Towards a graphene transparent conducting electrode for perovskite/silicon tandem solar cells

Indium‐based transparent conducting electrodes (TCEs) are a major limiting factor in perovskite/silicon tandem cell scalability, while also limiting maximum cell efficiencies. In this work, we propose a novel TCE based on electrostatically doped graphene monolayers to circumvent these challenges. The electrode is enabled by a thin film dielectric that is charged and interfaced to a graphene film, optimally exploiting electrostatic doping. The field effect mechanism allows the modulation of charge carriers in monolayer graphene as a function of charge concentration in the dielectric thin film. Electrostatic charge was deposited on SiO2 membranes, and graphene transferred onto them exhibited a reduction in sheet resistance because of the induced charge carriers. We show a reduction in sheet resistance of graphene by 60% in just 3 min of dielectric charging, without impacting the transmission of light through the film stack. Hall effect measurements indicated that the mobility of the films was not significantly degraded. The deposition of negative electrostatic charge reversed this effect, allowing for precise tunability of charge concentration from n‐ to p‐type. We develop a model to determine the required sheet resistance of a graphene TCE with 97% transmittance in a perovskite/silicon tandem cell. As the technique here reported does not impact transmittance, a graphene TCE with a sheet resistance below 50 Ω/□ could enable efficiencies up to 44%, presenting a promising alternative to indium‐based TCEs.

The efficiency of single-junction silicon solar cells is approaching the practically achievable limit of 29.4%. 1 Yoshikawa et al achieved an efficiency of 26.7% with an IBC silicon heterojunction (SHJ) design, 2 and LONGi Solar have demonstrated efficiencies up to 26.81% for large-area industrially processed SHJ cells. 3As these efficiencies approach the practical limit, a tandem solar cell design can be employed to circumvent the limitations of single-junction cells. 4,5In a tandem cell, two cells of differing band gap (E g ) are stacked together to more effectively harvest solar energy.7][8] A promising combination of tandem subcells for widespread terrestrial applications involves using a large E g perovskite top cell and a lower E g SHJ bottom cell.Perovskites are particularly promising as the top cell in a tandem because of the large absorption coefficient, 9 large V OC potential, 10 and readily tuneable E g. 11 Of the available single-junction silicon cell architectures, the SHJ design is particularly advantageous in a tandem architecture.It has the highest efficiency potential, and the a-Si passivating layers are conductive, which avoids the requirements for localised interconnection. 2,12However, perovskites and the passivating layers in SHJ cells both have poor lateral conductivity; hence, they require additional layers with high lateral conductivity for efficient charge carrier collection at metal fingers. 13Such layers must also have high transmittance to minimise parasitic absorption losses.
5][16] Photocurrent losses in 'transparent conducting electrodes' (TCEs), referred to as parasitic absorption, can represent a major efficiency loss, contributing to a reduction of singlejunction module efficiency by 10% rel -25% rel . 17Additionally, the most frequently used TCEs, indium zinc oxide (IZO) and indium tin oxide (ITO), use scarce, unsustainable indium, which severely limits the manufacturing potential of cell designs requiring it. 18,19Producing lowcost, sustainable TCEs with optimised properties is crucial in achieving high-efficiency tandems with widespread applicability.Such innovations could enable an accelerated uptake of renewable energy and reduce global carbon emissions.Graphene is a material that is increasingly lowcost to produce and has a transmittance that exceeds that of ITO and IZO, yet has limited applications as a transparent conductor because of its relatively high resistivity. 20In this work, we demonstrate that a sufficiently-doped high-transmittance graphene layer could circumvent the issues with conventional TCEs that are currently limiting perovskite/silicon tandem uptake and efficiency losses.
Compared with single-junction cells, TCEs in tandem cells have more stringent optical requirements. 21All perovskite/silicon tandem configurations require a front TCE with high transmittance to light from ≈280 to 1100 nm to maximise light absorption across the air-mass 1.5 global (AM1.5G)spectrum in both perovskite and silicon subcells.In a single-TCE two-terminal monolithic perovskite/silicon tandem, its TCE can contribute >1 mA/cm 2 J SC loss because of parasitic absorption, equivalent to $1% abs loss in efficiency. 22,23The two-and four-terminal mechanically-stacked and three-terminal monolithic tandem configurations usually require one or two additional TCEs between the subcells, from which parasitic absorption may cause $3-4 mA/cm 2 loss in J SC. 21,22,24 This places significant pressure on TCE performance.As TCEs tend to be one of the most expensive components in solar cell fabrication, as well as multiple-terminals increasing balance-of-system costs, the single-TCE two-terminal monolithic configuration is preferable for large-scale commercial applications. 21The series connection of monolithic two-terminal cells requires current matching between the cells, constraining the bandgaps that can be used.However, the tunability of perovskite band gaps can mitigate this issue. 11To incorporate bifaciality in tandems, an extra TCE with high infrared (IR) transmittance and efficient light coupling is also needed at the rear. 12This is essential for high-efficiency SHJ bottom cells.Solar cell manufacturers must balance a trade-off between the high efficiencies of SHJ cells versus the high cost of an additional TCE.Low-cost TCEs with broadband transmittance would serve to eliminate this trade-off and enable higher efficiencies in tandem cell architectures.
Along with requiring broadband transmittance, TCEs in a tandem cell must contribute minimally to the series resistance (R S ) of the cell.
