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Point contact openings in surface passivated macroporous silicon layers
Solar Energy Materials & Solar Cells 105 (2012) 113–118
Contents lists available at SciVerse ScienceDirect
Solar Energy Materials & Solar Cells journal homepage: www.elsevier.com/locate/solmat
Point contact openings in surface passivated macroporous silicon layers Marco Ernst a,n, Urs Zywietz b, Rolf Brendel a,c a b c
Institute for Solar Energy Research Hamelin (ISFH), Am Ohrberg 1, D-31860 Emmerthal, Germany Laser Zentrum Hannover e.V. (LZH), Hollerithallee 8, D-30419 Hannover, Germany Department Solar Energy, Institute of Solid-State Physics, Leibniz Universit¨ at Hannover, Appelstr. 2, D-30167 Hannover, Germany
a r t i c l e i n f o
abstract
Article history: Received 9 December 2011 Accepted 24 May 2012 Available online 23 June 2012
In this paper we demonstrate the preparation of point contact openings in surface passivated macroporous silicon layers. In our experiments we control the etching parameters to vary the percentage of these non-passivated local openings from 0% to 1.6%. We investigate the impact of these local openings in the passivating layer on the effective carrier lifetime. These local openings reduce the measured effective carrier lifetime with increasing percentage of the non-passivated areas. We measure effective carrier lifetimes up to 10 ms on 29 mm-thick fully passivated macroporous silicon samples. We develop and apply a 3-dimensional numerical model to calculate carrier lifetimes as a function of pore morphology, surface recombination, percentage of non-passivated area, and bulk lifetime. The model agrees with the experimental measurements. We find a surface recombination velocity of þ 1:6 þ 1500 Þ cm s 1 for the passivated surfaces and Snp ¼ð22001400 Þ cm s 1 for the non-passivated ðSpass ¼ 22:81:4 surface. & 2012 Elsevier B.V. All rights reserved.
Keywords: Porous Si Macroporous Si Carrier transport Carrier lifetime Modeling Numerical modeling
1. Introduction The typical thickness of monocrystalline silicon solar cells is currently around 200 mm with an additional kerf loss of 150–200 mm. Since the silicon wafer makes around one-third of the module costs [1], it is highly desirable to reduce the wafer thickness and the kerf loss while maintaining the high efficiency potential of monocrystalline silicon [2]. Currently, several approaches in fabricating thin monocrystalline silicon solar cells are under investigation. One promising approach is the layer transfer process of epitaxially-grown thin crystalline silicon films [3,4]. Recently, high efficiencies over 19% were reported for a layer thickness of 43 mm using this technique [5]. Nevertheless, the non-availability of low-cost high throughput epitaxial reactors is still a barrier for an industrial application of this process. Henley et al. demonstrated a thin-film process that involves proton implantation and lift-off at a depth of a few tens of micrometers that yields (111)-oriented layers. However, this surface orientation does not show anisotropic etching and can therefore not be structured with conventional processes for light trapping [6]. Another approach applies macropores that are thermally reorganized at high temperatures. These macropores are fabricated by deep-UV lithography and reactive
n
Corresponding author. Tel.: þ49 5151 999 644; fax: þ 49 5151 999 400. E-mail address: [email protected] (M. Ernst).
0927-0248/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.solmat.2012.05.033
ion etching. Solar cells with efficiencies of up to 4.1% have been reported applying this technique [7]. The macroporous silicon process (MacPSi) [8], is a separation technique for detaching thin monocrystalline layers with thicknesses of around 20–30 mm from CZ silicon wafers. In this process, small cylindrical holes are etched into the surface of a silicon substrate by means of electrochemical etching. These holes are broadened in a depth of about 20–30 mm – the thickness of the later absorber layer – to form a highly porous separation layer. We investigate macroporous silicon as an absorber material for thin monocrystalline solar cells. Light-generated carriers in thin macroporous silicon absorbers recombine in the bulk or, more likely at the large surface of the pores. Understanding the measured effective carrier lifetime is important for process optimization and for designing a device. The surface recombination velocity of passivated silicon surfaces by thermally grown oxide layers depends on the crystallographic orientation [13]. Since the macroporous surface shows various surface orientations, the SRV cannot be determined using planar reference samples [11]. Instead an average SRV needs to be determined experimentally. In a recent paper we measured effective carrier lifetimes of passivated macroporous silicon layers and derived an analytical model to describe effective carrier lifetimes as a function of pore morphology, bulk recombination, and surface recombination [9]. Therein we investigated the impact of the layer thickness on the effective carrier lifetime of passivated macroporous silicon samples experimentally and applied our analytical model to determine an
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M. Ernst et al. / Solar Energy Materials & Solar Cells 105 (2012) 113–118
average surface recombination velocity (SRV) S¼75 cm s 1 on passivated macroporous silicon samples by fitting the model to the measurements. This surface recombination velocity was higher than the surface recombination velocity S¼24 cm s 1 that we measured on non-porous reference samples passivated in the same process. This discrepancy could not solely be explained by the various surface orientations. Instead, we explained the discrepancy in the surface recombination velocity with the existence of local openings in the passivating layer that we observed in scanning electron micrographs. However, such openings were not included in our previous model [9]. In this contribution we therefore develop a three-dimensional numerical model that accounts for the non-passivated openings. We verify the numerical model experimentally by preparing macroporous silicon samples with defined openings in the passivation layer.
