Mechanisms and computer modelling of transition element gettering in silicon

Solar Energy Materials & Solar Cells 72 (2002) 299–313

Mechanisms and computer modelling of transition element gettering in silicon . W. Schroter*, V. Kveder1, M. Seibt, A. Sattler, E. Spiecker2 IV. Physikalisches Institut der Universitat Bunsenstr. 13-15, D-37073 Gottingen, Germany . Gottingen, . .

Abstract This paper starts out by summarising the modelling and computer simulation of phosphorus diffusion gettering (PDG) of Au. The mobilisation of precipitated impurity atoms is discussed in the light of the silicon interstitial supersaturation provided by the phosphorus diffusion (PD). We then extend the gettering model to Co using bulk solubility data of highly P-doped Si, and find satisfactory agreement with experimental profiles of the total Co-concentration. Yet the pointed disagreement between the CoP/Cos-ratio obtained . through simulation and Mo
bauer data leads to the conclusion that, in the case of phosphorus silicate glass (PSG) growth, segregation alone cannot unambigiously account for the observed gettering efficiency. Instead, it is proposed that PD induced silicide formation provides a more suitable explanation of the high efficiency of PDG accompanied with PSG growth. r 2002 Elsevier Science B.V. All rights reserved. Keywords: PDG; Segregation; Transition metals; Solar cells; Injection-induced gettering

1. Introduction Low-cost silicon materials like multi-crystalline (mc) Si, solar-grade Cz–Si or Si sheets (EFG) are widely used for photo-voltaic applications or are in development like tri-crystalline Si or new Si sheets (RGS). One of the basic material parameters, which significantly influence the efficiency of solar cells, is the minority carrier lifetime [1]. In silicon materials it is generally controlled by non-radiative recombination at defects with deep electronic levels. Possible defect candidates in *Corresponding author. Fax: 49-0551-394574. . E-mail address: [email protected] (W. Schroter). 1 Permanent address: Institute of Solid State Physics, Chernogolovka, Moscow district. 2 New address: Institut fur . Mikrosturkturanalytik, Universit.at Kiel, D-24143, Kiel. 0927-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 4 8 ( 0 1 ) 0 0 1 7 8 - 7

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those materials are extended defects like dislocations, grain boundaries or precipitates and point defects like oxygen, carbon, and transition elements. It is the general view that dislocations and grain boundaries are not associated with deep extended states, since their cores are reconstructed, whereby extended core states are pushed out of the band gap of Si [2]. What remains is an electrical activity caused by core defects, which in the case of dislocations are reconstruction defects, core vacancies, jogs, and kinks. Annealing at or above 8001C strongly reduces the density of core defects and therewith their influence on the electrical parameters of the material. Extended defects may also act as preferred nucleation sites for precipitation from a supersaturated solution of Si/O or Si/transition element and thereby assume an electrical activity which results from that of the individual precipitates and their interaction with others at the extended defect. By their long-range strain field dislocations attract deep impurities, might become decorated by them, and then act as strong recombination centres. The influence of decorating impurities on the minority carrier lifetime has its origin in the attraction of minority carriers by the long-range electric fields of the dislocation and in the strong overlap of the deep impurity states with the shallow one-dimensional (1d) states, both of which exist in the dislocation strain field [3]. In silicon for solar cells, processes like phosphorus diffusion gettering (PDG) or aluminum gettering (AlG), aim to improve the solar cell efficiency. The above considerations show that such gettering processes should be able to significantly change the electrical properties of extended defects like dislocations, stacking faults, SiOx-precipitates, and grain boundaries, that have interacted with metallic impurities, oxygen, or carbon. The goal, one can hope to reach, is a purification of the extended defects from fast diffusing metallic impurities. This is a worthy goal, since there is good evidence now from EBIC and DLTS, that even slight decoration of extended defects by those impurities has a dramatic effect on their electrical properties and that e.g. clean dislocations have no EBIC contrast at room temperature [3] and almost no DLTS-signal. However, on the way to this goal four complex processes have to be quantified: (1) phosphorus diffusion (PD), (2) its effect on a homogeneous distribution of metallic impurities, either dissolved (M) or in precipitates, (3) the reaction between point and extended defects during annealing and more important during cooling, and (4) the effect of PD on a heterogeneous distribution of M. PDG applied to silicon for solar cells is composed of the action of these interconnected processes. Eight years ago Pe! richaud et al. [4] have demonstrated the complexity of that action, when they applied PDG to various materialsFPolix, Eurosolare, Silso, Semix, Cz wafers etc.Fand found that in some materials PDG leads to an improvement of the minority carrier diffusion length, in some not, and in some it even had detrimental effects. This result indicates a basic problem, when dealing with silicon for solar cells. In these materials PDG has to operate against a distribution of metallic impurities, which has been established in a process preceding PDG by relaxation during cooling, i.e. by segregation and precipitation at extended defects, where clouds of impurities, precipitates of silicide or even of silicate form, as has recently been observed [5,6].

