The Potential of Tandem Photovoltaic Solar Cells for Indoor Applications

Several studies have already determined the power potential of different types of photovoltaic solar cells for indoor applications. However, a detailed study whether or not the use of tandem solar cell (i.e. using two solar cells with different bandgaps in a row) is beneficial for indoor use is lacking. This paper attempts to fill this lacuna by comparing the power output of different tandem solar cells with single-junctions as reference. The comparisons are done by efficiency simulations of the solar cells and the light spectra of typical artificial light sources, i.e. a typical fluorescent tube, a high pressure sodium and metal halide lamp, a typical LED lamp and a common incandescent lamp, which are compared to the outdoor AM 1.5 spectrum as reference. More specifically, we study the influence of the energy levels of the bandgaps, not only for the usual monolithic configuration, but also for a stacked set-up. By determining the relative efficiency gain compared to single-junctions, we prove the limited usefulness of tandem solar cells for indoor applications.


Introduction
Nowadays, wireless communication networks focused towards indoor applications, use batteries as their source of energy.However, batteries have a limited lifetime and have to be replaced in due time.The lifetime of the battery is often the limiting factor for the lifetime of the device.Often, the cost of replacing the battery outweighs the cost of the device itself.Also from an environmental perspective, battery waste should be minimized if possible.The lifetime of the device can be extended if the device itself would be able to harvest energy from renewable resources in the environment.Photovoltaic (PV) solar energy can be an efficient natural energy source for indoor applications.
The different PV cells for applications on earth are rated by their power output under standard test conditions i.e. an illumination intensity of 10 3 W/m² under the global AM 1.5G spectrum, at a cell temperature of 25 °C.Although these conditions seldom appear at the same time, this characterization gives a reasonable guideline for comparing different solar cell types for outdoor conditions.However, the standard test conditions are not relevant for indoor applications.Typically, the light intensity under artificial lighting conditions found in offices and factories is less than 10 W/m 2 as compared to 100-1000 W/m 2 under outdoor conditions, depending on the type of and the distance from the light source.Moreover, the spectrum can be totally different from the outdoor solar spectrum.The spectrum depends not only on the type of light source, but also on the presence of reflected and diffused light.Unfortunately, there are no international norms which determine the way of characterizing solar cells for indoor applications.
Different authors discussed [1][2][3] and measured [4][5][6][7] the spectral mismatch between the absorption of solar cells and the spectrum of indoor light sources, but mainly only for single-junction solar cells.In this paper we quantify on a fundamental level the gain that can be achieved by using tandem cells instead of single-junction cells for indoor applications.More specifically, we study the influence of the energy levels of the bandgaps of the tandem cell for different indoor illuminations, not only for the usual monolithic configuration, but also for a stacked set-up.

