- Email: [email protected]
Optical properties of a-SiGe:H solar cells on textured substrates
Journal of Non-Crystalline Solids 227–230 Ž1998. 1262–1266
Optical properties of a-SiGe:H solar cells on textured substrates J.H. van den Berg ) , M. Zeman, J.W. Metselaar Delft UniÕersity of Technology - DIMES, P.O. Box 5053, 2600 GB Delft, The Netherlands
Abstract The optical numerical simulator for multi-layer structures with textured interfaces, GENPRO2, was improved and applied to determine the scattering parameters of textured interfaces of a-SiGe:H solar cells. A sensitivity study was carried out in which the relative effects of the various scattering parameters of the interfaces on the quantum efficiency ŽQE. of the solar cells were investigated. The optical properties of the separate layers were determined and extrapolated to energies at which they could not be measured accurately. A series of four a-SiGe:H solar cells with various thicknesses of the intrinsic layer was grown and their QE properties were measured. The contribution of the scattering of the various interfaces was determined by matching the measured and the simulated QE properties. The haze values of the transparent conductive oxiderp-doped layer ŽTCOrp. interface found by our simulations agree well with reports in the literature. In contrast to other model results, we show that besides the scattering at the TCOrp- and n-doped layerrAg interface, the scattering at the prinsulator and the insulatorrn interface also has to be taken into account in calculating the QE characteristics. q 1998 Elsevier Science B.V. All rights reserved. Keywords: a-SiGe:H; Optical properties; Modeling
1. Introduction To increase the absorption of incident light in hydrogenated amorphous silicon Ža-Si:H., based solar cells light trapping techniques have been implemented w1,2x. These include the introduction of textured substrates and the use of layers such as back reflectors. These developments have indicated a need for optical models that can calculate the optical behavior of the solar cells accurately. These models require knowledge of the scattering properties of the rough interfaces in the solar cells. However, these properties are not fully known and it is the purpose of this paper to gain more insight into this matter.
)
Corresponding author. Fax: q31-15 262 2163; e-mail: [email protected].
As far as we know, only a few optical models for multi-layer structures with textured interfaces have been developed w3–7x. A precise analytical solution of a device with textured interfaces requires that Maxwell’s equations are solved in three dimensions, because the morphology of the texture is three-dimensional. In practice, solving these equations is too complicated. Two-dimensional Ž2D. numerical approaches, however, have been reported w5,6x. For 2D approaches, the morphology of the texture, which is usually random, is described by a simple periodic function. In most optical simulations of a-Si:H solar cells on textured substrates, only the texture between the transparent conductive oxide ŽTCO. and the pdoped layer, and between the n-doped layer and the back contact are taken into account w3,7,8x. Because the other interfaces in the solar cells are also textured, this approach may not be correct.
0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 Ž 9 8 . 0 0 2 8 0 - 4
J.H. Õan den Berg et al.r Journal of Non-Crystalline Solids 227–230 (1998) 1262–1266
With an improved version of our optical numerical simulator, GENPRO2, we investigated the effects of textured interfaces on the quantum efficiency ŽQE. of a TCOrp–i–nrAg Ži ' insulator. a-SiGe:H solar cell. We simulated the QE properties of four a-SiGe:H solar cells with different i-layer thicknesses. By comparing the simulated data to the measured QE properties of these cells, we demonstrate that we can obtain the scattering properties of the textured interfaces.
