Issue 
EPJ Photovolt.
Volume 2, 2011



Article Number  20301  
Number of page(s)  6  
Section  Semiconductor Thin Films  
DOI  https://doi.org/10.1051/epjpv/2011001  
Published online  01 April 2011 
https://doi.org/10.1051/epjpv/2011001
Geometrical optimization and electrical performance comparison of thinfilm tandem structures based on pmSi:H and μcSi:H using computer simulation^{*}
^{1}
Institut d’Électronique du Solide et des Systèmes (InESS) CNRS, 23 rue du Loess, BP 20 CR, 67037 Strasbourg Cedex 2, France
^{2}
Laboratoire de Génie Électrique de Paris, CNRS UMR 8507, SUPELEC, Université ParisSud, UPMC Univ Paris VI, 11 rue JoliotCurie, Plateau de Moulon, 91192 GifsurYvette Cedex, France
^{3}
Laboratoire de Physique des Interfaces et Couches Minces, École polytechnique, CNRS, 91128 Palaiseau, France
^{a}
email: foudil.dadouche@iness.cstrasbourg.fr
Received: 1 July 2010
Accepted: 10 January 2011
Published online:
1
April
2011
This article investigates the optimal efficiency of a photovoltaic system based on a silicon thin film tandem cell using polymorphous and microcrystalline silicon for the top and bottom elementary cells, respectively. Two ways of connecting the cells are studied and compared: (1) a classical structure in which the two cells are electrically and optically coupled; and (2) a new structure for which the “currentmatching” constraint is released by the electrical decoupling of the two cells. For that purpose, we used a computer simulation to perform geometrical optimization of the studied structures as well as their electrical performance evaluation. The simulation results show that the second structure is more interesting in terms of efficiency.
© EDP Sciences 2011
This is an Open Access article distributed under the terms of the Creative Commons AttributionNoncommercial License 3.0, which permits unrestricted use, distribution, and reproduction in any noncommercial medium, provided the original work is properly cited.
1 Introduction
The technological progress that has been made in the development of thin film silicon solar cells has led to a significant reduction in the cost per peak watt generated by such devices. Thin film silicon materials such as hydrogenated amorphous (aSi:H), polymorphous (pmSi:H) and microcrystalline silicon (μcSi:H) have become a serious alternative to monocrystalline silicon for the fabrication of solar cells, as the production cost can be drastically reduced through numerous mechanisms: (i) in contrast to the high temperature process (>1400 °C) used in preparing mono or polycrystalline silicon, the plasma enhanced chemical vapor deposition (PECVD) technique, which is a widely used deposition process to fabricate thin film solar cells, needs relatively low temperatures (<300 °C); (ii) the thin film semiconductor can be deposited directly on lowcost largearea substrates; (iii) high deposition rates combined with low defect density silicon thin films have been obtained using PECVD or other deposition techniques [1, 2, 3, 4] leading to good efficiency solar cells.
To further decrease the cost per watt for thin film devices, a common design strategy is to increase conversion efficiency through the use of multijunction cells. In tandem devices, two PIN cells made with materials of different bandgap energies are fabricated in series [5, 6, 7]. A low bandgap material such as microcrystalline silicon can be used as the bottom cell in conjunction with amorphous silicon (top cell) to extend the spectral range of high collection efficiency [5, 8]. Also used as the top cell in such structures is polymorphous silicon, a nanostructured material deposited by PECVD at high pressure and RF power, in a regime where silicon clusters and nanocrystals synthesized in the plasma contribute to the growth along with silicon radicals [9]. It has been reported in previous studies that pmSi:H has better electronic properties and stability than conventional aSi:H [10, 11, 12, 13]. Moreover, the pmSi:H optical gap being slightly larger than the aSi:H one, the use of pmSi:H in a tandem structure in place of aSi:H allows one the possibility to increase the opencircuit voltage of the entire device and therefore to increase the electric output of the photovoltaic modules.
We present herein a comparative numerical modeling study of two tandem pmSi:H/μcSi:H cell structures: (1) a conventional tandem cell for which the two elementary PIN cells are superimposed by successive layer deposition; and (2) an assembly of two electrically decoupled PIN cells. After having introduced the two structures in detail, including the relevant cell parameters, we report on the simulation procedure used to optimize the power delivered by each structure, and finally discuss our results.
2 Technical details
