Enhanced broadband absorption is silicon micro structures by laser processing for solar cells

For silicon wafer solar cells, the high reflection at the front surface, due to its high refractive index, is a hindrance to the devices’ light collection efficiency.. high-of metallic n

ENHANCED BROADBAND ANTI-REFLECTION IN LASER PROCESSED SILICON NANO-STRUCTURE

ARRAYS FOR SOLAR CELLS

2014

ACKNOWLEDGEMENTS

I would like to express my heartfelt appreciation and gratitude to my supervisors, Prof Hong Minghui, Dr Bram Hoex and Dr Ian Marius Peter for their invaluable guidance and great support throughout my Master project Without their valuable advice and encouragements, the progress of this project will not be as smooth as it

is I am deeply grateful to Prof Hong Minghui for the high standard he held on

me Without his dedicate care, my research work would be slow down His acute sense and strict attitude in research field inspire and give me great help

It is my pleasure to recognize all the members in Laser Microprocessing Lab for sharing their experience in research and giving me kind help and useful discussion Special thanks would be expressed to Dr Luo Fangfang, Dr Du Zheren, Mr Yang Jing and Mr Wang Dacheng for your help in both my study and life, and I deeply appreciate the time shared with you I wish you best luck in your career

I am grateful to all the members from Monocrystalline Silicon Wafer Group and Simulation Group in Solar Energy Research Institute of Singapore (SERIS) for giving me their kind advice and experience in research The scholarship provided

by SERIS for my Master degree is gratefully acknowledged

Last but the most importantly, I would like to give my great thanks to my parents for their great encouragement and constant support during my years of pursuing degree in National University of Singapore

