for this increase in BDTT is that dislocation-dislocation interactions take a finite time to occur, and if sufficient time is not allowed for these interactions to occur, then the material will remain in a brittle state. The strain rate dependence of the BDTT into consideration, and that FLA introduces a strain rate many orders of magnitude higher than that experimentally shown to cause damage. It is entirely possible that the Si film never reaches the BDTT during the FLA process, and dislocations in the film that would allow for ductility at lower strain rates, end up being stress concentration points where mechanical failure starts.

The BDTT ranges from ~790K [Ritchie - 2003], to as high as 1000K [Pope - 2001] depending on the author, and applied strain-rate. At temperatures below the BDTT the yield stress of pc-Si (3-5 GPa) has been shown to be around a quarter of that for c-Si (~20 GPa). As stated above, the very high strain rate could lead to the Silicon not leaving the brittle state, even though it is above the BDTT. With this in mind, the yield stress, resulting in brittle failure of the Silicon is assumed to be 3-5 GPa, as given by [Ritchie, et al. - 2004].

There is a significant difference between the mechanical properties of single crystalline material and polycrystalline material. The difference arises from the relative ease of dislocations to diffuse within the material and the higher energy barrier seen by dislocations crossing grain boundaries. In materials with a smaller grain size, more grain boundaries are present per unit volume, and this has an effect of reducing the plasticity of the material. The yield stress of polycrystalline silicon films has been shown to follow a Hall-Petch relation [Krus - 1991], which is a direct result of higher energy barrier of dislocations at grain boundaries mentioned above. The Hall-Petch effect was independently observed and explained by E. Hall and N. Petch in the early 1950 and states that a reduction in grain size (down to 10’s of nanometers) results in an

- 102 - increase in yield stress. It is important to note that yield stress in the stress at which a material exhibits plasticity, not failure. In metals, plastic flow is usually observed before brittle fracture, which is indeed the case for Silicon at temperatures above the BDTT.

In thin films the number of dislocations through the depth of the film is significantly less than in the plane of the film. This results in less dislocation-dislocation interactions which means less work hardening occurring than in bulk material. Dislocations are more abundant in materials with smaller grain size, so films with fine grains will experience a higher level of work hardening compared to films with a grain size comparable to the film thickness [Krus - 1991]. The FLA experiment were carried out on films crystallised via solid phase crystallisation (SPC) which results in grains of the order of 10s to 100s of nanometres. The amount of work hardening in LPCSG material will be less evident because of the increased grain size.

The diffusion of dislocations through a grain and between grains, while contributing to the mechanical properties of the material, also changes the electrical properties, which is our primary concern. The theories outlined above propose that stress in pc-Si results in a dislocation migration to grain boundaries, where the majority are energetically limited from further diffusion into an adjacent grain. This is consistent with electrical activity of defect in pc-Si, seen in our experiments. After thermally induced dislocation diffusion to the grain boundaries little increase Open Circuit Voltage (Voc) is seen until Hydrogen passivation is conducted. This is because hydrogen passivation readily terminates dangling bonds between grain boundaries, which thermal annealing does not do. Therefore the effectiveness of thermal annealing can only be observed after samples have been hydrogenated, which is what is observed in our experiments.

- 103 -

Fracture Toughness (K) = 1 MPa.(m1/2)

140

120 (nm)

100

80 Length 60

40 Crack

0 Critical 0123456

Fracture Strength ()

Figure 43. The green circles show a constant value of fracture toughness (K = 1 MPa.(m1/2)), given the facture toughness on the x axis and critical crack length on the y axis. The Blue squares show that if the material has a Fracture toughness of 5GPa (x-axis), then if a crack exceeds a critical crack length of 13 nm (Y-axis), then it is energetically favourable for the crack to propagate, and the film to fail. Similarly, the Red diamonds show that for a material with a fracture strength of 3.1 GPa, then a crack length of 33 nm is required before the film will mechanically fail. If any combination of fracture strength and crack length, results in a K value that lies on the left of the Green line, then the film will not fail. If the calculated value of K lies on the right of the green line, then the film will be damaged.

Another important concept for determining the stress that will induce failure in our films can be found a presentation by Ritchie at the 13th Workshop on Crystalline Solar Cell Materials and Processes [Ritchie.et .al - 2004]. As stated earlier the fracture strength ( of pc-Si films is given as 3-5 GPa, where mechanical failure is statistically likely to increase from a low probability at 3GPa, and reach approximately 100% at a fracture strength of 5GPa. The probability of failure over this range is governed by ‘weakest link’ (Weibull) statistics. Given the fracture toughness, we can determine the fracture toughness by the equation;

. 56

We also know, from Ritchie’s presentation that 1 MPa.√, if 1, where Q is a geometry dependent factor. If this value of fracture toughness is plotted on an axis of fracture strength and critical crack length, as is presented by Ritchie, we get the figure reproduced below. It can be seen that for the fracture strength of pc-Si of 3-5 GPa, then a crack length of 13 to 33 nm will result in crack propagation and failure of the film. This explained why cracking begins at the edge of the sample and propagated inward. - 104 -

Cracks of a few 10’s of nanometres are common around the edge of the sample, and around laser scribed lines, making crack source points common. In the centre of the film, away from the edges, the uniformity is much higher, and cracks or other faults of around 33 nm are far less common. Cracks will still originate at the centre of the film, if enough stress is applied; this relationship between fracture strength, fracture toughness, and critical crack length tells us that a higher stress would be required to do so.

- 105 -

2.6 Model Assumptions and Simplifications A number of assumptions and simplifications had to be made to model the FLA process on Si on glass. These assumptions and simplifications are mainly related to the material properties of the Silicon and glass substrates. Assumptions were also made about the FLA process, and the initial stress state of the samples before the FLA pulse was applied to the sample.

Perhaps the most obvious and important simplification was reducing the dimensions of the problem from 3D to 2D. This was done only to reduce the computation time required for the simulation. During the FLA process the sample experiences a non- uniform temperature profile through the depth of the sample (y-axis), but the temperature profile parallel to the surface of the sample is uniform, making the x-axis and z- axis equal. Given this degeneracy in the temperature profile and that the materials under investigation are isotropic, the effect of solving for the 2D problem and inferring outcomes in the 3D case is a valid assumption.

As stated in section 2.4.2 the material properties of both the Silicon and the glass are temperature dependant, but are simplified to a value that is representative of that in the temperature range 600°C – 1400°C. The thermal and mechanical properties that are assumed to be constant in the simulation, vary by less than a factor of 2 over the investigated temperature range [Wu.et .al - 2010].

The absorption of Silicon increases drastically at high temperature compared to that at room temperature. The absorption coefficient is assumed to be constant for all wavelengths at temperatures above 600°C. This simplification is believed to have a negligible effect on the resulting temperature profile within the silicon film and the resulting structural modelling. This is because at temperatures above 600°C light from the flash lamp is absorbed completely within the Si film, and the thermal profile through the thickness of the film (2 µm) becomes uniform on the time scale of microseconds.

This model also assumes that the thermal energy radiated from the sample during the simulation is negligible. The thermally radiated energy was omitted from the model simply because the solver used in MATLAB was hyperbolic, and could not incorporate the parameters that are dependent on the temperature itself (as thermal emission of radiation is). The net amount of thermal energy radiated away from the silicon and - 106 - glass is dependent on its temperature relative to the ambient temperature. In these experiments the surrounding gas reaches the same preheat temperature as the sample. So at 600°C the loss of energy due to thermal radiation is approximately 0. The magnitude of the thermally emitted radiation is dependent on the 4th power of the temperature, and so increases very sharply above 600°C. At 800°C above the preheat temperature (1400°C), around 160 W/cm2 would be lost via thermal radiation. This energy loss is negligible because the sample is at an elevated temperature for only a very short time (maximum 40 milliseconds). The maximum possible energy lost from the sample over the duration of the flash lamp pulse is approximately 6 J/cm2, which is around 5% of the energy deposition required to reach 1400°C for a time during a 40 milliseconds. If longer pulse durations were to be investigated in the future, then the thermal emission of radiation from the sample would need to be taken into consideration.

The process of deforming a viscoelastic solid, results in energy lost as heat. In this simulation it is assumed that any resulting heat energy has a negligible effect on the overall temperature of the sample.

- 107 -

2.7 Results of Simulations

2.7.1 Thermal The thermal simulation, as expected shows a significant increase in temperature as the FLA pulse is switched on and a rapid decrease in temperature immediately following the end of the pulse.

The model shows that the peak temperature achieved in the Si is almost linearly dependent on the input energy density, as can be seen in Figure 44. The increase in the peak temperature achieved increases at a higher rate at shorter pulse durations compared to longer pulse durations. This can be explained by considering the higher thermal diffusion into the glass substrate over longer pulse durations.

Peak Temperature for a given Pulse Energy

1400

1300 (°C)

1200

1100 Pulse ‐ 3 ms ‐ Preheat ‐700°C 1000 Pulse ‐ 20 ms ‐ Preheat ‐700°C Temperature 900 Pulse ‐ 40 ms ‐ Preheat ‐700°C Pulse ‐ 100 ms ‐ Preheat ‐700°C Peak 800 Pulse ‐ 200 ms ‐ Preheat ‐700°C 700 0 50 100 150 200 250 300 Pulse Energy (J/cm2)

Figure 44 shows the peak temperature achieved with a given input pulse energy density (J/cm2). The three lines represent the 3 pulse durations investigated.

The temporal thermal profile in the silicon follows the heating pulse profile closely in the initial stages of the pulse. Then as thermal diffusion into the glass occurs, the temperature decays exponentially to a steady state temperature which is higher than the preheat temperature, but significantly lower than the peak temperature. Temporal thermal profiles in the Si film are shown in Figure 46 for multiple pulse durations.

- 108 -

The reason for the exponentially fast cooling time, after silicon has reached its peak temperature, is thermal diffusion in to the glass substrate. The thermal profile through the depth of the sample changes over the duration of the pulse. The energy required to reach a certain temperature increases as the pulse duration increases.

Pulse Energy Required to reach 1400 °C

250 ) 2 200 (J/cm 150

100 Energy

Pulse 0 0 50 100 150 200 Pulse Width (ms)

Figure 45 shows the pulse energy density required to reach 1400 °C from a preheat temperature of 700 °C for the given pulse durations.

Thermal Profile of Film Through Time

Figure 46 shows the thermal profile of the Si film, during the FLA pulse. It can be seen that short pulse durations lead to faster cooling of the film once the FLA pulse has ended. For longer pulse durations, the cooling time increases, as more thermal energy is retained by the glass substrate.

- 109 -

Temperature Profile at End of Various Pulse Durations

Figure 47 shows the thermal profile at the end of the FLA pulse. Longer pulse durations give the thermal energy more time to diffuse deeper into the glass substrate, which can be seen clearly in this figure. The pulse energy density of each pulse must be variedto achieve a peak temperature of around 1400°C for each pulse.

Temperature at 500 ms after the FLA pulse begins

Figure 48 shows the thermal profile through the depth of the sample at 500 after the start of theFLA pulse. The extra thermal energy deposited from the longer pulse durations, means that the temperature of the film (at the top) remains higher for longer. - 110 -

2D thermal profile

Figure 49 shows the 2D thermal profile of the Si film of glass at the end of a 100 ms pulse. The temperature is shown in the vertical axis, with higher temperatures shown in red, and lower temperatures shown in blue. The high temperatures are in the Si film and top of the glass substrate, and the temperature at the bottom of the film is at the preheat temperature. Also, the edges of the sample are shaded in this simulation, and thea low level of thermal diffusion laterally across the Si toward the sides of the sample can also be seen. This is expected because thermal energy diffuses mostly through the glass, and the thermal energy diffusion through the Si film has little effect of the resultant thermal profile. This simulation had a preheat temperature of 700°C, pulse energy density of 186 J/cm2, at 110 ms after the beginning of 100ms pulse.

The results of the thermal simulation presented in this section are relatively simple to understand. With Heat addition in the film, and thermal diffusion into the glass describing the thermal profile predicted for various pulse duration. It can also be seen that the increased pulse energy deposited on the film during longer pulse durations is required to reach 1400°C. This increased energy deposition increases the substrate temperature higher for longer, and the effect on stress in the film and substrate will vary with this changing thermal profile. Also, the increased temperature of the glass substrate for longer times will have an effect on the viscoelastic relaxation of the substrate. The issues surrounding the stresses in the glass and Si film are covered in the following subsection.

- 111 -

2.7.2 Structural

2.7.2.1 Stresses in the Film This subsection shows the results of the structural simulation away from the edges of the film and edges of the irradiated area. This simulation shows that the stresses induced during FLA are uniform across the irradiated area, and so the results at one point in the film are presented here for simplicity. At the edge of the irradiated area the film is constrained by Si and glass that does not receive any thermal energy directly from the FLA pulse, this induces large stress concentration points, which is discussed in the next subsection.

Early experiments into FLA showed that the sample needed to be preheated to temperatures above the glass transition temperature () of the substrate, to achieve any level of annealing before the onset of cracking. Increasing the preheat temperature above reduced the stress in the Si film by reducing the thermal energy required to reach the annealing temperature of the Si. This also allowed viscoelastic relaxation of the glass substrate to occur, which relieves stress in the glass, and Si film. Although the glass is a viscoelastic material, the results of a simulation assuming the glass is elastic is given first. From this basis, the viscoelastic nature of the glass is taken into consideration and compared and contrasted to the elastic case.

The results of the simulation in this section aim to first derive a relationship between the temperature profile, the induced stress, and the damage seen in experiments at pulse durations of 3 ms and 20 ms. From the FLA experiments covered in Chapter 1, the damage threshold of various pulse energy densities and pulse widths was determined. By combining the experimental data and the simulation results we can predict the threshold stress in the film that would result in damage. This relationship between damage and induced stress can be used to predict the level of damage likely to occur for pulse durations and pulse energies that are not experimentally available at this time.

If thermal energy were added to a viscoelastic material infinitely fast, and no time allowed for relaxation, then the stress profile within the sample would be exactly the same as the elastic simulation. So by comparing the viscoelastic result with the elastic result, we are analysing the effect of time on the induced stress profile. As the viscoelastic case and elastic case are equivalent while no time has elapsed, then we can - 112 - expect that as more time passes then the stress profile of the viscoelastic material to diverge from the elastic case. Also, by comparing the viscoelastic to elastic material model, then we can distinguish how FLA of thin films on glass differs from FLA of thin films on an elastic substrate with different CTE, such as a Germanium film on a Silicon wafer.

Below we can see the peak compressive and tensile stress induced in the film, for FLA pulses that raise the Si film temperature to a peak of 1400°C. The blue points represent the peak tensile stress that would be experienced when assuming an elastic material, and the red points represent the peak compressive stress induced in the film, still assuming elastic materials.

Peak Compressive / Tensile Stress in Si film vs. pulse Width - Elastic 180 130 80

(MPa) 30 ‐20 Film

in ‐70 ‐120

Stress ‐170

‐220 Max ‐270 ‐320 0 0.05 0.1 0.15 0.2 Pulse Duration (sec) film tension film compression

Figure 50 shows the peak stress experienced by the Si film. The Blue points represent the maximum tensile stress induced in the film during the FLA cycle. The Red circles represent the maximum compressive stress induced in the film during the same FLA process. These values represent the stress that would be experienced by the film should it reach a peak temperature of 1400 °C, assuming that the glass behaves elastically.

It can be seen that for longer pulses, in the elastic case, the peak compressive stress decreases steadily for an increase in pulse duration. Similarly, there is an increase in the maximum tensile stress seen in the film, with increasing pulse duration. It is important to note that the peak compressive stress during the FLA pulse, occurs at or before the time of peak temperature in the film, while the peak tensile stress occurs from 0.4 to 0.6 seconds after the pulse began. The compressive stress arises when the Si film has a much higher temperature than the glass substrate, which occurs early on in the FLA process, before thermal energy has diffused from the Si to the glass. The tensile stress

- 113 - arises when the temperature of the Si film as glass substrate are similar, because the thermal expansion coefficient of the glass is approximately 2.5 times larger than that of the Silicon. This situation occurs when enough time has elapsed to allow thermal diffusion from the Silicon to the glass, which is pulse duration dependent.