2. Sample preparation
Fig. 2. Etching current density profile to form an approximately 30 mm thick macroporous silicon layer with a highly porous separation layer. We use three different current densities between 18 (short dashed line) and 20 mA cm 2 (solid line) to form the separation layer with varied porosity.
We use (100)-oriented, n-type float zone crystalline Si wafers that have a resistivity of (7.570.1) O cm. The thickness of the wafer is (674710) mm. The wafer surface is structured with a hexagonal array of inverted pyramids as shown in Fig. 1. The pyramids are defined by photolithography. The distance of the pyramids is 8.3 mm and the edge length is 4 mm as measured by means of scanning electron microscope (SEM) analysis (S-4800 from Hitachi). A phosphorous diffusion at the rear side with a sheet resistance of 40 O/sq. improves the contact during electrochemical etching in 3 wt % hydrofluoric acid at 20 1C. Photogenerated holes are required for dissolving n-type Si in HF-containing electrolytes. Thus we use rear side illumination [10]. The illumination source is an array of LEDs which emit light at a wavelength of 880 nm. The etched area is circular with an area of 1 cm2. Fig. 2 shows the set values of the etching current density. By controlling the illumination intensity a current density of 6 mA cm 2 is generated and the pores start growing at the tips of the inverted pyramids with an etching rate of 0.68 mm min 1. The pore diameter is a function of the current density, therefore the pores are broadened in a depth of about 30 mm by increasing the illumination intensity. The current increases linearly from 6 mA cm 2 to values of 18–20 mA cm 2 within 6 min. At this level, the current is maintained for 6 min to form a highly porous separation layer. The porosity of the separation layer controls the width of the weak bridges between the substrate and the separation layer.
Fig. 3. Cross sectional SEM-images of prepared samples with separation layer current density of (a) 20 mA/cm2 and (b) 18 mA/cm2. The width of the weak bridges is approximately 800 nm in case (b).
Fig. 1. SEM-image showing an oblique view onto a silicon surface with inverted pyramids defined by photolithography. The distance of the pyramids tips is 8.3 mm.
Fig. 3a shows the 20 mA cm 2 case. The porosity of the separation layer is 100%, i.e. no weak bridges remain between the substrate and the macroporous layer. The layer is only attached to the substrate at the border of the etched area. Fig. 3b shows a cross-sectional SEMimage of the 18 mA cm 2 case. Here the width of the weak bridges is approximately 800 nm. We find 18 mA cm 2 to be the lower limit to remain the detachability of the macroporous layer. We prepare a set of three samples for each separation layer current density 18, 19, and 20 mA cm 2. Finally, dry thermal oxidization at 900 1C creates a 30 nm thick passivating SiO2-layer. The passivated macroporous silicon samples are subsequently detached by mechanical force and non-passivated areas remain at the broken bridges.
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3. Experimental results 3.1. Geometrical analysis We determine the percentage c of the non-passivated areas after detaching the macroporous silicon layer from the substrate by means of SEM image analysis. The local openings in the oxide layer are observable in the SEM images presented in Fig. 4. In case of a final etching current density of 20 mA cm 2 (Fig. 4a) the porosity of the separation layer is 100% and thus no nonpassivated areas remain. The brightness and contrast of the SEM image are adjusted in an image editing software (Corel PhotoPaint X4) to enhance the contrast between the passivated and non-passivated areas. Passivated and non-passivated areas appear as white and black areas respectively. Since pores and nonpassivated areas both appear black, we color non-passivated areas within the image editing software as shown in Fig. 5. The fraction of these colored pixels results in the percentage c of the non-passivated areas. Furthermore, we determine the geometrical parameters of the macroporous layer from cross-sectional SEM images as specified in Table 1.
Fig. 5. Top view SEM-image after image processing and colorizing the nonpassivated areas in green. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Fraction of the non-passivated areas and geometrical parameters of the macroporous layers. Parameter
Symbol
Value
Percentage of the non-passivated areas for 20 mA/cm2 Percentage of the non-passivated areas for 19 mA/cm2 Percentage of the non-passivated areas for 18 mA/cm2 Thickness of the macroporous layer Pore radius Pore distance
c1
0%
c2
(0.757 0.20)%
c3
(1.607 0.20)%
W rp d0
(297 1) mm (2.47 0.1) mm (8.37 0.1) mm
Fig. 6. Measured effective carrier lifetimes teff of passivated and detached macroporous silicon layers (dots) and numerical simulations (lines) as a function of the percentage c of non-passivated areas. The solid line A is the numerical simulation for the SRV given in the figure. The dashed lines B and C show numerical simulations for the upper and lower boundaries of Spass and Snp.
