As-grown iron precipitates and gettering in multicrystalline silicon

Materials Science and Engineering B 159–160 (2009) 248–252

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As-grown iron precipitates and gettering in multicrystalline silicon A. Haarahiltunen ∗ , H. Savin, M. Yli-Koski, H. Talvitie, M.I. Asghar, J. Sinkkonen Helsinki University of Technology, P.O. Box 3500, FI-02015 TKK, Finland

a r t i c l e

i n f o

Article history: Received 2 May 2008 Received in revised form 21 October 2008 Accepted 30 October 2008 Keywords: Multicrystalline silicon Iron Precipitation Gettering

a b s t r a c t We report here the results of a theoretical study concerning the iron precipitation in multicrystalline silicon during crystal growth and its implications on phosphorus gettering. In our model the average size and density of iron precipitates in the final structure depends on the growth method, initial iron concentration and the density of possible heterogeneous precipitation sites. With the same model we can simulate phosphorus diffusion gettering (PDG) of iron in cast multicrystalline silicon by using the iron precipitate size distribution obtained from crystal growth simulations as initial condition for gettering. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Multicrystalline silicon contains high concentrations of iron, typically in the range of 1014 to 1016 cm−3 . Iron is mostly precipitated at grain boundaries and at structural defects, and approximately only 1012 to 1013 cm−3 of iron remains in interstitial sites after crystal growth [1,2]. Diffusion of high concentration of phosphorus (P) is a well-known gettering technique for removing iron in silicon technology and it is a crucial part of a high efficiency solar cell process. Theoretical results of gettering of precipitated iron in multicrystalline silicon are presented in several papers [3,4]. Usually it is assumed that all iron is precipitated to some density of iron precipitates and a diffusion limited growth law is used to simulate the time evolution of average size of iron precipitates. In this paper we study theoretically the iron precipitation process during multicrystalline silicon growth using the heterogeneous precipitation model presented in Refs. [5,6], originally developed for single crystal silicon. Particularly, we consider into details the cooling rate, which depends on the crystal growth method, and its effect on the size distribution of as-grown iron precipitates and the efficiency of phosphorus diffusion gettering (PDG).

iron are more attractive gettering sites than the ones with no iron, simply because of a lower chemical potential of iron in large precipitates. This assumption, together with the Fokker-Planck Equation (FPE) used to simulate the cluster evolution, leads to a model that includes the nucleation and growth of iron precipitates. Here we use this model to simulate iron precipitation in multicrystalline silicon by adjusting the density of possible heterogeneous precipitation sites for iron, which includes also dislocations with a typical density of about 105 cm−2 [2,7]. The FPE is used to simulate the evolution of the size distribution of iron precipitates ∂ ∂f (n, t) = ∂t ∂n



∂f (n, t) −A(n, t)f (n, t) + B(n, t) ∂n



,

(1)

where f(n,t) is the density of heterogeneous precipitation sites containing n atoms of precipitated iron and A and B are given by A(n, t) = g(n, t) − d(n, t)

B(n, t) =

g(n, t) + d(n, t) . 2

(2)

The growth and dissolution rates g and d are given by the following equations:

 E  a

2. Modeling of heterogeneous iron precipitation and phosphorus gettering

g(n, t) = 4rc DCFe and d(n, t) = 4rc DCSol exp

In Refs. [5,6] we have presented a lumped model for heterogeneous precipitation of iron in single crystal silicon, which has been used to model internal gettering. The model assumes that the heterogeneous precipitation sites that already contain some

where D is the diffusion constant of iron, CFe is the interstitial iron concentration, CSol is the solubility of iron and factor Ea /n1/2 describes the fact that iron has a higher chemical potential in a small cluster than in a large cluster. rc is the average capture radius of the iron precipitate [8], and

∗ Corresponding author. Tel.: +358 9 4512330; fax: +358 9 4515008. E-mail address: antti.haarahiltunen@tkk.fi (A. Haarahiltunen). 0921-5107/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2008.10.053

rc = (rs + 5.1 × 10−9 (cm)n1/2 ), where rs is the radius of precipitation sites.

