- Email: [email protected]
Numerical simulations on the limits for the efficiency improvement of hybrid dye-microcrystalline silicon solar cells
Solar Energy Materials & Solar Cells 99 (2012) 345–348
Contents lists available at SciVerse ScienceDirect
Solar Energy Materials & Solar Cells journal homepage: www.elsevier.com/locate/solmat
Numerical simulations on the limits for the efficiency improvement of hybrid dye-microcrystalline silicon solar cells ¨ Sven Burdorf n, Gottfried Heinrich Bauer, Rudolf Bruggemann Institut f¨ ur Physik, Carl von Ossietzky Universit¨ at Oldenburg, D-26111 Oldenburg, Germany
a r t i c l e i n f o
abstract
Article history: Received 19 October 2010 Received in revised form 24 November 2011 Accepted 28 December 2011 Available online 14 January 2012
Composite material solar cells have been proposed and even recently processed with dye sensitizers embedded in a microcrystalline silicon thin film matrix to enhance absorption. In this contribution we present calculations to estimate the efficiency improvement of such hybrid dye-microcrystalline silicon solar cells compared to pure single junction pin microcrystalline solar cells. The simulation results for varying thicknesses of the dye-incorporated microcrystalline silicon layer demonstrate a potential efficiency improvement of almost 30% compared with a pure microcrystalline silicon cell. For the same efficiency, the thickness of the hybrid system can potentially be reduced to almost one-third of the pure microcrystalline layer. We discuss how these achievements depend on the photon energies of maximum absorption of the dye. & 2012 Elsevier B.V. All rights reserved.
Keywords: Microcrystalline silicon Organic dyes Sensitization Inorganic–organic composite
1. Introduction Photon absorption is one of the key features for any type of solar energy harvesting device. In thin film solar cells this feature is derogated by the reduced film thickness. Therefore many approaches are made to increase the absorption of thin film solar cells which result either in a higher conversion efficiency or a thinner photoactive layer being beneficial for production costs and speed and the open-circuit voltage. One approach is to improve light trapping and hence increase the path length of light inside the solar cell. For this approach angular selective filters made of photonic structures have been studied [1] or plasmonic effects are used to enhance light scattering [2]. Another approach is to directly increase the absorption coefficient in the low energy regime by the use of intermediate band solar cells [3]. Recently Mayer et al. proposed a microcrystalline silicon (mc-Si) pin-solar cell [4,5] with additional light absorbing dyes in the i-layer. Organic dyes show a high absorbance in the spectral range relevant for photovoltaic applications, however, the transport properties of charge carriers in dyes are quiet poor. Microcrystalline silicon mc-Si on the other hand has acceptable transport properties while the absorption especially in the low energy regime is poor. Thus the combination of these materials is very promising as a photoactive layer in a solar cell. This contribution aims to evaluate the potential of this solar cell design by a theoretical investigation of the achievable
n
Corresponding author. E-mail address: [email protected] (S. Burdorf).
0927-0248/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2011.12.026
efficiency improvement under optimum conditions, like perfect transfer of the dye excited state to mc-Si : H host matrix and no additionally introduced defects to the matrix. Further aspects can be found in the Simulation Details section. The working principle of hybrid dye-mc-Si : H as an absorber layer is sketched in Fig. 1 where CB and VB denote the conduction and valence band and LUMO and HOMO designate the lowest unoccupied molecular orbital and the highest occupied one. After a photon excited the dye molecule in the matrix the electron in the LUMO and the hole in the HOMO have to be transferred into the conduction and valence band of the matrix. This is an approach similar to the dye sensitized solar cell [6]. In the case presented here, hole transport occurs in the valence band of mc-Si : H silicon so there is no need for an electrolyte to regenerate the dye after the electron transfer. For an efficient and continuous process the rate constants ket for the electron transfer and kht for the hole transfer have to be much larger than any recombination rate constants of the dye. Therefore dyes with a LUMO level above the conduction band edge and a HOMO level below the valence band edge are desirable.