3.2. Effective carrier lifetime
Fig. 4. Top view SEM-images of surface passivated macroporous layers showing the surface facing the substrate prior to detachment. The etching current density for the separation layer is (a) 20 mA/cm2, (b) 19 mA/cm2 and (c) 18 mA/cm2. The non-passivated areas are visible in the magnifications.
We measure minority carrier lifetimes of detached passivated macroporous silicon layers using the transient photo-conductance decay (WT-2000 system from Semilab) technique. The samples are illuminated from the side that was facing to the substrate prior to detachment. The optical absorption length of the short pulse laser is approximately 30 mm in crystalline silicon and thus comparable to the layer thickness. Fig. 6 shows the measured effective carrier lifetimes (dots) for various percentages of non-passivated areas. The mean value of the effective lifetimes is calculated from a set of three samples for each percentage of the non-passivated areas. Note that our
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experimental points cover the experimentally feasible range due to limits in sample preparation. We assume a relative error in lifetime measurement of 5%. The highest effective lifetime measured is teff ¼(10.1 70.5) ms for a fully passivated sample.
recombination velocity is Spass for the surface passivated areas as shown in Fig. 8(a) of the macroporous layer, thus ! ! n Dp r p ¼ Spass p:
ð2Þ
! Here n is a unit vector perpendicular to the respective surface. The surface recombination velocity for the non-passivated areas as marked in red in Fig. 8(b) is Snp, thus
4. Numerical modeling We set up and apply a numerical finite element model in COMSOL Multiphysics [12] that accounts for the geometrical properties of macroporous silicon to determine the average SRV at the passivated and non-passivated areas. In the following sections we apply the numerical model to describe our measurements and simulate the effect of geometrical and electrical parameters on the effective carrier lifetime. 4.1. Geometry Fig. 7 schematically shows the hexagonal pattern of the macroporous structure with a pore distance d0. For our numerical model we assume cylindrical pores with radius rp and smooth surfaces. One unit cell is extruded from the triangular basis with a thickness W. The increased pore radius of the separation layer is approximated by subtracting three spheres at the top of the unit volume. The centers of the spheres lie on the pores axis. The breaking point of the weak bridge is marked in red in Fig. 7(d). Increasing the spheres radius leads to thinner bridges. This variation in the spheres radius corresponds to an experimental variation of the separation layer current density.
! ! n Dp r p ¼ Snp p:
ð3Þ
For symmetry reasons the perpendicular component of the ! derivate r p vanishes for the boundaries shown in Fig. 8(c), thus ! ! n Dp r p ¼ 0:
ð4Þ
The average excess carrier density pav is calculated by integrating the local excess carrier densities over the unit volume: Z 1 ! 3 pav ¼ pð x Þd x: ð5Þ V V
4.2. Equations and boundary conditions The inhomogeneous steady-state diffusion equation for the minority carriers is given by !
!
r ðDp r pÞ ¼ G
p
tp,bulk
:
ð1Þ
Here Dp is the diffusion coefficient of the minority carriers, p the excess carrier density, and tp,bulk the minority carrier bulk lifetime. We assume the generation rate G to be spatially homogeneous, since the optical absorption length of the short pulse laser used in our measurements is comparable to the layer thickness. In Fig. 8 the surfaces exhibiting identical boundary conditions are marked in identical colors schematically. The average surface
Fig. 8. Boundary conditions for the unit cell highlighted in red: (a) Passivated surfaces with an SRV Spass. (b) Non-passivated surface with SRV Snp. (c) Symmetric boundary conditions. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 7. (a) Schematic of the hexagonal array with pore distance d0 and pore radius rp. The orange triangular defines the unit cell used in the numerical simulations. (b) Extruded unit volume with thickness W. (c) The separation layer is approximated by subtracting three spheres from the extruded unit volume. The spheres center lies in the pores axis. (d) The area highlighted in red corresponds to the non-passivated areas of the passivated and detached macroporous silicon samples. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
M. Ernst et al. / Solar Energy Materials & Solar Cells 105 (2012) 113–118
We calculate the effective minority carrier lifetimes under steady state conditions by dividing the average excess carrier density and the average carrier generation rate G that we assumed to be spatially homogeneous:
tef f ðpav Þ ¼
pav : G
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and C show the 5% uncertainty in L of the numerical simulations for Spass and Snp.
