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Field Performance versus Standard Test Condition Efficiency of Tandem Solar Cells and the Specific Case of Perovskites/Silicon Devices Olivier Dupre, Björn Niesen, Stefaan De Wolf, and Christophe Ballif J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02277 • Publication Date (Web): 05 Jan 2018 Downloaded from http://pubs.acs.org on January 6, 2018

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The Journal of Physical Chemistry Letters is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry Letters

Field Performance versus Standard Test Condition Efficiency of Tandem Solar Cells and the Specific Case of Perovskites/Silicon Devices Olivier Dupré,1) Bjoern Niesen,1,2) Stefaan De Wolf,3) Christophe Ballif1,2) 1

École Polytechnique Fédérale de Lausanne (EPFL), Institute of Microengineering (IMT), Photovoltaics and Thin Film

Electronics Laboratory, Rue de la Maladière 71b, CH-2002 Neuchâtel, Switzerland 2

CSEM PV-Center, Jaquet-Droz 1, CH-2002 Neuchâtel, Switzerland

3

King Abdullah University of Science and Technology (KAUST), KAUST Solar Center (KSC), Thuwal, 23955-6900, Saudi Arabia

Abstract: Multi-junction cells may offer a cost-effective route to boost the efficiency of industrial photovoltaics. For any technology to be deployed in the field, its performance under actual operating conditions is extremely important. In this perspective, we evaluate the impact of spectrum, light intensity, and module temperature variations on the efficiency of tandem devices with crystalline silicon bottom cells with a particular focus on perovskite top cells. We consider devices with different efficiencies and calculate their energy yields using field data from Denver. We find that annual losses due to differences between operating conditions and standard test conditions are similar for single-junction and four-terminal tandem devices. The additional loss for the twoterminal tandem configuration caused by current mismatch reduces its performance ratio by only 1.7% when an optimal top cell bandgap is used. Additionally, the unusual bandgap temperature dependence of perovskites is shown to have a positive, compensating effect on current mismatch.

In recent years, multi-junction cells integrating silicon have reached impressive efficiencies of up to 32.8% in tandem-based III-V Si-cells.1 However, the path for reducing the cost of III-V on Si devices is not straightforward. This is why perovskite solar cells have attracted tremendous attention among academic researchers as a highly promising photovoltaic technology, thanks to their combination of high conversion efficiencies and potential low-cost fabrication.2–10 The perovskite materials used in the most efficient devices have a fairly wide bandgap (>1.5 eV) that can be further opened by compositional engineering (e.g., by 11–14

developing mixed-halide mixed-cation perovskite materials). 15

absorption,

Their tunable bandgap, absence of parasitic sub-bandgap

and lack of need for lattice matching in these thin-film devices make perovskites particularly attractive for

application as the top cell of low-cost tandem solar cells.

16

Such dual-junction devices aim at better exploitation of the solar

spectrum by reducing thermalization losses, compared to single-junction devices (see Figure 1).17 Crystalline silicon (c-Si) solar cells are likely the best candidate for bottom cells, because they are fabricated from stable, non-toxic, and earth-abundant materials, and their market penetration is very high. In addition, c-Si solar cells can achieve an excellent response in the red part of the solar spectrum.

18,19

Alternative bottom cells may be CIGS

20–23

and narrow-bandgap perovskites.

24–26

For all these material

combinations, essentially three device architectures are possible. In a monolithic tandem architecture, the top cell is directly processed onto the bottom cell. stacked

33–35

27–32

Alternatively, both sub cells are processed independently and then either mechanically

or arranged in a more complex geometry using a spectral beam splitter.36,37 Each of these architectures has its

specific advantages and challenges concerning peak performance, device fabrication, module reliability and system integration.38–40 In addition, the sub cells for each of these device architectures can be either electrically connected in series to form a two-terminal (2T) tandem or each sub cell can be individually contacted to form a four-terminal (4T) device (Figure 1).

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The 2T configuration has the advantages of featuring fewer transparent electrodes on the cell level (minimizing parasitic

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absorption losses),41 less electrical wiring on the module level and fewer electronics at the system level, but requires a design that guarantees current matching at the maximum power point of the sub cells. On the other hand, 4T tandems require additional components but offer higher operational flexibility as both sub cells can be kept at their maximum power point 32

14,29,42

individually without the need for current matching. The best results so far are over 23% for 2T and over 25% for 4T

, with

a strong upside potential. Whether tandems with perovskite top cells will eventually be able to challenge the market-established single-junction PV technologies is increasingly debated in the community.