In a conventional tandem device, the two elementary cells are directly stacked by successive layer deposition, which means that they are both optically and electrically coupled [5, 6, 7]. To provide the current to the load, this structure requires only two contact electrodes connected to the top cell P layer and to the bottom cell N layer. In the following, we will call this design the “twowire structure”. Using this interconnection design, the two cells are physically series connected and thus have the same current flowing through them. This introduces an important constraint, because the thickness of each cell has to be precisely chosen in order to share the same short circuit current. Otherwise, the cell with the higher short circuit current will have to work at a shifted operating point due to the lower current of the other cell. This will lead to a degraded performance compared to the optimal, currentmatched situation.
This design requirement leads to the idea of an electrical cell decoupling in order to independently target the maximum power of each cell, the currentmatching constraint being released. In this configuration, each cell has its own electrodes connected to its own P and N layers. Thus, the two cells in such a combination are optically coupled and electrically decoupled, and we will refer to this design as a “fourwire structure”. These two tandem cell structures are presented in Figure 1.
We focus here on tandem pmSi:H/μcSi:H cells. The pmSi:H PIN cell needs a small intrinsic layer (ilayer) thickness (several hundreds of nm) to convert its useful spectrum. This property is linked to the high absorption coefficient of this material due to its directlike bandgap. On the other hand, the μcSi:H PIN cell requires a thicker ilayer (a few μms) so as to compensate its lower absorption coefficient. In the tandem configuration, the solar spectrum is more used more efficiently, as the top pmSi:H cell will absorb the energy of photons with less thermalization loss, whereas the bottom μcSi:H cell will transfer the infrared energy that would normally go unabsorbed.
Fig. 1 Twowire versus fourwire tandem structures. 
In order to quantify the power benefit one can expect from using the fourwire structure instead of the traditional twowire one, we have used numerical modelling software dedicated to studying heterojunction solar cells, “AFORSHET” (Automat FOR Simulation of HETerostructures). This software has been developed by the HahnMeitner Institut (now Helmholtz Zentrum) in Berlin [14]. Macroscopic characteristics of different layer structures and layer interfaces can be simulated in the dark or under illumination, taking into account optical reflections at any existing interfaces. A different subgap defect density spectrum can be introduced for each layer.
In the case of a twowire structure, the tunnelrecombination effect which occurs at the N(pmSi:H)/P(μcSi:H) interface and which allows the passage of current between the two subcells is not included in the simulation. Thus, it is well adapted to the simulation of independent individual solar cells (fourwire structure) since the elementary cells are decoupled. For the twowire structure simulation, we calculated the JV characteristics of each cell separately, taking into account the optical coupling. The JV characteristics of the twowire structure are then reconstructed considering that the current is the same in each subcell (fundamental characteristic of a conventional tandem cell). The maximal power can then be calculated and compared to that of the fourwire tandem structure. Note that this procedure neglects the losses that might be due in practice from a non ideal tunnelrecombination between the cells, so the solar cell performance calculated on the twowire tandem might be somewhat overestimated.
Main electrical parameters of the pmSi:H and μcSi:H intrinsic layers introduced in the simulation.
Polymorphous silicon and microcrystalline silicon are both characterized by defects in their energy bandgap. Two kinds of defects can be mainly observed: the deep defects linked to the dangling bonds and the network defects linked to the weak bonds.
The first defect category, even if it is known to be of amphoteric type [15, 16], can be modelled by two Gaussian continuous distributions of monovalent states [17]: with a peak value D_{max}, peak position E_{max} and the standard deviation σ_{0} that depend on the quality of the film (that depends itself on the deposition conditions) as well as on the doping.
The second category is represented by an extension of the valence band and the conduction band on either side of the forbidden band. Those extensions are modelled by two exponential bandtails. The description of the valence bandtail is given by: where E_{UV} is the characteristic energy width of the tail, and G_{V0} the DOS at the valence band edge. An analogous expression holds for the conduction band tail, with a characteristic energy width E_{UD}.
The material parameters for the μcSi:H and pmSi:H cells used in the numerical calculations originate from several references [18, 19, 20, 21]. The main parameters of intrinsic layers introduced in our simulation are given in Table 1.