2. Description of the optical model parameters The optical numerical simulator, GENPRO2, is described in Ref. w4x. It differs from other semi-empirical models in that it can incorporate with multiple layers with textured interfaces. For each layer and interface, a range of input variables can be assigned. An improvement of this model was made to simulate the QE of multi-layer structures more accurately. 2.1. The input parameters of the optical model GENPRO2 Ž1. A description of the multi-layer structure that includes the thickness of the layers and the texture of the interface. Ž2. A definition of the incident light that can either be monochromatic with a defined photon flux or multi-chromatic with a defined wavelength spectrum. The angle distribution of the incident light is defined by the following angle dependent functions: uniform, linear, cos, cos 2 , or otherwise Žvia an external file.. Ž3. Optical files of the separate layers, containing the wavelength dependent refractive indices and extinction coefficients. Ž4. Interface scattering parameters that include: Ži. the angle distribution of the scattered light as function of the incident light angle f Ž u in .; Žii. the haze, C, that is the percentage of the total scattered light; and Žiii. the angle distribution of the scattered outgoing light f Ž uout .. Because the light can arrive at a rough interface from both media 1 and 2, four processes are taken into account: reflection in medium 1 ŽR 11 ., reflection in medium 2 ŽR 22 ., transmission
1263
from medium 1 to 2 ŽT12 . and transmission from medium 2 to 1 ŽT21 .. In all four processes, a part of the light is scattered and therefore a rough interface is described by four sets of the above mentioned scattering parameters. The output of GENPRO2 is an absorption profile as a function of depth. By calculating the absorption profile for a range of wavelengths and integrating this over the intrinsic layer, the optical QE properties are determined. Because the model is developed to simulate structures with ‘textured’ interfaces, the optical interference is of minor importance. Therefore, and to keep the model simple, an incoherent simulation is carried out. This simulation can, however, lead to small deviations in the QE properties for optical systems with little scattering. Before running the actual simulations, we carried out a sensitivity study of the model scattering parameters to obtain their relative contribution to the QE. We investigated this contribution in two parts of the light spectrum, i.e., below and above 600 nm. The sensitivity of each parameter was investigated by variation around a reference value and determining its effect on the QE. The reference values are zero for the haze parameters Žflat interface., a cos 2 function for the angle distribution of incident light and a uniform distribution function for the angle distribution of outgoing light. Since only one parameter was changed at a time, no cross correlation of the parameters was taken into account. The contributing parameters are summarized in Table 1.
Table 1 The relative contribution of the scattering parameters of GENPRO2 on the QE of an a-SiGe:H solar cell Interface
Parameter
QE Ž l -600 nm.
QE Ž l )600 nm.
TCOrp TCOrp prI prI prI irn irn nrAg
C T12 f T12 Ž u out. C T12 C T21 f T12 Ž u out. C T12 , C T21 f T21Ž u out. C R1 1
yy qq q 0 yyy 0 0 0
qqq y qqq qqq yyy qqq yyy qqq
The symbols have the following meaning: qqq, qq, q denote relative increase in the response Žqqq largest increase., and yyy, yy, y denote relative decrease in the response Žyyy largest decrease.. No contribution is indicated by a ‘0’.
1264
J.H. Õan den Berg et al.r Journal of Non-Crystalline Solids 227–230 (1998) 1262–1266
3. Experiments and simulations 3.1. Determination of the optical properties of the separate layers GENPRO2 needs the optical properties of each individual layer as input. Each optical input file contains the refractive index and the extinction coefficient as function of wavelength of a layer. For photon energies above the optical band gap, the reflection and transmission ŽRT. were measured, whereas for photon energies below the band gap dual beam photoconductivity ŽDBP. was employed. The measured data were smoothed and extrapolated to smaller energies to obtain the required optical files. The extinction coefficient and refractive index as function of wavelength for different layers that were used in our simulations are shown in Figs. 1 and 2, respectively. 3.2. Determination of the scattering parameters 3.2.1. Measurement of the quantum efficiency Four different a-SiGe:H solar cells, with a p Ž14 nm a-SiC:H.ri Ža-SiGe:H.rn Ž30 nm a-Si:H.rAg structure were deposited on a substrate ŽAsahi Utype.. The Tauc optical gap of the intrinsic a-SiGe:H layer was 1.5 eV. The thickness of the intrinsic layer was varied between 50 and 200 nm. The cells were made as simple as possible to carry out accurate simulations. In practice, this requirement means that
Fig. 1. Measured data Žpoints. and fitted curves Žsolid lines. of the extinction coefficient of the separate layers.