TABLE OF CONTENTS

ACKNOWLEDGEMENTS i

TABLE OF CONTENTS ii

SUMMARY vii

LIST OF FIGURES ix

LIST OF SYMBOLS xiii

CHAPTER 1 INTRODUCTION 1

1.1 Background 1

1.2 Motivation 2

1.3 Research objectives 4

1.4 Organization of thesis 5

CHAPTER 2 BACKGROUND AND LITERATURE REVIEW 7

2.1 Silicon solar cells 7

2.1.1 Introduction 7

2.1.2 Optical properties of silicon 8

2.1.3 Optical loss 11

2.1.4 Surface texturing 13

2.1.5 Light trapping 15

2.2 Light scattering by nanoparticles (NPs) 18

2.2.1 Properties of surface plasmons 19

2.2.2 Surface plasmon excitation 21

2.3 Numerical simulation 23

CHAPTER 3 EXPERIMENTAL SETUP AND FABRICATION DETAILS 27

3.1 Introduction 27

3.1.1 Laser micro-lens array (MLA) lithography 27

3.1.2 Laser interference lithography (LIL) 29

3.1.2.1 Principle of LIL 30

3.1.2.2 Lloyd’s mirror setup 31

3.1.3 Top-down fabrication of silicon nanowires 33

3.2 Fabrication details 36

3.2.1 Substrate selection and wafer cleaning 36

3.2.1.1 RCA I cleaning 36

3.2.1.2 RCA II cleaning 37

3.2.1.3 5% Hydrofluoric Acid Dip 37

3.2.2 Photoresist coating 38

3.2.3 Exposure and develop 40

3.2.3.1 Concentric rings nano-structure arrays 40

3.2.3.2 Silicon nanowire arrays 40

3.2.4 Metallic thin film deposition 41

3.2.5 Lift-off 43

3.2.6 Chemical etching and 3D nano-structures fabrication 46

CHAPTER 4 HYBRID 3D SILICON SURFACE NANO-STRUCTURE ARRAYS FOR SOLAR CELLS BY LASER MICRO/NANO-PROCESSING 49

4.1 Introduction 49

4.2 Characterization methods 50

4.2.1 Optical microscope (OM) imaging 50

4.2.2 Scanning electron microscope (SEM) imaging 51

4.2.2.1 Silicon concentric nano-rings array 51

4.2.2.2 Silicon nanowires array 53

4.2.3 UV-Vis spectroscopy 56

4.2.3.1 Silicon concentric nano-rings array 57

4.2.3.2 Silicon nanowires array with different pillar heights 59

4.2.3.3 Silicon nanowires array with different pillar diameters 62

4.3 “Mushroom”-shape silicon nanowires array 64

4.3.1 Scanning electron microscope (SEM) image 66

4.3.2 UV-Vis spectroscopy 67

4.4 Theoretical analyses of enhanced light trapping in hybrid 3D silicon nano-structures array 69

4.4.1 Optical performance 69

4.4.1.1 Reflectance of silicon nano-structures array 69

4.4.1.2 Absorption of silicon nano-structures array 71

4.4.2 E-field distribution in single standing nano-structure 72

4.5 Summary 76

CHAPTER 5 BROADBAND ENHANCEMENT OF ANTI-REFLECTION IN SILICON MICRO/NANO-STRUCTURES 78

5.1 Introduction 78

5.2 Experimental details 79

5.2.1 Metallic nanoparticles deposition 79

5.2.2 Pyramid micro-structures 79

5.2.3 Laser surface texturing 81

5.2.4 Thermal annealing of metallic nanoparticles 82

5.3 Characterization 84

5.3.1 Scanning electron microscope imaging 84

5.3.1.1 Flat silicon with metallic nanoparticles deposition 84

5.3.1.2 Pyramid micro-structure with metallic nanoparticles deposition 85

5.3.1.3 Laser surface texturing with metallic nanoparticles’ deposition 86

5.3.2 UV-Vis spectroscopy 89

5.3.2.1 Silicon micro/nano-structures with metallic nanoparticles’ deposition 89

5.3.2.2 Silicon back surface texturing 97

5.4 Summary 99

CHAPTER 6 CONCLUSIONS AND FUTURE WORK 101

6.1 Research achievements 101

6.2 Suggestion for the future work 103

References: 105

SUMMARY

Light collection efficiency act as a key factor affecting the performance of many optical and optical-electronic devices For silicon wafer solar cells, the high reflection at the front surface, due to its high refractive index, is a hindrance to the devices’ light collection efficiency To minimize unwanted reflection and increase light trapping, anti-reflection surfaces by micro/nano-texturing are one of the most promising candidates, which is featuring an improved anti-reflection as well

as enabling the probability of manufacturing high-efficiency solar cells on a large scale This thesis focuses on broadband enhancement of light absorption for solar cells by silicon surface texturing using laser micro/nano-processing

Laser technology has become one of the commonly applied techniques for efficiency silicon wafer solar cell fabrication In this thesis, laser interference lithography (LIL) and micro-lens array (MLA) lithography are adopted as mask-free and efficient techniques, associated with metal catalyst assisted chemical etching, to fabricate silicon nano-structures arrays The surface anti-reflection performance and light trapping are significantly improved by sub-wavelength structures at ultra-high aspect ratios, which create gradient refractive index from air ambient to wafer substrate Furthermore by varying the surface geometry and feature design of the nano-structures arrays, the light absorption in the nano-structures are boosted by extending the light travelling path and changing the silicon volume ratio at the nano-structures layers Meanwhile, with the decoration

high-of metallic nanoparticles on silicon nano-structures, the surface plasmon resonance can be excited to further enhance broadband anti-reflection, achieving

an ultra-low reflection across the broad spectrum from 300 to 1200 nm

LIST OF FIGURES

Chapter Two

Figure 2.1 Evolution of silicon solar cell efficiency [36] 7 Figure 2.2 In the wavelength regime 300 nm < λ < 1200 nm, which is relevant to silicon solar cell operation, the absorption coefficient 𝛼0 and correspondingly the absorption length 𝐿𝛼 of c-Si strongly depend on wavelength [39] 10 Figure 2.3 Schematic illustration of optical loss processes in a solar cell [43] 12 Figure 2.4 Comparison of light travelling path on flat and textured silicon surfaces 14 Figure 2.5 Silicon surface structures fabricated by (a) KOH etching, (b) catalyst-assisted chemical etching, (c) plasma etching and (d) femtosecond laser induced texturing [25] [48] 15 Figure 2.6 Schematic diagram illustrating reflection and transmission of light for a pyramidal textured silicon solar cell [43] 17 Figure 2.7 Schematic illustration of plasmon collective oscillation of a spherical gold colloid, showing the displacement of the conduction electron charge cloud relative to the nuclei [54] 20 Figure 2.8 SPP excitation configurations: (a) Otto geometry (b) Kretschmann geometry, (c) diffraction on a grating, and (d) diffraction on surface features [60] 21 Figure 2.9 Rayleigh expansion for the diffracted fields [70] 25

Chapter Three

Figure 3.1 Schematic of the experimental setup used for laser micro-lens array lithography 28