The refractive index of each layer, from which the absorption and the reflection of the incoming photons according to their wavelength can be calculated, has been derived from spectroscopic ellipsometry measurements. It should be noted that no light scattering due to texturing was used in this study, and therefore the absolute values of currentdensity for a given layer thickness will be lower than typically observed in devices using textured substrates.
3 Simulation procedure
To optimize the two cells so that the global structure (two or fourwire structures) can produce the maximum power, it is necessary to tune the thickness of each pmSi:H and μcSi:H ilayer. The thickness of the top pmSi:H cell plays the key role, as it additionally determines the part of the incident photon flux that is transmitted to the bottom μcSi:H cell. Moreover, in the micromorph tandem aSi:H/μcSi:H cell approach, the thickness of the μcSi:H cell is on the order of several micrometers [7, 22]. However, in order to reduce production costs, one should reduce the thickness of the μcSi:H layer as much as possible. Therefore, we have decided to fix the thickness of the intrinsic part of the μcSi:H cell at a reasonable value of 1.5 μm and to sweep the width of the intrinsic pmSi:H layer. The P and N layers are mainly used to create the junctions and the internal electrical field in the Ilayers, and should be kept as thin as possible. We also therefore fixed the thickness of these very thin layers at values that are typical for PIN cells. These values are summarized in Table 2. Moreover, both junctions are sandwiched between two SnO_{2} transparent electrodes. In order to enhance the photon absorption probability in the bottom cell, the microcrystalline cell is designed with an Ag back reflector.
Layer thicknesses for pmSi:H and μcSi:H cells as used in simulation.
To define the thickness range of the pmSi:H intrinsic layer, we took into account the ageing process, which occurs during the first months of solar illumination. Exposure to solar illumination causes the creation of new dangling bonds created by breaking weak bonds, observed as the socalled lightsoaking (LS) or StaeblerWronski effect [23]. The DOS of pmSi:H after lightsoaking was modeled by increasing the magnitude of the dangling bond Gaussian distribution (D_{max}). We present in Figure 2 the pmSi:H cell efficiency as a function of the pmSi:H layer thickness for different values of D_{max} introduced in the simulation.
Fig. 2 PmSi:H cell efficiency as a function of pmSi:H intrinsic layer thickness for three values of the Gaussian distribution peak value D_{max} (expressed in cm^{3} eV^{1}): 5 × 10^{15} (■), 1 × 10^{16} (°) and 1 × 10^{17} (△). 
It can be observed that for a constant ilayer thickness, the cell efficiency deteriorates with an increase in defect density, as caused by the light soaking process, as the DOS increase shortens the charged carriers’ diffusion length. For a given DOS, the efficiency shows an optimum in ilayer thickness due to recombination growing more quickly with thickness than the number of photogenerated electronhole pairs. This optimal thickness is lowered by an increase of the DOS. In our simulation, this optimal thickness is located beyond 4 μm for a low peak DOS in the pmSi:H I layer, representative of a cell in the asdeposited state (D_{max} = 5 × 10^{15}cm^{3} eV^{1}), then decreases to 2.7 μm after intermediate degradation caused by lightsoaking (D_{max} = 1 × 10^{16}cm^{3} eV^{1}), and finally stabilizes around 0.5 μm for a fully lightsoaked cell (D_{max} = 1 × 10^{17} cm^{3} eV^{1}). We need to take into account this last data which represents the point that will guarantee us the good function of the cell. After several months of utilization, a cell with Ilayer more than 500 nm thick would work far less efficiently than one with a thinner Ilayer.
To conclude, when thinking of a long term use, the ilayer thickness of the pmSi:H cell must not exceed 500 nm. This maximal thickness value is even thinner for greater values of the DOS. In this study, our lightsoaked cell is described by a D_{max} of 1 × 10^{17}cm^{3} eV^{1}, and so the maximal ilayer thickness is chosen as 450 nm. At the opposite side of the sweep range, technological considerations limit the thinnest possible ilayer to 50 nm. Consequently, we have varied the Ilayer thickness of the pmSi:H cell from 50 nm to 450 nm with a step of 50 nm.
Regarding the former results, we have optimized the top cell intrinsic layer thickness in both two and fourwire structures following the procedure illustrated in Figure 3 for the twowire cell and in Figure 4 for the fourwire cell.
Fig. 3 Simulation steps for a twowire tandem structure. 
Fig. 4 Simulation steps for a fourwire tandem structure. 
The different steps can be summarized as follows:

