Evaluation von laser bearbeiteten si nanopartikeldünnfilmen für den einsatz in der photovoltaik

MASTER THESIS Submitted in fulfillment of the requirements for the degree of Master of Science in Computer Science and Communications Engineering

Evaluation von Laser-bearbeiteten Si-nanopartikeld端nnfilmen f端r den Einsatz in der Photovoltaik by Levon Altunyan born on 26.11.1986 in Sofia, Bulgaria

Supervisors: Prof. Dr. rer. nat. Roland Schmechel Prof. Dr.-Ing. Einar Kruis

Duisburg, 17 January 2012

i

ABSTRACT

In this work, the potential of silicon (Si)-nanoparticles as back surface field (BSF) material for solar cells was investigated. The BSF layers were created with the help of an infra-red laser (λ = 808nm), with continuous wave length and maximum power of Pmax ≈ 452W. The optical heating of the spin-coated Si-nanoparticles took place over different substrates. For this purpose, commercially available polycrystalline silicon (poly-Si) cells from the company Solland Solar have been used. In particular, so called semi-ready structures were employed. Under this term, two types of solar cells (with and without anti-reflex coating and metal contacts) having no BSF allowed an evaluation of the discussed approaches. In addition, experiments of the Si-nanoparticles were done on several additional types of substrate materials such as glass, intrinsic Si-wafers and Kapton® foils.

The particle size distribution inside the dispersions has been evaluated to be Gaussian like, with a mean value around µ ≈ 100d.nm and a standard deviation of approximately σ ≈ 9d.nm. Thin films of the dispersed in ethanol, highly doped silicon nanoparticles were deposited on the solar cell substrates. The thickness of the spin-coated layers was determined to lie in the range of hSiNp = 650nm in the case of the commercially available cells from the company Solland Solar and hSiNP = 350nm when considering the intrinsic Si-wafers substrates used for conductivity measurements.

In addition, the parameters for the laser sintering procedure were found and optimized. Including, but not limited to, these included values concerning scan velocity, number of scans, need and advantages of a fast pre-heating step.

Furthermore, electrical characterizations of different samples have been carried out. Current-voltage (I-V) measurements under and without illumination of the semi-ready structures with Si nanoparticles as BSF were studied. Based on these curves important cell parameters are evaluated and presented. For some of the laser treated semi-ready structures from Solland Solar with anti-reflective coating, a fill factor of FF = 41%, short-circuit current Isc = −28, 76mA, an open-circuit voltage Voc = 0, 53V, power at maximum power point of Pmpp = 6, 4mW and an cell efficiency of around η = 6, 38% was obtained. In the case of a semi-ready structure without anti-reflective coating, the best result was comprising of a fill factor of FF = 27%, a short-circuit current Isc = −16, 81mA, an open-circuit voltage

ii

Voc = 0, 49V, power at maximum power point of Pmpp = 2, 21mW and an cell efficiency of around η = 2, 95%.

Different procedures to increase the efficiency of the cells in use were tested. Limiting parameters such as grain boundaries and parasitic resistances were examined. In addition, conductivity of the sintered S . layers was verified to be σtotal 6 2, 57 × 10−3 cm Scanning electron microscope pictures were used to further evaluate the change of particles and semi-ready cells by laser treatment. A 5µm layer of laser sintered BSF was achieved. Furthermore, important correlation between metalization type, parasitic resistances and cell efficiency were extracted.

Finally, to evaluate the possibility for a substantial cost reduction by employment of cheap substrates, the effect of laser sintering of the Si-nanoparticles on glass and Kapton® foil were briefly studied.

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The smallest act of kindness is worth more than the grandest intention. — Oscar Wilde

ACKNOWLEDGMENTS

I would like to take the opportunity to say THANK YOU to Prof. Dr. rer. nat. Roland Schmechel, Dr. Niels Benson and Dipl. Ing. Martin Meseth for their time and guidance during the development of this project. Without them this master thesis would not have been possible. Furthermore, I would like to thank the whole team of the Institute for Nano Structures and Technology (NST) for their support concerning my work in the laboratory. Their advices contributed to the pleasant and fruitful experience that I obtained during this time.

In addition, I would like to thank all those people that motivated me throughout the years to constantly try to make the best that I am capable of doing.

The words would not fully express my gratitude to my family for their continuous support during my academic studies. Therefore, I would like to give my special thanks to my parents which have provided me with the opportunity to learn and face so many new things. Last but not least, I would like to thank one special member of my family, namely my dog - Archi, for the inspiration he has been giving me, during the times of hopeless laziness, independently from the distance which is dividing us.

iv

CONTENTS

i introduction 1 1 introduction 2 1.1 Motivation 2 1.2 Problem Description 4 1.3 Chapters Outline 4 2 theoretical background 5 2.1 Insulators, Metals, Semiconductors 5 2.2 pn-Junction Diode 12 2.2.1 Energy Band Diagram and Charge Carrier Distribution 13 2.2.2 Mathematical Description for Current in a PNjunction 18 2.3 Photovoltaics 20 2.3.1 Back Surface Field 21 2.3.2 Important Cell Parameters 22 2.3.3 Limiting Factors 24 2.4 Shockley-Queisser Limit 25 3 experimental methods 28 3.1 Material Processing 28 3.1.1 Gas phase production of silicon nanoparticles 28 3.1.2 Substrates 30 3.1.3 Dispersing silicon nanoparticles 31 3.1.4 Substrates Cleaning, Spin-Coating and Profilometry 31 3.1.5 Laser Crystallization 33 3.2 Analytical Methods 35 3.2.1 Parasitic Resistances Extraction 35 3.2.2 Electrical Characterizations 36 3.3 Scanning electron microscope and Energy-dispersive X-ray 39 3.3.1 Energy-Dispersive X-ray Principle 41 4 results and evaluation 42 4.1 Semi-Ready Cells, Type I 42 4.1.1 Reference Cell, Type I 42 4.1.2 Reference Cell, Type I, with aluminum (Al) as BSF 42 4.2 Initial Trends 43 4.2.1 Si-nanoparticles Size 43

v

Contents

Layer Thickness 45 “Safe” Region Determination 47 Primary Observations 48 Samples Treatment - Procedures and Results 49 Scanning Electron Microscope Investigations 59 Conductivity, Laser Parameters and Color Considerations 64 4.2.8 Diffusion of Silver in Silicon Investigations 65 4.3 Semi-Ready Cell, Type II 68 4.3.1 Electrical Properties of Type II Cells 69 4.3.2 On-Off Current Ratio Comparisons 70 4.3.3 Conductivity Measurements 72 4.4 Kapton® Substrates 74 5 conclusion and future work 77 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.2.7

ii a b c

appendix 81 program code 82 additional graphs 83 sample pictures and tables

bibliography

92

90

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LIST OF FIGURES

Figure 1.1 Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6 Figure 2.7 Figure 2.8 Figure 2.9 Figure 2.10 Figure 2.11 Figure 2.12 Figure 2.13 Figure 3.1

Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7 Figure 3.8 Figure 3.9 Figure 3.10 Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4

Laser treating Si-nanoparticles - method for creating an efficient BSF 2 Band structure of dielectrics 6 Band structure of a monovalent metal 7 Band structure of a metal with overlapped bands 8 Excess of: (a)free electrons; (b)holes; in Si 9 Boron in Silicon - Excess of Holes 10 Temperature dependence of the electron concentration in a n-doped semiconductor [1] 11 A pn-junction (diode) 13 Current-voltage characteristic of a silicon diode 14 Energy band diagram and charge carrier distribution 15 Schematic Representation of Solar’s Cell Work Principles 20 Standard IV-characteristic of a Solar Cell 22 Solar Cell Equivalent Circuit 25 Shockley-Queisser Limit 26 a.) Transmission electron micrography of a typically obtained Si-nanoparticle; b). Schematic picture of a HWR system; 29 Spin Coater 32 XP-200 High Resolution Stylus-Type Surface Profilometer, Ambios Technologies 34 IR Laser 34 MBraun 200B Glove Box System 35 Determination of majority carriers 37 Four Point Measurement Schematic Picture 38 Four Point Resistance Determination Schematic 39 Principle of the scanning electron microscope 40 Principle of EDX 41 IV-Characteristic of Reference Cell (Type I) 43 Fully Processed Reference Cell Type I with Al BSF - Characteristic Behavior 44 Ball Milling and Dynamic Light Scattering Devices 44 Determination of the Si-nanoparticle size via DLS measurement 45

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List of Figures

Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10 Figure 4.11 Figure 4.12 Figure 4.13 Figure 4.14 Figure 4.15 Figure 4.16 Figure 4.17 Figure 4.18 Figure 4.19 Figure 4.20 Figure 4.21 Figure 4.22 Figure 4.23

Figure 4.24

Figure 4.25 Figure 4.26 Figure 4.27

Figure 4.28 Figure 4.29 Figure 5.1

Si Layer Thickness vs. Position on substrate

46 Si Layer Thickness vs. Position on Substrate, Top View 46 Si layer thickness vs. number of depositions 47 Si Layer Thickness vs. Spin Speed, One Spin Phase 48 Fill Factor vs Different Laser Intensities 50 Cell Efficiency vs Different Laser Intensities 50 IV Characteristic 51 Open Circuit Voltage and Short Circuit Current Applying Different Procedures 55 Fill Factor and Corresponding Efficiency Applying Different Procedures (see table.4.2) 55 Short Circuit Current Density (Jsc ) and Open Circuit Voltage (Voc ) 57 Fill Factor (FF) and Efficiency (ﾎｷ) 58 Micrograph-Uncoated Backside Surface View of a Sample 60 Micrography of Brownish Color Area of Sintered Coated Sample 61 Picture of the Characteristic Brownish Color Area after Sintering 62 Micrograph Sintered Coated Sample, Transition (Untreated-Treated-Untreated) Region 62 Highly vs. Low Reflective Area Comparison 64 EDX on the Front Surface of the Sample 66 Diffusion Coefficient of silver (Ag) in Si 67 IV-Characteristic of a Solar Cell Without Antireflective Coating, Sintered Si-nanoparticles(Isintern = 15% @ Vsintern = 1m/min) 69 IV-Characteristic of a Solar Cell Without Antireflective Coating, Sintered Si-nanoparticles(Isintern = 35% @ Vsintern = 1m/min) 70 On-Off Ratio, Comparison of Cells With and Without Si-nanoparticles 71 Efficiency of Type II samples with Si-nanoparticles 72 Conductivity (ﾏフotal ) of Si-nanoparticles Spincoated on Intrinsic Si-wafers Irradiated for Different Laser Intensities 73 Conductivity of samples in different medium 74 Kaptonﾂｮ films after sintering 75 PERL (passivated emitter, rear locally-diffused) cell structure 79

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Figure B.1 Figure B.2 Figure B.3 Figure B.4 Figure B.5 Figure B.6 Figure B.7 Figure B.8 Figure B.9 Figure B.10 Figure B.11 Figure B.12 Figure B.13 Figure C.1 Figure C.2 Figure C.3

“Slim” Version - Efficiency (η) vs Different Treatment Combinations 83 Legend for Samples Evaluated on 24.08.2011 84 IV-Characteristic (Step 2), Sample No 03 84 IV-Characteristic, Reference Cell with Step 1 85 IV-Characteristic (Step 3), Sample No 05 85 IV-Characteristic (Step 1), Sample No 04 86 IV-Characteristic (Step 4), Sample No 03 86 IV-Characteristic (Step 2-Acetone), Sample 04 87 Front Side (Step 2-Acetone), Sample 04 87 IV-Characteristic (Step 2-Acetone), Sample 05 88 Front Side (Step 2-Acetone), Sample 05 88 IV-Characteristic (Step 2-Acetone), Sample 06 89 Front Side (Step 2-Acetone), Sample 06 89 Back Surface of the Solar Cells (Type I) After Sintering - 01.06.2011 90 Back Surface of the Solar Cells (Type I) After Sintering, 14.06.2011 91 Back Surface of the Solar Cells (Type II) After Sintering, 21.09.2011 91

L I S T O F TA B L E S

Table 2.1 Table 3.1 Table 4.1 Table 4.2 Table 4.3 Table 4.4 Table 4.5 Table 4.6 Table C.1

Band gaps Eg of several semiconductor materials 27 Filter Paper (parameters) 31 Sample Preparation Parameters (Fill Factor) 49 Combination Nomenclature, (Average Fill Factor) 54 Combinations’ Nomenclature, (24.08.2011) 57 Solar Cells Sintering Parameters - Created on 21.09.2011 65 Diffusivity of Ag in Al 66 Si-nanoparticles sintered on Kapton® substrates (parameters) 75 Back Surface of the Solar Cells After Sintering - 01.06.2011 (parameters) 90

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acronyms

Table C.2

Back Surface of the Solar Cells After Sintering - 14.06.2011 (parameters) 91

ACRONYMS

Ag

silver

Al

aluminum

B

boron

BSF

back surface field

EDX

energy-dispersive x-ray spectroscopy

HWR

hot wall reactor

O

oxygen

P

phosphorus

SEM

scanning electron microscope

Si

silicon

Zn

zinc

x

Part I INTRODUCTION

1

INTRODUCTION

Even a ball of wool has a beginning. — Proverb For a photovoltaic power generation system to be economically competitive the total costs of an installed PV system must be maximum $1/W, which translates to 5-6 cents per kilowatt-hour. The current costs (2011) for a photovoltaic system are $3,40/W. This number is projected to decrease to $2,20/W by 2016 [2]. Therefore, decreasing manufacturing costs is a crucial factor in photovoltaics industry and research.

In order to reduce the cost for solar energy there is a continuous drive to reduce the thickness of the silicon wafers. This is to reduce the cost of silicon fraction of the cell and thus overall solar energy costs. Besides handling and bowing problems associated with thinner wafers a major drawback is the increased influence of the wafer back surface on the overall cell performance.[3] 1.1

motivation

A schematic representation of a typical photovoltaic cell with back surface field (BSF) structure can be seen on fig.1.1a. The cell consists

(a) Schematic drawing of a solar cell with

(b) Sintering [4]

BSF

Figure 1.1: Laser treating Si-nanoparticles - method for creating an efficient BSF

of a bottom metal contact, p and n doped semiconductor layers and

2

1.1 motivation

a top contact grid. Between the areas of opposite polarity (p and n) a space charge region is formed. One of the possibilities of increasing solar cell efficiency is by minimizing electron recombination in the rear contacts.

In general, contacts are considered as a highly defective area at which recombination of minority charge carriers will immediately take place. To reduce the losses on the back side of the p-doped layer an additional p+ layer can be applied. The theory predicts, sharing of the applied voltage among the two junctions (the n-p and the p-p+ junction) [5]. The BSF acts as a mirror, that reflects back into the cell the minority charge carriers, thus ensuring that the probability of recombination is reduced. Therefore, the absolute value of the short-circuit current would be as well increased when comparing to an ordinary solar cell (pn-junction).

The general trend in solar cell industry is the use of thick (typically over 10Âľm) aluminum (Al) film as BSF doping material. For thin Si solar cells (6 250Âľm), the Al films have a significant negative impact [6].

As discussed by Murray et al., the Al-Si phase diagram is a straight forward, classic example of a eutectic system where each element has little, if any solubility in the other [7]. Due to the different expansion coefficients of Al and Si, warping of the cell is observed. This negative result, leads to difficulties in subsequent production and increases the probability of breakage. For these reasons it is unlikely that high efficiency cells on thin silicon wafers will use Al as BSF doping material [6].

For photovoltaics research and industry the reduction in cost per watt is of utter most importance. Therefore the applicability of other materials has to be evaluated. The usage of Si-nanoparticles is a promising alternative approach. Si is a non-toxic material and it is abundant in the nature. It represents one of the most investigated materials for building electronic devices. Furthermore, due to its strongly reduced size, Si-nanoparticles can easily be converted into printable dispersions.

Furthermore, although laser crystallization contains a high potential for the annealing of Si-nanoparticles, only little evaluation of this method has been performed till now [8]. A great advantage of laser crystallization is the possibility to crystallize only a very thin film of silicon on almost arbitrary substrates [8]. This opens possibilities of new cost-effective technologies that can be utilized as well as for processing on cheap substrates such as polymer foils.

3

1.2 problem description

1.2

problem description

Due to fact, that classical solutions have a significant negative impact on thin solar cells, in this work new materials such as Si-nanoparticles are investigated. Therefore, it is suggested, that on top of the p-region, highly boron (B) doped, Si-nanoparticles are spin-coated. Thereafter, the nanoparticles can be sintered with the Silicon layer by controlled, brief, local heating to create a highly doped p+ -type region over the bulk semiconductor. This approach is intended to achieve a key benefit in cost per watt reduction when manufacturing silicon-based photovoltaic elements.

1.3

chapters outline

The aim of this work is to evaluate the potential of laser treated highly p-doped, Si-nanoparticles in the field of photovoltaics. Chapter 2 presents a brief introduction to metals, insulators and semiconductors. In addition the basic operational principles of a pn-junction are explained. Furthermore, important quantities in photovoltaics such as fill factor and cell efficiency are covered.

The experimental details and methods applied during this thesis will be presented in Chapter 3. Here, the preparation of the Sinanoparticles, the formation of dispersions and the techniques applied to characterize the physical properties will be highlighted.

Chapter 4 introduces details about electrical properties of the laser treated films. Evaluation of the results of the different semi-ready structures is given. Furthermore, conductivity after laser annealing is discussed. In addition, the behavior of Kapton速 films is shortly investigated. In the final Chapter 5 the potential of the material for further research and optimization will be highlighted.

4

THEORETICAL BACKGROUND

Fundamental progress has to do with the reinterpretation of basic ideas.

— Alfred North Whitehead

2.1

insulators, metals, semiconductors

The electrical properties of a large group of materials are highly dependent on different conditions such as temperature, illumination, presence of impurities, etc. Furthermore, their specific electrical resistance is considerably higher than that of conductors and lower than that of dielectrics. These materials are called semiconductors.

To it belong some chemical elements (e.g. Ge, Si) and many chemical compounds (e.g. GaAs, InP, CdS, ZnSe). More complex materials consist of three or four kinds of atoms are called ternary (e.g. AlGaAs, InGaP) and quaternary (e.g. InGaAsP) semiconductors, respectively [1]. By changing the composition of ternary and quaternary semiconductors their physical properties (like lattice constant or band gap) can be varied. The main difference between insulators and semiconductors is quantitative and will be characterized by the value of the band gap (Wg ) separating the valence and the conduction band [9].

As defined in literature, an atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom [10]. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom’s nucleus.

