Nonlinear static and dynamic analysis of mulltilayer nanocomposite structures in solar cell

VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY VU MINH ANH NONLINEAR STATIC AND DYNAMIC ANALYSIS OF MULTILAYER NANOCOMPOSITES STRUCTURES IN SOLAR CELL MASTER’S THESIS

VIETNAM NATIONAL UNIVERSITY, HANOI

VIETNAM JAPAN UNIVERSITY

VU MINH ANH

NONLINEAR STATIC AND DYNAMIC

ANALYSIS OF MULTILAYER NANOCOMPOSITES STRUCTURES IN

SOLAR CELL

MASTER’S THESIS

Ha Noi, 2019

VIETNAM NATIONAL UNIVERSITY, HANOI

VIETNAM JAPAN UNIVERSITY

VU MINH ANH

NONLINEAR STATIC AND DYNAMIC

ANALYSIS OF MULTILAYER NANOCOMPOSITES STRUCTURES IN

I

ACKNOWLEDGEMENT

Firstly, I want to send deep gratitude to my instructor, Professor Nguyen Dinh Duc, who has extended his arms to receive and inspire me to carry out his thesis over the years Despite many difficulties and failures in implementing this thesis, this thesis is still completed with his dedicated guidance as well as help with time, ideas and in-depth knowledge I will remember his sharing, helping, guiding me with enthusiasm

I would like to thank all the teachers who came from Infrastructure Engineering Program: Professor Kato, Professor Dao Nhu Mai, Professor Nagai, Doctor Phan Le Binh and Doctor Nguyen Tien Dung The professors and doctors have always given me great advice, orientations, pointing out the irrational points in the thesis to get me the best, most useful thesis Besides, I was always assisted by the program assistant Bui Hoang Tan In particular, in the process of studying and implementing the thesis, I always get support from Vietnam Japan University, I feel happy and happy for that Indispensably, I want to say thank you to Doctor Tran Quoc Quan, Doctor Nguyen Thi Thuy Anh for not only giving valuable reviews but also making new developments in world studies to help my thesis have more attractions through discussions at the laboratory meetings I would like to thank all VJU students, classmate for the happy time, for sharing and helping, Finally, I sincerely thank my family, close friends who are always by my side motivate and help me complete this thesis

II

TABLE OF CONTENTS

ACKNOWLEDGEMENT I

LIST OF FIGURES IV

LIST OF TABLES VI

NOMENCLATURES AND ABBREVIATIONS VII

ABSTRACT VIII

CHAPTER 1: INTRODUCTION 1

1.1. Background 1

1.2. Research objectives 7

1.3. The layout of the thesis 7

CHAPTER 2: LITERATURE REVIEW 9

2.1. Literature review in Outside Vietnam 9

2.2. Literature review in Vietnam 13

CHAPTER 3: METHODOLOGY 15

3.1. Modelling of SC 15

3.2. Methodology 16

3.3. Basic Equation 17

3.4. Boundary Conditions 22

3.5. Nonlinear Dynamic Analysis 23

3.6. Nonlinear Static Stability 25

CHAPTER 4: RESULTS AND DISCUSSION 27

4.1. Introduction 27

III

4.2. Natural frequency 27

4.3. Dynamic response 28

4.4. Frequency – amplitude relation 32

4.5. Nonlinear Static 33

4.6. Critical buckling load 35

CHAPTER 5: CONCLUSIONS AND FURTHER WORKS 37

5.1. Conclusions 37

5.2. Future works 37

APPENDIX 39

PUBLICATIONS 40

REFERENCES 40

IV

LIST OF FIGURES

Figure 1.1 Modelling of surface transitions organic solar cell 4

Figure 1.2 Modelling of a solar cell using perovskite as a light-sensitive substance and structure of the energy zone of the solar cell 6

Figure 3.1 Geometry and coordinate system of nanocomposite multilayer SC 16

Figure 4.1 Influence of ratio a b/ on the SC’s nonlinear dynamic response (P x =0,P y =0 ) 29