2. Simulation details Numerical simulations on mc-Si : H pin-structures were performed with the program AFORS-HET 2.4.1 [7]. AFORS-HET solves the coupled continuity equations for electrons and holes and the Poisson equation. Details of the parameters of the mc-Si : H can be found in Table 1. The parameters have been chosen such that the simulation results in efficiency, open-circuit voltage V OC ,
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Fig. 1. Excitation of a dye and subsequent electron and hole transfer to the conduction band (CB) and valence band (VB) with rate constants ket and kht .
Table 1 Input parameters of the baseline mc-Si : H pin structure used for the modeling of the current–voltage curves and external quantum efficiencies. Parameter
p-layer
i-layer
n-layer
Thickness (nm) Electron affinity (eV) Dielectric constant Band gap (eV) Effective DOS CB (cm 3) Effective DOS VB (cm 3) Electron mobility (cm2V 1s 1) Hole mobility (cm2V 1s 1) Fermi level EC Ef (eV)
5 3.9 11.9 1.4 1020 1020 20 5 1.1
100y2000 3.9 11.9 1.4 1020 1020 20 5 0.61
5 3.9 11.9 1.4 1020 1020 20 5 0.2
2:4 1020 120
9:4 1019 30
1:88 1020 94
Band tail states parameters VB trap density (cm 3) VB tail characteristic energy (meV) Electron capture cross section (cm2)
7 1016
7 1016
7 1016
Hole capture cross section (cm2)
7 1016
7 1016
7 1016
CB trap density (cm 3)
2:4 1020 80
6:4 1019 20
1:36 1020 68
CB tail characteristic energy (meV) Electron capture cross section (cm2)
7 1016
7 1016
7 1016
Hole capture cross section (cm2)
7 1016
7 1016
7 1016
Defect states parameters Position EC Et , acceptor (eV) Defect density (cm 3)
0.5
0.5
0.5
6:9 1019 0.21
1015 0.144
6:9 1019 0.21
3 1015
1015
3 1015
14
14
3 1014 0.6
Standard deviation (Gaussian) (eV) Electron capture cross section (cm2) Hole capture cross section (cm2) Position EC Et , donor (eV) Defect density (cm 3) Standard deviation (Gaussian) (eV) Electron capture cross section (cm2) Hole capture cross section (cm2)
3 10 0.6
6:9 1019 0.21
10 0.7 1015
3 1014
0.144 10 14
6:9 1019 0.21 10 14
3 1015
10 15
10 14
short-circuit current density JSC and fill factor FF are in fair agreement with the results in [8] where the cells were also intentionally contaminated. The optical generation profile is calculated according to Lambert–Beer’s law where we neglected any reflection occurring either on the front or back side. The artificial absorption cross section sA of four dyes are presented in Fig. 2. Each sA is represented by three Gaussians. For simplification we assume that the separation between the HOMO and the LUMO level of the dyes increases symmetrically with respect to the conduction band and valence band edge when the HOMO–LUMO gap of the dye is increased (i.e. from dye A to dye D). Therefore both charge injection processes into the semiconductor remain possible as long as the HOMO–LUMO gap is not smaller than the band gap of the i-layer. This requirement also sets a lower limit for the photon energy of maximum
Fig. 2. Absorption cross sections sA for four artificial dyes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. Absorption coefficient a of the mc-Si : H silicon matrix (black dashed line) and the hybrid mc-Si-dye layer (colors correspond to the dyes in Fig. 2).
absorption of the dye. Hence we decided not to use any dyes which have a photon energy of maximum absorption below the band gap of the mc-Si : H host matrix of 1.4 eV. For the simulation, we assume that (i) the incorporated dye in the mc-Si : H i-layer does neither change the absorption properties nor the electronic properties of the Si-matrix, (ii) every photon absorbed by a dye leads to an injected electron–hole pair in the mc-Si : H matrix and (iii) the dye molecules are homogeneously distributed in the mc-Si : H matrix. With these assumptions we can model the hybrid mc-Si : H-dye layer by exchanging the absorption coefficient aSi of mc-Si : H with a ¼ aSi þ sA c where c is the concentration of the dye molecules. Fig. 3 shows the corresponding absorption coefficients for the different dyes in the Si-matrix used for the simulation. The absorption coefficient of pure mc-Si : H (black dashed line) was obtained by optical transmission measurements with a Cary 5E spectrophotometer and subsequent analysis with the evaluation program Diplot [9]. The crystalline volume fraction rc determined
S. Burdorf et al. / Solar Energy Materials & Solar Cells 99 (2012) 345–348
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by Raman measurements was 0.553. The concentration c of the dye molecules in the Si-matrix was chosen such that the dye/ silicon ratio was 103 where we made the simplification that the size of the dye molecules is independent of their absorption cross section. Since we are only interested in the limits for the efficiency improvement we neglect the impact of the incorporated dye molecules on defect properties like an increased density of dangling bonds or band-tail states.