When a solid is being formed, the orbitals of the outer (so-called valence) electrons will interact with each other. Thus, in solids the levels form continuous bands of energy rather than the discrete energy levels of the atoms in isolation. The core levels remain shielded [2]. Thus, two important bands are defined: • the top most filled with electrons energy level is called the valence band; • the bottom most empty band, named conduction band; Furthermore, it is usually accepted to use the following naming:

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2

2.1 insulators, metals, semiconductors

W Conduction Band

Wc Wg

Valence Band

Wv

x Figure 2.1: Band structure of dielectrics

• Wc the lowest energy level in the conduction band; • Wg the energy band gap separating the valence and the conduction band; • Wv as the topmost energy level of the valence band; The current-carrying electrons in the conduction band are called "free electrons", or "electrons" if context allows this usage to be clear.

In general, electrical conductivity in a solid could be considered as caused by their movement. In order to be involved in an electrical current, an electron must first get enough energy. Its amount is equivalent to the transition of this electron to a higher energy level.

Three major types of materials are to be identified depending on the band gap between the valence and the conduction band, namely: insulators, metals and semiconductors.

1. Insulators (dielectrics): At T = 0K the valence band in insulators is completely filled with electrons and the highest conduction band is absolute empty (fig. 2.1). Therefore, the nearest level to be filled can be found in the conduction band only. The band gap in the case of insulators is very large (e.g. WgSiO2 = 8.9eV, WgSi3 N4 = 5.1eV) [11]. Thus, electrons need larger energies to be excited into the conduction band making current flow impossible under low applied voltages.

2. Metals: In metals like Cu, the valence band is partially filled (fig. 2.2),

6

2.1 insulators, metals, semiconductors

W

Conduction Band

Valence Band

Wv Wc x

Figure 2.2: Band structure of a monovalent metal

whereas in other metals the conduction band and the valence band overlap each other (fig. 2.3), so that the uppermost electrons in the top part of the valence band can be excited in the next-higher available energy level already at T = 0K by applying an electric field. The energies required are much lower than in the cases of insulators and semiconductors. In principle, the electrons can be excited and contribute to the electrical current because there are many unoccupied states above filled states in the valence band. By this way, the free electron concentration in metals is much higher than in intrinsic semiconductors resulting in a very high electrical conductivity [10].

3. Semiconductors: The electrical properties of semiconductors are determined by their structure. Some typical semiconductor material examples are Si (WgSi = 1, 12), Ge (WgGe = 0, 8), InP (WgInp = 1, 3) and GaAs (WgGaAs = 1, 5) [11]. The material with highest practical relevance in semiconductor devices is silicon (Si) [1]. In the ideal Si crystal at temperature of T=0 K all electrons are bonded in electron pairs, therefore there are no free charge carriers and it behaves as a dielectric. To get free, the electron should receive a certain amount of energy. The electron may receive such energy as a result of the interaction between the particles during their thermal motion (e.g. at T > 0 K) or during illumination of the crystal [9].

Each release of an electron is related to the emerge of a vacant place (free, unoccupied bond). Around the vacant place a noncompensated positive charge of the nucleus is left. This charge

7

2.1 insulators, metals, semiconductors

W Conduction Band

Wc Wg

Valence Band

Unoccupied states

Wv

Occupied states x

Figure 2.3: Band structure of a metal with overlapped bands

can attract an electron from a neighboring atom, so that the bond is filled [1]. Therefore, a new vacant place in the nearby atom is created, in which an electron from another atom might come. Thus, the vacant place makes a chaotic motion inside the crystal similar to the thermal motion of free electrons. This imaginary positive charge is called p-carrier or hole [2].

By applying an electric field the free electrons start a directed motion - current flows. The electric field ~E influences also the electrons from the covalent bonds and facilitates their jumps in the vacant places in direction, opposite to the direction of the intensity ~E of the field [2]. Therefore, the places themselves are moving into the direction of the intensity ~E. Instead of considering the real motion of the bonded electrons it is much easier to look at the motion of the vacant places. It is equivalent to the motion of a positive charge with a magnitude of the electron, into the direction of the field [1].

Therefore, in semiconductors the electrical conductivity is accomplished by the help of two types of charge carriers: free electrons and holes.

Extrinsic semiconductors Intrinsic semiconductors are only a subject of theoretical consideration, since materials with required purity do not exist in the nature and can not be realized using modern technology as well. However, for most important applications, the semiconductors with a defined amount of artificially introduced impurities (doping) is a prerequisite. Introducing different impurity atoms (e.g. phosphorus in Si), n-type or p-type (e.g.

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2.1 insulators, metals, semiconductors

boron in Si) semiconductors can be fabricated [10].

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Figure 2.4: Excess of: (a)free electrons; (b)holes; in Si

Donors Let us assume that in a Si crystal, one atom of a P is substituting one atom of Si. P has five valent electrons, four of them form common electron pairs with the neighboring Si atoms. The fifth electron is not taking part in the covalent bonds. When considering the band structure, such impurities “create” an energy level within the band gap, close to the conduction band.

This is called “shallow” level - a level that is very close to the conduction band, so the energy required to ionize an atom is small and a sizable fraction of donor atoms will be ionized at room temperature. For its transition from connected into free state condition a much smaller amount of energy is needed compared with the covalent bonded electrons. As reported in literature by Chen et al. [12], in the case of P the donor level is ED = 0, 045eV. Therefore, at room temperature the energy of thermal motion is sufficient for impurity atoms to loose their “superfluous” electrons and to convert themselves into positively charged ions P+ . Impurity atoms, which give electrons are called donors. The electrical current is mainly due to the directed motion of free electrons received from the donors.

Semiconductors, in which conductivity is defined by the free electrons received from the donors, are called semiconductors with electrical (n-type) conductivity or shortly n-type semiconductors [9].

Acceptors Fig. 2.4b shows the crystal lattice with a B atom replacing a Si atom. Since B has 3 valence electrons, one bond with neighboring Si atoms is occupied by one electron only. This positively charged vacant bond corresponds to a hole and can move in

9

2.1 insulators, metals, semiconductors

the crystal capturing an electron of the neighbor’s bond and “jumping” on its place. Thus, an atom with three valence elec-

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Figure 2.5: Boron in Silicon - Excess of Holes

trons acts in Si as an acceptor. It creates an energy level in the band gap close to the top of the valence band and can be occupied by an electron from the valence band. In the case of, B the “shallow” level is EA = 0, 045eV [12]. Doping with acceptors leads to a p-type semiconductor with excess of holes.

Temperature dependence of the charge carrier concentration Furthermore, semiconductors are having a dependency on temperature. For example, the charge carrier concentration is strongly related to the previously mentioned parameter. In the case of an n-doped semiconductor the temperature dependence can be separated in to three characteristic areas. Namely, these are the freeze-out, saturation and intrinsic regions (see fig.2.6).

As seen in the given plot, with the temperature increase the electron concentration significantly increases too. Still not ionized donors provide electrons to the conduction band, and at the temperature Tmin the semiconductors pass into the saturation region with the following relation [9]: n = ND

(2.1)

If the temperature increases up to Tmax , electron-hole pairs will be created by the band-to-band excitation, as it happens in intrinsic semiconductors [1]. In this temperature region the electrical behavior depends on the intrinsic conductivity. The electron concentration in this region will be given by: p ni = Nc Nv e−Wg /2kB T (2.2) Electronic devices based on doped semiconductors operate in the depletion region, i.e. between Tmin and Tmax [1]. Otherwise, the

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Introduction to Solid-State Electronics 11

3-22

2.1 insulators, metals, semiconductors

n (log)

∝ (-∆WG/2)

saturation region

freeze-outregion

intrinsic range

ND

∝ (-∆WD/2)

ni Tmax

Tmin

1/T

Fig. 3.18 Temperature dependence of the electronofconcentration a n-doped semicoductor Figure 2.6: Temperature dependence the electron in concentration in a ndoped semiconductor [1]

devices with a pn-junction will loss their functionality above Tmax , 3.3 Chargebecause carrierthe transport amountin ofsolids thermally generated (i.e. not impurity related) electrons and holes will exceed the doping concentration [11]. For Charge carrier concentration and velocity of charge carriers are most important parameters temperatures below Tmin charge carriers are frozen out and the having an influence on the electrical conductivity.

If the ion flow can be neglected, the electrical electrical conductivity drastically decreases. current in a solid is caused by electron and hole flows only.

A similar consideration can be performed for a p-type semiconductor.

The interested reader referredform to the The current density will be written in is a common as given literature [1, 9, 11] for further information.

J = −qThe n v nresults + q p vof p comparison between dielectrics, semiconductors and (3.44) cancarrier be summarized where n , metals p : charge concentrationas follows: In :respect electrical conductivity - q (1) +1. q (2) chargeof ofthe electrons (1) and holes (2), there is a qualitative difference between dielectrics and semiconductors. Quantitatively v n , v p : velocity electrons and holes, respectively. they of can be characterized by the value of the band gap. For both kinds of solids the number in thepositive conduction An external electrical field applied to the solid results of in electrons a force moving charges (holes) uur band determine the electrical conductivity. with a velocity v parallel and negative charges (electrons) with a velocity v anti-parallel to the p

n

field. Thus, to define current flows should be added.

2. In the metals allboth electrons take part in electrical conductivity becauseenergy, the number ofand unoccupied directly above thealso va-without an Because of the thermal electrons holes movestates with significant velocity lence band is in the same order as the number of electrons. external force. The mean thermal energy of each charge carrier is h k  3 1 1 2  = m*  Wth = kT = m* vth  m*  2 2 2  

2

or, in terms of „thermal” velocity:

vth =

3kT

m*

(3.45)

2.2 pn-junction diode

2.2

pn-junction diode

A p-n junction is occurring at the boundary between a p and an n-type semiconductor material. The p region contains holes which are mobile, and negatively charged impurity ions which are immobile. Similarly, the n-region has positively charged ions which are immobile and mobile electrons. As soon as a pn-junction is formed, electrons from n-type material and holes from p-type material diffuse into p-type and n-type material, respectively. As a result the positive donor ions in the n-region and the negative acceptor ions in the pregion are left uncompensated. Around the pn-junction a region with very few charge carriers is created. This region forms the depletion region also called the space charge region (see fig.2.9a)). It is named so because it is depleted of mobile charge carriers. Therefore, this region has a very high electrical resistance. The holes e.g. trying to enter the p-region are repelled by the uncompensated positive charge on the donor ions. As a result a potential (band diagram heights) difference is established across the junction. Soon, it becomes large enough to prevent any further movement of charge carriers. This is called potential barrier or junction barrier. It gives rise to an electric field that prevents the respective majority carriers from crossing the barrier region.

Consider connecting the p-region of the diode on a higher electrical potential than the n-region as seen in fig.2.7a. Due to the influence of the electric field the holes of the p-region and the electrons from the n-region start moving towards the pn-junction. The reduction of the potential difference and the width of the depletion region causes a large number of majority charge carriers to diffuse across the junction. An electric current flows through the diode. Connecting the diode in this way is called forward bias, and the applied voltage forward-bias voltage [13].

On the other hand, if connect the p-region with ground and the n-region with the positive pole (high electrical potential) respectively (see fig.2.7b), under the influence of the applied electric field, the free charge carriers are moving away from the pn-junction. Thus, the potential barrier is increased. Practically, the current which flows through the diode is almost zero. In this arrangement, the diode is operated in reverse biased mode, and the applied voltage is called reverse-bias voltage.

The current-voltage characteristic of a typical Si diode is shown in fig.2.8. A non-linear characteristic can be observed. Initially, the current which flows in the forward bias increases slowly with increasing voltage. From a given voltage value on it increases much faster. This shows, that the resistance of a diode is variable. It is high at low voltages and decreases with increasing voltage U. From the graphic,

12

2.2 pn-junction diode

E

E +

+

-

+ +

-

+

+

+

-

-

+

- ‐

+ +

‐ ‐ ‐ ‐ ‐ ‐ ‐

+ +

(a) in forward bias

+

+

‐

+ +

+ ‐ depletion depletion p‐doped region

‐

-

+

+

‐ ‐ ‐

‐

n‐doped

+

(b) in reverse bias

Figure 2.7: A pn-junction (diode)

it can be seen that through the diode also a reverse current Irev flows but it is typically thousand times [13] lower than the current in the forward bias. The property of diodes to pass current only in one direction is of great practical importance for electronics. The forward current Iforward rises exponentially with voltage (for U 3 kBqT ), so that it may be approximately described as [1]: Iforward = I0 × (eqU/kB T )

(2.3)

The approximation above is valid for a voltage smaller than the flat band voltage only, i.e. for silicon up to about U ≈ 0, 6V [11].

If this voltage is exceeded, the additionally applied voltage will drop primarily across the semiconductor outside the interface barrier region. The exact complete current voltage characteristic is given by [9]: I = I0 × (eqU/kB T − 1)

(2.4)

2.2.1 Energy Band Diagram and Charge Carrier Distribution In the following the mechanisms that are responsible for electrical current in a pn-junction are described. Electric field or charge carrier diffusion, or their combination is the main reason for this phenomenon. Assume without loss of generality the following [1] : 1. Abrupt doping profile: At the junction interface an abrupt change of the doping concentrations ND (net doping on p-side) and NA (net doping on n-side) takes place.

2. All doping atoms are ionized.

13

2.2 pn-junction diode

I, mA 120 100 80 60 40 20 -U, V

+U, V

0 6 4 2

0,2 0,4 0,6 2

Irev, ÂľA Figure 2.8: Current-voltage characteristic of a silicon diode [13] (Note: reverse and forward bias currents are given in a different scale)

3. There are no defects, especially at the interface.

The case of thermodynamic equilibrium (voltage U = 0V and current I = 0A) is denoted by the use of an index 0. The intrinsic density of carriers is specified by ni . np0 = 0 =

pn0

n2 n2i = i Minority charge carriers (electrons) in p-region pp0 NA (2.5)

n2i n2i =0= = Minority charge carriers (holes) in n-region nn0 ND (2.6)

where, pp0 Majority charge carriers (holes) in p-region nn0 Majority charge carriers (electrons) in n-region NA is the acceptor concentration in the p-doped region ND is the donor concentration in the n-doped region The term used to describe the topmost electron energy level at absolute zero temperature is "Fermi level" and it is usually abbreviated as WF . In the case of thermal equilibrium the reference "Fermi level" is constant (WF = const.). Near the junction, the concentration of free charge carriers does not follow the sharp profile of the doping atom distribution because of their non-zero mobility. Diffusion drives

14

2.2 pn-junction diode

Figure 2.9: Energy band diagram and charge carrier distribution

a) Space charge region b) Band structure profile of an abrupt pn-junction c) Space charge distribution d) Potential- and field distribution [1]

15

2.2 pn-junction diode

electrons from n- to p- region and the holes from p- to n-region, respectively. According to Poisson’s equation (see eq.2.7), this effect results in a band bending (fig. 2.9b) and a build-in electric field (fig.

2.9d), counter acting the diffusion process of electrons and holes and, therefore, leading to the equilibrium state. Using Poisson’s equation, the diffusion current caused by n and p gradients across the junction, as well as the field-dependent current from the band structure profile (i.e. potential profile) can be calculated: Ď âˆ†Ď† = −div~E = − 0 r

(2.7)

where: ~E is the electric field φ is the electric potential Ď is the charge density 0 = 8.85 Ă— 10−12 F/m is the permittivity in vacuum r is the relative permittivity of the material q is the elementary charge = 1.60 Ă— 10−19 C The potential difference UD that electrons and holes have to pass when moving through a pn-junction can be calculated as: !

NA ND UD = Uth ln (2.8) n2i where, UD is the difference between “built-in� and external applied voltage

where the thermal voltage Uth =

kB T q

(2.9)

UD > 0 corresponds to the voltage which has to be applied externally so that a flat band profile will be achieved. Furthermore, − Ď = q[N+ D (x) + p(x) − NA (x) − n(x)]

(2.10)

Therefore, equation 2.7 and equation 2.10, lead to:   Ď q − =  0 r  

 n −p | 0 {z }0 equilibrium concentration difference of free charges (≈0)

+

N− − N+ | A {z D} concentration difference of acceptor and donor atoms

    

(2.11)

16

2.2 pn-junction diode

After using the above defined simplifications (see p.13) a more compact form can be expressed as: Ď = qN+ D for lg 6 x 6 ln0 (n − doped region)

(2.12)

where: ln0 is the length of the space charge region in the n-doped region.

For acceptors, one can define in similar manner: Ď = −qN+ A for lp0 6 x 6 lg (p − doped region)

(2.13)

where: lp0 is the length of the space charge region in the p-doped region; These results are shown on fig.2.9c). The whole length of the space charge region can be defined as [1]: s 2 0 r 1 1 p l0 = (2.14) ( + ) UD q NA ND Fig. 2.9d) shows the distribution of the electric field across the junction. It is increasing with doping and is determined primarily by the lower level of doping. A maximal value is obtained at x = lg .

Emax = −

qND qNA (lg − lp0 ) = − (ln0 − lg ) 0 r 0 r

(2.15)

Using the conduction and the valence band, the distribution of free charge carriers n(x) and p(x) can be calculated as: "

# 1 ln0 − x 2 for lg 6 x 6 ln0 (2.16) nn (x) = ND exp − 2 LDp and "

1 pp (x) = NA exp − 2

x − lp0 LDn

2 # for lp0 6 x 6 lg

(2.17)

where, pp (x) Majorities (holes) in p-region depending on the length x nn (x) Majorities (electrons) in n-region depending on the length x LDn is the Debye length (the distance over which significant charge separation can occur) in n-region LDp is the Debye length in p-region The concentration of minority charge carriers can be obtained from the following equations: nn pn = n2i and np pp = n2i

(2.18)

17

2.2 pn-junction diode

Therefore using equations 2.16, 2.17 and 2.18, follows: "

#

n2i UD 1 x − lp0 2 np (x) = = ND exp exp − for lp0 6 x 6 lg pp (x) Uth 2 LDn (2.19) ,where nn (x) Majority charge carriers (electrons) in p-region depending on the length x, and "

#

n2i UD 1 ln0 − x 2 for lg 6 x 6 ln0 pn (x) = = NA exp exp − nn (x) Uth 2 LDp (2.20) ,where pp (x) Majority charge carriers (electrons) in p-region depending on the length x.

2.2.2 Mathematical Description for Current in a PN-junction In contrast to the equilibrium conditions, under operational conditions a net electrical current flows through a semiconductor device.

Contributions from the different electron transport mechanisms exist.

