Numerical Simulation of the Solar Cell Based on the Quaternary System Cu(In,Ga)Se₂

Abstract

Energy in one form or another has been and remains an essential vital element for humanity. It is positioned as the essential propellant for the accomplishment of any human activity. Its sources have diversified over time to meet the ever-increasing needs of industry and consumers. This chapter deals with the solar cell based on copper, indium, gallium, and diselenide (CIGS), which is a photovoltaic technology in constant evolution and demonstrates very interesting record yields. The aim is to show through the results obtained from the numerical simulation that the solar cells based on CIGS have the capacity in terms of energy conversion to meet part of the energy needs of the world population. In this chapter, after describing and modeling the Mo/Cu(In,Ga)Se₂/CdS/ZnO structure, we noted from the obtained results that Shockley-Read-Hall (SRH) recombination is the predominant mode of recombination in the CIGS solar cell, and these recombinations more affect the performance of the solar cell inside the space charge region (SCR).

1. Introduction

Energy is at the center of all human activity; its transformation has been and still remains a great concern. It is increasingly used, especially in developed countries. Currently, more than 80% of the energy consumed in the world is of fossil origin [1, 2, 3]. In 2017, non-renewable energy sources constituted approximately 86% of global energy demand and nearly 48% of energy demand in Africa [4]. The rest of the energy (52%) used in Africa comes from essentially renewable energy in general and more particularly PV solar, wind, solar thermic but, above all hydraulic and biomass [4]. We see that fossil energy sources are limited in nature. In addition, the use of fossil fuels causes numerous social and environmental problems, including the degradation of the ozone layer, the main protector of the earth’s atmosphere.

The move toward sustainable alternative energies is more relevant than ever [5]. The promotion of renewable energies, including photovoltaic, has become more than a necessity. This trend accelerated following the ratification of the Kyoto Protocol in 2002. Many countries then intensified research and development of alternative energies that do not emit carbon dioxide (CO₂) [5]. The Paris Agreement announced by the United Nations organization in 2015 on climate strengthens the Kyoto Protocol and aims to significantly reduce the risks and effects of climate change, and this involves limiting the rise in temperature at 1.5°C compared to pre-industrial levels. This will be made possible for low greenhouse gas emissions and will promote investment in the development of renewable energies. Solar photovoltaic (PV) energy is one of the most powerful alternatives for the future of large-scale electricity production. Solar cells based on Cu(In,Ga)Se₂ (copper, indium, gallium, and selenium) abbreviated CIGS from the second generation are among the most promising. They are developed with the aim of properly converting the maximum amount of light energy received into electrical energy, effectively reducing electrical and optical losses, and optimizing surface properties. It meets the current objectives in the field of photovoltaic: low cost, high conversion efficiency, mass production, and accessibility for all [6]. The development of a stable, high-efficiency solar cell remains the ultimate objective of researchers in the PV field. To improve their performance and increase their yields, we focus our study on the buffer layer.

In this chapter, the main objective is to contribute to a better understanding of the role of the cadmium sulfide (CdS) buffer layer and the recombination mechanisms in the operation of the thin-film solar cell based on CIGS.

The chapter is structured into several sections following the specific objectives of the study. The first section (2.1) addresses photovoltaic solar energy and photovoltaic sectors. In Section 2.2, we discuss the history of thin-film solar cells based on copper and indium diselenide. We further describe the structure of the solar cell, highlighting the role of each layer. We then discuss the operating principle of the solar cell and the effects of temperature on its operation.

Section 2.3 develops a numerical simulation methodology. We highlight the basic equations that govern the phenomenon of charge carrier transport in semiconductors and we discuss the process of solving these equations.

In Section 2.4, we emphasize the need for a numerical method and present simulation software. Section 2.5 describes the two solar cell characterization techniques used in this work, namely current-voltage density and quantum efficiency characterizations.

In the last section (2.6), we present the results of the numerical simulation with solar cell capacitance simulator in one-dimensional (SCAPS-1D) of the Mo/Cu(In,Ga)Se₂/CdS/ZnO structure. We study the evolution of the charge carrier recombination rate across the thickness of the buffer layer. Likewise, we study the effects of the outside temperature on the performance of the solar cell. Finally, we determine the dominant recombination mechanism and its area of predominance.

2. Modeling and simulation of the Mo/CIGS/CdS/ZnO solar cell

2.1 Polycrystalline sector with thin layers of chalcopyrite

In the thin-film polycrystalline sector, three options stand out: cadmium telluride CdTe technology [5, 7, 8], copper indium diselenide technology CuInSe₂ (abbreviated CIS), and copper, zinc, tin, and selenium technology (Cu₂ZnSnSe₄) [9, 10, 11, 12]. Copper and indium sulfide (CIS) is a ternary material of type I-III-VI, with a chalcopyrite structure. It is increasingly promising for the mass production of thin-film modules, which is essentially explained by the interesting properties and the prospect of miniaturization of the solar device. The absorption coefficient of the (n)CdS-(p)CuInSe₂ heterojunction has approximately the same threshold as that of crystalline silicon (c-Si), but CIS is 100–1000 times more absorbent in the range of 1.1–2.6 eV than crystalline silicon. This allows an absorber thickness of 1–2 μm to absorb the maximum of photons from the solar spectrum [13, 14].