3. Results and discussion Each of the simulations of the current–voltage characteristics and external quantum efficiencies in this paper were done at a device temperature T¼300 K. Fig. 4 shows the current–voltage curves under AM1.5G conditions of a cell with an i-layer thickness di ¼ 1778 nm. The black dashed line corresponds to a pure mc-Si : H i-layer while the colored lines represent the current–voltage curves for the different hybrid dye doped mc-Si : H layers. The current–voltage curve for the i-layer containing dye A (red line) shows a strong increase of 4.87 mA in the short-circuit current density J SC compared with the pure mc-Si : H i-layer while there is only a minor increase in the open-circuit voltage V OC . The increase in the J SC becomes smaller for the dyes B (orange line) and C (green line) and is smallest for the dye D (blue line). The reason for the difference in the J SC for the different hybrid mc-Si : H-dye layers can be seen in Fig. 5 where the simulated external quantum efficiencies (EQE) are presented. The EQE of the cell with the mc-Si : H i-layer containing dye A (red line) shows the largest difference to the EQE of the pure mc-Si : H i-layer. With increasing HOMO-LUMO gap of the dye (dye B to D) this difference becomes smaller (orange, green and blue lines). This behavior of the EQE is directly related to the absorption coefficients introduced in Fig. 3. The EQE of the pure mc-Si : H baseline cell has only one maximum at Eph ¼ 2:25 eV which agrees with what is found in the literature [10]. Cells containing dyes show maxima that have the same energetic position as the maxima in the absorption coefficient. It should be noted that the unusual high EQE in the high energy regime is due to the fact that we omitted a TCO-layer on the front side of the cell which would absorb high energy photons. Fig. 6 summarizes the results of the current–voltage curves with the dyes A to D for different i-layer thicknesses di ranging from 100 nm to 2mm. The colored lines represent the results of
Fig. 5. External quantum efficiencies (EQE) of mc-Si pin structures (black dashed line for pure mc-Si : H and colored lines for hybrid layers with dyes) with an i-layer thickness di ¼ 1778 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Open-circuit voltage V OC (a), short-circuit current density J SC (b), fill factor (c) and efficiency (d) for different i-layer thicknesses di . Black lines and circles for pure mc-Si : H and colored lines and circles for hybrid layers with dyes A to D. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Current-voltage-curves of mc-Si pin structures (black dashed line for pure mc-Si : H and colored lines for hybrid layers with dyes) under AM1.5G conditions with an i-layer thickness di ¼ 1778 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the dyes A to D where the colors are allocated as before. The black symbols represent the mc-Si : H baseline cell. From Fig. 6a it can be seen that maximum improvement for the open-circuit voltage V OC is less than 10 mV when dye A is incorporated in the i-layer compared to the baseline cell. Since additional charge carriers generated by dyes enter only logarithmically in the open-circuit voltage this number is expected.
