Bothe, Karsten

Herlufsen, Sandra

MacDonald, Daniel

Schmidt, Jan

The Australian National University

27th European Photovoltaic Solar Energy Conference, Frankfurt, Germany, 24-28 September 2012, 2AV.4.27  IMAGING OF THE INTERSTITIAL IRON CONCENTRATION IN B-DOPED C-SI  BASED ON TIME-DEPENDENT PHOTOLUMINESCCENCE IMAGING   Sandra Herlufsen1, Daniel Macdonald2, Karsten Bothe1, and Jan Schmidt1, 3 1Institute for Solar Energy Research Hamelin (ISFH), Am Ohrberg 1, D-31860 Emmerthal, Germany Tel: +49 5151 999 414; Fax: +49 5151 999 400; Email: herlufsen@isfh.de 2 Research School of Engineering, The Australian National University, Canberra, ACT 0200, Australia 3Institute for Solid-State Physics, Leibniz University Hannover, Appelstraße 2, D-30167 Hannover, Germany   ABSTRACT: We report on measurements of the interstitial iron concentration in boron-doped crystalline silicon by measuring the dissociation rate of iron-boron pairs using a camera-based photoluminescence setup (dynamic Fei imag-ing). This approach enables us to identify the interstitial iron concentration without measuring absolute values of the carrier lifetime and without knowing the recombination properties of interstitial iron and iron-boron pairs in silicon. We take advantage of the dependence of the dissociation rate of iron-boron pairs on the interstitial iron concentration. Furthermore, we exploit the linear relationship between the excess carrier density and photoluminescence signal at low injection levels. This allows the determination of the relative FeB pair concentration directly from the measured PL signals in the associated and dissociated state of the FeB pairs without an additional calibration of the PL signal to excess carrier density.  Keywords: photoluminescence, multicrystalline silicon, impurities   1 INTRODUCTION  Iron is a well-known and detrimental impurity in crystalline silicon (c-Si) for solar cells, especially in block-cast multicrystalline silicon (mc-Si). So far, most measurement techniques used to determine the concentra-tion of interstitial iron (Fei) in boron-doped Si wafers are based on measurements of the carrier lifetimes or diffusion lengths before and after iron-boron (FeB) pair dissociation [1 - 3]. We report on measurements of the interstitial iron concentration in B-doped c-Si by measur-ing the dissociation rate of FeB pairs using a photolumi-nescence (PL) camera signal (dynamic Fei imaging) [4]. An interesting aspect arises from the fact that the sensitivity of the dynamic Fei technique does not depend on the interstitial iron concentration. A combined analysis of the time constant of the FeB pair dissociation process and the noise behavior of the PL setup yields optimum injection conditions for the dynamic Fei technique.   2 BASIC PRINCIPLE OF THE DYNAMIC APPROACH  In previous techniques, the interstitial  iron concen-tration [Fei] of passivated B-doped Si wafers was mostly determined by measuring absolute values of the carrier lifetime  with the Fei in two different states, namely (i)FeB, when the Fei  is bound to B dopant atoms to form FeB pairs and (ii) Fei, after complete dissociation of the FeB pairs. Due to the different recombination properties of the iron in these two states, the Fei concentration can be deduced from the difference of the inverse bulk lifetimes [1–3]:  ,11]Fe[FeBFeiSRHi C            (1)  with CSRH being a prefactor which depends on the doping and excess carrier concentration [3]. Figure 1 shows the expected effective carrier lifetime if the interstitial iron is in the associated or dissociated state with the boron dopants, considering Shockley-Read-Hall statistics [5, 6] with an interstitial iron concentration of [Fei] = 1012 cm-3 and the impact of Auger recombination processes [7].   If PL imaging [8] is used for the determination of the interstitial iron concentration [9], the lifetime in the two different states of the Fei is typically measured at a constant generation rate and therefore for different injection densities as indicated in Fig. 1 by the tilted gray arrow.   Figure 1: Expected effective carrier lifetimes in a B-doped Si wafer with [Fei] = 1012 cm-3 for the Fei in the dissociated and the associated state (FeB pairs). Typical injection ranges are indicated by arrows for the dynamic Fei technique and for [Fei] imaging [9] based on PL lifetime imaging [10].  Geerligs and Macdonald [11] investigated the dynam-ics of light-induced FeB pair dissociation and revealed a quadratic dependence of the dissociation rate Rdiss on the average photogeneration rate Gav and an inverse propor-tionality on the square of the interstitial iron concentra-tion [Fei]:  27th European Photovoltaic Solar Energy Conference, Frankfurt, Germany, 24-28 September 2012, 2AV.4.27  ,]Fe[ 2i2avdissdissGCR              (2)  with a proportionality constant Cdiss that Geerligs and Macdonald [11] determined to be Cdiss = 5 × 10−15 s. The time-dependent relative iron-boron concentration [FeB]rel after complete iron-boron pair bonding is established, is described by an exponential function [11]:  dissreprep)(dissrepdissreldissrepe)(]FeB[RRRRRRt tRR  , (3)  considering the dissociation rate Rdiss and a repairing rate Rrep [12, 13]. Exemplarily, we show in Fig. 2 the ex-pected time-dependent behavior of the relative FeB concentration, simulated for different interstitial iron concentrations, using Eq. (2) for Rdiss and Rrep of Ref. 13.    