kTn1/2

(3)

(4)

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Iron precipitation was modeled using parameters which we have found to be appropriate for internal gettering simulations [5], although some of the parameters might depend on the doping level or on the properties of the precipitation sites. Previously, we have used for the iron solubility a value of 4.3 × 1022 exp(−2.10 eV/kT) cm−3 (Ref. [9]), in this study we use instead an iron solubility value of 8.4 × 1022 exp(−2.86 eV/kT) cm−3 (Ref. [10]) at temperatures higher than 890 ◦ C. In PDG simulations the diffusion and segregation of iron are calculated using an algorithm that is described in Ref. [11]. The diffusion of high concentrations of P in silicon follows so-called kink and tail profile, which can be simulated quite accurately using the model suggested by Bentzen et al. [12]. In this model P diffuses mainly via self-interstitial mechanism at low concentrations while at high P concentration the diffusivity is associated with doubly negative vacancies. Above solid solubility of P, the diffusivity decreases due to the formation of P clusters, however, this has only a minor impact on simulation of P diffusion. The driving force for iron segregation during PDG is the chemical potential gradient caused by the difference in solubility of iron in lightly B-doped and heavily P-doped silicon. The physical background for calculating the iron solubility in heavily P-doped silicon, which is proposed in Ref. [13], is based on reactions of (i) vacancies with interstitial iron and (ii) substitutional iron with phosphorus. The proposed model is very closely linked to the recently published model for phosphorus diffusion by Bentzen et al. [12] and ab initio calculations [14] of iron reactions with pre-existing vacancies. The proposed physics behind this model, however, needs further examination and experimental evidence, although PDG can be quantitatively modeled at temperatures above 700 ◦ C as shown in Ref. [13]. In our model the effect of phosphorus doping on iron precipitation arises completely from the change in solubility and diffusivity (Eq. (4)) in similar manner as we have proposed in the case of boron [8,15]. The as-grown iron precipitates dissolve quickly in P-rich layer as the solubility is typically rather high (Eq. (4)) and we assume that diffusion constant in P-rich layer is same as in bulk. In general, modeling includes also iron precipitation in the emitter, which indeed might occur during a low temperature processing if the segregation

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coefficient does not increase very strongly at lower temperatures and iron diffusion from the bulk is sufficiently fast [15].

3. Results and discussion 3.1. As-grown iron precipitates At the moment several crystal growth techniques are in use, such as String Ribbon (SR), edge-defined film-fed (EFG), and directionally solidified ingot growth. SR and EFG growth techniques have faster cooling rates after crystallization than ingot growth [1]. Thus, we made a series of simulations assuming either fast (45 ◦ C/min) or slow (1 ◦ C/min) cooling during crystal growth [16]. The initial iron concentration and the density of heterogeneous precipitation sites were varied between 1014 to 1015 cm−3 and 107 to 1012 cm−3 , respectively. The radius of precipitation sites was kept at 10 nm. The density and the average radius of iron precipitates were calculated for iron precipitates that consist more than 103 iron atoms. Simulation results at slow and fast cooling rates are presented in Figs. 1 and 2, respectively. Purpose of these simulations was (i) to confirm that iron precipitation model [5,6] developed for single crystal silicon can be extended to multicrystalline silicon, (ii) to find out possible limitations and (iii) to find appropriate values for the precipitation site density in various multicrystalline silicon materials. We present here a comparison between our simulation results and a collection of typical experimental results [1,2,17] mainly from synchrotron X-ray fluorescence microscopy (␮-XRF) studies. Firstly, the measured average dissolved iron concentration after the crystal growth in both slowly and rapidly cooled samples is few times 1012 cm−3 when the average total iron concentration is about 1014 cm−3 [2]. This indicates that the average density of precipitation sites is about 108 cm−3 , in slowly cooled crystals (Fig. 1a)). However, in the rapidly cooled crystal the final dissolved iron concentration remains too high as compared to experimental value [2] even at the precipitation site density of 1010 cm−3 as seen in Fig. 2a. This may indicate that (i) in the case of fast cooling a better approximation than a linear cooling rate should be used and (ii) the density of precipitation sites is typically larger in the rapidly cooled crystals.