TCEs must have a low sheet resistance (R sheet ), as well as a low contact resistance to the metal fingers.The R sheet in units of Ω/□ can be approximated, assuming uniform carrier generation, as described by Equation 1: where σ is electrical conductivity, μ and n are majority carrier mobility and concentration respectively, q is the charge of the majority carrier, and t is the thickness of the film. 15,25Equation 1 illustrates that to minimise R sheet , one must choose a film with large μ, n and t.However, increasing t reduces transmittance.Similarly, increasing n increases free-carrier absorption (FCA), reducing overall transmittance. 13,26This motivates the need for TCEs with high mobility, so that R sheet is low without inducing free carrier absorption from high carrier concentrations.These fundamental trade-offs in TCE properties must be balanced for optimum performance in tandem cells.
TCEs in tandems must also be stable and compatible with the processing of other cell materials.Perovskite layers have poor stability to moisture, UV light and temperatures as low as 85 C, 27 whereas SHJ processing must occur at temperatures <250 C because of the poor thermal stability of the amorphous silicon based passivation. 28TCE materials for tandems must fit within the processing constraints of the other layers.
Furthermore, all materials and processing steps in producing a tandem cell must be sustainable, to realise terawatt-scale photovoltaic global production capacity.This would enable notable reductions in global carbon emissions while meeting energy demand. 18O is the dominant TCE used in optoelectronics. 29,30This transparent conducting oxide (TCO) has high transmittance to visible light ≈80%-90% because of its low absorption coefficient and low R sheet ≈ 10-100 Ω/□ because of its high carrier concentration n ≈ 10 20 -10 21 cm À3 and moderately high mobility μ ≈ 20-50 cm 2 / Vs. [31][32][33][34][35][36] However, this high carrier concentration causes high parasitic FCA in the near-UV and IR regions, which is severely detrimental to tandem performance. 13,26,37It is therefore critical to prioritise TCOs with high carrier mobility over high carrier concentration to maintain high transmittance with low R sheet. 38IZO is the most frequently used top TCE in perovskite/silicon tandem because of its high mobility ≈60 cm 2 /Vs, but it suffers from reduced transmittance in the ultraviolet-visible (UV-Vis) range. 13Zirconium oxide doped In 2 O 3 (IZRO) is a promising TCO for tandems, with high mobility ≈77 cm 2 / Vs. 26,39 It exhibits reduced FCA in the NIR region, resulting in an efficiency increase of 2.3% abs in perovskite/silicon tandems. 26Similarly, hydrogen-doped indium oxide (IO:H) offers very low FCA because of high mobility ≈100 cm 2 /Vs, but suffers from poor stability. 13Other indium-based TCOs with high mobility and NIR transmittance that may be suitable for tandems include cerium/hydrogen and tungsten/ hydrogen co-doped In 2 O 3 , although these require high-temperature annealing steps incompatible with many tandem designs. 13,26,40However, crucially, there are insufficient global indium reserves to meet the demand for future terawatt-scale photovoltaic capacity. 18Zhang et al calculated that the annual manufacturing capacity for SHJ cells using ITO was only 37 GW. 18Using perovskite/silicon tandems offers some scope for improvement, yet are limited to just 29-177 GW/ year, indicating that indium cannot be used in any significant PV manufacturing capacity. 18,19 Indium-free TCOs such as fluorine-doped tin oxide (FTO) and aluminium-doped ZnO (AZO) suffer from high FCA because of low mobility, with AZO additionally suffering from instability. 13,34Moreover, the relatively expensive sputter deposition process of TCOs damages perovskite layers. 38,41This necessitates an additional buffer layer such as MoO x , increasing processing time and costs, and often reducing stability and transmittance. 38,413][44] Silver nanowires (AgNWs) can be deposited as a dense conductive mesh for carrier transport to metal fingers, leaving voids for light transmission, attaining properties comparable with ITO. 13,45However, AgNWs suffer from poor stability, and increasing the use of Ag in solar cells is prohibitively expensive and unsustainable. 18,38Alternatives such as copper nanowires and carbon nanotubes also exhibit poor stability, as well as high contact resistance and poor substrate adhesion. 13,45A viable indium-free TCE must overcome these issues to achieve success in tandems.