39,43–51

As new materials and processes are reported on a daily basis and

record efficiencies with increasingly acceptable stability are still rising at a fast pace, it may be too soon to draw a final conclusion. Also, the question whether the 2T or 4T configuration is the most promising is still debated and uncertainty remains about the losses caused by current mismatch. Several basic questions in these discussions remain unanswered… What is a fair methodology to compare single-junction cells with tandems and various tandem configurations with each other? Is it sufficient to compare peak performance measured under standardized conditions? How do the actual outdoor operating conditions, including spectral and intensity as well as temperature fluctuations, affect the actual energy output of these different devices in different locations? Can we make assumptions based on existing tandem cell technologies, such as thin-film silicon solar cells and III-V semiconductor multijunction cells, or is there a fundamental difference between these established technologies and emerging perovskite-based tandem cells?


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The Journal of Physical Chemistry Letters In this perspective, we aim to establish which factors affect 2T and 4T perovskite / c-Si tandem performance and how to

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estimate their impact for given locations / climatic conditions. Firstly, we describe the effects of irradiance, spectrum and temperature variations separately. Next, by using field data, we show that these parameters (i.e., irradiance, the spectrum’s average photon energy and module temperature) are correlated and discuss the implications for the different devices considered. To draw long-lasting conclusions, independent of any particular perovskite / c-Si tandem design, we first focus on ideal tandem cells, which operate in the radiative limit (i.e., the so-called Shockley-Queisser or detailed-balance limit).17,52 Note that the analysis also applies to III-V top cells but inherent differences will be highlighted. The efficiencies and, subsequently, the energy yields and annual performance ratios are calculated using a detailed-balance model that includes the radiative coupling 17

between the sub cells (as in ). A series of simulations enables us to quantify the impact of each operating condition on the field performance of the different devices. Following this, we then take into account non-radiative recombination by including external radiative efficiencies53 in our model to provide a basis of comparison of the actual field performances of devices with various STC efficiencies.

Figure 1 Illustration of the differences in photon absorption and charge carrier thermalization between single junction and tandem photovoltaic devices. Sketches adapted from 54.

To start our discussion, Figure 2 illustrates how the AM1.5G solar spectrum is selectively absorbed in an ‘ideal’ tandem device. The top cell absorbs the visible part of the spectrum while the bottom cell mostly absorbs the infrared. In the ideal case, each absorbed photon results in exactly one collected electron-hole pair. In an actual tandem device, absorption might be different from the ideal case shown in the figure due to reflection, incomplete absorption or parasitic absorption losses in the surrounding transparent electrodes, or in the electron and hole transport materials.

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In addition, it is also possible that a

fraction of the photogenerated electron-hole pairs is not collected, which may happen, for example, if the carrier diffusion length is too short. However, the conclusions derived from our ideal tandem approach can be easily extended to real devices by using more refined optical simulations (as, e.g., demonstrated in 39) and additional diode parameters (as, e.g. in 55). In any case,


The Journal of Physical Chemistry Letters to evaluate correctly the impact of current mismatch on the efficiency of tandem devices, it is not sufficient to calculate the

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difference in short-circuit current (Isc) between both sub cells. The reason for this is that the fill factor (FF) of tandem devices 56

reaches its minimum value under current-matched conditions. This latter effect somewhat compensates for the Isc loss due to current mismatch and, in certain cases, the actual maximum power point of a tandem can be obtained with a slightly currentmismatched device design.56 Therefore, it is necessary to consider all J-V parameters when evaluating the impact of current mismatch.

Figure 2 Photon-flux density of the AM1.5G spectrum. The colored areas show the photons absorbed in each sub cell of an ideal (EQE=1) tandem device perfectly current-matched at 25°C. The red arrows show the directions of changes in bandgaps with increasing temperature. The green arrows show the directions of changes of the incident photon flux density with increased average photon energy (APE).

Figure 3 Radiative-limit efficiency of tandems (two-terminal and four-terminal configurations) with a c-Si bottom cell (Eg=1.12 eV at 25°C) as a function of the top cell bandgap. The efficiency limit of a c-Si single junction cell is also shown for comparison.


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The Journal of Physical Chemistry Letters Figure 3 shows that under standard test conditions (STC: AM1.5G spectrum, 1000 W m-2, 25°C), the radiative efficiency limits for both tandem

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configurations are nearly identical, assuming that the bandgap of the perovskite cell used on top of the c-Si cell can be tuned at will

