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

MASTER THESIS

Submitted in fulfillment of therequirements for the degree of

Master of Sciencein Computer Science and Communications Engineering

Evaluation von Laser-bearbeitetenSi-nanopartikeldünnfilmen für den Einsatz

in der Photovoltaik

by

Levon Altunyanborn on 26.11.1986 in Sofia, Bulgaria

Supervisors:

Prof. Dr. rer. nat. Roland SchmechelProf. Dr.-Ing. Einar Kruis

Duisburg, 17 January 2012

i

A B S T R A C T

In this work, the potential of silicon (Si)-nanoparticles as back surfacefield (BSF) material for solar cells was investigated. The BSF layerswere created with the help of an infra-red laser (λ = 808nm), withcontinuous wave length and maximum power of Pmax ≈ 452W. Theoptical heating of the spin-coated Si-nanoparticles took place overdifferent substrates. For this purpose, commercially available poly-crystalline silicon (poly-Si) cells from the company Solland Solarhave been used. In particular, so called semi-ready structures wereemployed. Under this term, two types of solar cells (with and with-out anti-reflex coating and metal contacts) having no BSF allowed anevaluation of the discussed approaches. In addition, experiments ofthe Si-nanoparticles were done on several additional types of sub-strate materials such as glass, intrinsic Si-wafers and Kapton® foils.The particle size distribution inside the dispersions has been eval-uated to be Gaussian like, with a mean value around µ ≈ 100d.nmand a standard deviation of approximately σ ≈ 9d.nm. Thin films ofthe dispersed in ethanol, highly doped silicon nanoparticles were de-posited on the solar cell substrates. The thickness of the spin-coatedlayers was determined to lie in the range of hSiNp = 650nm in thecase of the commercially available cells from the company SollandSolar and hSiNP = 350nm when considering the intrinsic Si-waferssubstrates used for conductivity measurements.In addition, the parameters for the laser sintering procedure werefound and optimized. Including, but not limited to, these includedvalues concerning scan velocity, number of scans, need and advan-tages of a fast pre-heating step.Furthermore, electrical characterizations of different samples havebeen carried out. Current-voltage (I-V) measurements under andwithout illumination of the semi-ready structures with Si nanopar-ticles as BSF were studied. Based on these curves important cell pa-rameters are evaluated and presented. For some of the laser treatedsemi-ready structures from Solland Solar with anti-reflective coating,a fill factor of FF = 41%, short-circuit current Isc = −28, 76mA, anopen-circuit voltage Voc = 0, 53V , power at maximum power pointof Pmpp = 6, 4mW and an cell efficiency of around η = 6, 38% wasobtained. In the case of a semi-ready structure without anti-reflectivecoating, 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, 21mWand an cell efficiency of around η = 2, 95%.Different procedures to increase the efficiency of the cells in use weretested. Limiting parameters such as grain boundaries and parasiticresistances were examined. In addition, conductivity of the sinteredlayers was verified to be σtotal 6 2, 57× 10−3 Scm .Scanning electron microscope pictures were used to further evaluatethe change of particles and semi-ready cells by laser treatment. A5µm layer of laser sintered BSF was achieved. Furthermore, impor-tant correlation between metalization type, parasitic resistances andcell efficiency were extracted.Finally, to evaluate the possibility for a substantial cost reduction byemployment of cheap substrates, the effect of laser sintering of theSi-nanoparticles on glass and Kapton® foil were briefly studied.

iii

The smallest act of kindnessis worth more than

the grandest intention.

— Oscar Wilde

A C K N O W L E D G M E N T S

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

In addition, I would like to thank all those people that motivatedme throughout the years to constantly try to make the best that I amcapable of doing.The words would not fully express my gratitude to my family fortheir continuous support during my academic studies. Therefore,I would like to give my special thanks to my parents which haveprovided me with the opportunity to learn and face so many newthings. Last but not least, I would like to thank one special memberof my family, namely my dog - Archi, for the inspiration he hasbeen giving me, during the times of hopeless laziness, independentlyfrom the distance which is dividing us.

iv

C O N T E N T S

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 Dis-tribution 13

2.2.2 Mathematical Description for Current in a PN-junction 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 Pro-filometry 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-dispersiveX-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) asBSF 42

4.2 Initial Trends 43

4.2.1 Si-nanoparticles Size 43

v

Contents vi

4.2.2 Layer Thickness 45

4.2.3 “Safe” Region Determination 47

4.2.4 Primary Observations 48

4.2.5 Samples Treatment - Procedures and Results 49

4.2.6 Scanning Electron Microscope Investigations 59

4.2.7 Conductivity, Laser Parameters and Color Con-siderations 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

ii appendix 81

a program code 82

b additional graphs 83

c sample pictures and tables 90

bibliography 92

L I S T O F F I G U R E S

Figure 1.1 Laser treating Si-nanoparticles - method for cre-ating an efficient BSF 2

Figure 2.1 Band structure of dielectrics 6

Figure 2.2 Band structure of a monovalent metal 7

Figure 2.3 Band structure of a metal with overlapped bands 8

Figure 2.4 Excess of: (a)free electrons; (b)holes; in Si 9

Figure 2.5 Boron in Silicon - Excess of Holes 10

Figure 2.6 Temperature dependence of the electron con-centration in a n-doped semiconductor [1] 11

Figure 2.7 A pn-junction (diode) 13

Figure 2.8 Current-voltage characteristic of a silicon diode 14

Figure 2.9 Energy band diagram and charge carrier dis-tribution 15

Figure 2.10 Schematic Representation of Solar’s Cell WorkPrinciples 20

Figure 2.11 Standard IV-characteristic of a Solar Cell 22

Figure 2.12 Solar Cell Equivalent Circuit 25

Figure 2.13 Shockley-Queisser Limit 26

Figure 3.1 a.) Transmission electron micrography of a typ-ically obtained Si-nanoparticle; b). Schematicpicture of a HWR system; 29

Figure 3.2 Spin Coater 32

Figure 3.3 XP-200 High Resolution Stylus-Type SurfaceProfilometer, Ambios Technologies 34

Figure 3.4 IR Laser 34

Figure 3.5 MBraun 200B Glove Box System 35

Figure 3.6 Determination of majority carriers 37

Figure 3.7 Four Point Measurement Schematic Picture 38

Figure 3.8 Four Point Resistance Determination Schematic 39

Figure 3.9 Principle of the scanning electron microscope 40

Figure 3.10 Principle of EDX 41

Figure 4.1 IV-Characteristic of Reference Cell (Type I) 43

Figure 4.2 Fully Processed Reference Cell Type I with AlBSF - Characteristic Behavior 44

Figure 4.3 Ball Milling and Dynamic Light Scattering De-vices 44

Figure 4.4 Determination of the Si-nanoparticle size viaDLS measurement 45

vii

List of Figures viii

Figure 4.5 Si Layer Thickness vs. Position on substrate 46

Figure 4.6 Si Layer Thickness vs. Position on Substrate,Top View 46

Figure 4.7 Si layer thickness vs. number of depositions 47

Figure 4.8 Si Layer Thickness vs. Spin Speed, One SpinPhase 48

Figure 4.9 Fill Factor vs Different Laser Intensities 50

Figure 4.10 Cell Efficiency vs Different Laser Intensities 50

Figure 4.11 IV Characteristic 51

Figure 4.12 Open Circuit Voltage and Short Circuit CurrentApplying Different Procedures 55

Figure 4.13 Fill Factor and Corresponding Efficiency Ap-plying Different Procedures (see table.4.2) 55

Figure 4.14 Short Circuit Current Density (Jsc) and OpenCircuit Voltage (Voc) 57

Figure 4.15 Fill Factor (FF) and Efficiency (η) 58

Figure 4.16 Micrograph-Uncoated Backside Surface Viewof a Sample 60

Figure 4.17 Micrography of Brownish Color Area of Sin-tered Coated Sample 61

Figure 4.18 Picture of the Characteristic Brownish ColorArea after Sintering 62

Figure 4.19 Micrograph Sintered Coated Sample, Transition(Untreated-Treated-Untreated) Region 62

Figure 4.20 Highly vs. Low Reflective Area Comparison 64

Figure 4.21 EDX on the Front Surface of the Sample 66

Figure 4.22 Diffusion Coefficient of silver (Ag) in Si 67

Figure 4.23 IV-Characteristic of a Solar Cell Without Anti-reflective Coating, Sintered Si-nanoparticles(Isintern =

15% @ Vsintern = 1m/min) 69

Figure 4.24 IV-Characteristic of a Solar Cell Without Anti-reflective Coating, Sintered Si-nanoparticles(Isintern =

35% @ Vsintern = 1m/min) 70

Figure 4.25 On-Off Ratio, Comparison of Cells With andWithout Si-nanoparticles 71

Figure 4.26 Efficiency of Type II samples with Si-nanoparticles 72

Figure 4.27 Conductivity (σtotal) of Si-nanoparticles Spin-coated on Intrinsic Si-wafers Irradiated for Dif-ferent Laser Intensities 73

Figure 4.28 Conductivity of samples in different medium 74

Figure 4.29 Kapton® films after sintering 75

Figure 5.1 PERL (passivated emitter, rear locally-diffused)cell structure 79

Figure B.1 “Slim” Version - Efficiency (η) vs Different Treat-ment Combinations 83

Figure B.2 Legend for Samples Evaluated on 24.08.2011 84

Figure B.3 IV-Characteristic (Step 2), Sample No 03 84

Figure B.4 IV-Characteristic, Reference Cell with Step 1 85




Figure B.8 IV-Characteristic (Step 2-Acetone), Sample 04 87

Figure B.9 Front Side (Step 2-Acetone), Sample 04 87





Figure C.1 Back Surface of the Solar Cells (Type I) AfterSintering - 01.06.2011 90

Figure C.2 Back Surface of the Solar Cells (Type I) AfterSintering, 14.06.2011 91

Figure C.3 Back Surface of the Solar Cells (Type II) AfterSintering, 21.09.2011 91

L I S T O F TA B L E S

Table 2.1 Band gaps Eg of several semiconductor materi-als 27

Table 3.1 Filter Paper (parameters) 31

Table 4.1 Sample Preparation Parameters (Fill Factor) 49

Table 4.2 Combination Nomenclature, (Average Fill Fac-tor) 54

Table 4.3 Combinations’ Nomenclature, (24.08.2011) 57

Table 4.4 Solar Cells Sintering Parameters - Created on21.09.2011 65

Table 4.5 Diffusivity of Ag in Al 66

Table 4.6 Si-nanoparticles sintered on Kapton® substrates(parameters) 75

Table C.1 Back Surface of the Solar Cells After Sintering- 01.06.2011 (parameters) 90

ix

acronyms x

Table C.2 Back Surface of the Solar Cells After Sintering- 14.06.2011 (parameters) 91

A C R O N Y M S

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

Part I

I N T R O D U C T I O N

1I N T R O D U C T I O N

Even a ball of wool has a beginning.

— Proverb

For a photovoltaic power generation system to be economicallycompetitive the total costs of an installed PV system must be max-imum $1/W, which translates to 5-6 cents per kilowatt-hour. Thecurrent costs (2011) for a photovoltaic system are $3,40/W. Thisnumber is projected to decrease to $2,20/W by 2016 [2]. Therefore,decreasing manufacturing costs is a crucial factor in photovoltaicsindustry and research.In order to reduce the cost for solar energy there is a continuousdrive to reduce the thickness of the silicon wafers. This is to reducethe cost of silicon fraction of the cell and thus overall solar energycosts. Besides handling and bowing problems associated with thin-ner wafers a major drawback is the increased influence of the waferback surface on the overall cell performance.[3]

1.1 motivation

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

(a) Schematic drawing of a solar cell withBSF

(b) Sintering [4]

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

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

2

1.1 motivation 3

a top contact grid. Between the areas of opposite polarity (p and n) aspace charge region is formed. One of the possibilities of increasingsolar cell efficiency is by minimizing electron recombination in therear contacts.In general, contacts are considered as a highly defective area atwhich recombination of minority charge carriers will immediatelytake place. To reduce the losses on the back side of the p-doped layeran additional p+ layer can be applied. The theory predicts, sharingof the applied voltage among the two junctions (the n-p and thep-p+ junction) [5]. The BSF acts as a mirror, that reflects back into thecell the minority charge carriers, thus ensuring that the probabilityof recombination is reduced. Therefore, the absolute value of theshort-circuit current would be as well increased when comparing toan ordinary solar cell (pn-junction).The general trend in solar cell industry is the use of thick (typicallyover 10µm) aluminum (Al) film as BSF doping material. For thin Sisolar cells (6 250µm), the Al films have a significant negative impact[6].As discussed by Murray et al., the Al-Si phase diagram is a straightforward, classic example of a eutectic system where each elementhas little, if any solubility in the other [7]. Due to the different expan-sion coefficients of Al and Si, warping of the cell is observed. Thisnegative result, leads to difficulties in subsequent production andincreases the probability of breakage. For these reasons it is unlikelythat high efficiency cells on thin silicon wafers will use Al as BSFdoping material [6].For photovoltaics research and industry the reduction in cost perwatt is of utter most importance. Therefore the applicability of othermaterials has to be evaluated. The usage of Si-nanoparticles is apromising alternative approach. Si is a non-toxic material and it isabundant in the nature. It represents one of the most investigatedmaterials for building electronic devices. Furthermore, due to itsstrongly reduced size, Si-nanoparticles can easily be converted intoprintable dispersions.Furthermore, although laser crystallization contains a high potentialfor the annealing of Si-nanoparticles, only little evaluation of thismethod has been performed till now [8]. A great advantage of lasercrystallization is the possibility to crystallize only a very thin filmof silicon on almost arbitrary substrates [8]. This opens possibilitiesof new cost-effective technologies that can be utilized as well as forprocessing on cheap substrates such as polymer foils.

1.2 problem description 4

1.2 problem description

Due to fact, that classical solutions have a significant negative impacton thin solar cells, in this work new materials such as Si-nanoparticlesare 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 overthe bulk semiconductor. This approach is intended to achieve a keybenefit in cost per watt reduction when manufacturing silicon-basedphotovoltaic elements.

1.3 chapters outline

The aim of this work is to evaluate the potential of laser treatedhighly p-doped, Si-nanoparticles in the field of photovoltaics. Chap-ter 2 presents a brief introduction to metals, insulators and semicon-ductors. In addition the basic operational principles of a pn-junctionare explained. Furthermore, important quantities in photovoltaicssuch as fill factor and cell efficiency are covered.The experimental details and methods applied during this thesiswill be presented in Chapter 3. Here, the preparation of the Si-nanoparticles, the formation of dispersions and the techniques ap-plied to characterize the physical properties will be highlighted.Chapter 4 introduces details about electrical properties of the lasertreated films. Evaluation of the results of the different semi-readystructures is given. Furthermore, conductivity after laser annealingis discussed. In addition, the behavior of Kapton® films is shortlyinvestigated. In the final Chapter 5 the potential of the material forfurther research and optimization will be highlighted.