| Graphene as a TCE
A promising indium-free TCE for tandem solar cells is graphene. 46om a processing perspective, there are several advantages to using graphene.Graphene is becoming increasingly affordable to produce using chemical vapour deposition (CVD) in dimensions comparable with industrial solar cell processing.Sheets can be processed and deposited using roll-to-roll techniques compatible with perovskite solution and roll-to-roll processing. 32,479][50][51][52][53][54][55] Similarly, mono-and multilayerreduced graphene oxide sheets have been effectively deposited directly on perovskite and yielded functioning perovskite cells without a separate HTL. 56Additionally, graphene flakes have been effectively interfaced as an additive for TiO 2 in perovskite cell ETLs, in this case not acting as the TCE layer. 57,580][61] The strong sp 2 carbon bonds in graphene give it high chemical and mechanical stability. 62Graphene is impermeable to gas and water, providing additional stability as an encapsulating layer for components susceptible to moisture, such as perovskites. 27,62Graphene is sustainable, consisting entirely of an atomically-thick carbon layer.CVD graphene can be grown on relatively inexpensive copper sheets, which can be reused, requiring less energy and lower carbon emissions to produce than ITO films. 46ble 1 displays a comparison between the material properties of monolayer graphene, ITO and IZO.Note that the values are given as ranges, which depend on fabrication conditions.Table 1 serves to highlight the primary differences between these materials.From an optical standpoint, graphene is clearly advantageous, with typical broadband transmittance >97% for monolayer graphene. 63This is much higher than ITO or IZO and could lead to substantially reduced parasitic absorption losses in a tandem solar cell.Unlocking the potential of graphene could thus substantially improve the efficiency of perovskite/silicon tandems.ITO and IZO are capable of achieving R sheet as low as 10 and 40 Ω/□, respectively, which is required to reduce electrical losses.In contrast, the R sheet of graphene is too high to act as an effective TCE in tandem solar cells.As discussed above, the R sheet is determined by both the carrier concentration and mobility of majority carriers.The mobility of graphene is very high, in the range from 1000 to 40,000 cm 2 /Vs on SiO 2 at room temperature. 71wever, the R sheet is limited by its carrier concentration, which is the order of magnitude lower than ITO or IZO.For graphene to T A B L E 1 Comparison of typical material properties of monolayer graphene on SiO 2 , ITO and IZO for photovoltaic applications, at standard temperature and pressure.
become a viable alternative as a TCE, this critical issue must be resolved.
The conventional approach to increase the carrier concentration in graphene is by chemical doping.However, chemical doping is often unstable, difficult to control and typically reduces the transmittance and mobility of graphene because of the disruption of its lattice by dopant atoms. 25,65,72Graphene's R sheet can also be reduced if multiple graphene layers are used, but this degrades the transmittance significantly (2.3% transmittance reduction with each layer). 64,65Lang et al demonstrated that CVD graphene TCE integration in perovskite/ silicon tandems is possible without damaging the perovskite layer, but its R sheet was too high. 4851][52]54 However, these approaches did not lead to a sufficient increase in its carrier concentration, resulting in low efficiencies relative to cells with indium-based TCEs.Doping with AuCl 3 in a perovskite cell was shown to reduce the R sheet stack significantly, offering performance that rivals ITO. 55,58However, aggregated Au particles increase light scattering, minimising the maximum efficiency potential, particularly deleterious if incorporated in a tandem cell stack. 55,58'Transfer-free' graphene for flexible substrates was doped using NiO x , enabling sheet resistances <100 Ω/□, while preserving high transmittance. 53But this result is limited to flexible substrates and hole carrier transport, limiting its applicability in tandem cells.Therefore, it is critical to develop alternative approaches that can sufficiently dope graphene TCEs in different parts of a tandem device stack, so that carrier concentration is increased and the desired R sheet can be achieved without impacting the transmittance or mobility.
An alternative approach to doping graphene is to use the field effect or electrostatic mechanism.By establishing an electrostatic field in the vicinity of graphene using a gate bias, a mirror charge is induced in it.This increases the carrier concentration and has been shown to reduce R sheet to values as low as 100 Ω/□. 73In field-effect doping the mobility is reduced, but to a less significant extent than when using chemical doping techniques.In chemical doping, species either directly disturb the graphene lattice structure or cause charge impurity scattering. 31,72,74,75In field-effect doping, however, the R sheet reduction only occurs when the power supply is switched on, meaning this technique is not applicable in the context of tandem cell fabrication.Paradisi et al demonstrated that under applied bias and high temperature, charged ions could be migrated in a thick glass film to permanently electrostatically dope graphene, enabling carrier concentration modulation >10 14 cm À2.76However, this requires an opaque metal electrode and was only shown to be possible on thick silica films, hindering its applicability for perovskite/silicon tandem cells.In recent years, Bonilla et al demonstrated that using corona charge and solid-state alkali ions, it is possible to permanently embed large concentrations of charge in thin films of SiO 2 . 77,78This establishes a permanent electrostatic field in the thin dielectric film, generating field effect surface passivation that is stable on commercial timescales. 78 this work, we reveal how electrostatic corona charge deposited on a thin SiO 2 film can generate a field effect large enough to manipulate the carrier concentration of graphene.Although field-effect doping of graphene has been known for nearly two decades, 73 the key novelty in this work is the way in which the doping is achieved.We introduce here a new technique that we refer to as 'ion-charged dielectric' (ICD) doping.In this case, the magnitude of the electric field effect can be precisely controlled by varying the amount of charge deposited on a dielectric thin film.Figure 1 depicts how this technique can be used to enhance conductivity in graphene, where positive and negative charges induce n-and p-type doping, respectively.This allows for tailored carrier concentration so that low R sheet graphene can be produced without detrimentally affecting transmittance or mobility.The process is rapid, inexpensive and compatible with the processing conditions required of perovskites and SHJ cells.Such developments offer the path towards a viable indium-free, graphene TCE in perovskite/silicon tandem cells.

| EXPERIMENTAL METHODOLOGY
Demonstrating ICD-doping of graphene requires the manufacture of a device in which a close interface can be formed between a thin film dielectric and a monolayer of graphene.Figure 2A shows the device architecture used in this work to achieve this.A 0.4 Â 0.4 cm 2 CVD monolayer graphene sheet is transferred to a 0.5 Â 0.5 cm 2 p-type Si/SiO 2 substrate using a standard wet-transfer method (see Section-S1, Supplementary Material). 79The 300 nm SiO 2 layer is unsupported application in photovoltaic devices. 82We use this to predict the required sheet resistances for an electrostatically doped monolayer graphene film in a two-terminal monolithic stack tandem cell and compare this with frequently used TCO materials.The details of the model can be found in Sections S6 and S7 of the Supplementary Material.