Figure 3. The ideal top cell bandgap is 1.73 and 1.82 eV for 2T and 4T devices, respectively. These values should be considered as targets for devices operating close to the radiative limit. In the short term, the optimal bandgaps can be lower if the quality of the top cell is lower than that of the bottom cell. A recent study55 evaluated the optimal bandgap for 2T between 1.65 and 1.7 eV for devices with realistically constrained diode characteristics. Also, as explained in this work, the optimal bandgap decreases when spectra become more red rich. This is the case in real devices because the transparent electrode and charge transport layers in the top cell absorb some of the UV. Additionally, actual conversion efficiencies – and as a result the ideal bandgap for the top cell (as well as its ideal thickness in a more realistic consideration) – depend on field-specific operating conditions, such as light spectrum, intensity and operating device temperature. In the following, we quantify the effects of each of these conditions on the field performance of different device configurations (operating in the radiative limit). The devices under comparison in this work are a single junction c-Si cell (Eg=1.12 eV at 25°C) and tandems with a c-Si bottom cell and the top cells with the determined ideal bandgaps under STC: i.e., Eg=1.73 eV (at 25°C) for the 2T configuration and Eg=1.82 eV (at 25°C) for the 4T configuration. Note that, because the operating conditions have seasonal variations, quantifying their impact on PV production requires taking at least a full year into account. To compare the performance of these different PV technologies, we use the concept of harvesting efficiency, defined as the ratio of the time-integrated produced energy divided by the timeintegrated incident energy. This metric corresponds to an average efficiency in terms of energy output and enables a direct comparison of locations with different annual irradiation conditions. To quantify the various losses, we also use the Performance Ratio (PR) metric, which corresponds to the ratio between harvesting efficiency and STC efficiency. In contrast to their 4T counterparts, 2T tandems may suffer from current mismatch when there are spectral variations, as indicated by the more pronounced decrease in efficiency at STC when deviating from the ideal top cell bandgap as compared to 4T devices (Figure 3). This current mismatch loss can only be calculated for a specific location as it depends on daily as well as seasonal variations of the incident spectrum. As an example, Figure 4 illustrates typical spectral variations during outdoor 57

operation based on data from Denver, Colorado, USA. On a clear day, the spectrum shifts towards the blue during the morning until noon, as the sun rises, and then shifts to the red as the sun sets (see Figure 4a). This spectral effect is caused by Rayleigh scattering of sunlight in the atmosphere, which especially attenuates the shorter wavelengths and depends upon the atmospheric distance the sunlight traverses. For the same reason, and because the Sun’s arc is higher above the horizon in summer than in winter, the spectra reaching Earth in summer are on average bluer than their winter counterparts. This is illustrated in Figure 4b in which PV energy output distributions in August and in January are shown as a function of the average photon energy (APE) of the incident spectrum. The irradiation spectra received at a given location also depend on other factors such as humidity. Indeed, the broad absorption lines of water vapor significantly reduce the infrared part of the solar 58

spectrum. As a result, devices operating in tropical locations like Singapore are exposed to spectra that are significantly bluer than the AM1.5G spectrum. This effect of the climate is illustrated in Figure 5 where the PV energy output distributions in



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Denver and in Singapore are shown a function of APE. Figure 5 also shows the impact of APE on the efficiency of different device

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configurations, optimized for maximum efficiency in STC (with a perovskite bandgap of 1.73 eV for 2T and 1.82 eV for 4T). Because of the current matching constraint, the efficiency of the 2T tandem decreases as the APE diverges from the value it was designed for, while the efficiency of the 4T tandem is almost insensitive to APE variations. Over a year, the loss in harvesting efficiency caused by current mismatch is thus dependent on the distribution of APE, which depends on the location, and on the tandem design for which the bandgaps and the absorber thicknesses of the sub cells define the optimal operating spectrum. Figure 5 highlights that a 2T device optimized for the STC would suffer a much larger loss due to current mismatch if it was operating in Singapore rather than in Denver. However, it is possible to optimize a device design specifically for any operating condition. Such optimization enables the green curve in Figure 5 to be shifted so that the maximum coincides with the average 1

operating APE. For example, the optimal top cell bandgap for the average spectrum in Denver is 1.73 eV, slightly higher than the optimal value for the AM1.5G spectrum. This value shifts to 1.76 eV for the average spectrum in Singapore. The optimal spectral condition can also be modified by fine-tuning the absorber thickness of the top cell.59,60 Liu et al. showed numerically that optimizing for operation in Singapore a 2T GaAs/Si tandem with 27% in STC reduces the loss in annual harvesting efficiency 61

due current mismatch from 1.1% to 0.4%, corresponding to a PR loss reduction from 4.1% to 1.5%.

a.

b.

Figure 4 a. daily (morning until noon, a reverse shift occurs from noon until evening) and b. seasonal spectral variations, expressed as a function 62

57

of average photon energy (APE). Spectral data for Denver are from NREL SRRL and available online.

1

Note that these simulations consider a perfect optical absorption. In real devices, optical absorption in the active layers depends on the 83 thicknesses of the different layers and the angle of incident light (and thus the diffuse light fraction) because of thin film interferences. Thus, the current mismatch loss and the optimum value might vary depending on the considered device structure.


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Figure 5 Energy output distribution in Denver and Singapore as well as conversion efficiencies of single-junction and tandem devices as a function of average photon energy (APE). Data for Denver were taken from 62; data for Singapore from 61. The efficiency curves were calculated 61

using the characteristic set of spectra for Denver from .

