Thin film absorbers for tandem solar cells: an industrial perspective

Tandem solar cells have received a lot attention from academia and industrial researchers as the potential next-generation PV technology, with higher efficiency above the limit of single-junction solar cells. Thin-film/thin-film (TF/TF) tandems are attractive due to similar toolset and processes producing the top and bottom cells, which improve scalability and promote cost reduction compared to TF/wafer tandem technologies. TF/TF/tandems additionally offer more absorber bandgap flexibility that promotes photovoltaic conversion efficiency optimization. Many materials not suitable for single junction solar cells can be explored as tandem top or bottom cells. To assess the practical efficiency potential of tandem solar cells limited by non-ideal material and device quality, we present a Shockley–Queisser-like efficiency calculation for tandem devices consisting of non-ideal top and bottom cells and with a range of absorber band gaps. The non-ideality is introduced through an experimentally measurable external radiative quantum efficiency (ERE). We find that a range of top and bottom cell band gaps enabling the highest tandem efficiency shifts from the ideal Shockley–Queisser case and depends on the top and bottom cell ERE. Furthermore, tandem cell efficiency greater than 37% can be achieved with very modest top/bottom cell EREs, for example of only 0.008%/0.5% which is typical for CdTe/CIS cells. Our results indicate that high efficiency tandem solar cells have good probability to be manufactured at high volume within a foreseeable future, despite non-ideal material and device quality due to early stages of development or constraint by manufacturing requirements. Finally, we review a number of mature and emerging thin film absorber material candidates for tandem applications. We discuss properties of these materials and the corresponding device performance as well as the associated technological challenges. We concludes on the promise of each of these materials for tandem applications that is expected to provide guidance to the photovoltaic research community.


Single-junction thin-film (TF) solar cells
Presently photovoltaics (PV) is one of the cheapest energy resources based on the levelized cost of energy (LCOE).LCOE is a measure of the cost of electricity generation for a particular system averaged over its lifetime.The LCOE includes cost of equipment manufacturing, installation, operation and maintenance, decommissioning and other costs offset by the cost of the actual energy delivered.Factors affecting solar module energy production include the initial efficiency, degradation rate, temperature coefficient, spectrum response, the bifaciality, etc.In the recent LAZARD's LCOE analysis [1], the LCOE of utility scale solar farm ranged from $30 to $41 MWh −1 for Si PV, while the LCOE for thin film PV (mostly CdTe) ranged from $28 to $37 MWh −1 .Thin film PV has fundamentally better cost structures due to 98%-99% reduction in semiconductor material consumption.Its lower energy and water usage enables lower carbon footprint and faster energy payback time.The manufacturing line can be fully integrated, and the monolithic design of thin film module allows the coating of an entire module area at a time unlike in the production of separate Si cells requiring subsequent integration into a module.With First Solar's CdTe module manufacturing process, glass-in to module-out usually can be achieved in less than 4.5 h, while for conventional crystalline silicon batch technologies it may take up to 3 d.
Among thin film PV technologies, CdTe, CIGS, and GaAs have been extensively studied in laboratories and corresponding cell efficiencies are well above 20%.In the last decade, significant progress was made developing perovskite solar cells with record efficiencies reaching 25.7%.Attempts to commercialize the perovskite technology are ongoing.
It is worth noting that high solar cell efficiencies demonstrated in the R&D labs or at pilot lines do not guarantee commercial success of a particular technology at large scale.For example, record efficiency of GaAs solar cells is higher than that of Si.Nevertheless, the annual module production capacity of GaAs is minuscule compared with the capacity of Si production that exceeded 200 GW in 2021.CdTe and CIGS cells have very similar record efficiencies.Production capacity of CdTe is approaching 20 GW while for CIGS it is less than 1 GW and shrinking.This can be largely attributed to the degree of complexity of the selected material system, in particular the absorber.For high volume manufacturing, a highly defect tolerant material system often means lower cost because of larger process windows, higher product yield, higher equipment uptime, and likely lower capital equipment investment.
Looking at the phase diagrams (figure 1) it is obvious that CIGS material system is more complex than Si or CdTe.Both CdTe and Si thermodynamically favor pure and energetically stable phases.This means that lower densities of detrimental absorber defects can be expected.On the other hand, phase diagram of the CIGS materials system is very complex and higher defect density can be expected.This in turn implies an inherently narrow manufacturing process window, poor production yield and more expensive equipment.Taking another example, low defect density GaAs absorber can be deposited, but only on single-crystal wafers with an expensive lift-off technique.Despite high efficiency in manufacturing environment, GaAs technology is at a cost disadvantage compared to Si or CdTe.One could argue that the perovskite material system has evolved and become more complex over time.There are many defects in perovskite, and nevertheless it appears more defect tolerant than other PV absorber materials as most of the defect levels fall within conduction and valence bands in as-made perovskite cells.However, little is known about the role these impurities play in perovskite device long-term performance degradation.