Fig. 2. Measured data Žpoints. and fitted curves Žsolid lines. of the refractive index of the separate layers.
no graded layers and no buffer layers have been implemented, so the cells were not optimized for maximum efficiency. The absolute external QE was measured for wavelengths in the range between 380 and 950 nm. QE is defined as: QE ex ,abs Ž l . s
Ý
QE op Ž l . hg Ž l . QE el Ž l . ,
Ž 1.
layers
where QE op is the optical QE and is a measure for the probability of a photon being absorbed while hg is the generation QE that represents the number of electron-hole pairs generated by one absorbed photon and is assumed to be unity. QE el is the electrical QE and reflects the probability of a photogenerated carrier being collected. By applying a negative bias, we assume that QE el is unity and that a measurement of the QE represents the optical QE. 3.2.2. Simulations of the quantum efficiency The simulations were carried out using the obtained optical files of the layers as input and varying the haze for TCOrp interface Ž C T12 ., pri interface Ž C T12 , C T21 ., irn interface Ž C T12 , C T21 ., nrAg interface Ž C R11 ., and varying the angle-distribution of pri and irn interfaces Ž f T12 Ž uout ., f T21Ž uout ... The other haze parameters were set to zero, following the results of the sensitivity study. The haze parameters in this study were assumed to be wavelength independent. The angle distribution of the incident light was set to a cos 2 function for both reflection and
J.H. Õan den Berg et al.r Journal of Non-Crystalline Solids 227–230 (1998) 1262–1266
1265
f T21Ž uout ., of the pri and the irn interfaces were found to be uniform. Fig. 4 shows the difference between the QE of the 150 nm solar cell simulated with the determined parameters and the reference.
4. Discussion
Fig. 3. Measured data Žpoints. and fitted curves Žsolid lines. of the optical QE of four a-SiGe:H solar cells with various thickness of the intrinsic layer.
transmission and for the angle distribution of the outgoing light a Lambertian distribution was taken. 3.2.3. Results of the measurements and simulations Since the four a-SiGe:H solar cells only differed in thickness of the intrinsic layer, we assumed that the interface scattering parameters are the same in each cell. With this assumption, we obtained a good matching between the measurement and simulated QE, as shown in Fig. 3, with the following values: 15% haze for the TCOrp interface, 5% haze for the pri and irn interfaces, and 0% haze for the nrAg interface. The angle distributions, f T12 Ž uout . and
Comparing the measured and simulated QE of the a-SiGe:H solar cells with textured interfaces shows that all textured interfaces of the solar cell should be considered. The resulting haze value of 15% for the TCOrp interface is in agreement with values in literature w9–11x. For the first time, the haze value of the pri and irn interfaces have been determined and we found a value of 5%. The fitted QE curves of the 100 nm and 150 nm solar cells are better than for 50 nm and 200 nm cells, although not perfect. Due to the magnitude of haze, a part of the light in the solar cells is specular and, thus, gives rise to interference. These interference patterns can be clearly observed in Fig. 3 in the measured QE properties. We used GENPRO1 for multi-layer structures with flat interfaces for simulations of the QE of the four cells to examine the interference patterns. The position of resulting interference maxima agreed well with those measured. In addition, the assumption that the scattering parameters of all interfaces are the same for the four test structures is not entirely correct. Because a thicker intrinsic layer makes the morphology smoother, the scattering parameters of the irn and nrAg interface can differ slightly with varying i-layer thickness. Finally, to obtain a good fit, it is necessary to match the measurements and simulations by inverse modeling w12x. In this case, also the wavelength dependence of the haze should be taken into account.
5. Conclusions
Fig. 4. The influence of the interface scattering on the simulation results of QE for a-SiGe:H solar cell with 150 nm thick intrinsic layer.
We found that besides the scattering at the TCOrp interface, also the scattering at the other interfaces should be taken into account to obtain a good fit between the measured and simulated QE characteristics. Haze values found by our modeling are in good agreement with results of other groups. These
1266
J.H. Õan den Berg et al.r Journal of Non-Crystalline Solids 227–230 (1998) 1262–1266
results offer a good estimation of more detailed determination of haze profiles, in which account for wavelength and i-layer thickness dependence can be made.
w3x w4x w5x
Acknowledgements w6x
The authors wish to thank Rene´ van Swaaij for valuable discussions and acknowledge the financial support from the Netherlands Agency for Energy and the Environment ŽNOVEM. and the Netherlands Organisation for Scientific Research ŽNWO. for the research of a-Si:H based solar cells.
