Overview and loss analysis of III – V single-junction and multi-junction solar cells

. The development of high-performance solar cells offers a promising pathway toward achieving high power per unit cost for many applications. Because state-of-the-art ef ﬁ ciencies of single-junction solar cells are approaching the Shockley-Queisser limit, the multi-junction (MJ) solar cells are very attractive for high-ef ﬁ ciency solar cells. This paper reviews progress in III – V compound single-junction and MJ solar cells. In addition, analytical results for ef ﬁ ciency potential and non-radiative recombination and resistance losses in III – V compound single-junction and MJ solar cells are presented for further understanding and decreasing major losses in III – V compound materials and MJ solar cells. GaAs single-junction, III – V 2-junction and III – V 3-junction solar cells are shown to have potential ef ﬁ ciencies of 30%, 37% and 47%, respectively. Although in initial stage of developments, GaAs single-junction 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 sub-cells are shown to be necessary for further improvements in ef ﬁ ciencies of MJ solar cells.


Introduction
The development of high-performance solar cells offers a promising pathway toward achieving high power per unit cost for many applications. Because state-of-the-art efficiencies of single-junction solar cells are approaching the Shockley-Queisser limit [1], the multi-junction (MJ) solar cells [2] are very attractive for high-efficiency 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 high-efficiency MJ solar cells composed of other materials like perovskite, II-VI compounds and chalcogenides.
This paper reviews progress in III-V compound singlejunction and multi-junction solar cells. In addition, analytical results for efficiency potential and non-radiative recombination and resistance losses in III-V compound single-junction and multi-junction solar cells are presented for further understanding and decreasing major losses in III-V compound materials and multi-junction solar cells.
2 Overview for III-V single-junction and multi-junction solar cells  [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: where h(t) is the time-dependent efficiency, h L limiting asymptotic maximum efficiency, a 0 is the year for which h(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 [2] in comparison with efficiency data (best laboratory efficiencies [3]). (Reproduced with permission from Ref. [2]. Updated). loss. The open-circuit voltage V oc drop compared to bandgap energy (Eg/q À V oc ) is dependent upon non-radiative voltage loss (V oc , nrad ) that is expressed by external radiative efficiency (ERE). Open-circuit voltage is expressed by [6-10] where the second term on the right-hand side of equation (2) is denoted as V oc,nrad because it is associated to the voltageloss due to non-radiative recombination and V oc,rad is radiative open-circuit voltage and is given by [6][7][8][9][10] V oc;rad ¼ ðkT =qÞlnðJ L ðV oc;rad Þ=J 0;rad þ 1Þ; ð3Þ where J L (V oc,rad ) is photo-current at open-circuit 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][9][10] for III-V compounds and perovskite, and 0.26 V [8][9][10] for Si solar cells were used as DV oc, rad (= E g /q À V oc,rad ) in this study. In the case of multi-junction tandem solar cells, we define average ERE (ERE ave ) by using average V oc loss [11]: X ðV oc;n À V oc;rad;n Þ=n ¼ ðkT =qÞlnðERE ave Þ; ð4Þ 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], where v oc is normalized open-circuit voltage and is given by 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 where r s and r sh are normalized series resistance and normalized shunt resistance, respectively and are given by The characteristic resistance R CH is expressed by [12] 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. Figure 3 shows calculated efficiencies of GaAs singlejunction, III-V 2-junction, III-V/Ge 3-junction and III-V/ InGaAs 3-junction solar cells as a function of average external radiative efficiency (ERE) in comparison with the state-of-the art efficiencies of those solar cells [3] including chronological efficiency improvements [5]. GaAs singlejunction, III-V 2-junction and III-V 3-junction solar cells have potential efficiencies of 30%, 37% and 47%, respectively. Highest efficiency of 39.5% [3,13] has been demonstrated with III-V 3-junction solar cells under 1-sun 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 single-junction, III-V 2-junction, III-V/Ge 3-junction and III-V/InGaAs 3-junction 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 single-junction solar cells, hetero-face 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 sub-cells are necessary for further improvements in efficiencies of MJ solar cells. For example, in the case of 6-junction solar cell [16], ERE (1.3 Â 10 À4 %) 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 Al-related cells are thought to be due to oxygen-related non-radiative recombination center [17].    Figure 6, estimated average ERE values for GaAs single-junction [3,14], III-V 2-junction [3,18], III-V 3-junction [3,13], III-V 5-junction [3,19], III-V 6-junction [3,16], III-V/Si 2-junction [3,20], III-V/Si 3-junction [3,21], perovskite single-junction [3] and perovskite/Si 2-junction [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 sub-cells 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 wide-bandgap sub-cell layer is suggested to be lower ERE due to oxygen-related non-radiative recombination center [17]. In this paper, non-recombination center behavior of AlGaInP top cell and AlGaAs 2nd layer solar cells was analyzed by using data for molecular-beam 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: where t rad is the radiative recombination lifetime and expressed by where N is carrier concentration and B is radiative recombination probability (2 Â 10 À10 cm 3 /s for GaAs [24]). Effective lifetime t eff is expressed by where t nonrad is non-radiative recombination lifetime and given by where sn is minority-carrier thermal velocity, s is capture cross section of non-radiative recombination centers, and N r is density of non-radiative recombination centers. In this analysis, 10 À10 cm 2 was used as capture cross section of oxygen related non-radiative 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][26][27] and our result. As shown in Table 2, it is clear that oxygen-related 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 non-radiative recombination center by using double carrier pulse DLTS (Deep Level Transient Spectroscopy) in our previous study [17]. Density of non-recombination center density N r in 2.19 eV AlGaInP top cell and 1.76eV AlGaAs 2nd layer cell of 6-junction solar cell [16] was estimated by equations (11)- (14) and was compared with data for MBE-grown 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 6-junction solar cell [16] and MBE-grown 1.77 eV AlGaAs single-junction solar cell [23] as a function of non-radiative recombination centers estimated by using equations (11)- (14). Because ERE (1.3 Â 10 À4 %) 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 6-junction solar cell [16], reduction in density of non-recombination center in Al-contained wide-bandgap layer is necessary as pointed out by one of co-authors [17]. Lower ERE values for Al-contained solar cells are thought to be due to oxygenrelated non-radiative 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 2-junction [3,18], III-V 3-junction [3,22], III-V 5-junction [3,19], III-V 6-junction [3,16], III-V/Si 2-junction [3,20], III-V/Si 3-junction [3,21], perovskite single-junction [3] and perovskite/Si 2-junction [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   7. Changes in external radiative efficiency ERE for AlGaInP top cell and AlGaAs 2nd layer cell of 6-junction solar cell [16] and MBE-grown AlGaAs single-junction solar cell [18] as a function of non-radiative recombination centers estimated by using equations (11)- (14).  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 2-junction solar cell [29]. Calculated results for series resistance of perovskite single-junction solar cell were estimated by using equations (5)- (10). Difference between measured values and calculated results for perovskite single-junction 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.

Summary
This paper overviewed progress in III-V multi-junction (MJ) solar cells. In addition, analytical results for efficiency potential of III-V MJ solar cells were presented and nonradiative recombination and resistance losses of III-V MJ solar cells were discussed in this paper. GaAs singlejunction, III-V 2-junction and III-V 3-junction solar cells have potential efficiencies of 30%, 37% and 47%, respectively. Although in initial stage of developments, GaAs single-junction 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 sub-cells were shown to be necessary for further improvements in efficiencies of MJ solar cells. Especially, Al contained wide-bandgap subcell layer showed lower ERE due to oxygen-related nonradiative recombination center.