Figure 55 shows only the stress that would be expected if the stress reached a peak temperature of 1400°C during the FLA process. In our experiments, the energy density required to reach 1400°C varies with pulse duration and caused significant cracking of the film. The peak temperature reached in the Si film in any of our experiments, where a Voc could still be measured was approximately 1280°C. It was found that the peak compressive and tensile stress induced in the film was linearly related to the peak temperature reached, when not accounting for viscoelastic relaxation. This can clearly be seen in Figure 51 and Figure 52 showing the tensile peak stress and compressive peak stress, respectively.

We can find the extremes of the expected compressive stress by assuming that the heating of the Silicon is infinitesimally short, and no heating of the glass occurs, and similarly, we can find the maximum possible tensile stress in the Silicon by assuming a sufficiently long pulse to assume that the temperature across the film is uniform. The maximum compressive stress is given by:

.∆ 57

Where is the coefficient of thermal expansion (CTE), and ∆ is the temperature change from the zero stress point. Assuming that the stress in the sample has completely relaxed at 700°C, and the Silicon reaches a temperature of 1400°C, and the CTE of Silicon is 4E-6, then the maximum possible compressive stress is -455 MPa.

As the CTE of the glass substrate is larger than the CTE of Si, the tensile stress in an elastic film on an elastic substrate away from the edges, can be found by the following equation, given by Hutchinson [Hutchinson - 1996].

.∆.∆ 58

Where ∆ is the difference in CTE between the film and the substrate, E is Young’s modulus, and is Poisson’s Ratio. For calculating the maximum tensile stress we

- 114 -

assume ∆ 410 – 9.75 10 , 0.2, 130 10 , and ∆ 700, same as above. The resulting peak tensile stress in the film is 654 MPa.

Thus a compressive stress of -455 MPa, and a tensile stress of 654 MPa are the limits of realistic stress that would be observed in the film under the extremes of FLA processing of thin film Si on Borosilicate glass. The results of our simulations shown in this section, give values that are well within the Stress limits calculated here.

Peak Elastic Compressive Stress in Film vs. Peak Temperature

‐50 (MPa)

film ‐100

in ‐150 Stress ‐200

‐250 Maximum ‐300 800 900 1000 1100 1200 1300 1400 Peak Temperature (°C)

3 ms film tension 20 ms film tension 40 ms film tension 100 ms film tension 200 ms film tension

Figure 51 shows the peak compressive stress in the film induced when a certain peak temperature is reached. Each line colour represents different pulse durations from 3ms to 200 ms. This graph assumes the glass behaves elastically.

- 115 -

Peak Elastic Tensile Stress in Film vs. Peak Temperature

160

140

120 (MPa)

100 film

in 80

60 Stress

20 Maximum 0 800 900 1000 1100 1200 1300 1400 Peak Temperature (°C) 3 ms film compression 20 ms film compression 40 ms film compression 100 ms film compression 200 ms film compression

Figure 52 shows the peak tensile stress in the film induced when a the peak temperature on the x axis is reached. This graph assumes the glass behaves elastically.

From the above graphs, we can clearly see the linear relationship between the peak temperature and stress. If we look at the gradient of these curves we can see that if constant heating was applied, and a peak temperature of 1400°C was reached, then the peak compressive stress would approach zero, and the max tensile stress would approach a constant value of 654MPa.

The below figures show the stress in the Si film through time for a number of pulse durations. It can be seen that the stress follows closely, the FLA pulse for short pulse durations (3ms to20 ms). However at longer pulse durations, thermal diffusion into the glass reduces compressive stress and tends to larger tensile stress. The tendency of compressive stress to be minimised for longer pulse durations, also means that a larger tensile stress is induced in the film.

- 116 -

Stress in the Silicon Film Through Time - Elastic

Figure 53 shows the evolution of strain through time, over the first second of the FLA process. Elastic properties of the glass are assumed. It can be seen that for short pulse durations, a relatively large compressive stress is attained early in the process. In longer pulses a larger tensile stress is induced, and this tensile stress occurs later in the FLA process (approximately 0.5 seconds). These stress profiles emerge when the peak Temperature of the film is 1400°C.

In contrast to the above stress profiles, the stress in the glass closely follows the thermal profile, with the peak compressive stress occurring at the same time as the peak temperature (at the end of the pulse). Also, the relative thinness of the Si film means that the pressure exerted on the substrate by the film has little effect on the temporal stress profile. As a result, even though the film would be pulling the glass substrate to be in tension early in the pulse, the substrate stress does not become tensile at any point during the pulse. It should be noted that the stress shown in the following figure is taken from immediately below the Si film. At greater depths into the film, the stress does in fact become tensile, which is discussed in more depth later in this section.

- 117 -

Stress in the Glass Substrate Through Time - Elastic

Figure 54 shows the evolution of strain through time, over the first ½ second of the FLA process. Elastic properties of the glass are assumed. It can be seen that the glass experiences compressive stress that closely follows the temporal thermal profile of the FLA pulse. These stress profiles emerge when the peak Temperature of the film is 1400°C.

As time elapses and viscoelastic relaxation occurs, the stress in the glass begins to deviate from that of an elastic material which has been shown above. The below figure shows the evolution of stress within the glass through time, for assuming the glass is an elastic material (Red), and a viscoelastic material (Blue).

- 118 -

Stress in glass during a 3ms FLA pulse

Figure 55 shows the elastic (red) and viscoelastic (blue) stress in the glass, just under the silicon film through time, for a 3ms pulse. As shown earlier, the stress in the 3 ms pulse follows closely, that of the FLA pulse, and so the viscoelastic relaxation of the glass follows a clear relaxation of the peak stress, and maintains this relaxed stress after the pulse has ended. This stress profile is that induced when a peak temperature of 1400°C is reached in the Si film.

Stress in glass during a 100ms FLA pulse

Figure 56 shows the elastic (red) and viscoelastic (Blue) stress profiles of the glass, just below the Silicon film, for a 100 ms FLA pulse. This stress profile is that induced when a peak temperature of 1400°C is reached in the Si film.

It can be seen that the stress in the glass drops to approximately half that predicted by the elastic case. This is because the viscoelastic relaxation time at 1400°Cis approximately 1.8 microseconds (See Table 13). This is 3 orders of magnitude shorter - 119 - than the pulse duration, and more than enough time elapses to allow the stress in the glass to relax, even at the shortest of pulse durations investigated. The same trend can be seen in the stress profile of the glass from the 100 ms pulse shown above.

From the above graphs we can conclude that the stress in the glass immediately below the Si film is compressive, and when the viscoelastic nature of the glass is taken into consideration, the magnitude of the stress reduces, but the overall trend remains is unchanged. Now we will look at the stress profile in the glass through the depth of the glass substrate.

Through the depth of the glass, a complex pattern of tensile and compressive stress exists as a result of the non-uniform thermal profile that exists within the glass. Below are three depth profiles taken from the centre line of the sample, to show how viscoelastic relaxation effects the viscoelastic stress profile within the glass substrate, for various pulse durations.

Elastic vs. Viscoelastic Stress in Glass substrate – 3ms pulse – Time = 3ms

Figure 57 shows the stress profile through the thickness of the glass substrate, for a 3ms pulse. This stress profile is taken at 3ms into the FLA process, at the point of maximum stress. It can be seen that the viscoelastic stress profile (Blue) varies only slightly from the elastic model simulation.

Comparing the stress profile in Figure 57 (above) with that in Figure 58 (below), we can see that due to the longer relaxation time, more viscoelastic relaxation has occurred in the stress profile of the 100 ms pulse. This might seem like a contradiction to the conclusion made above about the temporal stress profiles of the glass just below the Si

- 120 - film, where we saw the maximum viscoelastic stress drop by half over the elastic stress. However, at increasing depths into the glass substrate the temperature decreases, which in turn increases the viscosity, and time required for viscoelastic relaxation to occur.

Elastic vs. Viscoelastic Stress in Glass substrate – 100ms pulse – Time = 100ms

Figure 58 shows the stress profile over the depth of the glass substrate at 100ms into 100ms pulse FLA process. Comparing this stress profile to that of the 3ms pulse above, we can see that a lot more stress relaxation has occurred, in the glass.

Elastic vs. Viscoelastic Stress in Glass substrate – 100ms pulse

Figure 59 shows the stress profile over the depth of the glass substrate of a 100 ms pulse. The red curve represents the elastic stress profile through the depth of the glass substrate at 100ms into the process (end of the pulse). The blue curve represents the viscoelastic stress as 100 ms into the FLA process. The green curve represents the stress in the glass substrate 200msinto the FLA process.

- 121 -

The general stress feature of compressive stress at the bottom and top, and tensile stress at some depth in the glass can be seen in both the 3ms and 100 ms stress profiles. Although not shown here, this general stress profile also occurs in the other pulse durations investigated.

In Figure 59, the stress over the depth of the glass is shown for a 100ms pulse at 100ms and 200ms after the beginning of the pulse. This figure confirms that the viscoelastic relaxation reduces the stress further as more time elapses. Also, the depth of peak tensile stress has moved downward below 2mm from the top of the glass. The increased depth of the tensile strain peak can be attributed to the additional thermal diffusion from the top of the sample in the time that has elapsed.

More stress relaxation in the glass occurs, as expected, for longer time periods, and at higher temperatures. As shown in section 2.7.1 the film and substrate temperature plateau is higher for longer pulses, due to the higher level of thermal energy deposited by the FLA pulse. This has the effect of keeping the glass at an elevated temperature for a longer time, reducing stress built up in the glass substrate. If however the pulse duration is increased too much then the viscoelastic nature of the glass with begin to deform the sample, and make the resulting solar cell unusable.

Having quantified the viscoelastic relaxation in the glass expected from theory, our attention now focuses on the stress in the film. The Si film is an elastic material, and although structural changes occur in the film as a result of the annealing process, any deviation from pure elastic behaviour would be small. It is shown that the viscoelastic relaxation in the glass substrate serves to increase the compressive stress in the glass rather than relax it.

From Figure 60 we can see that the compressive stress in the Si film increases with increasing FLA pulse duration, up to 200 ms. Experience with glass melts tells us that at longer pulse durations than that investigated here, the peak compressive stress induced in the film would begin to decrease as the viscoelastic relaxation outpaces the induced thermal stress.

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Stress in Si film – Taking the Viscoelastic Relaxation of Glass in Account

0.0E+00

‐5.0E+07 (Pa) ‐1.0E+08 3 ms Film ‐1.5E+08 20 ms in 40 ms ‐2.0E+08 100 ms Stress ‐2.5E+08 200 ms ‐3.0E+08 0 0.1 0.2 0.3 0.4 0.5 Time (Seconds)

Figure 60 shows the temporal stress profile in the Si film taking into account the viscoelastic nature of the glass. From this graph we can clearly see that the compressive stress in the film increases with increasing pulse duration up to 200 ms. This temporal stress profile in the Si taking the viscoelasticity of the glass into account is in complete contrast to the trend seen with increasing pulse duration when considering the glass to be an elastic material. The magnitude of the stress in the Si film increases with increasing pulse duration in the viscoelastic case, where as it decreases in the elastic case.

Stress in Si film - Elastic and Viscoelastic Substrate

‐1.00E+07

‐6.00E+07

(Pa) ‐1.10E+08

‐1.60E+08 Stress

‐2.10E+08

‐2.60E+08 0 20406080100120140160180200 Pulse Duration (ms)

Stress in Si film ‐ elastic substrate Stress inn Si film ‐ Viscoelastic Substrate

Figure 61 shows the peak compressive stress in the Si film, while undergoing FLA heating. The Blue line represents the peak stress in the Si film assuming the glass behaves elastically. The Green line shows the peak stress in the film taking the viscoelastic nature of the glass into consideration.

- 123 -

Stress in Si Film 3ms Pulse - Elastic - Viscoelastic

5.0E+07

0.0E+00

‐5.0E+07 (Pa)

‐1.0E+08 Film

in ‐1.5E+08

‐2.0E+08 Stress ‐2.5E+08

‐3.0E+08 0 0.02 0.04 0.06 0.08 0.1 Time (Seconds) 3 ms ‐ viscoelastic 3 ms ‐ elastic

Figure 62 shows the viscoelastic stress in the Si film taking into account the viscoelastic nature of the glass. The temporal stress profile assuming the glass is an elastic material is also shown for comparison

Stress in Si Film 200 ms Pulse - Elastic - Viscoelastic

2.0E+08 1.5E+08 1.0E+08 5.0E+07 (Pa)

0.0E+00 ‐5.0E+07 Film ‐1.0E+08 in ‐1.5E+08 ‐2.0E+08 Stress ‐2.5E+08 ‐3.0E+08 00.511.522.53 Time (Seconds)

200 ms ‐ Viscoelastic 200 ms ‐ elastic

Figure 63 shows the stress in the Si film taking into account the viscoelastic nature of the glass (Solid Line). The temporal stress profile assuming the glass is elastic, is shown for comparison (Dashed line). It should be noted that the stress profile for the 200 ms pulse is shown for 3 seconds after the beginning of the process, where as the stress profile for the 3ms pulse above is shown only for 0.1 seconds after the beginning of the process.

Figure 62 and Figure 63, above shows the relaxation in the silicon film for a 3ms and 200ms pulse, assuming viscoelastic properties of the glass substrate (solid line), and elastic properties for the glass, for comparison (dashed line). Taking the viscoelastic nature of the glass into consideration, the magnitude of the stress in the film also - 124 - relaxes, for the 3ms case. Also, it can be seen that the stress in the film remains compressive for a time after the pulse has ended.

The stress profile in the Si film from a 200 ms FLA pulse, when the viscoelasticity of the substrate is taken into account, begins to deviate from the elastic case after approximately 70 ms from the beginning of the pulse. In the elastic case, enough thermal energy has diffused into the glass, at 70 ms to allow the thermal expansion of the glass to begin to reduce the compressive stress in the film. Also in the elastic case, as the temperature in the film and substrate becomes more uniform, the higher thermal expansion in the glass drives the stress in the film to become tensile. In the viscoelastic case, it was seen in Figure 55 to Figure 59 that the compressive stress in the glass just below the film decreases significantly due to viscoelastic relaxation. This means that the force on the Si film, from the glass substrate is also reduced. This reduction in force means that the glass does not expand in the horizontal direction, which leads to the stress in the film remaining compressive, even when the film and substrate have attained the same temperature. The following section discusses the results shown above, and aims to give the reader an understanding of how the viscoelastic nature of glass alters the results from the elastic case so dramatically.

2.7.2.2 Stresses at the boundary of the irradiated area In viscoelastic materials the shear stress relaxes, but the dilatational (volume changing) stresses do not directly relax. In the case investigated, some of the dilatational stresses are dissipated because the sample is unconstrained in the vertical direction, as discussed earlier. At the edges of the illuminated area, during FLA, the viscous transformation of horizontal stress to vertical displacement creates strong shear stress in the film. Although the film is unconstrained in the vertical direction, and the vertical stress component is approximately equal to zeros ( 0. At the edge fo the irradiated area the film is constrained by unheated glass and Si. This area of high stress induced at the boundary of the illuminated area and the shaded area can be seen in the elastic model of stress shown below, and it is certainly enhanced when taking the viscoelastic nature of the glass into consideration. In the figure shown the stress the edges of the irradiated area are induced by a 3ms pulse, and the profile shown, is 3ms into the FLA process. Two large peak stress points can be seen at the edges of the irradiated area, in the film, and two lines of increased stress continue vertically down into the glass

- 125 - substrate. This stress exists for all pulse durations, and is almost certainly the cause of the cracking seen around the edge of the irradiated area when shading is used to prevent cracks originating at the edge of the sample. To effectively remove this stress from the sample, the transition from the irradiated are to a non-irradiated are must be made more gradual. The effect this would have on the stress at the boundary was not investigated further in this thesis. It is also important to note that the stress in the vertical direction at the boundary of the irradiated are is still at least an order of magnitude less that the stress parallel to the film, but because it is concentrated over such a small area, the likely hood of damage is relatively high.

Vertical Component of Stress in Si film – 3ms into a 3ms pulse.