Similarly to the incident spectrum, the illumination intensity shows daily and seasonal variations, which strongly depend on location. Figure 6 illustrates the range of irradiance relevant to photovoltaic energy conversion in Denver and Singapore. This 63

figure also shows the well-known logarithmic dependency of the efficiency on irradiance, observed for both single- and multijunction devices. Additional effects in actual modules caused by shunts and series resistances or partial shading are not -2

discussed here for the sake of simplicity. The average irradiance in terms of annual energy output is about 750 W m in Denver, -2

which is less than the 1000 W m irradiance under STC. The operation at low irradiance accounts for an annual harvesting efficiency loss of about 0.7% for all the device configurations considered.2 This corresponds to a performance ratio loss of 2.1% for the SJ device and 1.6% for the tandems. Figure 6 shows that this “low irradiance loss” would be larger in a more cloudy location, such as Singapore, where a larger fraction of the total electricity is produced under low irradiance conditions, with an -2

average irradiance of 640 W m .

2

This number corresponds to devices installed on fixed arrays mounted with the optimum tilt angle for each location. The loss due to low irradiances would be smaller for installations with tracking systems.


The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Figure 6 Energy output distributions in Denver and Singapore with conversion efficiencies of single-junction and tandem devices as a function of 62

61

irradiance. Data for Denver were taken from ; data for Singapore from .

The operating temperature of PV devices also undergoes daily and seasonal variations. The magnitudes of these variations depend on the climatic conditions, such as ambient temperature and wind speed, under which the device operates and on certain design parameters, such as the mounting configuration and the type of back sheet.

64

Figure 7 shows the PV energy

output distribution of modules operating in three locations as a function of their operating temperature. On average, the PV module installed in Agder (Norway) operates at the lowest temperature of the three compared locations, followed by the module installed in Denver (Colorado, USA) with intermediate operating temperatures. The module installed in the desert in USA operates under considerably higher temperatures on average. These differences in operating temperature affect the harvesting efficiencies and can be estimated easily by considering the so-called temperature coefficients of the devices. The efficiencies of the different devices are plotted in relation to temperature in Figure 7. From these efficiencies and the operating temperature distributions, we can estimate the loss in annual harvesting efficiency (compared to STC efficiency) due to operation at high temperature in the different locations. This loss amounts to about 1.3% in the desert in SW USA and 0.5% in Denver, and is negligible in Agder for all the devices (the loss in performance ratio can be calculated using the STC efficiencies, e.g., 3.0 %, 1.2% and 0.0% for the 2T tandem). It is important to recall that the efficiencies plotted in Figure 7 are those of devices operating in the Shockley-Queisser limit -1

where only radiative recombination is considered. We see that the temperature coefficients in this case, -0.15% K and -0.13% -1

K for the c-Si single junction and the tandems respectively, are significantly lower than those of actual c-Si modules of ≈-0.30 to -0.45% K

-1

65

(for silicon heterojunction and diffused-junction technologies, respectively).

This stems from the fact that

temperature coefficients generally improve as the device’s quality improves because the rates of most recombination mechanisms increase with temperature.64,66 This observation means that for actual devices, which even when defect-free still suffer from Auger recombination in addition to radiative recombination, the loss due to high temperature operation is greater than that calculated above. Depending on the selected solar cell technology, the presence of defect recombination can further inflate the temperature coefficient.

65

Also, it is noteworthy that the temperature distributions shown in Figure 7 were obtained from measurements on different installed modules. As mentioned above, the operating temperature of a PV device also depends on its design (this is partially shown through the Nominal Operating Cell Temperature (NOCT) parameter).64 For example, part of the heat generated within a module depends on the fraction of sub-bandgap photons that is parasitically absorbed, e.g., in the rear metal electrode. This is one reason why – under identical outdoor conditions - passivated emitter rear contact (PERC) or Si heterojunction (SHJ) cells


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The Journal of Physical Chemistry Letters operate at lower temperatures than do Al back-surface field cells, because PERC and SHJ solar cells reflect infrared light better

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67

out of the device than do Al cells. The other reason for this “thermal advantage” of PERC and even more for SHJ cells is their higher conversion efficiencies. This is because there remains less energy to heat up a device that converts a larger fraction of the incident energy into electricity, resulting in a lower operating temperature. This has an evident beneficial impact on the annual harvesting efficiency and it will also reduce the degradation rate and therefore improve the device’s lifetime.64 Overall, these arguments suggest the use of high-efficiency silicon technology in tandem solar cells, especially when they are intended for deployment in hot climates.

Figure 7 Energy output distribution in Agder (Norway), Denver (USA) and a desert in the SW USA and conversion efficiencies of single junction and tandem devices as a function of module temperature. Data for Norway are from the Energy Materials Group at the University of Agder, 68

Norway. Data for Denver are from PVDAQ.