Why TF/TF tandem solar cells
Presently, most of the tandem cell research is focused on perovskite/Si absorber materials combination.The choice is natural given the maturity of Si single-junction technology.However, Si bottom cell is not an ideal partner of the thin film top cell, in either of the common monolithically integrated or mechanically stacked perovskite/Si tandem architectures.The former requires current matching of the top and bottom cells, which is achieved at standard test conditions by varying perovskite cell bandgap and thickness.Current matching is broken under non-AM1.5 conditions with either the top or bottom cell limiting tandem cell current and leading to large energy losses that are variable during the day and seasonally.Manufacturing scale-up is difficult because, for the best performance, sub-micrometer thick perovskite device layers need to be uniformly and continuously deposited on highly textured Si cells.
Mechanically stacked tandem can be current-or voltage-matched.The former will suffer from the same spectral sensitivity as the monolithically integrated tandem.Voltage matching of top perovskite and bottom Si submodules requires many fewer perovskite cells per submodule compared to the number of Si cells due to the approximately two times higher per cell voltage of the former.Wafer-based Si bottom submodule provides very little voltage variation flexibility in voltage-matched tandem.The number of cells per wafer is usually limited to 2 or 3 due to cutting-related efficiency and reliability losses, as well as production throughput concerns.Four-terminal tandem does not require submodule matching thus allowing for greater optimization flexibility.However, it requires additional maximum power point tracking, and therefore, higher balance of system costs.
TF/TF tandem presents an opportunity that is free from these disadvantages.In TF/TF tandem the cells in both the top and bottom submodule will be integrated using series or series-parallel connection by laser scribes.This monolithic integration approach provides broad flexibility of submodule voltage and current adjustment for the submodule electrical matching.Top-bottom submodule interconnect is also expected to be significantly simpler in TF/TF vs wafer-based tandem due to the similar top and bottom module layouts.
In addition, the top and bottom cell candidates can be individually selected and optimized for tandem instead of single junction applications.This approach may open a field of new absorber materials with the band gaps that are suitable for tandem but not ideal for single junction devices.One can tailor existing single junction absorber materials or explore new materials candidates suitable for tandem applications.Several materials systems suitable for thin film top and bottom cells have broadly adjustable band gaps.
Furthermore, TF/TF tandem is expected to have a lower bill of materials (BOMs) versus a wafer-based Si-tandem.The cost of Si cell fabrication is more than 50% of the total Si module cost [2].For CdTe, the cost of semiconductor is much lower and is around 10% of the BOMs [2].Monolithic integration of thin film cells in the module further reduces the BOM.The fact that bottom Si submodule generates much less energy than a single junction Si module further amplifies Si bottom cell cost disadvantage.In TF/TF tandem, both top and bottom cells can use similar manufacturing equipment and processes.Therefore, TF/TF tandem is fundamentally simpler to manufacture and scale up.