Figure 3.2 Schematic illlustration of a standing wave generated by the

interference of two coherent laser beams 31

Figure 3.3 Schematic illlustration of a Lloyd's mirror setup for laser interference lithography of periodic structures on photoresist 32

Figure 3.4 Scanning electron micrographs showing (a) the arrays of silicon nanowires prepared by using inductively coupled plasma etching [81]; and (b) the arrays of silicon nanopillars fabricated by optical lithography and reactive ion etching [82] 33

Figure 3.5 Scanning electron micrographs of Ag–Si after treatment in an aqueous solution containing (a) 5.3 M HF and 0.18 M H2O2 for 1 min; (b) 5.3M HF and 1.8M H2O2 for 1 min Inset shows an enlarged image at the top surface region [89] 35

Figure 3.6 Measurement of the film thickness using a step profiler 39

Figure 3.7 Schematic drawing of an electron beam evaporator 42

Figure 3.8 Process flow for the single-layer lift-off process 45

Figure 3.9 Schematic illustration of catalyst assisted wet etching process 47

Figure 3.10 Schematic diagram depicting the experimental setup for catalyst assisted wet etching 48

Chapter Four Figure 4.1 Optical microscope top view images of fabricated (a) silicon concentric nano-rings array and (b) silicon nanowires array 51

Figure 4.2 SEM micrographs of silicon concentric nano-rings arrays fabricated at heights of (a) 750 nm, (b) 3 µm and (c) 12µm 53

Figure 4.3 SEM micrographs of silicon nanowires array fabricated with (a) 300 nm diameter and pillars’ height of (b) 300 nm, (c) 1 µm, (d) 6 µm, (e) 12 µm and (f) 40 µm 54

Figure 4.4 SEM image of silicon nanowires array fabricated with (a) less than half period, (b) half period and (c) larger than half period diameters of the pillars at the same height 56

Figure 4.5 Reflectance spectra of silicon concentric nano-rings arrays with (a)

750 nm, (b) 3 µm and (c) 12 µm ring heights 58 Figure 4.6 Measured reflectance spectra of silicon nanowires arrays with (a) 1

µm, (b) 6 µm, (c) 12 µm and (d) 40 µm pillar heights 61 Figure 4.7 Measured reflectance spectra of silicon nanowires array with pillar diameters of (a) less than, (b) equal to and (c) larger than half period 63 Figure 4.8 Schematically cross section view of LIL-based lift -up process 64 Figure 4.9 Schematic process flow for the fabrication of 3D silicon nano-

structures array fabrication without using a lift off process 65 Figure 4.10 SEM micrograph of a "mushroom"-shape silicon nanowires array 67 Figure 4.11 Measured reflection spectra of silicon nanowires array with and without the "mushroom"-shape crowns 68

Figure 4.12 Measured spectrally resolved reflectance of planar silicon, normal and “mushroom”-shape silicon nanowires 70

Figure 4.13 Measured spectrally resolved absorption spectra of planar, normal and “mushroom”-shape silicon nanowires 72

Figure 4.14 Plot of the simulated absolute value of square of electric field in direction (abs(Ey)2) for (a) planar and (b) “mushroom”-shape nanowires structures

y-at wavelengths of 300 nm and (c) 1000 nm 75

Chapter Five

Figure 5.1 (a) Top view and (b) cross section SEM images of the KOH etched silicon surface 80 Figure 5.2 (a) Schematic diagram of the laser ablation for silicon surface texturing and (b) a SEM image of the resulting c-Si surface 82 Figure 5.3 Schematic of silicon nanowires array with metallic nanoparticles' decoration 83 Figure 5.4 SEM images of (a) Ag, (b) Au, (c)Ag/Au and (d) Cu/Ag/Au metallic nanoparticles' decoration of flat silicon surfaces 84

Figure 5.5 SEM images of metallic nanoparticles' decoration of the KOH etched silicon surface 85

Figure 5.6 SEM images of the laser-textured silicon surfaces being decorated with

(a) Ag/Au, and (b) Cu/Ag/Au alloy nanoparticles 86 Figure 5.7 SEM images of metallic nanoparticles' decoration of the silicon

nanowires array at heights of (a) 500 nm, (b) 3 µm, (c) 12 µm and (d) 40 µm 88 Figure 5.8 Measured reflection spectra of flat silicon surfaces with and without the metallic nanoparticles' decoration 89 Figure 5.9 Measured reflection spectra of the KOH etched silicon surface with and without metallic nanoparticles' decoration 92 Figure 5.10 Measured reflection spectra of laser textured silicon surfaces with and without metallic nanoparticles' decoration 93 Figure 5.11 (a) SEM image and (b) Measured reflection spectra of silicon

nanowires arrays with and without metallic nanoparticles' decoration 95 Figure 5.12 Measured reflection spectra of 320 µm-thick laser-textured Si front surfaces without and with the backside surface texturing 98 Figure 5.13 Measured reflection spectra of 320, 530, 890 µm-thick front side laser-textured Si sample with the backside surface texturing 99