In the best current devices, Cu(In,Ga)Se₂ has a gap of the order of 1.2 eV obtained for [Ga]/[Ga] + [In]) =0.3 [15, 16]. In addition to the high conversion efficiencies that it promises, CIGS cells have good stability [1]. The interest in these thin layers comes essentially from the economical use of materials in relation to the physical properties and the simplicity of the technologies used for their production: easy and inexpensive development.

2.2 Solar cell based on the Cu(In,Ga)Se₂ quaternary system

2.2.1 Structure of the solar cell

We distinguish from bottom to top (Figure 1) [17, 18, 19, 20]: substrate layer, rear contact layer, absorber layer, buffer layer, conductive transparent oxide layer, and front contact layer. To these elements is added a magnesium fluoride (MgF₂) anti-reflection layer.

Figure 1.

Structure of a solar cell based on CIGS.

2.2.1.1 Substrate

The soda glass substrate layer is the support of the device (Figure 1), and its thermal expansion coefficient is adapted to the growth of the CIGS layers. As early as 1993, the importance of contamination of the CIGS absorber by the sodium (Na) contained in the substrate was reported by Hedström et al. [16]. The sodium contained in the glass in the form of sodium oxide (Na₂O₂) plays a determining role both in the growth and performance of the cell [15, 21, 22, 23]. Sodium mainly improves the efficiency of the CIGS cell by increasing the open circuit voltage (V_OC) and the fill factor [22], other studies also reported an increase in the grain size.

2.2.1.2 Back contact

The rear contact layer is made up of molybdenum (Mo) (Figure 1), it ensures the collection of positive charges that result from the conversion of incident photons into electron-hole pairs. The permeability of this layer allows the sodium atoms to diffuse and contribute to the better growth of the absorber at low and high temperatures [15, 22, 24, 25, 26]. Likewise, the selenium and gallium from the absorber diffuse into the molybdenum and form compounds such as molybdenum diselenide (MoSe₂) in very small quantities after annealing at 600°C [27, 28, 29]. The good ohmic and electronic behavior of the Mo/CIGS interface is due to the formation of the thin layer of MoSe₂ [23, 25, 28], which allows better adhesion of the molybdenum layer on the glass. The role of the MoSe₂ layer with a thickness of around 10 nm has been discussed within the scientific community [27, 29], and it is now proven that MoSe₂ is essential to facilitate the formation of a quasi-ohmic electrical contact at the interface between CIGS and molybdenum [27].

2.2.1.3 Absorber layer

The absorber layer, the most important of the device (Figure 1), is made up of indium gallium copper diselenide (Cu(In,Ga)Se₂). With p-type conductivity and a large absorption coefficient of around 10⁵ cm⁻¹ [1], it allows optimal conversion of incident photons into electron-hole pairs and ensures their separation. CuInGaSe₂ is the key material in CIGS solar cells, which is why its structural and optoelectronic properties have been and will be the subject of several studies. The performance of solar cells based on CIGS depends considerably on the structure of the material, the doping used, the insertion of gallium, or even the different interactions produced at the two interfaces of this layer, CuInGaSe₂/Mo and CdS/CuInGaSe₂.

2.2.1.4 Buffer layer

The buffer layer constituted by the cadmium sulphide (CdS) is n-type (Figure 1). It creates the heterogeneous p-n junction with the absorber layer [30]. Optimizing the performance of the CIGS-based solar cell necessarily requires understanding the mechanism of the formation of this p-n junction. CdS films have the advantage of having high optical transparency and low electrical resistivity, and the gap of 2.4 eV is among the largest [30]. The CdS layer passivates the defects on any free surface of the CIGS absorber and protects it during the deposition of the ZnO layer by cathode sputtering [25, 23]. The CdS layer provides a good quality interface with the CIGS layer and makes it possible to control the phenomenon of diffusion of defects toward this interface. It has been reported that the element cadmium present in cadmium sulfide diffuses into the absorber at about 10 nm depth and brings positive effects [31, 32].

2.2.1.5 Transparent conductive oxide layer

There are two main requirements for transparent conductive oxides (TCO) used in CIGS solar cells [16], sufficient transparency to allow enough light to reach the CIGS layer and conductivity high enough to be able to transport the photocurrent generated to an external circuit.

For our study, TCO is made up of zinc oxide (ZnO) (Figure 1). We distinguish n-ZnO doped TCO with a wide gap of 3.3 eV and high transparency. It mobilizes the maximum number of incident photons from the incident light toward the absorber. The presence of the intrinsic TCO i-ZnO in the solar cell based on Cu(In,Ga)Se₂ reinforces the protection of the absorber and also protects the buffer layer during the deposition of energetic ions from n-ZnO by sputtering cathodic. The i-ZnO layer has been shown to increase device performance due to increased open circuit voltage (V_OC) [16, 33].

