Issue 
EPJ Photovolt.
Volume 13, 2022
Special Issue on ‘WCPEC8: State of the Art and Developments in Photovoltaics’, edited by Alessandra Scognamiglio, Robert Kenny, Shuzi Hayase and Arno Smets



Article Number  22  
Number of page(s)  8  
Section  High Efficiency Materials and Devices  New concepts  
DOI  https://doi.org/10.1051/epjpv/2022020  
Published online  14 October 2022 
https://doi.org/10.1051/epjpv/2022020
Regular Article
Overview and loss analysis of III–V singlejunction and multijunction solar cells
^{1}
Toyota Technological Institute, Nagoya 4688511, Japan
^{2}
Fraunhofer Institute for Solar Energy Systems ISE, Freiburg 79110, Germany
^{3}
University of New South Wales, Sydney 2052, Australia
^{*} email: masafumi@toyotati.ac.jp
Received:
2
June
2022
Received in final form:
26
July
2022
Accepted:
29
August
2022
Published online: 14 October 2022
The development of highperformance solar cells offers a promising pathway toward achieving high power per unit cost for many applications. Because stateoftheart efficiencies of singlejunction solar cells are approaching the ShockleyQueisser limit, the multijunction (MJ) solar cells are very attractive for highefficiency solar cells. This paper reviews progress in III–V compound singlejunction and MJ solar cells. In addition, analytical results for efficiency potential and nonradiative recombination and resistance losses in III–V compound singlejunction and MJ solar cells are presented for further understanding and decreasing major losses in III–V compound materials and MJ solar cells. GaAs singlejunction, III–V 2junction and III–V 3junction solar cells are shown to have potential efficiencies of 30%, 37% and 47%, respectively. Although in initial stage of developments, GaAs singlejunction and III–V MJ solar cells have shown low ERE values, ERE values have been improved as a result of several technology development such as device structure and material quality developments. In the case of III–V MJ solar cells, improvements in ERE of subcells are shown to be necessary for further improvements in efficiencies of MJ solar cells.
Key words: Highefficiency / singejunction solar cells / multijunction solar cells / loss analysis
© M. Yamaguchi et al., Published by EDP Sciences, 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
The development of highperformance solar cells offers a promising pathway toward achieving high power per unit cost for many applications. Because stateoftheart efficiencies of single junction solar cells are approaching the ShockleyQueisser limit [1], the multijunction (MJ) solar cells [2] are very attractive for highefficiency solar cells as shown in Figure 1. Although the concept of MJ solar cells was first and most successfully implemented using III–V compound materials, there is a need to further improve their conversion efficiency of III–V MJ solar cells and to show guidelines for realizing highefficiency MJ solar cells composed of other materials like perovskite, IIVI compounds and chalcogenides.
This paper reviews progress in III–V compound singlejunction and multijunction solar cells. In addition, analytical results for efficiency potential and nonradiative recombination and resistance losses in III–V compound singlejunction and multijunction solar cells are presented for further understanding and decreasing major losses in III–V compound materials and multi junction solar cells.
Fig. 1 Calculated efficiencies of III–V compound MJ solar cells under 1sun condition as a function of the number of junction and average external radiative efficiency (ERE) [2] in comparison with efficiency data (best laboratory efficiencies [3]). (Reproduced with permission from Ref. [2]. Updated). 
2 Overview for III–V singlejunction and multijunction solar cells
Figure 2 summarizes chronological improvements in conversion efficiencies of Si, GaAs, CIGS and perovskite singlejunction solar cells and III–V compound multijunction solar cells under 1sun operation [3] and future efficiency predictions of those solar cells (original idea by Professor A. Goetzberger et al. [4] and modified by M. Yamaguchi et al. [5]).
The function chosen here (Eq. (1)) is derived from the diode equation:
$$\eta (t)=\eta L\{1\mathrm{exp}[({a}_{0}a)/c]\}\text{,}$$(1)
where η(t) is the timedependent efficiency, η _{L} limiting asymptotic maximum efficiency, a _{0} is the year for which η(t) is zero, a is the calendar year and c is a characteristic development time. Fitting of the curve is done with three parameters which are given in Table 1. For example, 43% for η _{L} , 17 for a _{0} and 1975 for c were used in the case of III–V compound multijunction solar cells. The function can be fitted relatively well to the past development of best laboratory efficiencies of various solar cells under 1sun condition.
Fig. 2 Chronological efficiency improvements of crystalline Si, GaAs, CIGS, and perovskite singlejunction solar cells and III–V compound multijunction (MJ) solar cells under 1sun condition. 
Fitting parameters for different technologies.