FCA Free Carrier Absorption

SPR Surface Plasmon Resonance

SPPs Surface Plasmon polaritons

TIR Total Internal Reflection

MLA Micro-lens Array

ROC Radius of Curvature

LIL Laser Interference Lithography

SEM Scanning Electron Microscopy

RCWA Rigorous coupled-wave analysis

a different media, it is partially reflected due to the refractive index (RI) mismatching In this case, high reflection at the interfaces affects the performance

of the devices [8-11] Therefore, the surface anti-reflection becomes an important factor to enhance its cell efficiency [12-14] In order to minimize unwanted reflection and improve the light absorption efficiency, different types of anti-

reflection surfaces have been widely studied for solar cells, like anti-reflection thin film deposition and surface texturing Among all of these, nano-structures have received steadily growing research interest due to their unique optical properties and potential applications superior to their bulk counterparts [15-17] Recent advances in surface micro/nano-fabrication and thin film deposition technologies provide versatile approaches to decorate silicon surfaces with engineered structures to reduce optical reflection, especially for silicon solar cells with an absorber layer of a few micrometers

Following Feynman’s challenge that “there is plenty of room at the bottom” [18], the capability in sculpting silicon with extraordinary precision and efficiency is very much needed for the development of nanotechnology Extensive effort has been devoted by various research groups in the quest for greater structural control

at the nanometer level [19] to precisely generate such miniscule structures The resulting nano-structures show complex and interesting optical properties, which lead to a large number of opportunities, including but not limited to the potential applications in the areas of optical and opto-electrical devices

1.2 Motivation

For monocrystalline silicon solar cells, the most commonly adopted light trapping structures are pyramidal textures [20, 21], which have feature sizes of a few micrometers (2~10 µm) However, with reducing the thickness of silicon solar cells to no thicker than a few micrometers, they are no longer favored as absorber

layers Meanwhile, the crystalline silicon (c-Si) solar cells exhibit a comparably weaker absorption at near-bandgap spectrum due to the indirect bandgap of silicon, which results in a narrow absorption spectrum To bypass these limitations, nano-scale textured silicon surface provides the better solution for omnidirectional and broadband anti-reflection [2, 22-28] As photon management schemes for c-Si solar cells with thin absorber layers, such silicon nano-structures usually possess unique photon management properties to compensate for light absorption loss when arranged into random or regular arrays

With the fabrication of surface nano-structure arrays on silicon substrates, high optical absorption is indicated because of the strong light trapping by multiple scattering of the incident light among silicon nano-structures and the optical antenna effect [29-32] Therefore, the surface anti-reflection properties can be further improved by the effective graded refractive index (RI) from sub-wavelength structures The effective RI depends on the volume fraction of silicon and air to compensate the RI mismatching at the interface [33, 34] This causes low reflectance and eliminates antireflective coating step required in the manufacturing process With further adopting the metallic nanoparticles together with the nano-structures, a broadband reflection spectrum can be promised Hence, the fabrication of c-Si solar cells decorated with three-dimensional (3D) nano-structures, which vary in features, has attracted a great deal of interest among researchers as it renders the design of high-efficiency solar cells with possibly reduced material cost

1.3 Research objectives

The aim of this study was to explore the techniques for the fabrication of precisely located and well-arranged 3D nano-structures arrays on silicon using micro-lens array (MLA) and laser interference lithography (LIL) To further improve the antireflection performance and light trapping efficiency of silicon based solar cells

The focus of this research can be divided into several parts Firstly, this study focuses on the large-area synthesis of silicon nanowire arrays with tunable size, length and period This approach ma kes use of interference lithography, anisotropic etching of silicon, electron-beam (E-beam) evaporation of Ag and Au layer, lift-off, and catalyst assisted etching

Secondly, a study is carried out to investigate the optical performance of the silicon nano-structured surfaces when various surface geometries were applied The methods of MLA, LIL and multiple etching are adopted to fabricate the nanorings array and “mushroom”-shape silicon nanowires with varying feature sizes and periods