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However the trend is observable that the increase in the opencircuit voltage decreases from dye A to D. The short circuit current density J SC , given in Fig. 6b, of pure mc-Si improves for thicker i-layers due to more absorbed radiation. The difference in JSC between pure mc-Si : H and hybrid dyemc-Si : H layers increases with enlarging i-layer thickness because of more absorbing dye molecules in a thicker layer. When dye A is incorporated in the mc-Si : H matrix a dramatic increase in J SC of 5.07 mA/cm2 in comparison with the pure mc-Si : H baseline cell for an i-layer thickness of 2 mm is observed. This is a relative increase of nearly 29%. From dye B to D the improvement in J SC becomes smaller ending up in an absolute increase in J SC of 0.37 mA/cm2 (relative improvement 2.1%). As we can see from Fig. 6c there is almost no effect of incorporated dyes in the mc-Si matrix compared to pure mc-Si on the fill factor. The parameter mainly affecting the fill factor is the increasing i-layer thickness which is also observed experimentally [10] (please note that we omitted the symbols in Fig. 6a–c for clarity). The respective conversion efficiencies are given in Fig. 6d with a peak efficiency i-layer thickness of 1778 nm. Here, the efficiency strongly increases from 6.531% for the baseline cell to 8.474% for a hybrid i-layer with dye A which is a relative improvement of almost 30%. The horizontal black line represents the maximum efficiency of the baseline cell. The efficiency curve for dye A intersects the horizontal line at a thickness of 600 nm. For the dyes B to D the ilayer thickness necessary to obtain an efficiency equal to that of the baseline cell increases to 685 nm, 830 nm and 1120 nm respectively. The slight decrease of the efficiency for larger i-layer thicknesses larger than 1778 nm is due to the decrease in the fill factor. So far all interfaces in the simulation are flat surfaces. In a realistic solar cell rough interfaces are used which increase the spectral response in the low energy regime due to optical scattering and hence the overall efficiency by enlarging the path length [11]. The maximum path length enlargement is given by the Yablonovitch limit and states that it cannot be enlarged by more than a factor 4n2 where n is the refractive index. Therefore the maximum path length enlargement in mc-Si : H with a refraction index of n ¼ 3:5, . . . ,3:6 is about a factor of 50. The amount of the efficiency improvement for the composite system compared to the pure mc-Si : H depends on the path length enlargement and the difference between the absorption coefficients between the two materials. Using Lambert–Beer’s law with the absorption coefficients shown in Fig. 3 we find that for moderate path length enlargement factors (factor two for an ilayer thickness of 2 mm) the beneficial effect of the dye pigments to the absorption increases compared to the mc-Si : H layer since there is a larger probability that scattered radiation is absorbed by the dye. Only at values for the path length enhancement close to the Yablonovitch limit the additional absorption of the dye is masked by the enhanced absorption of mc-Si : H.
4. Conclusions Numerical simulations on hybrid dye-mc-Si : H pin-structures to exploit their potential were performed. Our results indicate that this cell design by Mayer et al. shows great potential of improving the efficiency or reducing the thickness of the photoactive layer and therefore this approach might be beneficial for production speed and cost even in the case of rough surfaces and increased optical scattering. However, our knowledge about the impact of incorporated dyes on the structural and electronic properties of the mc-Si : H host matrix is still very limited. Future work should therefore take into account defects in the matrix associated with incorporated dyes.
Acknowledgments The authors like to thank A. Decker from TU Darmstadt for
mc-Si thin film layer samples preparation and Raman measurements. Financial support by the BMBF contract 035F0339-B is gratefully acknowledged.