Optimal top and bottom cell bandgaps
The theoretical Shockley-Queisser efficiency limit of single junction solar cells ranges from approximately 30% to approximately 32%, with an optimal absorber band gap between 1.0 and 1.6 eV.It is believed that the practical efficiency limit is around 28% for Si [3], CdTe [4], and GaAs [5].Tandem solar cells can break this efficiency limit, with Shockley-Queisser-like theoretical efficiencies greater than 40% achievable in a broad range of top/bottom cell absorber band gap combinations [6].Similar to single junction cells, practical tandem Eff limit is lower than predicted by the Shockley-Queisser model.One important factor limiting either the single junction or tandem cell efficiency is absorber material and interface quality which are often characterized by the external radiation efficiency (ERE).We present calculated tandem cell efficiency for a range of absorber bandgaps and for the ERE values typical of several tandem technologies.The results suggest that even with the ERE that are worse than that of the best Si or GaAs cells, a tandem cell efficiency >35% can be readily achieved.
We use the Shockley-Queisser model to predict optimal tandem top and bottom cell bandgap combinations and to calculate conversion efficiencies of these tandems.Tandem cells are assumed to be mechanically stacked and in four-terminal (4T) configuration so that any top-bottom cell current or voltage mismatch losses can be neglected.The Shockley-Queisser formalism is used in its original form for the top cell efficiency calculations.For the bottom cell, the formalism is modified in the usual way so that only light with energies between the top and bottom cell energy gaps is absorbed by the cell [6].
The calculation is additionally made more realistic by accounting for nonradiative recombination losses by varying the Shockley-Queisser radiation fraction parameter f c .Radiation intensity emitted by such non-ideal cell as a fraction of the radiation emitted by similar cell with zero nonradiative recombination, i.e. at Shockley-Queisser radiative recombination limit, is what is often reported as ERE in photo-and electroluminescence experiments.The impact of nonradiative recombination and cell ERE on single-junction theoretical maximum conversion efficiency was recently studied by Green and Ho-Baillie for various single-junction PV cell technologies [7].
ERE is a measure of the quasi-Fermi level splitting, or free energy of the electron-hole pairs, in solar cell absorber.Conversion of this energy into electrical energy in practical single-junction and tandem cells is subject to additional carrier extraction selectivity and resistive losses.There are several other loss components that are present in practical tandem devices.One is optical losses in and between tandem top and bottom cells.Another is injection dependence of non-radiative recombination fraction or the ERE.The latter is important when comparing bottom cell operating under filtered light and maximum power point rather than at 1 sun open circuit conditions that are often used for ERE estimations.None of these additional losses are accounted for in the analysis that we present.However, given that nonradiative recombination (ERE ≪ 1) is a major source of losses beyond the Shockley-Queisser limit for many practical top and bottom cell candidates, the predictions presented below are expected to provide an accurate absorber material selection guidance.
We first calculate 4T mechanically stacked tandem Shockley-Queisser efficiency versus top and bottom cell bandgaps for the ideal case of ERE = 1; the results are shown in figure 2. Maximum tandem efficiency of about 45% is achieved for top and bottom cell bandgaps close to 1.7 eV and 0.95 eV, respectively, similarly to earlier studies [6].The maximum efficiency is achieved because of a tradeoff between the free carrier thermalization losses (defined here as the energy of the absorbed photon minus the free energy of the electron-hole pair) in the top and bottom cells.
Next, we calculate tandem efficiencies for top and bottom cells with ERE less than 1.In Shockley-Queisser model, the ERE or the radiation fraction parameter enters through the dark saturation current, which directly impacts cell V oc .One can, therefore, choose ERE values that provide V oc typical for a particular solar cell technology.For example, record 22.1% CdTe cell V oc of 887 mV [8] is achieved with an ERE of 0.008%; record 19.2% 1.0 eV CIS cell V oc of 609 mV [9] is achieved with an ERE = 0.5%; 26.7% 738 mV Si cell [8] is achieved with an ERE = 1.6%; 25.7% 1.18 V perovskite cell [8] is achieved with an ERE = 9.2% (assuming the bandgap of 1.53 eV from an earlier publication by the same group [10]).Since we neglect losses other than those resulting from nonradiative recombination, these ERE values may be somewhat underestimated.This analysis, nevertheless, provides useful tandem optimization guidance.
Using these practically achievable ERE values demonstrated by CdTe (0.008%), Si (1.6%), perovskite (9.2%), and CIS (0.5%), we re-calculate the Shockley-Queisser efficiencies for tandem cells with various top and bottom cell bandgaps.The top/bottom ERE pairs of 0.008%/0.5%,9.2%/0.5% and 9.2%/1.6%are used.The results are plotted in figure 3. Peak tandem Eff is reduced to about 37% in the first case and to 40%-41% in the second and third.Even though these efficiencies are lower than the theoretical 45% tandem efficiency limit, they are still in all cases well above the efficiencies of the corresponding single-junction constituents.Optimal bandgap combinations are also different from the ERE = 1 case and achieved for top/bottom cell bandgaps of 1.95/1.15eV for the lowest ERE pair.For higher EREs optimal bandgaps remain close to the ERE = 1 case but the second maximum with an almost equal efficiency at 1.8/1.15eV becomes almost as pronounced.
Most of the recently published tandem Eff research was focused on 2T monolithic perovskite/Si tandems.Our analysis applies to 2T tandems provided current mismatch losses are minimized, which should be the  case for the best performing tandem cells.The 2T perovskite/Si Eff record of 33.7% is currently held by KAUST [8].The 4T perovskite/Si tandem Eff of 30.3% was reported by Duong et al [11], while 27.0% 4T perovskite/CIGS tandem was reported by Wahl et al [12].Perovskite top cell bandgap was not reported for KAUST 2T tandem while the bandgap was 1.55 eV in the 4T perovskite/Si device and 1.65 eV in the 4T perovskite/CIGS device, both of which are close to the optimal according to our calculation.We will also mention that calculated top cell bandgap range, enabling tandem Eff that is close to the maximum, is broad.In all the referenced cases tandem cell Eff were significantly below their calculated non-ideal Schockley-Queisser-like limits suggesting that additional optical or resistive losses were present in these devices.We are not aware of any published CdTe/CIS 2T tandem reports.There is one 4T CdTe/CIS tandem report and the result is listed in table 1. Figure 4 gives guidance on the range of suitable band gaps for both top sub-cell and bottom sub-cells.Obviously, the optimal range of bandgaps of tandem are different from that of single junction cells, which is between 1 and 1.6 eV.The optimal range of top cell band gap is 1.5-2.2eV, where the optimal range of bottom cell is 0.9-1.2eV.
Shockley-Queisser model assumes infinite cell absorber thicknesses and complete absorption of light with photon energies above the bandgap energy.Practical devices with finite absorber thicknesses will have incomplete absorption near their absorption edge which can be thought of as an effective broadening of the absorber bandgap.This may change the choice of optimal bandgaps for tandem top and bottom cells.The effective bandgap broadening is expected to be smaller for direct-bandgap devices with large absorption coefficients but may still be relevant for typical perovskite absorbers with thicknesses of a few hundred nanometers.For indirect bandgap cells with smaller absorption coefficients near the absorption edge in particular the effective bandgap broadening vs the infinitely thick absorber is expected to be larger.