Finally, in order to reduce the reflection in a broadband region, metallic nanoparticles are deposited to the aforementioned nano-structures The tunability

in the size and distribution of the synthesized metallic nanoparticles are examined

by varying the deposited film thickness and annealing temperature Meanwhile, a back surface texturing is applied to further enhance the reflection reduction at a broadband range

1.4 Organization of thesis

This thesis is divided into six chapters and their contents are listed as follows:

Chapter One gives an introduction on the anti-reflection performance of optical and opto-electrical devices, especially solar cells An introduction of the c-Si surface micro/nano-structures fabrication is indicated The motivation, objective and contribution of this study are also addressed

Chapter Two describes the fundamental physics of antireflection for silicon based solar cell The optical properties of silicon solar cell are introduced The current antireflection and light trapping techniques are discussed with their advantages and limitations A theoretical introduction of light scattering and absorption affected by metallic nanoparticles deposited on the substrate are also included

Chapter Three describes the methods and techniques of the fabrication process A detailed procedure of the fabrication of silicon micro/nano-structures arrays by laser processing is presented

Chapter Four investigated the fabricated silicon surface structures for their reflection performance The reflection in the silicon surface nano-structures arrays are shown according to different designs of their features in both experimental measurement and numerical simulation

anti-Chapter Five investigates the anti-reflection enhancement of the silicon micro/nano-structures by two means, which are metallic nanoparticles deposition and back surface texturing Their anti-reflection performance is discussed

Chapter Six provides the conclusions of this study as well as recommendation for future work

CHAPTER 2

BACKGROUND AND LITERATURE REVIEW

2.1 Silicon solar cells

2.1.1 Introduction

Silicon wafer solar cells currently dominate the photovoltaic market with a market

share of ~ 90% The first silicon wafer solar cell with a pn junction was fabricated

in the 1950s at Bell Labs by Chapin et al [35] This solar cell only had an energy

conversion efficiency of 6% but as can be seen in Figure 2.1 the efficiency of the c-Si wafer solar cell has been improved significantly in recent years up to 25.6%

[36]

Figure 2.1 Evolution of silicon solar cell efficiency [36]

Optimizing the solar cell efficiency is all about minimization of losses Therefore, the boost of silicon solar cells efficiency comes with its priority in our study The dominant losses of a silicon wafer solar cell are optical, resistive, and recombination losses In this thesis we will only focus on a reduction of optical losses particularly for ultrathin c-Si solar cells

2.1.2 Optical properties of silicon

When light impinges on the silicon surface, it is partially reflected due to the optical contrast between c-Si and air The reflection coefficient 𝑅𝑆𝑖can be calculated by the well know Fresnel equations The transmitted light penetrates into the material, where it is attenuated due to absorption The rate of absorption

is determined by the law of Lambert-Beer,

𝐼(𝑥) = (1 − 𝑅𝑆𝑖)𝑒(−𝛼𝑒𝑓𝑓𝑥)𝐼0 （2.1）

which characterizes the intensity of a light beam that has traveled a distance 𝑥 inside a material with effective absorption coefficient 𝛼𝑒𝑓𝑓, relative to an incident intensity 𝐼0 The absorbed photons either lose their energy by generating electron/hole pairs at a rate 𝐺 = 1 𝑡⁄ (optical generation), where 𝑡𝑒 𝑒 is the excitation time constant, or by exciting free carriers (free carrier absorption, FCA) The excited carriers eventually thermalize and transfer their energy as heat in the lattice by carrier/lattice collisions The optically generated electron/hole pairs eventually recombine radiatively, or likewise produce heat by non-radiative

recombination, unless they are extracted out of the material as e.g happens in a solar cell The time constant for recombination is denoted by the carrier lifetime 𝜏 The most important quantities and dependencies of the energy transfer of light to silicon will be described as following

 Absorption by optical generation of charge carriers

In opto-electric semiconductors, the generation of electron/hole pairs occurs for incident photons with energies ℎ𝜈 > 𝐸𝑔 The generation rate is 𝐺 =𝐼𝜎𝑜𝑝𝑡⁄ℎ𝜈, with 𝐼 being the absorbed intensity, 𝜎𝑜𝑝𝑡 the optical absorption cross section and

ℎ𝜈 the photon energy For silicon, the photon energies required for optical generation are ℎ𝜈 > 𝐸𝑔 = 1.12 eV (corresponding to 𝜆 = 1107 nm)