Figure 64 shows the vertical component of stress in the silicon film (Top) and glass substrate (bottom). It can be seen that sharp stress concentration points exist at the irradiated area boundary, and this stress continues vertically in the glass substrate with a lower magnitude. This stress concentration at the irradiated area boundary is most likely the cause of the cracking seen in our sample, in this area.

The viscoelastic relaxation in the horizontal axis results in an increase in strain in the glass, along the vertical axis. As stated earlier this does not increase the stress in the film away from the edges of the sample, as the Si film is not confined in this dimension. However, at the boundary between the irradiated area, and the shaded area that exists at the edge of our simulated sample, there is a sharp change in the vertical component of strain. This results in a large component of stress in the Si film, around the shaded edge boundary. It is this stress which is believed to be responsible for the damage seen in

- 126 - experiments where cracks originate and run parallel to this shading boundary. An example of the resulting cracks can be seen in chapter 1, section 1.5.3.

This stress arising at the boundary is increased by the viscoelastic relaxation of glass, as vertical displacement of the film increases over that which would be experienced in elastic materials. The mechanism for this is the increase in the vertical stress component of the glass which is discussed earlier. Away from the shading boundary, the transfer of strain from the horizontal to vertical components reduces the overall strain, because the vertical component is unconstrained, and vertical displacement is uniform across the Si film. At the shading boundary however, the Si is constrained, and an additional vertical stress component is induce in the film. A diagram showing this increased vertical stress component is shown below in Figure 65.

Diagram of increased vertical stress component at Shading Boundary

Figure 65 shows a diagram showing increased vertical displacement in the irradiated area, relative to the shaded area. The gradient of the displacement at the shading boundary induces a sharp stress in the film, which has been shown to result in cracking in our FLA experiments. The thermally induced displacement of the sample is shown in blue, and the corresponding stress/strain is shown in red.

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2.7.3 Discussion of Structural Modelling Results The following discussion aims to give the reader a conceptual view of what is occurring in the sample during FLA, and how the viscoelastic nature of the glass impacts on the induced stress.

From the 2D thermal profile (Figure 49) we can see that the glass substrate is heated locally at the top of the sample, and during the FLA pulse, the bottom of the substrate and the sides of the substrate remain at the preheat temperature. At the preheat temperature of 700°C the viscoelastic relaxation time is approximately 0.8 seconds. So over the pulse durations considered here, the amount of relaxation at the edges of the glass is minimal. For this conceptual model we are also not taking sample bending into consideration. If we consider an elastic material confined on 3 sides and allowed to expand freely in the vertical direction (Shown in Figure 66) we can visualise the forces involved that give rise to the stress profile in the elastic simulation. We can see that the horizontal force component is large relative to the vertical force component, as most of that force is dissipated by free expansion of the material along that axis. It may seem like an obvious statement at this stage, but allowing thermal expansion in the vertical direction does not allow dissipation of the horizontal stress.

Heated Elastic Material Confined on 3 Sides

Figure 66 shows the large horizontal force component and relatively small vertical force component when an elastic material is heated and confined on 3 sides and allowed to expand freely in 1 direction. The thin solid line shows the position of the top surface of the film before heating, and the dashed line shows the position after vertical expansion. - 128 -

Allowing thermal expansion in the vertical direction gives rise to shear stress, and this shear stress is not relaxed in elastic materials, but is relaxed in viscoelastic materials. It is by this mechanism of shear stress relaxation in viscoelastic materials that the force in the horizontal direction is dissipated in viscoelastic materials. The following figure shows the same situation as shown in Figure 66, only with a viscoelastic material replacing the elastic material. It can be seen that the stress in the horizontal direction decreases as the dissipation of shear strain in the material transfers this stress from a horizontal to vertical. The magnitude of the force exerted on the confining box is represented by the size of the red arrows in the elastic material and green arrows in the viscoelastic material below. This additional vertical stress increases the expansion of the material along this direction, thus dissipating the stress.

Heated Viscoelastic Material Confined on 3 Sides

Figure 67 shows the large horizontal force component and relatively small vertical force component when an elastic material is heated and confined on 3 sides and allowed to expand freely in 1 direction. The thin solid line shows the position of the top surface of the film before heating, and the dashed line shows the position after vertical expansion.

The lower the viscosity of the glass, or the longer time is allowed to elapse, the more relaxation of shear stress occurs, and the more expansion would be seen in the vertical direction of Figure 64.

- 129 -

Viscoelastic relaxation is a form of plastic deformation and is non-reversible. It can be seen in Figure 55 and Figure 56 that after viscoelastic relaxation has occurred in the glass, the stress in the Si film does not returns to the stress state predicted by an elastic material, nor does it return to the stress free state experienced before the Flash Lamp heating pulse. This is because the viscoelastic relaxation occurring in the glass at each time step is cumulative, and returning to a stress free state requires additional plastic deformation. The viscoelastic relaxation retards thermal expansion in the horizontal direction. Assuming that that same peak temperature is achieved in the film, then less viscoelastic relaxation occurs in the glass, by the end of the pulse. If less viscoelastic relaxation occurs then more force exists in the glass for thermal expansion along the horizontal axis and thus, more expansion of the glass occurs along axis, which relaxes the compressive stress in the film.

For the viscoelastic case we see that longer pulse durations resulted in an increased stress in the Si film, implying that longer pulse durations would induce a higher compressive stress in the film. This is not consistent with our experience, as heating to temperatures of above 1100°C on a belt furnace, have been shown to result in crack free samples, while heating over a pulse duration of 3 ms to 20 ms to the same temperature results in significant damage to the Si film. The time scale of this simulation is from 3 ms to 200 ms, and over this timescale the force exerted on the glass is very small compared to the internal forces within the glass. So the deformation, and stress profile within the glass and film is dominated by the dynamics of the glass. Over longer timescales the force exerted on the glass substrate by the Si film becomes comparable to the internal forces of the glass, and the Si film then induces viscoelastic relaxation, that serves to reduce film stress. This time scale is dependent on the viscosity of the glass which is temperature dependent, and the thermal diffusivity of the glass, but must occur at some point between the 200 ms time scale investigated here, and the time- temperature annealing conditions used for belt furnace annealing outlined in Chapter 1.

After the FLA pulse has ended then stress relaxation begins. The rate at which this happens is dependent on the speed at which thermal energy diffuses through the sample and into the surrounding environment, and viscoelastic relaxation within the glass. If the glass is held at the preheat temperature after FLA, then the stress profile within the glass would mostly be dissipated by additional viscoelastic relaxation. However, if the

- 130 - sample is cooled immediately following the FLA pulse the unique mix of tensile and compressive stresses through the depth of the glass is ‘frozen’ in to the material altering its mechanical properties from those immediately preceding the FLA heating process. As no damage was observed in the borosilicate glass samples, it is assumed that if this mixed compressive/tensile stress profile exists in the glass, then it is of a sufficiently low magnitude to not cause failure of the sample. It is important to note the difference between stress in the Si film that affects the electrical properties, and stress within the glass substrate which can remain in the glass with minimal impact on the performance of the thin film solar cell, assuming that the stresses are too low to cause major deformation or failure of the glass.

2.7.4 Pulse Energy Density Damage Threshold The pulse Energy Density Damage threshold, is the maximum pulse energy density of the flash lamp that can be used to anneal our thin film Si on glass samples without causing damage to the film.

From the Experiments outlined in Chapter 1 we have data on what pulse energy density coincides with the onset of cracking in our films. By using the results previously mentioned in this section, and cross referencing them with data collected from our experiments with Prof. Skorupa at HZDR we can determine the maximum possible stress the Si film can withstand before cracking, under FLA processing conditions.

From the experimental data presented in Chapter 1 we can see that the maximum pulse energy density used on our samples before damage occurs was 21.5 J/cm2 for a 3 ms pulse, and 35.8 J/cm2 for a 20 ms pulse. It is worth noting that the pulse energy density damage threshold was independent of the preheat temperature. So samples annealed with a preheat temperature of 700°C reach a peak temperature 100°C higher than samples preheated to 600°C before damage is observed. Although 40 ms pulse experiments were conducted, the pulse energy density was too low to induce damage on the Si film, so it is not considered here.

- 131 -

Preheat Temperature (°C) Peak Compressive Stress - Peak Compressive stress - Damage Threshold Pulse Peak Tensile Stress - Pulse Duration (ms) Viscoelastic (MPa) Temperature (°C) Estimated Peak Energy Density Elastic (MPa) Elastic (MPa)

3 700 21.5 1155 14.4 196 59.8

20 700 35.8 890 23.1 110 61.3

Table 14 shows the experimental parameters where the onset of damage is observed. It can be seen that the maximum compressive stress observed in the film when processed with a pulse energy density at the damage threshold is predicted to be approximately 60 MPa by the presented model. From the simulations presented earlier in this section we can find the stress in the film for the threshold pulse energy densities. These results are summarised in Table 14 above. It can be seen that the viscoelastic model presented predicts failure in the Si film at roughly the same magnitude of stress in the film (~60 MPa). If the viscoelastic nature of glass is not taken into account, then the stress in the film that will induce damage varies quite significantly. The comparison of the results of the viscoelastic model experimentally derived pulse energy density damage thresholds, suggests that the model is quite accurate. We also see that not taking the viscoelastic nature of glass into account results in large deviations in the predicted maximum stresses in the film. 60 MPa may seem like a low stress to induce failure in the film, but when taking into account discussed in section 2.5, it can be seen that failure of thin film Si can occur at much lower stresses if high rates of induced strain are present.

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2.8 Implications for FLA on Thin Film Si on Glass and Discussion The simulations have shown that the stresses involved in FLA of Si thin film on glass are of the order of 10s to 100s of MPa depending on the pulse duration, and peak temperature reached during the process. As discussed in section 2.7.2, the fast rate of the stress being induced, is believed to be the cause of the mechanical failure of the film, rather than just the magnitude of the stress itself. Because of the lack of experimental data around strain rates in thin film Si over time intervals of milliseconds, it is unclear whether longer pulse durations (of the order of 100’s of milliseconds) would allow damage free FLA processing of Si thin films. This investigation has shown that longer pulse durations and the effect of viscoelastic relaxation of the glass results in an increase in film stress with increasing pulse duration. The pulse duration investigated were not increased past 200 ms because at heating durations longer than this, flash lamp annealing equipment is no longer the optimal method of heating the sample. High power continuous lamps would be more appropriate, which requires different equipment.

In Chapter 1, section 1.3, we saw that the optimal annealing temperature and times follow an Arrhenius like relationship. When extrapolating this to temperatures near the melting point of Silicon, this relationship predicts that pulses of the scale of 100’s of milliseconds will result in optimal annealing conditions. The results of this simulation suggests that the optimal parameter space for reducing damage and achieving the highest possible level of annealing is for shorter pulse duration of 3 to 20 ms, not 100 to 200 ms. This would suggest that flash lamp annealing, is incompatible with the thermal profiles required to anneal defects with Si film solar cells on a glass substrate. This is backed up by the investigations presented in Chapter 1, where we failed to show experimentally that FLA is a viable option for replacement of the belt furnace annealing process.

- 133 -

Chapter 3

Photoluminescence Imaging of Thin Film Silicon on Glass Solar Cells

- 134 -

3.1 Introduction Photoluminescence imaging is a characterisation technique that produces a spatially resolved map of the light generated from a semiconductor. Silicon luminescence is in the range 900-1200nm.

Photoluminescence (PL) Imaging has become an important part of wafer based solar cell characterisation in recent years. The technique is able to quantify many important solar cell parameters including minority carrier lifetime [Würfel, et al. - 1995], implied

Voc [Trupke, et al. - 2005], effective series resistance [Kampwerth, et al. - 2008] and emitter sheet resistance [Kampwerth - 2010].

The focus of this chapter is to report on the first results of PL imaging done on LPCSG (Liquid Phase Crystalline Silicon on Glass) thin film silicon solar cell on glass. This is the first time PL imaging has been successfully attempted on this material to extract cell parameters. This is due in part, to the development of thin film solar cells at UNSW and Suntech R&D Australia (formally CSG), who have increased the Silicon film quality to a point where PL imaging is possible. PL Imaging was not previously possible because the carrier lifetime of the Si films was very low.

In the following sections an overview of photoluminescence is given, with a focus on how its application as a characterisation tool on silicon thin film, differs from that on silicon wafers. The reader will be directed to relevant papers on topics related to PL imaging, where the content is not directly relevant to its application on thin film Silicon.

Luminescence refers to all light emission not resulting from heat, and luminescence is not limited exclusive to light emission from semiconductors, however other subcategories of fluorescence are not relevant and not considered here. In this thesis Photoluminescence (PL) refers to the light emitted during recombination of electrons and holes across the band gap, also known as Band to band emission, and occurs at a wavelength of 900- 1200 nm. PL emission in other spectral ranges all so occurs in solar cell during the process of trap assisted recombination. Analysis of the PL spectrum can also be used as a valuable solar cell characterisation technique [Tajima - 1978]. The prefix ‘photo’ refers to the method of excitation of the luminescence. Similarly excitation via an electrical current is electroluminescence, and in animals and bacteria, the light emitted is referred to as bioluminescence. - 135 -

3.2 Samples Investigated PL Imaging of thin film Si on glass was predominantly investigated on LPCSG (Liquid Phase Crystallised Silicon on Glass) Si films. These films are very similar to the SPC (Solid Phase Crystallised) thin film Si described in section 1.2, with a few important differences.

Firstly as the names suggest, LPCSG is crystallised from a liquid, and SPC material is crystallised from a solid a-Si state. LPCSG leads to much larger grains relative to SPC films, and a much higher electrical quality. Secondly, the Si film is 10µm in LPCSG samples, and only 2µm thick in SPC samples. This thickness variation must be taken into consideration in PL imaging, and is discussed in the following sections.

The manufacturing process of LPCSG samples begins with Borosilicate glass. The glass substrate for LPCSG films is the same as that used for SPC films, and poses the same changes for PL Imaging. An intermediate layer of SiO, SiN, or a combination of the two is then deposited on glass substrate. This intermediate layer does not interfere with the excitation light from the PL Imaging system, as it is completely absorbed in the Si film. However the surface passivation provided by the intermediate layer does play a role in the intensity of the PL signal.

The Si film itself is deposited on the intermediate layer via e-beam thermal evaporation, resulting in an a-Si film. This film is then crystallised with a high power laser beam, approximately 180µm wide and 11mm long. The film is doped with a boron concentration of approximately 1E16 cm-1, during the film deposition, or from a highly doped intermediate layer. During the crystallisation, the Si is liquid for a time of microseconds to milliseconds, and in that time, the boron doping diffuses uniformly through the film. The sample is then spin coated with a phosphorous dopant source, and an emitter is thermally diffused on the air side of the film. The resulting dopant profile is shown in Figure 80.

As well as LPCSG material, some SPC samples which had undergone FLA processing were also investigated. The SPC samples are described in more detail in Chapter 1.

- 136 -

3.3 Key Differences between PL on wafers and PL on thin film Si on glass The first and most obvious difference is the reduced thickness of the Silicon film, relative to that of a wafer. The thicknesses of the films investigated in this study are typically between 2 µm and 10 µm. Compared to a solar cell of 180 µm to300 µm, the volume of material contributing to PL is reduced by 1 to 2 orders of magnitude. This means that the PL intensity we can expect from a thin film Si solar cell will be less than an equivalent wafer solar cell.

Excitation wavelength = 280 nm Excitation wavelength = 488 nm

Excitation wavelength = 365 nm Excitation wavelength = 610 nm

Figure 68, luminescence from Borofloat, and other Glasses from Schott. These graphs are taken directly from the Borofloat brochure.

- 137 -

The second important and obvious difference is that the film is on a borosilicate glass substrate. This has implications for PL imaging because the glass luminesces when illuminated with visible light. The spectral shape of the fluorescence from the glass depends strongly on illumination wavelength, as shown in Figure 68, above. The term fluorescence is deliberately used to describe light emission from the glass to distinguish it from photoluminescence from the Silicon film. It is equally true that the fluorescence from the glass could be described as photoluminescence.