Tandem based on existing PV technologies
Our simulation shows that one can have a wide choice of bandgaps to achieve an efficiency entitlement well exceeding those of Si, CdTe and CIGS single junction cells.Another important conclusion is that tandem efficiency significantly exceeding that of single junction cells can be achieved even if top and bottom cell absorbers are far from ideal (ERE ≪ 1).As shown in figure 3, a greater than 35% tandem cell can be achieved with 0.008% ERE CdTe top cell and 1.6% ERE Si bottom cell.This lowers the requirement of top and bottom cell efficiencies needed for commercial production.The optimal range of tandem top cell band gap is 1.5-2.2eV, where the optimal range of tandem bottom cell is 0.9-1.2eV. Figure 5.A high-level rating is assigned to each of four essential qualities as 1-low/2-medium/3-high following this scale: efficiency = record-cell efficiency as <20%/20%-25%/>25%; stability = typical warranted annual degradation rate as >1%/0.5%-1%/<0.5%;manufacturability = (record-cell efficiency) − (record-module efficiency) as >5%/3%-5%/<3%; bandgap tunability as impossible/significant development required/demonstrated.Record-cell and module efficiency values refer to single-junction devices from Green et al [8] tables 1 and 4, respectively.For this comparison, only record cells with areas 1 cm 2 or larger are considered [13].Reprinted from Weiss, Copyright (2021), with permission from Elsevier.
To build tandem cells upon existing PV technologies, Weiss evaluated tandems using either perovskite or CdTe as top sub-cells; and using either Si or CIGS as bottom sub-cells [13].Figure 5 summarizes his assessment with respect to four essential quantities: efficiency, band gap tunability, manufacturability and stability.
Perovskite/Si is the most studied top-bottom cell combination.The perovskite with its tunable bandgap is a very suitable top cell candidate while the well-established Si solar cell with its smaller bandgap can be the bottom cell.The highest demonstrated perovskite/Si cell Eff is 33.7% [8].The reliability and manufacturability of perovskite solar cells are however to be proven.
Mailoa et al [6] modeled II-VI based TF tandem solar cells under realistic operating conditions.In the ideal case (ERE = 1), the best 4T efficiency is 45.1% with the 1.7/0.95eV band gap combination.The efficiency is 42.4% with CdTe/CIGS.They also found that the 4T CdTe/CIGS tandem offers the best energy-yield even in humid climate where the infrared light absorption due to the atmospheric water vapor limits the bottom-cell performance.