The electrical currents are generated in a semiconductor due to the transport of charge from place to place by electrons and holes. The two basic transport mechanisms in a semiconductor are drift and diffusion (see fig.2.9b)) [14].

The drift current is defined as the flow of electric current due to the motion of the charge carriers under the influence of an external electric field. The mathematical description for current in a pn-junction diode follows the following relations.

Jn,Drift = −qnµn~E

(2.21)

,where Jn,Drift is the drift current density µn is the electron mobility ~E is the electric field Carrier diffusion is due to the thermal energy, kB T, which causes the carriers to move at random even when no field is applied. This random motion does not yield a net flow of carriers nor does it yield a net current in material with a uniform carrier density since any carrier which leaves a specific location is on average replace by

18

2.2 pn-junction diode

another one. However if a carrier gradient is present, the diffusion process will even out the carrier density variations: carriers diffuse from regions where the density is high to regions where the density is low. The diffusion process is not unlike the motion of sand on a vibrating table; hills as well as valleys are smoothed out over time [9].

As a final result of complex derivations for the diffusion current holds: Jn,Diff = qDn ∇n

(2.22)

,where Dn is the electron diffusion coefficient n is the electron concentration Similar expressions exist for the hole-related current. In case of thermodynamic equilibrium, the total current through the junction is equal to zero: Jtotal = 0 = JDrift + JDiff = Jn,Diff + Jn,Drift + Jp,Diff + Jp,Drift (2.23) Since each process (for electrons and holes individually) has to be in equilibrium, this equation can be split into parts. Namely,: Jn = Jn,Diff + Jn,Drift = 0

(2.24)

Jp = Jp,Drift + Jp,Diff = 0 at U = 0

(2.25)

Combining the characteristics of a pn-junction with the photoelectric effect leads to the field of photovoltaics which is described in the following section.

19

2.3 photovoltaics

2.3

photovoltaics

The photovoltaic effect is based on the properties of a pn-junction and light. In the following the operation of solar cell in a simplified form (see fig.2.10) is discussed.

Figure 2.10: Schematic representation of the charge carrier generation in a solar cell. In the left part is the generation of the charge carrier pairs and the recombination process represented. The schematic band structure of an pn-junction on the right side shows the collection of charge carriers in a solar cell. [15]

In a pn-junction being in an equilibrium state, the build-in potential barrier holds most of the electrons in the n-side, whereas the holes on the p-side. If a positive voltage on p-side is applied by an external source (forward bias), the energy barriers are lowered. Therefore, there is a higher probability of electrons getting over the barrier from n to p-side. As a consequence of this, there are many more electrons in the p-side than there were in the equilibrium state. This leads to an excess of minority charge carriers on the p-side. The same holds for holes which have migrated to the n-type region. Some of the excess minority electron charge carriers injected across the junction may recombine in the bulk of the p-side region.

There are many reasons for which this might happen. The most common in Si is that there might be defects corresponding to energy states inside the band gap of the p-region [2]. Therefore, an electron may land to that intermediate state, and thereafter fall down once again. Thus it would fill up a hole state in the valence band.

When an electron gets into the p-type region, the system is not anymore electrostatically neutral. Therefore, it reacts by kicking an electron out of the valence band into the conduction band to create a new hole. The resulting electron flows through the connected load back to the conduction band of the n-side and so replaces the missing electron.

Usually contacts are characterized as highly defective areas. Therefore, recombination can take place in the contact regions as well.

In conclusion, if an excess of minority charge carriers is observed, the pn-junction system may react by promoting a recombination process.

Thus, if an electron and a hole recombine, one electron flows in the

20

2.3 photovoltaics

external circuit.

Sunlight is composed of photons, or “packets” of energy. When irradiated, some of the photons are absorbed by the photovoltaic cell. If they get absorbed the energy from the photon is transfered to an electron of an atom of the solar cell. When in semiconductor material a photon having sufficient energy is absorbed an electron in the valence band is lifted to the conduction band. Thus, an empty state in the valence band (a hole) is created.

The photo-generated current flows in opposite direction to the one created by the diode’s forward bias voltage. If a load is connected the following effect is observed: the electrons move towards the n side and the holes move towards the p side in direction of the junction. In the ideal case the photo current has essentially a negative constant value.

2.3.1 Back Surface Field The generated minority carriers are useful if they are created near the collecting pn-junction. A lot of recombination occurs at the back contact. This surfaces have a lot of defects and it can be assumed that once reached, a recombination will immediately occur. As obtained by different simulations of a typical crystalline solar cell under short circuit conditions around 49% of the hole-electron pairs are generated in the base and near the rear contact region. In addition, around 23% of them recombine and are lost in the same area. Under open circuit conditions, the recombination losses are much higher. They are accounted to lie in the range of 80% [16].

According to Beer-Lambert law, the intensity of an electromagnetic wave inside a material falls off exponentially from the surface as I(z) = I0 × e−αz

(2.26)

,where I0 is the intensity of an electromagnetic wave; α is the wavelength; z is the distance inside the material; If δp denotes the penetration depth, we have: δp =

1 α

(2.27)

Furthermore, as a consequence of this law longer incident light wavelengths are absorbed more deeply in a Si solar cell [17]. Therefore, they are more sensitive for recombination at the back surface contact.

Thus, it is important to improve the performance by shutting off some recombination processes.

21

2.3 photovoltaics

One possible way to reduce losses and thus increase the efficiency of a cell is the so called Back Surface Field. Applying a BSF acts as a mirroring of the minority charge carriers back to the pn-junction.

Therefore, this method is an important technological step to increase a solar cell’s efficiency.

Assume, a p-type as a base material of the cell. BSF is achieved, by heavily p-type region doping at the rear side of the cell. Therefore, the Fermi level would get closer to the valence band. Thus, an additional energy barrier is inserted that the electrons have to jump over.

In general, recombination depends on the speed at which a minority charge carrier diffuses towards the back contact [16]. BSF acts as a minority carrier mirror which prevents some of them reaching the back contact. Thus, the probability of diffusion towards the collecting pn-junction is increased. In addition, when comparing the behavior of a cell with and without extra p+ -type layer doping, more current at longer wavelengths is obtained in favor of BSF treated cells [16].

2.3.2 Important Cell Parameters An IV characteristic of an ideal solar cell can be seen in fig.2.11. Two

Figure 2.11: Standard IV-characteristic of a Solar Cell

important quantities to characterize a cell that can be observed in the graph are: 1. Open circuit voltage (Voc ), represents the maximum voltage available from a solar cell;

22

2.3 photovoltaics

2. Short circuit current (Isc ), gives the largest current which may be drawn from the solar cell; As a solar cell contains a pn-junction, it can be modeled mathematically in a similar way as a diode. For a crystalline Si cell, the pn-junction collection mechanism can be considered as independent of the voltage applied on the cell. Therefore, the total induced current under illumination is obtained by a superposition between the current in the dark and the light generated current. Thus, the current density can be approximated as a combination of the short circuit current and the dark current density of an ideal diode: J = Jsc − J0 (eqV/kB T − 1), where

(2.28)

J0 is the reverse bias saturation current density; Jsc is the short circuit current density; V is the voltage between the terminals; In the case of an open circuit no current (J=0) flows between the terminals. Therefore,

kB T Jsc Voc = ln +1 (2.29) q J0 A solar cell converts light, a flow of photons, to electric current, a flow of electrons. Therefore, higher light intensity would mean more photons, which in turn means more electrons and higher short circuit current. Jsc is inversely proportional to the effective area (A) of the solar cell. Thus, the short circuit current density is given as: Jsc = Isc /A

(2.30)

Furthermore, this parameter is often used to compare solar cells.

From the fourth quadrant of the coordinate system (fig. 2.11) it can be seen that for a positive voltage V, the current I is negative. Therefore, the corresponding product of the two quantities would be smaller than zero (P = I ∗ V < 0). Thus, it can be concluded that the solar cell generates power. Somewhere between these two characteristic points the maximum power of a solar cell is situated.

The maximum power density is simply: PMPP = Jmp Vmp

(2.31)

where, Jmp and Vmp are the current density and voltage at Maximum Power Point (MPP). It gives the optimal place to operate the device.

As it can be noticed PMPP is less than the product of the open circuit voltage Voc and the short circuit current density Jsc . The amount of “utilized” open circuit voltage and short circuit current at maximum

23

2.3 photovoltaics

power is given by the fill factor, FF. It is a measure of how ideal a solar cell is.

PMPP = Jmp Vmp = Jsc Voc FF

(2.32)

Therefore, FF =

Jmp Vmp Jsc Voc

(2.33)

If the device is operated at its optimum, then the efficiency is defined as the ratio between output Pout and input power Pin . η=

Jmp Vmp Pout = Pin Pin

(2.34)

where, Pin is the power density of incoming light. Furthermore, one can express efficiency by using the fill factor: η=

Jsc Voc FF Pin

(2.35)

The four quantities Jsc , Voc , FF and η are frequently used to characterize the performance of a solar cell.

The starting point for an evaluation is a measurement of the cell under light conditions. Under different illumination intensities the cell current will vary. As an example, the air mass coefficient defines the direct optical path length through the Earth’s atmosphere, expressed as a ratio relative to the path length vertically upwards, i.e. at the zenith. A typical value of Θx = 48, 2◦ for mid-latitudes is considered as a useful representation of the overall yearly average.

It corresponds to an air mass coefficient of 1,5. Therefore, standard lighting conditions for terrestrial solar cells have been defined. Under this term it is normed an air mass 1.5 spectrum, light flux of 1000W/m2 and temperature of 25◦ C[2].

2.3.3 Limiting Factors In addition, important for the evaluation of solar cells are limiting factors which can be modeled as parasitic resistances as showed in fig.2.12.

Parasitic Resistances In general, to collect most of the sunlight and thus generate a lot of power, a large pn-junction would be preferred in the design of a solar cell. It is highly probable that there are shorts, shunt paths,

24

2.4 shockley-queisser limit

Figure 2.12: Solar Cell Equivalent Circuit

leakage mechanisms and defects in the diode. All these undesired characteristics would lower the performance of the cell in consideration. Their behavior, can be summarized in a shunt resistance (Rsh ) connected in parallel to the solar cell (mainly due to the pn-junction interface). In addition, the contacts, the p region, the n region and the pn-junction itself, would introduce some parasitic effects as well.

Their total effect can be modeled by a series resistance (Rs ). The effect of the series and shunt resistances would lower the current and voltage and therefore degrade the cellâ&#x20AC;&#x2122;s fill factor. That is why reducing negative influences such as material contamination, surface and crystal defects are of utter most importance.

2.4

shockley-queisser limit

Solar cells are sensitive to different wavelengths of light (i.e., photons of different energies) as a function of the materials they are built from. Accordingly, some cells are better performers outdoors (i.e., optimized for sunlight), while others are better performers indoors (optimized for fluorescent light). As predicted by Shockley and Queisser [18] the maximum conversion efficiency of a solar cell lies around 33.7% assuming a p-n junction band gap of around 1.1 eV. It can be seen from fig. 2.13, that as the band-gap is increased there are fewer and fewer photons that can be absorbed, but the open circuit voltage is increasing. As the band-gap is increased furthermore, the voltage is increased as well. Nevertheless, the number of photons that can be absorbed decreases. Therefore, the current is reduced as well. As it can be extracted from the graph, the optimum lies around the band-gap of Si. Solar cells made from single crystal silicon are currently limited to about 25% efficiency because they

25

2.4 shockley-queisser limit

0,4

CuInSe 2

Si

19

26

CuGaSe 2

0,3

0,2

0,1

0,0

0

1

2

Eg [eV]

3

Figure 2.13: Shockley-Queisser Limit [15]

Abbildung 1.2: Abha¨ngigkeit des theoretischen Wirkungsgrades von der

are most sensitive to infrared light, and radiation in this region of Bandlu Eg [2]. Die Bandlu ¨cke spectrum ¨ckenenergien the electromagnetic is relatively low in energy der [19].HalbleitermaAside from single crystal there exist other commonly used types of silicon terialien Si, CuInSe2 und CuGaSe2 sind durch Linien gekennsuch as polycrystalline and amorphous.

The reason for this is their zeichnet. lower cost at acceptable efficiency. Polysilicon, is a material consisting of small silicon crystals. It is commonly accepted in photovoltaic industry to use the term multi-crystalline (mc-Si) as a naming synonym. Thinder filmplasmatechnologischen cells have a number of advantages, including konnten easier Fu Barriereschichten typische ¨r die Entwicklung deposition and assembly, the ability to be deposited on inexpensive Kenngr¨oßensubstrates, fu herangezogen werden.and Sothe gibt diesuitability Leerlaufspannung Uoc ¨r Solarzellen the ease of mass production, high to large Since amorphous silicon cells have no crystal eines Moduls z.B.applications.

Auskunft dar u ob in einer Isolationsschicht Fehler vorliegen. ¨ber, structure at all, their efficiencies are presently only about 10% due to Der Kurzschlußstrom Moduls bewertet z.B. die Barrierewirkung sc einesenergy significant Iinternal losses [19]. Nevertheless, they are used, gegen Verdue to providing an acceptable efficiency at good price. unreinigungen.

A number of other materials can also be used to make solar cells.

Eine wichtige Kenngr o¨ße beiare Solarzellen ist die maximale Leistung Pmpp (engl. maTypical examples gallium arsenide, copper indium diselenide and cadmium telluride nameSolarzelle a few. In table 2.1 the band gaps kann. of ximum power point, mpp), die vontoeiner entnommen werden Es gilt: several typical semiconductor materials is presented.

Pmpp = Umpp · Impp

(1.7)

Eine weitere Gr¨oße ist der Fu ¨llfaktor ff . Er bewertet, wie nah sich die StromSpannungs-Kennlinie der Solarzelle an die Idealform ann¨ahert: Umpp · Impp Uoc · Isc

(1.8)

ff · Uoc · Isc Pmpp = PLicht PLicht

(1.9)

ff =

Daraus ergibt sich der Wirkungsgrad zu: η=

Die typischen Gr¨oßen, mit denen man eine Solarzelle oder ganze Photovoltaikmodule

2.4 shockley-queisser limit

27

Table 2.1: Band gaps Eg of several semiconductor materials [15, 20â&#x20AC;&#x201C;22]

Material: Band gap: Power conversion efficiency [%] Technology Ge 0,66 eV CuInSe2 1,05 eV Si 1,12 eV 10-17 Crystalline GaAs 1,42 eV 20-29 Crystalline CdTe 1,45 eV 10-17 Thin-film CuGaSe2 1,68 eV a-Si:H â&#x2030;&#x2C6; 1, 7 eV 8-13 Thin-film CdS 2,4 eV There are several reasons due to which Si is the preferred choice in solar cell industry. It is a well known, inexpensive, non-toxic material. Furthermore, it has its band gap value (Wg = 1, 12eV), near to the point at which the theoretical efficiency maximum predicted

by Shockley and Queisser can be obtained.

3

E X P E R I M E N TA L M E T H O D S

A theory is something nobody believes, except the person who made it.

An experiment is something everybody believes, except the person who made it.

— Albert Einstein

3.1

material processing

In this section the methods used through this thesis are described.

Furthermore, the information and procedures needed to replicate the build up of the structures is explained. Moreover, the equipment and materials needed are listed. Finally, the reasons, limitations and assumptions which influenced the choice of the methods in use is stated.

3.1.1 Gas phase production of silicon nanoparticles Several methods to grow Si-nanoparticles have been reported. Typical examples reported in literature are: • Embedded clusters [23, 24] • Nanoporous silicon [25] • Colloidal chemistry [26, 27] • Laser ablation [28] • Gas phase growth [29] One of the methods which is scalable to an industrial production level is the gas phase growth and in particular, the use of a hot wall reactor (HWR) system [8]. The Si-nanoparticles used throughout this work have been produced by this method.

The schematic illustration of a HWR system used for the growth of silicon nanoparticles is given in fig.3.1b. A typical Si HWR produced nano-particle can be seen in fig.3.1a. In the following the procedure to obtain the B-doped Si-nanoparticles is described.

The particles have been obtained by pyrolysis of pure monosilane and a mixture of 1% diborane gas in hydrogen. Both precursors

28

3.1 material processing

4 Properties of Silicon Nanoparticle Layers

(a) Transmission electron micrography (b) Schematic illustration of a HWR sysfor the growth of silicon inset shows the electron diffraction nanoparticles [30]. of the indicated [30] in between sinmaterial, which will be pattern outlined below.

The large amount ofregion internal interfaces Figure 4.1: Transmissionof electron micrograph of a HWR silicon nanoparticle.The The inset shows eleca HWR silicon nanoparticle. temtheused tron diffraction pattern of the indicated region [Wig01].

tered silicon nuclei will have consequences on the defect properties of hot wall silicon nanoparticles as will be Figure discussed in3.1: Section a.)4.1.4.

Transmission electron micrography

Si-nanoparticle;

Microwave reactor silicon nanocrystals

of a typically obtained b). Schematic picture of a HWR system;

In contrast, a completely different sample morphology is present for silicon nanocrystals grown in the microwave reactor systems. As Figure 4.2 demonstrates, these exhibit a clearly spherical shape and consist of only one crystalline domain, thus being real single nanocrystals. The TEM micrograph shows the crystalline interference fringes from the lattice planes in the nanocrystalline volume, but also an outer shell showing no signs of crystalline order is evident. This shell is considered as the surface oxide (consisting of silicon suboxide, SiOx , with 1 < x â&#x2030;¤ 2), which is usually present on samples that have been subject to oxidation at ambient atmosphere, such as the shown samples, which were prepared for the TEM measurements under room conditions.

The natural oxide shell is typically 1 nm in thickness and serves as a passivation layer for further oxidation of the silicon nanocrystals similar to the case of bulk crystalline silicon surfaces.

When oxidized at high temperatures, the oxide thickness can increase to significantly thicker

74

29

3.1 material processing

were mixed and fed into a tabular hot-wall reactor with six heating zones and total heating length of 1 m. An additional flow of nitrogen prevented particle deposition inside the reactor and served also as a carrier gas. The furnace temperature was set to 1050◦ C and the reactor pressure was adjusted to 400 mbar using a vacuum pump and a regulating valve. The particles were transported with the gas flow to a separator and collected on porous stainless filter elements.

After the experiment the material was filled automatically into plastic containers by back purging the filter. The production rate was around 600 g per hour.[30] 3.1.2 Substrates The experimental investigations of the Si-nanoparticles took place on different types of substrate materials. For the initial studies thermo scientific microscope slides, with ground edges 90◦ and thickness of 0,8 - 1,0 mm were used. The substrates were cut into a square shape, 10 × 10mm2 .