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Furthermore, in solar cell processing PD is applied for gettering and at the same time for the formation of the front-side p–n-junction, whose operation should not be affected by the deposition of metallic impurities in the P-doped region. To match the competing requirements of effective gettering and of appropriate p–n-junction operation requires computer modelling of PDG which has been initiated recently. This paper provides a brief report on the status of this effort and on its near future problems.

2. Computer modelling of PDG: status Computer modelling is a tool to deal with complex systems, whose properties are too involved to be accessible by an analytic treatment. In order not to lose the physical significance of the model, the number of its free parameters has to be kept sufficiently small to arrive at a critical check of the model by comparing its results with experimental data and even come to predictions whose incompatibilty with experiment should lead to modifications of the model. By this strategy, physical parameters, which are relevant for the description of the experimental results, are distinguished from those that are of secondary importance. One may then hope to disclose the relevant physical mechanisms and to incorporate them into the computer model. To our present knowledge, the system Si/P has to be considered as a complex one as soon as the surface concentration ½PðsurfÞ exceeds a critical value ½PðcritÞ : This value is determined by the condition that the self-interstitial (I) generation by P-diffusion begins to outbalance the processes which bring [I] back to its equilibrium value. For ½PðsurfÞ > ½PðcritÞ ; diffusion of phosphorus becomes strongly coupled to nonequilibrium concentration of silicon interstitials and vacancies, which mathematically means the coupling of transport equations to rate equations describing nonlinear reactions. 2.1. Modelling of phosphorus diffusion Computer modelling of PD and PDG of Au in FZ-Si has already been presented at the EMRS meeting 1998 by Kveder et al. [7], wherefore we restrict ourselves to a brief summary of their results. The presently accepted model of PD has been proposed by Morehead and Lever [8] in 1986. The transport of positively charged substitutional phosphorus, PðþÞ s starts ðþÞ ð0Þ with the kick-out reaction: PðþÞ þ eðÞ -Pð0Þ through reaction s þI i ; whereby Ps with a silicon interstitial I ð0Þ and an electron is transformed into its highly mobile ðþÞ interstitial species Pð0Þ i : The back-reaction prevails in the region of low ½Ps  thus acting as a source of self-interstitials which diffuse into the bulk or to the surface, at which thermodynamic equilibrium is assumed to hold, i.e. ½IðsurfÞ ¼ ½IðeqÞ : In addition I-recombination with vacancies established local equilibrium. As soon as selfdiffusion (SD) cannot balance any more the P-diffusion induced I-generation, i.e. DðSDÞ oDs ½PðsurfÞ ; where Ds is the effective diffusion coefficient of P at the surface,

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non-equilibrium I- and V-concentration modify the P-diffusion. The critical value of ½PðsurfÞ at 9001C is ½PðcritÞ E3  1019 cm3. For ½PðcritÞ o½PðsurfÞ p½PðeqÞ ; where ½PðeqÞ is the solubility of P in Si (E3  1020 cm3 at 9001C) the concentration profiles of P after diffusion show a new characteristics, which has been called ‘‘kink and tail’’. In the computer model, ðÞ developed by Kveder et al. [7], a new mobile species (PðþÞ with an estimated s Þ2 V ðbÞ binding energy of E X2:5 eV has been proposed to describe the kink and tail profiles. Since silicon vacancies and interstitials are coupled, the two P-diffusion mechanism compete with each other. This makes the evolution of the systems Si/P strongly non-linear, especially in the early stages of P-diffusion. The relevance of this model has been demonstrated by fitting to experimental data. Experimental results, obtained with varying temperature and at variable values of ½PðsurfÞ in the range of 1019–3  1020 P-atoms/cm3, have been used to determine three parameters, viz. two effective diffusion constants of Pi and P2 V
DPi