3 | RESULTS AND DISCUSSION

| Electrical characterisation
The first step in demonstrating ICD-doping of graphene was to ensure that a concentration of static charge can be built and maintained on top of the free-standing thin film membrane.Figure 3A depicts the contact potential difference (CPD) of the SiO 2 membrane, as it is held under an applied corona voltage of ±30 kV over 16 min of total charging time.As the charging time is increased, the CPD of opposite polarity increases in magnitude.The magnitude of the CPD is proportional to the amount of corona charge deposited on the surface of the SiO 2 membrane. 83After 6 min at +30 kV, the CPD saturates at about À12 V, whereas after 8 min at À30 kV, the CPD saturates at about +20 V.At this point, no additional charge can be deposited on the film, and the electric field generated is likely to be at its maximum.
Ten hours after positive charging, the CPD measured decayed by just 2.80% (see Figure S1, Section S2, Supplementary Material) Similarly, 12 h after negative charging, the CPD decayed by 7.82% (see Figure S1, Section S2, Supplementary Material).This stability allows R sheet measurements to be taken several minutes after each charging interval with confidence that the CPD will not have decayed substantially.The complete device was then manufactured including the graphene monolayer and contact electrodes and was subsequently charged under the corona discharge apparatus.Figure 3B shows how the R sheet of graphene varied as the dielectric membrane was charged under +30 kV voltage over time.The initial R sheet of $1740 Ω/□ is high for undoped CVD graphene.This is attributed to the difficulty of wet-transferring the graphene to substrates <1 cm 2 , resulting in a large number of wrinkles, cracks and defects in the film.Figure 3C shows the R sheet increase from 1740 to 1810 Ω/□ after 10 s of positive charging.This can be explained by the p-type nature of the undoped, as-transferred graphene.Graphene on SiO 2 is typically slightly p-doped because of the residual polymers left over from the transfer process, as well as interactions with moisture. 84 contamination, which reduces its mobility. 84,86,87This indicates that the quasi-permanent field induced in the graphene counteracts the effect of atmospheric contamination from increasing R sheet .When subjected to further positive charge deposition, the sheet resistance of the sample indicated in Figure 3B decreased further from 607 to $573 Ω/□ in 30 s.No further reductions were observed as positive charging time increased.This is a combined reduction of R sheet of 67% in the positively charged sample from the initial R sheet.The relative change of R sheet demonstrated in this novel doping technique is already approaching that of chemical doping, which typically reduces the R sheet by 70%-80%. 31,88Strategies for improving this technique beyond this work are described in Section 3.5.
Figure 3C shows how the R sheet of graphene varied as the dielectric membrane was charged under À30 kV corona voltage over 16 min.The R sheet decreases from 3.5 to 2.4 k Ω/□ after 3 min of negative charging time.This reduction in R sheet is assumed to occur because of the p-type doping effect of the negatively-charged substrate, where holes are the majority carrier in graphene.As the graphene was already likely slightly p-doped, there was no increase in R sheet as was observed with positive charging.The high initial R sheet is due to processing difficulties resulting from using small substrates, as was the case in the positively charged sample.Because of the equal electron and hole mobilities in graphene, 89 both p-and n-type graphene TCEs can be developed using this technique.Figure 3D depicts the change in R sheet of a graphene device subject to +30 kV for 2 min, followed by À30 kV for 2 min.Once again, the initial R sheet was in the order of 1.9 kΩ/□ because of the faulty or defective graphene monolayers.Despite such high resistance, it is evident that the doping effect provided by the corona charge is reversible.The addition of negative electrostatic charge counteracted the n-type doping provided by initially deposited positive charges.This could enable precise conductivity tailoring for particular device applications, where both nand p-type doping are required for better interconnection to active semiconductors.
Figure 4A depicts the variation in Hall carrier concentration and mobility of a graphene sheet as the membrane is charged with positive electrostatic charge over time.The initial charge carrier concentration of the graphene is high, at 1.56 Â 10 13 cm À2 , attributed to doping induced by remaining polymer residues. 84,90The initial mobility was relatively low at $213 cm 2 /Vs.We attribute this low mobility to a high density of defects, wrinkles and cracks induced by the graphene wet transfer onto such small films, as well as scattering by polymer residues. 84,86,87Such imperfections act as scattering centres that reduce the mean free path of the carriers and hence reduce mobility.
The defects, wrinkles and cracks are likely to be the primary factors contributing to the high initial R sheet observed in Figure 3A   bonded carbon in hexagonal rings. 31,91A third peak at $1350 cm À1 , 'D', is present because of the defects in graphene. 31,91The D/G intensity ratio is therefore used to provide an indication of the defect density in the film.atoms. 25,65,723][94] The slightly blueshifted G peak and decrease in full-width half maximum indicate that moderate doping has occurred. 92,94The redshift of the 2D peak indicates that that doping is n-type. 92,94 opens up the possibility for a highly transmissive TCE for tandem cell applications.
