Modelling and Simulation in Engineering

Volume 2019, Article ID 5090981, 9 pages

https://doi.org/10.1155/2019/5090981

## Simulating the Performance of Al_{0.3}Ga_{0.7}As/InP/Ge Multijunction Solar Cells under Variation of Spectral Irradiance and Temperature

Theoretical Physics Division, Department of Physics, Bogor Agricultural University, Jl. Meranti, Kampus IPB Dramaga, Bogor 16680, Indonesia

Correspondence should be addressed to Tony Sumaryada; di.ca.bpi@adayramust

Received 30 August 2018; Revised 15 December 2018; Accepted 8 January 2019; Published 5 February 2019

Academic Editor: Jing-song Hong

Copyright © 2019 Tony Sumaryada et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The effect of spectral irradiance and temperature variation on the performance of the mechanically stacked Al_{0.3}Ga_{0.7}As/InP/Ge multijunction solar cells was investigated using a simulation approach. The incoming and transmitted spectra of each subcell were simulated by using MATLAB codes, while PC1D software did the power-producing simulations. The incoming solar radiation on the first subcell was a multiplication of AM1.5d spectrum with the value of spectral irradiance multiplication factor (SIMF) 1, 5, 10, 50, 100, 150, and 200 suns. Each set of simulation was done at 25°C, 50°C, 75°C, and 100°C. The simulation results have shown a linear behavior of the open-circuit voltage and the efficiency of the solar cells upon variation of temperature, while the nonlinear response of the solar cells performance was obtained due to the change of SIMF. The simulation results also suggest that the spectral irradiance exposure at 100 suns and the operating temperature of 25°C give the highest efficiency.

#### 1. Introduction

Over the last couple of decades, the progress on the renewable energy research has significantly increased, especially in the field of solar photovoltaics. Various types of solar cells such as silicon-based material, CIGS-based (copper indium gallium arsenide) material, and III-V-based chemical group have been intensively studied to produce a highly efficient solar cell. Some recorded achievements such as References [1–4] have decorated the global effort to find a better solar cell which is capable of producing clean and sustainable energy for a better future.

The combination of the III-V-based solar cells materials such as GaInP, AlGaAs, InP, and GaAs in the form of multijunction solar cells (MJSCs) and their exposure to the several hundreds multiplication of solar radiation had produced the efficiency rate up to 46% at 508 suns for the GaInP/GaAs/GaInAsP/GaInAs system [4]. Some new experimental results and aspects in high-efficient solar cells such as the new design of a vertical epitaxial heterostructure architecture (which allows a high-efficient narrow band cells) [5, 6], the use of luminescent solar concentrators (LSCs) [7], or a six-junction solar cell [8] have also expanded our knowledge in solar cells research. Most of the experiments related to the high-efficient MJSC were done using a small specimen prototype, and their realization in the market and industrial scale is still far. More research related to multijunction solar cells are needed including the simulation and modeling aspect of MJSC performance under various conditions [9–13].

In a multijunction solar cell, several p-n junctions of semiconducting layers (or subcell) were put in order from top to bottom following the order of their bandgap energies. The first layer has the highest bandgap energy with the purpose to absorb the solar radiation in the small wavelength region, while the next layers with the smaller bandgap of energy were set to absorb solar radiation in the longer wavelength regions. Theoretically, a higher efficiency rate can be obtained by putting more subcells in the solar cells [14].

Based on their fabrication technique, there are several types of MJSC such as the monolithically integrated solar cells and the mechanically stacked solar cells. In monolithic multijunction solar cells, the electric current matching, lattice matching, and tunnel junction between subcells become the main issues which limit the overall performance of MJSC. In the mechanically stacked multijunction solar cells, the abovementioned problems can be overcome by applicating the separate load control for each subcell. The optical losses in the mechanically stacked multijunction solar cell are usually reduced by inserting an intermediate transparent and conductive layer such as ITO (indium titanium oxide) between two adjacent subcells.

There have been some experimental [15–18] and simulation studies [19–21] on the performance of multijunction solar cells under the variation of temperature and concentrated radiation, but to the best of author’s knowledge, none of them discuss the Al_{0.3}Ga_{0.7}As/InP/Ge solar cell. This paper is aimed at studying the performance of Al_{0.3}Ga_{0.7}As/InP/Ge MJSC under the variation of spectral irradiance (produced by concentrators) and temperature through a simulation approach using the PC1D program [22]. The use of the PC1D program for simulating the effects mentioned above on MJSC, again to the best of author’s knowledge, has never been found in the literature before. Hopefully, this study might help us in designing a robust, stable, and highly efficient solar cell in the future.