Furthermore, depending on the applied methods and as a consequence of the obtained results different semi-ready industrially prepared solar cells were used. Two different types of multicristalline silicon cells were employed. Both were provided by the company Solland Solar and were sawed into samples of 10 × 10mm2 .

At first, a semi-ready cell with anti-reflex coating (SiN), front silver (Ag) silver grid contacts and back Al layer metalization was used. The total thickness of the samples was 250µm. As reported

by Solland Solar, the anti-reflex coating had a refractive index between 2.0 and 2.2 and a thickness of 80 nm(±5nm). Furthermore, concerning the provided cells, the top 300 to 400 nm of the wafer were compensated with P atoms. Thus, an n-type layer was formed.

The doping concentration for this depth range was specified as ND = (1 × 1016 . . . 1 × 1017 )cm−3 . The thickness of the p-type layer corresponds to the wafer thickness minus the emitter. The number of B atoms was as high as ND = (1 × 1015 cm−3 . . . 1 × 1016 cm−3 ). The specific resistance was specified as ρ ≈ 0, 5 − 3.0 Ωcm. For naming purposes, through later chapters, the previously described semiready cell configuration will be defined as Type I. In addition, a second type of semi-ready cells was employed. The major difference with respect to the previously described cells was that they consisted of no anti-reflex coating and no metal contacts.

The total thickness of the samples was measured to be 250µm. Later on, they will be referred as semi-ready cells from Type II. For conductivity measurements, monocrystalline intrinsic (residual n-type doping) Si wafers were used. They had a thickness of 525µm and a square shape, 10 × 10mm2 . The orientation of the Si-wafer was

30

3.1 material processing

1 0 0. The p-type side was polished, whereas the n-type side was etched.

Cost-efficient technologies that can be utilized such as processing on thin polymer foils has been briefly investigated. For this purpose, due to their high thermal stability Kapton® films (10 × 10mm2 ) were employed. For stability during actual particle depositions, larger glass substrates were used. The Kapton® films were placed over UV Quality quartz glass substrates which had a square shape of 15 × 15mm2 , and a thickness of 1mm.

3.1.3 Dispersing silicon nanoparticles To produce stable dispersions of the Si-nanoparticles a defined quantity was mixed with dry ethanol. Thus, liquids of Si-nanoparticles 5%wt and 10%wt were prepared. To assure smooth layers after spincoating a ball milling procedure has been used. For this purpose, yttria stabilized zirconia (YTZ) beads (100µm) were utilized. To prevent obstruction of the slotted sieve filters a pre-dispersing step was employed. It included milling with courser beads (300µm). Thereafter, a 15 minutes of ultrasonic cleaning was applied. Thus, possibly existing bigger agglomerates have been destroyed. In addition, to prevent unwanted things like dust, big agglomerates, etc. a final filtering step has been utilized. For this purpose a glass fiber paper was used. Its properties can be summarized in the following table 3.1.

Table 3.1: Filter Paper (parameters)

Grade Weight[g/m2 ] Thickness[mm] Filtration speed [s] Average retention capacity [µm] Surface Applications and properties

MN 85/90 BF 90 0,4 15 0,5 Smooth Glass fiber filter without binder

3.1.4 Substrates Cleaning, Spin-Coating and Profilometry As a first step each of the samples was carefully cleaned so that oils and organic residues which appear on this type of surfaces are removed. The procedure that has been used involved the following ordered steps:

31

3.1 material processing

Cleaning 1. pouring on the surface of the sample which was glued to the wafer with ethanol; 2. rubbing the wetted surface with paper; 3. ultrasonic cleaning in acetone (10 min); 4. ultrasonic cleaning in ethanol (10 min); 5. ultrasonic cleaning in isopropanol (10 min); 6. blow drying with compressed nitrogen; Spin-coating The Si-nanoparticles have been spread onto the substrates by spincoating. All Si layer depositions were made on the "close bowl" designed Single Wafer Spin Processor for Manual Dispense (APTSPIN150-v3-NPP), seen on fig. 3.2. One of the most important factors

Figure 3.2: Spin Coater

in spin coating is repeatability. Subtle variations in the parameters that define the spin process can result in drastic variations in the coated film. Only a single step (static dispense) has been used. The rotational frequency during the spin-coating procedure was set to 2000 rpm. The acceleration of the spin coater in use was set to

32

3.1 material processing

1088rpm/s2 . The amount of material was selected in a way that the substrate is fully coated. As a general observation, once the substrate area was fully coated, the exact amount of material did not influence the final spin coated layer thickness. For measurements an estimated height of dSiNp = 650nm(±25nm) is assumed (see fig. fig.4.5 in the following sections). Therefore, a larger puddle, to ensure full coverage of the substrate during the high speed spin step, was preferred. By choosing one, instead of several smaller interlocking circular drops, reduced the contamination as well as air bubbles inside the final Si-nanoparticles layer. Thus, depositing a puddle of the Si-nanoparticles fluid near the center of the glass substrate was sufficient.

The final outcome which has been used for all Si particle depositions on all used substrates through this work could be summarized in the following procedure: 1. Use vacuum mode; 2. Use the top opening when depositing the particles; 3. Cover the whole substrate area; 4. After putting the Si drop on the substrate start immediately with the spin coating; 5. Reduce the "ramp" → Use a relatively high acceleration. (aactual = 1088 rpm ); s2 6. Use only one phase for tspin = 20 s; Profilometry The layer thickness achieved by this method has been determined using, a XP-200 High Resolution Stylus-Type Surface Profilometer from Ambios Technologies (see fig. 3.3a). To isolate vibration, a Micro 40 benchtop unit from Halcyonics was utilized. The devices needed for this step can be seen on fig. 3.3b. The stylus force used was F = 0, 10mg.

3.1.5 Laser Crystallization To crystallize the thin films of silicon nanoparticles by optical heating, an infra-red laser (λ = 808nm), with continuous wave length and maximum power of Pmax ≈ 452W was utilized (see fig. 3.4). The amount of gas flow inside the processing chamber (total volume Vchamber = (1 . . . 2)l, see fig.3.4) was measured with the help of a TSI 4000 Series Mass Flowmeter. Cheaper glasses were absorbing too much light due to imperfection of the material and were breaking

33

3.1 material processing

(a) Surface Morphology Measurement (b) Surface Profilometer and Benchtop Plate Vibration Insulator Instrument Set

Figure 3.3: XP-200 High Resolution Stylus-Type Surface Profilometer, Ambios Technologies

almost immediately leading to unstable stand for the samples. Therefore, each sample has been placed over a quartz glass (UV-quality) in the chamber of the infra-red laser so that stability during sintering was assured. The optimal focus of the laser has been defined in a

Figure 3.4: IR Laser

previous work [31]. Therefore, only the height (z-dimension) of the laser had to be adjusted with respect to the different substrates used.

Furthermore, a short program in the G programming language for the laser control (see appendix p. 82) has been developed. With its help, different parameters such as the intensity of the actual sintering step, its velocity and the number of scans have been controlled and varied.

34

3.2 analytical methods

Metal evaporation Before IV measurements were possible, contacts on the back side as well on the front side (when needed) of the solar cells were evaporated. In the case of Type I cells, only back side contacts were necessary. Thick contacts have been made by using 200nm layers of aluminum (ρ = 10, 49 g/cm3 ). They were metalized by thermal evaporation (see fig. 3.5a) under low pressure conditions of approximately 2 × 10−6 mbar. Typical deposition rates in the range of 3-5 Å/s were used. All metal evaporations were made inside the MB 200B glove box system’s chamber seen on fig. 3.5b. Back side contacts

(a) MBraun, Evaporation Chamber

(b) MBraun 200B Glove Box System

Figure 3.5: MBraun 200B Glove Box System

having an area of 9 × 9mm2 were prepared. Thus, on each side of the 10 × 10mm2 cells there were big enough windows, thus protecting the sample of short circuiting by connecting to the front side grid.

3.2

analytical methods

3.2.1 Parasitic Resistances Extraction As suggested by Goetzberger et al., approximate values for the parasitic resistances in a solar cell can be calculated from the inverse of the slopes of the I-V curves at Voc and Isc , respectively [32]. Therefore:

Rs =

∂I ∂V

−1 , slope around Voc

(3.1)

and

Rsh + Rs =

∂I ∂V

−1 , slope around Isc

(3.2)

35

3.2 analytical methods

Through this work, a slightly modified version of this method has been used. Concerning the series (Rs ) and the shunt (Rsh ) resistances, slopes were extracted when looking at the saturated parts of the respective characteristic curves under illumination instead at the intersections with the abscissa and ordinate axis.

In general, an ideal cell’s shunt resistance (Rsh ) would be infinite and would not provide an alternate path for current to flow, while the series resistance (Rs ) would be zero, resulting in no further voltage drop before the load. Usually a shunt resistance of Rsh > 1000Ω is regarded to be tolerable, whereas even small values of the series resistance (Rs ) are considerably degrading the efficiency of the cell [32].

3.2.2 Electrical Characterizations Fast Majority Charge Carrier Determination Due to the subtle difference in the colors of the p and n region sides, in semi-ready cells from Type II, each of the samples from the wafer has been tested by utilizing a fast majority charge carrier test. This procedure is based on the thermoelectric effect. The method was employing a voltmeter and two measurement tips, one of which could be heated up to 300 ◦ C whereas the other was kept at room temperature. It was regulated that by default the following shall be understood concerning the voltage-measuring device in use: • the anode is connected to the ”hot” side (iron soldering unit) • the cathode is connected to the ”cold” side For n-doped material the following phenomenon would be observed.

By heating one side (see fig.3.6) the majority charge carriers (for n-doped material- the electrons) would become more kinetic energy.

Therefore, the probability of moving away from the heated source in direction to the opposite side is increased as well. Thus, potential difference is created. Therefore, the voltage measuring device would display a positive voltage. If p-doped material was measured this would have led to the opposite result. The warming of one of the sides was achieved by the usage of a soldering iron unit. To confirm the measurement setup a test with the help of reference Si sample of known doping type was done.

Two Point Measurements After the first BSF structures were prepared and bottom contacts have been deposited IV-characterizations have been carried out. For the

36

3.2 analytical methods

e--excess (cold side)

e-

n-dopped

-

e--defficiency (hot side)

Measurement device +

> 0V Figure 3.6: Determination of majority carriers

measurements initially a Keithley 238 High Current Source Measurement Unit was used. Thereafter, it has been substituted in favor of a Keithley 4200-SCS Semiconductor Characterization System. Furthermore, to investigate hysteresis behavior dual sweep measurements were utilized. From the comparison of the obtained graphs, a quantitative conclusion concerning the amount of traps inside the semi conducting material was possible.

During measurements several difficulties have been faced, which were solved accordingly. For example, the front contact stripes of the commercially prepared cells were too thin. In addition, stability of the samples during measurements was needed. To overcome, these problems a "dirty" method of placing thicker top contacts made of silver paste was considered as possible solution. In addition, the samples were placed over bigger Al plate and glued to it by using silver paint droplets. Thus, it was insured stability as well as easier contacting of the back contacts during measurements. The front contacts were connected by a continuous thin silver paint stripe near to one of the edges of the sample.

The tests were driven in the ranges of -3 V to +3 V. The maximum current was capped to 100 mA corresponding to the limitations of the measurement device. The experiments were carried out in dark and under illumination conditions.For this purpose, the WACOM WXS-155S-10,AM1.5G solar simulator has been utilized. The irradi-

37

3.2 analytical methods W ance power was set to Pin = 0, 1 cm 2.

Four Point Measurements To characterize the electrical conductivity of thin-films of Si-nanoparticles over a Si wafer, after sintering, four point measurements were carried out. For this purpose, the geometry schematically shown in fig.3.7 was realized. The measurement consists of passing a known current

Figure 3.7: Four Point Measurement Schematic Picture

(I1 ) through the outer probes and measuring the potential difference (U23 ) through the inner ones. Thus, the relationship of the current and voltage values was dependent only on the resistivity of the material under test and not on the wire resistances (RL ) as represented on fig.3.7. Therefore, the four point measurement is a more robust method compared to the standard ones.

The electrical resistivity, ρ, can be derived as: ρtotal =

U23 A U23 dtotal ∗ s 1 = ∗ = ∗ I1 L I1 L σtotal

(3.3)

where, A is the area through which current flows. dtotal is the total thickness of the measured wafer s is the common contact length between the contact stripes L is the distance between the inner contact stripes; σtotal is the total conductivity of the material under test; According to Lechner, the conductivity of spin-coated layers strongly depends on the illumination level [8]. To assure, correctness of the results the measurements were carried out under no light conditions with the help of the Keithley 4200-SCS Semiconductor Characterization System.

38

3.3 scanning electron microscope and energy-dispersive x-ray

To extract the respective resistivity of the sintered Si-nanoparticles layer only, the following simplified model seen on fig.3.8 has been suggested. In this model, it is assumed that the current branches and

U

RL

RL

RL

RL

RL

RL Rtotal

U

Si-NP

RSi-NP Si Wafer RL

dSiNp

dwafer

RWafer

RL

Figure 3.8: Four Point Resistance Determination Schematic

flows through both the Si-wafer and the Si-nanoparticles which in total build the equivalent parallel resistance Rtotal . Thus, the resulting resistivity of the nanoparticles layer can be approximated as: ρSiNp =

ρtotal ∗ ρwafer ∗ dSiNp ∗ 100Ωcm (3.4) ρwafer ∗ dtotal − ρtotal ∗ dwafer

Furthermore, σSiNp =

1 ρSiNp

(3.5)

Nevertheless, the evaluated values were in the negative range. Thus, it can be concluded, that this model, does not fully resemble the actual layout.

3.3

scanning electron microscope and energy-dispersive x-ray

The schematic principle of an scanning electron microscope (SEM) device as presented by Reimer et al. [33], is shown in fig.3.9. At the top of an SEM, an electron gun is placed. A positively charged plate called the anode, attracts the emitted electrons. At the anode, there is a hole through which many of the electrons slip through [34]. Since the stream of electrons will bend at the magnetic field, circular electromagnets focus the flood into a tiny spot [35]. The focusing magnets act like lenses on the beam. At the bottom of the unit, is the stage for the specimen. The SEM, looks at the surface of

39

3.3 scanning electron microscope and energy-dispersive x-ray

Figure 3.9: Principle of the scanning electron microscope [33]

things. To insure a path for excess electrons the specimen usually has to be platted with a fine coating of metal [36]. Wherever the beam lands, it excites the specimen to give electrons of its own.

Depending on the angle of the surface of the specimen varying amounts of these secondary electrons are attracted towards the collector. Some electrons pass through the collector [33]. When this happens light is emitted. The light is piped to a photomultiplier tube.

The photomultiplier converts the light back into electrons. Thereafter, the secondary electron phenomenon is used to amplify the signal.

The amount output signal of photomultiplier is proportional to the number of electrons collected [36]. The number of electrons depend on the surface of the specimen when the electron beam hits it. Another set of electromagnets in the beams path deflects it left to right and up and down. As the beam scans the specimen the output signal changes its strength [33]. This signal is then displayed on a monitor. The interior of the microscope is at vacuum to avoid the electron beam crashing into air molecules. So the specimen has to be installed through an air lock. As the scanning size gets smaller the amount of magnification increases [34]. As seen on the schematic, the SEM device is capable of energy-dispersive x-ray spectroscopy (EDX) measurements as well.

40

3.3 scanning electron microscope and energy-dispersive x-ray

3.3.1 Energy-Dispersive X-ray Principle X-rays are waves of electromagnetic radiations similar to light waves.

X-rays are produced by shooting a high velocity stream of electrons at a target [37]. Thereafter, they collide with electrons in the investigated target (see fig. 3.10).

If an oncoming electron has the right velocity the target electrons

Figure 3.10: Simplified diagram of electron shells, following from the Bohr model of the atom. Some transitions leading to observed X-ray emission are indicated. [38]

are knock into a higher energy orbital. When the electrons fall back down to their lower orbitals, the energy differential is released as X-rays [38]. A detector is used to convert this energy into voltage signals. As the energy of the X-rays are characteristic of the difference in energy between the two shells, and of the atomic structure of the element from which they were emitted, this allows the elemental composition of the specimen to be measured [39].

41

4

R E S U LT S A N D E VA L U AT I O N

I was taught that the way of progress is neither swift nor easy.

— Marie Curie In this chapter it will be shown that well-defined silicon particle dispersions layers can be realized by spin coating. Furthermore, structural, and electrical quality of such films as BSF layers will be assessed. The results are based on measurements on the laser treated Si-nanoparticles on different commercially available substrates. Finally, an initial evaluation of the possibility, of using Kapton® foils is presented.

4.1

semi-ready cells, type i

As a first step, the characteristic behavior of reference solar cells from the company Solland Solar have been determined. Here, under a reference cell is to be understood a semi-ready cell with antireflex coating (SiN), front Ag silver grid contacts and back Al layer metalization. A more detailed description of the used substrate can be found in the methods section (see p.30). For naming purposes the previously described semi-ready cell configuration will be defined as Type I. 4.1.1 Reference Cell, Type I No nanoparticles have been deposited, as well as the cell has not been laser treated. A diode like behavior is clearly observed on fig.4.1. The reverse bias as well the forward bias regions are easily recognized.

Furthermore, the breakdown voltage can be extracted to be Vbr ≈ −8, 5V. As the cell has broken down, during the measurements under dark conditions, no illuminated IV-graph is presented.

4.1.2 Reference Cell, Type I, with Al as BSF As an additional reference, six fully processed solar cells from the company Solland Solar have been evaluated. These included, Type I substrates having anti-reflex coating (SiN), front Ag silver grid contacts, and fired Al paste, creating an Al:Si eutectic layer used

42

4.2 initial trends

Reference Cell by Solland Solar with Anti-Reflective Coating and Metal Contacts 0,10

Dark

Current [A]

0,05

0,00

-0,05

-0,10 -5

0

5

10

15

Voltage [V] Figure 4.1: IV-Characteristic of Reference Cell Type I (A Solar Cell With Anti-reflective Coating and Ag Front Contacts Grid, No Deposited Si-nanoparticles, No Laser Treatment)

as BSF material. Neither nano particles have been deposited nor laser treatment has taken place. All six cells IV-characteristics had a similar behavior to the one represented in fig. 4.2. As it can be read from the given graph, the open circuit voltage is Voc = 0, 59V. Furthermore, the short circuit current equals to Isc = −27, 78mA. The corresponding absolute value of the power at maximum power point is given as PMPP = 9, 7mW. From this information, a fill factor of FF = 59, 21% can be computed. Combining the previos data, and subtracting the front side metal contacts from the total area, an effective cell efficiency of η = 12, 93% was obtained.