The glass fluorescence signal whose wavelength component in the range 1000 nm to 1150 nm is that which contributes to noise. PL noise in the visible wavelength range is shown in Figure 68, and the intensity of the fluorescence of the glass in the wavelength range of interest can be directly measure with the PL imaging system. It was found that the PL intensity from the glass in the wavelength range of interest was linearly related to the excitation intensity. It was also found that shorter wavelength excitation resulted in a much higher PL noise signal relative to longer wavelengths for all glasses. The intensity dependence and the wavelength dependence of PL intensity can be seen in Figure 69, and Figure 70, respectively.

PL Intensity of various Glasses

100000

10000 Second

1000 /

100 Red Counts Green PL 10 Blue 1 5

mm) mm) mm) mm) mm)

KG (3 (3

(0.7 (0.7

BSG ‐ Text SLG Eagle BSG Quartz (2.2

Figure 69, show the fluorescent signal seen by the PL camera, from direct excitation of various glass substrates. The Green excitation wavelength is 530 nm and the Blue excitation wavelength is 465nm. The Intensity of the PL shown in the graph is measured over the wavelength range 1050nm to 1150nm. The intensity of the Blue and Green excitation sources are 0.23 W/cm2.

- 138 -

Two interesting notes from Figure 69 are that quartz has a very low fluorescence signal when illuminated by visible light, and the substrate of choice for our solar cells, has the highest of all glasses measured. This means that quartz can be used in the PL setup without problems, and any stray light illuminating the substrate of our samples could result in noise. Fluorescence from the glass excited through cracks in the silicon film is found to have little effect, and is discussed later.

Glass Fluorescence vs. Blue LED Excitation

2000

1500 Second

/ 1000 Counts 500 PL

0 1000 1500 2000 2500 3000 3500 4000 4500 Excitation Intensity (W/m2) Glass Fluorescence vs Blue LED Light Intensity

KG5 filter Fluorescence ‐ Blue Excitation

Figure 70, shows the Fluorescence intensity from 3mm thick BSG at various Blue LED excitation intensities. The fit of the data to a line gives an R² value = 0.9982. (R² = 1 is a perfect fit). The noise level of the Blue LED is given in this figure for reference (approximately 30 counts per second). The same trend is also found with Green and Red excitation.

PL Imaging of wafer based solar cells can be conducted at all stages of the cell manufacturing process. However, PL imaging can be performed on thin film silicon on glass solar cells up to the point where the cell is contacted. This is because the fluorescence of the glass is much higher than the silicon, and so the PL excitation light can only illuminate the silicon from the air side of the film. When the silicon is contacted, light can only enter the film from the glass side. After contacting the cell, electroluminescence could be used as a tool to measure the material quality. This method will be investigated as a characterisation technique in the near future, as a method of characterising the performance of the resultant cell.

Another important difference between Si thin film and wafers is the quality of the material. Wafers used in today’s solar cells typically have carrier lifetimes of 100’s of µs, whereas the lifetime of thin films, is at most on the order of 1 µs. This means that

- 139 - the PL signal from our thin films is expected to produce a lower PL signal relative to a standard wafer. Measurement of the PL intensity is useful because it is most fundamentally related to the separation of the quasi Fermi energy levels [Trupke, et al. - 2007]. However recombination of carriers in the bulk rather than the junction is not dependent on the Fermi energy levels, and analysis of the PL signal must incorporate a constant factor to the equations to account for these diffusion limited carriers [Trupke.et .al - 2007] [Kampwerth.et .al - 2008].

- 140 -

3.4 Solar Cell Specific Photoluminescence Theory Photoluminescence theory has been well covered by many authors with papers specifically pertaining to Silicon dating back as far as the 1970’s [Tajima - 1978]. This section aims to give an overview of the fundamentals of PL imaging, and how the PL signal has been utilised to measure solar cell parameters in wafers, and how these can be applied to Silicon thin film solar cells. For a more detailed discussion on the underlying physics, and application to solar cells, the reader is referred to the work of Wurfel, Trupke, and Cuevas.

In semiconductors the energy-momentum characteristics of electrons can be divided into three distinct regions. These are the valance band, where electrons are rigid within the lattice structure of the semiconductor, the conduction band, where electrons are move freely about the lattice, and the band gap, where electrons are quantum mechanically forbidden, in an ideal semiconductor.

At any temperature above 0 Kelvin, there is a transfer of electrons between the valance and conduction band, across the Band gap. The process of electron/hole recombination occurs via three mechanisms;

 Radiative Recombination,

 Auger Recombination, and

 Shockley-Read-Hall (SHR) Recombination.

The amount of recombination occurring via each of the above mentioned mechanism varies, and is dependent on a number of factors, including doping density [Altermatt, et al. - 2006], temperature [Trupke, et al. - 2003], and the excess carrier concentration [Kerr, et al. - 2003]. The effective carrier lifetime can be expressed as a combination of the above recombination mechanisms and surface recombination:

Where τ is the carrier lifetime in the bulk Silicon [Trupke.et .al - 2005]:

- 141 -

The bulk lifetime is an important material parameter to fully characterise a solar cell, and can be done with PL measurements through the following equations in this section.

Radiative recombination, as the name suggests, is when a photon is released during the process of an electron recombining with a hole. It is known as band to band recombination, and the photons emitted during this process are also known as band to band radiation. Silicon is an indirect band gap semiconductor, so the process of photon emission must involve an electron-hole pair, and a third particle for continuity of momentum to be satisfied. The other recombination mechanisms do not generate photons of the same energy as the band gap, although photon emission at longer wavelengths may be part of the recombination process associated with defects.

Auger recombination (also known as Impact recombination) is also a three particle interaction, whereby one electron recombines with a hole, but instead of the excess energy being emitted as a photon, it is transferred to a third particle, and subsequently lost as heat. The important thing to note about Auger recombination, from the point of view of PL, is that there is no photon emission in the process. Auger recombination becomes a significant form of recombination when high carrier concentrations are present. This is due to an increased probability of carrier-carrier collisions.

Shockley-Read-Hall (SRH) recombination (also known as trap-assisted recombination) occurs when there are impurities or other lattice defects within the forbidden band gap region. Electrons can decay to these defect levels within the band gap, and any photons that are emitted are of a lower energy than those emitted when an electron recombines band to band. Using the intensity and wavelength of the photons emitted during SRH recombination to characterise defects is known as spectral photoluminescence.

Under conditions of low excess carrier concentration rates, low doping, and room temperature conditions, the PL intensity (), is described by the following equation.

. . ∆.∆ 61 where is a calibration factor determined by experiment, is the radiative recombination coefficient, is the doping density, and ∆ is the excess minority carrier concentration [Trupke - 2005]. Equation 61 holds for all PL excitation conditions, however the radiative recombination coefficient () has been shown to be strongly dependent on the doping density, temperature, and carrier injection density - 142 -

[Altermatt.et .al - 2006]. In our case, the number of carriers we are injecting into the solar cell is in the range where can be assumed to be constant.

In the case of the thin film solar cells illuminated with approximately one sun intensity, the doping density is significantly larger than the excess minority carrier density,

≫∆, which means that the above equation can be simplified even further.

..∆ 62

This simplification will be used throughout the analysis and PC1D simulations. Also, as B and

are constants, they have been merged into the one constant B, for simplicity. From Figure 71 we can see that the PL intensity is linearly proportional to the excitation intensity. The data shown in this figure is the PL intensity measured when excited with the Blue LED, and clearly has an r2 value close to one when linear regression is performed on the data.

PL Intensity vs Excitation Intensity

600

500

400

(Counts/sec) 300

200

100 Intensity

PL 0 0 500 1000 1500 2000 2500 3000 Excitation Intensity (W/m2)

Figure 71, shows the linear relationship between excitation intensity and measured PL intensity. The sample was a standard LPCSG sample with junction. The sample was excited with 530 nm (green) light.

This linear relationship is expected from the PL equations outlined by Trupke [Trupke - 2005], given below. This linear relationship implies that no additional recombination mechanisms become apparent with an increase in the number of carriers. This linear relationship would break down at much higher generation rates as Auger recombination becomes more probable, and starts to dominate.

∆ 63

- 143 -

..∆... 64 where C is a constant, τ is the effective carrier lifetime, and is the Generation rate which is proportional to the excitation illumination intensity.

Many solar cell properties other than bulk lifetime can be measured with Luminescence Imaging. These include, minority carrier lifetime [Würfel.et .al - 1995], Voltage [Trupke.et .al - 2005], Series and Sheet Resistance [Trupke, et al. - 2007], [Kampwerth.et .al - 2008], Shunting, and the diffusion length of minority carriers in polycrystalline Silicon (pc-Si) [Würfel.et .al - 1995].

- 144 -

3.5 Physical Setup of PL Imaging System Two practical limitations guided the design of the excitation light source for PL imaging of thin film silicon on glass:

1. Excitation light illuminating the glass, must be minimised or eliminated.

2. The excitation light must be uniform, and have at least one sun photon flux.

The first limitation listed above comes from the fact that the glass substrate has a high luminescence intensity in the same wavelength range as the Silicon band-band transition, as can be seen in Figure 69. The first limitation listed above also means that the majority of the excitation wavelength must be completely absorbed within a depth, less than or equal to the thickness of the silicon film.

Light Intensity at depth in Silicon

1.E+02 1.E+01 1.E+00 1.E‐01 (%)

1.E‐02 1.E‐03 1.E‐04

Intensity 1.E‐05 1.E‐06 1.E‐07 1.E‐08 0246810 Penetration depth from surface (um) 465 nm 530 nm 630 nm 808nm

Figure 72, shows the intensity of the excitation light at various depths into the Si. It can be seen that wavelengths shorter than 630 nm are almost completely absorbed within the 10 µm Si film. 808 nm light is typically used for PL on wafers, but is not appropriate for thin film Si because a significant amount of light penetrated the Si and excited PL in the glass.

High power (100 W) LEDs were chosen as the excitation source instead of traditional method of using lasers. LEDs were chosen because many wavelengths from 465 nm to 630 nm were available at a price of approximately AU$70.00 each, from SatisLED.com. In our experience the LEDs have been of good quality and we have had only one failed

- 145 - during this investigation. The line width of lasers is typically less than 1 nm, while the line width of LEDs is typically from 3 to 10 nm. This is not a problem for PL Imaging because the excitation wavelength is very far from the PL emission wavelength of 1150 nm.

Although the input power of the LEDs is 100 W, the output power of these LEDs varies depending on the wavelength. The Blue LED has an output power of approximately 30 W, while the Green LED has 10 W, and the Red LED has an output power of 17 W. This difference is due to the different semiconductor material used in each LED. Also, the typical application of these LEDs is for lighting, and because the human eye is more sensitive to Green light, less optical power is required to obtain a similar Lux value of other wavelengths. For this reason the Green LEDs typically have a lower output power than either Red or Blue LEDs. The Green and Blue LEDs operate at between 32 – 36 V and a maximum current of 3.5 Amps. An image of the LEDs used in this investigation can be seen

100 W LED

Figure 73 is an image of the LEDs used in this investigation. The difference wavelength LEDs look the same when not turned on. The image was taken from the SatisLED.com website. The LED light is emitted from 100 discrete points on the yellow area, and the divergence of the light from each point is very high (approximately 140°).

A negative aspect of using these LEDs as the excitation source is that low intensity IR light is emitted, which is an additional source of noise in the PL signal. The IR emitted from the LED is intense enough to saturate the PL camera in 1 second, if illuminated directly. The IR from the LED was filtered out by using Schott glass filters KG3, and KG5. The transmission curves of these filters can be found in Figure 74, below. The - 146 - transmission of both filters between 400 and 650nm is above 80%, but the absorption coefficient for light above 1000 nm is at least an order of magnitude better for the KG5 filter. The first and second configuration of the PL excitation setup used KG3 filters because they were available at no cost, but when the KG5 filters were eventually put in the system, the noise reduced an order of magnitude, and is now only marginally higher than the dark current noise of the CCD camera.

Optical Density of KG3 and KG5 Schott Filters

1E+00

1E‐01

1E‐02 (O.D)

1E‐03

1E‐04 Transmission 1E‐05

1E‐06 300 400 500 600 700 800 900 1000 1100 1200 Wavelength (nm)

KG3 ‐ Transmission (O.D.) KG5 ‐ Transmission (O.D.)

Figure 74 shows the transmission curves of the KG3 filter and the KG5 filter from Schott. The data was taken directly from the KG3 and KG5 data sheets.

Excitation Parameters Blue Green Red IR Wavelength (nm) 465 530 630 808 Absorption depth (1/e) (µm) 0.52 1.27 3.06 12.9 Percentage of light absorbed in 10 µm Si film 100% 99.99% 98.4% 54% Percentage of light absorbed in 2 µm Si film 97.8% - - -

Table 15 shows parameters of the LED Excitation light. Also shown is the table is 808 nm light, which has historically been used for excitation of PL in Si wafers. The excitation light must enter the film on the silicon side, to avoid fluorescence noise from the glass, while the PL emission from the silicon can be collected from either the air or glass side. The first attempt at exciting PL in the Si film, projected the 100W LED onto the film, and imaged the PL signal from the same side, as shown in Figure

- 147 -

76. This is the same configuration used for PL excitation of wafers. The light emitted from the LEDs is highly divergent, and the collection and collimation optics used resulted in high losses, and non-uniformity on the Si surface, which can be seen in Figure 75. Because so much light was lost, and the excitation illumination intensity was so non-uniform a different configuration had to be found.

Non-Uniformity of LED Excitation light – Version 1

Figure 75, Non-Uniformity of PL excitation light projected onto the Si film.

- 148 -

Diagram of First PL Excitation Elements of Configuration 1 configuration 1. 100 W LED, 10 1 2. Telecope configuration to

9 focus LED onto Si film, 2 8 3. IR Blocking Filter (KG3),

4. Green or Blue LED Excitation 3 light, no IR Noise,

7 5. Overlap area,

4 6. Si film on glass, Si Side up,

5 7. Visible Light, and PL from Si film,

8. Visible Light Filter,

9. PL Signal from Si, no Visible 6 light,

10. Cooled Si CCD Camera.

Figure 76, shows the first configuration if PL excitation of thin films.

In the second configuration attempted, the excitation light enters the film on the air side and the PL signal is imaged on the glass side. With this configuration a photon flux 3 times higher than that of 1 sun (1 sun = 2.7E17 photons) could be achieved with the 100 W Red and Blue LEDs, and close to 2 suns with the green LED. The intensity achievable with the Red LED was not measured in the second configuration. The only downside of this configuration was that there was an appreciable amount of non- uniformity in the illumination intensity across the excitation area. This non-uniformity can be seen in Figure 78. The intensity of the light on the edge of the illumination area

- 149 - in configuration 2 was between 70% and 80% of the peak intensity. In version 3, the illumination intensity is within 3% or 4% of the maximum illumination intensity point.

Configuration Version 2 Configuration Version 3 Index 1. 100 W LED, 6 6 2. (a) Focusing Lens

5 5 2. (b) Light Integrating

Pipe 4 4 3. IR Blocking Filter 3 3 (KG3 or KG5),

2 a 4. Si film on glass, Si 2 b 1 Side down,

5. Visible Light Filter,

6. Cooled Si CCD

1 Camera.

Figure 77, shows the setup of version 2 and version 3. Both setups Excite PL on the Si side of the film, and images the PL signal from the glass side. Version 2 had issues with uniformity of illumination of the sample. This problem was solved in version 3 with the use of a light integrating pipe (2 b).

The illumination area of the setup is 40mm by 40mm. This size is ideal for the film currently being investigated, which are ~40mm x 40mm. The actual samples are ~50mm x 50mm, but the excitation light must be masked, as to not illuminate the glass edges directly, or a high noise signal will result in the PL image. The idea of using a light pipe to obtain a uniform flux is well established [Chen, et al. - 1963]. The size of the Illuminated area could easily be increased by simply adding more LEDs in a grid pattern, and using a larger area filter. The high divergence on the LEDs makes the illumination intensity naturally tend towards uniformity without the need for optics. The same usage of mirrors around the edge of the illumination area may be needed to increase the uniformity around the edges.

- 150 -

Uniformity Version 2 Uniformity Version 3

Figure 78, shows the excitation uniformity across the illumination area for configuration versions 2 and 3. The improved uniformity is clear in version 3.