Figure 4.2 Influence of ratio a/h on the SC’s nonlinear dynamic response(P x =0,P y =0 ) 29

Figure 4.3 Effect of the exciting force amplitude Q on the dynamic response of SC

Figure 4.6 Effect of initial imperfection W0 on the dynamic response of the SC 31

Figure 4.7 Influence of external force Fon SC’ frequency – amplitude curves 32

Figure 4.8 The influence of initial geometrical imperfection on the SC’ stability with uniaxial compressive load 33

Figure 4.9 The influence of a/b ratio the SC’ load – deflection amplitude curve 34

VI

LIST OF TABLES

Table 4 1 Initial thickness and properties materials of layers of SC 27

Table 4 2 Effects of the thickness of layers and modes on natural frequencies of the

nanocomposite multilayer organic solar cell 28

Table 4 3 Effects of the elastic foundations and ratio a/b on the critical buckling load

of the SC 35

VIII

ABSTRACT

This thesis focuses on the study of the mechanical behavior of Solar Cell (SC) As we know, SC is a sustainable solution for energy supply and greenhouse gas reduction Therefore, SC is currently hot topic that attracted a lot of interest from scientists worldwide Currently, there are many research about SC such as Replace component materials in OS or how to improve SC performance … However, there is very little research on mechanical properties, mechanical behavior of SC Therefore, this thesis will focus on investigation of mechanical behavior of SC SC are made by 5 layers under mechanical load Besides, SC are supported by elastic foundations: winker foundation and Pasternak foundation In details, nonlinear static and dynamic analysis

of multilayer nanocomposite structure in solar cell will be investigated By using classical plate theory, Glarkin method along with Runge - Kutta method, the effect of geometrical parameter, elastic foundation, load, and imperfection on the nonlinear static and dynamic analysis of multilayer nanocomposite structure in solar cell will be described in detail Besides, some numerical results as critical buckling load and natural frequency also will be shown

Key words: Dynamic Analysis, Nonlinear Static, Organic Solar Structures, The Classical Theory, Mechanical Load

Since 1953 when D Chapin, C Fuller and G Pearson Silicon introduced the 2 cm2 Si solar cell with power conversion efficiency 4%, this solar cell has been developed through many generations Now, it is commercial with power conversion efficiency 40% This attracts numerous researchers, which is represented through an increasing number of researches about solar cell in recent years Therefore, it is necessary to have better understand the operational methods and physics behaviors of solar cell to increase its power conversion efficiency

Nowadays, we are facing the threat of global climate change due to environmental pollution and the greenhouse effect Therefore, the search for new energy sources which are environmentally friendly and highly efficient enough to replace traditional fossil fuels such as oil, coal, etc., is an urgent matter Photovoltaic cells are fields that create new electrical energy by converting light into electricity based on technologies Beginning with the invention of photovoltaic cells, the first complete module of solar cells was successfully produced and published in 1954 Beside wind energy, solar cells are the most promising fields among the renewable energy sources because of its enormous potential One estimate suggests that a small area of less than 6% of the Sahara is sufficient to meet the world's energy needs Currently, energy is supplied primarily (over 80%) by petroleum There are two main issues of using fossil fuels Firstly, the fossil resources are limited and its distribution on the earth is unbalanced Secondly, burning fossil fuels produces CO2 But CO2 is the cause of global warming

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because it acts as a greenhouse gas The cause of the greenhouse effect is that the atmosphere reflects the infrared (heat radiation) back to Earth This effect is essential for life on Earth because radiation balances the sun, the atmosphere and surface of the Earth It leads to an average temperature of 14 0C on the earth's surface Without this effect, the surface temperature of the earth would be -15 0C (Würfel, 2009) The impact

of global warming is very serious and the potential consequence is the rise of sea level