However, silicon is an indirect band gap semiconductor, as the energy maximum

of the valence band and the energy minimum of the conduction band are located

at different values of crystal momentum [37] Therefore, the absorption of a photon with an energy below the direct bandgap of c-Si requires an interaction with the crystal lattice (phonon absorption or emission), which leads to a strong dependence of the band-to-band absorption coefficient 𝛼0 on 𝜆 Only for photon energies ℎ𝜈 > 3.4 eV ( 𝜆 = 365 nm), corresponding to the direct band gap of silicon, the absorption coefficient saturates around 𝛼0 ≈ 106 cm−1 Figure 2.2 depicts 𝛼0 as well as the corresponding penetration depth 𝐿𝛼 in the range 250 nm

< 𝜆 < 1300 nm [38]

Figure 2.2 In the wavelength regime 300 nm < λ < 1200 nm, which is relevant to silicon solar cell operation, the absorption coefficient 𝛼0 and correspondingly the absorption

length 𝐿𝛼 of c-Si strongly depend on wavelength [39]

 Absorption by free charge carriers

The absorption coefficient 𝛼0 can be significantly increased by the presence of a large number of free charge carriers 𝑁𝑓𝑐𝑐 due to FCA In such a case, an effective absorption coefficient 𝛼𝑒𝑓𝑓 = 𝛼0+ 𝑁𝑓𝑐𝑐𝜎𝐹𝐶 holds, with 𝜎𝐹𝐶 as the FCA cross section As 𝜎𝐹𝐶 increases approximately with 𝜆2, FCA predominantly plays a role for infrared light [40] and is therefore relatively less important in normal solar cell operation Relevant data is also found e.g in Refs [41] or [42]

As mentioned above, free carriers are either created optically or, alternatively, by doping, due to the dependence of the intrinsic carrier density 𝑛𝑖 on the temperature according to

short-Figure 2.3 Schematic illustration of optical loss processes in a solar cell [43]

However, in realistic manufacturing of solar cell, optical loss is yet to be eliminated Therefore, in order to achieve more promising performance of the cells, a number of ways can be applied to reduce the optical loss:

 Top contact coverage of the cell surface can be minimized for reducing light reflection at the surface contacts However, this potentially increases the resistive losses of the solar cell by an increase in series resistance

 Anti-reflection coatings (ARC) can be used on the top surface of the cell However, the ARC film is limited at one specific wavelength due to its fixed RI

 By surface texturing, the reflection of the incoming light can be significantly reduced

 The solar cell can be made thicker to increase absorption The optical path length in the solar cell may be increased by a combination of surface texturing at the front and rear surface

The reflection of a polished silicon surface in air is over 30% due to its high refractive index The reflectivity R between two materials of different refractive indices for normal incidence is determined by:

2.1.4 Surface texturing

For optical and photovoltaic applications, surface texturing, either in combination with an ARC layer or by itself, is commonly applied to reduce surface reflection and enhance the light travelling path as well The textured surface of a solar cell,

by means of “roughening”, reduces reflection by i ncreasing the chance that reflected light has another interaction with the sample, instead of being lost to the surrounding [44] Figure 2.4 shows this principle schematically for a standard pyramid textured surface where most of the light undergoes

Figure 2.4 Comparison of light travelling path on flat and textured silicon surfaces

Researchers have demonstrated several processing methods to modify the surface morphology of silicon surfaces [1, 8, 10, 25, 45, 46] The etching methods, including chemical, electrochemical and dry etching, have been widely employed [47, 48] as shown in Figure 2.5

Dynamic etching of porous silicon surfaces at the thickness of 100 nm was

demonstrated by Striemer et al to achieve an average reflection of 3.7% across

the terrestrial solar spectrum [48] Laser ablation also provides another dry processing to fabricate Si surfaces for anti-reflection [23-25, 27, 28] Black Si

surfaces fabricated by short pulse lasers were studied by Mazur et al [25] Conical

shape surface structures can be created by the laser processing, resulting in a reflection below 5% in the visible range of the spectrum

Figure 2.5 Silicon surface structures fabricated by (a) KOH etching, (b) catalyst-assisted chemical etching, (c) plasma etching and (d) femtosecond laser induced texturing [25]

[48]