Fig. 1. Simulation results of slowly cooled crystal: (a) dissolved iron concentration, (b) average radius of iron precipitates and (c) density of iron precipitates as a function of heterogeneous precipitation site density. Initial iron concentrations are 1014 cm−3 (solid line), 5 × 1014 cm−3 (dashed line) and 1015 cm−3 (dotted line).

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Fig. 2. Simulation results of rapidly cooled crystal: (a) dissolved iron concentration, (b) average radius of iron precipitates and (c) density of iron precipitates as a function of heterogeneous precipitation site density. Initial iron concentrations are 1014 cm−3 (solid line), 5 × 1014 cm−3 (dashed line) and 1015 cm−3 (dotted line).

Experimental results show that the diameter of iron precipitates is larger than 30 nm [1] in the slowly cooled crystals and the experimental results [17,18] from cast multicrystalline silicon indicate that the precipitate sizes of 800 nm are also possible. Thus, the values in Fig. 1b are reasonable only in cases of initial iron concentration of 1014 cm−3 and 5 × 1014 cm−3 (we discuss the reason for this later). According to the experiments in the rapidly cooled crystal at low contamination level the size of iron precipitates is below the detection limit (10–30 nm) of ␮-XRF technique [1]. At higher contamination levels the diameter of iron precipitates is about 50 nm

and the density of iron precipitates is much higher than in lowcontamination slowly cooled crystals [1]. We can clearly observe from Fig. 2b that iron precipitates are too small for detection at low contamination level, in agreement with the experiments. We can also notice from Fig. 2b and by comparing the simulated iron precipitate densities in Figs. 1 and 2c that the average density of precipitation sites in the rapidly cooled crystal is about 5 × 109 cm−3 , i.e., the size is in agreement with the experiments and the density of iron precipitates is about one decade higher than in the slowly cooled crystals. The adjustment of final dissolved iron concentra-

Fig. 3. Simulation results of slowly cooled crystal: (a) iron precipitate density and (b) dissolved iron concentration as a function of temperature. Heterogeneous precipitation site density is 108 cm−3 . Initial iron concentrations are 1014 cm−3 (solid line), 5 × 1014 cm−3 (dashed line) and 1015 cm−3 (dotted line).

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tion by manipulating the low temperature part of the crystal cooling would not change significantly the simulated radius or the density of iron precipitates. Note that the manipulated low temperature part might simply be a surface passivation (SiN growth) treatment, which is typically made at temperatures around 400 ◦ C. This annealing indeed decreases the interstitial iron concentration more in the rapidly cooled samples than in the slowly cooled samples due to the higher density of iron precipitates in the rapidly cooled crystal. The behavior of the final iron precipitate density and the average size as a function of the heterogeneous precipitation site density and the cooling rate is quite interesting. Firstly we can observe that a higher cooling rate generally leads to a larger density of smaller iron precipitates as compared to the slow cooling rate. This has a natural explanation as during slow cooling, the growth of existing iron precipitates slows down further nucleation. However, the exact explanation of the behavior of the final density and the average size of iron precipitates arises from the observation that quite often the nucleation of iron precipitates in simulations occurs in two stages as shown in Figs. 3 and 4. The first-stage of nucleation arises at rather high temperature >700 ◦ C and the temperature of the first-stage nucleation increases when the heterogeneous precipitation site density or initial iron concentration increases. The growth of the first-stage precipitates decreases supersaturation and prevents nucleation. However, when the temperature further decreases, the growth of the first-stage precipitates slows down and the growth-rate is not any more sufficient to prevent the second-stage nucleation (note that supersaturation is increasing due to the decrease in temperature). Two-stage nucleation also well explains the notch observed in the average size of precipitates (Figs. 1 and 2b). Naturally, the first-stage nucleation remains in some cases as the only nucleation stage. The final density of iron precipitates in Figs. 3 and 4a is consistent with the analysis of the density of metal silicide nanoprecipitates, which suggests that their density is about 4 × 107 to 108 cm−3 and 5 × 108 to 109 cm−3 [19] in cast and sheet multicrystalline silicon, respectively. Buonassisi et al. [18] have observed that multicrystalline silicon contains micron size iron oxide and iron-rich multiple