In addition, desertification and dehydration are likely to collapse the entire ecosystem, change in ocean currents; which lead to the imbalance of natural life Because of these risks, scientists have been looking for solutions to reduce greenhouse gas emissions The solution of using renewable energy sources has attracted large numbers of scientists and the field of solar cells has boomed (S Chu, 2017) The contribution of this energy source is increasing in total world energy demand At present, developed countries have used solar power plants to contribute to national energy such as the United States, Germany, Japan and China In Vietnam, we also have two solar power plants under construction in Quang Ngai and Binh Thuan province

Although the development of solar cells has gone through many development cycles,

we can divide it into three main generations:

§ The first generation of solar cell is wafer plate based on silicon crystals This is a technology that still accounts for 90% of the solar power today These solar cells are connected and protected by a layer of glass or other material Solar cells are made from semiconductor materials (light absorbers), such as crystalline silicon The electron flow is formed when the solar cell is stimulated by light photons The electrons "flow" out like direct currents Inverters convert the photovoltaic current into

an alternating current, which is how the grid works in the United States The number of solar cells and the size of the panels determine the electrical power that can be generated Silicon wafer based on photovoltaic phenomenon is non-toxic, abundant and

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high stability to the environment But the silicon wafer is not a good light absorber, so

it is usually thick and hard These solar panels are very complex to produce and relatively expensive But their efficiency is up to 25% - the highest level for commercial applications In addition, scientists have developed a multilayer configuration, different semiconductors with different band widths Their efficiency has reached 65% because it can absorb a wider range of solar spectrum

§ The second generation of solar cells consists of thin film solar cells which are primarily made of Cadmium Telluride (CdTe) and Copper Selium Indium Gallium (CIGS) Both of them are rare and toxic metals This type of solar cell is manufactured

by depositing one or more thin film photovoltaic materials onto glass, plastic or metal They absorb the light from 10 to 100 times as much as silicon, so the thickness of the photoelectric material is just a few micrometers (the thickness of human hair is 90 µm) The efficiency of these solar cells has reached more than 20% but they have the potential to achieve the same efficiency as the first generation of solar cells according

to scientists However, they are made of heavy metals, which have an adverse effect on the environment

§ The main goals of the third generation of solar cells are to improve the efficiency while keeping low costs The third generation includes thin film solar cells that use light-sensitive pigments, organic solar cells, quantum dot solar cells and peroskite solar cells The advantages of these solar cells are cheap, easy manufacturing Their efficiency has recently reached 20.1% and they have the potential to reach 31% This makes them to be the most promising photovoltaic technology today This shows the importance of the mechanical and physical behaviours study of the third generation

of solar cells

During the last few decades, conducting polymers have been attracted much attention

of researchers on the world to apply fabricating organic devices (OLED, OSC, OFET

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and OTFS due to their benefits such as abundant materials, large-scale, low-energy fabrication methods At present, organic solar cell (OSC) technology is considered as one of the most promising cost-effective alternative and environmentally friendly electric generation Nanocomposite materials will be novel materials in the near future because of their outstanding properties These are combined the advantages of both organic and inorganic materials as well as surmounted the disadvantages of them In term of mechanics, the composite materials are more stability than organic or inorganic materials They also give distinct properties in comparison with photovoltaic devices

By the ways, we would observe interesting effects and therefore having ability to open new application in the field of nanotechnology

The model of surface transitions organic solar cell

Figure 1.1 Modelling of surface transitions organic solar cell (google)

The basic structure of a surface transitions solar cell (Figure 1.1) consists of an anode, charge transmission layer, the animation layer which is created by Acceptor and Donor layers, hole transport layer and cathode electrodes which are usually made of ITO Hole transport layer and electronic transmission layer are used to regulate the discharge of the poles for the purpose of producing Ohmic contact The excitons are

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separated at the interface between Acceptor and Donnor Solar cell transitions face is the simplest structure of organic solar cells The advantage of transient solar cells is that it reduces the recombinant exciton by reducing the travel distance of the exciton