References ¨ [1] M. Peters, J. Goldschmidt, T. Kirchhartz, B. Blasi, The photonic light trap: improved light trapping in solar cells by angularly selective filters, Solar Energy Materials & Solar Cells 93 (2009) 1721–1727. [2] H.A. Atwater, A. Polman, Plasmonics for improved photovoltaic devices, Nature Materials 9 (2010) 205–213. [3] A. Luque, A. Martı´, Increasing the effiency of ideal solar cells by photon induced transitions at intermediate levels, Physical Review Letters 78 (1997) 5014–5017. ¨ [4] T. Mayer, U. Weiler, C. Kelting, D. Schlettwein, S. Makarov, D. Wohrle, O. Abdallah, M. Kunst, W. Jaegermann, Silicon-organic pigment material hybrids for photovoltaic application, Solar Energy Materials & Solar Cells 91 (2007) 1873–1886. [5] T. Mayer, U. Weiler, E. Mankel, W. Jaegermann, C. Kelting, D. Schlettwein, ¨ N. Baziakina, D. Wohrle, Organic–inorganic hybrid composites for photovoltaics: organic guest molecules embedded in mc-Si and ZnSe host matrices, Renewable Energy 33 (2008) 262–266. ¨ [6] B. O‘Regan, M. Gratzel, A low-cost, high effiency solar cell based on dye sensitized colloidal TiO2 films, Nature 353 (1991) 737–740. [7] R. Stangl, C. Leendertz, J. Haschke, Numerical simulation of solar cells and solar cell characterization methods: the open-source on demand program AFORS-HET, in: R.D. Rugescu (Ed.), Solar Energy, InTech, Rijeka, 2010, p. 432. [8] T. Kilper, W. Beyer, G. Brauer, T. Bronger, R. Carius, M. van den Donker, ¨ D. Hrunski, A. Lambertz, T. Merdzhanova, A. Muck, B. Rech, W. Reetz, R. Schmitz, U. Zastrow, A. Gordijn, Oxygen and nitrogen impurities in microcrystalline silicon deposited under optimized conditions: influence on material properties and solar cell performance, Journal of Applied Physics 105 (2009) 074509. [9] see /http://www.diplot.deS for details. [10] O. Vetterl, A. Lambertz, A. Dasgupta, F. Finger, B. Rech, O. Kluth, H. Wagner, Thickness dependence of microcrystalline silicon solar cell properties, Solar Energy Materials & Solar Cells 66 (2001) 345–351. ˇ [11] A. Poruba, A. Fejfar, Z. Remeˇs, J. Springer, M. Vanˇecˇek, J. Kocˇka, J. Meier, P. Torres, A. Shah, Optical absorption and light scattering in microcrystalline silicon thin films and solar cells, Journal of Applied Physics 88 (2000) 148.
Contents lists available at SciVerse ScienceDirect
Solar Energy Materials & Solar Cells journal homepage: www.elsevier.com/locate/solmat
Numerical simulations on the limits for the efficiency improvement of hybrid dye-microcrystalline silicon solar cells ¨ Sven Burdorf n, Gottfried Heinrich Bauer, Rudolf Bruggemann Institut f¨ ur Physik, Carl von Ossietzky Universit¨ at Oldenburg, D-26111 Oldenburg, Germany
a r t i c l e i n f o
abstract
Article history: Received 19 October 2010 Received in revised form 24 November 2011 Accepted 28 December 2011 Available online 14 January 2012
Composite material solar cells have been proposed and even recently processed with dye sensitizers embedded in a microcrystalline silicon thin film matrix to enhance absorption. In this contribution we present calculations to estimate the efficiency improvement of such hybrid dye-microcrystalline silicon solar cells compared to pure single junction pin microcrystalline solar cells. The simulation results for varying thicknesses of the dye-incorporated microcrystalline silicon layer demonstrate a potential efficiency improvement of almost 30% compared with a pure microcrystalline silicon cell. For the same efficiency, the thickness of the hybrid system can potentially be reduced to almost one-third of the pure microcrystalline layer. We discuss how these achievements depend on the photon energies of maximum absorption of the dye. & 2012 Elsevier B.V. All rights reserved.
Keywords: Microcrystalline silicon Organic dyes Sensitization Inorganic–organic composite
1. Introduction Photon absorption is one of the key features for any type of solar energy harvesting device. In thin film solar cells this feature is derogated by the reduced film thickness. Therefore many approaches are made to increase the absorption of thin film solar cells which result either in a higher conversion efficiency or a thinner photoactive layer being beneficial for production costs and speed and the open-circuit voltage. One approach is to improve light trapping and hence increase the path length of light inside the solar cell. For this approach angular selective filters made of photonic structures have been studied [1] or plasmonic effects are used to enhance light scattering [2]. Another approach is to directly increase the absorption coefficient in the low energy regime by the use of intermediate band solar cells [3]. Recently Mayer et al. proposed a microcrystalline silicon (mc-Si) pin-solar cell [4,5] with additional light absorbing dyes in the i-layer. Organic dyes show a high absorbance in the spectral range relevant for photovoltaic applications, however, the transport properties of charge carriers in dyes are quiet poor. Microcrystalline silicon mc-Si on the other hand has acceptable transport properties while the absorption especially in the low energy regime is poor. Thus the combination of these materials is very promising as a photoactive layer in a solar cell. This contribution aims to evaluate the potential of this solar cell design by a theoretical investigation of the achievable
n
Corresponding author. E-mail address: [email protected] (S. Burdorf).