69

Data for the US desert are from .

To accurately quantify the annual harvesting efficiency of a device, it is necessary to simulate the above described effects of the different operating conditions (spectrum, intensity and temperature) simultaneously. Indeed, as will be shown in the following, important correlations exist between these parameters. Figure 8 shows the results of simulations that use a full year of spectral and temperature data from Denver. The conversion efficiency of each device is calculated every 30 minutes during the full year using the detailed balance model described above, enabling the determination of the annual harvesting efficiencies. The different simulation parameters are summarized in Table 1. -2

The initial comparison point (Step 1 in Figure 8) shows the normalized efficiency under STC (AM1.5G spectrum, 1000 W m , °

25 C). In the second simulation step, the annual harvesting efficiencies are calculated using the full year of spectral data while keeping the operating temperature at 25°C to quantify the impact of spectral and intensity variations exclusively. The loss between Step 1 and 2 is thus only due to spectral variations and operation at reduced illumination intensity. As expected, this loss is larger for the 2T configuration, due to current mismatch. However, we remark that the harvesting efficiency of the 4T and the 2T configurations differ by only 0.6%, which corresponds to a 1.2% performance ratio loss.3 68

In the third simulation step, we include the effect of operating temperature. For this, we use the temperature measured on a commercial c-Si module operating in Denver. The loss between steps 2 and 3 is due to operation at high temperature and is – at

3

Note that these calculations are based on the in-plane irradiance on a fixed array mounted at 40° and facing south. Modules installed on tracking systems would produce more energy in the mornings and evenings. This would result in a different average spectrum distributions and different current mismatch losses.



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this stage of the simulation – directly proportional to the devices’ temperature coefficients (which are almost identical for all

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considered architectures as discussed above). Until this point, the bandgaps of the sub cells were assumed to be independent of temperature. In the fourth simulation step, we take into account the actual temperature dependencies of the respective bandgaps. It is noteworthy that perovskites differ from other typically used semiconductor materials because they have an opposite bandgap temperature sensitivity, i.e., their bandgap widens with temperature, which has been attributed to a reverse ordering of their band-edge states.7 The measured bandgap energies (Eg) of several perovskite compounds were found to increase linearly in the temperature (T) range of photovoltaic operation, with gradients (dEg/dT) ranging from 0.3 to 0.35 meV K-1.64,70–73 Based on this, we assume in the following calculations a positive bandgap temperature dependence of 0.32 meV K-1 for the perovskite top cells. In comparison, c-1

Si and GaAs feature bandgaps that narrow with temperature, with a slope of -0.27 and -0.55 meV K around room temperature, respectively

74,75

.

When a negative temperature dependence of the top cell bandgap is used in the simulation (dashed line in Figure 8, e.g., if GaAs were used), the annual harvesting efficiencies do not change significantly. However, when a positive bandgap temperature dependence – e.g., that of a perovskite compound – is assumed for the top cell, the performance ratio of the 2T tandem cell is increased by 0.2%, as shown by the full line from step 3 to 4 in Figure 8. Although the change is small in this configuration, it is worthwhile discussing it because it corresponds to a phenomenon specific to tandem cells that have one (and only one) perovskite sub cell. Indeed, this improvement of the annual harvesting efficiency comes from a thermally-induced current mismatch which partially counterbalances the current mismatch caused by spectral variations. To visualize why these effects compensate for one another, it is helpful to look at Figure 2 and describe the operating conditions during a standard sunny day. As mentioned above, the incident spectrum undergoes a blue shift during the morning. The current increases relatively more in the top cell than in the bottom cell. Additionally, as the sun rises, the irradiance increases as does the temperature of the module. This temperature rise causes the bandgap of the perovskite top cell to widen and that of the c-Si bottom cell to narrow. These bandgap variations result in an increase of the current generated by the c-Si cell, which compensates to a certain extent for the current mismatch induced by the spectral variations. The data from Denver as well as other data from other locations

76

show that despite the multiplicity of operating conditions (seasonal variations, different cloud cover, etc.), there exists a general correlation between APE and the temperature of the module. This “compensating effect”, which is specific to tandem cells with

one perovskite sub cell, might be more pronounced in actual devices, compared with our radiative-limited simulations. Indeed, the temperature coefficient of the short-circuit current of actual cells is not solely determined by its bandgap-temperature dependency but it also depends on mechanisms limiting carrier collection.

64

For example, the temperature coefficient of the

short circuit current of c-Si cells is usually significantly larger than the value that can be calculated from the bandgaptemperature dependence.