3 Analytical procedure for estimating efficiency potential of various solar cells
One of the problems to attain the higher efficiency MJ and Si tandem solar cells is to reduce nonradiative recombination loss. The opencircuit voltage V_{oc} drop compared to bandgap energy (Eg/q − V_{oc}) is dependent upon nonradiative voltage loss (V_{oc},_{nrad}) that is expressed by external radiative efficiency (ERE). Opencircuit voltage is expressed by [6–10]
$${V}_{\text{oc}}={V}_{\text{oc,rad}}+(kT/q)\mathrm{ln}(\text{ERE})\text{,}$$(2)
where the second term on the righthand side of equation (2) is denoted as V _{oc,nrad} because it is associated to the voltageloss due to nonradiative recombination and V _{oc,rad} is radiative opencircuit voltage and is given by [6–10]
$${V}_{\text{oc,rad}}=(kT/q)\mathrm{ln}({J}_{L}({V}_{\text{oc,rad}})/{J}_{0\text{,rad}}+1)\text{,}$$(3)
where J_{L} (V_{oc,rad}) is photocurrent at opencircuit in the case of only radiative recombination and J_{0,rad} is saturation current density in the case of only radiative recombination. 0.28 V [8–10] for III–V compounds and perovskite, and 0.26 V [8–10] for Si solar cells were used as ΔV_{oc, rad} (= E_{g}/q − V_{oc,rad}) in this study. In the case of multijunction tandem solar cells, we define average ERE (ERE_{ave}) by using average V_{oc} loss [11]:
$$\sum ({V}_{\text{oc},n}{V}_{\text{oc,rad},n})/n=(kT/q)\mathrm{ln}({\text{ERE}}_{\text{ave}})\text{,}$$(4)
where n is the number of junctions.
The resistance loss of a solar cell is estimated solely from the measured fill factor. Fill factor is dependent upon V _{oc} and ideal fill factor FF_{0} , defined as the fill factor without any resistance loss, used in the calculation is empirically expressed by [12],
$$\text{FF}0=[{v}_{\text{oc}}\mathrm{ln}({v}_{\text{oc}}+0.72)]/({v}_{\text{oc}}+1)\text{,}$$(5)
where v _{oc} is normalized opencircuit voltage and is given by
$${v}_{\text{oc}}={V}_{\text{oc}}/(nkT/q)\text{.}$$(6)
The measured fill factor FF is decreased as increase in series resistance R _{s} and decrease in shunt resistance R _{sh} of solar cell and approximated by
$$\text{FF}\approx \text{FF}0(1{r}_{s})(11/{r}_{sh})\approx \text{FF}0(1{r}_{s}1/{r}_{sh})\text{,}$$(7)
where r_{s} and r_{sh} are normalized series resistance and normalized shunt resistance, respectively and are given by
$${r}_{s}={R}_{s}/{R}_{\text{CH}}$$(8)
$${r}_{sh}={R}_{\text{sh}}/{R}_{\text{CH}}$$(9)
The characteristic resistance R _{CH} is expressed by [12]
$${R}_{\text{CH}}={V}_{\text{oc}}/{I}_{\text{sc}}\text{.}$$(10)
In the calculation, highest values obtained were used as J _{sc}. V _{oc} and FF were calculated by equations (2)–(10) and conversion efficiency potential of various solar cells were calculated as a function of ERE.
4 Analysis for nonradiative recombination loss and efficiency potential of III–V singlejunction and multijunction solar cells
Figure 3 shows calculated efficiencies of GaAs singlejunction, III–V 2junction, III–V/Ge 3junction and III–V/InGaAs 3junction solar cells as a function of average external radiative efficiency (ERE) in comparison with the stateofthe art efficiencies of those solar cells [3] including chronological efficiency improvements [5]. GaAs singlejunction, III–V 2junction and III–V 3junction solar cells have potential efficiencies of 30%, 37% and 47%, respectively. Highest efficiency of 39.5% [3,13] has been demonstrated with III–V 3junction solar cells under 1sun by NREL, further efficiency improvements in III–V multijunction solar cells by improving ERE and reducing resistance loss are expected. For this end, reduction on nonradiative recombination and resistance losses is necessary.
Figure 4 shows chronological ERE improvements of GaAs singlejunction, III–V 2junction, III–V/Ge 3junction and III–V/InGaAs 3junction solar cells.
Although in initial stage of developments, GaAs singlejunction and III–V MJ solar cells have shown low ERE values, ERE values have been improved as a result of several technology development. For example, in the case of GaAs singlejunction solar cells, heteroface and double hetero junction solar cells have been developed from homo junction solar cells. Recently, high ERE values have been realized by photon recycling [14,15].
In the case of III–V MJ solar cells, improvements in ERE of subcells are necessary for further improvements in efficiencies of MJ solar cells. For example, in the case of 6junction solar cell [16], ERE (1.3 × 10^{−4}%) for the 1st 2.19 eV AlGaInP cell 0.044% for the 2nd 1.76 eV AlGaAs cell are lower than 1.4% for the 3rd 1.42eV GaAs cell and 2.1% for 4th 1.19 eV GaInAs cell and 5th 0.97 eV GaInAs cell. Lower ERE values for Alrelated cells are thought to be due to oxygenrelated nonradiative recombination center [17].
Figure 5 shows chronological fill factor FF improvements of GaAs singlejunction, III–V 2junction, III–V/Ge 3junction and III–V/InGaAs 3junction solar cells.
Although in initial stage of developments, GaAs singlejunction and III–V MJ solar cells have shown low fill factor values, FF values have been improved as a results of improvements in series resistance and shunt resistance.