Uniformity of Excitation Illumination

1 0.9 0.8 0.7 (Arb)

0.6 0.5 0.4 0.3

Intensity 0.2 0.1 0 00.511.522.53 Distance (Pixels) Figure 79, shows a cross-section of the excitation uniformity, shown above. This figure shows a horizontal profile from the right image in Figure 78. This shows that the excitation uniformity is better than 90% across the entire illumination area.

The increased uniformity of the 3rd configuration attempted was due to the use of a short integrating light pipe between the LED and the illumination plane. To obtain a uniform illumination a relatively short light pipe (4 cm) was be used, because of the high divergence of the LEDs used (~140°). This meant that there are a fewer number of bounces of the light off the mirrors, and thus only a small amount of light is lost. The mirrors are cheap, and low quality, but any IR introduced by the glass on the mirrors is filtered out by the KG5 filters placed immediately before the Si film. The maximum possible illumination intensities and other parameters for the various LEDs and configurations are listed in Table 16, below. - 151 -

Configuration Uniformity Intensity Max Photon Flux (Photons/cm2) Blue Green Red Setup 1 Poor Poor ~ 1E16 ~1E16 - Setup 2 Poor High 1.0E18 6.2E17 1.6E18 Setup 3 Good Good 5.9E17 3.3E17 8.6E17

Table 16 shows the properties of the various attempted illumination configurations. Aluminium is used on the outside of the housing of the excitation light sources. This is because aluminium has a virtually no luminescence signal, and is relatively cheap. Other material such as plastic can give off a luminescence signal, and unnecessarily add noise to the system.

- 152 -

3.6 PL modelling in PC1D

3.6.1 Process Overview PC1D is a well-known simulation program for the photovoltaics industry, where fundamental Si properties, physical dimensions, doping concentration and profile are used to simulate the performance of different cell structures. The majority and minority carrier concentration through the depth of a sample can be simulated using PC1D, for different cell structures and excitation parameters, including monochromatic excitation. The PL intensity measured by the camera is essentially the sum of the PL emitted through the depth of the cell from that position of the film, which is directly related to the carrier concentration. This relationship is given in the following equation:

. .∆ .. . . 65

Where the doping density (, the excess minority carrier lifetime ∆, excess carrier concentration and hole concentration are functions of depth, through the thickness of the cell. PC1D models the material parameters through the thickness of the cell (1D), which makes it an adequate basis for investigating Photoluminescence.

PL modelling is conducted by inputting the known parameters of the solar cell into PC1D and running the program as standard. When the simulation is complete, the electron and hole carrier density information is then taken from the program and further processed in Excel. In Excel the electron and hole carrier concentration is integrated over the depth of the cell, which from the above equation, is proportional to the PL intensity. A value proportional to the PL intensity measured by the camera is the most that could be expected when comparing simulation to experiments, as all equations relating PL intensity to material properties contains a proportionality constant relating to the collection efficiency of imaging camera, which must be determined experimentally. [Trupke.et .al - 2005]

With the above mentioned process, the effect of excitation wavelength, surface passivation, carrier lifetime, doping density, etc., on the PL intensity can be evaluated.

- 153 -

3.6.2 Model Input Parameters A summary of the input parameters to the model are outlined in Table 17.

Material Parameters Value Thickness (µm) 10 Carrier Mobility (cm2/Vs) (Internal PC1D Model) - Electrons (Max) : 1417 - Holes (Max): 470 Band gap (eV) 1.124 Intrinsic conc. @ 300K (cm- 10E101 3) Refractive Index 3.582 Background doping (cm-3) 1E16 (P-type) Doping Concentration (cm-3) - Air side: 1E19 (N-type) - Glass side: 1E17 (P-type) Doping Depth (cm-3) - Air side (nm): 250 to 300 - Glass side (nm): 100 to 150 Bulk recom. time (µsec) 1E-4 to 10 Surf. Recom. Velocity - Air side (cm/s): 0 to 1E6 - Glass side (cm/s): 0 to 1E6

Table 17, shows the input parameters into the PC1D, PL simulation. The intrinsic carrier concentration (ni) used in the simulation is 10E10 cm-3, which is accurate enough for the purposes of the simulation. The dopant density and depth profile used in the PC1D simulations are based on SIMS data obtained from samples which had undergone the same dopant diffusion process as those in the PL investigation. As can be seen in the PL theory section above (Section 0), the measured PL intensity is linearly proportional to the dopant concentration, which

1 -3 The intrinsic carrier concentration (ni) used in the simulation is 10E10 cm , which is accurate enough for the purposes of the simulation, but can be more accurately given as 9.71E9 cm-3 [2003 – Trupke, J. Appl. Phys. 94, 4930] 2 The refractive index is wavelength dependent and varies from 4.54 at 465nm to 3.89 at 630nm which is the range of excitation wavelengths investigated [Aspnes and Studna 1983]. The effect of this discrepancy is expected to be minimal, the thickness of the film is many times larger than the wavelength of the excitation light. - 154 - is orders of magnitude larger (1020) in the junction of the cell compared to the bulk (1016).

Dopant Diffusion in thin film Si on Glass

1E+21 P

1E+20 P 900°C Diffusion 1E+19

1E+18 870°C Diffusion

1E+17

P CONCENTRATION (atoms/cc) CONCENTRATION P 1E+16 0 100 200 300 400 500

DEPTH (nm) Jul 25, 2012

Figure 80, is the rear (N type) doping concentration of the solar cells investigated by PL in this study. The carrier mobilities listed in Table 17 are the default values used for bulk Silicon by PC1D. The actual mobility of the thin films under investigation can vary significantly over the film. Hall measurements in areas where a relatively high PL intensity has been measured have shown that the minority carrier mobility can be as high as 490 cm2/Vs and as low as 175 cm2/Vs in areas of low PL intensity. It should be noted that the mobility measurements are carried out on cells with no junction. This does not mean that all high PL signal areas have a high mobility and all low PL signal areas have low mobility, but it does illustrate that favourable material qualities, such as high carrier mobility, coincide with areas of relatively high PL intensity.

The measured mobility of 490 cm2/Vs is actually 1.18 times larger than the mobility expected in bulk silicon at the dopant density seen in our films (1016cm-1). This mobility enhancement can be explained by taking into account strains present in the Si film. Strains in the Si crystal structure have been shown to enhance mobility up to 5 time that of bulk Silicon, as can be seen in Figure 81, below [Thompson, et al. - 2006]. If we assume that the mobility enhancement measured is caused by uniaxial compression of the (001) plane, then approximately 120 MPa of stress would be present - 155 - in the film. Although not directly measured in LPCSG material at this stage, it has been shown by Brazil that stresses as high as 159 MPa were present in SPC Silicon on glass [Brazil - 2009].

Mobility Enhancement Factor in Silicon

Figure 81, shows the mobility enhancement achievable when stress is applied to Silicon. The bulk minority carrier lifetime is the main property of interest for the PL simulations in PC1D and could range from nanoseconds to 10s of microseconds in our samples.

The bulk minority carrier lifetime is directly related to maximum possible Voc achievable in the solar cell, and the carrier collection efficiency. The surface recombination velocity on the air side is dependent on the surface passivation applied to the sample, and as such varies between values as low as 100s cm/s and as high as 106 cm/s. The surface passivation on the glass side of the film is believed to be good, but the effect on PL intensity of high and low glass side surface passivation can also be investigated in these simulations.

Excitation Parameters Blue Green Red Wavelength (nm) 465 530 630 Intensity (W cm-2) 0.1432 0.1238 0.1050 Photon Flux (photons/(cm2.sec)) 3.3E17 3.3E17 3.3E17

Table 18, shows the illumination parameters used in the simulation, and experiments. For comparison of the relative PL intensities between simulation and experiment, the excitation intensities and wavelengths must be known accurately. The excitation parameters given in Table 18 above are directly related to the experimental parameters used in the current investigation. - 156 -

A photon flux of 3.3E17 cm-2 is used for the experiments and simulations. This photon flux is the highest achievable with the Green LED, and the intensities of the Blue and Red LEDs were chosen to match. The excitation photon flux is of the same order as the photon flux from 1 sun (2.7E17 cm-2).

- 157 -

3.7 Results of Simulations

In this section the results of the simulations run in PC1D are given. These simulations cover the effect of minority carrier lifetime, surface passivation, and the effect of a diffused junction. A discussion of the results can be found in the following section.

3.7.1 Diffused Junction vs. No Junction

Adding a diffused junction the silicon film increases the measured PL signal. This can be understood by noting equation 62, where an increase in the doping density () increases the PL intensity (). This must be taken into consideration when trying to deduce the minority carrier concentration or lifetime from the PL intensity. A junction also helps to increase the surface passivation of the air side, which increases the PL intensity even further.

A more interesting effect of adding a junction to the cell is the variation in PL intensity with variation of the excitation wavelength. This effect is most clearly seen in films with a low bulk minority carrier lifetime, and diminishes as bulk lifetimes increase. This effect is clearly illustrated in Figure 82 below.

The variation in PL intensity at low bulk lifetimes is caused by the inability of the minority carriers to diffuse away from where they are created. Blue for example is absorbed primarily in the first 1 to 2 µm of the film, and the high doping in the junction, in that region results in a high PL signal. Longer wavelengths such as green or red light, are absorbed over a greater depth (see Figure 72), and thus the effect of a higher PL signal from the junction has less of an effect.

In the PL experiments carried out on LPCSG material, we do indeed see a variation in the measured PL intensity depending on the excitation wavelength. Unfortunately, the implication is that the lifetime of the bulk minority carriers is low, but it none-the-less allows the possibility of estimating the lifetime, simply by comparing the relative PL intensities. The relative PL intensities we can expect to see for various bulk lifetimes are shown in Figure 86, below. This technique effectively separates the minority carrier lifetime into three distinct regions, which are;

 1 ,

- 158 -

 1 1 μ, and  1 μ. While the material quality is being improved in the R&D stage, Excitation wavelength dependent PL intensities offer a simple way to evaluate the resulting material quality of various processes. A major limitation of the technique is the limited range of lifetimes that the technique can accurately determine.

PL Intensity - wavelength dependence

1E+27

1E+26 (Arb) 1E+25 Blue

1E+24 Green Intensity Red

PL 1E+23

1E+22 1.00E‐05 1.00E‐04 1.00E‐03 1.00E‐02 1.00E‐01 1.00E+00 1.00E+01 1.00E+02 Bulk Lifetime (µs)

Figure 82 shows the effect on PL intensity of excitation wavelength, on silicon with varying bulk lifetime.

Another limitation to the technique is that it requires an accurate estimate of the dopant diffusion profile to get an accurate estimation of the bulk lifetime. The dopant diffusion profile in our case is known from SIMS (Secondary Ion Mass Spectrometry) data, for the current standard process, but as novel dopant diffusion processes, such as laser diffusion become increasingly effective, additional SIMS data will be required. When the excitation wavelength dependent PL ratio approaches 1, then previously established methods of deducing the bulk lifetime from PL (discussed previously) could be used. This data will be easier to perform on high lifetime material as the intensities will be one to two orders of magnitude higher than the range where the excitation wavelength dependent PL ratio method could be used.

- 159 -

Ratio - PL Intensity excited at various wavelengths

1 0.9 0.8 (Arb) 0.7 0.6 0.5 Intensity 0.4 PL

‐ 0.3 0.2

Ratio 0.1 0 1.00E‐05 1.00E‐04 1.00E‐03 1.00E‐02 1.00E‐01 1.00E+00 1.00E+01 1.00E+02 Bulk Lifetime (µs) Green/Blue Red/Blue Red/Green

Figure 83 shows the relative PL intensities than could be expected between different excitation wavelengths, for various bulk minority carrier lifetimes.

Excitation wavelength dependent PL is not predicted to occur in films without a diffused junction on the air side. Adding a diffused junction on glass side would also alter the expected PL intensities excited at different wavelengths. In fact any change to the dopant profile would need to be known before an estimation of the bulk lifetime could be made.

3.7.2 Surface passivation

Surface Passivation reduces the number of electrons and holes that combine at the surface, and increases the effective lifetime of minority carriers. The standard measure of surface recombination is the surface recombination velocity, which has units of cm/s. A surface recombination velocity of <1000 cm/s is considered good, and a value above 1E4 cm/s is poor. Silicon with no surface passivation can have a surface recombination velocity of greater than 1E6 cm/s. The effective carrier lifetime () of a Si solar cell can be expressed as a combination of the bulk carrier lifetime (), and the lifetime of carriers at the surface ():

- 160 -

At low bulk lifetimes, the glass side surface recombination velocity has little influence on the PL intensity. This is because the number of carriers generated by the excitation light is higher on the air side of the silicon, and the low lifetime means that these carriers do not diffuse far enough to recombine at the glass side interface. At higher bulk lifetimes the glass side surface passivation becomes more influential, limiting the effective carrier lifetime, and hence the PL intensity.

The air side surface passivation affects the PL signal significantly at low bulk lifetimes, and less significantly at high bulk lifetimes relative to the glass side passivation. This is because the carriers are generated in close proximity to this surface. When a junction is diffused on the airside of the film, the diffusion of minority carriers to the airside surface is lessened, and recombination at this surface is lessened.

PL Intensity - Surface Passivation

1E+27

1E+26 (Arb) 1E+25

1E+24 Intensity

PL 1E+23

1E+22 1.00E‐05 1.00E‐04 1.00E‐03 1.00E‐02 1.00E‐01 1.00E+00 1.00E+01 1.00E+02 Bulk Lifetime (µs) Green ‐ Low Air Side ‐ Low Glass side Green ‐ High Air Side ‐ Low Glass side Green ‐ Low Air Side ‐ High Glass side Green ‐ High Air Side ‐ High Glass side

Figure 84, shows the PL intensity expected from a thin film Si sample with parameters outlined in Table 17. High means high recombination velocity, and Low means low recombination velocity.

The effect of surface recombination velocity on the PL intensity, for a thin film Si cell with a diffused junction is shown in Figure 84, above. The large circle data points represent a low glass side surface recombination velocity (well passivated), and the small circles conversely represent a high glass side recombination velocity (poorly passivated). Figure 84 shows us that the level of surface passivation on the glass side of the film has little effect on the PL intensity from the sample at low minority carrier lifetimes. At high minority carrier lifetimes however, the level of surface passivation on - 161 - the glass side of the film has a significant effect on the PL Intensity. The simulation results are for an excitation wavelength of 530nm (Green), but the same overall trends in PL intensity are seen for both 465nm (Blue) and 630nm (Red) excitation.

- 162 -

3.8 Discussion of Simulation

From Figure 84 we can see that there are four possible surface passivation states of the film, which are:

Possible Surface Passivation Glass side passivation - Glass side passivation States Good - Poor Air side passivation - Good 1 2 Air side passivation - Poor 3 4

Table 19 shows the possible surface passivation states. This is from each side of the cell having a good or poor surface passivation. We can describe the effect on the PL intensity for each of the four possible surface passivation states given in Table 19 above.

Surface Passivation Effect on low bulk lifetimes Effect on high bulk lifetimes States PL intensity influenced by Air PL intensity influenced by both Air side only. High PL signal side and glass side. Highest possible 1 relative to poor air side surface PL signal expected. passivation. PL intensity influenced by Air PL intensity reduced by high air side side only. High PL signal recombination, but PL intensity still 2 relative to poor air side surface high, due to passivation provided by passivation. the junction PL intensity influenced by Air High Glass side recombination results side only. Low PL signal in a relatively low PL intensity 3 & 4 relative to low quality air side regardless of airside passivation. surface passivation.

It is important to note that the PL excitation is from the opposite side from that which will be used when the solar cell is illuminated by the sun. And that at low bulk lifetimes, there is no influence on the PL intensity from the glass side surface passivation. However, when in operation the cell is illuminated from the glass side, and

- 163 - recombination would play a significant role in determining the voltage and current characteristics of the cell.

Further information on the spatial variation of PL intensity could be garnered by developing a model based on the simulations of PC2D. This however has not been attempted in this thesis.