In contrast, the downside of solar cell transitions is that the surface is small, which leads to the reduction of efficiency in exciton separation

The model of the solar cell uses perovskite as a light-sensitive substance

Perovskite material is used in solar cells for the first time using a light-sensitive substance In particular, perovskite nanocrystals are used as optical absorbers instead of light sensitive ones Perovskite nanoparticles will be adsorbed onto the surface of the capillary oxide layer as TiO2 and absorb light The electron transporter in this case is TiO2 and the hole transporter is a liquid electrolyte Perovskite in this case only takes

on a role of absorbing light The transfer of charge in the battery will be done by ETL and HTM The efficiency of this battery is about 3.8% and 3.1% by using CH3NH3PbI3 and CH3NH3PbBr3 as optical absorbers The efficiency of this solar cell is low and it goes down quickly within minutes The reason of this phenomenon is the rapid decomposition of perovskite in liquid electrolytes Therefore, liquid electrolytes have been replaced by solid-state carriers to improve the efficiency of the solar cell (Figure 1.2) The efficiency and the stability of the cell have been significantly improved by continuously improving the efficiency of the transportation and collecting holes in the HTM layer It has reached 9.7% (H.S Kim, 2012)by using Spiro-MeOTAD and 12% by replacing PTAA for HTM (J H Heo, 2013)

The adsorption of perovskite nanocrystals onto the capillary oxide layer is difficult to control and fabricate, which leads to changes in the perovskite crystal form In order to overcome this weakness, a small structural improvement has been made by taking advantage of the good electron transportability of perovskite (electron mobility in perovskite is 25 cm2/ Vs, 3-4 times higher than electron mobility in TiO2, 7.5 cm2/ Vs)

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Perovskite material, instead of absorbing on the capillary material, penetrates completely into the hollow spaces between the TiO2 nanoparticles efficiency of this structure was recorded up to 15% (J Burschka, 2013)

Figure 1.2 Modelling of a solar cell using perovskite as a light-sensitive substance and

structure of the energy zone of the solar cell (google)

Advantages of solar cells

Main advantages of organic solar:

• Cost of production is low because it can be made using roll to roll or low molecular weight technology (N N Dinh, 2017) (Nam, 2014)

• High flexibility and high performance

• Nontoxicity, rich materials, light weight (few grams per m2)

• Applications in mobile devices

• No refinement in fabrication

The main advantages of perovskite solar cells:

• High optical absorption coefficient

• Long length of charge diffusion

• The appropriate band width

• Easy to fabricate

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1.2 Research objectives

The research objective of this thesis is to study nonlinear static stability and dynamic response of organic solar subjected to mechanical load Therefore, in order to have remarkable results, this Master thesis will set goals that need to be achieved as below:

v Studies on nonlinear static stability of structure in solar cell subjected to mechanical load to determine the critical loads and the load – deflection curves The effects of geometrical parameters, material properties, imperfections, loads

on the nonlinear static stability of next-generation solar cells will be also discussed

v Investigations on nonlinear dynamic analysis on the structure in solar cell subjected to mechanical load The natural frequency of free and forced vibration, the deflection – time, frequency – amplitude curves and dynamic critical buckling loads of organic solar structures are determined In numerical results, the effects of the material properties, geometrical parameters, imperfections and loads on the nonlinear dynamic analysis on the structure in solar cell structures will be analyzed

1.3 The layout of the thesis

This thesis focuses on the investigation of nonlinear static and dynamic analysis of multilayer nanocomposites structure solar cell under mechanical load Classical plate theory and boundary condition are proposed to obtained the numerical results and figure results In order to understand the problem as well as to get the best results, this dissertation has taken steps according to the structure below:

Ø Chapter 1: Introduction

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The research background, the necessity of this thesis along with overview of research situation will mentioned Formation, development, types as well as advantages and disadvantages of OS will also be introduced