5. Conclusions ð6Þ
4.3. Experimental verification With the above model we calculate the effective carrier lifetimes as a function of the percentage of the non-passivated areas. The geometric parameters of the macroporous layers are those listed in Table 1. We use a bulk lifetime of tp,bulk ¼3 ms typical for lowly doped n-type Si substrates and the diffusion coefficient Dp ¼ 12 cm s 1. The model is fitted to the measured carrier lifetimes by varying the surface recombination velocities Spass of the passivated areas and Snp of the non-passivated areas. We calculate the mean average percentage error L between the calculated curve and the measurements: 3 1X ti,sim ti,exp : L¼ ð7Þ 3i¼1 ti,exp Fig. 9 shows this error as a function of an Spass and Snp in a contour plot. At the minimum of L (dot A) we find an average þ 1:6 surface recombination velocity Spass ¼ð22:81:4 Þ cm s 1 for the þ 1500 passivated surfaces and Snp ¼ð22001400 Þ cm s 1 for the nonpassivated surface within an experimental error of L o5%. The resulting uncertainty of Spass is approximately 7%. This high accuracy is due to the strong dependence of the effective carrier lifetime on the surface recombination velocity that originates from the large passivated surface area. The uncertainty of Snp is approximately 70%. This large relative error results from the fact, that the non-passivated area fraction is small with respect to the total area. The dots B and C lie inside the uncertainty range of Spass and Snp, respectively. Fig. 6 shows the measured effective carrier lifetimes (dots) and the numerical simulations (lines) as a function of the percentage of non-passivated areas. The numerical simulations agree with the experimental data within the uncertainty range of the experimental data. Line A is the numerical simulation with Spass and Snp for the minimum of L (dot A in Fig. 9). The dashed lines B
Fig. 9. Contour plot of the mean average percentage error L evaluated between the fit and experimental data for various surface recombination velocities. Within þ 1:6 a deviation o 5% we find Spass ¼ ð22:81:4 Þ cm s 1 for the passivated surfaces and þ 1500 Snp ¼ð22001400 Þ cm s 1 for the non-passivated surface.
In this paper we have demonstrated the preparation of point contact openings in surface passivated macroporous silicon layers. The percentage of these non-passivated local openings was experimentally varied in a range from 0% to 1.6% by controlling the etching parameters. The highest lifetime measured was (10.170.5) ms for a fully oxide passivated 29 mm thick macroporous silicon layer. A three-dimensional finite element numerical model has been developed to determine the surface recombination velocities of the macroporous surfaces and the local openings. The model agrees with the measurements within the measurement accuracy. We find þ 1:6 an average surface recombination velocity Spass ¼ð22:81:4 Þ cm s 1 for the passivated surfaces of macroporous silicon layers and a þ 1500 surface recombination velocity Snp ¼ ð22001400 Þ cm s 1 for the non-passivated areas. Thus the postulated reason for the discrepancy between the average surface recombination velocity of our analytical model and reference measurements [9] is verified and explained with the non-passivated areas. The surface recombination velocity Snp determined for the nonpassivated areas is surprisingly low. However, for low doping densities of 6 1014 cm–3 as in our case, M¨ackel and Cuevas [14] found effective surface recombination velocities from 1 103 cm s 1 to 3 104 cm s 1 for non-passivated surfaces depending on storage time after HF dip. This measurement is consistent with our result.
Acknowledgments This work is supported by the Federal Ministry for Environment, Nature Conservation and Nuclear Safety under the contract FKZ 0325147. References [1] P. Fath, S. Keller, P. Winter, W. Jooss, W. Herbst, Status and perspective of crystalline silicon solar cell production, in: 34th IEEE Photovoltaic Specialists Conference, IEEE, 2009, pp. 2471–2476. [2] T. Tiedje, E. Yablonovitch, G.D. Cody, B.G. Brooks, Limiting efficiency of silicon solar cells, IEEE Transactions on Electron Devices 31 (5) (1984) 711–716. [3] H. Tayanaka, T. Matsushita, Separation of thin epitaxial Si film on porous Si for solar cells, in: Proceedings of the 6th Sony Research Forum, Sony, 1996, p. 556 (in Japanese). [4] R. Brendel, A novel process for ultrathin monocrystalline silicon solar cells on glass, in: Proceedings of the 14th European Photovoltaic Solar Energy Conference, Information Press, Eynsham, UK, 1997 1354. [5] J. Petermann, D. Zielke, J. Schmidt, F. Haase, E. Garralaga Rojas, R. Brendel, 19% efficient and 43 mm-thick crystalline Si solar cell from layer transfer using porous silicon, Progress in Photovoltaics: Research and Applications 1 (2012) 1–5. [6] F. Henley, A. Brailove, A. Lamm, T. Heerwagen, E. Sauar, M. Nese, R. Steeman, B. Hammel, Kerf-free silicon wafering equipment configuration using beaminduced cleave technology, in: Proceedings of the 23rd European Photovoltaic Solar Energy Conference, Information Press, Eynsham, UK, 2008, p. 2017. [7] V. Depauw, Y. Qiu, K. van Nieuwenhuysen, I. Gordon, J. Poortmans, Epitaxyfree monocrystalline silicon thin film: first steps beyond proof-of-concept solar cells, Progress in Photovoltaics: Research and Applications 7 (2011) 844–850. [8] R. Brendel, M. Ernst, Macroporous Si as an absorber for thin-film solar cells, Physica Status Solidi (RRL) 4 (1–2) (2010) 40–42. [9] M. Ernst, R. Brendel, Modeling effective carrier lifetimes of passivated macroporous silicon layers, Solar Energy Materials and Solar Cells 95 (4) (2011) 1197–1202. ¨ Formation mechanism and properties of electrochemi[10] V. Lehmann, H. Foll, cally etched trenches in n-type silicon, Journal of the Electrochemical Society 137 (2) (1990) 653–659. [11] P. Hurley, B. O’Sullivan, F. Cubaynes, P. Stolk, Examination of the Si(111)–SiO2, Si(110)–SiO2, and Si(100)–SiO2 interfacial properties following rapid thermal annealing, Journal of the Electrochemical Society 149 (2002) G194–G197. [12] www.comsol.com (valid on October 26, 2011).