- 164 -

3.9 Practical Considerations for PL Images of Thin Film Si on Glass Photoluminescence is excited in our samples from the air side of the film, which is the opposite of how the film would be illuminated by the sun whilst in operation. Given the low bulk lifetime of the Si in the film, the diffused junction has a large effect on the measured PL intensity. When a junction is diffused on the cell, an asymmetry is introduced in the film, which would give different intensity PL signals if excited from the air side or glass side of the film (if excitation from the glass side were possible).

Light Absorption in 10 µm thick solar cell.

Figure 85, shows the current density from an ideal cell (red) and a cell 10 µm thick (blue). This image is a screen shot of the applet at http://www.pveducation.org/pvcdrom/design/material-thickness developed by Jeff Cotter and Stuart Bowden for PVCDROM. Another important aspect to consider is that the photon fluxes used in the PL investigation, are monochromatic, and absorbed completely in the depth of the film. This is not the case when the silicon is illuminated by sunlight, where a significant amount of light passes through the film. This can be seen in the applet at pveducation.org shown in Figure 85.

An important practical aspect of PL imaging to consider is dust. The PL signal given off by dust is very high, and can add significantly to the PL signal if not addressed properly. Cleaning with compressed nitrogen is sufficient to remove all the dust from

- 165 - the excitation filters and the samples before an image is taken. An example of the noise one can expect from dust in the system is shown in Figure 86, below.

Dust Particles In PL Image

Dust

Figure 86, shows the noise that dust can introduce into a PL image. The Intensity of luminescence from dust can be higher than the PL signal from the silicon under investigation, and so dust needs to be managed appropriately.

- 166 -

3.10 PL Imaging Equipment

The images of the thin films were taken using PL imaging equipment provided by BT Imaging. (www.btimaging.com) The camera and imaging software is all contained within the BTI tool, and is not discussed here. The only thing added to this equipment to make imaging of thin films possible was the high power LEDs discussed in section 3.5. Although The BTI software contains many functions for analysis of the resulting images, ImageJ (http://rsb.info.nih.gov/ij/) was also used heavily for the analysis of the images.

BTI Imaging Tool at CSG Solar Excitation Light source for Thin Films

Figure 87 shows the BTI tool used at Bay St to Figure 88 shows the LED light source that was perform the PL Imaging experiments carried out in developed for imaging of Si thin films. The two holes this thesis. in the top are where the Blue, green, or Red LED light emerges, after being made uniform, and all the IR is filtered out.

- 167 -

3.11 Surface passivation

In this round of experiments, SiN was coated on the air side of the film at various stages of the manufacturing process, as a form of surface passivation. This was done primarily to get better information on the material quality, rather than information on the level of surface passivation.

Using SiN as a method of surface passivation was successful for reducing the recombination of minority carriers at the surface. However, upon analysis of the data, it was found that the SiN film added a level of noise to the PL signal that is believed to be excitation wavelength dependent. This in turn made the estimate of the lifetime from multiple wavelength PL excitation inaccurate. In future experiments the SiN surface passivation will be replaced with another method of temporary surface passivation. These possible methods include HF, Quinhydrone methanol and/or Iodine

The SiN also has a wavelength dependent effect on reflection of the excitation light from the Si film surface. The SiN deposited is 90 nm thick, with a refractive index of approximately 2.1. The reflection of 460 nm, 530nm and 630nm light from this surface is 27%, 11% and 1% respectively. The simulations carried out in PC1D take the varying spectral reflectance into consideration implicitly, though adding an optical coating into the simulation, with the appropriate SiN properties (n = 2.1, thickness = 90nm).

- 168 -

3.12 PL Intensity at the various stages of production

The PL Intensity from the Si film varied greatly at the various stages of production. This means that as crystallised films will be imaged with a different exposure time (integration time) to films with a diffused junction. In the early stages of production with no surface passivation, an exposure time of as high as 45 seconds was used to obtain a good signal with low noise. Toward the end of the production process exposure times of two seconds were adequate to attain an image with high number of counts and little noise.

Average PL counts from Strip

2500

2000 Sample 8

second) Sample 6 KG5 Filter 1500

(per Crystallised ‐ No Junction ‐ 1000 ~85nm (315°C) SiN Passivation Crystallised ‐ With Junction ‐ 500 ~85nm (315°C) SiN Passivation counts

PL 0 0 5 10 15 20 25 Sample / Strip Number

Figure 89 shows the average PL intensity measured on each sample before and after a n+ junction has been diffused, and the noise floor produced by the KG5 filter. The excitation wavelength is 530 nm, and the intensity is approximately 1 sun. It can be seen that there is variation in the PL intensity from sample to sample before the junction is diffused, as represented by the green triangles, but this variation is magnified with the addition of a junction. The data above comes from 8 samples, which each contain three strips, as can be seen in Figure 94. Sample 6 and sample 8 are highlighted because they are analysed in more depth in following sections.

- 169 -

3.13 PL Imaging Results In this section PL images of a standard LPCSG (Liquid Phase Crystalline Si on Glass) lot are analysed. The lot contains 8 samples, giving a total of 24 individual crystallised strips which show a range material qualities, which can be easily quantified via PL Imaging.

3.13.1 Minority Carrier Lifetime from multi-wavelength PL Excitation ratio. The theory of how the minority carrier lifetime can be extracted from a comparison of the intensity of the emitted Photoluminescence when excited by multiple wavelengths, is covered in section 3.7.1. The theory basically states that by comparison of the intensity of the PL signal, when excited by different wavelengths, then the lifetime can be extracted when this information is compared to PC1D models.

In this subsection, the PL intensity of two samples is used to gauge the ability of this technique to accurately estimate the minority carrier lifetime. A single line through the sample was chosen to do analysis on the intensity profile because aligning all points over 2 dimensions would be difficult, and not much insight would be gained from investigating only a single point. Future designs of the PL imaging system will enable different wavelength excitation to be performed without moving the sample, so that this analysis is possible in 2 dimensions.

PL Image of Sample 8

Figure 90, shows a grey scale PL image of sample 8 from lot 5F117. The horizontal yellow line across the centre of the image is the line where the intensity profile in Figure 91 was taken. - 170 -

The resulting intensity profile is shown in Figure 91, with the three lines representing the PL intensity obtained from excitation of 465 nm (Blue), 530 nm (Green), and 630 nm (Red) LED light. The intensity of the excitation light varies for each wavelength, but the photon flux is constant at 3.3E17 photons/cm2 (1 sun = 2.7E17 photons /cm2).

PL Intensity - Various Excitation Wavelength

3000

2500

2000 (counts)

1500 Blue Green 1000

Intensity Red

PL 500

0 0 112233 Distance (mm) (approx)

Figure 91 shows a PL intensity profile taken horizontally across sample 8 from lot 5F117. The exact place on the sample where the profile was taken is shown in Figure 90. PL Image of Sample 6

Figure 92 shows a grey scale PL image of sample 6 from lot 5F117with 460nm (blue) excitation. The horizontal yellow rectangle across the lower part of the image is the line where the intensity profile in Figure 93 was taken.

- 171 -

Like Figure 91 it can be seen that the intensity of the PL signal induced by Blue excitation is higher than that from either the Green or the Red LED. It can be seen that the average of the PL intensity across sample 8 is higher than for sample 6, although the peak PL intensity for both is similar.

PL Intensity - Various Excitation Wavelength

3000

2500

2000 (arb)

1500 Blue Green Intensity

1000

PL Red 500

0 0 112233 Distance (mm) (approx)

Figure 93 shows a PL intensity profile taken horizontally across sample 6 from lot 5F117. The exact place on the sample where the profile was taken is shown in Figure 92.

Referring to Figure 89 we can see that the average PL intensity from sample 8 was much higher than the rest of the samples. Given that the profile crosses very low lifetime uncrystallised material (a-Si), between the laser crystallised strips. The PL intensity in the a-Si areas comes mainly from the dopant diffusion in that area, and can give us an indication of the contribution of the junction area to the PL signal in the crystallised areas.

By comparing the intensity of the PL signal from different wavelength excitation we can estimate the bulk minority carrier lifetime, as shown in Figure 83, in section 3.7. For simplicity, if we take the ratio of the maximum PL intensity points of each sample, then we could estimate the maximum bulk minority carrier lifetime in our samples. The ratios for each sample are given in Table 20, as well as the carrier lifetime this implies.

- 172 -

Sample 8 Sample 6 Colour Ratio Lifetime Colour Ratio Lifetime Red/Green 0.65 ~4 ns Red/Green 0.69 ~5 ns Red/Blue 0.34 ~2 ns Red/Blue 0.34 ~2 ns Green/Blue 0.52 ~ 2 ns Green/Blue 0.50 ~2 ns

Table 20 shows the PL intensity ratio from excitation of different wavelengths with the same photon flux. The larger of the PL intensity signals is always the denominator, to keep the ratio a value between 0 and 1. The lifetime listed in the above table is just an estimate of the actual value, which can be found by referencing Figure 83. These results predict a maximum pulk minority carrier lifetime of the order of a few nanoseconds, which is surprisingly low. In PC1D, as well as predicting the minority carrier concentration through the depth of the sample, we can also predict the Voc of the device. With lifetimes of this range the maximum possible Voc for the amterial would be of the order of 450 mV. This is in stark contrast to the observed Voc which is typically of the order of 500 to 530 mV.

After much analysis to resolve this apparent conflict, it was discovered that the SiN used to passivate the surface could itself be emitting PL [Deshpande, et al. - 1995, Kistner, et al. - 2011]. This PL signal has typically been measured in the visible part of the specturm, and is dependent on both the excitation intensity and wavelength. Any SiN signal would be present in PL Imaging of wafers, if a SiN anti-reflection coating was applied. However, excitation wavelength for wafers is typically 808 nm, and it appears from our investigation that the PL contribution from SiN is stronger for shorter wavelengh excitation. Also, the PL intensity of wafers is typically larger (at least an order of magnitude larger) than that measured on our thin films. This would mean that any contribution from the SiN film would be less obvious in wafer based PL measurements, and potentially passed off as noise.

It is unclear how much of the PL signal can be attributed to the SiN, or if this contribution is wavelength dependent. This question could be answered by looking at the PL spectrum, but unfortunately the spectral PL system at the university was offline at the time of completion of this thesis. The observed Voc of these samples implies a minority carrier lifetime of 10’s of nanoseconds, which is larger than that predicted by comparing various wavelength PL intensities. The ratio that predicts the longest carrier lifetime is the Red/Green data, and it is obvious from looking at Figure 91 and Figure 93 is can be seen that the Blue PL signal is typically from double to triple that of the PL - 173 - signal induced with Green (530 nm) excitation. From this, it would appear that the SiN contributes more to the PL signal when shorter wavelength excitation is used, compared to shorter wavelengths. However, there are not direct measurements confirming the SiN effect on PL from our investigation. Further investigation into PL Imaging using alternative temporary surface passivation techniques (Iodine [Sopori, et al. - 2008] and Quinhydrone methanol [Chhabra, et al. - 2010] were not investigated, because the PL Imaging tool was taken offline before this work could be completed.

3.13.2 PL intensity variation within a sample As discussed in section 3.12 the PL intensity in the images varies greatly over the various stages of production. We can also see a large variation of PL intensity within one sample. This variation can be seen in Figure 94.

Typical Image of PL from LPCSG material at the stage

Figure 94 shows a typical PL image taken of LPCSG material at the stage where a junction has been diffused, and surface passivation applied. The brighter areas represent a high PL intensity, and darker areas represent a lower PL intensity. The three vertical strips visible in the film are from the three passes of the laser used to crystallise the material. The dark vertical strips are amorphous Si material in between the crystallised areas. The bright horizontal line on the middle strip is a section where the Si film delaminated, and the PL from the borosilicate glass was excited directly. The image is of sample 8 from the lot 5F117.

The majority of the noise in a typical PL Image arises from the KG5 glass filter, and it typically around 30 5 counts per second. The variation in the PL signal from a sample at the stage where a junction is diffused and the surface is passivated is of the order of 100 to 120 counts per second. The variation in PL intensity inside the green rectangle, on the left strip, of the sample shown in Figure 94, is quantified below. - 174 -

Histogram of PL Intensity

Figure 95 shows a histogram of the intensity profile for the area enclosed by the Green rectangle in Figure 94. This histogram is a typical plot of the intensity variation seen in LPCSG material. The numbers on the grey scale bar represent the counts per second. Statistical analysis tools in ImageJ allow us to look at the Standard Deviation of the Intensity from its mean value. For the above histogram, the mean intensity value is 463 counts per, with a standard deviation of 93 counts per second. The standard deviation can be used to quantify the variation in material quality across a particular sample. Reducing the variation of material quality within a strip will make the film a more reliable base for subsequent processes, and make the overall production process more reliable.

Non-Uniformity of PL signal across strips

4000

3500 ) 3000 (arb 2500

2000

1500 Intensity 1000

PL Strip 2 Strip 3 500 Strip 1

0 00.511.522.5 Distance (mm) (approx) Figure 96 shows an intensity profile slice of a horizontal section of Figure 94.

- 175 -

It can be seen that crystallisation process results in a high level of non-uniformity of the material quality over the area of the film. This non uniformity is quantified in Figure 96 which shows an intensity profile slice of a horizontal section of Figure 94.

Bad Cracking Seen in PL Image of Sample Overlay of Cracking Early LPCSG Material shown to right with PL Image

Figure 97 shows an early version of LPCSG material with back cracking after the Laser crystallisation process. The centre images is the corresponding PL Image of the sample, with high intensity areas represented by Orange to white areas, and low PL intensity corresponding to Blue/Purple and black colours.

The areas of low PL intensity between the strips are a-Si material that was not crystallised, and some other areas where a low PL intensity is low can be attributed to cracks in the Si films. Early versions of LPCSG material contained cracks that typically ran parallel to the laser scan direction and ran the length of the sample.

An example of the cracking is shown in Figure 97, as well as the corresponding PL Image. The rightmost image shows an overlap of the two, and shows that cracks in the film correspond to regions of low PL intensity. This result also means that around cracks, the light getting through the film to the glass is not sufficient to excite a high level of PL in the glass. Also the material quality around cracks appears to be lower than areas where a crack has not formed. Areas of the film where a low PL signal is seen, shows no visible difference to other areas where a relatively high PL signal is observed. The variation observed in LPCSG material is similar to that observed in PL images of string ribbon Silicon [Trupke - 2006]. Further investigation into the similarities of LPCSG material and Ribbon silicon will be conducted in the near future.

The variation in thin film Si solar cells, PL imaging makes PL Imaging a much more valuable characterisation technique than a single PL intensity measurement of the whole - 176 - sample. Future experiments PL will be invaluable in making the material more uniform across the whole sample.

3.13.3 PL Intensity vs. Voltage It was stated earlier that the PL intensity is proportional to the carrier concentration, and so is the Open Circuit Voltage (Voc). The relationship between PL intensity and carrier concentration was given in section 0, and is given again here for reference:

. . ∆.∆ 67

Where is a calibration factor determined by experiment, is the radiative 3 recombination coefficient, is the doping density (dopants/cm ), and ∆ is the excess 3 minority carrier concentration (carriers/cm ) [Trupke - 2005]. The Voc of a solar cell can be approximated by the equation:

∆.∆ 68

Where is Boltzmann’s constant, is temperature (Kelvin), is the charge on an -3 electron, is the intrinsic carrier concentration = 8.6 10 (cm ) at room temperature [Sproul, et al. - 1991] and all other parameters are described above. At Room temperature 0.0258 [Sinton, et al. - 1996], which is typically a constant in our experiments. By combining these equations we find the relationship relating PL

Intensity to Voc:

. . . 69 ,

The constant must be determined experimentally before Voc can be determined directly from a PL Image. This equation shows that with a linear increase in Voc an exponential increase in PL intensity should be observed.

- 177 -

Voc vs. PL Intensity

1000

100 Counts

10 250 300 350 400 450 500 550 Open Circuit Voltage (mV)

FLA Annealed (E‐Beam samples) Belt Furnace Annealed LPCSG Filter Noise *

Figure 98, is an image of the PL intensity vs. Voc. The PL intensity measured of a number of samples, and is plotted against the measured Voc. It can be seen that there is good qualitative agreement with the Voltage and the PL intensity of the various films investigated. The blue data points represent FLA samples, the red data points represent RTA annealed samples, and the green represent a broad range of processing parameters investigated in relation to LPCSG material. FLA was not investigated on LPCSG material. This graph is also shown in Chapter 1 to shown the effect of FLA on the material quality.