Figure 2: Relative FeB concentration [FeB]rel in depend-ence on time for different interstitial iron concentrations [Fei] and therefore different FeB dissociation rates Rdiss.   As described in Ref. 11, Rdiss can be easily obtained by linear regression of the derivative of the natural logarithm of the FeB pair concentration [FeB]rel, normal-ized with respect to the total  FeB concentration at t = 0:  .)]]FeB[ln([diss0rel Rdtdt           (4)  Eq. (3) is valid for t = 0 or at least: t < (Rrep  + Rdiss )−1.   At low injection levels, the measured PL signal IPL is, within certain limits [14], proportional to the excess carrier density. Hence, for a constant photogeneration rate, IPL is proportional to the carrier lifetime. Using this knowledge and Eq. (1), we are able to calculate the relative FeB concentration [FeB]PL,rel(t) using only measured PL signals without requiring an additional calibration technique:  ,)(11)(]FeB[FeBPL,FeiPL,relPL, tIIt                            (5)  with IPL,Fei being the PL signal measured for the dissoci-ated state of the FeB pairs, and IPL,FeB(t) being the time-dependent PL signal after complete FeB pair association during constant photogeneration. The assumption that the prefactor CSRH of Eq. (1) is independent of injection is found to be valid for low-level injection conditions [3]. IPL,FeB(t)  is decreasing with time since the FeB pairs are separated due to the illumination during the PL meas-urement. The decrease of the FeB concentration leads to an increase of the Fei concentration and therefore results in a decreasing effective carrier lifetime as indicated by the tilted black arrow in Fig. 1. Typical illumination intensities of a PL measurement at low-level injection conditions are not sufficient for the dissociation of all FeB pairs in the sample as suggested by the capped black arrow.     3 EXPERIMENTAL CONDITIONS  Technical details of our camera-based PL setup have been published elsewhere [10, 15]. In this study, the associated state of the Fei with the substitutional boron is obtained by placing the sample on a hotplate at 50 °C for about 30 mins. After complete association of the FeB pairs, we record a sequence of PL images for the determination of [FeB]PL,rel(t) with Eq. (5). During the acquisition of the PL image sequence, the excitation source remains switched-on. The PL signal of the fully dissociated state is meas-ured after exposing the wafer to about 15 flashes of a photo flash lamp with an intensity of up to 100 W/cm2. All PL measurements were performed at a sample temperature of 25 °C. We use a calibrated Si solar cell to measure the photon flux laser during illumination with a laser. The average generation rate for excess carriers Gav in a Si wafer of thickness W and reflectivity Rlaser at the excitation wavelength is then calculated using   W/)1( laserlaserav RG   ,                          (6)  with Rlaser being the reflection of the exciting light at the front side of the Si sample.   4 RESULTS  We verified the results of Geerligs and Macdon-ald [11] by measuring the time-dependence of [FeB]PL,rel for different illumination intensities for a deliberately Fe-contaminated SiNx-passivated float-zone (FZ) Si wafer with a resistivity of 1 cm, a thickness of 385 m and [Fei] = 2.5  1012 cm-3. The iron was introduced by ion implantation and the Fei concentration was deduced from the implanted Fe dose. The dissociation rate of FeB pairs Rdiss is determined from [FeB]PL,rel by linear regression of ln([FeB]PL, rel) using Eq. (4).  In Fig. 3, the product of Rdiss, as obtained from our PL measurements, and [Fei]2, as calculated from the implanted dose, is plotted on a double logarithmic scale versus the measured photogeneration rate Gav. The dashed red line shows the dependence published by Geerligs and Macdonald [11]. The excellent agreement further justifies using Eq. (2) for the dynamic determina-tion of the interstitial iron concentration [Fei]dyn by measuring the dissociation rate Rdiss of the FeB pairs.   27th European Photovoltaic Solar Energy Conference, Frankfurt, Germany, 24-28 September 2012, 2AV.4.27    Figure 3: Product of the measured Rdiss and [Fei]2 in dependence on the average generation rate Gav for a deliberately Fe-contaminated FZ-Si wafer with [Fei] = 2.5  1012 cm-3. The red dashed line shows the depend-ence obtained in Ref. 11.  We demonstrate the applicability of the dynamic Fei approach for measuring [Fei]dyn by investigating a solar-grade SiNx-passivated, 15.6  15.6 cm2 sized mc-Si wafer with a resistivity of 1.3 cm and a thickness of 175 µm from a bottom region of a mc-Si brick. The measured [Fei]dyn image is shown in Fig. 4 (a). We use the infor-mation from four images for the linear regression [Eq. (4)] to determine Rdiss with a camera integration time for each image of tint = 10 s and an illumination intensity of about 0.4 suns (~ 27 mW/cm2). We averaged three measurements and applied 2  2 binning of the pixels to increase the signal-to-noise ratio. For comparison, we show in Fig. 4 (b) a PL image of the same wafer, acquired for the dissociated state of the FeB pairs.    