2.2.1.6 Front contact

Finally, the front contact layer which is made up of a metal grid made of aluminum (Al) and nickel (Ni) ensures good collection of electrons (Figure 1). This metal grid is made up of a succession of layers (Ni/Al/Ni). The first layer of nickel prevents the oxidation of the aluminum contained in the TCO. The aluminum layer represents the front ohmic contact of the device, and the second nickel layer prevents oxidation of the aluminum, which could create direct contact with the ZnO window layer [22].

2.2.2 Operating principle

Regarding the CIGS-based solar cell, photons with energy Eph < 3.3 eV pass through the ZnO layer. Those with an energy between 2.4 and 3.3 eV are absorbed in the CdS buffer layer. In general, the largest majority of photons will reach the CIGS absorber to be absorbed in the Space Charge Region (SCR) [6, 17]. The photo-generated electron-hole pairs in the SCR are separated by an internal electric field, which then accelerates and propels the electrons toward the n-type zone and the holes toward the p-type zone [34]. The electrons are collected at the front contact (metallic grid) (Figure 1) and the holes at the back contact (Mo) (Figure 1). These carriers give rise to a generation photocurrent [35]. The electron-hole pairs that are collected at the metal grid (front contact), and at the ohmic contact (rear contact) of the cell are delivered into the load (Figure 1).

2.2.3 Influence of temperature

Temperature is a limiting parameter for solar photovoltaic devices. Cells exposed to solar radiation heat up. The very energetic photons transfer the energy equivalent to the gap of the semiconductor material, and the excess energy is dissipated in the form of heat through the device [3]. The increase in the temperature of the cell causes an expansion of the crystal lattice of the semiconductor material. The value of the gap decreases, which causes an increase in the saturation current [36]. Conversely, photons are more absorbed at long wavelengths, which leads to a slight increase in the short-circuit current [36]. We note that more free electrons are produced in the conduction band (BC) to the benefit of the slight reduction in the gap. The instability of the gap at high temperature can accelerate the recombination between the valence band (BV) and the (BC) [37], and the open-circuit voltage of the cell decreases. Operating at the lowest possible temperature allows for better conversion efficiency.

2.3 Modeling of the thin-film solar cell based on CIGS

The performance of a solar cell depends on its various electrical parameters, which are the short circuit current density (J_SC), the open circuit voltage (V_OC), the fill factor (FF), and its conversion efficiency photoelectric (η). Obtaining these different parameters of the solar cell requires the resolution of a certain number of equations. In this section, we will first highlight the essential equations governing the operation of thin-film solar cells. We then discuss solving these equations.

2.3.1 Transport phenomenon in a semiconductor

The differential equations governing the operation and characterization of a solar cell can be reduced to three (3) [35]:

• Poisson’s equation:

  $$\nabla .\epsilon \nabla \mathrm{\Phi }=-q\left(p-n+N_D^{+}-N_A^{-}\right)$$E1

• the continuity equation for electrons:

  $$\nabla .{\overrightarrow{J}}_n=q\left(R-G\right)+q\frac{\partial n}{\partial t}$$E2

• the continuity equation for holes:

  $$\nabla .{\overrightarrow{J}}_p=-q\left(R-G\right)+q\frac{\partial p}{\partial t}$$E3

In these equations, $\epsilon$ is the dielectric constant, Ф the electrostatic potential, q the electrostatic charge; the terms n and p designate the concentrations of electrons and holes.

$N_D^{+}$ and $N_A^{-}$ are the densities of ionized donors and ionized acceptors, respectively; the terms J_n and J_p are the current densities of the electrons respectively of the holes. R is the recombination rate, and G is the generation rate.

In a particular case of operation in a static regime, we have:

$$\frac{\partial n}{\partial t}=\frac{\partial p}{\partial t}=0$$E4

Then Eqs. (2) and (3) become:

$$\nabla .{\overrightarrow{J}}_n=q\left(R-G\right)$$E5

$$\nabla .{\overrightarrow{J}}_p=-q\left(R-G\right)$$E6

The recombination term in Eqs. (2) and (3) is a function of the charge carrier density. Therefore Eqs. (1)–(3) are nonlinear differential.

2.3.2 Generation term

In our work, generation results from optical excitation. The density of the photon flux denoted $\mathrm{\Phi }$(z), decreases exponentially with the depth z of the device. The back reflection shows that a fraction of the absorbed light reaches the back contact. If $e_{\mathit{\text{CIGS}}}$ is the thickness of the absorber, the flux of the intensity of the reflected light has the expression [35]: ${\mathrm{\Phi }}_{r\acute{e}\mathit{\text{flexie}}}=R_B{\mathrm{\Phi }}_{e_{\mathit{\text{CIGS}}}}$, R_B is the reflection of the rear contact. The generation rate due to optical excitation is given by the following relationship:

$$G\left(z\right)=-\frac{d\mathrm{\Phi }}{\mathit{dz}}={\alpha }_x\mathrm{\Phi }\left(z_0\right)exp\left(-{\alpha }_x\left(z-z_0\right)\right)$$E7

In this equation, $\mathrm{\Phi }$ is the photon flux density per unit area and time, and ${\alpha }_x$ is the absorption constant, the subscript x denotes a given layer: ZnO, CdS, and CIGS.