4.2

initial trends

4.2.1 Si-nanoparticles Size The determination of the particle size was done by the dynamic light scattering method. After a curve fitting, the distribution inside the dispersions has been evaluated to be Gaussian like, with a mean value around µ ≈ 100d.nm. and a standard deviation of approximately σ ≈ 9d.nm. The long-term stability of the Si-nanoparticles dispersions and the tendency of building agglomerates has also been tested by evaluating the particle size after a dispersion has been milled as a function of time. On the given plot (see fig. 4.4), the ordi-

43

4.2 initial trends

0,12

Reference Cell with Anti-reflex Coating and Al BSF; No Si-nano Particles, No Sintering; Illuminated Dark

0,10

Current [A]

0,08 0,06

Rs = 5,9 立; Rsh = 2060,19 立;

0,04 0,02 0,00 -0,02 -0,04

-3

-2

-1

0

1

Voltage [V] Figure 4.2: IV-Characteristic of Reference Cell Type I with Al BSF (A Solar Cell With Anti-reflective Coating, Ag Front Contacts Grid and Al as BSF material, No Deposited Si-nanoparticles, No Laser Treatment)

(a) Circulation Milling Device, Netzsch (b) Dynamic Light Scattering Device, Malvern

Figure 4.3: Ball Milling and Dynamic Light Scattering Devices

44

4.2 initial trends

nate represents the mean number of particles inside the dispersion (in percent) that have a diameter equal to the corresponding x-axis value. As one can see from figure 4.4, the Si-nanoparticles do not tend to re-agglomerate even after three weeks have passed. It can be also observed that milling for about 75 min and reaching 3000 rpm (final mixing velocity) is sufficient for the optimal particle size that can be reached by utilizing this procedure.

Mean Number [%]

30

Filtered particles Measurement 3 weeks before rest of curves 45 min 2000 rpm 75 min 3000 rpm

20

10

0 10

100

1000

Size [d.nm] Figure 4.4: Determination of the Si-nanoparticle size via DLS measurement

4.2.2 Layer Thickness For the determination of the layer thickness, the Si-nanoparticles were spun on a different sized, bigger glass substrate (25 Ă&#x2014; 25mm2 ).

Across this sample seven more or less parallel scratch lines (A to G) were considered. On each of them points located through the center of the sample and ones closer to the outer edges of the substrate were measured (see fig.4.5). In this way local deviations in the Si hight could be detected and an average height of hSiNp = 650nm(Âą25nm) for the spun layer was found. Figure 4.5 shows the final outcome of this work. As a solution to the inhomogeneous layer distribution, mostly pronounced in the center of the sample, a deposition through the upper opening of the device was favored. Furthermore, as fast as possible actual spin-coating after the Si puddle has covered the substrate was preferred. With this, much more homogeneous layers were achieved.

45

4.2 initial trends

1000

Thickness [nm]

900 800 700

A - line near left substrate edge B C D - line near the middle E F G - line near right substrate edge

600 500 400 0,0

0,5

1,0

1,5

2,0

2,5

Position [cm] Figure 4.5: Si Layer Thickness vs. Position on substrate

Thickness [nm] 953 874 795 716 637 558 479 400

y-Position [cm]

2,0 1,5 1,0 0,5 0,0 0,0

0,5

1,0

1,5

2,0

x-Position [cm] Figure 4.6: Si Layer Thickness vs. Position on Substrate, Top View

46

4.2 initial trends

The resulting layer thickness versus the number of particle depositions via spin-coating has been shortly studied. The number of spin-coatings was varied from one to six layer depositions. The used Si-nanoparticles had a concentration of 10 wt%. The obtained results can be seen on fig.4.7. It can be noticed that after two spin-

3500 Thickness

Thickness [nm]

3000 2500 2000 1500 1000 1

2

3

4

5

6

Number of Spin-Coatings [-] Figure 4.7: Si layer thickness vs. number of depositions

coatings the resulting layers are tripling their thickness to around hSiNpDouble = 2120nm, whereas increasing further the number of depositions leads to a saturation of the layer height of around hSiNPMulti = 2440nm.

The discrepancy in the values concerning the layer thickness between fig.4.5 and fig.4.7 can be accounted to the different sample size used during the spin-coating procedure. In the case of fig.4.5 a square sample with a side size of a1 = 2, 5cm was used. On the other hand, in fig.4.7 the samples had a side length of a2 = 1cm. Therefore, it can be inferred that this could have affected the final thicknesses in both cases.

4.2.3 “Safe” Region Determination When using the laser some parts of the cell might ablate. Therefore, subjective operational “safe” regions have been defined as follows: • 0 - no visible laser illumination; • 1 - visible laser illumination/no change of the sample’s surface;

47

4.2 initial trends

• 2 - optimal = change to silver like color of the sample’s surface; • 3 - slightly scratched layer; • 4 - ablation of cell’s layer; • 5 - layer is totally removed; As a next step the “safe” regions have been determined. For this purpose the 10 × 10mm2 glass samples have been spin-coated and thereafter treated with the laser. To cross-check results some samples have been prepared and evaluated in different gas media. Typically these were argon and nitrogen. As seen on fig. 4.8 there is a good coincidence for the velocities between 1000 mm/min and 5000 mm/min. Due to the subjective nature of the evaluation of the safe

45

Lasser Inte ensity [[%]

40 35 30 25

"Eye" Eye Guideline Optimal Intensity Optimal p Intensity y Argon g Optimal Intensity Nitrogen

20 15

0

2000

4000

6000

8000

Scan Velocity [mm/min]

10000 7

Figure 4.8: Si Layer Thickness vs. Spin Speed, One Spin Phase

regions, some discrepancy for higher velocities is observed. Nevertheless, a good separation can be noticed. Glass ablation and layer cracks are lying above the data points represented as black squares, whereas lower intensities can be considered as safe.

4.2.4 Primary Observations After a suitable reference point, spin coating procedure and safe laser intensity regions have been defined, the actual evaluation of highly B doped Si-nanoparticles as possible material for BSF could be initiated.

Therefore, studies of the optimal laser sintering parameters of the

48

4.2 initial trends

spin-coated films over cells of Type I were thoroughly investigated.

To decide what is the best laser sintering parameter combination different samples have been prepared. Table 4.1 contains the parameters used for the evaluation of the Fill Factor versus the different laser intensities. The “continuous ↓↑”, designation corresponds to scanning of the sample from edge to edge and backwards in a continuous manner. As it can be seen from the resulting graphs (fig. 4.9 Table 4.1: Sample Preparation Parameters (Fill Factor) Sample Name Reference #0110 #11 #05 #08 #17 #0622062011 #13 #07 #06 20.06.11

In Figure a1 a2 a3 a4 a5 a6 a7 a8 a9 a10

Scan Parameters No Laser Treatment 1x10%100mm/min 1x10%100mm/min 1x15%100mm/min 1x17%100mm/min 1x17%100mm/min 1x18%100mm/min 1x18%100mm/min 1x19%100mm/min 6(continuous ↓↑)x50%10m/min 1x30%100mm/min

Nano Particles No Yes Yes Yes Yes Yes Yes Yes Yes No

and fig.4.10) the highest Fill Factor (FF ≈ 41%) and cell efficiency (η = 6, 38%) values were obtained at the parameters of a laser intensity of Iscan = 15% and a laser scan speed of Vscan = 100mm/min.

The corresponding IV-characteristic can be observed on fig. 4.11. It can be as well confirmed that this cell shows low series Rs = 9, 75Ω and high shunt Rsh = 689, 54Ω resistance values. Comparing this sample, with the ones processed at other laser intensities and in particular the resulting efficiency values it has been concluded that this would possibly represent the optimal parameters for the realization of an efficient BSF layer.

4.2.5 Samples Treatment - Procedures and Results Through this work, and especially with the samples from Type I, parasitic effects could be frequently observed. Therefore, taking into consideration the good IV-characteristic behavior (see fig.4.11), leaded to more detailed studies at single sintering steps (Iscan = 15@Vscan = 0, 1m/min).

Procedures While keeping laser parameters constant (1 scan, Iscan = 15@Vscan = 0, 1m/min), different procedures have been applied to decrease parasitic effects as well as to confirm reproducibility of the obtained results. The total procedure had a variable part (steps designated

49

4.2 initial trends

Fill Factor vs Laser Intensity a3

a4

40 a7

FF [%]

35

a10

a7 a6 a7

30

a8 a9 a9

25

a1 a2

20

a5 0

5

10

15

20

25

30

Laser Intensity [%] Figure 4.9: Fill Factor vs Different Laser Intensities

Cell Efficiency vs Laser Intensity 7 a4

6 a3 5

Ρ [%]

4 3 a8

2

a5

1

a7 a1

0 0

a2 5

10

a9

a5

15

a10 20

25

Laser Intensity [%] Figure 4.10: Cell Efficiency vs Different Laser Intensities

30

50

4.2 initial trends

Sample #05 from 22.06.2011 1xscan 15% @ 100mm/min Dark Illuminated

0,04

Current [A]

0,02

Rs = 9,75 Ω; Rsh = 689,54 Ω;

0,00

-0,02

-0,04

-0,9

-0,6

-0,3

0,0

0,3

0,6

0,9

Voltage [V] Figure 4.11: IV-Characteristic of Sample with Highest Measured Fill Factor (FF ≈ 41%) No 05, 22.06.2011 (A Solar Cell With Anti-reflective Coating and Ag Front Contacts Grid, Deposited Si-nanoparticles, Laser Treatment:Single Scan, Iscan = 15% Vscan = 0, 1m/min)

51

4.2 initial trends

with a number) and a constant part (steps that have been executed for any of the created samples). The overall algorithm can be summarized as follows: 1. grinding of the sample’s edges cleaning (see p.32); putting on an adhesive tape on the front side of the sample as protection measure; spin-coating (see p.33); 2. cleaning the edges with a Cotton Swab rinsed in Ethanol or Acetone; 3. grinding of the sample’s edges; laser sintering step (Iscan = 15% Vscan = 100mm/min); 4. cleaning the sample’s Si-nanoparticle thin film.

Grinding (Step 1): The grinding of the sample’s edges has been utilized so that it could be insured that defects and impurities introduced during the initial sawing (original size of 156 × 156mm2 ) of the samples into smaller substrates (10 × 10mm2 ) could be overcome. Each sample’s side has been grinded with a sanding paper. The average grit diameter particle size used was d = 15, 3µm (P1200).

Q-Tip/Cotton Swab (Step 2): Cleaning the edges with a cotton bud rinsed in Ethanol was used to remove only the undesired nanoparticles which have landed on the thin edges after spin-coating has taken place.

Grinding (Step 3): Nevertheless, there was still probability that not only the edges were cleaned but as well the outer areas of the back side of the sample.

This was not desired. Therefore, a further final grinding of the edges has been incorporated.

Cleaning with Acetone/Ethanol (Step 4): In addition, some of the samples have been as well cleaned with acetone or ethanol after an actual sintering has taken place. Thus, it has been assured that the number of nanoparticles which did not sinter i.e. contribute to the doping of the back surface and introduced additional resistivity of the layer, has been reduced.

Additional Measures: To prevent nanoparticle deposition each spin-coated cell front side was completely covered with an adhesive tape (mostly from the company “Tesa”). Nevertheless, the sample’s edges could not be

52

4.2 initial trends

always effectively protected.

Later on, for some samples, the Tesa film was glued on parts of the back side as continuation of the front side protection. Thus the edges of the sample were as well protected. In this way it has been assured that the probability that no nano particles are distributed at front side of the solar cells and or at the edges was higher.

General Observations Some general observations in the processing of the cells could be established. As previously discussed, the parameters concerning the actual sintering step have been fixed to treating the sample once mm with 15% laser intensity at 100 min velocity of the laser scan, using l approximately 55 min argon gas during the procedure. Due to the small chamber volume (Vchamber = (1 . . . 2)l), it can be assumed that a quite perfect atmosphere during each sintering step was achieved.

Due to the low laser intensity no additional â&#x20AC;&#x153;coolingâ&#x20AC;? phase after sintering with argon was needed. It could be observed that the front Ag contacts were melting on the surface of the quartz glass in use. This was cross-checked with further SEM investigations, presented in later sections (see p. 59). Even at low laser intensities, inhomogeneous morphologies introduced over the base quartz glass from previous sinterings were leading to the breaking of the cell in concideration.

Therefore, it can be assumed that temperatures during sintering are at least near the melting point of some of the materials inside the silver paste, for example Ag (Tmelt = 961.93â&#x2014;Ś C [40]), if not higher.

Therefore, each side of the quartz glass could be used only once.

After cleaning in isopropanol+potassium hydroxide solution, the quartz glasses could be re-used as stable surfaces inside the chamber.

To eliminate movements during sintering additional glasses were used to fix the sample in the chamber. Furthermore, it has been observed that the edge at which the laser-scan ends had a different color in all sintered samples.

The heat equation is a typical linear differential equation that arises in the field of physics. The superposition principle can be used to simplify the computations which describe these type of functions.

Therefore, the change in color could be easily explained with the superposition of heat distribution inside the substrate. Due to this phenomenon, at the end of the scanning range more energy was received than at any other part of the cell, leading to additional optical and as well structural changes (as verified with SEM investigations see p.59) in the appearance of the threated layer.

Concerning the evaluation of the measured data, the reduced effective area due to metal contacts and additionally introduced Ag stripes has been taken into account. Each of the resulting front contact areas was individually measured with the help of a caliper. The resulting

53

4.2 initial trends

area was then subtracted from the solar’s effective one. Thus, the actual efficiency and the current density of the samples were evaluated.

Furthermore, the number of front contact lines perpendicular to the thin Ag hand deposited stripe was almost always kept constant to three lines.

Initial IV-Characterization The evaluated combinations are summarized in table 4.2. The samTable 4.2: Combination Nomenclature, (Average Fill Factor) Combination

Included Optional Steps: 1 2 3 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14

X X X X X X X

15 16 17

Nano Particles Deposited, Not Sintered Only Grinded Wafer 1, No Particles Deposited, Not Sintered Only Grinded Wafer 2, No Particles Deposited, Not Sintered

X X X

X X X X

X X X X

X X X X

X X

X X X X

ples corresponding to combination 16 and 17, were produced to check if there was any difference between the samples from the first and second wafer (both Type I). For each of the combinations three samples have been prepared. The outcome of the evaluation of the sample’s measurements can be seen on fig.4.13. As it can be extracted from the figure, the highest efficiency has been obtained in the case of using only grinding the edges of the sample (Step 1).

Special attention, has been paid to the samples which have introduced larger deviations in the measured data concerning the corresponding fill factor value. It has been confirmed, that combinations 7, 13 and 14 are having high fill factors when comparing to combination 1 (FF ≈ 29%). Nevertheless, when taking into concideration other characteristic cell parameters (Isc and Voc ) represented

54

4.2 initial trends

Average Open Circuit Voltage and Short Circuit Current 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17

-0,020

Î&#x2122;sc[A]

-0,015 -0,010

Voc [V]

-0,005 0,55 0,50 0,45 0,40 0,35 0,30 0,25 0,20 0,15 0,10

Combination [-]

1

2

3

4

5

6

7

8

0,000

9 10 11 12 13 14 15 16 17

Combination [-]

Figure 4.12: Open Circuit Voltage and Short Circuit Current Applying Different Procedures (see table.4.2)

Average Fill Factor and Corresponding Efficiency 2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17

Combination [-]

3,0 2,5 2,0 1,5 1,0

Ρ [%]

1

FF [%]

0,5 0,55 0,50 0,45 0,40 0,35 0,30 0,25 0,20 0,15

0,0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17

Combination [-]

Figure 4.13: Fill Factor and Corresponding Efficiency Applying Different Procedures (see table.4.2)

55

4.2 initial trends

on fig.4.12, different final outcome is observed. After extracting the corresponding efficiency values based on the short circuit current and the open circuit voltage it could be stated that grinding stand alone gave probably the most effective procedure with η1 = 2, 44%.

As it can be seen on the given graphs, based on the characteristic parameters Isc and Voc of the threated cells, in all casses, a power conversion ratio, smaller to the one obtained in step 1 is observed. The corresponding efficiencies for combinations 7, 13 and 14 are much lower with η7 = 0, 56%, η13 = 0, 38% and η14 = 1, 19%. Therefore, it has been concluded, that grinding of the sample’s edges should be the preferred method for further more detailed investigations.

As a next step, to assure reproducibility of the obtained values, multiple samples treated with step 1 (grinding of the sample’s edges) as well as with other combinational steps have been created.

Therefore, the grinding step had been fixed as "constant" one and it was combined with additional treatments in newly prepared samples. The reason for this was, to easily compare steps which included it. After many samples have been created, measured and evaluated, getting a pronounced behavior in the evaluated data was in general not observed. In addition, comparing combination 16 and 17 it can be concluded that both (Type I) wafers behaved in a similar manner.

Furthermore, no trend in the efficiency versus the use of different treatments could be extracted. As this, behavior could be observed as well from the results from the following subsection, no further extra data is presented here.

Final IV-Characterizations Finally, it has been examined closely, just the behavior of the samples when only single of the optional steps have been utilized without making combinations out of them. From each of the single steps (Grinding (step 1); Cotton bud(step 2); Grinding after Spin-coating(step 3); Cleaning the layer after sintering with Acetone/Ethanol(step 4)) multiple samples have been prepared and measured. The naming nomenclature is given in table 4.3. Some typical, IV-characteristics from differently processed samples can be found in the appendix section (see p. 84-86). It can be seen that the superposition principle for the net current in a solar cell does not fully apply. In general, the total induced current under illumination is obtained by a simple addition between the current in the dark and the light generated current. Nevertheless, this behavior is not detected in the respective plots. Instead, a shift in the illuminated IVcharacteristic to the left can be observed. As suggested by Lindholm et al. [41], the series and shunt resistance must contribute negligibly to the cell current-voltage characteristics so that dark current could describe the one under illumination apart from a shift on the y-axis.

56

4.2 initial trends

Table 4.3: Combinations’ Nomenclature, (24.08.2011) Combination 1 2 3 4 5 6 7 8

Included Optional Steps Grinded (Step 01) and Sintered Samples, No Particles Deposited Cleaning the Edges With a Cotton Swab Rinsed in Acetone (Step 02) Cleaning the Edges With a Cotton Swab Rinsed in Ethanol (Step 02) Reference Cell, Grinded Only (Step 01), No Particles Deposited, Not Sintered Grinding of the Samples’ Edges, (Step 03) Grinding of the Samples’ Edges, (Step 01) Cleaning with Acetone the Samples’ Nanoparticle Thin Film, (Step 04) Cleaning with Ethanol the Samples’ Nanoparticle Thin Film, (Step 04)

For more detailed legend, please refer to the appendix section (see B.2)

In the given graphs this condition is not satisfied. This can be explained by the high parasitic resistances.