77

As the efficiency of photovoltaic devices improves, one often-overlooked associated benefit is the fact that the operating temperatures are reduced. This originates from a reduction in the heating under illumination; indeed, the energy extracted electrically from a device does not turn into heat. Reduced operating temperatures result in better energy yields as well as increased longevities of photovoltaic systems. In the fifth and final simulation step, we aim at illustrating this benefit in harvesting efficiency resulting from the efficiency gain of tandem cells compared with single-junction devices. For this, we first introduce a way to estimate the operating temperature expected for each device, instead of assuming that all devices operate at the same temperature; the operating temperatures of the different devices are calculated from a measured module temperature by subtracting a term corresponding to the heat source reduction that stems from the efficiency advantage:


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Tdevice = Tmeas −

( Pinc × (ηdevice −ηmeas )) , h

(1)

where Tdevice is the calculated from the operating temperature of a solar cell with efficiency STC ηdevice, Tmeas is the measured temperature of a solar module with ηmeas at STC, Pinc is the power incident on the module and h is a global heat transfer coefficient that accounts for all the heat transfer mechanisms between the module and its surroundings. This coefficient includes convective exchanges (which depend on parameters such as wind speed and direction, mounting configuration, etc.) and radiative exchanges (which depend on the module’s surroundings and the optical properties of its different layers).64 Because the tandem devices under consideration are significantly more efficient than the single-junction device (limiting efficiency ≈45% against 33% in STC), a smaller fraction of the incident solar irradiation turns into heat, which leads to lower operating temperatures. This gives them an advantage in terms of harvesting efficiency (see Step 5 in Figure 8). This “thermal -2

-1

benefit” strongly depends on h. We performed simulations for h = 10 and h = 20 W m K , which are representative of average field values for insulated and free-standing arrays, respectively. In both cases, the tandem devices operate at lower operating temperatures than the single junction devices operate at. This thermal benefit translates into a performance ratio advantage of 0.3% and 0.6% for h = 20 and h = 10 W m-2 K-1, respectively (corresponding to average operating temperature differences of 4 4

and 8°C, respectively) . This phenomenon could even more important in environments where heat transfer is severely limited, such as outer space applications.

Figure 8 Simulation results of the harvesting efficiencies in Denver in 2016 for a c-Si single junction, a two-terminal device and a four-terminal tandem device operating in the radiative limit. The data used include spectrum, intensity, and module temperature measurements taken from 62

68

and . The simulated devices are a single junction c-Si cell (Eg=1.12 eV at 25°C) and the tandems with a c-Si bottom cell and the top cells with

the ideal bandgaps under STC : i.e. Eg=1.73 eV (at 25°C) for the 2T and Eg=1.82 eV (at 25°C) for the 4T.

4

th

Some of the calculated harvesting efficiencies in this 5 simulation step are actually higher than their counterparts calculated at step 2 because the recalculated average operating temperatures are below 25°C. This stems from the very high efficiencies of the simulated devices. -2 -1 Also, the harvesting efficiencies calculated with h=10 W m K are higher than those calculated with h=20. This is because the operating temperatures are calculated from Eq. 1 in which the heat transfer coefficient, h, should always correspond to the measured module (whose temperature is Tmeas). The case h=10 is not representative of the measured module data but it is presented here to illustrate the particular importance of the heat source when heat transfer out of the module is limited.



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Table 1 Parameters used in the simulations. The resulting annual harvesting efficiencies are shown in Figure 8.

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Simulation parameters

Step

Tdevice

Description

Eg 1. reference calculation in the

1

Standard Test Conditions (STC) 25°C

2. takes into account assumed cst.

2

the spectra and irradiances over a whole year in Denver

3. takes into account 3

the module temperature dEg/dT= 4. shows the “compensating” curr

-0.55

Tmeas

4a

meV K

-1

(GaAs)

Tmeas-∆T 5a

(eq. 1

dEg/dT=

meV K-1

+0.32

perovskites

meV K-1 5. Shows the benefit (perovs of high efficiency

h=10)

kites)

Tmeas-∆T 5b

dependence of

=-0.27 (c-Si)

of the singular bandgap temperature

dEg/dT

4b

ent mismatch effect

stemming from reduced operating

(eq. 1

temperature

h=20)

The results presented in Figure 8 illustrate the differences that one can expect between the efficiency under STC and the actual annual harvesting efficiency for different PV technologies. For the sake of simplicity, the simulations presented so far were based on the assumption that the devices operate in the radiative limit (note that the single junction and tandem devices had significantly different efficiencies under STC, ≈33% compared with 45%). Next, we use the concept of external radiative 53,78

efficiency

in our detailed balance model to simulate devices with more realistic performance and assess the efficiency

reductions, compared to STC efficiency, caused by the operating conditions in Denver. The devices we simulated are:

•

a single junction c-Si cell rated at 19%STC, i.e. 19% efficiency under STC (similar to conventional products currently available in the market);

•

a single junction c-Si cell rated at 27%STC (which is close to the actual record80) and 27%STC efficient tandems based on 19%STC efficient c-Si bottom cells (these require a 18.2%STC efficient top cell in a 2T configuration and a 17%STC efficient top cell in a 4T configuration);

•

35%STC efficient tandems (which is a plausible target in tandem device development) based on 27%STC efficient c-Si bottom cells (these require a 22.2%STC efficient top cell in a 2T configuration and a 20.6%STC efficient top cell in a 4T configuration).