2T H E O R E T I C A L B A C K G R O U N D

Fundamental progresshas 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 highlydependent on different conditions such as temperature, illumination,presence of impurities, etc. Furthermore, their specific electrical re-sistance is considerably higher than that of conductors and lowerthan that of dielectrics. These materials are called semiconductors.To it belong some chemical elements (e.g. Ge, Si) and many chemicalcompounds (e.g. GaAs, InP, CdS, ZnSe). More complex materials con-sist 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 semicon-ductors their physical properties (like lattice constant or band gap)can be varied. The main difference between insulators and semicon-ductors is quantitative and will be characterized by the value of theband gap (Wg) separating the valence and the conduction band [9].As defined in literature, an atomic orbital is a mathematical functionthat describes the wave-like behavior of either one electron or a pairof electrons in an atom [10]. This function can be used to calculatethe probability of finding any electron of an atom in any specificregion around the atom’s nucleus.When a solid is being formed, the orbitals of the outer (so-calledvalence) electrons will interact with each other. Thus, in solids thelevels form continuous bands of energy rather than the discrete en-ergy 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 thevalence band;

• the bottom most empty band, named conduction band;

Furthermore, it is usually accepted to use the following naming:

5

2.1 insulators, metals, semiconductors 6

W

Conduction Band W

Wg

Wc

WValence 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 con-duction 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 ascaused by their movement. In order to be involved in an electricalcurrent, an electron must first get enough energy. Its amount isequivalent to the transition of this electron to a higher energy level.Three major types of materials are to be identified depending on theband 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 absoluteempty (fig. 2.1). Therefore, the nearest level to be filled can befound in the conduction band only. The band gap in the case ofinsulators is very large (e.g. WgSiO2

= 8.9eV ,WgSi3N4= 5.1eV)

[11]. Thus, electrons need larger energies to be excited into theconduction band making current flow impossible under lowapplied voltages.

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


W

W

Conduction Band Wc

WvValence Band

x

Figure 2.2: Band structure of a monovalent metal

whereas in other metals the conduction band and the valenceband overlap each other (fig. 2.3), so that the uppermost elec-trons in the top part of the valence band can be excited in thenext-higher available energy level already at T = 0K by apply-ing an electric field. The energies required are much lower thanin the cases of insulators and semiconductors. In principle, theelectrons can be excited and contribute to the electrical currentbecause there are many unoccupied states above filled states inthe valence band. By this way, the free electron concentrationin metals is much higher than in intrinsic semiconductors re-sulting in a very high electrical conductivity [10].

3. Semiconductors:The electrical properties of semiconductors are determined bytheir structure. Some typical semiconductor material examplesare Si (WgSi = 1, 12), Ge (WgGe = 0, 8), InP (WgInp = 1, 3) andGaAs (WgGaAs = 1, 5) [11]. The material with highest practicalrelevance in semiconductor devices is silicon (Si) [1]. In theideal Si crystal at temperature of T=0 K all electrons are bondedin electron pairs, therefore there are no free charge carriers andit behaves as a dielectric. To get free, the electron should receivea certain amount of energy. The electron may receive such en-ergy as a result of the interaction between the particles duringtheir thermal motion (e.g. at T > 0 K) or during illumination ofthe crystal [9].Each release of an electron is related to the emerge of a vacantplace (free, unoccupied bond). Around the vacant place a non-compensated positive charge of the nucleus is left. This charge


W

Conduction Band W

Wg

Wc

W

Valence Band

WvUnoccupied states

Occupied states

x

Figure 2.3: Band structure of a metal with overlapped bands

can attract an electron from a neighboring atom, so that thebond is filled [1]. Therefore, a new vacant place in the nearbyatom is created, in which an electron from another atom mightcome. Thus, the vacant place makes a chaotic motion insidethe crystal similar to the thermal motion of free electrons. Thisimaginary positive charge is called p-carrier or hole [2].By applying an electric field the free electrons start a directedmotion - current flows. The electric field ~E influences also theelectrons from the covalent bonds and facilitates their jumpsin the vacant places in direction, opposite to the direction ofthe intensity ~E of the field [2]. Therefore, the places themselvesare moving into the direction of the intensity ~E. Instead ofconsidering the real motion of the bonded electrons it is mucheasier to look at the motion of the vacant places. It is equivalentto the motion of a positive charge with a magnitude of theelectron, into the direction of the field [1].Therefore, in semiconductors the electrical conductivity is ac-complished by the help of two types of charge carriers: freeelectrons and holes.Extrinsic semiconductorsIntrinsic semiconductors are only a subject of theoretical con-sideration, since materials with required purity do not exist inthe nature and can not be realized using modern technologyas well. However, for most important applications, the semi-conductors with a defined amount of artificially introducedimpurities (doping) is a prerequisite. Introducing different im-purity atoms (e.g. phosphorus in Si), n-type or p-type (e.g.


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

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5th Valenceelectron of P Atom

(a) P in Si -> excess of electrons

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(b) B in Si -> excess of holes

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

DonorsLet us assume that in a Si crystal, one atom of a P is substitutingone atom of Si. P has five valent electrons, four of them formcommon electron pairs with the neighboring Si atoms. Thefifth electron is not taking part in the covalent bonds. Whenconsidering the band structure, such impurities “create” anenergy level within the band gap, close to the conduction band.This is called “shallow” level - a level that is very close to theconduction band, so the energy required to ionize an atom issmall and a sizable fraction of donor atoms will be ionized atroom temperature. For its transition from connected into freestate condition a much smaller amount of energy is neededcompared with the covalent bonded electrons. As reported inliterature by Chen et al. [12], in the case of P the donor levelis ED = 0, 045eV . Therefore, at room temperature the energyof thermal motion is sufficient for impurity atoms to loosetheir “superfluous” electrons and to convert themselves intopositively charged ions P+. Impurity atoms, which give elec-trons are called donors. The electrical current is mainly due tothe directed motion of free electrons received from the donors.Semiconductors, in which conductivity is defined by the freeelectrons received from the donors, are called semiconductorswith electrical (n-type) conductivity or shortly n-type semi-conductors [9].AcceptorsFig. 2.4b shows the crystal lattice with a B atom replacing a Siatom. Since B has 3 valence electrons, one bond with neighbor-ing Si atoms is occupied by one electron only. This positivelycharged vacant bond corresponds to a hole and can move in


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 theband gap close to the top of the valence band and can be occu-pied by an electron from the valence band. In the case of, B the“shallow” level is EA = 0, 045eV [12]. Doping with acceptorsleads to a p-type semiconductor with excess of holes.

Temperature dependence of the charge carrier concentrationFurthermore, semiconductors are having a dependency on tempera-ture. For example, the charge carrier concentration is strongly relatedto the previously mentioned parameter. In the case of an n-dopedsemiconductor the temperature dependence can be separated in tothree characteristic areas. Namely, these are the freeze-out, saturationand 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 donorsprovide electrons to the conduction band, and at the temperatureTmin the semiconductors pass into the saturation region with thefollowing relation [9]:

n = ND (2.1)

If the temperature increases up to Tmax, electron-hole pairs will becreated by the band-to-band excitation, as it happens in intrinsicsemiconductors [1]. In this temperature region the electrical behaviordepends on the intrinsic conductivity. The electron concentration inthis region will be given by:

ni =√NcNve

−Wg/2kBT (2.2)

Electronic devices based on doped semiconductors operate in thedepletion region, i.e. between Tmin and Tmax [1]. Otherwise, the

2.1 insulators, metals, semiconductors 113-22 Introduction to Solid-State Electronics

n(log)

1/TTmax Tmin

saturationregion

freeze-out-region

intri

nsic

rang

e

ni

ND

(-∆WD/2)∝

(-∆WG/2)∝

Fig. 3.18 Temperature dependence of the electron concentration in a n-doped semicoductor

3.3 Charge carrier transport in solids

Charge carrier concentration and velocity of charge carriers are most important parameters having an influence on the electrical conductivity. If the ion flow can be neglected, the electrical current in a solid is caused by electron and hole flows only.

The current density will be written in a common form as

pn vpqvnqJ +−= (3.44)

where n , p : charge carrier concentration

- q (1) + (2) : charge of electrons (1) and holes (2), q

nv , pv : velocity of electrons and holes, respectively.

An external electrical field applied to the solid results in a force moving positive charges (holes) with a velocity pv parallel and negative charges (electrons) with a velocity

uu anti-parallel to the

field. Thus, to define the current both flows should be added. nvr

Because of the thermal energy, electrons and holes move with significant velocity also without an external force. The mean thermal energy of each charge carrier is

2

**2*

21

21

23

===

mkmvmkTW thth

h

or, in terms of „thermal” velocity:

*mvth =

3kT (3.45)

Figure 2.6: Temperature dependence of the electron concentration in a n-doped semiconductor [1]

devices with a pn-junction will loss their functionality above Tmax,because the amount of thermally generated (i.e. not impurity related)electrons and holes will exceed the doping concentration [11]. Fortemperatures below Tmin charge carriers are frozen out and theelectrical conductivity drastically decreases.A similar consideration can be performed for a p-type semiconductor.The interested reader is referred to the given literature [1, 9, 11] forfurther information.The results of comparison between dielectrics, semiconductors andmetals can be summarized as follows:

1. In respect of the electrical conductivity there is a qualitative dif-ference between dielectrics and semiconductors. Quantitativelythey can be characterized by the value of the band gap. Forboth kinds of solids the number of electrons in the conductionband determine the electrical conductivity.

2. In metals all electrons take part in electrical conductivity be-cause the number of unoccupied states directly above the va-lence band is in the same order as the number of electrons.

2.2 pn-junction diode 12

2.2 pn-junction diode

A p-n junction is occurring at the boundary between a p and ann-type semiconductor material. The p region contains holes whichare mobile, and negatively charged impurity ions which are immo-bile. Similarly, the n-region has positively charged ions which areimmobile and mobile electrons. As soon as a pn-junction is formed,electrons from n-type material and holes from p-type material diffuseinto p-type and n-type material, respectively. As a result the positivedonor ions in the n-region and the negative acceptor ions in the p-region are left uncompensated. Around the pn-junction a region withvery few charge carriers is created. This region forms the depletionregion also called the space charge region (see fig.2.9a)). It is namedso because it is depleted of mobile charge carriers. Therefore, thisregion has a very high electrical resistance. The holes e.g. trying toenter the p-region are repelled by the uncompensated positive chargeon the donor ions. As a result a potential (band diagram heights)difference is established across the junction. Soon, it becomes largeenough to prevent any further movement of charge carriers. This iscalled potential barrier or junction barrier. It gives rise to an electricfield that prevents the respective majority carriers from crossing thebarrier region.Consider connecting the p-region of the diode on a higher electricalpotential than the n-region as seen in fig.2.7a. Due to the influenceof the electric field the holes of the p-region and the electrons fromthe n-region start moving towards the pn-junction. The reductionof the potential difference and the width of the depletion regioncauses a large number of majority charge carriers to diffuse acrossthe junction. An electric current flows through the diode. Connectingthe diode in this way is called forward bias, and the applied voltageforward-bias voltage [13].On the other hand, if connect the p-region with ground and then-region with the positive pole (high electrical potential) respectively(see fig.2.7b), under the influence of the applied electric field, thefree charge carriers are moving away from the pn-junction. Thus, thepotential barrier is increased. Practically, the current which flowsthrough the diode is almost zero. In this arrangement, the diode isoperated in reverse biased mode, and the applied voltage is calledreverse-bias voltage.The current-voltage characteristic of a typical Si diode is shown infig.2.8. A non-linear characteristic can be observed. Initially, the cur-rent which flows in the forward bias increases slowly with increasingvoltage. From a given voltage value on it increases much faster. Thisshows, that the resistance of a diode is variable. It is high at lowvoltages and decreases with increasing voltage U. From the graphic,


-

--

-

-

+

++

+

+

-+

E

+ -

(a) in forward bias

E

‐‐‐‐++++

+‐‐‐‐

‐

‐

++

+

‐‐‐‐

‐‐++++ ++

‐‐ +

+

+

‐depletion

p‐doped n‐dopeddepletion region

‐‐ +

(b) in reverse bias

Figure 2.7: A pn-junction (diode)

it can be seen that through the diode also a reverse current Irev flowsbut it is typically thousand times [13] lower than the current in theforward bias. The property of diodes to pass current only in onedirection is of great practical importance for electronics. The forwardcurrent Iforward rises exponentially with voltage (for U 3kBTq ), sothat it may be approximately described as [1]:

Iforward = I0 × (eqU/kBT ) (2.3)

The approximation above is valid for a voltage smaller than theflat band voltage only, i.e. for silicon up to about U ≈ 0, 6V [11].If this voltage is exceeded, the additionally applied voltage willdrop primarily across the semiconductor outside the interface barrierregion. The exact complete current voltage characteristic is given by[9]:

I = I0 × (eqU/kBT − 1) (2.4)

2.2.1 Energy Band Diagram and Charge Carrier Distribution

In the following the mechanisms that are responsible for electri-cal current in a pn-junction are described. Electric field or chargecarrier diffusion, or their combination is the main reason for thisphenomenon. Assume without loss of generality the following [1] :

1. Abrupt doping profile: At the junction interface an abruptchange 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.