w7x
w8x w9x w10x
References w1x D. Redfield, Appl. Phys. Lett. 25 Ž11. Ž1974. 647. w2x G. Tao, B.S. Girwar, G.E.N. Landweer, M. Zeman, J.W. Metselaar, in: E.A. Schiff et al. ŽEds.., Amorphous
w11x
w12x
Silicon Technology, MRS Symp. Proc., Vol. 297, 1993, pp. 854. F. Leblanc, J. Perrin, J. Schmitt, J. Appl. Physiol. 75 Ž2. Ž1994. 1074. G. Tao, M. Zeman, J.W. Metselaar, Sol. Energy Mater. Sol. Cells 34 Ž1994. 359–366. T. Sawada, N. Terada, T. Takahama, H. Tarui, M. Tanaka, S. Tsuda, S. Nakano, Sol. Energy Mater. Sol. Cells 34 Ž1994. 367. J. Furlan, S. Amon, P. Popovic, F. Smole, Proc. of WCPC-1, Hawaii, 1994, pp. 658. H. Stiebig, A. Kreidel, K. Winz, N. Schultz, C. Beneking, Th. Eickohoff, H. Wagner, Proc. of WCPC-1, Hawaii, 1994, pp. 603. M. Zeman, J.A. Willemen, L.L.A. Vosteen, G. Tao, J.W. Metselaar, Sol. Energy Mater. Sol. Cells 46 Ž1997. 81. M. Mizuhashi, Y. Gotoh, K. Adachi, Jpn. J. Appl. Phys. 27 Ž1988. 2053. J. Wallinga, J. Daey Ouwens, R.E.I. Schropp, W.F. van der Weg, Mater. Sci. Forum 173–174 Ž1995. 331. Y. Hishikawa, E. Maruyama, S. Yata, M. Tanaka, S. Kiyama, S. Tsuda, Technical Digest of the Int. PVSEC-9, Miyazaki, Japan, 1996, pp. 639. M. Zeman, J.A. Willemen, S. Solntsev, J.W. Metselaar, Sol. Energy Mater. Sol. Cells 34 Ž1994. 557.
Optical properties of a-SiGe:H solar cells on textured substrates J.H. van den Berg ) , M. Zeman, J.W. Metselaar Delft UniÕersity of Technology - DIMES, P.O. Box 5053, 2600 GB Delft, The Netherlands
Abstract The optical numerical simulator for multi-layer structures with textured interfaces, GENPRO2, was improved and applied to determine the scattering parameters of textured interfaces of a-SiGe:H solar cells. A sensitivity study was carried out in which the relative effects of the various scattering parameters of the interfaces on the quantum efficiency ŽQE. of the solar cells were investigated. The optical properties of the separate layers were determined and extrapolated to energies at which they could not be measured accurately. A series of four a-SiGe:H solar cells with various thicknesses of the intrinsic layer was grown and their QE properties were measured. The contribution of the scattering of the various interfaces was determined by matching the measured and the simulated QE properties. The haze values of the transparent conductive oxiderp-doped layer ŽTCOrp. interface found by our simulations agree well with reports in the literature. In contrast to other model results, we show that besides the scattering at the TCOrp- and n-doped layerrAg interface, the scattering at the prinsulator and the insulatorrn interface also has to be taken into account in calculating the QE characteristics. q 1998 Elsevier Science B.V. All rights reserved. Keywords: a-SiGe:H; Optical properties; Modeling
1. Introduction To increase the absorption of incident light in hydrogenated amorphous silicon Ža-Si:H., based solar cells light trapping techniques have been implemented w1,2x. These include the introduction of textured substrates and the use of layers such as back reflectors. These developments have indicated a need for optical models that can calculate the optical behavior of the solar cells accurately. These models require knowledge of the scattering properties of the rough interfaces in the solar cells. However, these properties are not fully known and it is the purpose of this paper to gain more insight into this matter.
)
Corresponding author. Fax: q31-15 262 2163; e-mail: [email protected].