An exponential fit to the above graph, of 4.789. exp 0.007. fits the above data with an R2 value of 0.867, which indicates that there is a correlation of the data with the exponential fit. The fit of the data to an exponential curve would be better if parameters, such as film thickness, surface passivation, and others were the same for each sample. The data presented in Figure 98 represents some of the data collected on various types of thin films investigated to date with PL. A higher degree of correlation between the PL data and the exponential fit needs to be found, before an implied Voc can be determined directly from the PL image.

It can be seen in Figure 98 that there is a large range of data points relating PL intensity to measured Voc for the LPCSG material (Green triangles). This deviation from the expected values can be explained by considering the non-uniformity seen in these samples. The PL intensity value is an average over a finite area, where the PL intensity varies significantly. In the above results the FLA annealed samples, and the belt furnace annealed samples, are 2 µm thick films, and the LPCSG material is 10 µm thick films. This could account for some of the discrepancy in the data from the expected value given by the above equation.

- 178 -

Another contributor to the discrepancy could be that trying to find the exact position where a voltage measurement is taken and the corresponding point in a PL data is difficult. The below Figure 99 shows the areas where Voc measurements were taken, and it can be seen that even within the small yellow circles a relatively large variation in PL intensity can be observed.

Points where measured Voc was correlated to PL Intensity.

Figure 99, shows the points where Voc was measured. The points are approximate, as there is not current method of relating the measured Voc to a specific point on the film to a corresponding point on the PL Image.

With a more accurate method of relating the point where the Voc is measured, to a corresponding PL intensity, then an increase in the correlation of the PL intensity to Voc is expected. Measures to improve the uniformity of the LPCSG material are also being attempted, and this will increase the uniformity of the PL signal, and make a Voc measurement more consistent across the sample.

- 179 -

3.14 Further PL imaging investigation In this thesis the imaging of PL from thin film Si on glass has been reported. However, there are improvements that could be made to the experiments carried out, and extensions to the work.

Firstly, as discussed in section 3.13.1, the estimated bulk minority carrier lifetime is low, and is most likely affected by the PL coming from the SiN used for surface passivation. Future experiments replacing SiN with Quinhydron Methanol, HF or Iodine for surface passivation, would allow us to make a more accurate prediction of the bulk lifetime.

On a practical level an improvement that could be made to the current PL setup, is to have the light source be interchangeable without altering the position of the sample. In this way comparison of the PL intensity from multiple wavelength excitation images could be achieved over the whole area of the film. This would extend the analysis shown in section 3.13.3 to include the whole film, giving greater insight into the quality of the film and decreasing the time spent on analysis.

An important part of PL Imaging is to verify that the light being imaged is indeed band- band luminescence from the solar cell under investigation. Although it is believed that the light is a PL signal from the cell, this should be confirmed by Spectral PL measurements. Spectral PL would be able to distinguish between a relatively narrow band-band luminescence from a solar cell, and the broad peak expected from the glass substrate. Other noise from the excitation LED would also be able to be quantified via this technique. Spectral PL would also be able to identify the extent of the PL noise signal coming from the SiN surface passivation, and the extent of this signal at other wavelengths.

With the camera available for PL Imaging, Electroluminescence (EL) Imaging would also be possible. By replacing the PL excitation LEDs with electrical excitation, the thin film Si could be characterised past the stage where Aluminium contacts are made. Electroluminescence can give insight into the carrier diffusion length of the material [Fuyuki, et al. - 2005], as well as areas where poor contact is made, and detection of shunts [Breitenstein, et al. - 2008].

- 180 -

3.15 PL Imaging Conclusions In this Chapter the subject of PL Imaging of thin film silicon solar cells on glass has been covered. It is found that the there is a strong correlation between Voc and measured PL Intensity, which is consistent with PL on solar cell theory. The basic overview of the theory behind PL is presented, with a focus on analysis of solar cells.

It was found that the luminescence of the glass substrate limits the ability to excite PL from out thin film from the glass side of our samples. For this reason, the PL excitation light illuminates the film from the air side. It was also found that a large portion of the excitation light was lost if the sample was far from the excitation LED, and optics to focus the LED light onto the sample resulted in poor illumination uniformity. For this reason the PL signal was imaged on through the glass side of the sample. This configuration blocked the excitation light from the glass to an extent where PL noise from the glass was less than that from the KG5 filter used to block IR from the LED, which was the main source of noise in the system. Another source of noise was dust in the PL image, from poor sample cleaning, which was easily identifiable and could be removed from the image with the use of Isopropanol and lint free wipes, or blowing the dust off with compressed air.

Typical PL Image of LPCSG Material

Figure 100, shows a typical PL image of LPCSG material. A very high intensity area can be seen on the left strip, which was found to correspond with high carrier mobility. The bright horizontal line on the centre strip is where delamination has occurred, and the bright PL intensity is from the glass substrate. This counts in this image are high, because the exposure time of the camera is 45 seconds. Three excitation LED wavelengths were investigated, which were Red (630 nm), Green (530 nm) and Blue (465 nm). From each LED the intensity at the Si film was more than 1 sun (2.7E17 photons or 0.1 W/cm2). It was found that the PL signal intensity of our - 181 - thin films, were strongly dependent on the excitation wavelength, and this is used as a means to estimate the minority carrier lifetime. Estimating the lifetime of the silicon also involved modelling the cells in PC1D and comparing this to experimental results. With this technique, the minority carrier lifetime can be determined over the entire area of the film, rather than just a single value for whole sample. With the high variability in the sample observed (see Figure 100), spatially resolved material quality is a valuable characterisation tool.

Variability in the PL intensity was also seen at various stages of the production process. With a barely detectable PL intensity from the as crystallised films, to a very strong PL signal from samples with a diffused junction and surface passivation.

It was already known that surface passivation has a significant impact on the PL signal of the sample. However, Noise in the PL signal is believed to come from the SiN surface passivation used. This will be investigated further in future experiments using alternate temporary surface passivation techniques.

The influence of cracks has also been addressed, and it is found that areas in the film where cracks appear correspond to a low PL intensity. This means that stray excitation light that travels through the cracks is not intense enough to excite a PL signal of the same order of magnitude as the PL intensity from the Si film.

Finally, possible future investigations into thin film Si on glass are discussed. These proposed experiments cover improvements that could be made to the existing PL Imaging setup, and extending the work to include electroluminescence, and spectral PL investigations.

- 182 -

Appendix A- Thermal Simulation Code

The following code calculates the thermal profile in the Si film and glass substrate during flash lamp heating over a 3 ms pulse. The code used for other pulse durations is not listed here, as only a small section of the code changes where the input energy in the film is changed. This can be supplied if the reader wishes to recreate the exact simulation conditions for the other pulses investigated in this thesis. function [points,edges,tri,u1] = si_on_gl_fla_3ms (preheat_temperature,pulse_energy_density,tlist,parameters)%(points_in ,edges_in,tri_in,t_start_in,u0_in) w = parameters(7);%0.02; %width h_si = parameters(8);%2*10^-6; %2um h_gl = parameters(9);%3*10^-3; %3mm h_tot = parameters(10);%h_si + h_gl; si_gl_dim = [w,h_si,h_gl,h_tot]; thickness_gl = h_gl; thickness_si = h_si; thickness_tot = thickness_gl+thickness_si; thickness_air = 0.003;width_gl = w; width_si_m = 0.011; width_si_l = 0.0045; width_si_r = width_si_l; rho_si = 2329; rho_gl = 2230;%density; %kg/m3 c_p_si = 1000; c_p_gl = 830;%heat capacity;(J/(kg.K)) value for c_p_gl and c_p_si k_si = 30; k_gl = 1.3; %%%%%%%%air%%%%%%%%%%%% rho_air = 0.5;%kg/m3 c_p_air = 1050;%J/(kg.K); k_air = (6*10^-5)*10^3;% (W/(m.K)) %convective heat transfer coefficient; h_si_to_gl = 41000;%41000; %W/(m2.K);2000 - Tempel - Thermal Conductivity of a Glass Measurement by the Glass–Metal Contact h_si_to_air = 1000; %not sure of this value h_gl_to_air = 100;%W/(m2.K); Wikipedia - Air - h = 10 to 100 W/(m2K); h_si = 0; h_gl = 0; h_air= 0; T_ext = preheat_temperature; reflection = 0.32; absorption_si = 10^(5.23); %(inverse metres. /100 to get inverse cm; x_vol_calc = 1; %1m y_vol_calc = 1; %1m z_vol_calc = thickness_si; transmission = (exp(-absorption_si*thickness_si)); pulse_energy = ((1-reflection)*(1- transmission)).*pulse_energy_density/(x_vol_calc*y_vol_calc*z_vol_calc ); %gd = the decomposed geometry matrix (must go counter clock % [3=square, 4 = four sides, x values y values gd_gl = [3;4; 0;width_gl;width_gl;0; 0;0;thickness_gl; thickness_gl]; gd_si_l = [3;4; 0;width_si_l;width_si_l;0;thickness_gl;thickness_gl;thickness_tot;thic kness_tot];% gd_si_r = [3;4; width_si_l+width_si_m;width_gl;width_gl;width_si_l+width_si_m;thicknes s_gl;thickness_gl;thickness_tot;thickness_tot];%

- 183 -

gd_si_m = [3;4; width_si_l;width_si_l+width_si_m;width_si_l+width_si_m;width_si_l;thic kness_gl;thickness_gl;thickness_tot;thickness_tot];% gd_air = [3;4; 0;width_gl;width_gl;0;thickness_tot;thickness_tot;thickness_tot+thickn ess_air;thickness_tot+thickness_air]; gd = [gd_gl,gd_si_l,gd_si_m,gd_si_r,gd_air]; name_space_bytes_g = unicode2native('g');% name_space_bytes_l = unicode2native('l');%same as above. name_space_bytes_s = unicode2native('s');%same as above. name_space_bytes_i = unicode2native('i');%same as above. name_space_bytes_a = unicode2native('a');%same as above. name_space_bytes_r = unicode2native('r');%same as above. name_space_bytes__ = unicode2native('_');%same as above. name_space_bytes_m = unicode2native('m');%same as above. ns_gl= [name_space_bytes_g;name_space_bytes_l; 0; 0];s_si_l = [name_space_bytes_s;name_space_bytes_i;name_space_bytes__;name_space_b ytes_l];ns_si_m=[name_space_bytes_s;name_space_bytes_i;name_space_byte s__;name_space_bytes_m];ns_si_r=[name_space_bytes_s;name_space_bytes_i ;name_space_bytes__;name_space_bytes_r];ns_air=[name_space_bytes_a;nam e_space_bytes_i;name_space_bytes_r; 0];ns = [ns_gl,ns_si_l,ns_si_m,ns_si_r,ns_air];sf = 'gl+si_l+si_m+si_r+air'; dl=decsg(gd,sf,ns); %boundary numbers given below: %______%| 2 | %|16 (5) 13| %|______| %| 8 | 9 | 10 | %|15 (4) |3 (1) |7 (3) |12 %|______|______|______| %| 4 5 6 | %|14 (2) 11| %|______| % 1 %define q g h and r; g_si_gl = unicode2native(num2str(h_si_to_gl))'; g_si_air=unicode2native(num2str(h_si_to_air))'; g_gl_air = unicode2native(num2str(h_gl_to_air))'; g_same = unicode2native(num2str(1e6))'; lg_si_gl = length(native2unicode(g_si_gl)); % length of g lg_si_air = length(native2unicode(g_si_air));% length of g lg_gl_air = length(native2unicode(g_gl_air));% length of g lg_same = length(native2unicode(g_same));% length of g

%q is always equal to 0; q = unicode2native('0')'; % lq = length(native2unicode(q));%% length of q %h is always equal to 1; h = unicode2native('1')';% 48 in unicode = 0; lh = length(native2unicode(h));%length of h; r = unicode2native(num2str(T_ext))'; lr = length(native2unicode(r)); % length of r (Text) no_of_boundaries = 16; %boundary_x = [N;M; length_q; length_g; length_h; length_r; q; g; h; r]; boundary_1 = [1;1; lq; 1; lh; lr; 48; 48; h; r];%bottom boundary_2 = [1;1; lq; 1; lh; lr; 48; 48; h; r];%top

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boundary_3 = [1;1; lq; lg_same; lh; lr; 48; g_same; h; r]; %si to si boundary_4 = [1;1; lq; lg_si_gl; lh; lr; 48; g_si_gl; h; r];%si to gl boundary_5 = [1;1; lq; lg_si_gl; lh; lr; 48; g_si_gl; h; r];%si to gl boundary_6 = [1;1; lq; lg_si_gl; lh; lr; 48; g_si_gl; h; r];%si to gl boundary_7 = [1;1; lq; lg_same; lh; lr; 48; g_same; h; r]; %si to si boundary_8 = [1;1; lq;lg_si_air; lh; lr; 48; g_si_air; h; r];%si to air boundary_9 = [1;1; lq;lg_si_air; lh; lr; 48; g_si_air; h; r];%si to air boundary_10 = [1;1; lq;lg_si_air; lh; lr; 48; g_si_air; h; r];%si to air boundary_11 = [1;1; lq;lg_gl_air; lh; lr; 48; g_gl_air; h; r];%gl to air boundary_12 = [1;1; lq;lg_si_air; lh; lr; 48; g_si_air; h; r];%si to air boundary_13 = [1;1; lq; 1; lh; lr; 48; 48; h; r];%top - side boundary_14 = [1;1; lq;lg_gl_air; lh; lr; 48; g_gl_air; h; r];%gl to air boundary_15 = [1;1; lq;lg_si_air; lh; lr; 48; g_si_air; h; r];%si to air boundary_16 = [1;1; lq; 1; lh; lr; 48; 48; h; r];%top - side len = zeros(1,no_of_boundaries); for counter = 1:no_of_boundaries strrr = eval(['boundary_' num2str(counter)]); len(counter) = length(strrr); end boundary_len = max(len); boundary_1 = padarray(boundary_1,(boundary_len - length(boundary_1)),'post'); boundary_2 = padarray(boundary_2,(boundary_len - length(boundary_2)),'post'); boundary_3 = padarray(boundary_3,(boundary_len - length(boundary_3)),'post'); boundary_4 = padarray(boundary_4,(boundary_len - length(boundary_4)),'post'); boundary_5 = padarray(boundary_5,(boundary_len - length(boundary_5)),'post'); boundary_6 = padarray(boundary_6,(boundary_len - length(boundary_6)),'post'); boundary_7 = padarray(boundary_7,(boundary_len - length(boundary_7)),'post'); boundary_8 = padarray(boundary_8,(boundary_len - length(boundary_8)),'post'); boundary_9 = padarray(boundary_9,(boundary_len - length(boundary_9)),'post'); boundary_10 = padarray(boundary_10,(boundary_len - length(boundary_10)),'post'); boundary_11 = padarray(boundary_11,(boundary_len - length(boundary_11)),'post'); boundary_12 = padarray(boundary_12,(boundary_len - length(boundary_12)),'post'); boundary_13 = padarray(boundary_13,(boundary_len - length(boundary_13)),'post');

- 185 - boundary_14 = padarray(boundary_14,(boundary_len - length(boundary_14)),'post'); boundary_15 = padarray(boundary_15,(boundary_len - length(boundary_15)),'post'); boundary_16 = padarray(boundary_16,(boundary_len - length(boundary_16)),'post'); boundary = [boundary_1,boundary_2,boundary_3,boundary_4,boundary_5,boundary_6,bou ndary_7,boundary_8,boundary_9,boundary_10,boundary_11,boundary_12,boun dary_13,boundary_14,boundary_15,boundary_16]; test = 0; boundary_mesh = boundary; %Coefficients: A_3ms = 0.4;b_3ms = 1.15*10^-3;w_3ms = 3.5*10^-4;c_3ms = 2*w_3ms^2; A1_3ms = 0.92; b1_3ms = 2.2*10^-3; w1_3ms = 8*10^-4; c1_3ms = 2*w1_3ms^2; A2_3ms = 0.15; b2_3ms = 4*10^-3; w2_3ms = 1.5*10^-3; c2_3ms = 2*w2_3ms^2; pulse_shape_3ms =[num2str(A_3ms) '.*(exp(-((t- ' num2str(b_3ms) ').^2)/ ' num2str(c_3ms) ')) + ' num2str(A1_3ms) '.*(exp(-((t- ' num2str(b1_3ms) ').^2)/ ' num2str(c1_3ms) ')) + ' num2str(A2_3ms) '.*(exp(-((t- ' num2str(b2_3ms) ').^2)/ ' num2str(c2_3ms) '))']; t = tlist; dt_small = tlist(2)-tlist(1); temp_tt = eval(pulse_shape_3ms)*dt_small; integal_of_pulse = sum(temp_tt);