120

100

8060

40

2

0

20

I, mA

-U, V +U, V

Irev, µA

0,2 0,4 0,6246

Figure 2.8: Current-voltage characteristic of a silicon diode [13] (Note: re-verse 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 currentI = 0A) is denoted by the use of an index 0. The intrinsic density ofcarriers is specified by ni.

np0 = 0 =n2ipp0

=n2iNA

Minority charge carriers (electrons) in p-region

(2.5)

pn0 = 0 =n2inn0

=n2iND

Minority charge carriers (holes) in n-region

(2.6)

where,pp0 Majority charge carriers (holes) in p-regionnn0 Majority charge carriers (electrons) in n-regionNA is the acceptor concentration in the p-doped regionND is the donor concentration in the n-doped regionThe term used to describe the topmost electron energy level at abso-lute zero temperature is "Fermi level" and it is usually abbreviatedas WF. In the case of thermal equilibrium the reference "Fermi level"is constant (WF = const.). Near the junction, the concentration offree charge carriers does not follow the sharp profile of the dopingatom distribution because of their non-zero mobility. Diffusion drives


Figure 2.9: Energy band diagram and charge carrier distributiona) Space charge region

b) Band structure profile of an abrupt pn-junctionc) Space charge distribution

d) Potential- and field distribution [1]


electrons from n- to p- region and the holes from p- to n-region, re-spectively. According to Poisson’s equation (see eq.2.7), this effectresults 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:

∆φ = −div~E = −ρ

ε0εr(2.7)

where:~E is the electric fieldφ is the electric potentialρ is the charge densityε0 = 8.85× 10−12 F/m is the permittivity in vacuumεr is the relative permittivity of the materialq is the elementary charge = 1.60× 10−19 CThe potential difference UD that electrons and holes have to passwhen moving through a pn-junction can be calculated as:

UD = Uth ln

(NAND

n2i

)(2.8)

where, UD is the difference between “built-in” and external appliedvoltage

where the thermal voltage Uth =kBT

q(2.9)

UD > 0 corresponds to the voltage which has to be applied externallyso that a flat band profile will be achieved. Furthermore,

ρ = q[N+D(x) + p(x) −N

−A(x) −n(x)] (2.10)

Therefore, equation 2.7 and equation 2.10, lead to:

−ρ

ε0εr=q

ε

n0 − p0︸︷︷︸equilibrium concentration

difference of free charges (≈0)

+ N−A −N+

D︸︷︷︸concentration difference

of acceptor and donor atoms

(2.11)


After using the above defined simplifications (see p.13) a morecompact form can be expressed as:

ρ = 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:

ρ = −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 spacecharge region can be defined as [1]:

l0 =

√2ε0εr

q(1

NA+

1

ND)√UD (2.14)

Fig. 2.9d) shows the distribution of the electric field across the junc-tion. It is increasing with doping and is determined primarily by thelower level of doping. A maximal value is obtained at x = lg.

Emax = −qNAε0εr

(lg − lp0) = −qNDε0εr

(ln0 − lg) (2.15)

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

nn(x) = ND exp

[−1

2

(ln0 − x

LDp

)2]for lg 6 x 6 ln0 (2.16)

and

pp(x) = NA exp

[−1

2

(x− lp0LDn

)2]for lp0 6 x 6 lg (2.17)

where,pp(x) Majorities (holes) in p-region depending on the length xnn(x) Majorities (electrons) in n-region depending on the length xLDn is the Debye length (the distance over which significant chargeseparation can occur) in n-regionLDp is the Debye length in p-regionThe concentration of minority charge carriers can be obtained fromthe following equations:

nnpn = n2i and nppp = n2i (2.18)


Therefore using equations 2.16, 2.17 and 2.18, follows:

np(x) =n2ipp(x)

= ND exp[UDUth

]exp

[−1

2

(x− lp0LDn

)2]for lp0 6 x 6 lg

(2.19)

,wherenn(x) Majority charge carriers (electrons) in p-region depending onthe length x, and

pn(x) =n2inn(x)

= NA exp[UDUth

]exp

[−1

2

(ln0 − x

LDp

)2]for lg 6 x 6 ln0

(2.20)

,wherepp(x) Majority charge carriers (electrons) in p-region depending onthe length x.

2.2.2 Mathematical Description for Current in a PN-junction

In contrast to the equilibrium conditions, under operational condi-tions 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 thetransport of charge from place to place by electrons and holes. Thetwo basic transport mechanisms in a semiconductor are drift anddiffusion (see fig.2.9b)) [14].The drift current is defined as the flow of electric current due to themotion of the charge carriers under the influence of an external elec-tric field. The mathematical description for current in a pn-junctiondiode follows the following relations.

Jn,Drift = −qnµn~E (2.21)

,whereJn,Drift is the drift current densityµn is the electron mobility~E is the electric fieldCarrier diffusion is due to the thermal energy, kBT, which causesthe carriers to move at random even when no field is applied. Thisrandom motion does not yield a net flow of carriers nor does ityield a net current in material with a uniform carrier density sinceany carrier which leaves a specific location is on average replace by


another one. However if a carrier gradient is present, the diffusionprocess will even out the carrier density variations: carriers diffusefrom regions where the density is high to regions where the densityis low. The diffusion process is not unlike the motion of sand on avibrating table; hills as well as valleys are smoothed out over time[9].As a final result of complex derivations for the diffusion currentholds:

Jn,Diff = qDn∇n (2.22)

,whereDn is the electron diffusion coefficientn is the electron concentrationSimilar expressions exist for the hole-related current. In case ofthermodynamic equilibrium, the total current through the junctionis 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 inequilibrium, 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 photoelectriceffect leads to the field of photovoltaics which is described in thefollowing section.

2.3 photovoltaics 20

2.3 photovoltaics

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

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

In a pn-junction being in an equilibrium state, the build-in potentialbarrier holds most of the electrons in the n-side, whereas the holeson the p-side. If a positive voltage on p-side is applied by an externalsource (forward bias), the energy barriers are lowered. Therefore,there is a higher probability of electrons getting over the barrier fromn to p-side. As a consequence of this, there are many more electronsin the p-side than there were in the equilibrium state. This leads toan excess of minority charge carriers on the p-side. The same holdsfor holes which have migrated to the n-type region. Some of theexcess minority electron charge carriers injected across the junctionmay recombine in the bulk of the p-side region.There are many reasons for which this might happen. The mostcommon in Si is that there might be defects corresponding to energystates inside the band gap of the p-region [2]. Therefore, an electronmay land to that intermediate state, and thereafter fall down onceagain. Thus it would fill up a hole state in the valence band.When an electron gets into the p-type region, the system is notanymore electrostatically neutral. Therefore, it reacts by kicking anelectron out of the valence band into the conduction band to create anew hole. The resulting electron flows through the connected loadback to the conduction band of the n-side and so replaces the missingelectron.Usually contacts are characterized as highly defective areas. There-fore, recombination can take place in the contact regions as well.In conclusion, if an excess of minority charge carriers is observed, thepn-junction system may react by promoting a recombination process.Thus, if an electron and a hole recombine, one electron flows in the


external circuit.Sunlight is composed of photons, or “packets” of energy. Whenirradiated, some of the photons are absorbed by the photovoltaiccell. If they get absorbed the energy from the photon is transferedto an electron of an atom of the solar cell. When in semiconductormaterial a photon having sufficient energy is absorbed an electron inthe valence band is lifted to the conduction band. Thus, an emptystate in the valence band (a hole) is created.The photo-generated current flows in opposite direction to the onecreated by the diode’s forward bias voltage. If a load is connected thefollowing effect is observed: the electrons move towards the n sideand the holes move towards the p side in direction of the junction. Inthe ideal case the photo current has essentially a negative constantvalue.

2.3.1 Back Surface Field

The generated minority carriers are useful if they are created nearthe collecting pn-junction. A lot of recombination occurs at the backcontact. This surfaces have a lot of defects and it can be assumed thatonce reached, a recombination will immediately occur. As obtainedby different simulations of a typical crystalline solar cell under shortcircuit conditions around 49% of the hole-electron pairs are generatedin the base and near the rear contact region. In addition, around23% of them recombine and are lost in the same area. Under opencircuit conditions, the recombination losses are much higher. Theyare accounted to lie in the range of 80% [16].According to Beer-Lambert law, the intensity of an electromagneticwave inside a material falls off exponentially from the surface as

I(z) = I0 × e−αz (2.26)

,whereI0 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 wave-lengths 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 offsome recombination processes.


One possible way to reduce losses and thus increase the efficiencyof a cell is the so called Back Surface Field. Applying a BSF acts asa mirroring of the minority charge carriers back to the pn-junction.Therefore, this method is an important technological step to increasea solar cell’s efficiency.Assume, a p-type as a base material of the cell. BSF is achieved, byheavily p-type region doping at the rear side of the cell. Therefore,the Fermi level would get closer to the valence band. Thus, an addi-tional energy barrier is inserted that the electrons have to jump over.In general, recombination depends on the speed at which a minoritycharge carrier diffuses towards the back contact [16]. BSF acts as aminority carrier mirror which prevents some of them reaching theback contact. Thus, the probability of diffusion towards the collectingpn-junction is increased. In addition, when comparing the behaviorof a cell with and without extra p+-type layer doping, more currentat 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 inthe graph are:

1. Open circuit voltage (Voc), represents the maximum voltageavailable from a solar cell;


2. Short circuit current (Isc), gives the largest current which maybe drawn from the solar cell;

As a solar cell contains a pn-junction, it can be modeled mathe-matically in a similar way as a diode. For a crystalline Si cell, thepn-junction collection mechanism can be considered as independentof the voltage applied on the cell. Therefore, the total induced cur-rent under illumination is obtained by a superposition between thecurrent in the dark and the light generated current. Thus, the currentdensity can be approximated as a combination of the short circuitcurrent and the dark current density of an ideal diode:

J = Jsc − J0(eqV/kBT − 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 theterminals. Therefore,

Voc =kBT

qln(Jsc

J0+ 1

)(2.29)

A solar cell converts light, a flow of photons, to electric current, aflow of electrons. Therefore, higher light intensity would mean morephotons, which in turn means more electrons and higher short circuitcurrent. Jsc is inversely proportional to the effective area (A) of thesolar 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 beseen that for a positive voltage V, the current I is negative. Therefore,the corresponding product of the two quantities would be smallerthan zero (P = I ∗ V < 0). Thus, it can be concluded that the solarcell generates power. Somewhere between these two characteristicpoints the maximum power of a solar cell is situated.The maximum power density is simply:

PMPP = JmpVmp (2.31)

where, Jmp and Vmp are the current density and voltage at MaximumPower 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 circuitvoltage Voc and the short circuit current density Jsc. The amount of“utilized” open circuit voltage and short circuit current at maximum


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

PMPP = JmpVmp = JscVocFF (2.32)

Therefore,

FF =JmpVmp

JscVoc(2.33)

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

η =Pout

Pin=JmpVmp

Pin(2.34)

where, Pin is the power density of incoming light. Furthermore, onecan express efficiency by using the fill factor:

η =JscVocFF

Pin(2.35)

The four quantities Jsc, Voc, FF and η are frequently used to charac-terize the performance of a solar cell.The starting point for an evaluation is a measurement of the cellunder light conditions. Under different illumination intensities thecell current will vary. As an example, the air mass coefficient de-fines 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 isconsidered as a useful representation of the overall yearly average.It corresponds to an air mass coefficient of 1,5. Therefore, standardlighting conditions for terrestrial solar cells have been defined. Un-der this term it is normed an air mass 1.5 spectrum, light flux of1000W/m2 and temperature of 25 C[2].

2.3.3 Limiting Factors

In addition, important for the evaluation of solar cells are limitingfactors which can be modeled as parasitic resistances as showed infig.2.12.

Parasitic Resistances

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

2.4 shockley-queisser limit 25

Figure 2.12: Solar Cell Equivalent Circuit

leakage mechanisms and defects in the diode. All these undesiredcharacteristics would lower the performance of the cell in considera-tion. Their behavior, can be summarized in a shunt resistance (Rsh)connected in parallel to the solar cell (mainly due to the pn-junctioninterface). In addition, the contacts, the p region, the n region andthe pn-junction itself, would introduce some parasitic effects as well.Their total effect can be modeled by a series resistance (Rs). Theeffect of the series and shunt resistances would lower the currentand voltage and therefore degrade the cell’s fill factor. That is whyreducing negative influences such as material contamination, surfaceand crystal defects are of utter most importance.

2.4 shockley-queisser limit

Solar cells are sensitive to different wavelengths of light (i.e., pho-tons of different energies) as a function of the materials they arebuilt from. Accordingly, some cells are better performers outdoors(i.e., optimized for sunlight), while others are better performers in-doors (optimized for fluorescent light). As predicted by Shockleyand Queisser [18] the maximum conversion efficiency of a solar celllies around 33.7% assuming a p-n junction band gap of around 1.1eV. It can be seen from fig. 2.13, that as the band-gap is increasedthere are fewer and fewer photons that can be absorbed, but theopen circuit voltage is increasing. As the band-gap is increased fur-thermore, the voltage is increased as well. Nevertheless, the numberof photons that can be absorbed decreases. Therefore, the current isreduced as well. As it can be extracted from the graph, the optimumlies around the band-gap of Si. Solar cells made from single crystalsilicon are currently limited to about 25% efficiency because they


0,4

0,3

0,2

0,1

0,00 1 2 3E [eV]g

SiCuInSe2

CuGaSe2

Abbildung 1.2: Abhangigkeit des theoretischen Wirkungsgrades von der

Bandlucke Eg [2]. Die Bandluckenenergien der Halbleiterma-

terialien Si, CuInSe2 und CuGaSe2 sind durch Linien gekenn-

zeichnet.

Fur die Entwicklung der plasmatechnologischen Barriereschichten konnten typische

Kenngroßen fur Solarzellen herangezogen werden. So gibt die Leerlaufspannung Uoc

eines Moduls z.B. Auskunft daruber, ob in einer Isolationsschicht Fehler vorliegen.

Der Kurzschlußstrom Isc eines Moduls bewertet z.B. die Barrierewirkung gegen Ver-

unreinigungen.

Eine wichtige Kenngroße bei Solarzellen ist die maximale Leistung Pmpp (engl. ma-

ximum power point, mpp), die von einer Solarzelle entnommen werden kann. Es gilt:

Pmpp = Umpp · Impp (1.7)

Eine weitere Große ist der Fullfaktor ff . Er bewertet, wie nah sich die Strom-

Spannungs-Kennlinie der Solarzelle an die Idealform annahert:

ff =Umpp · Impp

Uoc · Isc(1.8)

Daraus ergibt sich der Wirkungsgrad zu:

η =Pmpp

PLicht

=ff · Uoc · Isc

PLicht

(1.9)

Die typischen Großen, mit denen man eine Solarzelle oder ganze Photovoltaikmodule

charakterisiert, sind:

Figure 2.13: Shockley-Queisser Limit [15]

are most sensitive to infrared light, and radiation in this region ofthe electromagnetic spectrum is relatively low in energy [19]. Asidefrom single crystal there exist other commonly used types of siliconsuch as polycrystalline and amorphous. The reason for this is theirlower cost at acceptable efficiency. Polysilicon, is a material consist-ing of small silicon crystals. It is commonly accepted in photovoltaicindustry to use the term multi-crystalline (mc-Si) as a naming syn-onym. Thin film cells have a number of advantages, including easierdeposition and assembly, the ability to be deposited on inexpensivesubstrates, the ease of mass production, and the high suitability tolarge applications. Since amorphous silicon cells have no crystalstructure at all, their efficiencies are presently only about 10% due tosignificant internal energy losses [19]. Nevertheless, they are used,due to providing an acceptable efficiency at good price.A number of other materials can also be used to make solar cells.Typical examples are gallium arsenide, copper indium diselenideand cadmium telluride to name a few. In table 2.1 the band gaps ofseveral typical semiconductor materials is presented.