Figure 6 shows changes in average external radiative efficiency ERE for III–V multijunction, III–V/Si tandem solar cells and perovskite/Si tandem solar cells as a function of number of junctions. In Figure 6, estimated average ERE values for GaAs singlejunction [3,14], III–V 2junction [3,18], III–V 3junction [3,13], III–V 5junction [3,19], III–V 6junction [3,16], III–V/Si 2junction [3,20], III–V/Si 3junction [3,21], perovskite singlejunction [3] and perovskite/Si 2junction [3,22] solar cells were plotted. It is clear in Figure 6 that ERE for III–V MJ and Si tandem solar cells decreases as increase in number of junctions. Further improvements in ERE of subcells are necessary for further improvements in efficiencies of MJ and Si tandem solar cells. Especially, in the case of III–V based MJ solar cells, Al contained widebandgap subcell layer is suggested to be lower ERE due to oxygenrelated nonradiative recombination center [17].
In this paper, nonrecombination center behavior of AlGaInP top cell and AlGaAs 2nd layer solar cells was analyzed by using data for molecularbeam epitaxy grown Al_{l0.3}Ga_{0.7}As solar cells reported by one of the authors [23]. In this analysis, we assumed that the external radiative efficiency IRE is equal to the internal radiative efficiency IRE as follows:
$$\text{ERE}=\text{IRE}={\tau}_{\text{eff}}/{\tau}_{\text{rad}}\text{,}$$(11)
where τ _{rad} is the radiative recombination lifetime and expressed by
$${\tau}_{\text{rad}}=1/BN\text{,}$$(12)
where N is carrier concentration and B is radiative recombination probability (2 × 10^{−10} cm^{3}/s for GaAs [24]).
Effective lifetime τ _{eff} is expressed by
$$1/{\tau}_{\text{eff}}=1/{\tau}_{\text{rad}}+1/{\tau}_{\text{nonrad}}\text{,}$$(13)
where τ _{nonrad} is nonradiative recombination lifetime and given by
$$1/{\tau}_{\text{nonrad}}=\sigma \nu {N}_{r}\text{,}$$(14)
where σν is minoritycarrier thermal velocity, σ is capture cross section of nonradiative recombination centers, and N _{r} is density of nonradiative recombination centers. In this analysis, 10^{−10} cm^{2} was used as capture cross section of oxygen related nonradiative recombination center (E _{c} – 0.86 eV in AlGaAs) by fitting correlation curve between ERE and N _{r} as shown as dotted line in Figure 7 . ERE values were determined by using voltage loss expressed by equation (2). Table 2 shows activation energies and capture cross sections in AlGaAs [25–27] and our result. As shown in Table 2, it is clear that oxygenrelated defect in AlGaAs acts as very active defect center because it has higher capture cross section. In addition, the oxygen related defect in AlGaAs has been confirmed to act as a nonradiative recombination center by using double carrier pulse DLTS (Deep Level Transient Spectroscopy) in our previous study [17]. Density of nonrecombination center density N_{r} in 2.19 eV AlGaInP top cell and 1.76eV AlGaAs 2nd layer cell of 6junction solar cell [16] was estimated by equations (11)–(14) and was compared with data for MBEgrown 1.77 eV AlGaAs singlejunction solar cell [23].
Figure 7 shows changes in external radiative efficiency ERE for 2.1 eV AlGaInP top cell and 1.76 eV AlGaAs 2nd layer cell of 6junction solar cell [16] and MBEgrown 1.77 eV AlGaAs singlejunction solar cell [23] as a function of nonradiative recombination centers estimated by using equations (11)–(14). Because ERE (1.3 × 10^{−4}%) for the 1st 2.19 eV AlGaInP cell 0.044% for the 2nd 1.76 eV AlGaAs cell are lower than 1.4% for the 3rd 1.45 eV (Al)GaAs cell and 2.1% for 4th 1.19 eV GaInAs cell and 5th 0.97 eV GaInAs cell in the 6junction solar cell [16], reduction in density of nonrecombination center in Alcontained widebandgap layer is necessary as pointed out by one of coauthors [17]. Lower ERE values for Alcontained solar cells are thought to be due to oxygenrelated nonradiative recombination center [17].
Figure 8 shows changes in fill factor FF for III–V multijunction, III–V/Si tandem solar cells and perovskite/Si tandem solar cells as a function of number of junctions. In Figure 8, reported fill factor values for GaAs singlejunction [3,14], III–V 2junction [3,18], III–V 3junction [3,22], III–V 5junction [3,19], III–V 6junction [3,16], III–V/Si 2junction [3,20], III–V/Si 3junction [3,21], perovskite singlejunction [3] and perovskite/Si 2junction [3,22] solar cells were plotted. It is clear in Figure 8 that FF for III–V MJ and Si tandem solar cells decreases as increase in number of junctions. Further improvements in FF for III–V MJ solar cells and Si tandem solar cells are necessary by improvements in series resistance and shunt resistance.