2.3.3 Recombination term

There are several types of recombination: surface, trap, Auger-type volume, radiative-type volume, and Schockley-Read-Hall recombination [38].

Schockley-Read-Hall recombination appears to be the predominant mode of recombination in the solar cell. It introduces a step in the transition between the conduction and valence bands in the form of an intermediate electronic state located in the forbidden band. The recombination rate R can be described by the following equation [35]:

$$R=\frac{\left(\mathit{np}-n_i^2\right)}{{\tau }_h\left(n+n_1\right)+{\tau }_e\left(p+p_1\right)}$$E8

This equation expresses the recombination in the quasi-neutral regions of a doped semiconductor. Under these conditions, the recombination rate of carriers in materials n and p is expressed respectively:

$$R_n=\frac{\mathit{\Delta p}}{{\tau }_h}$$E9

$$R_p=\frac{\mathit{\Delta n}}{{\tau }_e}$$E10

With Δn and Δp, the excess concentrations of electrons and holes.

2.3.4 Solving of equations

Numerical simulation is an effective tool used to understand and solve very complex problems related to the structure of solar cells. It makes it possible to effectively model and improve the conversion efficiency of CIGS-based solar devices.

The unknowns of Eqs. (1)–(3) are the following state variables: the electrostatic potential $\mathrm{\Phi }$, the quasi-Fermi level energies for electrons, and holes $E_{\mathit{fn}}$ and $E_{\mathit{fp}}$. These three state variables are sufficient to describe the operation of the solar cell. The occupation of the conduction band by electrons and of the valence band by holes can be described by the Fermi-Dirac statistic:

$$f\left(E\right)=\frac{1}{1+exp\left(\frac{E-E_f}{\mathit{kT}}\right)}$$E11

This function describes the probability of occupation of the electron in the conduction band and the expression 1 − f(E) that of the hole in the valence band. With k the Boltzmann constant, T the temperature, E the energy of the electron for a given level, and E_f the energy for the Fermi level. The occupation of the Fermi level is given by the expressions for the densities of the donors n and that of the acceptors p [39]:

$$n=N_{C}exp\left(-\frac{E_C-E_f}{\mathit{kT}}\right)$$E12

$$p=N_{V}exp\left(-\frac{E_f-E_V}{\mathit{kT}}\right)$$E13

N_C and N_V are the effective densities of electrons in the conduction band and the effective densities of holes in the valence band and have the following expressions respectively:

$$N_C=2{\left(\frac{2\prod m_e^{\ast }\mathit{kT}}{h^2}\right)}^{3/2}$$E14

$$N_V=2{\left(\frac{2\prod m_h^{\ast }\mathit{kT}}{h^2}\right)}^{3/2}$$E15

In this equation, h is Planck’s constant, $m_e^{\ast }$ and $m_h^{\ast }$ are the effective masses of the electron and the hole. In equilibrium, the product of n and p is constant and depends only on the temperature, the effective masses, and the gap of the semiconductor:

$$\mathit{np}=n_i^2=N_C{N}_{V}exp\left(-\frac{E_g}{\mathit{kT}}\right)$$E16

In non-equilibrium situations, such as under illumination or during fault injection, there is no uniform Fermi level. In the steady state, the energies of the quasi-Fermi levels $E_{\mathit{fn}}$ and $E_{\mathit{fp}}$ can be introduced and the product np depends on the voltage:

$$\mathit{np}=n_i^{2}exp\left(\mathit{qV}/\mathit{kT}\right)$$E17

In the absence of a magnetic field and temperature gradient, the transport of a charge carrier in semiconductors occurs by diffusion and is expressed from the following equations relating to the current density of electrons and holes [35, 39]:

$$J_n=q\left({\mu }_n\mathit{n\epsilon }+D_n\nabla n\right)$$E18

$$J_p=q\left({\mu }_p\mathit{p\epsilon }-D_p\nabla p\right)$$E19

With ${\mu }_n$ and${\mu }_p$, the mobility of electrons and holes, respectively; the terms $D_n$ and $D_p$, diffusion constants of electrons and holes, respectively.