Table 2.1: Band gaps Eg of several semiconductor materials [15, 20–22]

Material: Band gap: Power conversion efficiency [%] TechnologyGe 0,66 eV

CuInSe2 1,05 eVSi 1,12 eV 10-17 Crystalline

GaAs 1,42 eV 20-29 CrystallineCdTe 1,45 eV 10-17 Thin-film

CuGaSe2 1,68 eVa-Si:H ≈ 1, 7 eV 8-13 Thin-filmCdS 2,4 eV

There are several reasons due to which Si is the preferred choicein solar cell industry. It is a well known, inexpensive, non-toxicmaterial. Furthermore, it has its band gap value (Wg = 1, 12eV), nearto the point at which the theoretical efficiency maximum predictedby Shockley and Queisser can be obtained.

3E 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 replicatethe build up of the structures is explained. Moreover, the equipmentand materials needed are listed. Finally, the reasons, limitations andassumptions which influenced the choice of the methods in use isstated.

3.1.1 Gas phase production of silicon nanoparticles

Several methods to grow Si-nanoparticles have been reported. Typicalexamples 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 productionlevel is the gas phase growth and in particular, the use of a hot wallreactor (HWR) system [8]. The Si-nanoparticles used throughout thiswork have been produced by this method.The schematic illustration of a HWR system used for the growth ofsilicon nanoparticles is given in fig.3.1b. A typical Si HWR producednano-particle can be seen in fig.3.1a. In the following the procedureto obtain the B-doped Si-nanoparticles is described.The particles have been obtained by pyrolysis of pure monosilaneand a mixture of 1% diborane gas in hydrogen. Both precursors

28

3.1 material processing 29

4 Properties of Silicon Nanoparticle Layers

Figure 4.1: Transmission electron micrograph of a HWR silicon nanoparticle. The inset shows the elec-tron diffraction pattern of the indicated region [Wig01].

material, which will be outlined below. The large amount of internal interfaces in between sin-tered silicon nuclei will have consequences on the defect properties of hot wall silicon nanopar-ticles as will be discussed in Section 4.1.4.

Microwave reactor silicon nanocrystals

In contrast, a completely different sample morphology is present for silicon nanocrystals grownin the microwave reactor systems. As Figure 4.2 demonstrates, these exhibit a clearly sphericalshape and consist of only one crystalline domain, thus being real single nanocrystals. The TEMmicrograph shows the crystalline interference fringes from the lattice planes in the nanocrys-talline volume, but also an outer shell showing no signs of crystalline order is evident. This shellis considered as the surface oxide (consisting of silicon suboxide, SiOx , with 1 < x ≤ 2), whichis usually present on samples that have been subject to oxidation at ambient atmosphere, suchas 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 fur-ther 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

(a) Transmission electron micrographyof a HWR silicon nanoparticle. Theinset shows the electron diffractionpattern of the indicated region [30]

(b) Schematic illustration of a HWR sys-tem used for the growth of siliconnanoparticles [30].

Figure 3.1: a.) Transmission electron micrography of a typically obtainedSi-nanoparticle; b). Schematic picture of a HWR system;


were mixed and fed into a tabular hot-wall reactor with six heatingzones and total heating length of 1 m. An additional flow of nitrogenprevented particle deposition inside the reactor and served also asa carrier gas. The furnace temperature was set to 1050C and thereactor pressure was adjusted to 400 mbar using a vacuum pumpand a regulating valve. The particles were transported with the gasflow to a separator and collected on porous stainless filter elements.After the experiment the material was filled automatically into plasticcontainers by back purging the filter. The production rate was around600 g per hour.[30]

3.1.2 Substrates

The experimental investigations of the Si-nanoparticles took place ondifferent types of substrate materials. For the initial studies thermoscientific microscope slides, with ground edges 90 and thickness of0,8 - 1,0 mm were used. The substrates were cut into a square shape,10× 10mm2.Furthermore, depending on the applied methods and as a conse-quence of the obtained results different semi-ready industrially pre-pared solar cells were used. Two different types of multicristallinesilicon cells were employed. Both were provided by the companySolland 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 wasused. The total thickness of the samples was 250µm. As reportedby Solland Solar, the anti-reflex coating had a refractive index be-tween 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 waferwere compensated with P atoms. Thus, an n-type layer was formed.The doping concentration for this depth range was specified asND = (1× 1016 . . . 1× 1017)cm−3. The thickness of the p-type layercorresponds to the wafer thickness minus the emitter. The number ofB atoms was as high as ND = (1× 1015cm−3 . . . 1× 1016cm−3). Thespecific resistance was specified as ρ ≈ 0, 5− 3.0 Ωcm. For namingpurposes, through later chapters, the previously described semi-ready cell configuration will be defined as Type I.In addition, a second type of semi-ready cells was employed. Themajor difference with respect to the previously described cells wasthat they consisted of no anti-reflex coating and no metal contacts.The total thickness of the samples was measured to be 250µm. Lateron, they will be referred as semi-ready cells from Type II.For conductivity measurements, monocrystalline intrinsic (residualn-type doping) Si wafers were used. They had a thickness of 525µmand a square shape, 10× 10mm2. The orientation of the Si-wafer was


1 0 0. The p-type side was polished, whereas the n-type side wasetched.Cost-efficient technologies that can be utilized such as processingon thin polymer foils has been briefly investigated. For this purpose,due to their high thermal stability Kapton® films (10× 10mm2) wereemployed. For stability during actual particle depositions, largerglass substrates were used. The Kapton® films were placed overUV Quality quartz glass substrates which had a square shape of15× 15mm2, and a thickness of 1mm.

3.1.3 Dispersing silicon nanoparticles

To produce stable dispersions of the Si-nanoparticles a defined quan-tity was mixed with dry ethanol. Thus, liquids of Si-nanoparticles5%wt and 10%wt were prepared. To assure smooth layers after spin-coating a ball milling procedure has been used. For this purpose,yttria stabilized zirconia (YTZ) beads (100µm) were utilized. To pre-vent obstruction of the slotted sieve filters a pre-dispersing step wasemployed. It included milling with courser beads (300µm). There-after, a 15 minutes of ultrasonic cleaning was applied. Thus, possiblyexisting bigger agglomerates have been destroyed. In addition, toprevent unwanted things like dust, big agglomerates, etc. a finalfiltering step has been utilized. For this purpose a glass fiber paperwas used. Its properties can be summarized in the following table3.1.

Table 3.1: Filter Paper (parameters)

Grade MN 85/90 BFWeight[g/m2] 90

Thickness[mm] 0,4Filtration speed [s] 15

Average retention capacity [µm] 0,5Surface Smooth

Applications and properties 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 thatoils and organic residues which appear on this type of surfaces areremoved. The procedure that has been used involved the followingordered steps:


Cleaning

1. pouring on the surface of the sample which was glued to thewafer 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 spin-coating. All Si layer depositions were made on the "close bowl"designed Single Wafer Spin Processor for Manual Dispense (APT-SPIN150-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 parametersthat define the spin process can result in drastic variations in thecoated film. Only a single step (static dispense) has been used. Therotational frequency during the spin-coating procedure was set to2000 rpm. The acceleration of the spin coater in use was set to


1088rpm/s2. The amount of material was selected in a way thatthe substrate is fully coated. As a general observation, once thesubstrate area was fully coated, the exact amount of material did notinfluence the final spin coated layer thickness. For measurementsan estimated height of dSiNp = 650nm(±25nm) is assumed (see fig.fig.4.5 in the following sections). Therefore, a larger puddle, to ensurefull coverage of the substrate during the high speed spin step, waspreferred. By choosing one, instead of several smaller interlockingcircular drops, reduced the contamination as well as air bubblesinside the final Si-nanoparticles layer. Thus, depositing a puddle ofthe Si-nanoparticles fluid near the center of the glass substrate wassufficient.The final outcome which has been used for all Si particle depositionson all used substrates through this work could be summarized inthe 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 immediatelywith 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 determinedusing, a XP-200 High Resolution Stylus-Type Surface Profilometerfrom Ambios Technologies (see fig. 3.3a). To isolate vibration, a Micro40 benchtop unit from Halcyonics was utilized. The devices neededfor this step can be seen on fig. 3.3b. The stylus force used wasF = 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 andmaximum power of Pmax ≈ 452W was utilized (see fig. 3.4). Theamount of gas flow inside the processing chamber (total volumeVchamber = (1 . . . 2)l, see fig.3.4) was measured with the help of aTSI 4000 Series Mass Flowmeter. Cheaper glasses were absorbing toomuch light due to imperfection of the material and were breaking


(a) Surface Morphology MeasurementPlate

(b) Surface Profilometer and BenchtopVibration Insulator Instrument Set

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

almost immediately leading to unstable stand for the samples. There-fore, each sample has been placed over a quartz glass (UV-quality)in the chamber of the infra-red laser so that stability during sinteringwas 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 thelaser had to be adjusted with respect to the different substrates used.Furthermore, a short program in the G programming language forthe laser control (see appendix p. 82) has been developed. With itshelp, different parameters such as the intensity of the actual sinteringstep, its velocity and the number of scans have been controlled andvaried.

3.2 analytical methods 35

Metal evaporation

Before IV measurements were possible, contacts on the back side aswell on the front side (when needed) of the solar cells were evap-orated. In the case of Type I cells, only back side contacts werenecessary. Thick contacts have been made by using 200nm layersof aluminum (ρ = 10, 49 g/cm3). They were metalized by thermalevaporation (see fig. 3.5a) under low pressure conditions of approx-imately 2× 10−6 mbar. Typical deposition rates in the range of 3-5Å/s were used. All metal evaporations were made inside the MB200B 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 ofthe 10× 10mm2 cells there were big enough windows, thus protect-ing 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 para-sitic resistances in a solar cell can be calculated from the inverse ofthe 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)


Through this work, a slightly modified version of this method hasbeen used. Concerning the series (Rs) and the shunt (Rsh) resistances,slopes were extracted when looking at the saturated parts of therespective characteristic curves under illumination instead at theintersections with the abscissa and ordinate axis.In general, an ideal cell’s shunt resistance (Rsh) would be infinite andwould not provide an alternate path for current to flow, while theseries resistance (Rs) would be zero, resulting in no further voltagedrop before the load. Usually a shunt resistance of Rsh > 1000Ω isregarded to be tolerable, whereas even small values of the seriesresistance (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 waferhas been tested by utilizing a fast majority charge carrier test. Thisprocedure is based on the thermoelectric effect. The method wasemploying a voltmeter and two measurement tips, one of whichcould be heated up to 300

C whereas the other was kept at roomtemperature. It was regulated that by default the following shall beunderstood 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 (forn-doped material- the electrons) would become more kinetic energy.Therefore, the probability of moving away from the heated sourcein direction to the opposite side is increased as well. Thus, potentialdifference is created. Therefore, the voltage measuring device woulddisplay a positive voltage. If p-doped material was measured thiswould have led to the opposite result. The warming of one of thesides was achieved by the usage of a soldering iron unit. To confirmthe measurement setup a test with the help of reference Si sample ofknown doping type was done.

Two Point Measurements

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


+ -

> 0V

n-dopped e- e--defficiency (hot side)

e--excess (cold side)

Measurement device

Figure 3.6: Determination of majority carriers

measurements initially a Keithley 238 High Current Source Measure-ment Unit was used. Thereafter, it has been substituted in favor of aKeithley 4200-SCS Semiconductor Characterization System. Further-more, to investigate hysteresis behavior dual sweep measurementswere utilized. From the comparison of the obtained graphs, a quan-titative conclusion concerning the amount of traps inside the semiconducting material was possible.During measurements several difficulties have been faced, whichwere solved accordingly. For example, the front contact stripes of thecommercially prepared cells were too thin. In addition, stability ofthe samples during measurements was needed. To overcome, theseproblems a "dirty" method of placing thicker top contacts made ofsilver paste was considered as possible solution. In addition, thesamples were placed over bigger Al plate and glued to it by usingsilver paint droplets. Thus, it was insured stability as well as easiercontacting of the back contacts during measurements. The front con-tacts were connected by a continuous thin silver paint stripe near toone of the edges of the sample.The tests were driven in the ranges of -3 V to +3 V. The maximumcurrent was capped to 100 mA corresponding to the limitations ofthe measurement device. The experiments were carried out in darkand under illumination conditions.For this purpose, the WACOMWXS-155S-10,AM1.5G solar simulator has been utilized. The irradi-


ance power was set to Pin = 0, 1 Wcm2 .

Four Point Measurements

To characterize the electrical conductivity of thin-films of Si-nanoparticlesover a Si wafer, after sintering, four point measurements were carriedout. For this purpose, the geometry schematically shown in fig.3.7was 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 currentand voltage values was dependent only on the resistivity of the ma-terial under test and not on the wire resistances (RL) as representedon fig.3.7. Therefore, the four point measurement is a more robustmethod compared to the standard ones.The electrical resistivity, ρ, can be derived as:

ρtotal =U23I1∗ AL

=U23I1∗ dtotal ∗ s

L=

1

σtotal(3.3)

where,A is the area through which current flows.dtotal is the total thickness of the measured wafers is the common contact length between the contact stripesL 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 stronglydepends on the illumination level [8]. To assure, correctness of theresults the measurements were carried out under no light conditionswith the help of the Keithley 4200-SCS Semiconductor Characteriza-tion System.

3.3 scanning electron microscope and energy-dispersive x-ray 39

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

Rtotal

RL

RL

RL

RL

UU

U

Si Wafer

Si-NP

RSi-NP

RWafer

RL RLRL RL

dSiNp

dwafer

Figure 3.8: Four Point Resistance Determination Schematic

flows through both the Si-wafer and the Si-nanoparticles which in to-tal build the equivalent parallel resistance Rtotal. Thus, the resultingresistivity of the nanoparticles layer can be approximated as:

ρSiNp =ρtotal ∗ ρwafer

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

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 theactual 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. Atthe top of an SEM, an electron gun is placed. A positively chargedplate 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]. Thefocusing magnets act like lenses on the beam. At the bottom of theunit, is the stage for the specimen. The SEM, looks at the surface of


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

things. To insure a path for excess electrons the specimen usuallyhas to be platted with a fine coating of metal [36]. Wherever thebeam lands, it excites the specimen to give electrons of its own.Depending on the angle of the surface of the specimen varyingamounts of these secondary electrons are attracted towards thecollector. Some electrons pass through the collector [33]. When thishappens 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 tothe number of electrons collected [36]. The number of electronsdepend on the surface of the specimen when the electron beam hitsit. Another set of electromagnets in the beams path deflects it left toright and up and down. As the beam scans the specimen the outputsignal changes its strength [33]. This signal is then displayed on amonitor. The interior of the microscope is at vacuum to avoid theelectron beam crashing into air molecules. So the specimen has to beinstalled through an air lock. As the scanning size gets smaller theamount of magnification increases [34]. As seen on the schematic, theSEM device is capable of energy-dispersive x-ray spectroscopy (EDX)measurements as well.