2.1.5 Light trapping

The need to absorb all the light is not the only parameter that needs to be considered when deciding your solar cell device thickness Also the bulk minority carrier diffusion length should be taken into account When the bulk minority carrier diffusion length is much shorter than the thickness of the solar cell increasing the thickness of the solar cell will not increase the short circuit current density In addition, a thinner solar cell may have a higher voltage by reducing the voltage losses due to the recombination Consequently, an optimized solar cell structure will typically have effective "light trapping" in which the optical path

length is several times of the actual device thickness The optical path length of a device, which is usually defined in terms of device thickness, refers to the total distance a photon could travel within the structure before it exits the device at the front or rear surface A solar cell with no light trapping features may have an optical path length that is only slight higher than the device thickness, while on the other hand, one with good light trapping may have an optical thickness of more than 50 times of device thickness

Effective light trapping is usually achieved by varying the angle at which light travels in the solar cell Applying an angled surface is one way A textured surface will not only reduce reflection as previously described but also couple light obliquely into the silicon, thus giving a longer optical path length than the physical device thickness The angle at which light is refracted into the semiconductor material is as follows, according to Snell's Law,

Figure 2.6 Schematic diagram illustrating reflection and transmission of light for a

pyramidal textured silicon solar cell [43]

The amount of light reflected at an interface is calculated from the Fresnel reflection formula For light polarized in parallel with the surface, the amount of reflected light is:

If light passes from a high refractive index medium to a low refractive index medium, there is the possibility of total internal reflection (TIR) The angle at which occurs is the critical angle and is found by setting 𝜃2 to 0 Using the TIR, light can be trapped inside the cell with multiple passes through the cell, thus allowing a high optical path length at the reduced thickness of the device

2.2 Light scattering by nanoparticles (NPs)

By the fabrication of the sub-wavelength structures, higher light absorption is achieved in visible and NIR range, which is significant for solar cells [47, 49, 50] Sub-wavelength structures, e.g hybrid moth-eye structures [34] and ZnO coated

Si nano-cone [51], have been shown to exhibit ultra-low reflection by numerical simulations Another point worth mentioning for anti-reflection performance of Si solar cell is metallic nanoparticles (NPs) induced surface plasmon resonance (SPR) With EM wave excitation, metallic NPs can be used in the anti -reflection surfaces to excite localized SPR to increase optical absorption by light trapping [2-4, 8, 22, 52] The localized EM field around metallic NPs can be significantly enhanced at the resonance [53] The light scattering properties become dominant for NPs at a large size Both effects contribute to the anti-reflection performance Generally, Au and Ag NPs are mostly used for their SPR excitations at visible range To reduce the material cost for anti-reflection surface fabrication, other metallic NPs, such as Al and Cu, were also investigated They are more suitable for the applications in UV and IR ranges at their SPR resonances [4, 52] To

reduce optical reflection in a wide wavelength range, alloyed NPs, like Ag-Au NPs, were also applied [8, 22] Nano-structured metallic particles show complex and interesting properties, which contribute to anti-reflection performance for photovoltaic applications by adopting surface plasmon resonance (SPR).With electromagnetic (EM) wave excitation, the deposited metallic NPs excite localized SPR, thereby enhance optical absorption by light trapping

2.2.1 Properties of surface plasmons

Surface plasmon polaritons (SPPs), often referred to as surface plasmons (SPs), are resonant electromagnetic field which are strongly confined to metallic surfaces that enable them to sustain coherent electron oscillations These electromagnetic surface waves arise via the coupling of the electromagnetic fields

to the electron plasma oscillations of the conductor [54, 55]

Localized surface plasmons (LSPs), a type of SPs, are charged density oscillations confined to metallic nanoparticles (sometimes referred to as metal clusters) and metallic nano-structures [54] LSPs are non-propagating excitations of the conduction electrons of the metallic nano-structures coupled to the electromagnetic field We will see that these modes arise naturally from the scattering problem of a small and sub-wavelength conductive nanoparticle in an oscillating electromagnetic field The curved surface of the particle exerts an effective restoring force on the driven electrons, so that a resonance can arise, leading to a field amplification both inside and in the near-field zone outside the

particle This resonance is called the localized surface plasmon or short localized plasmon resonance [56] Another consequence of the curved surface is that plasmon resonances can be excited by direct light illumination of appropriate frequency irrespective of the wave vector of the exciting light In contrast, an SPP mode can only be excited when both the frequency and wave vector of the exciting light match the frequency and wave vector of the SPP [57, 58]

Figure 2.7 Schematic illustration of plasmon collective oscillation of a spherical gold colloid, showing the displacement of the conduction electron charge cloud relative to the

nuclei [54]