Methodology
The power conversion efficiency of a solar cell can be significantly increased by using two solar cells with different bandgaps E g in a row, i.e. a tandem solar cell (Figure 1a).The solar cell with the highest optical bandgap is in front (side of the sun), thus E g1 > E g2 .High-energy photons with an energy hν > E g1 are absorbed by the first cell.The second cell, with a lower bandgap E g2 , absorbs the low-energy photons with energy between E g1 and E g2 .In this configuration, the photon energy is used more efficiently: the voltage at which electrical charge is collected in each subcell is closer to the energy of the photons absorbed in that subcell.
In the ideal configuration, the subcells are electrically separated.This is called the 4-terminal or stacked configuration (Figure 1a).However, this configuration is to date economical irrelevant.Indeed, experimental and commercial tandem solar cells are usually of the monolithic (integrated or 2terminal) type (Figure 1b).This means that the two cells are not only optically in series, but also electrically in series.This configuration will never reach an efficiency that is higher than that of a stacked tandem cell, because all single cells cannot operate at their optimal working point at the same time (unless they have an equal maximum-power current).
Because we want to investigate the relationship between on the one hand the energy levels of the subcells, and on the other hand the light harvesting potential of the configurations, we assume full absorption in each subcell (and consequently leaving the thickness of the subcells aside).We neglect interference and optical coupling of the subcells, thus overestimating the efficiency potential.Indeed, we only want to study the relative efficiency gain by using tandem cells instead of single-junction cells for indoor applications.For our simulations, the following fundamental assumptions are made about the stacked tandem cell (Figure 1a): • Every photon with an energy hν higher than the bandgap E g1 is absorbed by the first cell and leads to a useful energy E g1 .This assumption implies that each absorbed photon eventually leads to a free electron and a free hole, with an energy difference of E g1 between them.• Every photon with an energy hν between E g1 and E g2 is absorbed by the second cell and leads to a useful energy E g2 .
• Photons with an energy hν lower than E g2 are fully transmitted.
The maximum efficiency η max is therefore given by: with N(E) the incident photon flux.Note that the denominator is the total incident photon power density of the solar spectrum and does not depend on any bandgap.In this ideal scenario, the open circuit voltage V oc of the first and second subcell will be given by E g1 /q and E g2 /q respectively (with q the electric charge).The fill factor FF of both subcells is assumed to equal unity, as well as the external quantum efficiency EQE of the first cell for wavelengths below the cut-off wavelength λ g1 (corresponding with E g1 ).The EQE of the second cell equals unity for wavelengths between cut-off wavelength λ g1 and λ g2 (corresponding with E g2 ).Because these parameters are scalable, this idealization does not interfere with our goal to quantify the efficiency gain for tandem cells.To study the potential of tandem solar cells for indoor applications, we consider the following indoor light sources: • An incandescent lamp, represented by a black body on temperature T = 2856 K.
• A cool white fluorescent lamp with a correlated color temperature of 4230 K.They make up the majority of office illumination.• Two types of high pressure discharge lamps which are commonly used in commercial and industrial environments: a sodium lamp and a metal halide lamp.
We compare our results with the AM 1.5G spectrum (the outdoor standard spectrum) as reference [8].If we want to compare the same lighting conditions, we have to scale all the light sources to an equal illumination for the human eye to obtain a correct comparison.We choose a value of 500 lux because it is recommended for general offices.For the goal of our paper, the value itself is not important, as long as it is the same for all light sources.To make a correct comparison possible, we also scale the AM 1.5 spectrum to 500 lux.The spectra can be found in Figure 2. We refer to [9,10] for more details regarding the spectra.

Results
With the spectra and formulae above, we calculate the power conversion efficiency and the electrical power output of the single-junction and tandem solar cells under different indoor illuminations.We want to stress that the ideal efficiency from these calculations is not attainable in practice and the absolute value is only interesting from an academic point of view.However, the relative value of the single-junction compared to the tandem cell is relevant, as it describes the influence of one parameter only, namely the relative efficiency gain of adding an extra subcell to the configuration.
Figure 3 shows the maximum efficiency in this ideal scenario for a stacked and monolithic tandem cell with bandgaps E g1 and E g2 under the illumination of the AM 1.5 spectrum.A maximum efficiency of 65.2 % and 63.5 % is reached for a stacked and monolithic tandem cell respectively.As mentioned already, the efficiency of a monolithic configuration will never be higher than that of a stacked configuration.In comparison with a single-junction cell with an optimal bandgap of 1.1 eV, adding a second subcell results in a relative gain of about 1/3rd in power conversion efficiency [11].For higher bandgaps, less photons are being absorbed from the solar spectrum, but the useful output energy of each absorbed photon is higher.Hence, there is an optimum for each bandgap.This maximum occurs for the stacked and monolithic tandem cell at a configuration (E g1 , E g2 ) of (1.5 eV, 0.7 eV) and (1.6 eV, 0.9 eV) respectively.

Figure 1 .
Figure 1.(a) A 4-terminal or stacked tandem solar cell: the first single cell absorbs photons with an energy hν higher than E g1 .The second cell absorbs photons with an energy between E g1 and E g2 .Photons with an energy below E g2 are not absorbed.The two subcells are electrically separated.(b) A monolithic or 2-terminal tandem solar cell: the single cells are electrically connected in series.

Figure 3 .
Figure 3.The maximum efficiency for a stacked (left) and monolithic (right) tandem solar cell with bandgaps E g1 and E g2 under illumination of the AM 1.5 spectrum (top), an incandescent lamp (middle) and a fluorescent tube (bottom).

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