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 ata target [37]. Thereafter, they collide with electrons in the investigatedtarget (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 Bohrmodel of the atom. Some transitions leading to observed X-rayemission are indicated. [38]

are knock into a higher energy orbital. When the electrons fall backdown to their lower orbitals, the energy differential is released asX-rays [38]. A detector is used to convert this energy into voltagesignals. As the energy of the X-rays are characteristic of the differencein energy between the two shells, and of the atomic structure of theelement from which they were emitted, this allows the elementalcomposition of the specimen to be measured [39].

4R E S U LT S A N D E VA L U AT I O N

I was taught thatthe way of progress

is neither swift nor easy.

— Marie Curie

In this chapter it will be shown that well-defined silicon particledispersions layers can be realized by spin coating. Furthermore,structural, and electrical quality of such films as BSF layers will beassessed. The results are based on measurements on the laser treatedSi-nanoparticles on different commercially available substrates. Fi-nally, an initial evaluation of the possibility, of using Kapton® foilsis presented.

4.1 semi-ready cells, type i

As a first step, the characteristic behavior of reference solar cellsfrom the company Solland Solar have been determined. Here, undera reference cell is to be understood a semi-ready cell with anti-reflex coating (SiN), front Ag silver grid contacts and back Al layermetalization. A more detailed description of the used substrate canbe found in the methods section (see p.30). For naming purposes thepreviously described semi-ready cell configuration will be definedas Type I.

4.1.1 Reference Cell, Type I

No nanoparticles have been deposited, as well as the cell has not beenlaser treated. A diode like behavior is clearly observed on fig.4.1. Thereverse 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 underdark 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 thecompany Solland Solar have been evaluated. These included, TypeI substrates having anti-reflex coating (SiN), front Ag silver gridcontacts, and fired Al paste, creating an Al:Si eutectic layer used

42

4.2 initial trends 43

-5 0 5 10 15

-0,10

-0,05

0,00

0,05

0,10

Reference Cell by Solland Solarwith Anti-Reflective Coating and Metal Contacts

Dark

Cur

rent

[A]

Voltage [V]

Figure 4.1: IV-Characteristic of Reference Cell Type I (A Solar Cell WithAnti-reflective Coating and Ag Front Contacts Grid, No De-posited Si-nanoparticles, No Laser Treatment)

as BSF material. Neither nano particles have been deposited norlaser treatment has taken place. All six cells IV-characteristics hada similar behavior to the one represented in fig. 4.2. As it can beread 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 powerpoint is given as PMPP = 9, 7mW. From this information, a fill factorof FF = 59, 21% can be computed. Combining the previos data, andsubtracting the front side metal contacts from the total area, aneffective 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 lightscattering method. After a curve fitting, the distribution inside thedispersions has been evaluated to be Gaussian like, with a meanvalue around µ ≈ 100d.nm. and a standard deviation of approxi-mately σ ≈ 9d.nm. The long-term stability of the Si-nanoparticlesdispersions and the tendency of building agglomerates has also beentested by evaluating the particle size after a dispersion has beenmilled as a function of time. On the given plot (see fig. 4.4), the ordi-


-3 -2 -1 0 1-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

0,10

0,12

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

Cur

rent

[A]

Voltage [V]

Illuminated Dark

Rs = 5,9 Ω;Rsh = 2060,19 Ω;

Figure 4.2: IV-Characteristic of Reference Cell Type I with Al BSF (A SolarCell With Anti-reflective Coating, Ag Front Contacts Grid andAl as BSF material, No Deposited Si-nanoparticles, No LaserTreatment)

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

Figure 4.3: Ball Milling and Dynamic Light Scattering Devices


nate represents the mean number of particles inside the dispersion(in percent) that have a diameter equal to the corresponding x-axisvalue. As one can see from figure 4.4, the Si-nanoparticles do nottend to re-agglomerate even after three weeks have passed. It can bealso observed that milling for about 75 min and reaching 3000 rpm(final mixing velocity) is sufficient for the optimal particle size thatcan be reached by utilizing this procedure.

10 100 1000

0

10

20

30

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

Mea

n N

umbe

r [%

]

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-nanoparticleswere spun on a different sized, bigger glass substrate (25× 25mm2).Across this sample seven more or less parallel scratch lines (A to G)were considered. On each of them points located through the centerof the sample and ones closer to the outer edges of the substrate weremeasured (see fig.4.5). In this way local deviations in the Si hightcould be detected and an average height of hSiNp = 650nm(±25nm)for the spun layer was found. Figure 4.5 shows the final outcomeof this work. As a solution to the inhomogeneous layer distribution,mostly pronounced in the center of the sample, a deposition throughthe upper opening of the device was favored. Furthermore, as fastas possible actual spin-coating after the Si puddle has covered thesubstrate was preferred. With this, much more homogeneous layerswere achieved.


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

400

500

600

700

800

900

1000 A - line near left substrate edge B C D - line near the middle E F G - line near right substrate edge

Thic

knes

s [n

m]

Position [cm]

Figure 4.5: Si Layer Thickness vs. Position on substrate

400479558637716795874953

0,0 0,5 1,0 1,5 2,00,0

0,5

1,0

1,5

2,0

y-P

ositi

on [c

m]

x-Position [cm]

Thickness [nm]

Figure 4.6: Si Layer Thickness vs. Position on Substrate, Top View


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

1 2 3 4 5 6

1000

1500

2000

2500

3000

3500 Thickness

Thic

knes

s [n

m]

Number of Spin-Coatings [-]

Figure 4.7: Si layer thickness vs. number of depositions

coatings the resulting layers are tripling their thickness to aroundhSiNpDouble = 2120nm, whereas increasing further the number ofdepositions leads to a saturation of the layer height of aroundhSiNPMulti = 2440nm.The discrepancy in the values concerning the layer thickness betweenfig.4.5 and fig.4.7 can be accounted to the different sample size usedduring the spin-coating procedure. In the case of fig.4.5 a squaresample 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, itcan be inferred that this could have affected the final thicknesses inboth 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;


• 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 thispurpose the 10× 10mm2 glass samples have been spin-coated andthereafter treated with the laser. To cross-check results some sampleshave been prepared and evaluated in different gas media. Typi-cally these were argon and nitrogen. As seen on fig. 4.8 there is agood coincidence for the velocities between 1000 mm/min and 5000

mm/min. Due to the subjective nature of the evaluation of the safe

45

40

45

35[%]

30ensi

ty [

25"Eye" Guidelinese

r Int

e

20

Eye GuidelineOptimal IntensityOptimal Intensity Argon

Las

0 2000 4000 6000 8000 1000015

p y gOptimal Intensity Nitrogen

7

0 2000 4000 6000 8000 10000Scan Velocity [mm/min]

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

regions, some discrepancy for higher velocities is observed. Never-theless, a good separation can be noticed. Glass ablation and layercracks 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 laserintensity regions have been defined, the actual evaluation of highly Bdoped Si-nanoparticles as possible material for BSF could be initiated.Therefore, studies of the optimal laser sintering parameters of the


spin-coated films over cells of Type I were thoroughly investigated.To decide what is the best laser sintering parameter combinationdifferent samples have been prepared. Table 4.1 contains the param-eters used for the evaluation of the Fill Factor versus the differentlaser intensities. The “continuous ↓↑”, designation corresponds toscanning of the sample from edge to edge and backwards in a con-tinuous manner. As it can be seen from the resulting graphs (fig. 4.9

Table 4.1: Sample Preparation Parameters (Fill Factor)Sample Name In Figure Scan Parameters Nano Particles

Reference a1 No Laser Treatment No#0110 a2 1x10%100mm/min Yes#11 a3 1x10%100mm/min Yes#05 a4 1x15%100mm/min Yes#08 a5 1x17%100mm/min Yes#17 a6 1x17%100mm/min Yes

#0622062011 a7 1x18%100mm/min Yes#13 a8 1x18%100mm/min Yes#07 a9 1x19%100mm/min Yes

#06 20.06.11 a10 6(continuous ↓↑)x50%10m/min 1x30%100mm/min 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 inten-sity of Iscan = 15% and a laser scan speed of Vscan = 100mm/min.The corresponding IV-characteristic can be observed on fig. 4.11. Itcan be as well confirmed that this cell shows low series Rs = 9, 75Ωand high shunt Rsh = 689, 54Ω resistance values. Comparing thissample, with the ones processed at other laser intensities and in par-ticular the resulting efficiency values it has been concluded that thiswould possibly represent the optimal parameters for the realizationof 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, takinginto 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 par-asitic effects as well as to confirm reproducibility of the obtainedresults. The total procedure had a variable part (steps designated


0 5 10 15 20 25 30

20

25

30

35

40a4

a5

a2

a1

a3

a7

a9

a10

a7

a7a8

Fill Factor vs Laser Intensity

FF [%

]

Laser Intensity [%]

a9a6

Figure 4.9: Fill Factor vs Different Laser Intensities

0 5 10 15 20 25 30

0

1

2

3

4

5

6

7

a5

a4

a5a2a1

a3

a9

a10

a7

a8

η [%

]

Laser Intensity [%]

Cell Efficiency vs Laser Intensity

Figure 4.10: Cell Efficiency vs Different Laser Intensities


-0,9 -0,6 -0,3 0,0 0,3 0,6 0,9-0,04

-0,02

0,00

0,02

0,04

Rs = 9,75 Ω;Rsh = 689,54 Ω;

Cur

rent

[A]

Voltage [V]

Dark Illuminated

Sample #05 from 22.06.20111xscan 15% @ 100mm/min

Figure 4.11: IV-Characteristic of Sample with Highest Measured Fill Fac-tor (FF ≈ 41%) No 05, 22.06.2011 (A Solar Cell WithAnti-reflective Coating and Ag Front Contacts Grid, De-posited Si-nanoparticles, Laser Treatment:Single Scan, Iscan =15% Vscan = 0, 1m/min)


with a number) and a constant part (steps that have been executedfor any of the created samples). The overall algorithm can be sum-marized 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 pro-tection measure;spin-coating (see p.33);

2. cleaning the edges with a Cotton Swab rinsed in Ethanol orAcetone;

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 couldbe insured that defects and impurities introduced during the initialsawing (original size of 156× 156mm2) of the samples into smallersubstrates (10 × 10mm2) could be overcome. Each sample’s sidehas been grinded with a sanding paper. The average grit diameterparticle 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 toremove only the undesired nanoparticles which have landed on thethin edges after spin-coating has taken place.Grinding (Step 3):Nevertheless, there was still probability that not only the edges werecleaned but as well the outer areas of the back side of the sample.This was not desired. Therefore, a further final grinding of the edgeshas been incorporated.Cleaning with Acetone/Ethanol (Step 4):In addition, some of the samples have been as well cleaned withacetone or ethanol after an actual sintering has taken place. Thus, ithas been assured that the number of nanoparticles which did notsinter i.e. contribute to the doping of the back surface and introducedadditional resistivity of the layer, has been reduced.Additional Measures:To prevent nanoparticle deposition each spin-coated cell front sidewas completely covered with an adhesive tape (mostly from thecompany “Tesa”). Nevertheless, the sample’s edges could not be


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

General Observations

Some general observations in the processing of the cells could beestablished. As previously discussed, the parameters concerning theactual sintering step have been fixed to treating the sample oncewith 15% laser intensity at 100mmmin velocity of the laser scan, usingapproximately 55 l

min argon gas during the procedure. Due to thesmall chamber volume (Vchamber = (1 . . . 2)l), it can be assumed thata quite perfect atmosphere during each sintering step was achieved.Due to the low laser intensity no additional “cooling” phase after sin-tering with argon was needed. It could be observed that the front Agcontacts were melting on the surface of the quartz glass in use. Thiswas cross-checked with further SEM investigations, presented in latersections (see p. 59). Even at low laser intensities, inhomogeneousmorphologies introduced over the base quartz glass from previoussinterings were leading to the breaking of the cell in concideration.Therefore, it can be assumed that temperatures during sintering areat least near the melting point of some of the materials inside thesilver paste, for example Ag (Tmelt = 961.93C [40]), if not higher.Therefore, each side of the quartz glass could be used only once.After cleaning in isopropanol+potassium hydroxide solution, thequartz glasses could be re-used as stable surfaces inside the chamber.To eliminate movements during sintering additional glasses wereused to fix the sample in the chamber. Furthermore, it has beenobserved that the edge at which the laser-scan ends had a differentcolor in all sintered samples.The heat equation is a typical linear differential equation that arisesin the field of physics. The superposition principle can be used tosimplify the computations which describe these type of functions.Therefore, the change in color could be easily explained with thesuperposition of heat distribution inside the substrate. Due to thisphenomenon, at the end of the scanning range more energy was re-ceived than at any other part of the cell, leading to additional opticaland as well structural changes (as verified with SEM investigationssee p.59) in the appearance of the threated layer.Concerning the evaluation of the measured data, the reduced effec-tive area due to metal contacts and additionally introduced Ag stripeshas been taken into account. Each of the resulting front contact areaswas individually measured with the help of a caliper. The resulting


area was then subtracted from the solar’s effective one. Thus, the ac-tual efficiency and the current density of the samples were evaluated.Furthermore, the number of front contact lines perpendicular to thethin Ag hand deposited stripe was almost always kept constant tothree lines.