A typical example is shown in Figure 2.7, where the conduction electrons of a spherical gold colloid oscillate coherently in response to the electric field of the incident light [54] Excitation of LSPs by an electric field (light) at an incident wavelength, where resonance occurs, results in strong light scattering, in the appearance of intense SP absorption bands, and an enhancement of the local electromagnetic field The frequency and intensity of the SP absorption bands are characteristic of the type of materials (typically, gold, silver, or platinum), and are highly sensitive to the size, its distribution, and shape of the nano-structures, as well as to its surrounding environment [59]

2.2.2 Surface plasmon excitation

Figure 2.8 SPP excitation configurations: (a) Otto geometry (b) Kretschmann geometry,

(c) diffraction on a grating, and (d) diffraction on surface features [60]

As seen from the SPP dispersion relations, the SPP wavevector is larger than the photon wavevector in the adjacent dielectric medium Thus, light illumination a smooth surface cannot be directly coupled to surface polaritons Special experimental arrangements have been designed to provide the conservation of the wave vector The photon and SPP wavevector can be matched using either photon tunneling in the total internal reflection geometry (e.g by a prism) or diffraction effects (e.g via a grating or on surface defects) as shown in Figure 2.8

There are three main techniques by which the missing momentum can be provided The first makes use of prism coupling to enhance the momentum of the incident light [61, 62] The second makes use of a periodic corrugation in the surface of the metal [63] The third involves scattering from a topological defect

on the surface, such as a sub-wavelength protrusion or hole, which provides a convenient way to generate SPs locally [59, 64]

In the prism coupling technique, incident light passes thro ugh an optically dense medium In this case, a prism, to increase its wave vector momentum Under suitable wavelength and angles, total internal reflection (TIR) can be achieved where the incident beam reflects off at an interface between the optically dense glass and less dense dielectric [Otto configuration as shown Figure 2.8 (a)] or metallic layer [Kretchmann configuration as shown in Figure 2.8 (b)] Although

no light comes out of the prism in TIR, the electrical field of the photons extends about a quarter of a wavelength beyond the reflecting surface The coupling gap provides the evanescent tunnel barrier across which the radiation couples, allowing the surface plasmons to be excited at the dielectric metal interface [60]

The second method to overcome momentum mismatch is periodic corrugation, such as grating coupling, as shown in Figure 2.8 (c) This involves incident light being directed towards a grating with spatial periodicity similar to the incident irradiation The incident beam is either diffracted away from the grating or produces an evanescent mode that travels along the interface This evanescent mode has wave vectors parallel to the interface with reciprocal lattice vectors

added or subtracted from it Numerically, these vectors are represented by 2𝑛𝜋

where n is an integer and D gratings dimensions [65]

On a rough surface, the SPP excitation conditions can be achieved without any special arrangements Diffraction of light on surface features can provide coupling to the SPP modes on both the air-metal and glass-metal interfaces [Figure 2.8 (d)] This is possible since in the near field region, all wave vectors of diffractive components of light are present [65-67] Thus, SPPs can be excited in conventionally illuminated rough surfaces The problem with random roughness

is the irregular SPP excitation conditions, resulting in the low efficiency of to-SPP coupling This is a non-resonant excitation and there is a strong presence

light-of the reflected excitation light close to the surface Depending on the metal film thickness and depth of the defect, SPPs can be excited on both interfaces of the film Such non-resonant SPP excitation processes result in a complex field distribution over the surface due to interference of SPPs excited on different interfaces of the film and the illumination light [67]

2.3 Numerical simulation

In this study, the Rigorous Coupled Wave Analysis (RCWA) [68, 69] method was applied to investigate the optical properties of the silicon nano-structures This numerical simulation provides an insight of reflection and absorption conditions

in the nano-structure as well as its electric-field distribution

RCWA is a rigorous method to solve Maxwell’s equations by performing a Fourier transform of both the electromagnetic field and the structure In general terms, RCWA solves the diffraction problem by a grating defined by a stack of layers which have all identical periods in the x- and y-directions When defining the structures, a single period is approximated as a stack of uniform layers in the z-direction and repeated infinitely in x- and y-directions to form the whole structure, which describes a 3D spatial variation of the complex refractive index

Reflectance R, transmittance T and absorptance A of the structures can then be

retrieved The calculation returns the diffraction efficiencies of the transmitted and reflected orders for an incident plane wave from the top and for an incident plane wave from the bottom, both for TM and TE polarizations, by the grating of the following incident plane wave:

i If incident from the top layer,