3.4 | Target R sheet for ICD-doped graphene TCEs for two-terminal monolithic perovskite/silicon tandem solar cells The transmittance of graphene is uniquely broadband, offering optical advantages over ITO and IZO alternatives.In this work, we have shown experimental data indicating that ICD-doping of graphene does not impact its transmittance.Therefore, it is not expected that ICDdoped graphene would require an R sheet as low as that of ITO or IZO to remain competitive for application as a TCE in tandem cells.To evaluate the R sheet required for a graphene TCE to match the performance of an ITO or IZO film, we have modelled the ultimate tandem cell performance following the approach recently published by Anand et al. 82 In this model, the theoretical performance of the cell is calculated for variations in the transmittance and sheet resistance of the TCE.This allows a comparison between the theoretical efficiency achieved in tandem cells when they incorporate different TCEs.with silicon as the bottom cell.This is the most suitable device to focus on when drawing conclusions relevant to perovskite-silicon tandem solar cells.Figure 8 illustrates the unit domain used for the calculation, where two possible architectures are proposed.In the first architecture (Figure 8A), a front TCE is placed on the surface of the perovskite semiconductor, collecting current and driving it to localised front metal contacts.The current flow is assumed to be completely vertical because of the presence of a suitable optoelectronic link or an interconnection layer.This is often referred to as the recombination layer, but here, it is generalised to a layer(s) fulfilling both conduction and optical coupling functions.When vertical current flow is desired in the silicon absorber, a second TCE must be present at the rear surface as is typical in SHJ technology.A possible second approach (Figure 8B) uses surface doping in the silicon sub-cell to enable flow of charge carriers to a local contact both at the front and rear.This architecture would reflect the use of a different silicon bottom cell, for example, a passivated emitter and rear cell PERC or a tunnelling oxide passivating contact (TOPCon) architecture.Here, the rear TCE is present on top of the optoelectronic link to indicate that the current collected in the perovskite semiconductor must be conducted to the local contact at the front of the silicon sub-cell.Such a design was originally used to produce perovskite/silicon tandem cells, 23 making it highly relevant to the current large-scale production of solar panels.
For both cases in Figure 8A,B, each TCE accounts for one additional series resistance such that the effective series resistance must include two contributions, as detailed in Section S6, Supplementary Material.
Optically, the case in Figure 8A is more favourable as front light only passes through a single TCE.Accordingly, here, we have modelled the ultimate theoretical efficiency assuming the case of Figure 8A.This is used to determine the R sheet required for a graphene TCE with broadband transmittance to negligibly contribute to electrical losses when implemented in such tandem cell architectures.
Figure 9 shows the results of the model when applied to several potential TCEs.Here, a contour map of the upper efficiency limit for a two-terminal perovskite/silicon tandem is illustrated as a function of uniform spectral transmittance (280-1100 nm), using a 1 Sun weighted averaging to account for wavelength dependence.The y-axis of Figure 9   In the next section, we shall discuss strategies to realistically achieve a reduction in R sheet in ICD-doped graphene from ≈600 to ≈50 Ω/□, to practically enable the predictions of the model and its feasibility to integrate into a tandem cell device.

| Discussion
The proof-of-principle graphene TCE device proposed in this work exhibited a decrease in R sheet of nearly 70% through the corona discharge induction of an electrostatic field in an interfacing SiO 2 thin film.This occurs as the Fermi level of 2D materials such as graphene is easily disturbed under application of an electric field. 73 are now commercially available, 98 and graphene transfer on A4-sized sheets has now been demonstrated. 101,102As corona charge deposition and dielectric synthesis can occur on wafer-scale dimensions, this demonstrates the feasibility of producing ICD-doped graphene on industrially relevant scales.This shows that by ICD-doping such highquality CVD graphene sheets, R sheet < 150 Ω/□ with transmittance >95% in graphene on dimensions large enough for typical solar cells could be facilitated.This assumes that with a maximum CPD of about -12 V, as measured in this work, the same relative reduction in R sheet would occur because of an increase of carrier concentration by a factor of three.
A higher charge concentration can be deposited on the film, providing a stronger electrostatic doping effect.We have shown that a maximum CPD of about -80 V is attainable on these membranes when the membrane is positively charged from the top side (see Figures S2 and S3, Section S3, Supplementary Material).This is a near-sevenfold increase in CPD as compared with the films used in this work.CPD of this magnitude was not attained when charged from the rear, because of the screening of corona charge by the 100 nm SiO 2 layer on the Si support (see Section S3, Supplementary Material).This 100 nm SiO 2 layer on the Si support is closer to the discharge electrode, resulting in significant charge build-up on the support, which repelled the deposition of additional ionic charge.
However, in a practical perovskite/silicon tandem device, this screening effect would not occur as the distance between the discharge electrode and the target dielectric would be the minimum distance.In such cases, a uniform thin film dielectric would be deposited and embedded with a concentration of charge, leading to the possibility of much larger area TCEs with low sheet resistance.This would also avoid the intrinsic difficulties of working with small, suspended SiO 2 membranes.Therefore, we expect that a reduction in sheet resistance from 150 to 50 Ω/□ is practically achievable by optimising the charge deposition conditions.