As far as we know, only a few optical models for multi-layer structures with textured interfaces have been developed w3–7x. A precise analytical solution of a device with textured interfaces requires that Maxwell’s equations are solved in three dimensions, because the morphology of the texture is three-dimensional. In practice, solving these equations is too complicated. Two-dimensional Ž2D. numerical approaches, however, have been reported w5,6x. For 2D approaches, the morphology of the texture, which is usually random, is described by a simple periodic function. In most optical simulations of a-Si:H solar cells on textured substrates, only the texture between the transparent conductive oxide ŽTCO. and the pdoped layer, and between the n-doped layer and the back contact are taken into account w3,7,8x. Because the other interfaces in the solar cells are also textured, this approach may not be correct.
0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 Ž 9 8 . 0 0 2 8 0 - 4
J.H. Õan den Berg et al.r Journal of Non-Crystalline Solids 227–230 (1998) 1262–1266
With an improved version of our optical numerical simulator, GENPRO2, we investigated the effects of textured interfaces on the quantum efficiency ŽQE. of a TCOrp–i–nrAg Ži ' insulator. a-SiGe:H solar cell. We simulated the QE properties of four a-SiGe:H solar cells with different i-layer thicknesses. By comparing the simulated data to the measured QE properties of these cells, we demonstrate that we can obtain the scattering properties of the textured interfaces.
2. Description of the optical model parameters The optical numerical simulator, GENPRO2, is described in Ref. w4x. It differs from other semi-empirical models in that it can incorporate with multiple layers with textured interfaces. For each layer and interface, a range of input variables can be assigned. An improvement of this model was made to simulate the QE of multi-layer structures more accurately. 2.1. The input parameters of the optical model GENPRO2 Ž1. A description of the multi-layer structure that includes the thickness of the layers and the texture of the interface. Ž2. A definition of the incident light that can either be monochromatic with a defined photon flux or multi-chromatic with a defined wavelength spectrum. The angle distribution of the incident light is defined by the following angle dependent functions: uniform, linear, cos, cos 2 , or otherwise Žvia an external file.. Ž3. Optical files of the separate layers, containing the wavelength dependent refractive indices and extinction coefficients. Ž4. Interface scattering parameters that include: Ži. the angle distribution of the scattered light as function of the incident light angle f Ž u in .; Žii. the haze, C, that is the percentage of the total scattered light; and Žiii. the angle distribution of the scattered outgoing light f Ž uout .. Because the light can arrive at a rough interface from both media 1 and 2, four processes are taken into account: reflection in medium 1 ŽR 11 ., reflection in medium 2 ŽR 22 ., transmission
1263
from medium 1 to 2 ŽT12 . and transmission from medium 2 to 1 ŽT21 .. In all four processes, a part of the light is scattered and therefore a rough interface is described by four sets of the above mentioned scattering parameters. The output of GENPRO2 is an absorption profile as a function of depth. By calculating the absorption profile for a range of wavelengths and integrating this over the intrinsic layer, the optical QE properties are determined. Because the model is developed to simulate structures with ‘textured’ interfaces, the optical interference is of minor importance. Therefore, and to keep the model simple, an incoherent simulation is carried out. This simulation can, however, lead to small deviations in the QE properties for optical systems with little scattering. Before running the actual simulations, we carried out a sensitivity study of the model scattering parameters to obtain their relative contribution to the QE. We investigated this contribution in two parts of the light spectrum, i.e., below and above 600 nm. The sensitivity of each parameter was investigated by variation around a reference value and determining its effect on the QE. The reference values are zero for the haze parameters Žflat interface., a cos 2 function for the angle distribution of incident light and a uniform distribution function for the angle distribution of outgoing light. Since only one parameter was changed at a time, no cross correlation of the parameters was taken into account. The contributing parameters are summarized in Table 1.
Table 1 The relative contribution of the scattering parameters of GENPRO2 on the QE of an a-SiGe:H solar cell Interface
Parameter
QE Ž l -600 nm.
QE Ž l )600 nm.