Research directions of thin film tandem absorber candidates 2.4.1. Bandgap engineering of II-VI and I-III-VI compounds
Both CdTe and CIGS have demonstrated bandgap tunability, allowing them to be effectively tailored for tandem top and/or bottom cell applications.This absorber bandgap tunability is particularly helpful when adopting mature PV technologies for tandem applications, when the absorber materials have been well studied but are not at the optimal single-junction Shockley-Queisser bandgap.
The bandgap of CdTe is 1.5 eV at room temperature.Wider bandgap can be achieved by alloying with other group II or group VI elements such as Se and Zn with the corresponding binary CdSe and ZnTe compound bandgaps at 1.7 eV and 2.27 eV, respectively.Alloying with MnTe or MgTe can also increase bandgap of CdTe, up to 2.1 and 2.6 eV respectively.Lattice constants of both MnTe and MgTe nearly match that of CdTe and both Te compounds form continuous alloys with CdTe over a large concentration range.
CdMgTe has a direct bandgap.Several groups have studied Cd 1−x Mg x Te.Mg concentration (x) was limited to ∼0.7 because high Mg alloys are hygroscopic and difficult to work with.Figure 6 shows the bandgap versus Mg composition [14 -17].
CdMnTe also has a direct bandgap.Khoi and Gaj [18] measured the bandgap of Cd 1−x Mn x Te and found that the bandgap increases linearly with x, reaching a maximum of 2.1 eV at x = 0.5.Solar cells using CdMgTe and CdMnTe as absorbers had been made (see supplementary information).
Lower bandgap can be achieved by alloying with Se or Hg [19].CdTe alloying with CdSe can result in bandgap from 1.4 eV to 1.7 eV as shown in figure 7 [20].Similarly, alloying CdTe with HgTe results in bandgap from 0 eV to 1.5 eV including a semimetal phase (bandgap < 0) at low Cd concentrations as shown in figure 8 [21].Lattice constant of HgTe nearly matches that of CdTe.
In chalcopyrite Cu(In,Ga)Se 2 , bandgap tunability is achieved by varying Ga and In fractions and profiles providing the bandgap range from 1.0 eV for CuInSe 2 to 1.68 eV for CuGaSe 2 .Additional bandgap tunability is provided by replacing Ga or In with Al, and Se with S [22] as shown in figure 9.The quaternary   [22].Adapted from [22], with permission from Springer Nature.chalcogenide Cu 2 ZnSn(S,Se) 4 (CZTS, kesterite) with the bivalent Zn and quadrivalent Sn replacing In and Ga is also of interest.The bandgap can be tuned from 1.0 to 1.5 eV by going from all Se to all S [23].Kesterite was also used for tandem applications [24,25].
Among these various alloy systems, the Cu(In,Ga)Se 2 system has been studied extensively in relation to tandem development.For bottom cell applications, Feurer et al [9] reported a 19.2% 1.00 eV gap CuInSe 2 cell with Ga back grading.Jost et al [26] successfully combined a 1.68 eV gap perovskite and a 1.1 eV Cu(In,Ga)Se 2 absorber and achieved a record 24.2% tandem cell.
CuGaSe 2 which has a bandgap ∼1.68 eV is suitable for the top cell.Larssen et al [27] reported an efficiency of 11.9%.The 15.2% efficiency with a bandgap of 1.6 eV was reported by Shukla et al [28] with Cu(In,Ga)S 2 absorbers.They studied compounds with CGI ([Cu]/[Ga + In]) between 0.93-1.29 and GGI ([Ga]/[Ga + In]) of 0.12-0.18that resulted in bandgaps 1.57-1.61eV.They found that the key to the high efficiency was Cu deficiency with CGI = 0.93 together with the use of Zn(O,S) buffer layer.
Jeong et al [29] reported a monolithic 2T CuGaSe 2 /c-Si tandem solar cell with 9.7% efficiency.Wi et al [30] reported 4.32% efficiency for a monolithic CuGaSe 2 /Cu(In,Ga)Se 2 tandem cell.We note that efficient CuGaSe 2 cells are normally grown on Mo back contacts.The CuGaSe 2 top sub-cells had to be grown on transparent conducting oxides (TCOs) indium tin oxide (ITO) and aluminum doped zinc oxide (AZO).The efficiency of the CuGaSe 2 cell was only 4.2% and 2.72% respectively in these studies.How to make high quality CuGaSe 2 cells or Cu(In,Ga)S 2 cells on TCOs is an area that needs further research.
Table 1 compiles a short list of published work on chalcogenide or chalcopyrite tandems.More detailed discussion can be found in reviews of the subject, for example [31,32] and [33].