Page 13 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 9 and 10 show the results of several simulations that enable us to quantify the losses due to the operating conditions. The details

of

the

simulations

are

given

in

the

caption

of

Figure 9. The results highlight that: •

In general, the performance ratios are better for more efficient devices. This stems mainly from the reduction in operating temperature described above (the calculated average operating temperatures are about 33°C, 30°C and 27°C for the 19%STC, the 27%STC and the 35%STC devices, respectively). Additionally, the loss due to low irradiance remains the same

so

the

relative

drop

in

performance

is

lower


for

more

efficient

devices

(compare


Page 14 of 21

Figure 9 and 10). •

When comparing devices with similar STC efficiency (27%STC), there is no significant difference in the annual losses due to operating conditions between single junctions and 4T tandems. Note that this is different from the results obtained for ideal devices shown in Figure 8 because the devices in this case have similar efficiencies and therefore similar operating temperatures. We note that the loss due to operation at high temperature is slightly larger for the tandem than for the single junction devices, by about 0.2%abs, i.e. relative to the total incident illumination. This stems from lower temperature coefficients for the tandems which come from the fact that the quality of their sub cells (e.g. the 19%STC c-Si bottom cell), quantified by their external radiative efficiencies in this work, is comparatively lower than the quality of the 27%STC single junction cell. In the case of the 4T tandem, this additional high temperature loss is compensated by a 0.2%abs gain from spectral effects. Indeed, the average spectrum in Denver is bluer than the AM1.5 spectrum and can thus be converted more efficiently by tandem devices (because there is less thermalization in the cSi bottom cell).

•

The additional annual loss for the 2T tandem configuration caused by current mismatch accounts for only about 0.5%abs efficiency or 1.7%rel, i.e. in performance ratio. This is in line with previous reports for other multi-junction technologies.

61,81

This current mismatch loss for the 2T configuration needs to be weighed against the additional

requirements and losses of a 4T configuration (parasitic absorption in the intermediate electrode layer, additional connections, etc.), which were not taken into account in this work. •

Because of their unusual bandgap-temperature dependencies, perovskites benefit from a small advantage, compared with III-V materials such as GaAs, when used in two-terminal tandems with c-Si. As discussed above, this advantage results from a temperature-induced effect that somewhat compensates for the spectral mismatch inevitably occurring under real operating conditions. The simulations show that this advantage, shown in light blue in the figures, amounts to 0.2%abs or 0.6%rel in Denver for 2T devices with 27%STC efficiencies. For more efficient devices, this phenomenon is reduced because the operating temperature variations are attenuated.


Page 15 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 9 Loss breakdown of the harvesting efficiency of single junction and tandem devices with different efficiencies under STC simulated for 62 68 2016 in Denver. The data include spectrum, intensity, and module temperature measurements taken from and . The bandgaps of the sub cells were 1.12eV, 1.73 eV and 1.82 eV at 25°C for the c-Si, the top cell in the 2T configuration and the top cell in the 4T configuration, respectively. The simulations were performed as follows: First, the spectral effect was quantified (shown in purple) by calculating the efficiency of each device under the spectra received in Denver over the entire year of 2016. The spectra are normalized so that the number of photons above the bandgap of c-Si remains equals to its value under the AM1.5 spectrum. This way, irradiance and spectral effects are completely decorrelated. Next, the measured irradiances are included in the simulation together with the spectra. The loss shown in orange can be solely attributed to the lower efficiency at low irradiances. Next, the temperatures of the devices (calculated with Eq. 1) are included in the simulation -1 and the bandgap-temperature dependence of the top-cells is set to +0.32 meV K to mimic the behavior of perovskite compounds. The temperature coefficients are outputs of the model and depend upon the bandgaps and the external radiative efficiencies.66 The drops in harvesting efficiency due to operation at temperatures above 25°C are shown in red. The final harvesting efficiencies are shown in green for single junctions and perovskite/c-Si tandems. Finally, the same simulation (spectrum, irradiance and temperature) is done with the bandgap -1 temperature dependence of the top-cells set to -0.55 meV K to mimic the behavior of a “regular” semiconductor such as GaAs. The difference with the previous simulation is shown in cyan.

Figure 10 Loss breakdown of the performance ratio of single junction and tandem devices with different efficiencies in STC, simulated for 2016 in Denver. The details of the calculations are given in the caption of Figure 9.