Initial IV-Characterization

The evaluated combinations are summarized in table 4.2. The sam-

Table 4.2: Combination Nomenclature, (Average Fill Factor)Combination Included Optional Steps:

1 2 3 4

1 X2 X X3 X X X4 X X X5 X X6 X X X7 X X8 X9 X X10 X X X11 X X12 X13 X X14 X

15 Nano Particles Deposited, Not Sintered16 Only Grinded Wafer 1, No Particles Deposited, Not Sintered17 Only Grinded Wafer 2, No Particles Deposited, Not Sintered

ples corresponding to combination 16 and 17, were produced tocheck if there was any difference between the samples from the firstand second wafer (both Type I). For each of the combinations threesamples have been prepared. The outcome of the evaluation of thesample’s measurements can be seen on fig.4.13. As it can be extractedfrom the figure, the highest efficiency has been obtained in the caseof using only grinding the edges of the sample (Step 1).Special attention, has been paid to the samples which have in-

troduced larger deviations in the measured data concerning thecorresponding fill factor value. It has been confirmed, that combi-nations 7, 13 and 14 are having high fill factors when comparing tocombination 1 (FF ≈ 29%). Nevertheless, when taking into concider-ation other characteristic cell parameters (Isc and Voc) represented


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170,100,150,200,250,300,350,400,450,500,55

Voc

[V]

Combination [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0,000

-0,005

-0,010

-0,015

-0,020

Average Open Circuit Voltage and Short Circuit Current

Combination [-]

Ιsc[

A]

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170,150,200,250,300,350,400,450,500,55

FF [%

]

Combination [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0,00,51,01,52,02,53,0

Average Fill Factor and Corresponding Efficiency

Combination [-]

η [%

]

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


on fig.4.12, different final outcome is observed. After extracting thecorresponding efficiency values based on the short circuit currentand the open circuit voltage it could be stated that grinding standalone gave probably the most effective procedure with η1 = 2, 44%.As it can be seen on the given graphs, based on the characteristicparameters Isc and Voc of the threated cells, in all casses, a power con-version ratio, smaller to the one obtained in step 1 is observed. Thecorresponding efficiencies for combinations 7, 13 and 14 are muchlower with η7 = 0, 56%,η13 = 0, 38% and η14 = 1, 19%. Therefore, ithas been concluded, that grinding of the sample’s edges should bethe preferred method for further more detailed investigations.As a next step, to assure reproducibility of the obtained values, mul-tiple samples treated with step 1 (grinding of the sample’s edges) aswell as with other combinational steps have been created.Therefore, the grinding step had been fixed as "constant" one and itwas combined with additional treatments in newly prepared sam-ples. The reason for this was, to easily compare steps which includedit. After many samples have been created, measured and evaluated,getting a pronounced behavior in the evaluated data was in generalnot observed. In addition, comparing combination 16 and 17 it canbe concluded that both (Type I) wafers behaved in a similar manner.Furthermore, no trend in the efficiency versus the use of differenttreatments could be extracted. As this, behavior could be observedas well from the results from the following subsection, no furtherextra data is presented here.

Final IV-Characterizations

Finally, it has been examined closely, just the behavior of the sam-ples when only single of the optional steps have been utilizedwithout making combinations out of them. From each of the sin-gle steps (Grinding (step 1); Cotton bud(step 2); Grinding afterSpin-coating(step 3); Cleaning the layer after sintering with Ace-tone/Ethanol(step 4)) multiple samples have been prepared andmeasured. The naming nomenclature is given in table 4.3. Sometypical, IV-characteristics from differently processed samples can befound in the appendix section (see p. 84-86). It can be seen that thesuperposition principle for the net current in a solar cell does notfully apply. In general, the total induced current under illuminationis obtained by a simple addition between the current in the darkand the light generated current. Nevertheless, this behavior is notdetected in the respective plots. Instead, a shift in the illuminated IV-characteristic to the left can be observed. As suggested by Lindholmet al. [41], the series and shunt resistance must contribute negligiblyto the cell current-voltage characteristics so that dark current coulddescribe the one under illumination apart from a shift on the y-axis.


Table 4.3: Combinations’ Nomenclature, (24.08.2011)Combination Included Optional Steps

1 Grinded (Step 01) and Sintered Samples, No Particles Deposited2 Cleaning the Edges With a Cotton Swab Rinsed in Acetone (Step 02)3 Cleaning the Edges With a Cotton Swab Rinsed in Ethanol (Step 02)4 Reference Cell, Grinded Only (Step 01), No Particles Deposited, Not Sintered5 Grinding of the Samples’ Edges, (Step 03)6 Grinding of the Samples’ Edges, (Step 01)7 Cleaning with Acetone the Samples’ Nanoparticle Thin Film, (Step 04)8 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 ex-plained by the high parasitic resistances.Again, it was expected that repeatability as well a trend in the effi-ciency values could be observed. The respective short circuit currentdensity, open circuit voltage, fill factor, and efficiency are shownon figure 4.14 and figure 4.15, respectively. Due to space considera-tions, a detailed nomenclature concerning each point in the previousgraphs can be found in the appendix section (see B.2). The namingof the combination steps is summarized in table 4.3.As it can be observed extracting a pronounced trend in the givengraphs is difficult. The obtained results tend to be distributed in arandom manner. Therefore, further investigations relating grain sizeand cell behavior have been carried out.

1 2 3 4 5 6 7 80,000

-0,005

-0,010

-0,015

-0,020

Jsc

[A/c

m2 ]

Combination [-]

1 2 3 4 5 6 7 8

0,00,10,20,30,40,50,6

Combination [-]

Voc

[V]

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


1 2 3 4 5 6 7 816

18

20

22

24

26

FF [%

]

Combination [-]

1 2 3 4 5 6 7 8

0,0

0,5

1,0

1,5

2,0

2,5

Combination [-]

η [%

]

Figure 4.15: Fill Factor (FF) and Efficiency (η) vs Different Treatment Com-binations (see table 4.3), Detailed Legend Concerning EachSample (see fig.B.2)

Crystallinity

As suggested by Karpov et al. [42], a micro sized grain boundarydefect affects the response of current significantly. In addition, itsnegative effect can span in a great length. Furthermore, these nonuniformities impact the performance and stability of the diode. There-fore, it has been studied if the crystallinity of the samples underinvestigation could be correlated with the goodness of the measureddiode behavior of the respective cell. For this purpose, samples whichwere treated with the very same steps have been compared. Threedifferent samples (front side) and their respective IV-characteristicgraphs can be seen on fig.B.8, B.10 and B.12 in the appendix sec-tion. Clearly the boundaries between the crystals could be identified.Nevertheless, when comparing the graphs with the respective frontside structures no clear correlation between their number and therespective IV-characteristics could be observed. It seems as if in thefirst front side picture (fig.B.9) the number of boundaries is smallerthan the one observed in the second one (fig.B.11). Furthermore,the IV-characteristics of both graphs follow this trend - better diodelike behavior in case one (fig.B.8), compared to case two (fig.B.10).Nevertheless, when comparing both graphs to a third one for whichthe front side (see fig.B.13) shows as few boundaries as in the firstcase, but much worse diode behavior, dominated by high parasitic


resistances, no final statement can be made.As a final outcome from these and other samples investigations itcould be concluded that no pronounced dependence between crys-tallinity size and diode behavior could been extracted. Therefore,as a possible further reason for the non-ideal behavior diffusivityconsiderations are presented briefly as well (see p.65).As suggested by Karpov et al. [42] a possible solution to this issue isthe promotion of uniformity by thermal heating. Therefore, this wayof annealing the samples could be a solution for improvement of thedisordered structure of the polycrystalline Si layers. By introducinglow intensity treatments of the cell possibly increased and equalizedgrain 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 correlationbetween crystallinity size and diode behavior are carried out. It issuggested that an image manipulation program with pattern recog-nition capabilities that can measure the number of boundaries moreprecisely 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. Theaccelerating voltage of the involved field emission electron sourcewas typically 5 kV, enabling resolutions down to 100 nm. If notexplicitly mentioned otherwise, the micrographs were recorded un-der normal angle in top view (over the surface of the sample). Inaddition, 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 canbe seen on fig.4.16. The represented cell (Type I) has Ag front metalcontacts, as well as an anti-reflective coating. The pictures are takenat the same substrate position in different magnification factors.A semi-toroid like structure can be easily identified on the micro-

graph. Therefore, when Si-nanoparticles are spin-coated over theback side of the cell, they retain the hills and valleys structure of thebulk silicon.


1 µm 1 µm

10 µm 10 µm

Figure 4.16: Semi-ready Solar Cell with Anti-reflex coating and Pre-deposited Front Side Ag contacts; Uncoated Backside SurfaceView of the Sample. All micrographs are taken at the sameposition (Note: Difference in Magnification Factor - ZoomingOut from 1 to 10µm)


Treated Cell and Si-nanoparticles Morphology

As presented in fig.4.17, typical nano particle structures over the backside of a cell can be distinguished. The structure of grown in a hotwall reactor particles is highly characteristic. These particles exhibitan elongated and branched structure and often consist of severalrandomly oriented arms or side chains. Nevertheless, a continuous,well-defined thin-film layer is achieved after spin-coating [8]. There-fore, areas over which Si-nanoparticles have been deposited can beeasily recognized. It can be observed that they follow the hills andvalleys introduced by the substrate over which they are spin-coated.In conclusion, it can be stated that if the introduced energy duringsintering was not sufficient to molten the Si-nanoparticles with theback surface of the solar cell, similar structures as the ones observedin fig.4.17 shall be expected.

1 µm100 nm

10 µm1µm

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 atthe Same Possition

Furthermore, additional pictures of the same solar cell were exam-ined (see fig.4.18 and fig.4.19). The represented sample has been6 times preheated (Ipreheat = 50%@Vpreheat = 10m/min) and oncean actual sinter scan has taken place (Isintern = 30%@Vsintern =1m/min). Here (see fig.4.18) areas which can be clearly mapped


Sample 20110901 ‐ 08

Scan unbehandeltScan unbehandelt –hochreflektierend – unbehandelt

100 µm

Figure 4.18: Picture of the Characteristic Brownish Color Area after Sinter-ing

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 (Untreated-Treated-Untreated) Regions (Note: Same Magnification for allpictures)


to regions which are ordered in untreated-treated-untreated man-ner can be seen. In addition, the corresponding SEM pictures (seefig.4.19) justify this arrangement. When scanning the sample, start-ing at one of its edges, first typical Si-nanoparticle structures can beobserved which at some point (highly reflective area) have moltenand thereafter again an untreated region can be recognized (near tothe middle) which continuous to the end of the sample as seen infig.4.18.More convincing this behavior can be observed when looking closelyat the surface of an additional sample with similar parameters. Inthis case they were a laser intensity of Ipreheat = 50% and a scanvelocity of Vpreheat = 10m/min, followed by a single sintering scanof Isintern = 30% @ Vsintern = 0, 2m/min. Looking closely at fig.4.20

it can be indeed stated that no Si-nanoparticles can be differenti-ated anymore. The given picture suggests that in the dark areas ofthe micrograph melting of the Si-nanoparticles with the bulk Si hastaken place. The resulting film is not continuous and thus cannot beused for applications where lateral transport through the silicon isrequired. The rest of the sample’s surface retains the morphology ofan untreated one with unchanged nanoparticles spin-coated over it.An interesting property of the highly reflective area is its completesmoothness even when examined under maximum magnification ofthe SEM device. After pictures of the backside with sintered nanopar-ticles have been evaluated it can be concluded that only a smallfraction of the sample’s surface has actually received enough energyso that the nanoparticles and the bulk silicon layer could have meltedin each other.Furthermore, investigations of the two regions were undertakenby cross-sectional sample pictures. The highly and the region withlower reflectiveness have been compared. It is important to noticethat, under the region which shows highly reflective characteristic,an approximately 5µm layer can be observed (see fig.4.20). Fromthis it can be concluded, that this highly reflective layer area mightconsist of the parameters concerning doping with the help of laser il-lumination of highly doped with boron Si-nanoparticles. Therefore, agood starting point for further investigations in this direction wouldbe 6 times preheating step with laser intensity of Ipreheat = 50% andscan velocity of Vpreheat = 10m/min, followed by a single sinteringscan of: Isintern = 30% @ Vsintern = 0, 2m/min, corresponding to theparameters of the sample observed in fig.4.20.Thus, finer scanning of the optimum parameters leading to the de-sired layer structure can be studied. Therefore, to facilitate featurework in this direction, additional samples for further SEM investiga-tions which shall be carried out have been fabricated. Intentionally,they were constructed having the same parameters as in table 4.4.


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

Furthermore, the reasons for high parasitic resistances observed inmany of the previously evaluated data was investigated with thehelp of the SEM investigations. It was confirmed that no nanoparticleshave melted for the rest of the sample’s area. Therefore, it can beconcluded that unsintered nano-particles were the reason for thehigh series resistances observed. This was cross-checked with thehelp of conductivity measurements and their corresponding valuesfurther through the course of this work.

4.2.7 Conductivity, Laser Parameters and Color Considerations

As previous works (paper in progress) concerning the conductivity ofthe laser sintered layers have shown, a silver like color corresponds tobetter layer conductivity. Thus, a change in laser parameters towardsthis behavior was made. Therefore, obtaining silver in color surfaceswith only single actual sintering step have been investigated. Assuggested by Lechner [8] the detailed number of laser scans was notfound to be a critical parameter, and no systematic differences couldbe observed. Therefore, their number was kept as low as a singlesintering step. Before the actual sintering, an additional six times fastpre-heating procedure (10 000 mm/min, 50% laser power) has been


incorporated. Many different cells, with the previously mentionedoptical requirement were achieved under different laser paramaters.The silver like color can be observed on pictures C.1, C.2 and C.3 inthe appendix section. The corresponding process parameters can besummurized 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[%] 29[%]

10000[mm/min] 1000[mm/min]

04 50[%] 39[%]

10000[mm/min] 1000[mm/min]

06 50[%] 40[%]

10000[mm/min] 1000[mm/min]

08 50[%] 41[%]

10000[mm/min] 1000[mm/min]

10 50[%] 42[%]

10000[mm/min] 1000[mm/min]

12 50[%] 43[%]

10000[mm/min] 1000[mm/min]

14 50[%] 44[%]

10000[mm/min] 1000[mm/min]

16 50[%] 45[%]

10000[mm/min] 1000[mm/min]

18 50[%] 46[%]

10000[mm/min] 1000[mm/min]

4.2.8 Diffusion of Silver in Silicon Investigations

The diffusion coefficient in solids at different temperatures is oftenfound to be well predicted by the help of an Arrhenius equation ofthe form:

D(T) = D0 × exp(−Ea

κBT

), (4.1)

,whereD is the diffusion coefficientD0 is a pre-exponential coefficientEa is the activation energyT is the absolute temperatureκB = 8.6173324(78)× 10−5 eVK is the Boltzmann constantFor the case of diffusion of Ag in Si the forms summarized in table4.5 have been suggested.