The introduction of the Fermi potential ${\mathrm{\Phi }}_{\mathit{fn}}$ and ${\mathrm{\Phi }}_{\mathit{fp}}$, respectively for electrons and holes as a function of the energy of the quasi Fermi level $E_{\mathit{fn}}$ and $E_{\mathit{fp}}$, makes it possible to simplify Eqs. (18) and (19):

$${\mathrm{\Phi }}_{\mathit{fn}}=-E_{\mathit{fn}}/q$$E20

$${\mathrm{\Phi }}_{\mathit{fp}}=E_{\mathit{fp}}/q$$E21

$$J_n=-q{\mu }_{n}n\nabla {\mathrm{\Phi }}_{\mathit{fn}}$$E22

$$J_p=-q{\mu }_{p}p\nabla {\mathrm{\Phi }}_{\mathit{fp}}$$E23

Expressions (20) and (21), applied to Eqs. (1)–(3), describe the equation for the transport of charge carriers in the structure.

Eqs. (1)–(3) are subject to the conditions on the potential Φ and the current density J at the contacts. In a one-dimensional case, we have the following expressions [40]:

$$\mathrm{\Phi }\left(0\right)={\mathrm{\Phi }}_0-V$$E24

$$\mathrm{\Phi }\left(L\right)=0$$E25

$$J_p\left(0\right)=-{\mathit{qS}}_{p0}\left(p_0\left(0\right)-p\left(0\right)\right)$$E26

$$J_p\left(L\right)={\mathit{qS}}_{\mathit{pL}}\left(p\left(L\right)-p_0\left(L\right)\right)$$E27

$$J_n\left(0\right)={\mathit{qS}}_{n0}\left(n\left(0\right)-n_0\left(0\right)\right)$$E28

$$J_n\left(L\right)=-{\mathit{qS}}_{\mathit{nL}}\left(n_0\left(L\right)-n\left(L\right)\right)$$E29

p₀(0) and p₀(L) are the populations (density of holes) of the valence band respectively at the position X = 0 and the thermodynamic equilibrium position X = L. n₀(0) and n₀(L), the electron density of the conduction band at X = 0 and at thermodynamic equilibrium X = L. The quantities p(0) and p(L) correspond to the population of holes encountered at X = 0 and X = L. The quantities n(0) and n(p) correspond to the population of electrons found in the region delimited by X = 0 and X = L. The terms $S_{P0}$, $S_{\mathit{pl}}$, $S_{n0}$, and $S_{\mathit{nL}}$ are the effective recombination speeds on the surface of holes and electrons at the respective positions X = 0 and X = L [40].

2.4 Problematic of solving equations in thin layers

2.4.1 Need for a numerical method

Eqs. (1)–(3) are highly non-linear partial differential equations (PDE). The fact of having several nested layers, each with different input parameters, complicates the equations and prevents analytical solutions. These input parameters are of three types:

• the parameters that act on the entire device such as the temperature, the speed of thermal agitation, and the reflection coefficient;

• the parameters that apply to a particular region of the device such as the properties of the materials, the mobility of electrons and holes, and the width of the gap;

• the parameters that apply to the light spectrum such as light, wavelength, and absorption coefficient.

A complete solution to Eqs. (1)–(3) must correctly describe the possible discontinuities in the energy bands at the layer interface. Likewise, the effect of deep energy states (defects) in the majority of layers must be fully addressed and an explanation regarding recombination in the space charge region must be provided. In addition, the solution to Eqs. (1)–(3) must allow the determination of the state variables, $\epsilon \left(x\right)$, n(x), and p(x), which completely define the system at each point x. Given all of the above, an analytical solution to this problem is then excluded. Numerical methods appear essential for solving these equations. A typical methodology includes the following approach:

• discretization (mesh) of the device;

• discretization of the Poisson equation and the continuity equations for electrons and holes;

• application of contact boundary conditions and initial conditions;

• solution of the resulting matrix equation by iteration (Newton-Raphson method, Picard).

In short, a simulation program for thin-film solar cells must take into account the presence of several layers, and the recombination phenomena in volume and at the interface of the layers must be considered. It must also correctly deal with the recombination problem and the generation-recombination centers in the deep states of the volume of the layers. It must also offer the simulated opto-electrical characteristics (J-V, QE-λ, C-V, and C-f) and allow a comparison with the experimental measurements carried out.

2.4.2 Simulation software

Among the solar cell simulation software, we have AMPS, PC, SCAPS, and AFORS-HET at our disposal. Software is used directly or indirectly to evaluate the performance of the cell in one dimension [41]. All software in its diversity uses the equations described above. In the following lines, we will describe AMPS and SCAPS. The latter two are used specifically for chalcopyrite thin-film solar cells.

2.4.2.1 Analysis of microelectronic and photonic structures-1D

Analysis of microelectronic and photonic structures-1D (AMPS-1D) is the work of the team of Professor Stephen J. Fonash, from Pennsylvania State University with the support of the Electric Power Research Institute [1]. It makes it possible to obtain the response of any optoelectronic device to a given excitation: light, bias voltage, or temperature [42]. Among these devices, we distinguish:

• homo-junctions and heterojunctions p-n, p-i-n, n-i-n, and p-i-p;

• microelectronic structures;

• detector structures, and solar cell structures.