The results shown in Figures 9 and 10 include the harvesting efficiencies of different devices (SJ, 2T, 4T) with the same efficiencies under STC. Another question that one may ask is: what is the efficiency under STC that each tandem configuration



Page 16 of 21

needs to achieve to have the same annual energy output in the field as a single junction solar cell with a given efficiency under

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

STC? Figure 9 shows that a c-Si single junction cell with 27%STC would have a 26.1% annual harvesting efficiency in Denver. To have the same annual harvesting efficiency as this single-junction cell, we calculated5 that a tandem device with a 19%STC c-Si bottom cell would require a 27%STC efficiency in a 4T configuration and a 27.5%STC efficiency in a 2T configuration. These results can serve as guidelines to estimate the actual field performances of different type of PV devices (for operation in climates similar 6

to Denver): single junction and 4T tandems efficiencies under STC can be compared and a “malus” of about 0.5%abs should be subtracted for 2T devices because of current mismatch losses in operating conditions. The case of Singapore, shown in Figure 5, illustrates that the current mismatch loss occurring for 2T tandems is larger in locations where incident spectra show a relatively large discrepancy, compared to the reference AM1.5 spectrum. However, this loss can be kept around 0.5%abs in most locations if the devices are designed specifically for the appropriate operating conditions. The optimum bandgap range for most terrestrial applications remains between 1.7 and 1.8 eV (for highly efficient devices), which is easily reachable with currently available perovskite materials. However, at present, perovskite compounds in this bandgap range do not yet yield their full operating voltage potential.82 Further work is thus necessary on this topic to maximize the efficiency of perovskite-based tandem devices. Ultimately, economics will dictate whether it is worthwhile manufacturing different products adapted to various climate zones. The exact value of the loss due to current mismatch depends on the daily and seasonal spectral variations, with temperature having a minor effect. One would expect larger spectral variations for locations at high latitudes but other factors, such as humidity, make it challenging to derive any general rule. For example, Singapore at a latitude of 1° and Denver at a latitude of 40° have similarly broad APE distributions (Figure 5). Therefore, to quantify accurately the losses and to determine the optimum device designs, detailed calculations have to be performed for every location and for every tracking system7 of interest. For this purpose, a consistent set of data from each location that includes spectrum, irradiance, and temperature8 measurements recorded at least every 30 minutes is necessary. Unfortunately, very few spectral databases are available and accessible to the community to date. To conclude, we describe a practical way of directly comparing different device performances by calculating each device’s annual harvesting efficiencies rather than simply looking at their efficiencies under STC. This metric requires taking the various effects of the operating conditions on the efficiency into account. The simulations presented in this perspective confirm previous works that showed the small magnitude of the loss due to current mismatch in 2T tandem devices. The results also highlight the opportunity of boosting the energy yields of 2T tandem devices by designing devices specific to the given set of operating conditions representative of the location they are to be installed in. Additionally, the comprehensive analysis of the different phenomena happening during operation in the field demonstrates a “compensating effect” specific to 2T tandem devices that have one perovskite sub cell. Finally, we emphasize that high-efficiency devices such as tandems will benefit from an additional boost in harvesting efficiency that stems from lower operating temperatures compared to lower efficiency devices.

5 6

Using simulations (that include the different effects described previously) in an iterative process to converge towards the desired harvesting efficiencies. Spectral mismatch losses may be quite different in certain devices (e.g., a really good bottom cell in combination with a poor top cell) as this loss also strongly

depends on the combination of the fill factors of both sub cells56 7

Indeed, tracking systems change the amount of illumination received by PV devices significantly as a function of time. They therefore have a significant impact

on spectral mismatch effect.


Page 17 of 21


Proposition of quotes:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

•

…interesting phenomenon specific to tandem cells that have one perovskite sub cell… improvement of the annual harvesting efficiency comes from a thermally induced current mismatch that partially counterbalances the current mismatch caused by spectral variations

•

When comparing devices with similar STC efficiency … there is no significant difference in the annual losses due to operating conditions between single junctions and 4T tandems

•

The additional annual loss for the 2T tandem configuration caused by current mismatch accounts to only about 0.5%abs efficiency

•

As the efficiency of photovoltaic devices improves, one often-overlooked associated benefit is the fact that operating temperatures are reduced, resulting in better energy yields as well as increased durability of the photovoltaic system.

Acknowledgments: O.D. would like to thank Sarah Kurtz and Haohui Liu for kindly sharing their data. Special thanks also to Lionel Bloch for his help with big data management. This work was partially funded by the Nano-Tera.ch “Synergy” project, the Swiss Federal Office of Energy under Grant SI/501072-01, and the Swiss National Science Foundation via the NRP70 “Energy Turnaround” project “PV2050.

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