Perovskites
One of the great technology advances in thin film PV in the last decade is the hybrid organic-inorganic metal-halide perovskite.The certified efficiency has reached as high as 26.08% (certified 25.73%) [37].The metal-halide perovskites have a general formula of ABX 3 where A is a monovalent cation such as methylammonium (MA), formamidinium (FA) or Cs, B is usually Pb or Sn, X is I, Br or Cl.The device stack is quite like that for CdTe.There are two configurations.The n-i-p configuration is TCO/ETL/perovskite/HTL/electrode.The p-i-n configuration is TCO/HTL/perovskite/ETL/electrode.(ETL: electron transport layer, HTL: hole transport layer).The efficiency for n-i-p cell has reached 26.08% [37].The efficiency for p-i-n cell has reached 25.35% [38].Bifacial perovskite solar cells have also been demonstrated.Song et al reported a bifacial p-i-n cell with front efficiency of 18.4%, back efficiency of 17.5%, and bifacial factor (back efficiency/front efficiency) of 95% [39].
The use of two-dimensional (2D) perovskites in photovoltaics is also a very active area of research.The 2D perovskites can effectively passivate 3D perovskites and improve cell stability.There are many good reviews on this subject, for example, by Mahmud et al [40] and by Zhao et al [41].An interesting example is Cs 0.2 FA 0.8 Pb(I 0.7 Br 0.3 ) 3 with 1.75 eV bandgap which is potentially of interest for the top cell of a tandem cell.Yu et al [42] used 4-fluoro-phenylethylammonium iodide to coat the 3D grains with a 2D layer to improve crystallization and passivation.An impressive efficiency of 19.1% was reported.The 2D perovskites can also be an absorber with bandgap tunability.For example, Liang et al [43] worked with BA 2 MA 3 Pb 4 I 13 (BA: butylammonium) with a bandgap ∼1.8 eV.They reported a efficiency of 16.25%.Liu et al [44] reported a 15.41% efficiency for their BA 2 (MA 0.9 GA 0.1 ) 3 Pb 4 I 13 based solar cell (GA: guanidinium).Their data suggested a bandgap of ∼1.6 eV which can also be of interest for tandem.
All-inorganic CsPbBr x I 3−x system has attracted a lot of attention [45] because of its potentially higher stability.CsPbI 3 has 1.73 eV bandgap.Zhao et al [46] reported a highly stable all-inorganic CsPbI 3 cell with an effcieincy of 17.4%.They projected that T 80 (time to degrade to 80% of initial value) to exceed 50 000 h.Recently Mali et al [47] reported a β-CsPbI 3 /γ-CsPbI 3 phase heterojunction solar cell with an efficiency of 21.59%.They reported an operational stability >200 h.CsPbBr 3 has a bandgap of 2.3 eV and is highly stable at room temperature.An efficiency of 11.08% was reported [48].
Compositional engineering of mixed perovskites can provide opportunities in changing the energy gap and the operational stability.In perovskite, bandgap is largely dictated by Pb and the halide.Replacing Pb with Sn reduces bandgap.Adding Br or Cl significantly increases the bandgap.The size of A-cation has a smaller impact on the bandgap.The bandgap trend for the monovalent ion is FA < MA < Cs.The typical bandgap range for the metal halide perovskites are from 1.2 to 3 eV, of which the lowest are tin iodide-based perovskites, and the highest are chloride-containing perovskites.The broad range of bandgaps for perovskite makes all perovskite tandem an interesting option, despite some material composition with preferred bandgap may not be as stable as others.For example, Sn-based perovskites with bandgaps suitable for the bottom cell of a tandem are less stable because of the ease of oxidation of tin.But much progress has been made recently.Lin et al [49] recently reported a 26.4% efficiency 2-terminal tandem cell using a 1.8 eV Pb-based perovskite for the top cell while using a 1.2 eV Pb-Sn based perovskite for the bottom cell.The cell retained 90% of the initial efficiency after 600 h of operation.The same group also reported a 28.5% all perovskite tandem cell recently [50].For more details, readers can consult review articles on perovskites tandems cells, for example [51][52][53][54].Table 2 is a short list of recent published results on perovskite tandem cells with different combinations of absorbers.