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[13] F. Schuurmans, A. Schonecker, J. Eikelboom, W. Sinke, Crystal-orientation dependence of surface recombination velocity for silicon nitride passivated silicon wafers, in: 25th IEEE Photovoltaic Specialists Conference IEEE, 1996, pp. 485–488.
¨ [14] H. Mackel, A. Cuevas, Determination of the surface recombination velocity of unpassivated silicon from spectral photoconductance measurements, in: Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion, Osaka, Japan, 2003, pp. 71–74.
Contents lists available at SciVerse ScienceDirect
Solar Energy Materials & Solar Cells journal homepage: www.elsevier.com/locate/solmat
Point contact openings in surface passivated macroporous silicon layers Marco Ernst a,n, Urs Zywietz b, Rolf Brendel a,c a b c
Institute for Solar Energy Research Hamelin (ISFH), Am Ohrberg 1, D-31860 Emmerthal, Germany Laser Zentrum Hannover e.V. (LZH), Hollerithallee 8, D-30419 Hannover, Germany Department Solar Energy, Institute of Solid-State Physics, Leibniz Universit¨ at Hannover, Appelstr. 2, D-30167 Hannover, Germany
a r t i c l e i n f o
abstract
Article history: Received 9 December 2011 Accepted 24 May 2012 Available online 23 June 2012
In this paper we demonstrate the preparation of point contact openings in surface passivated macroporous silicon layers. In our experiments we control the etching parameters to vary the percentage of these non-passivated local openings from 0% to 1.6%. We investigate the impact of these local openings in the passivating layer on the effective carrier lifetime. These local openings reduce the measured effective carrier lifetime with increasing percentage of the non-passivated areas. We measure effective carrier lifetimes up to 10 ms on 29 mm-thick fully passivated macroporous silicon samples. We develop and apply a 3-dimensional numerical model to calculate carrier lifetimes as a function of pore morphology, surface recombination, percentage of non-passivated area, and bulk lifetime. The model agrees with the experimental measurements. We find a surface recombination velocity of þ 1:6 þ 1500 Þ cm s 1 for the passivated surfaces and Snp ¼ð22001400 Þ cm s 1 for the non-passivated ðSpass ¼ 22:81:4 surface. & 2012 Elsevier B.V. All rights reserved.
Keywords: Porous Si Macroporous Si Carrier transport Carrier lifetime Modeling Numerical modeling
1. Introduction The typical thickness of monocrystalline silicon solar cells is currently around 200 mm with an additional kerf loss of 150–200 mm. Since the silicon wafer makes around one-third of the module costs [1], it is highly desirable to reduce the wafer thickness and the kerf loss while maintaining the high efficiency potential of monocrystalline silicon [2]. Currently, several approaches in fabricating thin monocrystalline silicon solar cells are under investigation. One promising approach is the layer transfer process of epitaxially-grown thin crystalline silicon films [3,4]. Recently, high efficiencies over 19% were reported for a layer thickness of 43 mm using this technique [5]. Nevertheless, the non-availability of low-cost high throughput epitaxial reactors is still a barrier for an industrial application of this process. Henley et al. demonstrated a thin-film process that involves proton implantation and lift-off at a depth of a few tens of micrometers that yields (111)-oriented layers. However, this surface orientation does not show anisotropic etching and can therefore not be structured with conventional processes for light trapping [6]. Another approach applies macropores that are thermally reorganized at high temperatures. These macropores are fabricated by deep-UV lithography and reactive
n
Corresponding author. Tel.: þ49 5151 999 644; fax: þ 49 5151 999 400. E-mail address: [email protected] (M. Ernst).