The maximum CPD attainable on a 300 nm SiO 2 membrane should exceed 100 V and is only limited by its dielectric breakdown strength. 103,104In a practical device, the membrane would not be suspended but instead incorporated in an optoelectronic device stack.We demonstrated that the maximum CPD attainable on SiO 2 on substrates used in this work was -100 V when supported by Si, reached after just 3 min of positive charging (see Figure S4, Supplementary Material).This demonstrates a significant increase in doping potential beyond what has been demonstrated in this work.With improved dielectric synthesis techniques, the amount of charge deposited on the film can be increased to meet this limit.Such improvements should enable sheet resistances <50 Ω/□ to be F I G U R E 9 Plot of the maximum efficiency that can be obtained using a top perovskite cell of E g = 1.73 eV, two transparent conducting electrodes (TCEs) (one front and one rear), with a variation in sheet resistance and integrated transmittance across the air-mass 1.5 global (AM1.5G)spectrum.Tyagi (graphene), 97 Grolltex (graphene), 98 Bianco (graphene), 31 indium tin oxide (ITO) a (lightly doped, n = 6.5 Â 10 19 cm À3 ), 69 ITO b (heavily doped, n = 6.1 Â 10 20 cm À3 ), 69 hydrogen-doped indium oxide (IO:H), 99 tungsten-doped indium oxide (IWO), 100 IZO 66 and Zirconium oxide doped In 2 O 3 (IZRO). 26btained.Using Bonilla et al's method to permanently embed large concentrations of charge in thin films of SiO 2 with corona charge and solid-state alkali ions, 77,78 this graphene doping technique could be stabilised on commercial timescales.Electrostatic ICD doping of graphene is also applicable to other materials that store corona charge.An ionic charge concentration comparable to that used for graphene doping in this work can be deposited on SiN x dielectric membranes with a thickness of 100 nm, as shown in Supplementary Material Section S3, Figure S5.The thickness can be reduced significantly without compromising charge deposition on the film, as the amount of charge that can be deposited on a dielectric only depends on the dielectric constant and dielectric strength of the material (see Supplementary Material Section S5).This provides opportunities for varied device requirements and potential combination of ICD-doped TCEs with anti-reflection layers.For example, a charged SiN x layer of 75 nm thickness could be used as an anti-reflection layer, while also electrostatically doping the graphene which is interfaced with the perovskite HTL or ETL at the front of a perovskite/silicon tandem.
We envision device integration involving the replacement of a conventional TCE layer in a tandem cell stack with an ICD placed adjacent to a monolayer graphene sheet.In a two-terminal monolithic perovskite/silicon tandem, this ICD-doped graphene layer could be placed at the top of the perovskite subcell and at the rear of the silicon bottom cell.Note that such a TCE could not replace the recombination layer in a two-terminal tandem, as doing so would impede vertical charge transport.In a four-terminal mechanically-stacked perovskite/silicon tandem, such an ICD-doped graphene layer could also be positioned under the perovskite or on top of the silicon subcells.In all cases, the graphene layer would be oriented to the absorber to collect charge carriers, as the dielectric layer would impede vertical charge transport.Because of the compatibility of graphene with several HTL and ETL materials and the ambipolarity of the doping technique, ICD-doped graphene could be integrated in either p-i-n or n-i-p perovskite cell configuration, offering wide adaptability for different device processing constraints. 58In a solar cell device, the metal electrode could be positioned in between the ICD and conductive graphene or the metal could be laser-fired through the dielectric to form an electrical contact with the graphene.Several technical limitations remain before such an electrode could be fabricated at industrially relevant speeds.The production of CVD graphene is currently relatively slow compared with TCOs, typically requiring separate steps for production and transfer to the target device. 105High-quality, large-area CVD graphene can be transferred to flexible substrates via roll-to-roll techniques, at speeds up to 500 mm/min, 32,105,106 and transferred to rigid substrates within 15 min. 107The fabrication and charging of the dielectric layer would involve an additional step.Whereas engineering challenges remain for ICD-doped graphene TCEs to match the industrial speeds of TCOs, graphene fabrication and transfer benefits from being less energy intensive than fabricating indiumbased TCOs and is inherently less expensive because of not requiring scarce materials. 46

| CONCLUSION
In this work, we present results detailing a novel graphene doping technique that could enable a promising TCE compatible with tandem cells.This technique can lead to the production of graphene-based TCEs with optical and electrical properties competitive with ITO and IZO.Electrostatic charge deposition on a supporting dielectric substrate is used to tune the conductivity of graphene.We observe that the sheet resistance of graphene can be reduced by 60% in just 3 miutes of positive electrostatic charging of the underlying dielectric film.This technique does not impact transmittance, does not disturb the graphene lattice and can be stabilised on commercially relevant timescales.The doping is tuneable and readily reversible in less than 5 min, so that it can be tailored to different device applications.Using theoretical modelling, we showed that high-quality graphene doped with our novel technique could enable efficiencies up to 44% if R sheet < 50 Ω/□ can be obtained without impacting transmittance.This is a significant increase in efficiency potential as compared with current alternatives while also eliminating the unsustainable use of indium in next-generation solar cells.
This technique and material are compatible with tandem solar cells and aim to provide a low-cost, sustainable alternative to indiumbased TCEs for photovoltaic capacity at terawatt-scales.Such advantages could markedly improve cell efficiencies and price-performance ratios.The ease and rapid processing of this technique could enable faster, more economically viable and energy-efficient tandem cell production.This can facilitate a more accelerated uptake of renewable energy sources in the face of the current climate crisis.