Other absorber candidates
Figure 3 shows that high efficiency tandem cells can be achieved using absorber materials within a large range of bandgaps.Throughout the years, many absorber candidates suitable for single junction solar cells have been explored.However, materials with bandgaps not suitable for single junction solar cells have not received as much attention.The application of tandem cells opens new opportunities for these materials previously under explored.Based on the above simulation results, we constrained our material survey to candidates with bandgap of 1.5-2.2eV (top cells), and 0.9-1.2eV (bottom cells).We have limited them to inorganic thin film materials, and we also have not included III-V materials.The following tables list some of these candidates.In the supplementary information (SI), we provide further details such as the bandgap, efficiency, device structure, advantages, and challenges.Tables 3 and 4 summarize the bandgaps and reported efficiencys for a list of top and bottom cell candidates from our discussion above.

Outlook and concluding remarks
PV has become one of the cheapest electricity sources and will likely dominate future electricity supply.Currently the market is led by Si and CdTe technologies.Thin film PV has fundamentally lower cost structure, proven by the commercial success of CdTe.To further improve device and module efficiency, we must overcome the Shockley-Queisser limit and go beyond single junction solar cells.Thin film tandem solar cell is a strong contender of the next generation PV technology, due to high efficiency, less demanding in material defect tolerance, and lower cost compared to Si based tandem cells.Our model and calculations using practically achievable ERE values show that within a wide range of bandgap materials, greater than 37% 4T tandem solar cell efficiency can be demonstrated.This also brings to the table a large variety of suitable new absorbers for future exploration.
To qualify as a promising absorber candidate, the material must meet certain criteria on critical properties such as bandgap, bulk lifetime, doping, and surface recombination velocity.Exploration of carrier selective contact materials comes next, prior to demonstrating high efficiency devices.Such a structured approach helps us focus on the right technical challenges step by step, and not rush into device fabrication without understanding the practical potential versus limitation of materials such as ERE, doping, band alignment etc. Learning curves for new absorber material exploration and device fabrication can be shortened by leveraging experiences from established thin film PV technologies such as CdTe, CIGS, GaAs and perovskite.From the perspective of device structures, a few common challenges and solutions are shared among technologies, for example interface and grain boundary passivation strategies, candidates as carrier selective contacts, light management etc.In general, we feel optimistic about the TF/TF tandem solar cells and believe this is a fruitful R&D direction for the thin film PV community.

Figure 2 .
Figure 2. Efficiency limit of 4T mechanically stacked tandem solar cells versus top and bottom cell bandgaps for the ideal case of ERE = 1.

Figure 4 .
Figure 4.The range of suitable band gaps for single junction and tandem top/bottom cells.(a) The optimal range of bandgaps for single junction cells, which is between 1 and 1.6 eV.(b)The optimal range of tandem top cell band gap is 1.5-2.2eV, where the optimal range of tandem bottom cell is 0.9-1.2eV.

Figure 6 .
Figure 6.Comparison of bandgap values for Cd 1−x MgxTe as a function of x from four [14-17].

Figure 8 .
Figure 8. Energy gap Eg vs composition for Hg 1−x CdxTe.Reproduced from [21], with the permission of AIP Publishing.

Figure 9 .
Figure 9.Lattice constant vs bandgap of the CIGS alloy system.Bandgaps of 1.15-1.2eV are used for usual single junction solar cells.Redrawn from figure2of[22].Adapted from[22], with permission from Springer Nature.

Table 1 .
List of some published results on chalcogenide and chalcopyrite tandem cells.

Table 2 .
Some recently published results on perovskite tandem cells.The composition and bandgaps of the absorbers are listed when available.

Table 3 .
List of suitable top-cell absorbers.

Table 4 .
List of suitable bottom-cell absorbers.