0927-0248/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2011.12.026
efficiency improvement under optimum conditions, like perfect transfer of the dye excited state to mc-Si : H host matrix and no additionally introduced defects to the matrix. Further aspects can be found in the Simulation Details section. The working principle of hybrid dye-mc-Si : H as an absorber layer is sketched in Fig. 1 where CB and VB denote the conduction and valence band and LUMO and HOMO designate the lowest unoccupied molecular orbital and the highest occupied one. After a photon excited the dye molecule in the matrix the electron in the LUMO and the hole in the HOMO have to be transferred into the conduction and valence band of the matrix. This is an approach similar to the dye sensitized solar cell [6]. In the case presented here, hole transport occurs in the valence band of mc-Si : H silicon so there is no need for an electrolyte to regenerate the dye after the electron transfer. For an efficient and continuous process the rate constants ket for the electron transfer and kht for the hole transfer have to be much larger than any recombination rate constants of the dye. Therefore dyes with a LUMO level above the conduction band edge and a HOMO level below the valence band edge are desirable.
2. Simulation details Numerical simulations on mc-Si : H pin-structures were performed with the program AFORS-HET 2.4.1 [7]. AFORS-HET solves the coupled continuity equations for electrons and holes and the Poisson equation. Details of the parameters of the mc-Si : H can be found in Table 1. The parameters have been chosen such that the simulation results in efficiency, open-circuit voltage V OC ,
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Fig. 1. Excitation of a dye and subsequent electron and hole transfer to the conduction band (CB) and valence band (VB) with rate constants ket and kht .
Table 1 Input parameters of the baseline mc-Si : H pin structure used for the modeling of the current–voltage curves and external quantum efficiencies. Parameter
p-layer
i-layer
n-layer
Thickness (nm) Electron affinity (eV) Dielectric constant Band gap (eV) Effective DOS CB (cm 3) Effective DOS VB (cm 3) Electron mobility (cm2V 1s 1) Hole mobility (cm2V 1s 1) Fermi level EC Ef (eV)
5 3.9 11.9 1.4 1020 1020 20 5 1.1
100y2000 3.9 11.9 1.4 1020 1020 20 5 0.61
5 3.9 11.9 1.4 1020 1020 20 5 0.2
2:4 1020 120
9:4 1019 30
1:88 1020 94
Band tail states parameters VB trap density (cm 3) VB tail characteristic energy (meV) Electron capture cross section (cm2)
7 1016
7 1016
7 1016
Hole capture cross section (cm2)
7 1016
7 1016
7 1016
CB trap density (cm 3)
2:4 1020 80
6:4 1019 20
1:36 1020 68
CB tail characteristic energy (meV) Electron capture cross section (cm2)
7 1016
7 1016
7 1016
Hole capture cross section (cm2)
7 1016
7 1016
7 1016
Defect states parameters Position EC Et , acceptor (eV) Defect density (cm 3)
0.5
0.5
0.5
6:9 1019 0.21
1015 0.144
6:9 1019 0.21
3 1015
1015
3 1015
14
14
3 1014 0.6
Standard deviation (Gaussian) (eV) Electron capture cross section (cm2) Hole capture cross section (cm2) Position EC Et , donor (eV) Defect density (cm 3) Standard deviation (Gaussian) (eV) Electron capture cross section (cm2) Hole capture cross section (cm2)
3 10 0.6
6:9 1019 0.21
10 0.7 1015
3 1014
0.144 10 14
6:9 1019 0.21 10 14
3 1015
10 15
10 14
short-circuit current density JSC and fill factor FF are in fair agreement with the results in [8] where the cells were also intentionally contaminated. The optical generation profile is calculated according to Lambert–Beer’s law where we neglected any reflection occurring either on the front or back side. The artificial absorption cross section sA of four dyes are presented in Fig. 2. Each sA is represented by three Gaussians. For simplification we assume that the separation between the HOMO and the LUMO level of the dyes increases symmetrically with respect to the conduction band and valence band edge when the HOMO–LUMO gap of the dye is increased (i.e. from dye A to dye D). Therefore both charge injection processes into the semiconductor remain possible as long as the HOMO–LUMO gap is not smaller than the band gap of the i-layer. This requirement also sets a lower limit for the photon energy of maximum
Fig. 2. Absorption cross sections sA for four artificial dyes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. Absorption coefficient a of the mc-Si : H silicon matrix (black dashed line) and the hybrid mc-Si-dye layer (colors correspond to the dyes in Fig. 2).