Although resistance loss is composed of absorber, interface, contact, interconnection and grid of solar cells, especially, fill factor of perovskite/Si tandem solar cells is dependent on contact resistance of interconnection of subcells such as transparent conductive oxide layer, recombination junction and so forth. Figure 9 shows correlation between fill factor and series resistance of perovskite singlejunction solar cell [28] and perovskite/Si 2junction solar cell [29]. Calculated results for series resistance of perovskite singlejunction solar cell were estimated by using equations (5)–(10). Difference between measured values and calculated results for perovskite singlejunction solar cells are thought to be attributed from shunt resistance. Further improvements in FF for perovskite/Si tandem solar cells are necessary by improvements in series resistance and shunt resistance.
Fig. 3 Calculated efficiencies of GaAs singlejunction, III–V 2junction, III–V/Ge 3junction and III–V/InGaAs 3junction solar cells as a function of average ERE in comparison with the stateof theart efficiencies of those solar cells including chronological efficiency improvements. 
Fig. 4 Chronological ERE improvements of GaAs singlejunction, III–V 2junction, III–V/Ge 3junction and III–V/InGaAs 3junction solar cells. 
Fig. 5 Chronological fill factor improvements of GaAs singlejunction, III–V 2junction, III–V/Ge 3junction and III–V/InGaAs 3junction solar cells. 
Fig. 6 Changes in average external radiative efficiency ERE for III–V multijunction, III–V/Si tandem solar cells and perovskite/Si tandem solar cells as a function of number of junctions. 
Fig. 7 Changes in external radiative efficiency ERE for AlGaInP top cell and AlGaAs 2nd layer cell of 6junction solar cell [16] and MBEgrown AlGaAs singlejunction solar cell [18] as a function of nonradiative recombination centers estimated by using equations (11)–(14). 
Fig. 8 Changes in fill factor for III–V multijunction, III–V/Si tandem solar cells and perovskite/Si tandem solar cells as a function of number of junctions. 
Fig. 9 Correlation between fill factor and contact resistivity of perovskite singlejunction and perovskite/Si 2junction solar cells. 
5 Summary
This paper overviewed progress in III–V multijunction (MJ) solar cells. In addition, analytical results for efficiency potential of III–V MJ solar cells were presented and non radiative recombination and resistance losses of III–V MJ solar cells were discussed in this paper. GaAs singlejunction, III–V 2junction and III–V 3junction solar cells have potential efficiencies of 30%, 37% and 47%, respectively. Although in initial stage of developments, GaAs singlejunction and III–V MJ solar cells have shown low external radiative efficiency ERE values, ERE values have been improved as a result of several technology development such as device structure and material quality developments. It was shown in this study that ERE and fill factor FF for III–V MJ and Si tandem solar cells decreases as increase in number of junctions. Further improvements in FF for III–V MJ solar cells and Si tandem solar cells are necessary by improvements in series resistance and shunt resistance. Improvements in ERE of subcells were shown to be necessary for further improvements in efficiencies of MJ solar cells. Especially, Al contained widebandgap subcell layer showed lower ERE due to oxygenrelated nonradiative recombination center.
Conflict of interest
The authors declare no conflict of interest.
Supporting Information
Supporting Information is available from the Wiley Online Library or from the authors.
Data availability
The data that support the findings of this study are available upon reasonable request from the authors.
Author contribution statement
The supervision of the project was ensured by M. Yamaguchi. The experiments were conducted by M. Yamaguchi, N. EkinsDaukes and N. Kojima. The analysis was conducted by M. Yamaguchi, F. Dimroth and N. Ohshita. Discussion on results was conducted by all coauthors. The writing of the manuscript and proof reading were done by all coauthors.
The authors would like to express sincere thanks to Dr. J.F. Geisz, Dr. M.A. Steiner and Dr. R. France, NREL for their fruitful discussion, to the NEDO for their support and to Dr. T. Takamoto, Sharp, Dr. K. Araki and Dr. KH. Lee, former Toyota Tech. Inst., Prof. A. Yamamoto, Dr. H. Sugiura, Prof. K. Ando, Dr. C. Amano, Prof. S. Katsumoto and Dr. M. Sugo, Former NTT Labs., Dr. M. AlJassim, Dr. R. Ahrienkiel, Dr. J. Olson, Dr. S.R. Kurtz and Dr. D.J. Friedman, NREL, Prof. A. Luque and Prof. G. Sala, UPM, Dr. A. Bett and Dr. G. Siefer, FhGISE, Dr. Y. Hishikawa, AIST, Prof. Y. Okada and Prof. M. Sugiyama, Univ. Tokyo, Prof K. Nishioka and Prof. Y. Ota, Univ. Miyazaki for their helpful discussion and collaboration.
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Cite this article as: Masafumi Yamaguchi, Frank Dimroth, Nicholas J. EkinsDaukes, Nobuaki Kojima, Yoshio Ohshita, Overview and loss analysis of III–V singlejunction and multijunction solar cells, EPJ Photovoltaics 13, 22 (2022)
All Tables
All Figures
Fig. 1 Calculated efficiencies of III–V compound MJ solar cells under 1sun condition as a function of the number of junction and average external radiative efficiency (ERE) [2] in comparison with efficiency data (best laboratory efficiencies [3]). (Reproduced with permission from Ref. [2]. Updated). 