1.
Application of standard AM1.5 illumination at the toppmSi:H cell.

2.
Variations of the intrinsic layer thickness from 50 nm to 450 nm with a 50 nm step.

3.
For each thickness, the output light flux of the pmSi:H cell is calculated and is used as an input flux of the μcSi:H cell. JV and PV curves are then computed for both cells.

4.
For the fourwire structure, using the PV curves, the maximum power is determined by adding the maximum power of elementary cells.

5.
For the twowire structure, the output currents have to be matched. So, we first determine the common current range in both cells. We then get for each current density J, the voltage of the global multijunction structure V_{pm − Si:H} + V_{μc − Si:H}. We hence plot the J − (V_{pm − Si:H} + V_{μc − Si:H}) and P − (V_{pm − Si:H} + V_{μc − Si:H}) curves of the twowire tandem structure. From this data, we can establish the maximum power of the structure.
4 Results and discussion
We present in this section simulation results for both elementary cells and for both two and fourwire tandem structures.
The pmSi:H and μcSi:H PIN cell simulations allow us to compute the variation in maximum device output power with polymorphous cell ilayer thickness. These variations are plotted in Figure 5 for the thickness range under consideration (50 nm to 450 nm) for the pmSi:H ilayer. Our initial assumptions are confirmed:

for a pmSi:H cell in the asdeposited (AD) state, the wider theintrinsic layer, the better the efficiency,

the LS pmSi:H cell provides its maximum power for a 300 nm thick intrinsic layer,