Again, it was expected that repeatability as well a trend in the efficiency values could be observed. The respective short circuit current density, open circuit voltage, fill factor, and efficiency are shown on figure 4.14 and figure 4.15, respectively. Due to space considerations, a detailed nomenclature concerning each point in the previous graphs can be found in the appendix section (see B.2). The naming of the combination steps is summarized in table 4.3.

As it can be observed extracting a pronounced trend in the given graphs is difficult. The obtained results tend to be distributed in a random manner. Therefore, further investigations relating grain size and cell behavior have been carried out.

2

3

4

5

6

7

8

1

2

3

4

5

6

7

8

0,6 0,5 0,4 0,3 0,2 0,1 0,0

Voc [V]

Combination [-] 1

2

Jsc [A/cm ]

-0,020 -0,015 -0,010 -0,005 0,000

Combination [-]

Figure 4.14: Short Circuit Current Density (Jsc ) and Open Circuit Voltage (Voc ) vs Different Treatment Combinations (see table 4.3), Detailed Legend Concerning Each Sample (see fig.B.2)

57

4.2 initial trends

Combination [-] 1

2

3

4

5

6

7

8

2,5

1,5

Ρ

1,0

[%]

2,0

0,5 0,0

26

FF [%]

24 22 20 18 16 1

2

3

4

5

6

7

8

Combination [-] Figure 4.15: Fill Factor (FF) and Efficiency (Ρ) vs Different Treatment Combinations (see table 4.3), Detailed Legend Concerning Each Sample (see fig.B.2)

Crystallinity As suggested by Karpov et al. [42], a micro sized grain boundary defect affects the response of current significantly. In addition, its negative effect can span in a great length. Furthermore, these non uniformities impact the performance and stability of the diode. Therefore, it has been studied if the crystallinity of the samples under investigation could be correlated with the goodness of the measured diode behavior of the respective cell. For this purpose, samples which were treated with the very same steps have been compared. Three different samples (front side) and their respective IV-characteristic graphs can be seen on fig.B.8, B.10 and B.12 in the appendix section. Clearly the boundaries between the crystals could be identified.

Nevertheless, when comparing the graphs with the respective front side structures no clear correlation between their number and the respective IV-characteristics could be observed. It seems as if in the first front side picture (fig.B.9) the number of boundaries is smaller than the one observed in the second one (fig.B.11). Furthermore, the IV-characteristics of both graphs follow this trend - better diode like behavior in case one (fig.B.8), compared to case two (fig.B.10).

Nevertheless, when comparing both graphs to a third one for which the front side (see fig.B.13) shows as few boundaries as in the first case, but much worse diode behavior, dominated by high parasitic

58

4.2 initial trends

resistances, no final statement can be made.

As a final outcome from these and other samples investigations it could be concluded that no pronounced dependence between crystallinity size and diode behavior could been extracted. Therefore, as a possible further reason for the non-ideal behavior diffusivity considerations are presented briefly as well (see p.65).

As suggested by Karpov et al. [42] a possible solution to this issue is the promotion of uniformity by thermal heating. Therefore, this way of annealing the samples could be a solution for improvement of the disordered structure of the polycrystalline Si layers. By introducing low intensity treatments of the cell possibly increased and equalized grain sizes are obtained. As described in following sections (see 4.3.2) good results were obtained for laser treated cells (at low intensities) from Type II, which in principle follow this idea.

Nevertheless, it is important that further studies of the correlation between crystallinity size and diode behavior are carried out. It is suggested that an image manipulation program with pattern recognition capabilities that can measure the number of boundaries more precisely can be involved for this purpose.

4.2.6 Scanning Electron Microscope Investigations The behavior of Si-nanoparticles after laser treatment were examined.

For this purpose, electron micrograph images were recorded. The accelerating voltage of the involved field emission electron source was typically 5 kV, enabling resolutions down to 100 nm. If not explicitly mentioned otherwise, the micrographs were recorded under normal angle in top view (over the surface of the sample). In addition, scanning electron microscope (SEM) pictures of the back (p-doped) side have been taken as well.

Untreated Cell and Si-nanoparticles Morphology The uncoated morphology of the back side of a solar cell samples can be seen on fig.4.16. The represented cell (Type I) has Ag front metal contacts, as well as an anti-reflective coating. The pictures are taken at the same substrate position in different magnification factors.

A semi-toroid like structure can be easily identified on the micrograph. Therefore, when Si-nanoparticles are spin-coated over the back side of the cell, they retain the hills and valleys structure of the bulk silicon.

59

4.2 initial trends

1 µm

10 µm

1 µm

10 µm

Figure 4.16: Semi-ready Solar Cell with Anti-reflex coating and Predeposited Front Side Ag contacts; Uncoated Backside Surface View of the Sample. All micrographs are taken at the same position (Note: Difference in Magnification Factor - Zooming Out from 1 to 10µm)

60

4.2 initial trends

Treated Cell and Si-nanoparticles Morphology As presented in fig.4.17, typical nano particle structures over the back side of a cell can be distinguished. The structure of grown in a hot wall reactor particles is highly characteristic. These particles exhibit an elongated and branched structure and often consist of several randomly oriented arms or side chains. Nevertheless, a continuous, well-defined thin-film layer is achieved after spin-coating [8]. Therefore, areas over which Si-nanoparticles have been deposited can be easily recognized. It can be observed that they follow the hills and valleys introduced by the substrate over which they are spin-coated.

In conclusion, it can be stated that if the introduced energy during sintering was not sufficient to molten the Si-nanoparticles with the back surface of the solar cell, similar structures as the ones observed in fig.4.17 shall be expected.

100 nm

1µm

1 µm

10 µm

Figure 4.17: Semi-ready Solar Cell (6× preheating: Ipreheat = 50%@Vpreheat = 10m/min , 1 sinter scan: Isintern = 30%@Vsintern = 1m/min); Top View Backside of the Sample, Brownish Color Area (see fig. 4.18). All micrographs Taken at the Same Possition

Furthermore, additional pictures of the same solar cell were examined (see fig.4.18 and fig.4.19). The represented sample has been 6 times preheated (Ipreheat = 50%@Vpreheat = 10m/min) and once an actual sinter scan has taken place (Isintern = 30%@Vsintern = 1m/min). Here (see fig.4.18) areas which can be clearly mapped

61

Scan unbehandelt – Scan unbehandelt 4.2 initial trends hochreflektierend – unbehandelt

100 µm

Figure 4.18: Picture of the Characteristic Brownish Color Area after Sintering

10 µm

10 µm

10 µm

Figure 4.19: Backside of Solar Cell (No 08, 01.09.2011: 6× preheating: Ipreheat = 50%@Vpreheat = 10m/min , 1 sinter scan: Isintern = 30%@Vsintern = 1m/min); Top Surface View, Backside of Sintered Coated Sample, Transition (UntreatedTreated-Untreated) Regions (Note: Same Magnification for all pictures)

62

4.2 initial trends

to regions which are ordered in untreated-treated-untreated manner can be seen. In addition, the corresponding SEM pictures (see fig.4.19) justify this arrangement. When scanning the sample, starting at one of its edges, first typical Si-nanoparticle structures can be observed which at some point (highly reflective area) have molten and thereafter again an untreated region can be recognized (near to the middle) which continuous to the end of the sample as seen in fig.4.18.

More convincing this behavior can be observed when looking closely at the surface of an additional sample with similar parameters. In this case they were a laser intensity of Ipreheat = 50% and a scan velocity of Vpreheat = 10m/min, followed by a single sintering scan of Isintern = 30% @ Vsintern = 0, 2m/min. Looking closely at fig.4.20 it can be indeed stated that no Si-nanoparticles can be differentiated anymore. The given picture suggests that in the dark areas of the micrograph melting of the Si-nanoparticles with the bulk Si has taken place. The resulting film is not continuous and thus cannot be used for applications where lateral transport through the silicon is required. The rest of the sampleâ&#x20AC;&#x2122;s surface retains the morphology of an untreated one with unchanged nanoparticles spin-coated over it.

An interesting property of the highly reflective area is its complete smoothness even when examined under maximum magnification of the SEM device. After pictures of the backside with sintered nanoparticles have been evaluated it can be concluded that only a small fraction of the sampleâ&#x20AC;&#x2122;s surface has actually received enough energy so that the nanoparticles and the bulk silicon layer could have melted in each other.

Furthermore, investigations of the two regions were undertaken by cross-sectional sample pictures. The highly and the region with lower reflectiveness have been compared. It is important to notice that, under the region which shows highly reflective characteristic, an approximately 5Âľm layer can be observed (see fig.4.20). From this it can be concluded, that this highly reflective layer area might consist of the parameters concerning doping with the help of laser illumination of highly doped with boron Si-nanoparticles. Therefore, a good starting point for further investigations in this direction would be 6 times preheating step with laser intensity of Ipreheat = 50% and scan velocity of Vpreheat = 10m/min, followed by a single sintering scan of: Isintern = 30% @ Vsintern = 0, 2m/min, corresponding to the parameters of the sample observed in fig.4.20.

Thus, finer scanning of the optimum parameters leading to the desired layer structure can be studied. Therefore, to facilitate feature work in this direction, additional samples for further SEM investigations which shall be carried out have been fabricated. Intentionally, they were constructed having the same parameters as in table 4.4.

63

4.2 initial trends

Figure 4.20: Highly vs. Low Reflective Area Comparison; Semi-ready Solar Cell with Anti-reflex Coating and Pre-deposited Front Side Ag Contacts (Sample No 10, 01.09.2011: 6Ă&#x2014; preheating, Ipreheat = 50% @ Vpreheat = 10m/min; 1 sinter scan, Isintern = 30% @ Vsintern = 0, 2m/min);

Furthermore, the reasons for high parasitic resistances observed in many of the previously evaluated data was investigated with the help of the SEM investigations. It was confirmed that no nanoparticles have melted for the rest of the sampleâ&#x20AC;&#x2122;s area. Therefore, it can be concluded that unsintered nano-particles were the reason for the high series resistances observed. This was cross-checked with the help of conductivity measurements and their corresponding values further through the course of this work.

4.2.7 Conductivity, Laser Parameters and Color Considerations As previous works (paper in progress) concerning the conductivity of the laser sintered layers have shown, a silver like color corresponds to better layer conductivity. Thus, a change in laser parameters towards this behavior was made. Therefore, obtaining silver in color surfaces with only single actual sintering step have been investigated. As suggested by Lechner [8] the detailed number of laser scans was not found to be a critical parameter, and no systematic differences could be observed. Therefore, their number was kept as low as a single sintering step. Before the actual sintering, an additional six times fast pre-heating procedure (10 000 mm/min, 50% laser power) has been

64

4.2 initial trends

incorporated. Many different cells, with the previously mentioned optical requirement were achieved under different laser paramaters.

The silver like color can be observed on pictures C.1, C.2 and C.3 in the appendix section. The corresponding process parameters can be summurized in tables C.1, C.2 and 4.4.

Table 4.4: Solar Cells Sintering Parameters - Created on 21.09.2011 Name:

Pre-Heating Step (6 scans):

Sintering Step(1 scan):

02

50[%] 10000[mm/min] 50[%] 10000[mm/min] 50[%] 10000[mm/min] 50[%] 10000[mm/min] 50[%] 10000[mm/min] 50[%] 10000[mm/min] 50[%] 10000[mm/min] 50[%] 10000[mm/min] 50[%] 10000[mm/min]

29[%] 1000[mm/min] 39[%] 1000[mm/min] 40[%] 1000[mm/min] 41[%] 1000[mm/min] 42[%] 1000[mm/min] 43[%] 1000[mm/min] 44[%] 1000[mm/min] 45[%] 1000[mm/min] 46[%] 1000[mm/min]

04 06 08 10 12 14 16 18

4.2.8 Diffusion of Silver in Silicon Investigations The diffusion coefficient in solids at different temperatures is often found to be well predicted by the help of an Arrhenius equation of the form:

Ea D(T ) = D0 × exp − , (4.1) κB T ,where D is the diffusion coefficient D0 is a pre-exponential coefficient Ea is the activation energy T is the absolute temperature κB = 8.6173324(78) × 10−5 eV K is the Boltzmann constant For the case of diffusion of Ag in Si the forms summarized in table 4.5 have been suggested.

65

4.2 initial trends

Table 4.5: Diffusivity of Ag in Al Temperature range (◦ C) 1100-1300 1100-1300 Not specified

D0 (cm2 /s) 2 × 10−3 2 × 10−3 6 × 10−5

Ea (eV) 1,59 1,6 1,15

Mechanism Interstitial Interstitial Not specified

Reference [43, 44] [45, 46] [47]

Energy-Dispersive X-ray Spectroscopy Energy-dispersive X-ray spectroscopy was used for the elemental analysis of several samples, and in particular the behavior of the top Ag contacts after sintering has taken place. The materials that have been found can be seen on fig.4.21. Normally, in the total firing

1 µm

O

C

N Ti

Ag

Si

Zn

Figure 4.21: EDX on the Front Surface Side of the Sample; Semi-ready Solar Cell with Anti-reflex Coating and Pre-deposited Front Side Ag Contacts (Sample No 10, 01.09.2011: 6× preheating, Ipreheat = 50% @ Vpreheat = 10m/min; 1 sinter scan, Isintern = 30% @ Vsintern = 0, 2m/min);

process of the front contact’s Ag grid, a glass frit is used [8]. The EDX analysis showed that this layer consists of the elements zinc (Zn) and oxygen (O) as well. Furthermore, it can be seen that the top contacts still have good contact to the slightly (ND = 1 × 1013 cm−3 [9]) n-doped (with P atoms) Si-layer. Nevertheless, due to the high temperature during sintering, it is highly probable that a diffusion of Ag contacts in Si n-type region takes place. As suggested by Green et al.[17], a wavelength of λ = 810nm (near the one of the infra-red

66

4.2 initial trends

laser in use) corresponds to an absorption depth of dabsorb = 12, 9µm.

Therefore, the power introduced, would heat efficiently not only the absorbing layer, as the thickness of the spin-coated Si-nanoparticles was estimated around hSiNP = 0, 65µm, but part of the substrate as well. In addition, the front Ag contacts were observed on top of the base quartz glasses after each laser treatment. Therefore, a temperature of at least Ag (Tmelt = 961, 93◦ C [40]) can be assumed.

Furthermore, as previously discussed, the temperature in the substrate is superimposed during sintering. As the n-type layer is only 0,3 to 0,4 µm thick, temperatures in the range T = (1074 . . . 1115)◦ C may lead to a decremental effect to the solar cells when considering the diffusivity model (see p. 65) suggested by Smith [47]. If we consider the best case scenario and utilize the specially investigated temperature region model suggested by Jones [45] we could go to a slightly increased range of about T = (1111 . . . 1141)◦ C. Exceeding these temperatures during sintering increases the probability of diffusion of the Ag front contacts through the complete n-type layer.

Furthermore, from the discussed (see section 4.2.8 and table 4.5) models, it can be found that at the melting point of Si (Tmelt = 1414◦ C) 2

corresponds a diffusivity of at least D = 2, 201 µm s in the case of the parameters suggested by Smith [47]. If we extrapolate the model suggested by Boltaks [44] to the same temperature (see fig.4.22) then 2

2 in the worst case D = 3, 557 µm s . In case of a sample (10 × 10mm )

2

Diffusion Coefficient [μm /s]

10

Diffusion Coefficient of Silver in Silicon vs Temperature

1

0,1

-3

[43, 44] [45, 46] [47]

0,01 800

-8

-3

-8

2

2*10 *exp{-1,6/(κb*T)}*10 μm /s -5

-8

2

6*10 *exp{-1,15/(κb*T)}*10 μm /s Extrapolation of

1000

2

2*10 *exp{-1,59/(κb*T)}*10 μm /s

1200

graph

1400

Temperature [°C] Figure 4.22: Diffusion Coefficient of Ag in Si

which is scanned with velocity of Vsintern = 1m/min a total time of

67

4.3 semi-ready cell, type ii

tscan = 0, 6s is needed. When introducing more energy inside the Si-nanoparticles layer by slower speeds (e.g. Vsintern = 0, 2m/min) the needed time is as well increased to tscan = 3s.

When considering the above mentioned points, the superposition of temperature inside the substrates, as well as the n-type thickness of only 0,3 to 0,4Âľm, it can be reasoned out that it is possible that a diffusion of the contacts into the n-layer takes place. More importantly, there exists a probability that the front contacts get even further to the p-layer. This would lead to a destroyed pn-junction and naturally no ideal diode like behavior should be expected. Therefore, the reasons for low shunt resistances can be accounted to a damage introduced to the p-n junction of the cells during sintering.

Considering the previously described behavior, extracted from the EDX investigations of the front contacts, it can be concluded that semi-ready cells from Type I, are not a good candidate for further experiments. Therefore, the top metalization had to be deposited after the sintering step has been concluded, so that the probability of diffusion of the front contacts is eliminated.

In this subsection, it was argued that a possible explanation of the non-ideal behavior of the semi-ready cells from Type I can be found with the help of different diffusivity models of Ag in Si. As a summary, it can be stated that, it is highly probable that the temperature during sintering is at least in a range at which diffusion of the Ag front contacts through the complete n-type layer is possible. Therefore, a different cell structure shall be preferred. For this purpose, semi-ready cells of Type II were studied and their behavior is presented in the following subsection.

4.3

semi-ready cell, type ii

As a possible solution, to previously observed limitations a new type of cell was introduced. For naming purposes they are labeled as semi-ready cells from Type II. Under this term, cells consisting of no anti-reflex coating and no metal contacts shall be understood. Cleaning and spin-coating of the samples was performed as described in previous sections (see p.32 and p.33). Major difference, during sintering of the deposited Si-nanoparticles, using this type of cell was the possibility of reaching much higher laser intensities (I â&#x2030;&#x2C6; 70%) before cracks could be observed. Therefore, it can be concluded that they should be the preferred choice when much higher laser intensities during sintering without sample breakage or ablation of the Si-nanoparticles layer shall be needed. Since, no contacts were available during laser treatment, no possibility of metal diffusion existed.

Therefore, no constant quartz glass change was needed anymore. In addition, by using this type of cells, it was cross-checked if damage

68

4.3 semi-ready cell, type ii

of the pn-junction was caused by diffusion of the top contacts grid.