Table 4.5: Diffusivity of Ag in Al

Temperature range (C) D0(cm2/s) Ea(eV) Mechanism Reference

1100-1300 2× 10−3 1,59 Interstitial [43, 44]1100-1300 2× 10−3 1,6 Interstitial [45, 46]

Not specified 6× 10−5 1,15 Not specified [47]

Energy-Dispersive X-ray Spectroscopy

Energy-dispersive X-ray spectroscopy was used for the elementalanalysis of several samples, and in particular the behavior of thetop Ag contacts after sintering has taken place. The materials thathave been found can be seen on fig.4.21. Normally, in the total firing

1 µm1 µm

O

NCTi

SiAg Zn

Figure 4.21: EDX on the Front Surface Side of the Sample; Semi-ready SolarCell with Anti-reflex Coating and Pre-deposited Front Side AgContacts (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]. TheEDX analysis showed that this layer consists of the elements zinc (Zn)and oxygen (O) as well. Furthermore, it can be seen that the topcontacts still have good contact to the slightly (ND = 1× 1013cm−3

[9]) n-doped (with P atoms) Si-layer. Nevertheless, due to the hightemperature during sintering, it is highly probable that a diffusionof Ag contacts in Si n-type region takes place. As suggested by Greenet al.[17], a wavelength of λ = 810nm (near the one of the infra-red


laser in use) corresponds to an absorption depth of dabsorb = 12, 9µm.Therefore, the power introduced, would heat efficiently not only theabsorbing layer, as the thickness of the spin-coated Si-nanoparticleswas estimated around hSiNP = 0, 65µm, but part of the substrateas well. In addition, the front Ag contacts were observed on topof the base quartz glasses after each laser treatment. Therefore, atemperature of at least Ag (Tmelt = 961, 93C [40]) can be assumed.Furthermore, as previously discussed, the temperature in the sub-strate is superimposed during sintering. As the n-type layer is only0,3 to 0,4 µm thick, temperatures in the range T = (1074 . . . 1115)Cmay lead to a decremental effect to the solar cells when consider-ing the diffusivity model (see p. 65) suggested by Smith [47]. If weconsider the best case scenario and utilize the specially investigatedtemperature region model suggested by Jones [45] we could go toa slightly increased range of about T = (1111 . . . 1141)C. Exceedingthese temperatures during sintering increases the probability of dif-fusion of the Ag front contacts through the complete n-type layer.Furthermore, from the discussed (see section 4.2.8 and table 4.5) mod-els, it can be found that at the melting point of Si (Tmelt = 1414

C)

corresponds a diffusivity of at least D = 2, 201µm2

s in the case of theparameters suggested by Smith [47]. If we extrapolate the modelsuggested by Boltaks [44] to the same temperature (see fig.4.22) thenin the worst case D = 3, 557µm

2

s . In case of a sample (10× 10mm2)

800 1000 1200 14000,01

0,1

1

10

2*10-3*exp-1,59/(κb*T)*10-8 μm2/s

2*10-3*exp-1,6/(κb*T)*10-8 μm2/s

6*10-5*exp-1,15/(κb*T)*10-8 μm2/s Extrapolation of graph

Diff

usio

n C

oeffi

cien

t [μm

2 /s]

Temperature [°C]

Diffusion Coefficient ofSilver in Silicon vs Temperature

[43, 44][45, 46]

[47]

Figure 4.22: Diffusion Coefficient of Ag in Si

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

4.3 semi-ready cell, type ii 68

tscan = 0, 6s is needed. When introducing more energy inside theSi-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 oftemperature inside the substrates, as well as the n-type thickness ofonly 0,3 to 0,4µm, it can be reasoned out that it is possible that a dif-fusion 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 nat-urally no ideal diode like behavior should be expected. Therefore,the reasons for low shunt resistances can be accounted to a damageintroduced to the p-n junction of the cells during sintering.Considering the previously described behavior, extracted from theEDX investigations of the front contacts, it can be concluded thatsemi-ready cells from Type I, are not a good candidate for furtherexperiments. Therefore, the top metalization had to be depositedafter the sintering step has been concluded, so that the probabilityof diffusion of the front contacts is eliminated.In this subsection, it was argued that a possible explanation of thenon-ideal behavior of the semi-ready cells from Type I can be foundwith the help of different diffusivity models of Ag in Si. As a sum-mary, it can be stated that, it is highly probable that the temperatureduring sintering is at least in a range at which diffusion of the Agfront contacts through the complete n-type layer is possible. There-fore, a different cell structure shall be preferred. For this purpose,semi-ready cells of Type II were studied and their behavior is pre-sented in the following subsection.

4.3 semi-ready cell, type ii

As a possible solution, to previously observed limitations a new typeof cell was introduced. For naming purposes they are labeled assemi-ready cells from Type II. Under this term, cells consisting of noanti-reflex coating and no metal contacts shall be understood. Clean-ing and spin-coating of the samples was performed as describedin previous sections (see p.32 and p.33). Major difference, duringsintering of the deposited Si-nanoparticles, using this type of cell wasthe possibility of reaching much higher laser intensities (I ≈ 70%)before cracks could be observed. Therefore, it can be concluded thatthey should be the preferred choice when much higher laser inten-sities during sintering without sample breakage or ablation of theSi-nanoparticles layer shall be needed. Since, no contacts were avail-able during laser treatment, no possibility of metal diffusion existed.Therefore, no constant quartz glass change was needed anymore. Inaddition, by using this type of cells, it was cross-checked if damage


of the pn-junction was caused by diffusion of the top contacts grid.Before IV measurements were carried out Al ≈ 200nm contacts onboth sides were evaporated.

4.3.1 Electrical Properties of Type II Cells

As a next step, samples from Type II cells with Si-nanoparticles lasertreated surfaces (except for a reference cell) have been created. In ad-dition, back and front side Al contacts have been evaporated. A fixedpre-heating (6scans, Ipreheat = 50%@VpreHeat = 10000mm/min)and an actual scan (1scan@Vscan = 1000mm/min) at variable inten-sities were compared. Some characteristic IV-graphs can be observedin fig.4.23 and fig.4.24.

-3 -2 -1 0 1 2-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

0,10

0,12

Rs = 18,88 Ω;Rsh = 1204,54 Ω;

15% 1scan with Si-nano Particles

Cur

rent

[A]

Voltage [V]

Dark Illuminated

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

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


-3 -2 -1 0 1 2

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

0,10

0,12

Rs = 23,38 Ω;Rsh = 76,21 Ω;

Dark Illuminated

35% 1scan with Si-nano Particles

Cur

rent

[A]

Voltage [V]

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

These conciderations, lead in the case of fig.4.24 to the values ofRs = 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 consid-erably degrading the efficiency of the cell. Therefore, the obtainedshunt resistance value can be in general concidered as tollerable,whereas the series one is decrementing the efficiency of the cellseverely.

4.3.2 On-Off Current Ratio Comparisons

On fig. 4.25, the results of on-off current ratios measurements fordifferent laser intensities are represented. The voltages at whichthe values of the dark cell characteristic behaviors were comparedwere at -1V and +1V. With increasing the laser intensity, the non-ideal cell behavior could be observed more pronounced. This meansthat the negative influence of parasitic resistances has increased. Onthe other hand, good values can be extracted for low laser intensi-ties. Therefore, it can be concluded that when slightly heating (atlow intensities) the cells, possibly some build-in defects (e.g. grainboundaries) 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-


15 20 25 30 35 40 450,01

0,1

1

10

100 With Particles - Initial Study from 13.09.2011 With Particles - Samples from 16.09.2011 Without Particles - Samples from 16.09.2011

On-Off Current Ratio - Samples With and Without Nanoparticles

Rat

io [+

1/-1

]

Laser Intensity [%]

Figure 4.25: On-Off Ratio, Comparison of Cells With and Without Si-nanoparticles

tensities, can be explained with an increase of the probability ofdamaging the cell’s structure. This phenomenon can be related to thecorresponding rise in temperature, which after surpassing a certainthreshold value does not lead to the removal of build-in defects butrather harms the pn-junction (e.g. R+1/−1 = 1, 77, @ laser intensityI=45%).In addition a comparison between cells with and without nanoparti-cles at 15% and 25% has been carried out see fig.4.25. As expectedfrom previously discussed SEM investigations (see p.61) at low in-tensities the Si-nanoparticles would not melt, thus leading to higherresistivity of the layer and introducing lower on-off ratios. At slightlyhigher intensities, the probability that there are already some regionswith melted particles on the cell, leads to higher values in favor tothe threated samples.Since, all important cell characteristics can be combined in the powerconversion ratio parameter, an efficiency comparison for higher laserintensities has been carried out as well (see fig.4.26). Combining theideas that a highly reflective area represents a successfully dopedBSF region with the given plot, leads to the conclusion, that the opti-mal laser parameters should lie somewhere in the region betweenIscan = (29 . . . 40)%, @Vscan = 1000mm/min with a pre-heating stepof six scans with Ipreheat = 50%, @Vpreheat = 10000mm/min.


0 10 20 30 40 50 60 700,0

0,5

1,0

1,5

2,0

2,5

3,0

Laser Intensity [%]

Effi

cien

cy [%

]

Efficiency vs 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 threatedSi-nanoparticle layers are conductive, contacts of the type schemat-ically given on fig.3.7 for four point measurements were prepared.Furthermore, with these experiments the correctness of the SEM in-vestigations (see p.59) could be cross-checked.The four point measurements have been carried out on samples hav-ing the same parameters as the ones for the fine SEM investigations,but at different substrate. Namely these were, six pre-heating stepswith Ipreheat = 50%,Vpreheat = 10000mm/min and an actual scan ofIscan = (29; 39 . . . 46)%, @Vscan = 1000mm/min (see table4.4). The Si-nanoparticles have been spin-coated on intrinsic Si-wafers, and thensintered. The layer thickness of the Si-nanoparticles was measuredwith the help of the profilometer to be dSiNp = 350nm(±25nm). TheSi-wafer had a thickness of dwafer = 525µm. The determination ofthe resistivity of the sintered nanoparticles was carried out with thehelp of the four-terminal sensing method. Therefore, for the compu-tation of the total layer dark conductivity ρtotal can be evaluated asfollows:

ρtotal =U23I1∗ AL

=U23I1∗ dtotal ∗ s

L(4.2)

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


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

25 30 35 40 45 50 5510-4

10-3

10-2Total Conductivity vs Laser Intensity

Con

duct

ivity

[Ω−1

cm−1

]

Laser Intensity [%]

Figure 4.27: Conductivity (σtotal) of Si-nanoparticles Spin-coated on Intrin-sic Si-wafers Irradiated for Different Laser Intensities

ues (σtotal 6 2, 57× 10−3 Scm) are comparable with the conductivityof nanoparticle-coated Si-wafer pieces not treated with an IR-laser(σNoLaser 6 3, 52× 10−3 Scm) reported in literature [31] (see fig.4.28).In addition, the conductivity of the Si-wafer itself has been measuredto be σwafer = 0, 0137 S

cm .During measurements current might flow through the intrinsic waferas well. Therefore, calculations for obtaining the conductivity of theSi-nanoparticles only, based on the suggested model described in themethods section (see p.39) have been carried out. Since the evaluatedvalues were in the negative range, it can be concluded, that thatmodel, does not fully resemble the actual layout.As already found by SEM investigations, it can be stated that, sin-gle scans with low intensities are not sufficient for melting most ofthe deposited Si-nanoparticles. Furthermore, none of the spin-coatedsamples was treated with a hexafluorosilicic acid step. As reported inliterature [8] even after the dispersion and milling process in ethanol,the silicon nanoparticles exhibit an oxide shell. Since silicon oxideis an isolator with a very large band gap of Eg ≈ 9eV [8], the oxideinterfaces is equivalent to high energy barriers for the electronictransport. The main reason for the high resistivity can be found in

4.4 kapton® substrates 74

Argon N2 Si Si+Np (no laser) Al10-3

10-2

10-1

100

5x105106

Con

duct

ivity

[Ω-1cm

-1]

Parameters

Conductivity of samples treated in Ar, N2,

without laser treatment with Si-NP spincoated only

Comparisson: Al(data from Handbook of Chemistry and Physics 90th ed.)

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

the numerous oxide interfaces between the loosely interconnectedsilicon nanoparticles in the only coated layers.Based on the previous considerations, it is suggested for furthersamples that, before laser treatment takes place, the spin-coatedSi-nanoparticles are etched so that the native silicon surface oxide isremoved with the help of piranha solution or hydrofluoric acid. Thismight be identified as a crucial technological step in achieving betterconductive films after laser annealing.As a summary, it can be stated that, the conductivity of the lay-ers depends on the extent in which the deposited Si-nanoparticleshave sintered. It was proved that single, low intensity scans are notsufficient for melting them over the substrate. Therefore, a combina-tion of higher number of steps and illumination intensities shall bepreferred. Furthermore, an additional chemical cleaning which willreduce the resistivity of the layers might be incorporated.

4.4 kapton® substrates

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


been confirmed that it is possible to spin-coat the Si-nanoparticlesover 10× 10mm2 Kapton® films. The Kapton® films were placedover UV Quality quartz glass substrates. For stability during actualdepositions, larger glass substrates were used. The substrates hada square shape, 15× 15mm2, and thickness of 1 mm. As a first stepeach of the glasses was carefully cleaned so that oils and organicresidues are removed. By not completely blow-drying the glass sub-strates, it was assured an excellent adhesion of the Kapton® filmsduring spin-coating. Thereafter, the thin (dKapton = 0, 1mm) foilsof Kapton® have been sintered by using different laser parameters.Nevertheless, even at low intensities the thin Kapton® films werestarting to shrink and bend during sintering. Different, samples canbe 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 10% 2000

05 8% 2000

09 9% 2000

03 13% 2000

02 18% 2000

It is highly unprobable that nanoparticles would have melt un-der these parameters. Therefore, the possibility of pre-shrinking theKapton® films by thermal heating, and thus keeping them stableduring actual sintering was examined. For this purpose, differenttemperatures and durations of a hot-plate appliance were compared.As an outcome of this, no shrinkage of the Kapton® substrates could


be observed. Most probably the maximum temperature used (cappedby the heating element) (TMaxused ≈ 300C) is still under the materialdependent one (TKapton = 450C [48]).A possible idea for future experiments is the heating with a furnaceto higher temperatures as a method for the pre-shrinking step. Fur-thermore, it is important that this material would be investigatedfor example with a laser with shorter wavelength used in pulsedmode. This opportunity can be further studied with an ultraviolet(UV) laser. For example, the ATLEX Si 300 (λ(KrF) = 248nm) havinga pulse duration of 4-6 ns and a maximum repetition rate of 300 Hzwould be a suitable candidate. According to Green et al. [17], thiswould correspond to an absorption depth of dabsorb = 5, 43nm. Dueto the short pulse duration, the power introduced, would heat effi-ciently only the absorbing layer, as the thickness of the spin-coatedSi-nanoparticles was estimated around hSiNP = 650nm(±25nm). Insuch a way during sintering much lower temperatures inside thesubstrate can be expected. Furthermore, this would allow a muchwider variety, including plastic foils, to be used.