1
Representation of doping in 2D materials using ion-charged dielectrics (ICDs) compared with conventional chemical doping.(A) Undoped.(B) Chemical 'surface absorption' doping.This work: (C) N-type ICD doping and (D) P-type ICD doping.in the central 0.5 Â 0.5 mm 2 region, referred to as the 'membrane window', which allowed for electrostatic charge deposition.A 1064 nm IR laser (Linxuan LX-A1-20W) was used to remove the graphene from the area around the SiO 2 membrane window.Aluminium metal contacts of thickness 500 nm for electrical characterisation were thermally evaporated at the corners of the graphene using a shadow mask.Samples were stored in a low-pressure chamber purged with nitrogen to minimise moisture-induced degradation and were only removed during characterisation.Figure2Bshows a schematic of the electrostatic doping apparatus, constructed in-house.Devices are placed graphene-side down on a ground electrode, at a known distance over a point discharge electrode.A constant voltage is applied between the ground and discharge electrode.This ionises the air around the discharge electrode and accelerates electrostatic charge towards the sample.Positive applied voltage deposits positively charged corona ions (mostly (H 2 O) n H + ) on the surface of the SiO 2 membrane, whereas a negative applied voltage deposits negatively charged corona ions (mostly CO 3 -).80,81The quantity of charge deposited is controlled by varying the total time for which the device was held under constant voltage.A KP Technology Scanning Kelvin Probe SKP5050 with a 50 μm tip was used to characterise the quantity of corona charge deposited on the SiO 2 membrane.The sheet resistance of graphene was measured after varying amounts of corona charge were deposited using the Van der Pauw method.The carrier concentration and mobility were calculated by measuring the Hall effect of the films under a perpendicular magnetic field of 0.3 T. For Van der Pauw and Hall effect measurement, signal generation and measurement were carried out using a Keysight B2901A Source measuring unit, controlled via a virtual instrument programmed in LabVIEW.A LabRam Aramis HORIBA Jobin Yvon Raman spectrometer with a 532 nm laser was used to determine the defect density and doping behaviour of the graphene.The transmittance of the graphene film before and after electrostatic doping was determined using an Ocean Optics FLAME-T-XR1-ES spectrophotometer with a DH-2000-BAL light source.All characterisation was carried out in standard laboratory conditions of room temperature and pressure.This work aims to demonstrate how electrostatic ICD-doping can reduce the sheet resistance of graphene to a level competitive with TCOs without impacting transmittance.As the transmittance of monolayer graphene exceeds ITO and IZO, it is not expected to need as high an R sheet to match the overall performance of ITO films in tandem solar cells, assuming that its high transmittance can be maintained.We present a model depicting tandem cell efficiency as a function of TCE transmittance and R sheet based on the work of Anand et al where an 'exact Figure of Merit' is calculated to compare TCE Corona charging SiO 2 membrane for graphene doping.(A) Graphene device structure (cross-section).(B) Graphene device structure (3D cutaway view).(C) Apparatus used for corona charging of the SiO 2 membrane.
The 10 s of positive charging may have induced an n-type field effect large enough to reduce the p-type doping effect in the graphene, but insufficient for n-type behaviour.Increasing the amount of positive charge deposited on the membrane rapidly decreased the sheet resistance.It is assumed that the reduction of R sheet observed is because of n-type electrostatic doping of the carriers in graphene by the positively charged dielectric substrate.In under 3 min, the R sheet of graphene was reduced by $60% from 1810 to $759 Ω/□.After leaving this sample in a low-pressure nitrogenated chamber for 2 months, the sheet resistance decreased further, down to $607 Ω/□ (20% reduction).This is similar to the behaviour observed by Yu et al when investigating R sheet reductions in ICD-charged dielectric nanolayers in inversion layer solar cells.85It is likely that the quasi-permanent field established causes further reductions of graphene's R sheet over time.A device charged in the same way but stored in standard atmosphere and pressure, experienced a 2% (1910-1881 Ω/□) reduction in R sheet after 2 months.For comparison, a set of uncharged devices experienced a 10%-15% increase R sheet when held in standard laboratory conditions during the same time period, likely because of atmospheric F I G U R E 3 (A) Change in contact potential difference over time held under constant ±30 kV voltage, for a SiO 2 membrane measured by Kelvin probe microscopy.Inset: Kelvin probe microscopy measurement configuration.(B) Graphene sheet resistance over time held under constant +30 kV voltage.(C) Graphene sheet resistance over time held under constant À30 kV voltage.(D) Graphene sheet resistance as a function of time held under positive (red) and negative (blue) charge at ±30 kV.