In the numerical simulation, AMPS-1D takes into account several layers in the case of heterojunctions. The simulation of a solar cell with AMPS-1D gives the current density-voltage characteristics under illumination and darkness as well as the charge collection efficiency as a function of voltage. Furthermore, important information such as free and trapped electric field distributions, recombination profiles, and densities of each current carrier as a function of position are extracted from the simulation.

2.4.2.2 Solar cell capacitance simulator

Solar cell capacitance simulator (SCAPS-1D) is the work of Marc Burgelman’s team from the Department of Electronics and Information Systems (ELIS) at the Ghent University in Belgium. SCAPS-1D, one-dimensional numerical simulation software, is developed to obtain the electrical characteristics of heterojunction and thin-film solar cells. Its development is inspired by work on solar cells based on CdTe and Cu(In,Ga)Se₂ [19, 43]. The simulated and measured results were in very good agreement with the results in the literature [20, 41]. With SCAPS, it is possible to simulate structures consisting of seven intermediate layers, front and back contacts with different doping profiles, and energy distributions of given donor or acceptor levels. All physical and electronic properties can be viewed and edited in a separate window. SCAPS-1D, through numerical simulation, studies the most sensitive parameters of the solar cell, namely J(V), C(V), C(f), and QE(λ) under illumination and in the dark [43]. This feature makes SCAPS a very attractive program that catches our attention.

2.5 Characterization of a thin-film solar cell based on CIGS with SCAPS-1D

Characterization of CIGS-based solar devices is necessary to determine the sources of losses and suggest ways to minimize them. We investigate two characterization techniques in this manual: J-V and QE-λ.

2.5.1 Characterization of current density-voltage J-V

The current density-voltage characteristic of the solar cell is described by a standard diode equation. The diode current density is limited by Shokley-Read-Hall recombinations across states of the CIGS space charge zone and leads in the simplified case to the following equation [4]:

$$J=J_{0}exp\left[\mathit{qV}/\mathit{AkT}\right]-J_{\mathit{ph}}$$E30

J₀ is the diode saturation current density, A is the quality factor, J_ph is the photogenerated current density (J_ph = J_SC), k is the Boltzmann constant, and T is the temperature. The simplest and most effective way to describe the operation of a solar cell is to use its current density-voltage characteristics. There are two modes of current density-voltage characterization (Figure 2):

• Under darkness, the J-V curve follows the exponential diode law. SCAPS makes it possible to monitor the effects of series and shunt resistances on the performance of the solar cell.

• Under illumination, the J-V curve is shifted downward by an amount designated by J_ph called photogenerated current density, which in the ideal case is independent of the open-circuit voltage (V_OC) and the short current density circuit (J_SC). SCAPS allows us to directly access the main electrical parameters which are J_SC, V_OC, FF, and η.

Figure 2.

Characteristics (J-V) under darkness and illumination [4].

2.5.2 Quantum efficiency.

Quantum efficiency (QE) or quantum yield is defined as the ratio of charge carriers collected to photons incident on a surface at each wavelength. In the ideal case, each photon creates an electron-hole pair that contributes to the photocurrent. For an ideal cell, the highest energy photons (hυ > Eg) give an efficiency of 100% and 0% for the lower energy photons (hυ < Eg). This is not the case for a real cell because of reflection losses and losses due to incomplete collection of charge carriers (Figure 3). Photons whose energy is lower than the band gap therefore do not contribute to the current density.

Figure 3.

Quantum efficiency with current losses.

Losses at short wavelengths are the result of absorption in the CdS layer (λ < 520 nm) and in the ZnO layer (λ < 375 nm) because most of the carriers generated in these layers are generally not collected [1]. The spectral response is the ratio between the density of the collected current and the density of the incident photons, for each wavelength of light radiation. It depends much more on the optical properties of the materials than on the spectral distribution of the light received; it makes it possible to evaluate the quantum efficiency of the cell as a function of the wavelength of the incident light. Its optimization requires improvement in the front and even rear surfaces.

The internal spectral response (IQE) and the external spectral response (EQE), are strongly linked to surface and volume recombination, the diffusion length of the carriers, and the thickness of the region concerned [16]. External quantum efficiency takes into account optical loss effects such as unabsorbed light and reflected light. It is given by the equation:

$$\mathit{RQE}\left(\lambda \right)=\frac{J_{\mathit{ph}}\left(\lambda \right)}{q{\mathrm{\Phi }}_0\left(\lambda \right)}$$E31

The ratio between the number of electron-hole pairs collected and the number of absorbed photons provided is the internal spectral response [1]. It makes it possible to evaluate the quality of the different regions of the solar cell and is given by Eq. (32) [36, 44].

$$\mathit{RQI}\left(\lambda \right)=\frac{\mathit{RQE}\left(\lambda \right)}{\left(1-R\left(\lambda \right)\right)}=\frac{1}{\left(1-R\left(\lambda \right)\right)}\frac{J_{\mathit{ph}}\left(\lambda \right)}{q{\mathrm{\Phi }}_0\left(\lambda \right)}$$E32

These two forms of spectral response are strongly linked to surface and volume recombination, the carrier diffusion length, and the thickness of the layers of the solar cell [16].