0927-0248/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.solmat.2012.05.033
ion etching. Solar cells with efficiencies of up to 4.1% have been reported applying this technique [7]. The macroporous silicon process (MacPSi) [8], is a separation technique for detaching thin monocrystalline layers with thicknesses of around 20–30 mm from CZ silicon wafers. In this process, small cylindrical holes are etched into the surface of a silicon substrate by means of electrochemical etching. These holes are broadened in a depth of about 20–30 mm – the thickness of the later absorber layer – to form a highly porous separation layer. We investigate macroporous silicon as an absorber material for thin monocrystalline solar cells. Light-generated carriers in thin macroporous silicon absorbers recombine in the bulk or, more likely at the large surface of the pores. Understanding the measured effective carrier lifetime is important for process optimization and for designing a device. The surface recombination velocity of passivated silicon surfaces by thermally grown oxide layers depends on the crystallographic orientation [13]. Since the macroporous surface shows various surface orientations, the SRV cannot be determined using planar reference samples [11]. Instead an average SRV needs to be determined experimentally. In a recent paper we measured effective carrier lifetimes of passivated macroporous silicon layers and derived an analytical model to describe effective carrier lifetimes as a function of pore morphology, bulk recombination, and surface recombination [9]. Therein we investigated the impact of the layer thickness on the effective carrier lifetime of passivated macroporous silicon samples experimentally and applied our analytical model to determine an
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average surface recombination velocity (SRV) S¼75 cm s 1 on passivated macroporous silicon samples by fitting the model to the measurements. This surface recombination velocity was higher than the surface recombination velocity S¼24 cm s 1 that we measured on non-porous reference samples passivated in the same process. This discrepancy could not solely be explained by the various surface orientations. Instead, we explained the discrepancy in the surface recombination velocity with the existence of local openings in the passivating layer that we observed in scanning electron micrographs. However, such openings were not included in our previous model [9]. In this contribution we therefore develop a three-dimensional numerical model that accounts for the non-passivated openings. We verify the numerical model experimentally by preparing macroporous silicon samples with defined openings in the passivation layer.
2. Sample preparation
Fig. 2. Etching current density profile to form an approximately 30 mm thick macroporous silicon layer with a highly porous separation layer. We use three different current densities between 18 (short dashed line) and 20 mA cm 2 (solid line) to form the separation layer with varied porosity.
We use (100)-oriented, n-type float zone crystalline Si wafers that have a resistivity of (7.570.1) O cm. The thickness of the wafer is (674710) mm. The wafer surface is structured with a hexagonal array of inverted pyramids as shown in Fig. 1. The pyramids are defined by photolithography. The distance of the pyramids is 8.3 mm and the edge length is 4 mm as measured by means of scanning electron microscope (SEM) analysis (S-4800 from Hitachi). A phosphorous diffusion at the rear side with a sheet resistance of 40 O/sq. improves the contact during electrochemical etching in 3 wt % hydrofluoric acid at 20 1C. Photogenerated holes are required for dissolving n-type Si in HF-containing electrolytes. Thus we use rear side illumination [10]. The illumination source is an array of LEDs which emit light at a wavelength of 880 nm. The etched area is circular with an area of 1 cm2. Fig. 2 shows the set values of the etching current density. By controlling the illumination intensity a current density of 6 mA cm 2 is generated and the pores start growing at the tips of the inverted pyramids with an etching rate of 0.68 mm min 1. The pore diameter is a function of the current density, therefore the pores are broadened in a depth of about 30 mm by increasing the illumination intensity. The current increases linearly from 6 mA cm 2 to values of 18–20 mA cm 2 within 6 min. At this level, the current is maintained for 6 min to form a highly porous separation layer. The porosity of the separation layer controls the width of the weak bridges between the substrate and the separation layer.
Fig. 3. Cross sectional SEM-images of prepared samples with separation layer current density of (a) 20 mA/cm2 and (b) 18 mA/cm2. The width of the weak bridges is approximately 800 nm in case (b).
Fig. 1. SEM-image showing an oblique view onto a silicon surface with inverted pyramids defined by photolithography. The distance of the pyramids tips is 8.3 mm.
Fig. 3a shows the 20 mA cm 2 case. The porosity of the separation layer is 100%, i.e. no weak bridges remain between the substrate and the macroporous layer. The layer is only attached to the substrate at the border of the etched area. Fig. 3b shows a cross-sectional SEMimage of the 18 mA cm 2 case. Here the width of the weak bridges is approximately 800 nm. We find 18 mA cm 2 to be the lower limit to remain the detachability of the macroporous layer. We prepare a set of three samples for each separation layer current density 18, 19, and 20 mA cm 2. Finally, dry thermal oxidization at 900 1C creates a 30 nm thick passivating SiO2-layer. The passivated macroporous silicon samples are subsequently detached by mechanical force and non-passivated areas remain at the broken bridges.