TCOrp TCOrp prI prI prI irn irn nrAg
C T12 f T12 Ž u out. C T12 C T21 f T12 Ž u out. C T12 , C T21 f T21Ž u out. C R1 1
yy qq q 0 yyy 0 0 0
qqq y qqq qqq yyy qqq yyy qqq
The symbols have the following meaning: qqq, qq, q denote relative increase in the response Žqqq largest increase., and yyy, yy, y denote relative decrease in the response Žyyy largest decrease.. No contribution is indicated by a ‘0’.
1264
J.H. Õan den Berg et al.r Journal of Non-Crystalline Solids 227–230 (1998) 1262–1266
3. Experiments and simulations 3.1. Determination of the optical properties of the separate layers GENPRO2 needs the optical properties of each individual layer as input. Each optical input file contains the refractive index and the extinction coefficient as function of wavelength of a layer. For photon energies above the optical band gap, the reflection and transmission ŽRT. were measured, whereas for photon energies below the band gap dual beam photoconductivity ŽDBP. was employed. The measured data were smoothed and extrapolated to smaller energies to obtain the required optical files. The extinction coefficient and refractive index as function of wavelength for different layers that were used in our simulations are shown in Figs. 1 and 2, respectively. 3.2. Determination of the scattering parameters 3.2.1. Measurement of the quantum efficiency Four different a-SiGe:H solar cells, with a p Ž14 nm a-SiC:H.ri Ža-SiGe:H.rn Ž30 nm a-Si:H.rAg structure were deposited on a substrate ŽAsahi Utype.. The Tauc optical gap of the intrinsic a-SiGe:H layer was 1.5 eV. The thickness of the intrinsic layer was varied between 50 and 200 nm. The cells were made as simple as possible to carry out accurate simulations. In practice, this requirement means that
Fig. 1. Measured data Žpoints. and fitted curves Žsolid lines. of the extinction coefficient of the separate layers.
Fig. 2. Measured data Žpoints. and fitted curves Žsolid lines. of the refractive index of the separate layers.
no graded layers and no buffer layers have been implemented, so the cells were not optimized for maximum efficiency. The absolute external QE was measured for wavelengths in the range between 380 and 950 nm. QE is defined as: QE ex ,abs Ž l . s
Ý
QE op Ž l . hg Ž l . QE el Ž l . ,
Ž 1.
layers
where QE op is the optical QE and is a measure for the probability of a photon being absorbed while hg is the generation QE that represents the number of electron-hole pairs generated by one absorbed photon and is assumed to be unity. QE el is the electrical QE and reflects the probability of a photogenerated carrier being collected. By applying a negative bias, we assume that QE el is unity and that a measurement of the QE represents the optical QE. 3.2.2. Simulations of the quantum efficiency The simulations were carried out using the obtained optical files of the layers as input and varying the haze for TCOrp interface Ž C T12 ., pri interface Ž C T12 , C T21 ., irn interface Ž C T12 , C T21 ., nrAg interface Ž C R11 ., and varying the angle-distribution of pri and irn interfaces Ž f T12 Ž uout ., f T21Ž uout ... The other haze parameters were set to zero, following the results of the sensitivity study. The haze parameters in this study were assumed to be wavelength independent. The angle distribution of the incident light was set to a cos 2 function for both reflection and
J.H. Õan den Berg et al.r Journal of Non-Crystalline Solids 227–230 (1998) 1262–1266
1265
f T21Ž uout ., of the pri and the irn interfaces were found to be uniform. Fig. 4 shows the difference between the QE of the 150 nm solar cell simulated with the determined parameters and the reference.
4. Discussion
Fig. 3. Measured data Žpoints. and fitted curves Žsolid lines. of the optical QE of four a-SiGe:H solar cells with various thickness of the intrinsic layer.