Before IV measurements were carried out Al ≈ 200nm contacts on both sides were evaporated.

4.3.1 Electrical Properties of Type II Cells As a next step, samples from Type II cells with Si-nanoparticles laser treated surfaces (except for a reference cell) have been created. In addition, back and front side Al contacts have been evaporated. A fixed pre-heating (6scans, Ipreheat = 50%@VpreHeat = 10000mm/min) and an actual scan (1scan@Vscan = 1000mm/min) at variable intensities were compared. Some characteristic IV-graphs can be observed in fig.4.23 and fig.4.24.

15% 1scan with Si-nano Particles

0,12

Dark Illuminated

0,10

Current [A]

0,08 0,06 0,04 0,02

Rs = 18,88 Ω; Rsh = 1204,54 Ω;

0,00 -0,02 -0,04

-3

-2

-1

0

1

2

Voltage [V] Figure 4.23: IV-Characteristic of a Sollar Cell Without Anti-reflective Coating and No Initially Deposited Metal Contacts. Deposited and Sintered Si-nanoparticles(Isintern = 15% @ Vsintern = 1m/min)

Values for the series Rs and shunt Rsh parasitic resistances were extracted from the IV-characteristics of the 15% plot (fig.4.23). Using the slightly modified version of the method suggested by Goetzberger et al. [32], the approximate values were calculated as described in the methods section. Concerning the series (Rs ) and the shunt (Rsh ) resistances, slopes were extracted when looking at the saturated parts of the respective characteristic curves under illumination instead at the intersections with the abscisa and ordinate axis.

69

4.3 semi-ready cell, type ii

0,12

35% 1scan with Si-nano Particles Dark Illuminated

0,10 0,08

Current [A]

0,06 0,04

Rs = 23,38 Ω; Rsh = 76,21 Ω;

0,02 0,00 -0,02 -0,04 -0,06 -3

-2

-1

0

1

2

Voltage [V] Figure 4.24: IV-Characteristic of a Sollar Cell Without Anti-reflective Coating and No Initially Deposited Metal Contacts. Deposited and Sintered Si-nanoparticles(Isintern = 35%@Vsintern = 1m/min)

These conciderations, lead in the case of fig.4.24 to the values of Rs = 18, 88Ω and Rsh = 1204, 54Ω. According to Goetzberger et al.

[32], a shunt resistance of Rsh > 1000Ω is regarded to be tolerable, whereas even small values of the series resistance (Rs ) are considerably degrading the efficiency of the cell. Therefore, the obtained shunt resistance value can be in general concidered as tollerable, whereas the series one is decrementing the efficiency of the cell severely.

4.3.2 On-Off Current Ratio Comparisons On fig. 4.25, the results of on-off current ratios measurements for different laser intensities are represented. The voltages at which the values of the dark cell characteristic behaviors were compared were at -1V and +1V. With increasing the laser intensity, the nonideal cell behavior could be observed more pronounced. This means that the negative influence of parasitic resistances has increased. On the other hand, good values can be extracted for low laser intensities. Therefore, it can be concluded that when slightly heating (at low intensities) the cells, possibly some build-in defects (e.g. grain boundaries) are removed, thus leading to better on-off ratios (e.g.

R+1/−1 = 29, 68, @ laser intensity I=25%). The decay at higher in-

70

4.3 semi-ready cell, type ii

On-Off Current Ratio - Samples With and Without Nanoparticles With Particles - Initial Study from 13.09.2011 With Particles - Samples from 16.09.2011 Without Particles - Samples from 16.09.2011

100

Ratio [+1/-1]

10

1

0,1

0,01

15

20

25

30

35

40

45

Laser Intensity [%] Figure 4.25: On-Off Ratio, Comparison of Cells With and Without Sinanoparticles

tensities, can be explained with an increase of the probability of damaging the cellâ&#x20AC;&#x2122;s structure. This phenomenon can be related to the corresponding rise in temperature, which after surpassing a certain threshold value does not lead to the removal of build-in defects but rather harms the pn-junction (e.g. R+1/â&#x2C6;&#x2019;1 = 1, 77, @ laser intensity I=45%).

In addition a comparison between cells with and without nanoparticles at 15% and 25% has been carried out see fig.4.25. As expected from previously discussed SEM investigations (see p.61) at low intensities the Si-nanoparticles would not melt, thus leading to higher resistivity of the layer and introducing lower on-off ratios. At slightly higher intensities, the probability that there are already some regions with melted particles on the cell, leads to higher values in favor to the threated samples.

Since, all important cell characteristics can be combined in the power conversion ratio parameter, an efficiency comparison for higher laser intensities has been carried out as well (see fig.4.26). Combining the ideas that a highly reflective area represents a successfully doped BSF region with the given plot, leads to the conclusion, that the optimal laser parameters should lie somewhere in the region between Iscan = (29 . . . 40)%, @Vscan = 1000mm/min with a pre-heating step of six scans with Ipreheat = 50%, @Vpreheat = 10000mm/min.

71

4.3 semi-ready cell, type ii

Efficiency vs Laser Intensity 3,0

Efficiency [%]

2,5 2,0 1,5 1,0 0,5 0,0

0

10

20

30

40

50

60

70

Laser Intensity [%] Figure 4.26: Efficiency of Type II samples with Si-nanoparticles

4.3.3 Conductivity Measurements In addition, in order to justify to what extent the laser threated Si-nanoparticle layers are conductive, contacts of the type schematically given on fig.3.7 for four point measurements were prepared.

Furthermore, with these experiments the correctness of the SEM investigations (see p.59) could be cross-checked.

The four point measurements have been carried out on samples having the same parameters as the ones for the fine SEM investigations, but at different substrate. Namely these were, six pre-heating steps with Ipreheat = 50%, Vpreheat = 10000mm/min and an actual scan of Iscan = (29; 39 . . . 46)%, @Vscan = 1000mm/min (see table4.4). The Sinanoparticles have been spin-coated on intrinsic Si-wafers, and then sintered. The layer thickness of the Si-nanoparticles was measured with the help of the profilometer to be dSiNp = 350nm(±25nm). The Si-wafer had a thickness of dwafer = 525µm. The determination of the resistivity of the sintered nanoparticles was carried out with the help of the four-terminal sensing method. Therefore, for the computation of the total layer dark conductivity ρtotal can be evaluated as follows: ρtotal =

U23 A U23 dtotal ∗ s ∗ = ∗ I1 L I1 L

where A is the area through which current flows. dtotal = dwafer + dSiNp

(4.2)

72

4.3 semi-ready cell, type ii

10

-2

10

-3

10

-4

Total Conductivity vs Laser Intensity

−1

−1

Conductivity [Ω cm ]

s = 7, 4mm is the common contact length between the contact stripes L = 100µm is the distance between the inner contact stripes; The result of electrical conductivity measurements as a function of the applied laser energy is displayed in fig.4.27. The obtained val-

25

30

35

40

45

50

55

Laser Intensity [%] Figure 4.27: Conductivity (σtotal ) of Si-nanoparticles Spin-coated on Intrinsic Si-wafers Irradiated for Different Laser Intensities S ues (σtotal 6 2, 57 × 10−3 cm ) are comparable with the conductivity of nanoparticle-coated Si-wafer pieces not treated with an IR-laser S (σNoLaser 6 3, 52 × 10−3 cm ) reported in literature [31] (see fig.4.28).

In addition, the conductivity of the Si-wafer itself has been measured S . to be σwafer = 0, 0137 cm During measurements current might flow through the intrinsic wafer as well. Therefore, calculations for obtaining the conductivity of the Si-nanoparticles only, based on the suggested model described in the methods section (see p.39) have been carried out. Since the evaluated values were in the negative range, it can be concluded, that that model, does not fully resemble the actual layout.

As already found by SEM investigations, it can be stated that, single scans with low intensities are not sufficient for melting most of the deposited Si-nanoparticles. Furthermore, none of the spin-coated samples was treated with a hexafluorosilicic acid step. As reported in literature [8] even after the dispersion and milling process in ethanol, the silicon nanoparticles exhibit an oxide shell. Since silicon oxide is an isolator with a very large band gap of Eg ≈ 9eV [8], the oxide interfaces is equivalent to high energy barriers for the electronic transport. The main reason for the high resistivity can be found in

73

4.4 kapton速 substrates Conductivity of samples treated in Ar, N2, 6

10

without laser treatment with Si-NP spincoated only

Comparisson: Al (data from Handbook of

0

th

Chemistry and Physics 90 ed.)

-1

-1

Conductivity [立 cm ]

10 5 5x10

10

-1

10

-2

10

-3

Argon

N2

Si

Si+Np (no laser)

Al

Parameters Figure 4.28: Conductivity of samples in different medium [31]

the numerous oxide interfaces between the loosely interconnected silicon nanoparticles in the only coated layers.

Based on the previous considerations, it is suggested for further samples that, before laser treatment takes place, the spin-coated Si-nanoparticles are etched so that the native silicon surface oxide is removed with the help of piranha solution or hydrofluoric acid. This might be identified as a crucial technological step in achieving better conductive films after laser annealing.

As a summary, it can be stated that, the conductivity of the layers depends on the extent in which the deposited Si-nanoparticles have sintered. It was proved that single, low intensity scans are not sufficient for melting them over the substrate. Therefore, a combination of higher number of steps and illumination intensities shall be preferred. Furthermore, an additional chemical cleaning which will reduce the resistivity of the layers might be incorporated.

4.4

kapton速 substrates

Furthermore, thinking of new cost-efficient technologies that can be utilized such as processing Si-nanoparticles on thin polymer foils has been briefly investigated. Due to its high thermal and chemical stability (including many organic solvents such as acetone) Kapton速 polyimide foils were chosen. Before their initial use, a thorough cleaning procedure was performed which comprised washing in acetone, ethanol, isopropanol and subsequent drying with nitrogen. It has

74

4.4 kapton® substrates

been confirmed that it is possible to spin-coat the Si-nanoparticles over 10 × 10mm2 Kapton® films. The Kapton® films were placed over UV Quality quartz glass substrates. For stability during actual depositions, larger glass substrates were used. The substrates had a square shape, 15 × 15mm2 , and thickness of 1 mm. As a first step each of the glasses was carefully cleaned so that oils and organic residues are removed. By not completely blow-drying the glass substrates, it was assured an excellent adhesion of the Kapton® films during spin-coating. Thereafter, the thin (dKapton = 0, 1mm) foils of Kapton® have been sintered by using different laser parameters.

Nevertheless, even at low intensities the thin Kapton® films were starting to shrink and bend during sintering. Different, samples can be seen on fig.4.29.

Figure 4.29: Kapton® films after sintering

Table 4.6: Si-nanoparticles sintered on Kapton® substrates (parameters)

Number:

Laser Intensity [%]:

Velocity[mm/min]:

18 05 09 03 02

10% 8% 9% 13% 18%

2000 2000 2000 2000 2000

It is highly unprobable that nanoparticles would have melt under these parameters. Therefore, the possibility of pre-shrinking the Kapton® films by thermal heating, and thus keeping them stable during actual sintering was examined. For this purpose, different temperatures and durations of a hot-plate appliance were compared.

As an outcome of this, no shrinkage of the Kapton® substrates could

75

4.4 kapton® substrates

be observed. Most probably the maximum temperature used (capped by the heating element) (TMaxused ≈ 300◦ C) is still under the material dependent one (TKapton = 450◦ C [48]).

A possible idea for future experiments is the heating with a furnace to higher temperatures as a method for the pre-shrinking step. Furthermore, it is important that this material would be investigated for example with a laser with shorter wavelength used in pulsed mode. This opportunity can be further studied with an ultraviolet (UV) laser. For example, the ATLEX Si 300 (λ(KrF) = 248nm) having a pulse duration of 4-6 ns and a maximum repetition rate of 300 Hz would be a suitable candidate. According to Green et al. [17], this would correspond to an absorption depth of dabsorb = 5, 43nm. Due to the short pulse duration, the power introduced, would heat efficiently only the absorbing layer, as the thickness of the spin-coated Si-nanoparticles was estimated around hSiNP = 650nm(±25nm). In such a way during sintering much lower temperatures inside the substrate can be expected. Furthermore, this would allow a much wider variety, including plastic foils, to be used.

76

5

CONCLUSION AND FUTURE WORK

Every end is a new beginning.

— Proverb In this thesis, the properties of boron (B)-doped silicon (Si)-nano particles as possible material for back surface field (BSF) were studied. The dispersions of nanoparticles, in combination with a laser treatment, have been evaluated for possible use in photovoltaic thinfilm applications. First, the size and stability of the particles inside the dispersion was determined. The particle size distribution inside the dispersions has been evaluated to be Gaussian like distributed, with a mean value around µ ≈ 100d.nm. and a standard deviation of approximately σ ≈ 9d.nm. The Si-nanoparticles shown a stable behavior - they did not tend to re-agglomerate even after three weeks have passed. In addition, the material behavior concerning spin coating has been examined. When spin-coating on square substrates (a = 25mm) an average height of hSiNp = 650nm was found. Furthermore, it was noticed that after two spin-coatings the resulting layers are tripling their thickness to around hSiNpDouble = 2120nm, whereas increasing further the number of depositions leaded to an average saturation of the layer height of around hSiNpMulti = 2440nm.

As a result, smooth and compact thin films of Si-nanoparticles were obtained.

Moreover, different structures were implemented. At first, a semiready cell with an anti-reflex coating (SiN), front Ag silver grid contacts and back Al layer metalization was used. In addition, a second type of semi-ready cells was employed. The major difference with respect to the previously described cells was that they consisted of no anti-reflex coating and no metal contacts. Both types of cells were provided by the company Solar Solland. The total thickness of the samples was measured to be 250µm. Furthermore, cost-efficient technologies that can be utilized such as processing on thin polymer foils has been briefly investigated. For this purpose, due to their high thermal stability Kapton® films (10 × 10mm2 ) were employed.

Throughout this work, different technological problems were faced and were accordingly solved. Combinations of different contact materials were examined and their feasibility was studied.

The studies of current-voltage (I-V) relationships of the semi-ready structures (with and without anti-reflex coating) has given useful information about the behavior of the cells. For some of the

77

conclusion and future work

laser treated semi-ready structures from Solland Solar with antireflective coating, a fill factor of FF ≈ 41%, short-circuit current Isc = −28, 76mA, an open-circuit voltage Voc = 0, 53V, power at maximum power point of Pmpp = 6, 4mW and an cell efficiency of around η ≈ 6, 38% was obtained. In the case of a semi-ready structure without anti-reflective coating, the best result was comprising of a fill factor of FF ≈ 27%, a short-circuit current Isc = −16, 81mA, an open-circuit voltage Voc = 0, 49V, power at maximum power point of Pmpp = 2, 21mW and an cell efficiency of around η ≈ 2, 95%.

Furthermore, the morphology of cell and the particles were studied using SEM measurements. It was concluded that during laser treatment Ag is dissolving into the n-region of the cell, thus breaking the pn-junction. In addition, it was confirmed that only small areas of the back surface have sintered at the intensities used (I 6 30%).

An important result of this work, measured by the four-terminal sensing method, was the verification of the conductivity (σ) of the Si-nanoparticles in use. The Si-nanoparticles have been spincoated on intrinsic Si-wafers, and then sintered with the help of the infra-red laser (λ = 808nm, Pmax ≈ 452W). The layer thickness of the Si-nanoparticles was measured with the help of the profilometer to be dSiNp = 350nm(±25nm). The Si-wafer had a thickness of dwafer = 525µm. An average value of σSiNPaverage 6 S 2, 57 × 10−3 cm has been evaluated for samples treated with different laser intensities (Iscan = (29; 39 . . . 46)%, @Vscan = 1000mm/min), single actual sintering step, with a pre-heating of six scans (Ipreheat = 50%, @Vpreheat = 10000mm/min). The obtained results correspond well to the data given in literature [31] in the case of particles treated with no laser. Therefore, it can be clearly concluded, that a single scan is not sufficient to bring enough energy which would completely sinter the deposited Si-nanoparticles.

With the help of SEM measurements, an approximately 5µm thick layer was observed under regions characterized by a highly reflective surface. In conclusion, it was confirmed that the realization of small area regions with back doping using boron-doped Si-nanoparticles and a laser operated in the infra-red wavelength range is possible. A further study in this direction, could be the verification of the laser parameters which correspond to the observed highly reflective area.

When comparing this thickness with typical commercially available cell BSF heights (hBSF = 0, 8µm [2]) it can be argued that the obtained layer might be even too thick when optimal efficiency parameters are concerned. In general, the life time in such type of regions tends to be very short. Considering that the layer is heavily p+ doped, it can be inferred the volume of low life-time material where minority carriers may recombine is increased. Therefore, the optimal BSF thickness which takes into account this considerations should be calculated in

78

conclusion and future work

future works.

In addition, it is suggested that rear contacts are reduced in size as in the high-efficiency cell structure seen on fig.5.1 (PERL, η = 24, 5%) introduced by Zhao, et al. [49]. Thus, feature Si nanoparticles deposi-

Figure 5.1: PERL (passivated emitter, rear locally-diffused) cell structure [49]

tions should not cover the hole back surface of the solar cell. Rather, by using an adhesive tape during spin-coating, only small windows of the cell should be coated with nanoparticles. Thus, only very small contact areas would be needed. Due to this, the total area of the contact’s would be a small fraction of the total back side surface.

Therefore, the performance of the cell would be improved by shutting off some recombination processes. Furthermore, by additional passivation low surface recombination velocity can be achieved. In other words, the rate of recombination between electrons and holes at the surface of the semiconductor would be decreased. In addition, by designing the thickness of the oxide in an optimized way, efficiency of the cell can be increased.

Due to the limitations imposed by the Ag front contacts grid (only low laser intensity possible, high parasitic resistances observed) different type of semi-ready cells was preferred. They were involving no preready anti-reflex coating or metal contacts. It was found that this type of cells, can withstand much higher laser intensities (I 6 70%) during sintering without sample breakage or ablation of the Si-nanoparticles layer. By utilizing samples without front contact grids during laser treatment, the influence of parisitic resistances was efficiently prevented (Rs < 19Ω, Rsh > 1200Ω). As an outcome of this work, it can be suggested that a structure having initially no anti-reflexcoating or contacts should be used as for further experiments utilizing the

79

conclusion and future work

IR laser system. Such an arrangement has proved itself as an advantageous design. As a good starting point a six times pre-heating step (Ipreheat = 50%, Vpreheat = 10000mm/min), and an actual scan in the range of Iscan = (29 . . . 40)%, @Vscan = 1000mm/min is suggested.