Ø Chapter 2: Literature review

Chapter 2 will show some research papers are related to this thesis’s topic In those research papers, they also pointed out the outstanding results obtained from their research as well as those research’s limitation Since then, the objective of the thesis will be more clearly defined This chapter also explains why an investigation of nonlinear static and dynamic analysis of OS is important

Ø Chapter 3: Methodology

Chapter 3 will introduce the method used to approach and solve problems In details, classical plate theory along with some basic equation such as Hook’Law, the nonlinear equilibrium equations… will be used Besides, boundary conditions also will be described Additionally, the results are helped by some software

Ø Chapter 4: Numerical results and discussion

In this chapter, the numerical results such as critical buckling load and natural frequency will be shown Furthermore, the effect of geometrical parameters, material properties, imperfections, loads also will considered in the form of figures The results shown will also include discussion

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CHAPTER 2: LITERATURE REVIEW

2.1 Literature review in Outside Vietnam

In 1953, the first sillic solar cell with a performance of about 4% was fabricated at Bell laboratories after six years of p-n junctions’ discovery by William B Shockley, Walther H Brattain and John Bardeen The first module of solar cell was built as a power source for the spacecraft five years later In 1960, commercial modules were produced with power conversion efficiency 14% These modules are mainly used as power supplies for telecommunication systems In the early years of development, this source of energy was very expensive with an estimate of 100 EUR/W However, the price of this energy source has declined in recent years Therefore, it can be widely spread all over the world For example, the price of a module of solar cell dropped from 3 USD/W in 2008 (the price of a module of solar cell to generate 1W of energy under 1 sun sunlight density) to about 0.5 USD/W in 2017 (pvXchange, 2017)

The first research on the electronic properties of organic materials was on enthracene in the early 20th century In the early 1970s, conductive polymer was discovered (C K Chiang, 1977) Allan J Heeger, Alan G MacDiarmid and Hideki Shirakawa were awarded a Nobel Prize in chemistry in 2000 for contributions to the development of conductive polymers Photovoltaic was first observed in anthracene by Kalman and Pope in 1959 Several organo photovoltaic devices were announced two decades later They are made of metal-organic transition with a performance lower than 0.1% (Chamberlain, 1983) The first breakthrough for adopting organic semiconductors into solar cells was by Ching Tang who announced a donor-acceptor solar cell with performance lower than 1% (Tang, 1986) Solar cell of Tang is composed of a transition of two different materials with a layer that accepts electrons and a layer that transmits holes (tetracarboxylic derivative perylene and copper phthalocyanine) The

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second breakthrough was the invention of transient block heterostructure by simultaneously depositing two materials of different electrical properties After these achievements, the number of publications has grown exponentially over the past decade Photoelectric conversion efficiency was above 10% (Green et al, 2017), (He et

al, 2015), (Hou, Inganäs, Friend, & Gao, 2018), (Pelzer & Darling, 2016), (Yusoff et al, 2015), (Zhao et al, 2016), (Zheng et al, 2018), (Zheng et al, 2017), (Zimmermann et al, 2014) The reason for these successes is the enormous potential applications of organic semiconductor materials (Dinh, 2016), (Lu et al, 2015), (Mazzio & Luscombe, 2015) Generally, Perovskite is an oxide layer with the chemical formula ABX3 This material has the well-known and widely studied physical properties as magnetic, ferroelectric, and two-dimensional conductive material Recently, halide perovskite has attracted considerable interest in the fields of materials research as well as chemistry and physics This is explained by the high performance of solid-state solar cells based on perovskite halide, reaching 17.9% in 2014 after reaching 9.7% for the first time in 2012 In 2009, Miyakasa and his colleagues used a perovskite CH3NH3PbI3 metal-organic hybrid in a solar cell using a light-sensitive colorant with an efficiency of 3.8% By using surface-active CH3NH3PbI3 and TiO2 nanoparticles, research group of Park gained a 6.5% performance in 2011 In 2012, Park and Gratzel (Kim et al, 2012) replaced hole transport layer based on liquid by solid Spiro-MeOTAD due to corrosion problems related to liquid electrolytes Unexpectedly, this increased the efficiency up to 9.7% Lee and Snaith (Lee, Teuscher, Miyasaka, Murakami, & Snaith, 2012) gained an efficiency of 7.6% by using a similar structure They also found that the efficiency could be as high as 10.9% by replacing the conductive layer TiO2 with insulating oxide