absorption of the dye. Hence we decided not to use any dyes which have a photon energy of maximum absorption below the band gap of the mc-Si : H host matrix of 1.4 eV. For the simulation, we assume that (i) the incorporated dye in the mc-Si : H i-layer does neither change the absorption properties nor the electronic properties of the Si-matrix, (ii) every photon absorbed by a dye leads to an injected electron–hole pair in the mc-Si : H matrix and (iii) the dye molecules are homogeneously distributed in the mc-Si : H matrix. With these assumptions we can model the hybrid mc-Si : H-dye layer by exchanging the absorption coefficient aSi of mc-Si : H with a ¼ aSi þ sA c where c is the concentration of the dye molecules. Fig. 3 shows the corresponding absorption coefficients for the different dyes in the Si-matrix used for the simulation. The absorption coefficient of pure mc-Si : H (black dashed line) was obtained by optical transmission measurements with a Cary 5E spectrophotometer and subsequent analysis with the evaluation program Diplot [9]. The crystalline volume fraction rc determined
S. Burdorf et al. / Solar Energy Materials & Solar Cells 99 (2012) 345–348
347
by Raman measurements was 0.553. The concentration c of the dye molecules in the Si-matrix was chosen such that the dye/ silicon ratio was 103 where we made the simplification that the size of the dye molecules is independent of their absorption cross section. Since we are only interested in the limits for the efficiency improvement we neglect the impact of the incorporated dye molecules on defect properties like an increased density of dangling bonds or band-tail states.
3. Results and discussion Each of the simulations of the current–voltage characteristics and external quantum efficiencies in this paper were done at a device temperature T¼300 K. Fig. 4 shows the current–voltage curves under AM1.5G conditions of a cell with an i-layer thickness di ¼ 1778 nm. The black dashed line corresponds to a pure mc-Si : H i-layer while the colored lines represent the current–voltage curves for the different hybrid dye doped mc-Si : H layers. The current–voltage curve for the i-layer containing dye A (red line) shows a strong increase of 4.87 mA in the short-circuit current density J SC compared with the pure mc-Si : H i-layer while there is only a minor increase in the open-circuit voltage V OC . The increase in the J SC becomes smaller for the dyes B (orange line) and C (green line) and is smallest for the dye D (blue line). The reason for the difference in the J SC for the different hybrid mc-Si : H-dye layers can be seen in Fig. 5 where the simulated external quantum efficiencies (EQE) are presented. The EQE of the cell with the mc-Si : H i-layer containing dye A (red line) shows the largest difference to the EQE of the pure mc-Si : H i-layer. With increasing HOMO-LUMO gap of the dye (dye B to D) this difference becomes smaller (orange, green and blue lines). This behavior of the EQE is directly related to the absorption coefficients introduced in Fig. 3. The EQE of the pure mc-Si : H baseline cell has only one maximum at Eph ¼ 2:25 eV which agrees with what is found in the literature [10]. Cells containing dyes show maxima that have the same energetic position as the maxima in the absorption coefficient. It should be noted that the unusual high EQE in the high energy regime is due to the fact that we omitted a TCO-layer on the front side of the cell which would absorb high energy photons. Fig. 6 summarizes the results of the current–voltage curves with the dyes A to D for different i-layer thicknesses di ranging from 100 nm to 2mm. The colored lines represent the results of
Fig. 5. External quantum efficiencies (EQE) of mc-Si pin structures (black dashed line for pure mc-Si : H and colored lines for hybrid layers with dyes) with an i-layer thickness di ¼ 1778 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Open-circuit voltage V OC (a), short-circuit current density J SC (b), fill factor (c) and efficiency (d) for different i-layer thicknesses di . Black lines and circles for pure mc-Si : H and colored lines and circles for hybrid layers with dyes A to D. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Current-voltage-curves of mc-Si pin structures (black dashed line for pure mc-Si : H and colored lines for hybrid layers with dyes) under AM1.5G conditions with an i-layer thickness di ¼ 1778 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the dyes A to D where the colors are allocated as before. The black symbols represent the mc-Si : H baseline cell. From Fig. 6a it can be seen that maximum improvement for the open-circuit voltage V OC is less than 10 mV when dye A is incorporated in the i-layer compared to the baseline cell. Since additional charge carriers generated by dyes enter only logarithmically in the open-circuit voltage this number is expected.