Figure 4: (a) Spatially resolved interstitial iron concen-tration [Fei] for a wafer from the bottom region of a mc-Si brick, determined from the dissociation rate Rdiss of FeB pairs. (b) PL image, acquired for the dissociated state of the FeB pairs.  We observe a strong anticorrelation between PL sig-nal (proportional to the carrier lifetime) and the Fei concentration. This behavior is expected if the Fei is the limiting defect for the carrier lifetime and often observed for mc-Si wafers from top or bottom regions of mc-Si bricks [9]. The dark edges in the PL image are very likely caused by high impurity concentrations since these sides were close to the crucible wall during the formation of the mc-Si brick. Figure 5 exemplarily shows ln([FeB]PL,rel) (t) for two regions of the mc-Si wafer with different [Fei], marked in Fig. 4 (a) with a red square and a blue circle, respectively.    Figure 5: Natural logarithm of [FeB]rel,PL(t) in depend-ence on time for two different regions, marked in Fig. 4 (a) with a red square and a blue circle, with different Rdiss and therefore different [Fei]. The dashed lines show the linear regression for the filled symbols.   5 SENSITIVITY ANALYSIS  Due to the specific dependence of the dissociation rate Rdiss on the interstitial iron concentration and the generation rate [Eq. (2)], the sensitivity of the dynamic approach should not depend on [Fei] but only on the injection density of the PL measurement.  This results from the linear dependence of the carrier lifetime from the inverse impurity concentration [5, 6]. To obtain the same injection density for different interstitial iron concentrations, the generation rate has to be scaled proportionally to the interstitial iron concentra-tion, leaving the dissociation rate being a function of the excess carrier density:  2diss nR  .                               (7)  In Fig. 6, we show a comparison of the camera inte-gration time tint, necessary to achieve a certain signal-to-noise ratio SNR, and the time constant of the dissociation process t0 = (Rrep + Rdiss)-1 [Eq. (3)] in dependence on the injection density for full association of the FeB pairs. The time constant t0 is the upper limit for the validity of Eq. (4). The required camera integration time for a certain signal-to-noise ratio was simulated using the SNR model and parameter from Ref. 15. By dividing those two functions: t0(n)/tint(n), we obtain the number of measurements that can be done before exp(-1) ≈ 36.7% of the FeB pairs are dissociated and a linear regression of the measured data is still possible. The ratio t0/tint is shown in the inset of Fig. 6 and illustrates the best suitable injection density for the application of the dynamic Fei approach. Hence, the optimal measurement condition for a p-type Si wafer at a temperature of 25 °C with a resistivity of 1.3 cm is at an injection density of 2  1012 cm-3.  This result implies that basically every interstitial iron concentration is measurable with the dynamic Fei 27th European Photovoltaic Solar Energy Conference, Frankfurt, Germany, 24-28 September 2012, 2AV.4.27  approach if only an appropriate excitation source is available, providing the required excess carrier density.     Figure 6: Comparison of camera integration time tint, necessary for a certain signal-to-noise ratio SNR [15] with the time constants t0 = (Rrep + Rdiss)-1 [Eq. (3)]. The time constant t0 specifies the upper limit of the validity of Eq. (4). Inset: The ratio t0 /tint represents the number of data points that are maximum available for the linear regression.   7 CONCLUSION  We report on measurements of the interstitial iron concentration in boron-doped Si wafers by investigating the dissociation rate of FeB pairs. The dynamic Fei technique is verified by measuring the interstitial iron concentration of a deliberately Fe-contaminated FZ-Si wafer. Additionally, we generate an image of the interstitial iron concentration of a mc-Si wafer from the measurement of the dissociation rate. Interestingly, the sensitivity of the dynamic Fei technique is not a function of the interstitial iron concentration but only of the injection density. An analysis of the sensitivity shows that the optimum measurement condition for a p-type Si wafer with a resistivity of 1.3 cm is at an injection density of 2  1012 cm-3.   ACKNOWLEDGEMENTS  This work was funded by the German State of Lower Saxony and the German Federal Ministry for the Envi-ronment, Nature Conservation, and Nuclear Safety and by industry partners within the research cluster “SolarWinS” (Contract No. 0325270E). The content is the responsibility of the authors.   8 REFERENCES  [1] M. Kittler, W. Seifert, K. Schmalz, and K. Tittelbach Helmrich, physica status solidi (a) 96, K133 (1986). [2] G. Zoth and W. Bergholz, Jounal of Applied Physics 11, 6764 (1990). [3] D. H. Macdonald, L. J. 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Imaging of the interstitial iron concentration in B-doped c-Si based on time-dependent photoluminescence imaging

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