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metal (stainless steel) inclusions. The inclusions are believed to originate from a foreign source such as the growth surfaces, production equipment, or feedstock, and they might contain the majority of iron whereas iron concentration observed in silicide nanoprecipitates is typically on the order of 1014 cm−3 and 1015 cm−3 in cast and sheet material, respectively [18,19]. Nobody has not, however, reported any observation of several micron size metal silicide precipitates, which is suggested in our simulations at higher initial contamination level in slowly cooled crystal (Fig. 1b). Thus the experimentally observed iron concentration in silicide nanoprecipitates [18,19] can be considered as an upper limit for initial iron concentration in our simulations when the simulations are compared to the experimental results. The iron concentration difference in nanoprecipitates between sheet and ingot material is understandable as iron from the growth surfaces is able to diffuse through the entire thickness of the sheet material causing larger dissolved iron contamination [18]. 3.2. Phosphorus gettering Fig. 5 shows a comparison between our simulation and the experimental results [20] of PDG of cast grown multicrystalline silicon wafer. The wafer thickness is 200 ␮m and gettering occurs from both wafer surfaces [20]. We get a rather good agreement between experiments and simulations just by using parameters which we defined previously as typical values, i.e., the density of heterogeneous precipitation sites of 108 cm−3 and cooling rate of 1 ◦ C/min. Our fitted initial contamination level of iron is 1.2 × 1014 cm−3 (Fig. 5) which is in agreement with experimental value 1.5 × 1014 cm−3 measured after additional contamination [20]. Important is to note that the results of Shabani et al. [20] are in agreement with the results of Macdonald et al. [21] obtained by neutron activation analysis. In above simulation of PDG we have assumed the same diffusivity for iron both in the bulk and in the P-layer. However, we are aware that besides the solubility, phosphorus doping affects the diffusivity of iron in n-Si. We have noticed that even use of effective diffusivity (Deff = D/kseg ), i.e., assuming immobile substitutional

Fig. 4. Simulation results of rapidly cooled crystal: (a) iron precipitate density and (b) dissolved iron concentration as a function of temperature. Heterogeneous precipitation site density is 5 × 109 cm−3 . Initial iron concentrations are 1014 cm−3 (solid line), 5 × 1014 cm−3 (dashed line) and 1015 cm−3 (dotted line).

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Acknowledgements The authors acknowledge the financial support from the Finnish National Technology Agency, Academy of Finland, Okmetic Oyj, Endeas Oy, Semilab Inc. and VTI Technologies Oy. References

Fig. 5. Comparison between our simulation and experimental results of PDG of cast grown multicrystalline silicon wafer. Initial iron concentration in simulation is 1.1 × 1014 cm−3 . Experimental results are from Ref. [20].

iron, did not have an impact on the simulation results shown in Fig. 5. This means that even with highly decreased diffusivity in P-layer, the diffusion through bulk of the wafer, which is much thicker than P-layer, remains here as the limiting factor in the gettering process. The effective diffusivity still remains an important parameter as it affects the iron precipitation/dissolution behavior in the P-layer. For instance using Deff = D, iron precipitates dissolute “instantly” in the P-layer whereas using Deff = D/kseg , some iron precipitates remain stable even after 90 min of gettering at 900 ◦ C. 4. Conclusions We have made a series of simulations of iron precipitation during multicrystalline silicon growth. We have observed that we can interpret in a reasonable way the published experimental results of iron silicide precipitates although for simplification we have used a point-size simulation for iron precipitation during multicrystalline silicon growth. We have shown that PDG of iron can be simulated in cast multicrystalline silicon by combining the initial conditions from point-size crystal growth and 1D simulations of iron segregation to phosphorus layer.

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