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3. Experimental results 3.1. Geometrical analysis We determine the percentage c of the non-passivated areas after detaching the macroporous silicon layer from the substrate by means of SEM image analysis. The local openings in the oxide layer are observable in the SEM images presented in Fig. 4. In case of a final etching current density of 20 mA cm 2 (Fig. 4a) the porosity of the separation layer is 100% and thus no nonpassivated areas remain. The brightness and contrast of the SEM image are adjusted in an image editing software (Corel PhotoPaint X4) to enhance the contrast between the passivated and non-passivated areas. Passivated and non-passivated areas appear as white and black areas respectively. Since pores and nonpassivated areas both appear black, we color non-passivated areas within the image editing software as shown in Fig. 5. The fraction of these colored pixels results in the percentage c of the non-passivated areas. Furthermore, we determine the geometrical parameters of the macroporous layer from cross-sectional SEM images as specified in Table 1.
Fig. 5. Top view SEM-image after image processing and colorizing the nonpassivated areas in green. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Fraction of the non-passivated areas and geometrical parameters of the macroporous layers. Parameter
Symbol
Value
Percentage of the non-passivated areas for 20 mA/cm2 Percentage of the non-passivated areas for 19 mA/cm2 Percentage of the non-passivated areas for 18 mA/cm2 Thickness of the macroporous layer Pore radius Pore distance
c1
0%
c2
(0.757 0.20)%
c3
(1.607 0.20)%
W rp d0
(297 1) mm (2.47 0.1) mm (8.37 0.1) mm
Fig. 6. Measured effective carrier lifetimes teff of passivated and detached macroporous silicon layers (dots) and numerical simulations (lines) as a function of the percentage c of non-passivated areas. The solid line A is the numerical simulation for the SRV given in the figure. The dashed lines B and C show numerical simulations for the upper and lower boundaries of Spass and Snp.
3.2. Effective carrier lifetime
Fig. 4. Top view SEM-images of surface passivated macroporous layers showing the surface facing the substrate prior to detachment. The etching current density for the separation layer is (a) 20 mA/cm2, (b) 19 mA/cm2 and (c) 18 mA/cm2. The non-passivated areas are visible in the magnifications.
We measure minority carrier lifetimes of detached passivated macroporous silicon layers using the transient photo-conductance decay (WT-2000 system from Semilab) technique. The samples are illuminated from the side that was facing to the substrate prior to detachment. The optical absorption length of the short pulse laser is approximately 30 mm in crystalline silicon and thus comparable to the layer thickness. Fig. 6 shows the measured effective carrier lifetimes (dots) for various percentages of non-passivated areas. The mean value of the effective lifetimes is calculated from a set of three samples for each percentage of the non-passivated areas. Note that our
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experimental points cover the experimentally feasible range due to limits in sample preparation. We assume a relative error in lifetime measurement of 5%. The highest effective lifetime measured is teff ¼(10.1 70.5) ms for a fully passivated sample.
recombination velocity is Spass for the surface passivated areas as shown in Fig. 8(a) of the macroporous layer, thus ! ! n Dp r p ¼ Spass p:
ð2Þ
! Here n is a unit vector perpendicular to the respective surface. The surface recombination velocity for the non-passivated areas as marked in red in Fig. 8(b) is Snp, thus
4. Numerical modeling We set up and apply a numerical finite element model in COMSOL Multiphysics [12] that accounts for the geometrical properties of macroporous silicon to determine the average SRV at the passivated and non-passivated areas. In the following sections we apply the numerical model to describe our measurements and simulate the effect of geometrical and electrical parameters on the effective carrier lifetime. 4.1. Geometry Fig. 7 schematically shows the hexagonal pattern of the macroporous structure with a pore distance d0. For our numerical model we assume cylindrical pores with radius rp and smooth surfaces. One unit cell is extruded from the triangular basis with a thickness W. The increased pore radius of the separation layer is approximated by subtracting three spheres at the top of the unit volume. The centers of the spheres lie on the pores axis. The breaking point of the weak bridge is marked in red in Fig. 7(d). Increasing the spheres radius leads to thinner bridges. This variation in the spheres radius corresponds to an experimental variation of the separation layer current density.
! ! n Dp r p ¼ Snp p:
ð3Þ
For symmetry reasons the perpendicular component of the ! derivate r p vanishes for the boundaries shown in Fig. 8(c), thus ! ! n Dp r p ¼ 0:
ð4Þ
The average excess carrier density pav is calculated by integrating the local excess carrier densities over the unit volume: Z 1 ! 3 pav ¼ pð x Þd x: ð5Þ V V
4.2. Equations and boundary conditions The inhomogeneous steady-state diffusion equation for the minority carriers is given by !