Q_si_plus_h_times_T_ext = [num2str(pulse_energy) '.*(' pulse_shape_3ms ')/' num2str(integal_of_pulse)]; Q_si_plus_h_times_T_ext_no_laser = ['0']; Q_gl_plus_h_times_T_ext = ['0']; Q_air_plus_h_times_T_ext = ['0']; temp_tt = eval(Q_si_plus_h_times_T_ext)*dt_small; integal_of_pulse = sum(temp_tt);

%%%The coefficients need to be actual number strings, not variables... the %%%following code changes the variables to a string of the values it represents. a_domain_1 = num2str(h_si);a_domain_2 = num2str(h_gl); a_domain_3 = num2str(h_si);a_domain_4 = num2str(h_si); a_domain_5 = num2str(h_air); a = [a_domain_1 '!' a_domain_2 '!' a_domain_3 '!' a_domain_4 '!' a_domain_5]; %a is equal to convective heat transfer coefficient (h) W/(m2K)(h); c_domain_1 = num2str(k_si); c_domain_2 = num2str(k_gl); c_domain_3 = num2str(k_si);c_domain_4 = num2str(k_si); c_domain_5 = num2str(k_air); c = [c_domain_1 '!' c_domain_2 '!' c_domain_3 '!' c_domain_4 '!' c_domain_5]; %c is the convective heat transfer coefficient (k)(W/(m.K)); f_domain_1 = Q_si_plus_h_times_T_ext; f_domain_2 = Q_gl_plus_h_times_T_ext; f_domain_3 = Q_si_plus_h_times_T_ext_no_laser; f_domain_4 = Q_si_plus_h_times_T_ext_no_laser;f_domain_5 = Q_air_plus_h_times_T_ext; f = [f_domain_1 '!' f_domain_2 '!' f_domain_3 '!' f_domain_4 '!' f_domain_5]; %f is equal to heat source + (h * Temperature_external); d_domain_1 = num2str(c_p_si.*rho_si); d_domain_2 = num2str(c_p_gl.*rho_gl); d_domain_3 = num2str(c_p_si.*rho_si);d_domain_4 = num2str(c_p_si.*rho_si); - 186 - d_domain_5 = num2str(c_p_air.*rho_air);d = [d_domain_1 '!' d_domain_2 '!' d_domain_3 '!' d_domain_4 '!' d_domain_5]; f_mesh='10000!0!0!0!0'; max_triangles = 12000; [points,edges,tri]=initmesh(dl,'Init','on','Jiggle','on','Hgrad',1.999 ); [u,points,edges,tri]=adaptmesh(dl,boundary_mesh,c,a,f_mesh,'Mesh',poin ts,edges,tri,'Maxt', max_triangles,'Ngen',60,'Init',preheat_temperature); [u,points,edges,tri]=adaptmesh(dl,boundary_mesh,c,a,f_mesh,'Mesh',poin ts,edges,tri,'Maxt', max_triangles,'Ngen',60,'Init',preheat_temperature); points = jigglemesh(points,edges,tri); points = jigglemesh(points,edges,tri); points = jigglemesh(points,edges,tri); [points,edges,tri]=refinemesh(dl,points,edges,tri,1);%refines subdomain points = jigglemesh(points,edges,tri); rtol = 0.001;%default parameters of MATLAB atol = 0.0001;%default parameters of MATLAB f_preheat = ['0!0!0!0!0']; u01 = preheat_temperature .* ones(size(points,2),1); u00=parabolic(u01,[0.1,2],boundary,points,edges,tri,c,a,f_preheat,d,rt ol,atol); u0 = u00(:,2); u1=parabolic(u0,tlist,boundary,points,edges,tri,c,a,f,d,rtol,atol);

Appendix B – Stress Simulation Code

This appendix contains only the code written for simulation the stress involved in FLA processing of thin film Si on a glass substrate. Some code used in the simulation is derived from code developed by Peter Krysl called FAESOR. This code is freely available at http://hogwarts.ucsd.edu/~pkrysl/faesor/faesor_publish.html. This code takes the thermal simulation data, and calculates the displacement of each point from its original point in space at time = 0. It is important to note that the thermal simulation takes into account thermal diffusion into the surrounding air, but the thermal profile information of the air is disregarded from the structural simulation, as any change to the properties of the surrounding air is not important. The code that removes the air temperature information, and formatting the thermal data for input into the structural simulation code is not shown here. From this displacement data, the strain, and stress can be calculated. Calculating the stress and strain from the displacement, the viscoelastic relaxation of the glass, and the final step of calculating the stress in the Si film after taking the viscoelastic nature of the glass into consideration is given here. Also supplied here is a variation on example code written by Peter Krysl, alusteel. This

- 187 - example simulation calculates the thermal stress on aluminium and steel coupled and uniformly heated. The variation I created is to allow a non-uniform thermal profile across two materials, and the material properties of the aluminium and steel are changed to pc-Si and glass.

Running the simulations over a large 2D area, for 5 pulse durations, 2 preheat conditions, and no less than 90 time steps creates a lot of raw data (Approximately 150 GB worth). This data is saved in various ‘.mat’ files which are loaded to MATLAB as required. This prevents the RAM from filling up, and making the computer run slower than is optimal. By using this method, the various function calls do not return any data, they save the results to memory to be called by subsequent functions. The thermal profile is created by the code given in Appendix A, and is saved, and loaded as required by the structural simulation code. So any time the load() command is called, than that data has already been created by a preceding function. In the interests of brevity, not all code for all pulse durations is shown here, because there is little variation between them, only the saved data called and processed is changed. Additional functions were written to shape the data into a format that could be plotted. These functions are also not shown here. This code can be supplied to the reader if required.

The functions created for simulating the FLA process are the following:

 si_on_gl_fla_3ms o shown in the Appendix A  si_gl_AT_v8 o To calculate the displacement of each point from its zero strain point  calc_2D_visco_stress_in_glass_and_film_v6 o To calculate the viscoelastic relaxation of the glass from the elastic simulation carried out by si_gl_AT_v8. This function also calculates the stress in the film after calculating the stress in the glass.

si_gl_AT_v8 function u_out = si_gl_AT_v8(temperature_in, time_in, u_in, fens_in, gcells_in, groups_in, edge_gcells_in, edge_groups_in,mater_gl,mater_si,si_gl_dim) %%%%%%%%%%%%%%%% NO AIR input%%%%%%%%% run remove_subregions.m to remove air. disp(['code altered from alusteel.m - Aluminum/steel assembly. now simulates Silicon film on glass \n' ...

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'the result at each time step is passed to code that takes account of the viscoelasitc nature of the glass']); %calculates the stress induced from the temperature profile calculated by si_on_gl_fla_3ms integration_order = 3; % Finite element block feb_gl = feblock_defor_ss (struct ('mater',mater_gl,... 'gcells',subset(gcells_in,groups_in{1}),... 'integration_rule',tri_rule (integration_order),'stabfact',0)); feb_si = feblock_defor_ss (struct ('mater',mater_si,... 'gcells',subset(gcells_in,groups_in{2}),... 'integration_rule',tri_rule (integration_order),'stabfact',0)); %change fens to 2D from 3D (The 3rd dimesnion is all zeros anyway.) geom = field(struct ('name',['geom'], 'dim', 2, 'fens',fens_in)); u = clone(geom,'u'); u = set(u,'values',u_in); for n = 1:1% Apply EBC's %si_gl_dim = [w,h_si,h_gl,h_tot]; w = si_gl_dim(1); h_si = si_gl_dim(2); h_gl = si_gl_dim(3); h_tot = si_gl_dim(4); % ______%| 4 | %|9 (2) |6 %|______| %| 3 | %not sure if this is right %|8 (1) 5| %|______| % 1 u = apply_ebc (u); u = numbereqns (u); % Temperature field dT data given as an input dT = field(struct ('name',['dT'], 'dim', 1,'data',temperature_in)); % Assemble the system matrix K = start (sparse_sysmat, get(u, 'neqns')); cat_stiffness = cat(2,stiffness(feb_gl, geom, u),stiffness(feb_si, geom, u)); K = assemble (K,cat_stiffness); % Load F = start (sysvec, get(u, 'neqns')); F = assemble (F, cat(2,thermal_strain_loads(feb_gl, geom, u, dT),... thermal_strain_loads(feb_si, geom, u, dT))); % Solve u = scatter_sysvec(u, get(K,'mat')\get(F,'vec'));

%define output parameters u_out = u;

calc_2D_visco_stress_in_glass_and_film_v6 function calc_2D_visco_stress_in_glass_and_film_v6 % Input Parameters: E_si=130E9; %more realistic for polysilicon - Brazil Thesis %150e9;%Pa - 2010 - Hopcroft - What is the Young’s Modulus of Silicon nu_si=0.2;%(unitless - 2010 - Hopcroft - What is the Young’s Modulus of Silicon alpha_si= 4E-6;%this value is an approximation actual thermal expansion is 3.8E-6 at 600°C and 4.2E-6 at 1000°C - 189 -

E_gl=20E9;%64e9; nu_gl=0.2; alpha_gl= 9.75E-6; %this value is 3 time alpha_gl below the glass transition temperature(which is 3.25e-6)%3.25e-6;% Approximation from [Wu 2010] %this is the C.T.E. of borofloat below ~600°C from borofloat brochure w = 0.02; %width h_si = 2*10^-6; %2um h_gl = 3*10^-3; %3mm h_tot = h_si + h_gl; parameters=[E_si,nu_si,alpha_si,E_gl,nu_gl,alpha_gl,w,h_si,h_gl,h_tot] ; K_si = E_si/(2.*(1-nu_si)); %bulk modulus K_gl = E_gl/(2.*(1-nu_gl)); G_si = E_si/(2.*(1+nu_si)); %Shear modulus G_gl = E_gl/(2.*(1+nu_gl)); counter_a = 0; stress_visco_x_through_time_gl = zeros(2*5*9,110); stress_visco_x_through_time_si = zeros(2*5*9,110); stress_elast_x_through_time_gl = zeros(2*5*9,110); stress_elast_x_through_time_si = zeros(2*5*9,110); max_stress_array = zeros(2*5*9,8); %% 3 ms simulation pulse_width = 0.003; preheat_temperature = 700; for counter = 1:9%min temperature = 836(20J/m2); and max temp = 1423(105J/m2) pulse_energy_density = (20+28*(counter-1))*10^4; for ccc = 1 disp(['pulse width = ' num2str(pulse_width) '. Preheat = ' num2str(preheat_temperature) '. sequnce number ' num2str(counter) ' of 9.']); info_name = [num2str(pulse_width*1000) 'ms']; load([info_name '_temperature_grid_and_axis' '_preheat_' num2str(preheat_temperature) '_pulse_energy_' num2str(pulse_energy_density) '_Jperm2']); %temperature profile to see how closs the stress follows the temperature load([info_name '_elastic_stress_strain_v4' '_preheat_' num2str(preheat_temperature) '_pulse_energy_' num2str(pulse_energy_density) '_Jperm2']); load([info_name '_free_strain_preheat_' num2str(preheat_temperature) '_pulse_energy_' num2str(pulse_energy_density) 'Jperm2']);%import Free strain [l_time,l_row,l_col]= size(temp_out_grid); viscosity_const_A = 0; viscosity_const_B = -4200; viscosity_const_T0 = 250; viscous_x_stress_gl = zeros(l_time,l_col); viscous_y_stress_gl = zeros(l_time,l_col); viscous_x_stress_si = zeros(l_time,l_col); viscous_y_stress_si = zeros(l_time,l_col); for counter2 = 1:l_row if y_axis_grid(counter2) == h_gl; interface_index = counter2; end end %Calc viscous relaxation in glass just below film for counter1 = 2:l_time del_t = time_array(counter1) - time_array(counter1-1); for counter3 = 1:l_col

- 190 -

viscosity_temp = 10^(viscosity_const_A - (viscosity_const_B/(temp_out_grid(counter1,interface_index-1,counter3) - viscosity_const_T0))); tau = 10*viscosity_temp./G_gl; del_x_strain = reshape(elastic_x_strain(counter1,interface_index-1,counter3)- elastic_x_strain(counter1-1,interface_index-1,counter3),1,1); del_y_strain = reshape(elastic_y_strain(counter1,interface_index-1,counter3)- elastic_y_strain(counter1-1,interface_index-1,counter3),1,1);

del_viscous_x_stress = (K_gl*(del_x_strain+del_y_strain)) + ... (2*tau*G_gl)*(del_x_strain-del_y_strain)*(1- (1+sqrt(del_t/tau))*exp(-sqrt(del_t/tau))); viscous_x_stress_gl(counter1,counter3) = del_viscous_x_stress + viscous_x_stress_gl(counter1-1,counter3);

del_viscous_y_stress = (K_gl*(del_x_strain+del_y_strain)) + ... (2*tau*G_gl)*(del_y_strain-del_x_strain)*(1- (1+sqrt(del_t/tau))*exp(-sqrt(del_t/tau))); viscous_y_stress_gl(counter1,counter3) =del_viscous_y_stress + viscous_y_stress_gl(counter1-1,counter3); end end stress_in_gl = viscous_x_stress_gl; del_free_strain = reshape(free_x_strain(:,interface_index- 1,:),l_time,l_col) - reshape(free_x_strain(:,interface_index+1,:),l_time,l_col); viscous_x_stress_si = -(E_si./E_gl.*stress_in_gl + E_si*del_free_strain); elastic_x_stress_si = reshape(elastic_x_stress(:,interface_index+1,:),l_time,l_col); elastic_x_stress_gl = reshape(elastic_x_stress(:,interface_index-1,:),l_time,l_col); save([info_name '_viscous_stress_gl_and_si_v6' '_preheat_' num2str(preheat_temperature) '_pulse_energy_' num2str(pulse_energy_density) '_Jperm2'], ...

'viscous_x_stress_gl','elastic_x_stress_gl','viscous_x_stress_si','ela stic_x_stress_si','y_axis_grid','x_axis_grid','time_array','temp_out_g rid'); test=0; end for cccc = 1 info_name = [num2str(pulse_width*1000) 'ms']; load([info_name '_viscous_stress_gl_and_si_v6' '_preheat_' num2str(preheat_temperature) '_pulse_energy_' num2str(pulse_energy_density) '_Jperm2']); counter_a = counter_a + 1; [l_time,l_row,l_col] = size(temp_out_grid); for counter1 = 1:l_time stress_visco_x_through_time_gl(counter_a,counter1) = viscous_x_stress_gl(counter1,200); stress_visco_x_through_time_si(counter_a,counter1) = viscous_x_stress_si(counter1,200); stress_elast_x_through_time_gl(counter_a,counter1) = elastic_x_stress_gl(counter1,200);

- 191 -

stress_elast_x_through_time_si(counter_a,counter1) = elastic_x_stress_si(counter1,200); end max_stress_array(counter_a,1) = max(max(max(temp_out_grid))); max_stress_array(counter_a,2) = min(min(stress_visco_x_through_time_gl)); max_stress_array(counter_a,3) = min(min(stress_visco_x_through_time_si)); max_stress_array(counter_a,4) = min(min(stress_elast_x_through_time_gl)); max_stress_array(counter_a,5) = min(min(stress_elast_x_through_time_si)); max_stress_array(counter_a,6) = pulse_width; max_stress_array(counter_a,7) = preheat_temperature; max_stress_array(counter_a,8) = pulse_energy_density;

end end

- 192 -

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