Figure
Figure4Bdepicts the variation in Hall carrier concentration and mobility of graphene as the membrane is charged with negative electrostatic charge over time.This device was first charged with positive charge, then negative charge.The carrier concentration initially decreases with applied negative charge concentration, indicating that this particular graphene film, unlike those in Figure3, presented an initial level of n-type doping, which was compensated by the p-doping produced by negative charge on the SiO 2 membrane.Further negative

3. 2 |
Raman spectroscopyDefects in graphene are major scattering centres that can reduce mobility by reducing the mean free path of charge carriers.Raman spectroscopy allows the determination of whether the doping process introduced defects into the film, reducing mobility.The Raman spectrum of pristine graphene typically features two prominent peaks: the G peak at $1580 cm À1 , which arises because of in-plane vibrations of sp 2 bonded carbon in the graphene lattice; and the 2D peak, at $2690 cm À1 , which arises because of the breathing mode of sp2

Figure 5
Figure 5 depicts the Raman spectrum of a device before and after positive electrostatic charging of the SiO 2 layer.The presence of the D peak in the uncharged device indicates that the initial high sheet resistance of 1740 Ω/□ was due to a high density of defects, reducing mobility, as discussed in Section 3.1.When charged, the D/G intensity ratio did not increase, indicating that no additional defects were induced by the electrostatic doping process.This contrasts with chemical doping techniques, which often induce additional defects in the graphene film because of lattice disruptions by dopant

94 3. 3 |
Figure7Adisplays the experimental setup used to measure the transmission of the graphene devices on SiO 2 membranes.Figure7Bcompares the transmission of 350-800 nm light between an undoped graphene film, a graphene film doped with a corona-charged SiO 2 membrane, ITO and IZO.The doping by corona-charged SiO 2 did not impact the >95% broadband transmissivity of graphene.This contrasts with most doping techniques that tend to cause transmissivity reductions because of the addition of dopant atoms.25,65,72The ability to alter the R sheet of graphene rapidly and reversibly without impacting transmittance is significant, as it offers the potential to eliminate the challenging requirement to balance a trade-off between R sheet and transmittance in TCEs.Due to the limitations of in-house equipment, we were unable to measure the transmittance outside of the 350-800 nm window.Further work should include transmittance measurements across the entire AM1.5G spectrum before and after doping, to enable more meaningful comparisons between the optical properties of TCOs and ICD-doped graphene for tandem applications.The transmittance of undoped graphene remains broadband from 200 to 3000 nm, encompassing all light absorption within the AM1.5G spectrum.95,96If the ICD doping does not affect the transmittance of these regions, it Anand et al's work uses a detailed balance calculation to obtain the maximum power conversion efficiency of a single-junction solar cell with a given band gap, absorbing the AM1.5G spectrum.In this work, such detailed balance calculation is extended to the absorption and collection taking place in a two-terminal monolithic tandem device F I G U R E 6 Raman intensity versus wavenumber for a graphene device with a negatively charged SiO 2 substrate and an uncharged control.(A) G peak Raman shift.(B) 2D peak Raman shift.F I G U R E 7 (A) Schematic of spectrophotometry transmission measurement of graphene film.(B) Transmission of undoped graphene, ioncharged dielectric (ICD)-doped graphene, a typical indium tin oxide (ITO) film (ITO data 65 ) and a typical indium zinc oxide (IZO) film (IZO data 66 ).
The typical target sheet resistance for TCEs in optoelectronics is ≈10 Ω/□.Isolating this value on the x-axis, we can see that increasing the transmittance impacts the maximum efficiency significantly.At 10 Ω/□, increasing transmittance by 7% rel from 90% to 97% increases the efficiency potential from 40.5% to >44%.At 97% transmittance, reducing the R sheet by 500% rel from 50 to 10 Ω/□ would have a negligible impact on maximum efficiency.In this work, the graphene displays broadband transmittance >95%.This results in a maximum efficiency potential of >42% for R sheet less than ≈573 Ω/□.Optimizing the performance of ICD-doped graphene to have a transmittance of 97.5% and an R sheet ≈ 50 Ω/□ could facilitate maximum power conversion efficiencies as high as 44%.Thus, if graphene could be harnessed as a TCE for two-terminal perovskite/silicon tandem cells, the strict requirement on R sheet could be significantly relaxed, as well as providing increasing sustainability by eliminating indium from the cell.
Using theoretical modelling, we demonstrated that a maximum perovskite/silicon F I G U R E 8 Unit domains of two-terminal tandem solar cells with d representing the finger width and l the finger pitch.(A) Lateral view of two-terminal tandem with front and rear transparent conducting electrode (TCE) for bifacial configuration.(B) Lateral view of twoterminal tandem solar cell with front TCE and TCE between subcells.tandemefficiency of up to 44% could be realised if R sheet < 50 Ω/□ could be obtained in graphene without impacting its transmittance.In this work, despite not impacting transmittance, the measured R sheet of the ICD-doped graphene was ≈573 Ω/□, an order of magnitude above our target R sheet of <50 Ω/□.Fortunately, there are several ways to improve the ICD doping of graphene that could facilitate R sheet < 50 Ω/□.A key limitation of this work was the small 0.5 Â 0.5 cm 2 size of the substrates used.It is challenging to carry out the wet transfer process on substrates <1 cm 2 because of the increased manual dexterity required.Transferring the small 0.4 Â 0.4 cm 2 sheet to this substrate likely subjected the graphene to additional strain, resulting in the formation of additional wrinkles, cracks and holes.The presence of such deformations is supported by the prominent D peaks in its Raman spectra, which indicate a high density of defects.This high defect density resulted in a lower mobility and R sheet than is typical of monolayer CVD graphene.For perovskite/silicon tandem cell applications, a larger area sheet with a lower R sheet can be transferred.For example, monolayer CVD graphene films on Si/SiO 2 with undoped R sheet 430 ± 50 Ω/□ in areas up to 200 mm