transmission and for the angle distribution of the outgoing light a Lambertian distribution was taken. 3.2.3. Results of the measurements and simulations Since the four a-SiGe:H solar cells only differed in thickness of the intrinsic layer, we assumed that the interface scattering parameters are the same in each cell. With this assumption, we obtained a good matching between the measurement and simulated QE, as shown in Fig. 3, with the following values: 15% haze for the TCOrp interface, 5% haze for the pri and irn interfaces, and 0% haze for the nrAg interface. The angle distributions, f T12 Ž uout . and
Comparing the measured and simulated QE of the a-SiGe:H solar cells with textured interfaces shows that all textured interfaces of the solar cell should be considered. The resulting haze value of 15% for the TCOrp interface is in agreement with values in literature w9–11x. For the first time, the haze value of the pri and irn interfaces have been determined and we found a value of 5%. The fitted QE curves of the 100 nm and 150 nm solar cells are better than for 50 nm and 200 nm cells, although not perfect. Due to the magnitude of haze, a part of the light in the solar cells is specular and, thus, gives rise to interference. These interference patterns can be clearly observed in Fig. 3 in the measured QE properties. We used GENPRO1 for multi-layer structures with flat interfaces for simulations of the QE of the four cells to examine the interference patterns. The position of resulting interference maxima agreed well with those measured. In addition, the assumption that the scattering parameters of all interfaces are the same for the four test structures is not entirely correct. Because a thicker intrinsic layer makes the morphology smoother, the scattering parameters of the irn and nrAg interface can differ slightly with varying i-layer thickness. Finally, to obtain a good fit, it is necessary to match the measurements and simulations by inverse modeling w12x. In this case, also the wavelength dependence of the haze should be taken into account.
5. Conclusions
Fig. 4. The influence of the interface scattering on the simulation results of QE for a-SiGe:H solar cell with 150 nm thick intrinsic layer.
We found that besides the scattering at the TCOrp interface, also the scattering at the other interfaces should be taken into account to obtain a good fit between the measured and simulated QE characteristics. Haze values found by our modeling are in good agreement with results of other groups. These
1266
J.H. Õan den Berg et al.r Journal of Non-Crystalline Solids 227–230 (1998) 1262–1266
results offer a good estimation of more detailed determination of haze profiles, in which account for wavelength and i-layer thickness dependence can be made.
w3x w4x w5x
Acknowledgements w6x
The authors wish to thank Rene´ van Swaaij for valuable discussions and acknowledge the financial support from the Netherlands Agency for Energy and the Environment ŽNOVEM. and the Netherlands Organisation for Scientific Research ŽNWO. for the research of a-Si:H based solar cells.
w7x
w8x w9x w10x
References w1x D. Redfield, Appl. Phys. Lett. 25 Ž11. Ž1974. 647. w2x G. Tao, B.S. Girwar, G.E.N. Landweer, M. Zeman, J.W. Metselaar, in: E.A. Schiff et al. ŽEds.., Amorphous
w11x
w12x
Silicon Technology, MRS Symp. Proc., Vol. 297, 1993, pp. 854. F. Leblanc, J. Perrin, J. Schmitt, J. Appl. Physiol. 75 Ž2. Ž1994. 1074. G. Tao, M. Zeman, J.W. Metselaar, Sol. Energy Mater. Sol. Cells 34 Ž1994. 359–366. T. Sawada, N. Terada, T. Takahama, H. Tarui, M. Tanaka, S. Tsuda, S. Nakano, Sol. Energy Mater. Sol. Cells 34 Ž1994. 367. J. Furlan, S. Amon, P. Popovic, F. Smole, Proc. of WCPC-1, Hawaii, 1994, pp. 658. H. Stiebig, A. Kreidel, K. Winz, N. Schultz, C. Beneking, Th. Eickohoff, H. Wagner, Proc. of WCPC-1, Hawaii, 1994, pp. 603. M. Zeman, J.A. Willemen, L.L.A. Vosteen, G. Tao, J.W. Metselaar, Sol. Energy Mater. Sol. Cells 46 Ž1997. 81. M. Mizuhashi, Y. Gotoh, K. Adachi, Jpn. J. Appl. Phys. 27 Ž1988. 2053. J. Wallinga, J. Daey Ouwens, R.E.I. Schropp, W.F. van der Weg, Mater. Sci. Forum 173–174 Ž1995. 331. Y. Hishikawa, E. Maruyama, S. Yata, M. Tanaka, S. Kiyama, S. Tsuda, Technical Digest of the Int. PVSEC-9, Miyazaki, Japan, 1996, pp. 639. M. Zeman, J.A. Willemen, S. Solntsev, J.W. Metselaar, Sol. Energy Mater. Sol. Cells 34 Ž1994. 557.