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However the trend is observable that the increase in the opencircuit voltage decreases from dye A to D. The short circuit current density J SC , given in Fig. 6b, of pure mc-Si improves for thicker i-layers due to more absorbed radiation. The difference in JSC between pure mc-Si : H and hybrid dyemc-Si : H layers increases with enlarging i-layer thickness because of more absorbing dye molecules in a thicker layer. When dye A is incorporated in the mc-Si : H matrix a dramatic increase in J SC of 5.07 mA/cm2 in comparison with the pure mc-Si : H baseline cell for an i-layer thickness of 2 mm is observed. This is a relative increase of nearly 29%. From dye B to D the improvement in J SC becomes smaller ending up in an absolute increase in J SC of 0.37 mA/cm2 (relative improvement 2.1%). As we can see from Fig. 6c there is almost no effect of incorporated dyes in the mc-Si matrix compared to pure mc-Si on the fill factor. The parameter mainly affecting the fill factor is the increasing i-layer thickness which is also observed experimentally [10] (please note that we omitted the symbols in Fig. 6a–c for clarity). The respective conversion efficiencies are given in Fig. 6d with a peak efficiency i-layer thickness of 1778 nm. Here, the efficiency strongly increases from 6.531% for the baseline cell to 8.474% for a hybrid i-layer with dye A which is a relative improvement of almost 30%. The horizontal black line represents the maximum efficiency of the baseline cell. The efficiency curve for dye A intersects the horizontal line at a thickness of 600 nm. For the dyes B to D the ilayer thickness necessary to obtain an efficiency equal to that of the baseline cell increases to 685 nm, 830 nm and 1120 nm respectively. The slight decrease of the efficiency for larger i-layer thicknesses larger than 1778 nm is due to the decrease in the fill factor. So far all interfaces in the simulation are flat surfaces. In a realistic solar cell rough interfaces are used which increase the spectral response in the low energy regime due to optical scattering and hence the overall efficiency by enlarging the path length [11]. The maximum path length enlargement is given by the Yablonovitch limit and states that it cannot be enlarged by more than a factor 4n2 where n is the refractive index. Therefore the maximum path length enlargement in mc-Si : H with a refraction index of n ¼ 3:5, . . . ,3:6 is about a factor of 50. The amount of the efficiency improvement for the composite system compared to the pure mc-Si : H depends on the path length enlargement and the difference between the absorption coefficients between the two materials. Using Lambert–Beer’s law with the absorption coefficients shown in Fig. 3 we find that for moderate path length enlargement factors (factor two for an ilayer thickness of 2 mm) the beneficial effect of the dye pigments to the absorption increases compared to the mc-Si : H layer since there is a larger probability that scattered radiation is absorbed by the dye. Only at values for the path length enhancement close to the Yablonovitch limit the additional absorption of the dye is masked by the enhanced absorption of mc-Si : H.
4. Conclusions Numerical simulations on hybrid dye-mc-Si : H pin-structures to exploit their potential were performed. Our results indicate that this cell design by Mayer et al. shows great potential of improving the efficiency or reducing the thickness of the photoactive layer and therefore this approach might be beneficial for production speed and cost even in the case of rough surfaces and increased optical scattering. However, our knowledge about the impact of incorporated dyes on the structural and electronic properties of the mc-Si : H host matrix is still very limited. Future work should therefore take into account defects in the matrix associated with incorporated dyes.
Acknowledgments The authors like to thank A. Decker from TU Darmstadt for
mc-Si thin film layer samples preparation and Raman measurements. Financial support by the BMBF contract 035F0339-B is gratefully acknowledged.
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