the μcSi:H cell maximum power is directly linked to the number of photons coming out of the top pmSi:H cell. By this simple fact, the thinner the top cell, the more efficient the bottom cell.
As described in Figures 3 and 4, we determined the maximal power of two and fourwire structures as a function of the pmSi:H ilayer thickness. These results are presented in Figure 6 in both the AD and LS state.
Fig. 5 Maximum output power of elementary cells versus pmSi:H ilayer thickness. 
Fig. 6 Maximum output power of both tandem structures as a function of pmSi:H ilayer thickness (AD and LS state shown). 
This figure reveals interesting differences between the two structures. In the case of the asdeposited top pmSi:H cell, we notice that the fourwire structure is always more efficient, regardless of top cell thickness. The maximum power delivered by the fourwire structure monotonically increases with increasing top cell thickness, as all photons absorbed in the top cell are used more efficiently than those in the bottom cell due to less thermalization loss. No offsetting effect is present due to very low defect density. The twowire structure must cope with the current matching constraint, so the twowire structure performance depicts a maximum point around 100 nm as this constraint prevents the pmSi:H cell from operating at its maximum power point. Under the condition of good pmSi:H electronic properties, we can draw a 12.6% gain by using the fourwire structure in comparison to the traditional twowire structure. This gain may be even greater in the case of a thicker top pmSi:H cell.
In reality, the pmSi:H cell thickness will be limited by the StaeblerWronski effect. This is observed for the case of a lightsoaked pmSi:H cell, where the fourwire device output power exhibits a maximum at 200 nm. Again, the absolute value of these numbers will be shifted with respect to actual values, as no lightdiffusion by textured substrates is included.
We must also underline that in the fourwire structure, the total device efficiency is more robust with respect to variations of the pmSi:H thickness. The maximum power fluctuations do not exceed 7.5% for this structure, whereas for the twowire structure the decrease is more pronounced and reaches 23%. This parametric robustness of the fourwire structure is typical of the fact that even though one cell faces electronic defects, the second one is not modified.
In the lightsoaked case, the benefit of using a fourwire structure instead of a twowire one seems to be small, about 4% for the optimum thickness. But this value may be actually much more important. First, the simulation software does not take into account the tunnelrecombination junction effect which occurs in the N(pmSi:H)/P(μcSi:H) junction and which degrades the twowire tandem structure performance. Second, all the simulations have been implemented with the standard AM1.5 solar flux whereas the incident solar spectrum is subject to extensive variations due to influences such as incidence angle, cloud cover, etc. These variations influence the power delivered by of each cell and hence make the “currentmatching” condition that much more limiting. As shown by the above simulations, the fourwire structure will be much less sensitive to such variations due to the decoupling of the elementary cells.
5 Summary and conclusions
Through numerical simulation, we have performed a comparative study of thin film pmSi:H/μcSi:H tandem cells with two different interconnection designs: a conventional, “twowire” structure where the two PIN cells are superimposed and electrically coupled, and a “fourwire” structure where the two PIN cells are optically coupled but electrically decoupled. The aim of this study was to quantify the output power benefit one can expect from using the fourwire structure instead of the traditional twowire one. This benefit was studied both before and after material degradation through light soaking.
The results reveal that the fourwire structure is more efficient in both asdeposited and lightsoaked state, although the obtained power benefit of the fourwire structure is only 4% when comparing optimized structures in the lightsoaked state. However, this benefit may be underestimated, as variations in the photon flux due to outdoor conditions were not modeled. Moreover, we note the robustness of the fourwire design to ilayer thickness variations; its peak output power fluctuations do not exceed 7.5% for the range studied, whereas the thickness effect on the twowire structure is more pronounced, and results in an output power decrease up to 23%. This may have important consequences regarding robustness to fluctuations during the cell fabrication process.
Acknowledgments
The work was carried out under the project “Association Tandem Optimisée pour le Solaire (ATOS)” supported by “Agence Nationale de la Recherche (ANR)”.
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All Tables
Main electrical parameters of the pmSi:H and μcSi:H intrinsic layers introduced in the simulation.
All Figures
Fig. 1 Twowire versus fourwire tandem structures. 

In the text 
Fig. 2 PmSi:H cell efficiency as a function of pmSi:H intrinsic layer thickness for three values of the Gaussian distribution peak value D_{max} (expressed in cm^{3} eV^{1}): 5 × 10^{15} (■), 1 × 10^{16} (°) and 1 × 10^{17} (△). 

In the text 
Fig. 3 Simulation steps for a twowire tandem structure. 

In the text 
Fig. 4 Simulation steps for a fourwire tandem structure. 

In the text 
Fig. 5 Maximum output power of elementary cells versus pmSi:H ilayer thickness. 

In the text 
Fig. 6 Maximum output power of both tandem structures as a function of pmSi:H ilayer thickness (AD and LS state shown). 

In the text 
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