Possibility for future development is the implementation of the suggested methods for thin-film substrates such as Kapton速. Initial studies in this direction were carried out. Nevertheless, even at relatively low intensities (I 6 8%) bending and melting of foils was observed.Therefore, it can be concluded that for the semi-finished (Type I) products of Solland Solar as well as for thin-film foil substrates such as Kapton a different laser type should be preferred. A better candidate for this purpose would be a pulsed UV-Laser treatment, which would reduce the thermal load during the sintering step.

In addition, realization of solar cells made of pure Si-nanoparticles is suggested. A combination of these approaches would provide an additional set of observations which could be used for the further evaluation of the Si-nanoparticles.

80

Part II APPENDIX

A

PROGRAM CODE

%001(LEVON ALTUNYAN) G90 (Set ABSOLUTE Position Coordinates) MF1=R1 (Gas Flow=R1%) G01 XR7 YR8 F5000 (Go to x=R7 y=R8 Velocity=5000 mm/min) M12 (Gas Flow On) G04 10 (Wait for 10 Sec) $FOR R100=0,R3,1 (Pre-Heating Steps, e.g. R3=2->6PreScans) G01 XR7 YR8 F1000 (Go to x=R7 y=R8 Velocity=1000 mm/min) G01 ZR9 F1000 (Go to Z=R9 Velocity=1000 mm/min) M14 (Laser On) G01 XR7 YR8+16 FR5 (‘‘Forward’’ Scan Velocity=R5) G01 XR7 YR8 FR5 (‘‘Backward’’ Scan Velocity=R5) M15 (Laser off) $ENDFOR $FOR R100=0,R4,1 (Actual Sintering Steps, e.g. R4=0->1scan) G01 XR7 YR8 F1000 (Go to x=R7 y=R8 Velocity=1000 mm/min) G01 ZR9 F1000 (Go to z=R9 set‘‘focus’’) M14 (Laser On) G01 XR7 YR8+15 FR11 (Sintern the Sample) (G01 XR7 YR8 FR11) (If needed for continuous/multiple scans) M15 (Laser Off) $ENDFOR (G04 30) (Wait for sample to cool down 30 Sec) M13 (Gas Flow Off) G01 X0 Y0 Z0 F7500 (Go To Initial Position) M30 (Main Program END)

82

B

ADDITIONAL GRAPHS

Efficiency vs Combination

2,0

η [%]

1,5 Q-tip Acetton (Step 02) Sample#04 Q-tip Acetton (Step 02) Sample#05 Q-tip Acetton (Step 02) Sample#06 Q-tip Ethanol (Step 02) Reference Grinded Cell Grinding (Step 03) Sample#05 Grinding (Step 01) Sample#04 Cleaning Ethanol (Step 04) Sample#03

1,0

0,5

0,0 2

3

4

5

6

7

8

Combination [-] Figure B.1: “Slim” Version - Efficiency (η) vs Different Treatment Combinations (see table 4.3)

83

FF [-]

additional graphs

Grinded (Step 01) and Sintered Sample, No Partciles Deposited, #01 Grinded (Step 01) and Sintered Sample, No Partciles Deposited, #02 Grinded (Step 01) and Sintered, No Partciles #03 Fill Factor vsDeposited, Combination 0,26 Cleaning the Edges With a Q-Tip Rinsed in Acetone (Step 02), #04 Cleaning the Edges With a Q-Tip Rinsed in Acetone (Step 02), #05 Cleaning the Edges With a Q-Tip Rinsed in Acetone (Step 02), #06 Cleaning the Edges With a Q-Tip Rinsed in Ethanol (Step 02), #02 0,24 Cleaning the Edges With a Q-Tip Rinsed in Ethanol (Step 02), #03 Reference Cell, Grinded Only (Step 01), No Partciles Deposited, Not Sintered #01 Reference Cell, Grinded Only (Step 01), No Partciles Deposited, Not Sintered #02 Reference Cell, Grinded Only (Step 01), No Partciles Deposited, Not Sintered #03 0,22 Grinding of the Sample’s Edges, (Step 03), #01 Grinding of the Sample’s Edges, (Step 03), #02 Grinding of the Sample’s Edges, (Step 03), #03 Grinding of the Sample’s Edges, (Step 03), #04 0,20 Grinding of the Sample’s Edges, (Step 03), #05 Grinding of the Sample’s Edges, (Step 03), #06 Grinding of the Sample’s Edges, (Step 01), #02 Grinding of the Sample’s Edges, (Step 01), #03 0,18 Grinding of the Sample’s Edges, (Step 01), #04 Grinding of the Sample’s Edges, (Step 01), #05 Grinding of the Sample’s Edges, (Step 01), #06 Cleaning with Acetone the Sample’s Si Nanoparticle Thin Film, (Step 04), #04 0,16 Cleaning with Acetone the Sample’s Si Nanoparticle Thin Film, (Step 04), #05 Cleaning with Acetone the Sample’s Si Nanoparticle Thin Film, (Step 04), #06 2 the Sample’s 3 5 Thin Film, 6 (Step704), #01 8 Cleaning 1 with Ethanol Si 4 Nanoparticle Cleaning with Ethanol the Sample’s Si Nanoparticle Thin Film, (Step 04), #02 Combination [-] Film, (Step 04), #03 Cleaning with Ethanol the Sample’s Si Nanoparticle Thin

Figure B.2: Legend for Samples Evaluated on 24.08.2011

Cotton Swab (Ethanol) Sample #03 0,08 Illuminated(1) Dark(1) Illuminated(2) Dark(2)

0,06

Current [A]

0,04 0,02 0,00 -0,02 -0,04 -3

-2

-1

0

1

2

3

Voltage [V] Figure B.3: IV-Characteristic (Step 2-Cleaning the Edges With a Cotton Swab Rinsed in Ethanol, Sample No 03)

84

additional graphs

Reference Cell Grinded Only (Step 01) Sample #02 0,04

Illuminated(1) Dark(1) Illuminated(2) Dark(2)

0,03

Current [A]

0,02 0,01 0,00 -0,01 -0,02 -0,03 -0,04

-3

-2

-1

0

1

2

3

Voltage [V] Figure B.4: IV-Characteristic, Reference Cell (Grinded Only, Step 1, No Particles Deposited, Not Sintered, Sample No 02)

Grinding of the sampleâ&#x20AC;&#x2122;s edges Sample #05 0,10

Illuminated(1) Dark(1) Illuminated(2) Dark(2)

0,08

Current [A]

0,06 0,04 0,02 0,00 -0,02 -0,04 -3

-2

-1

0

1

2

3

Voltage [V] Figure B.5: IV-Characteristic (Step 3-Grinding of the Sampleâ&#x20AC;&#x2122;s Edges, Sample No 05)

85

additional graphs

Grinding (Step 1) Sample #04 Illuminated(1) Dark(1) Illuminated(2) Dark(2) Illuminated(3)

0,10 0,08

Current [A]

0,06 0,04 0,02 0,00 -0,02 -0,04 -3

-2

-1

0

1

2

3

Voltage [V] Figure B.6: IV-Characteristic (Step 1-Grinding of the Sample’s Edges, Sample No 04)

Cleaning (Ethanol) the sample’s Si-np thinn-film Sample #03 Illuminated(1) Dark(1) Illuminated(2) Dark(2)

0,06

Current [A]

0,04 0,02 0,00 -0,02 -0,04 -3

-2

-1

0

1

2

3

Voltage [V] Figure B.7: IV-Characteristic (Step 4-Cleaning with Ethanol the Sample’s Si Nanoparticle Thin Film, Sample No 03)

86

additional graphs

Cotton Swab (Acetton) Sample #04 Illuminated(1) Dark(1) Illuminated(2) Dark(2) Illuminated(3) Dark(3)

0,10

Current [A]

0,05

0,00

-0,05

-0,10 -3

-2

-1

0

1

2

3

Voltage [V] Figure B.8: IV-Characteristic (Step 2-Cleaning the Edges With a Cotton Swab Rinsed in Acetone, Sample 04)

Figure B.9: Front Side (Step 2-Cleaning the Edges With a Cotton Swab Rinsed in Acetone, Sample 04)

87

additional graphs

Q-tip (Acetton) Sample #05 0,06 Illuminated(1) Dark(1) Illuminated(2) Dark(2) Illuminated(3) Dark(3)

0,04

Current [A]

0,02 0,00 -0,02 -0,04 -0,06

-3

-2

-1

0

1

2

3

Voltage [V] Figure B.10: IV-Characteristic (Step 2-Cleaning the Edges With a Cotton Swab Rinsed in Acetone, Sample 05)

Figure B.11: Front Side (Step 2-Cleaning the Edges With a Cotton Swab Rinsed in Acetone, Sample 05)

88

additional graphs

Q-tip (Acetton) Sample #06 0,005 0,000 -0,005

Current [A]

-0,010 -0,015 -0,020 Illuminated (1) Dark(1) Illuminated(2) Dark(2) Illuminated(3) Dark(3)

-0,025 -0,030 -0,035 -0,040 -3

-2

-1

0

1

2

3

Voltage [V] Figure B.12: IV-Characteristic (Step 2-Cleaning the Edges With a Cotton Swab Rinsed in Acetone, Sample 06)

Figure B.13: Front Side (Step 2-Cleaning the Edges With a Cotton Swab Rinsed in Acetone, Sample 06)

89

C

S A M P L E P I C T U R E S A N D TA B L E S

Figure C.1: Back Surface of the Solar Cells (Type I) After Sintering 01.06.2011

Table C.1: Back Surface of the Solar Cells After Sintering - 01.06.2011 (parameters)

Number:

Pre-Heating Step 6 scans:

Sintering Step 1 scan:

13

50[%] 10000mm/min 50[%] 10000[mm/min] 50[%] 10000[mm/min] 50[%] 10000[mm/min] 50[%] 10000[mm/min]

40[%] 2000mm/min 40[%] 1000[mm/min] 40[%] 1000[mm/min] 45[%] 1000[mm/min] 50[%] 1000[mm/min]

14 15 16 17

90

sample pictures and tables

Figure C.2: Back Surface of the Solar Cells (Type I) After Sintering, 14.06.2011

Table C.2: Back Surface of the Solar Cells After Sintering - 14.06.2011 (parameters)

Number:

Pre-Heating Step (6 scans):

Sintering Step(1 scan):

11

50[%] 10000[mm/min] 50[%] 10000[mm/min]

30[%] 175[mm/min] 30[%] 200[mm/min]

13

Figure C.3: Back Surface of the Solar Cells (Type II) After Sintering, 21.09.2011

91

BIBLIOGRAPHY

[1] F. J. Tegude. Festkörperelektronik Skript zur Vorlesung, Lecture.

2001.

[2] M. Lundstrom. Lecture 1: Introduction to Solar Cells; Introduction to Photovolataics, Lecture. 2011.

[3] K. Albertsen, P. van Eijk, H. Kerp, N. Merchant, and A. Shaikh.

Development of Al-BSF Paste to Fire-Through Dielectric Passivation Layers, Conference. 2007.

[4] N. Benson. NETZ Vollversammlung, Conference. 2011.

[5] O. von Roos. A simple theory of back surface field (BSF) solar cells. J. Appl. Phys., 49(6), 1978. doi: 10.1063/1.325262.

[6] O. N. Hartley, R. Russell, K. C. Heasman, N. B. Mason, and T. M. Bruton. Investigation of thin aluminium films on the rear of monocrystalline silicon solar cells for back surface field formation, Conference. 2002. ISBN 0780374711. doi: 10.1109.

[7] J.L. Murray and A.J. McAlister. Technical Report 5, 1984.

[8] R. W. Lechner. Silicon Nanocrystal Films for Electronic Applications. PhD thesis, Walter Schottky Institut, 2008.

[9] S. M. Sze and K. K. Ng. Physics of Semiconductor Devices, 3rd Edition. Wiley-Interscience, 2006. ISBN 978-0-471-14323-9.

[10] R. S. Macomber, A. Pinhas, and R. M. Wilson. The Vocabulary and Concepts of Organic Chemistry. John Wiley & Sons, Inc., 2005.

[11] J. J. Quinn and K.-S. Yi. Solid State Physics: Principles and Modern Applications. Springer Berlin Heidelberg, 2009.

[12] J.-W. Chen and A. G. Milnes. Energy levels in silicon. Ann. Rev. Mater. Sci., 10:157 – 228, 1980.

[13] M. Maksimov and G. Hristakudis. Physics. Bulvest 2000, 2001.

ISBN 978-9-541-80200-7.

[14] D. A. Neaman. Semiconductor Physiscs and Devices: Basic principles. McGraw-Hill, 2003.

[15] A. Schulz. Plasmapolymerisierte Barriereschichten aus einer skalierbaren Mikrowellen-Plasmaquelle für flexible Solarzellenmodule. PhD thesis, Universität Stuttgart, 2005.

92

bibliography

[16] M. Lundstrom. Lecture 2: Physics Crystalline Solar Cells; Solar Cell Physics: recombination and generation, Lecture. 2011.

[17] M. A. Green and M. Keevers. Optical properties of intrinsic silicon at 300 K. Progress in Photovoltaics, 3(3):189 – 192, 1995.

[18] W. Shockley and H. J. Queisser. Detailed Balance Limit of Efficiency of p-n Junction Solar Cells . J. Appl. Phys., 32(3):510 – 519, 1961. doi: 10.1063/1.1736034.

[19] E. Seale. Solar Cells - Shedding a little light on photovoltaics.

2003. URL http://www.solarbotics.net/starting/200202_ solar_cells/200202_solar_cell_types.html.

[20] P. Würfel. Physik der Solarzellen. 2. Spektrum, 2000.

[21] H.-J. Lewerenz and H. Jungblut. Photovoltaik. Springer, 1995.

[22] C. Kittel. Einführung in die Festkörperphysik. Oldenbourg Wissenschaftsverlag, 1993.

[23] D. Yu, S. Lee, and G. S. Hwang. On the origin of Si nanocrystal formation in a Si suboxide matrix. J. Appl. Phys., 102, 2007.

[24] D. Yu, S. Lee, G. S. Hwang, M. Fujii, Y. Yamaguchi, Y. Takase, K. Ninomiya, and S. Hayashi. Control of photoluminescence properties of Si nanocrystals by simultaneously doping n- and p-type impurities. Appl. Phys. Lett., 85, 2004.

[25] L. T. Canham. Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers. Appl. Phys. Lett., 57, 1990.

[26] J. R. Heath. A liquid-solution-phase synthesis of crystalline silicon. Science, 258, 1992.

[27] C.-S. Yang, R. A. Bley, S. M. Kauzlarich, H. W. H. Lee, and G. R. Delgado. Synthesis of alkyl-terminated silicon nanoclusters by a solution route. J. Am. Chem. Soc., (121), 1999.

[28] E. Werwa, A. A. Seraphin, L. A. Chiu, C. Zhou, and K. D. Kolenbrander. Synthesis and processing of silicon nanocrystallites using a pulsed laser ablation supersonic expansion method.

Appl. Phys. Lett., (64), 1994.

[29] Z. Shen, T. Kim, U. Kortshagen, P. H. McMurry, and S. A. Campbell. Formation of highly uniform silicon nanoparticles in high density silane plasmas. J. Appl. Phys., 94:2277, 2004.

93

bibliography

[30] H. Wiggers, R. Starke, and P. Roth. Silicon Particle Formation

by Pyrolysis of Silane in a Hot Wall Gasphase Reactor. Chem.

Eng. Technol., 24:261 – 264, 2001.

[31] K. Lamine. Realisierung funktionaler Si-Dünnfilme durch Laserkristalisation von nanopartikulärem Silizium, Bachelor Thesis. 2012.

[32] A. Goetzberger, B. Voß, and J. Knobloch. Sonnenenergie: Photovoltaik. Teubner Studienbücher Physik, 1994.

[33] L. Reimer and P. W. Hawkes. Scanning Electron Microscopy: Physics of Image Formation and Microanalysis. Springer Berlin Heidelberg, 1998.

[34] J. Goldstein, D. E. Newbury, D. C. Joy, and C. E. Lyman. Scanning Electron Microscopy and X-ray Microanalysis. Springer US, 2007.

[35] C. E. Lyman and D. E. Newbury. Scanning Electron Microscopy, X-Ray Microanalysis, and Analytical Electron Microscopy: A Laboratory Workbook. Springer Verlag, 1990.

[36] P. Echlin. Handbook of Sample Preparation for Scanning Electron Microscopy and X-Ray Microanalysis. Springer US, 2009.

[37] J. C. Russ. Fundamentals of Energy Dispersive X-Ray Analysis (Monographs in Materials). Butterworth-Heinemann Ltd, 1984.

[38] A. J. Garratt-Reed and D. C. Bell. Energy Dispersive X-Ray Analysis in the Electron Microscope (Microscopy Handbooks). Bios Scientific Publ, 2003.

[39] K. Tsuji, J. Injuk, and R. Van Grieken. X-Ray Spectrometry: Recent Technological Advances. John Wiley & Sons, 2004.

[40] B. Belval. Silver (Understanding the Elements of the Periodic Table).

Rosen Pub Group, 2006.

[41] F. A. Lindholm, J. G. Fossum, and E. L. Burgess. Application of the superposition principle to solar-cell analysis. IEEE Transactions on Electron Devices, 26:165–171, 1979.

[42] V. G. Karpov, A. D. Compaan, and D. Shvydka. Random diode arrays and mesoscale physics of large-area semiconductor devices. Physical Review B, 69(045325), 2004.

[43] L. Chen, Y. Zeng, P. Nyugen, and T. L. Alford. Silver diffusion and defect formation in Si (1 1 1) substrate at elevated temperatures. Materials Chemistry and Physics, 76, 2001.

94

bibliography

[44] B. I. Boltaks and S.-Y. Hsueh. Solid State 2. Sov. Phys., 2:2383, 1961.

[45] S. W. Jones. Diffusion in Silicon, Unpublished Book. 2000.

[46] B. L. Sharma. Diffusion in Semiconductors. Trans. Tech. Publications, 1970. doi: 10.1002.

[47] D. D. Smith. Review of Issues for Development of Self-Doping Metallizations, Technical Report. Sandia National Laboratories, 1999.

[48] DuPont™Kapton®PV9101 polyimide film. Technical report, 2011. URL kapton.dupont.com.

[49] J. Zhao, A. Wang, and M. A. Green. 24.5% efficiency silicon pert cells on mcz substrates and 24.7% efficiency perl cells on fz substrates. Prog. Photovolt: Res. Appl, (7):471–474, 1999.

95