#### 2. Methods

Three steps need to be done in this research. First, the preparation of the incoming spectrum; second, the calculation of the absorption coefficient and the transmitted radiation; and the last step is the power-producing simulation. The first two steps were done numerically by solving some related formulas using MATLAB while the next step was done using a freely available PC1D program [22]. All these steps must be done for each subcell.

The incident spectral irradiance on the first subcell for one sun radiation was taken from AM1.5d direct solar spectrum (ASTM G173-03), while the multiplied spectral irradiances (5, 10, 50, 100, 150, and 200 suns) were obtained by multiplying this spectrum with its corresponding amplification factor. The freely available AM1.5d data in the web have a drawback due to discontinuous steps in the wavelength. To overcome this problem and to gain a smooth AM1.5d spectral irradiance, we must first reconstruct the radiation spectrum by using a blackbody radiation formula in Equation (1) and determine the constant , where for blackbody radiation and for the actual spectral irradiance. The temperature of blackbody radiation was set to *T* = 6000 K. The spectral irradiance (intensity divided by wavelength) of blackbody radiation received by the earth’s surface (terrestrial) is expressed as follows:where is the radius of the sun, is the distance between the center of the sun and the earth’s surface, is Planck’s constant, and is Boltzmann’s constant. By integrating the whole spectrum using a trapezoid method and setting the intensity value to 989.9 W/m^{2} (the total intensity of AM1.5d spectrum is the entire area under the versus curve), we can get the value of and reconstruct the smoothed AM1.5d spectrum using interpolation method.

The coefficient of absorption of each subcell was calculated using Equation (2) following the reference [23]:where is the coefficient absorption as a function of the wavelength, is the bandgap energy of the corresponding subcell, and is the incoming photon energy at a particular wavelength.

The transmitted intensity to the next subcell depends on the amount of the previous solar radiation , the thickness of the previous subcell , and the absorption coefficient of the previous subcell , which is as follows:where is the incoming spectral irradiance at the first subcell, is the incoming spectral irradiance at the second subcell, and is the incoming spectral irradiance at the third subcell. The thickness of the cell, , was calculated using the PC1D program. Since this program can only simulate one layer at a time, several simulations must be performed, depending on the number of junctions involved. The incoming multiplied radiation is then calculated using the following equation:where is defined as the multiplied incoming spectral irradiance. The SIMF (spectral irradiance multiplication factor) was set to 1, 5, 10, 50, 100, 150, and 200 and has the unit of suns. For each set of simulation (at a specific value of SIMF and temperature), we simulated the electrical performance of the MJSC in the form of the short circuit current (), the open circuit voltage (), the output power of each subcell (), and the total efficiency (). The total efficiency of the mechanically stacked multijunction solar cells is then calculated using the following equation:

There are two types of MJSC simulation. First, the identical electric current model, and second, the nonidentical electric current model [13]. In an identical current model (a series connection of the subcells), the amount of current flowing in each subcell is set to be the same. The current in the last subcell will dictate the amount of current in the whole MJSC because the last subcell (in the bottom layer) receives the least amount of spectral irradiance and produces the smallest current, and as a consequence, the output and the total efficiency of the MJSC will be dragged down in this model. The nonidentical electric current model, such as the case of mechanically stacked multijunction solar cells, in contrast, will maximize the output power in each subcell and increase the total efficiency of the solar cells. This nonidentical current model can increase the total efficiency by a factor of 1.7 as reported in Reference [13]. If the current record of MJSC’s efficiency is 45%, then the expected efficiency of the nonidentical current model can reach above 70%. This high value of solar cells efficiency under concentrated radiation has been theoretically predicted before, as can be found in Reference [24]. Although in reality, the nonidentical current model (harvesting the power from each subcell independently) seems unrealistic as compared to the identical current model, choosing this model does not change the intrinsic properties of MJSC in responding to the variation of temperature and incoming spectral irradiance. Note that this modeling can be considered as a toy model since some idealizations have been used here. The nonuniformity factors at the cell level which creates problems such as the occurrence of hotspots, the current mismatch between subcells, and the increase of resistive losses [25] were not taken into account in this paper.

#### 3. Results and Discussions

The spectrum of incoming radiation was calculated using Equations (1) and (3). In Figure 1, the solar radiation spectrum at the temperature of 25°C and SIMF = 1 and 200 were chosen to represent the entire spectra. As the SIMF value increased, the maximum spectral irradiance and intensity received by the MJSC. The energy gap and the absorption coefficient of each subcell will limit the spectrum range of absorbed spectral irradiance following the cutoff wavelength of each junction (). Based on that cutoff wavelength, the absorbed spectrum of Al_{0.3}Ga_{0.7}As was found within 280 nm to 685 nm range while for InP, within 598 to 841 nm and for Ge, within 872 to 1773 nm spectral range. Some overlapped regions between two adjacent subcells cannot be seen in Figure 1 due to overlapping colors.