In the text 
Fig. 2 Chronological efficiency improvements of crystalline Si, GaAs, CIGS, and perovskite singlejunction solar cells and III–V compound multijunction (MJ) solar cells under 1sun condition. 

In the text 
Fig. 3 Calculated efficiencies of GaAs singlejunction, III–V 2junction, III–V/Ge 3junction and III–V/InGaAs 3junction solar cells as a function of average ERE in comparison with the stateof theart efficiencies of those solar cells including chronological efficiency improvements. 

In the text 
Fig. 4 Chronological ERE improvements of GaAs singlejunction, III–V 2junction, III–V/Ge 3junction and III–V/InGaAs 3junction solar cells. 

In the text 
Fig. 5 Chronological fill factor improvements of GaAs singlejunction, III–V 2junction, III–V/Ge 3junction and III–V/InGaAs 3junction solar cells. 

In the text 
Fig. 6 Changes in average external radiative efficiency ERE for III–V multijunction, III–V/Si tandem solar cells and perovskite/Si tandem solar cells as a function of number of junctions. 

In the text 
Fig. 7 Changes in external radiative efficiency ERE for AlGaInP top cell and AlGaAs 2nd layer cell of 6junction solar cell [16] and MBEgrown AlGaAs singlejunction solar cell [18] as a function of nonradiative recombination centers estimated by using equations (11)–(14). 

In the text 
Fig. 8 Changes in fill factor for III–V multijunction, III–V/Si tandem solar cells and perovskite/Si tandem solar cells as a function of number of junctions. 

In the text 
Fig. 9 Correlation between fill factor and contact resistivity of perovskite singlejunction and perovskite/Si 2junction solar cells. 

In the text 
Current usage metrics show cumulative count of Article Views (fulltext article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
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Initial download of the metrics may take a while.