Al2O3 Although there is still debate over the efficiency of solar cells between the use

of Al2O3 and TiO2, this finding also indicates that perovskite can transport electrons efficiently From this finding, Liu and Snaith have created perovskite solar cells without the presence of electron transport, by using vapor phase deposition This solar

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cell gained a 15.4% efficiency (M Liu, 2013) Recently, Seok and his colleagues used the CH3NH3Pb(I1-xBrx) composite material and their efficiency hit a record of 16.2% to 17.9% by adjusting the thickness ratio of the layers and chemical composition (http://www.nrel.gov/ncpv/images/efficiency_chart.jpg) Other developmental directions of perovskite include adjusting the properties of perovskite by controlling the chemical composition, developing effective manufacturing methods and optimizing the hole transport layer and properties at the interface surfaces

Unlike p-n junctions in semiconductor such as p-n (Si) or n-p (GaP), heterojunctions are a junction formed between two dissimilar crystalline semiconductors Solar nanocomposite materials include heterojunctions of inorganic semiconductors and organic semiconductor Different types of nanocomposite materials are increasingly being studied because they are widely applied in many types of components with specific properties Some new photovoltaic materials and components using layered structure are gradually replace traditional inorganic electric components, forming the field of “organic electrics” Typical solar cells consist of inorganic solar cell, organic solar cell, perovskite solar cell, etc (Burlakov, Kawata, Assender, Briggs, & Samuel, 2005) There are processes occurring in solar cell: excitons created by light absorption, they diffuse and separate into free electrons and free holes, electrons and holes move to the corresponding electrodes to generate a photovoltaic (for organic solar cell)

Apart from the ability to raise optical conversion efficiency, multilayer structures also help to raise the mechanical stability and the life of components Thickness optimization of each layer and thermal stress of this structure in solar cell has been investigated The charge separation process is improved by implanting layers in nanoscale thickness which include materials such as C60 (Kawata, et al, 2005), (Salafsky, 1999), dyes (Huynh, Alivisatos, & P.Alivisatos, 2002), (Ma, Yang, X Gong,

& Heeger), nanocrystals (Yu & Heeger, 1995) The fact that results obtained in the

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layered structure give higher conversion efficiency than monolithic structures Environmentally friendly materials and lower costs than traditional structures (Haugeneder et al, 1999), (Dittmer et al, 2000) In the world, the research on monolayer and layered nanomaterials has attracted interest from many research groups, for example in USA, UK, France, Germany, Italy, Canada, Japan, Singapore, Korea, etc Based on nanocomposite thin films, high-quality and environmentally friendly solar cells such as organic solar cell and perovskite solar cell are being researched, developed and applied in practice

Experimentally, authors at Stanford University (Kline & McGehee, 2006) showed that

in conjugated polymers (CP), the surface morphology and thickness strongly affect the capacity for carrier transport Low-order CP thin films give higher carrier mobility The change in surface structure at the boundary between two CP layers change the mobility of electrons and holes moving through contact boundary CP is used to fabricate organic solar cells and perovskite solar cells The carrier trapping distribution was studied using the technique “Thermally stimulated current- TSC" (Wurzburg University, Germany) (Schafferhans, Baumann, Deibel, & Dyakonov, 2008) The research on carrier transport through contact boundary of the P3HT polymer / electrodes demonstrated that the charge separation process is strongly depend on electron and hole mobility (National Institute of Standards and Technology, Gaithersburg, Maryland, USA) (Germack et al, 2009) These processes are strongly influenced by mechanical and thermal loading