2.6 Results of the numerical simulation with SCAPS-1D

2.6.1 Study of the CdS buffer layer

In this part, we vary the thickness of the buffer layer and we obtain the curves relating to the electrical and optical characteristics respectively, J-V and QE-λ.

2.6.1.1 Influence of the thickness of the CdS on the electrical characteristics

At T = 300 K, we obtain Figure 4 and Table 1 which represent the influence of the thickness of the buffer layer on the J-V characteristic.

Figure 4.

J-V characteristic as a function of the thickness of the CdS [6].

WCdS (nm)	0	10	20	30	40	50	100	1000
VOC (V)	0.806	0.796	0.787	0.782	0.779	0.778	0.776	0.774
JSC (mA/cm^−2)	35.74	35.28	34.77	34.30	33.88	33.51	32.14	29.83
FF (%)	85.34	83.69	81.71	79.80	78.37	77.54	76.46	76.28
η (%)	24.60	23.51	22.38	21.42	20.70	20.22	19.27	18.27

Table 1.

Values of electrical parameters depending on the thickness of the CdS at 300 K [6].

From the results in Table 1 and Figure 4, we see a decrease in the values of all electrical parameters with the increase in the thickness of the CdS buffer layer [6]. However, we note a weak influence of the thickness of the CdS layer on the V_OC. In addition, the results show that the values of all the electrical parameters are greater for the small thickness of the CdS.

These results can be explained, on the one hand, by a reduction in the quantity of incident photons arriving at the absorber. This decrease is due to the absorption of incident photons in the CdS layer, which becomes important with the increase in the thickness of the CdS [6]. On the other hand, the value of the series resistance increases in the solar cell, which increases with the increase in the thickness of the CdS.

2.6.1.2 Influence of the thickness of the CdS on the quantum efficiency

Figure 5 shows that for small thicknesses (10 ≤ W_CdS ≤ 50 nm), the range of wavelengths absorbed in the CIGS layer goes from 380 nm to 1100 nm. When the thickness of the CdS is greater than 50 nm, the absorption in the buffer layer becomes very important. For a sufficiently large thickness (1000 nm) of the CdS, we see from Figure 5 that the length limiting absorption wave of the buffer layer is approximately 500 nm. As a consequence, all incident photons with a wavelength less than or equal to 500 nm are absorbed in this layer (CdS) [6].

Figure 5.

Spectral response as a function of the thickness of the CdS [6].

Unfortunately, the majority of electron-hole pairs photogenerated in the CdS layer recombine and are not collected at the contact levels. This explains the low values of J_SC and η observed in Table 1. We emphasize that the significant reduction in conversion efficiency (Table 1) is a direct consequence of the losses linked to J_SC and V_OC [6]. It appears from the study carried out on the buffer layer that the recombination inside the CdS layer and the interface of the CdS/CIGS layers become more and more important when the thickness of the CdS increases [19]. A thin layer of 10–40 nm of CdS is important for obtaining better performance and good stability [6].

2.6.2 Influence of temperature on the performance of the CIGS solar cell

2.6.2.1 J-V and quantum efficiency characteristics

Temperature is a limiting factor for the proper functioning of the solar cell. The present work effectively demonstrates that the J-V characteristic is affected by the temperature, in particular the open-circuit voltage of the device. We observed from the J-V characteristic (Figure 6a) [6], a significant decrease in V_OC with the increase in temperature. From the results in Table 2, in addition to V_OC, the values of FF and η decrease with increasing temperature [6], on the other hand, J_SC increases slightly.

Figure 6.

(a) Current density-voltage characteristics and (b) quantum efficiency for different temperatures [6].

T (K)	260	280	300	320	340	360	380
VOC (V)	0.8491	0.8159	0.7824	0.7482	0.7139	0.6794	0.6441
JSC (mA/cm^−2)	34.300	34.301	34.301	34.303	34.304	34.307	34.310
FF (%)	82.004	80.923	79.805	78.660	77.428	76.096	74.701
η (%)	23.890	22.652	21.419	20.189	18.96	17.732	16.504

Table 2.

Evolution of electrical parameters as a function of temperature [6].

2.6.2.2 Electricals parameters

We assume that a reduction in the quantity of photons absorbed at the absorber or a significant recombination of electron-hole pairs inside the SCR may be responsible for these results. However, the quantum efficiency of the solar cell appears not to be affected by the temperature variation as shown in Figure 6b. The quantity of photons absorbed in the absorber is therefore not reduced [6]. In reality, when the temperature increases, the mobility of the charge carriers decreases according to Eq. (3) and leads to significant recombination of the charge carriers. In addition, at high temperatures the gap of semiconductor materials decreases and leads to low performance of the solar cell. The slight increase in J_SC values is due precisely to this reduction in the gap of the absorber with temperature (Table 2).

$${\mu }_{n,p}=D\frac{q}{\mathit{kT}}$$E33

The analysis of these results shows that the losses in the performance of our solar cell model as a function of temperature are linked to the recombination of electron-hole pairs inside the SCR. The performance losses at the maximum power point are approximately: 0.35–0.5%/°C for a solar cell based on crystalline silicon [36, 45]; 0.27–0.32%/°C for a CIGS-based solar cell [37]. For our model, losses as a function of temperature are estimated at 0.1%/°C [34].