5C O N C L U S I O N A N D F U T U R E W O R K

Every end is a new beginning.

— Proverb

In this thesis, the properties of boron (B)-doped silicon (Si)-nanoparticles as possible material for back surface field (BSF) were stud-ied. The dispersions of nanoparticles, in combination with a lasertreatment, have been evaluated for possible use in photovoltaic thin-film applications. First, the size and stability of the particles insidethe dispersion was determined. The particle size distribution insidethe dispersions has been evaluated to be Gaussian like distributed,with a mean value around µ ≈ 100d.nm. and a standard deviationof approximately σ ≈ 9d.nm. The Si-nanoparticles shown a stablebehavior - they did not tend to re-agglomerate even after three weekshave passed. In addition, the material behavior concerning spin coat-ing has been examined. When spin-coating on square substrates(a = 25mm) an average height of hSiNp = 650nm was found. Fur-thermore, it was noticed that after two spin-coatings the resultinglayers are tripling their thickness to around hSiNpDouble = 2120nm,whereas increasing further the number of depositions leaded to an av-erage saturation of the layer height of around hSiNpMulti = 2440nm.As a result, smooth and compact thin films of Si-nanoparticles wereobtained.Moreover, different structures were implemented. At first, a semi-ready cell with an anti-reflex coating (SiN), front Ag silver gridcontacts and back Al layer metalization was used. In addition, asecond type of semi-ready cells was employed. The major differencewith respect to the previously described cells was that they consistedof no anti-reflex coating and no metal contacts. Both types of cellswere provided by the company Solar Solland. The total thickness ofthe samples was measured to be 250µm. Furthermore, cost-efficienttechnologies that can be utilized such as processing on thin polymerfoils has been briefly investigated. For this purpose, due to their highthermal stability Kapton® films (10× 10mm2) were employed.Throughout this work, different technological problems were facedand were accordingly solved. Combinations of different contact ma-terials were examined and their feasibility was studied.The studies of current-voltage (I-V) relationships of the semi-readystructures (with and without anti-reflex coating) has given use-ful information about the behavior of the cells. For some of the

77

conclusion and future work 78

laser treated semi-ready structures from Solland Solar with anti-reflective coating, a fill factor of FF ≈ 41%, short-circuit currentIsc = −28, 76mA, an open-circuit voltage Voc = 0, 53V , power atmaximum power point of Pmpp = 6, 4mW and an cell efficiency ofaround η ≈ 6, 38% was obtained. In the case of a semi-ready struc-ture without anti-reflective coating, the best result was comprising ofa fill factor of FF ≈ 27%, a short-circuit current Isc = −16, 81mA, anopen-circuit voltage Voc = 0, 49V , power at maximum power pointof Pmpp = 2, 21mW and an cell efficiency of around η ≈ 2, 95%.Furthermore, the morphology of cell and the particles were studiedusing SEM measurements. It was concluded that during laser treat-ment Ag is dissolving into the n-region of the cell, thus breaking thepn-junction. In addition, it was confirmed that only small areas ofthe back surface have sintered at the intensities used (I 6 30%).An important result of this work, measured by the four-terminalsensing method, was the verification of the conductivity (σ) ofthe Si-nanoparticles in use. The Si-nanoparticles have been spin-coated on intrinsic Si-wafers, and then sintered with the help ofthe infra-red laser (λ = 808nm, Pmax ≈ 452W). The layer thick-ness of the Si-nanoparticles was measured with the help of theprofilometer to be dSiNp = 350nm(±25nm). The Si-wafer had athickness of dwafer = 525µm. An average value of σSiNPaverage 62, 57× 10−3 Scm has been evaluated for samples treated with differentlaser 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 correspondwell to the data given in literature [31] in the case of particles treatedwith no laser. Therefore, it can be clearly concluded, that a single scanis not sufficient to bring enough energy which would completelysinter the deposited Si-nanoparticles.With the help of SEM measurements, an approximately 5µm thicklayer was observed under regions characterized by a highly reflectivesurface. In conclusion, it was confirmed that the realization of smallarea regions with back doping using boron-doped Si-nanoparticlesand a laser operated in the infra-red wavelength range is possible. Afurther study in this direction, could be the verification of the laserparameters which correspond to the observed highly reflective area.When comparing this thickness with typical commercially availablecell BSF heights (hBSF = 0, 8µm [2]) it can be argued that the obtainedlayer might be even too thick when optimal efficiency parameters areconcerned. In general, the life time in such type of regions tends to bevery short. Considering that the layer is heavily p+doped, it can beinferred the volume of low life-time material where minority carriersmay recombine is increased. Therefore, the optimal BSF thicknesswhich takes into account this considerations should be calculated in


future works.In addition, it is suggested that rear contacts are reduced in size asin 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 windowsof the cell should be coated with nanoparticles. Thus, only verysmall contact areas would be needed. Due to this, the total area ofthe contact’s would be a small fraction of the total back side surface.Therefore, the performance of the cell would be improved by shut-ting off some recombination processes. Furthermore, by additionalpassivation low surface recombination velocity can be achieved. Inother words, the rate of recombination between electrons and holesat the surface of the semiconductor would be decreased. In addition,by designing the thickness of the oxide in an optimized way, effi-ciency of the cell can be increased.Due to the limitations imposed by the Ag front contacts grid (only lowlaser intensity possible, high parasitic resistances observed) differenttype of semi-ready cells was preferred. They were involving no pre-ready anti-reflex coating or metal contacts. It was found that this typeof cells, can withstand much higher laser intensities (I 6 70%) duringsintering without sample breakage or ablation of the Si-nanoparticleslayer. By utilizing samples without front contact grids during lasertreatment, the influence of parisitic resistances was efficiently pre-vented (Rs < 19Ω,Rsh > 1200Ω). As an outcome of this work, it canbe suggested that a structure having initially no anti-reflexcoatingor contacts should be used as for further experiments utilizing the


IR laser system. Such an arrangement has proved itself as an ad-vantageous design. As a good starting point a six times pre-heatingstep (Ipreheat = 50%,Vpreheat = 10000mm/min), and an actual scanin the range of Iscan = (29 . . . 40)%, @Vscan = 1000mm/min is sug-gested.Possibility for future development is the implementation of the sug-gested methods for thin-film substrates such as Kapton®. Initialstudies in this direction were carried out. Nevertheless, even at rel-atively low intensities (I 6 8%) bending and melting of foils wasobserved.Therefore, it can be concluded that for the semi-finished(Type I) products of Solland Solar as well as for thin-film foil sub-strates such as Kapton a different laser type should be preferred. Abetter candidate for this purpose would be a pulsed UV-Laser treat-ment, which would reduce the thermal load during the sintering step.In addition, realization of solar cells made of pure Si-nanoparticlesis suggested. A combination of these approaches would provide anadditional set of observations which could be used for the furtherevaluation of the Si-nanoparticles.

Part II

A P P E N D I X

AP R O G R A M C O D E

%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

BA D D I T I O N A L G R A P H S

2 3 4 5 6 7 80,0

0,5

1,0

1,5

2,0

Efficiency vs Combination

η [%

]

Combination [-]

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

Figure B.1: “Slim” Version - Efficiency (η) vs Different Treatment Combina-tions (see table 4.3)

83

additional graphs 84

1 2 3 4 5 6 7 8

0,16

0,18

0,20

0,22

0,24

0,26FF

[-]

Combination [-]

Fill Factor vs Combination 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 Deposited, #03 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 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 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 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 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 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 Cleaning with Ethanol the Sample’s Si Nanoparticle Thin Film, (Step 04), #01 Cleaning with Ethanol the Sample’s Si Nanoparticle Thin Film, (Step 04), #02 Cleaning with Ethanol the Sample’s Si Nanoparticle Thin Film, (Step 04), #03

Figure B.2: Legend for Samples Evaluated on 24.08.2011

-3 -2 -1 0 1 2 3

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08Cotton Swab (Ethanol) Sample #03

Cur

rent

[A]

Voltage [V]

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

Figure B.3: IV-Characteristic (Step 2-Cleaning the Edges With a CottonSwab Rinsed in Ethanol, Sample No 03)


-3 -2 -1 0 1 2 3-0,04

-0,03

-0,02

-0,01

0,00

0,01

0,02

0,03

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

Cur

rent

[A]

Voltage [V]


Figure B.4: IV-Characteristic, Reference Cell (Grinded Only, Step 1, NoParticles Deposited, Not Sintered, Sample No 02)

-3 -2 -1 0 1 2 3

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

0,10

Grinding of the sample’s edges Sample #05

Cur

rent

[A]

Voltage [V]


Figure B.5: IV-Characteristic (Step 3-Grinding of the Sample’s Edges, Sam-ple No 05)


-3 -2 -1 0 1 2 3

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

0,10

Grinding (Step 1) Sample #04

Cur

rent

[A]

Voltage [V]

Illuminated(1) Dark(1) Illuminated(2) Dark(2) Illuminated(3)

Figure B.6: IV-Characteristic (Step 1-Grinding of the Sample’s Edges, Sam-ple No 04)

-3 -2 -1 0 1 2 3

-0,04

-0,02

0,00

0,02

0,04

0,06

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

Cur

rent

[A]

Voltage [V]


Figure B.7: IV-Characteristic (Step 4-Cleaning with Ethanol the Sample’s SiNanoparticle Thin Film, Sample No 03)


-3 -2 -1 0 1 2 3

-0,10

-0,05

0,00

0,05

0,10

Cotton Swab (Acetton) Sample #04

Cur

rent

[A]

Voltage [V]

Illuminated(1) Dark(1) Illuminated(2) Dark(2) Illuminated(3) Dark(3)

Figure B.8: IV-Characteristic (Step 2-Cleaning the Edges With a CottonSwab Rinsed in Acetone, Sample 04)

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


-3 -2 -1 0 1 2 3-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06Q-tip (Acetton) Sample #05

Cur

rent

[A]

Voltage [V]

Illuminated(1) Dark(1) Illuminated(2) Dark(2) Illuminated(3) Dark(3)




-3 -2 -1 0 1 2 3

-0,040

-0,035

-0,030

-0,025

-0,020

-0,015

-0,010

-0,005

0,000

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

Cur

rent

[A]

Voltage [V]

Illuminated (1) Dark(1) Illuminated(2) Dark(2) Illuminated(3) Dark(3)



CS 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 (pa-rameters)

Number: Pre-Heating Step 6 scans: Sintering Step 1 scan:

13 50[%] 40[%]

10000mm/min 2000mm/min

14 50[%] 40[%]

10000[mm/min] 1000[mm/min]

15 50[%] 40[%]

10000[mm/min] 1000[mm/min]

16 50[%] 45[%]

10000[mm/min] 1000[mm/min]

17 50[%] 50[%]

10000[mm/min] 1000[mm/min]

90

sample pictures and tables 91

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 (pa-rameters)

Number: Pre-Heating Step (6 scans): Sintering Step(1 scan):

11 50[%] 30[%]

10000[mm/min] 175[mm/min]

13 50[%] 30[%]

10000[mm/min] 200[mm/min]

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

B I B L I O G R A P H Y

[1] F. J. Tegude. Festkörperelektronik Skript zur Vorlesung, Lecture.2001.

[2] M. Lundstrom. Lecture 1: Introduction to Solar Cells; Introduc-tion 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 Passi-vation Layers, Conference. 2007.

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

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

[6] O. N. Hartley, R. Russell, K. C. Heasman, N. B. Mason, andT. M. Bruton. Investigation of thin aluminium films on therear of monocrystalline silicon solar cells for back surface fieldformation, 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 Applica-tions. PhD thesis, Walter Schottky Institut, 2008.

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

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

[11] J. J. Quinn and K.-S. Yi. Solid State Physics: Principles and ModernApplications. 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 princi-ples. McGraw-Hill, 2003.

[15] A. Schulz. Plasmapolymerisierte Barriereschichten aus einer skalier-baren Mikrowellen-Plasmaquelle für flexible Solarzellenmodule. PhDthesis, Universität Stuttgart, 2005.

92

bibliography 93

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

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

[18] W. Shockley and H. J. Queisser. Detailed Balance Limit ofEfficiency 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 Wis-senschaftsverlag, 1993.

[23] D. Yu, S. Lee, and G. S. Hwang. On the origin of Si nanocrystalformation 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 photoluminescenceproperties of Si nanocrystals by simultaneously doping n- andp-type impurities. Appl. Phys. Lett., 85, 2004.

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

[26] J. R. Heath. A liquid-solution-phase synthesis of crystallinesilicon. 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 bya solution route. J. Am. Chem. Soc., (121), 1999.

[28] E. Werwa, A. A. Seraphin, L. A. Chiu, C. Zhou, and K. D. Kolen-brander. Synthesis and processing of silicon nanocrystallitesusing 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. Camp-bell. Formation of highly uniform silicon nanoparticles in highdensity silane plasmas. J. Appl. Phys., 94:2277, 2004.

http://www.solarbotics.net/starting/200202_solar_cells/200202_solar_cell_types.html

http://www.solarbotics.net/starting/200202_solar_cells/200202_solar_cell_types.html

bibliography 94

[30] H. Wiggers, R. Starke, and P. Roth. Silicon Particle Formationby Pyrolysis of Silane in a Hot Wall Gasphase Reactor. Chem.Eng. Technol., 24:261 – 264, 2001.

[31] K. Lamine. Realisierung funktionaler Si-Dünnfilme durchLaserkristalisation von nanopartikulärem Silizium, BachelorThesis. 2012.

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

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

[34] J. Goldstein, D. E. Newbury, D. C. Joy, and C. E. Lyman. Scan-ning 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 Labo-ratory Workbook. Springer Verlag, 1990.

[36] P. Echlin. Handbook of Sample Preparation for Scanning ElectronMicroscopy 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 Anal-ysis in the Electron Microscope (Microscopy Handbooks). Bios Sci-entific Publ, 2003.

[39] K. Tsuji, J. Injuk, and R. Van Grieken. X-Ray Spectrometry: RecentTechnological 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 ofthe superposition principle to solar-cell analysis. IEEE Transac-tions on Electron Devices, 26:165–171, 1979.

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

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

bibliography 95

[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. Publica-tions, 1970. doi: 10.1002.

[47] D. D. Smith. Review of Issues for Development of Self-DopingMetallizations, 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 siliconpert cells on mcz substrates and 24.7% efficiency perl cells on fzsubstrates. Prog. Photovolt: Res. Appl, (7):471–474, 1999.

kapton.dupont.com

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