!
r ðDp r pÞ ¼ G
p
tp,bulk
:
ð1Þ
Here Dp is the diffusion coefficient of the minority carriers, p the excess carrier density, and tp,bulk the minority carrier bulk lifetime. We assume the generation rate G to be spatially homogeneous, since the optical absorption length of the short pulse laser used in our measurements is comparable to the layer thickness. In Fig. 8 the surfaces exhibiting identical boundary conditions are marked in identical colors schematically. The average surface
Fig. 8. Boundary conditions for the unit cell highlighted in red: (a) Passivated surfaces with an SRV Spass. (b) Non-passivated surface with SRV Snp. (c) Symmetric boundary conditions. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 7. (a) Schematic of the hexagonal array with pore distance d0 and pore radius rp. The orange triangular defines the unit cell used in the numerical simulations. (b) Extruded unit volume with thickness W. (c) The separation layer is approximated by subtracting three spheres from the extruded unit volume. The spheres center lies in the pores axis. (d) The area highlighted in red corresponds to the non-passivated areas of the passivated and detached macroporous silicon samples. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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We calculate the effective minority carrier lifetimes under steady state conditions by dividing the average excess carrier density and the average carrier generation rate G that we assumed to be spatially homogeneous:
tef f ðpav Þ ¼
pav : G
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and C show the 5% uncertainty in L of the numerical simulations for Spass and Snp.
5. Conclusions ð6Þ
4.3. Experimental verification With the above model we calculate the effective carrier lifetimes as a function of the percentage of the non-passivated areas. The geometric parameters of the macroporous layers are those listed in Table 1. We use a bulk lifetime of tp,bulk ¼3 ms typical for lowly doped n-type Si substrates and the diffusion coefficient Dp ¼ 12 cm s 1. The model is fitted to the measured carrier lifetimes by varying the surface recombination velocities Spass of the passivated areas and Snp of the non-passivated areas. We calculate the mean average percentage error L between the calculated curve and the measurements: 3 1X ti,sim ti,exp : L¼ ð7Þ 3i¼1 ti,exp Fig. 9 shows this error as a function of an Spass and Snp in a contour plot. At the minimum of L (dot A) we find an average þ 1:6 surface recombination velocity Spass ¼ð22:81:4 Þ cm s 1 for the þ 1500 passivated surfaces and Snp ¼ð22001400 Þ cm s 1 for the nonpassivated surface within an experimental error of L o5%. The resulting uncertainty of Spass is approximately 7%. This high accuracy is due to the strong dependence of the effective carrier lifetime on the surface recombination velocity that originates from the large passivated surface area. The uncertainty of Snp is approximately 70%. This large relative error results from the fact, that the non-passivated area fraction is small with respect to the total area. The dots B and C lie inside the uncertainty range of Spass and Snp, respectively. Fig. 6 shows the measured effective carrier lifetimes (dots) and the numerical simulations (lines) as a function of the percentage of non-passivated areas. The numerical simulations agree with the experimental data within the uncertainty range of the experimental data. Line A is the numerical simulation with Spass and Snp for the minimum of L (dot A in Fig. 9). The dashed lines B
Fig. 9. Contour plot of the mean average percentage error L evaluated between the fit and experimental data for various surface recombination velocities. Within þ 1:6 a deviation o 5% we find Spass ¼ ð22:81:4 Þ cm s 1 for the passivated surfaces and þ 1500 Snp ¼ð22001400 Þ cm s 1 for the non-passivated surface.
In this paper we have demonstrated the preparation of point contact openings in surface passivated macroporous silicon layers. The percentage of these non-passivated local openings was experimentally varied in a range from 0% to 1.6% by controlling the etching parameters. The highest lifetime measured was (10.170.5) ms for a fully oxide passivated 29 mm thick macroporous silicon layer. A three-dimensional finite element numerical model has been developed to determine the surface recombination velocities of the macroporous surfaces and the local openings. The model agrees with the measurements within the measurement accuracy. We find þ 1:6 an average surface recombination velocity Spass ¼ð22:81:4 Þ cm s 1 for the passivated surfaces of macroporous silicon layers and a þ 1500 surface recombination velocity Snp ¼ ð22001400 Þ cm s 1 for the non-passivated areas. Thus the postulated reason for the discrepancy between the average surface recombination velocity of our analytical model and reference measurements [9] is verified and explained with the non-passivated areas. The surface recombination velocity Snp determined for the nonpassivated areas is surprisingly low. However, for low doping densities of 6 1014 cm–3 as in our case, M¨ackel and Cuevas [14] found effective surface recombination velocities from 1 103 cm s 1 to 3 104 cm s 1 for non-passivated surfaces depending on storage time after HF dip. This measurement is consistent with our result.
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