Besides, the investigation of mechanical behaviors of material structure has important role It affects the durability and stability of operation Therefore, there are many researches about mechanical behaviors of material in the world For example, the using Kirchhoff’s plate theory along with the finite element model and mechanics of materials, the mechanical behavior such as dynamic response and static stability of

2.2 Literature review in Vietnam

For organic solar cells, recently, there are some domestic research groups such as Dr Dinh Van Chau’s group at VNU-University of Engineering and Technology, Prof Le Van Hieu’s group at Ho Chi Minh National University, Prof Pham Thu Nga, Prof Pham Duy Long’s group at Institute of Material Science They have been interested in this field during two last decades For perovskite solar cells, there are some research groups such as Nguyen Duc Cuong et al from VNU-University of Engineering and Technology, and Dr Nguyen Tran Thuat at VNU-Hanoi University of Science

The above research groups have successfully fabricated the solar cell samples which were measured in the certain great conditions This prototype solar cells also were investigated electrical properties (J-V), absorption spectrum, and power conversion efficiency In order to obtain more efficient, Nguyen Duc Cuong and co-workers are performing simulate organic solar cell based on multilayer structure to find optimal thickness of each layer in devices

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In term of situation, the research projects in Vietnam have the same research direction compared with foreign countries The difference in between Vietnam and other countries is that researchers in foreign countries were furnished modern devices with high qualification As a result, the quality of scientific research from aboard is more dominant than Vietnam However, it is able to see that domestic research are also

gradually integrating into the research of advanced groups in the world For example,

there are a lot of articles were published on international respected papers such as Composite structure, Journal of Sandwich Structures and Materials, Journal of Vibration and Control, Thin Solid Films, Solar Energy Materials & Solar Cells, J Nanomaterials, J Nanotechnology, v.v Beside that Vietnamese researchers were also invited to take international meetings and workshops in specific fields Based on initial results, we can apply to stabilize layer structure during fabrication process, although PCE and active area were still limited (ex: OSCs were fabricated in Faculty of Engineering Physics and Nanotechnology, VNU-University of Engineering and Technology)

From the above overview, we can see the importance of studying the mechanical behavior of solar cell structures So far, studies on nonlinear stability analysis of inorganic solar cell structures have received considerable attention from scientists around the world But there are very few studies on mechanical behavior of solar cell structures Therefore, we have chosen this topic for this thesis

Consider SC with total thickness h, length a,and width b is placed in the spatial coordinate system (x y z as shown in the figure 3.1a From figure 3.1a can see that , , )

SC is formed by 5 layers: Al, P3HT: PCBM, PEDOT: PSS, ITO and Glass as well as

SC is rested on elastic foundations Besides, in the figure 3.1, zdirection is attached in the thickness direction of the SC while ( )x y plane will be attached to the middle face ,

of SC

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a)

b)

Figure 3.1 Geometry and coordinate system of nanocomposite multilayer SC

a) 2D model b) 3D model

3.2 Methodology

In order to obtain the proposed purpose, analytical method is used I assume that the deflection of structures is relatively large, the material is elastic and the structural damage does not occur Depending on the form of structures, the problems are posed in terms of stress and deflection functions Basic equations will be established taking into account the influences of geometric nonlinearity and initial imperfection Specifically, the Donnell’s classical shell plate and shell theory is used for thin solar cell structures and higher order shear deformation plate and shell theory is used for thick solar cell structures Then these equations are solved by the Galerkin method for nonlinear static stability and the combination of the Galerkin method and the Runge-Kutta method for nonlinear dynamic response The value of the dynamic critical load is obtained by using the Budiansky-Roth criterion Researchers also use popular software to calculate

2 0 2 0

2 0 0

2 0

2 0

;2

x x

y y

xy xy

w x w z y w

2

0

2 0

2 0

121

in which u v are the displacement components along the ,0, 0 x y directions, respectively

Hooke’s Law for the k layers of SC are defined as