2.6.3 Recombination in CIGS solar cells

In this part of our chapter, our objective is to determine the type of recombination mechanism (Auger, radiative, or SRH) dominant in our solar cell model. In addition, we seek to understand in which part of the cell (CdS layer, SCR, CIGS/Mo, or CdS/CIGS interfaces) this type of recombination mechanism most affects the performance of the solar cell.

2.6.3.1 Dominant recombination mechanism

Charge carrier recombination plays a major role in CIGS-based solar cells. Controlling the different recombination mechanisms is very important for better performance of solar cells. The recombination of a charge carrier depends on its lifetime (τ), its mobility (μ), its diffusion length (L), and its recombination speed (υ_th). There are radiative, Auger, and Shockley Read Hall (SRH) type recombination mechanisms. The simulation with SCAPS-1D allows us to obtain Figure 7, which highlights the effects of the different recombination mechanisms on the J-V characteristic. From Figure 7, we see a significant loss of J_SC by SRH-type recombination. We deduce from these results that SRH type recombinations are dominant within the present solar cell model. Based on the results of Figure 7 we affirm that the different recombinations encountered in the previous sections are of the SRH type.

Figure 7.

Recombination current density.

2.6.3.2 Activation energy

The activation energy, denoted Ea, is a phenomenological parameter used to locate the place of the predominance of SRH-type recombination mechanisms in the CIGS solar cell. In the literature, several methods exist for determining the recombination activation energy [16, 17, 46, 47]:

The method that inspired us consists of plotting the V_OC curve as a function of temperature; we graphically obtain the activation energy by extrapolating the curve up to the temperature of 0 K at the origin of the benchmark (Figure 8). The V_OC value read corresponds to the value of the activation energy to a factor of 1/q (V_OC = Ea/q) (Figure 8). We make the following hypotheses:

1. If the activation energy is lower than the absorber gap (Ea < Eg), the interface recombination mechanisms (CdS/CIGS, CIGS/Mo) are dominant;

2. If the activation energy is substantially equal to or greater than the gap of the absorber, the recombination mechanisms inside the SCR dominate.

Figure 8.

Method for determining the activation energy.

From Figure 8 obtained from the numerical simulation, we see that the activation energy of the model studied has a value of approximately 1.3 eV. This value is greater than the gap value of the absorber studied (E.g. = 1.2 eV). In conclusion, the present model is affected more by SRH type recombinations in volume, more precisely inside the SCR.

3. Conclusion

In this manuscript, we proposed a theoretical framework for characterizing the CIGS-based solar cell based on the CdS buffer layer. We have set ourselves the objective of clearly explaining the different recombination phenomena that affect the performance of CIGS-based PV solar cells.

We described the polycrystalline sector with thin chalcopyrite layers and we presented the role of the different layers constituting the CIGS-based structure. Then, we discussed the operating principle as well as the influence of temperature on the Mo/CIGS/CdS/ZnO structure.

In the following sections, we modeled the CIGS-based solar cell from the basic equations that govern the transport phenomenon of charge carriers in a semiconductor. We also explained the terms of generation and recombination and underlined the need for a numerical method for solving the equations. We then gave an overview of the basic concepts of numerical simulation and described the SCAPS-1D and AMPS-1D simulation software. Finally, we presented the J-V and QE characterization techniques used for the numerical simulation.

We finally presented the results on the Mo/CIGS/CdS/ZnO structure in numerical simulation. The results show that the presence of a large thickness of the buffer layer reduces the quantity of photons arriving at the absorber. It also leads to recombinations inside the CdS layer of photogenerated charge carriers. We found that the electrical parameters decrease with increasing temperature, with the exception of J_SC, which observes a slight increase. In addition, the increase in temperature leads to recombination inside the SCR and greatly limits the performance of solar cells. Overall, we were able to show that SRH-type recombination is the predominant mode of recombination in CIGS-based solar cells. Our results further show that recombinations inside the SCR affect the performance of the solar cell.

It appears from this study that for good performance of our model, a thickness of 30 nm of the CdS layer is necessary. We retain the range of 300–360 K for the proper functioning of the chalcopyrite cell based on the Cu(In,Ga)Se₂ quaternary system.

Acknowledgments

The authors acknowledge the use of SCAPS-1D program developed by Marc Burgelman and colleagues at the Ghent University in all the simulations reported in this paper.

Conflict of interest

The authors declare no conflict of interest.