½Pi ðeqÞ ½Ps ðeqÞ

ðint rÞ


 3:31 eV ¼ 6:4  102 exp  cm2 =s kT

and

ðint rÞ ½P2 VðeqÞ 3:01 eV 24 DP2 V ¼ ½Ps  5:25  10 exp  cm2 =s; kT ½Ps ðeqÞ respectively, and ½PðsurfÞ : Values for DI ½IðeqÞ and (DV ½VðeqÞ ÞðintrÞ have been taken from the literature. 2.2. PDG and segregation of Au in Si Gold and some other 4d- and 5d-transition elements dissolve in silicon mainly on lattice sites, i.e. as substitutional species Aus, and with a small fraction on interstitial sites as Aui, so that ð½Aui ðeqÞ =½Aus ðeqÞ Þðint rÞ 51: Aus is a slow diffuser, even on moderate quenching from high temperatures it stays as Aus, which for PDG in FZ-Si is a simple initial distribution of a metallic impurity. Diffusion of Au starts with a kick-out reaction, fast diffusion of Aui (D0 ¼ 2:4  104 cm2/s, migration energy QðmiÞ ¼ 0:39 eV) and ends with the back-reaction. One basic mechanism of PDG is segregation [9]. The solubility increase due to charged species and pairing of Aus with Ps contributes to the segregation coefficient S; which compares the solubility of all gold species at the surface with those in intrinsic silicon, S ðsurfÞ ¼ ð½AuðeqÞ ÞðsurfÞ =ð½AuðeqÞ Þðint rÞ : Aus has an acceptor level so that its concentration becomes dependent on the position of the Fermi level EF ; i.e. [Aus](eq)(EF,T). It also forms pairs with phosphorus, e.g. via the reaction ðþÞ ðÞ Auð0Þ 2ðPs Aus Þð0Þ þIð0Þ : i þPs þ e PDG of Au for ½PðsurfÞ p½PðeqÞ has been carefully studied experimentally by . Sveinbjornsson et al. [10]. The authors demonstrated that the gettering efficiency G :¼ ½AuðsurfÞ =½AuðbulkÞ is by more than two orders of magnitude larger than the

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segregation coefficient, estimated by means of available models for the Fermi level effect and for pairing [11–13]. . On the basis of the experimental results of Sveinbjornsson et al. [10], Spiecker et al. [14] have proposed and formulated one new and important gettering mechanism. It has been called the diffusion mode of injection-induced gettering. It results from the interaction of Aus with self-interstitials which are injected into the bulk by PD. It leads to a drift current of Au from the bulk to the P-doped layer, which is proportional to the total concentration of Au, [Au] and the gradient of selfinterstitial supersaturation, ½I=½IðeqÞ : This mechanism has been shown to be the key for understanding the large observed gettering efficiency G of up to 106, which is larger by a factor up to 100 than what has been estimated from the segregation coefficient SðsurfÞ [10]. . To arrive at a quantitative check by means of the data of Sveinbjornsson et al. [10], computer modelling of the interrelated processes of P-diffusion, segregation and injection-induced gettering has been developed and applied by Kveder et al. [7] and has revealed as a surprising point the important role of the cooling rate. Taking from the literature the binding energy E ðbÞ ¼ 0:87 eV for the (AusPs)-pairs, the acceptor level Ec  0:55 eV for Aus, and for the effective diffusion constant of Aui [15] ðeqÞ =½Aus ðeqÞ Þðint rÞ ¼ 6:7  103 expð1:21 eV=kTÞ cm2 =s DðeffÞ Aui ¼ DAui ð½Aui 

they have reproduced without further fitting parameters the P- and associated Au. profiles, which have been measured by Sveinbjornsson et al. [10]. However, as Kveder et al. [7] showed, the cooling rate had a striking impact on the profiles and therefore had to be explicitly taken into account.

3. PDG of Co in Si Different from Au, the 3d-elements (M) in Si have a much larger solubility on interstitial than on substitutional sites, i.e. ½Mi ðeqÞ =½Ms ðeqÞ b1 in intrinsic silicon. As a consequence, the dominating species of M dissolved in silicon is decoupled from the silicon interstitial supersaturation in the bulk. Does then PDG of these 3d-elements reduce to segregation or is there any experimental evidence that a further gettering mechanism is operative? The answer to the second question is yes, if PDG is applied under phosphorus surface concentration beyond the solubility limit, i.e. for ½PðsurfÞ > ½PðeqÞ ; giving rise to SiP-growth in the near-surface region [16]. Cross-section high-resolution electron microscopy has clearly shown for Ni [17], Fe [18], and Pt [19,20] that near to SiP particles at the Si/PGS interface silicide precipitates form. This ‘‘precipitation mode’’ of PDG has been shown to occur with the injection of silicon interstitials at the Si/ SiP interface. A possible mechanism has been derived from the coupling between local I-currents and cobalt on substitutional sites [21,22]. But it appears that also for PDG operating under the condition ½PðsurfÞ p½PðeqÞ and under oxidising conditions, so that a phosphorus silicate glass (PSG) layer grows on top of the Si-surface, the answer is probably yes. The experimental evidence has

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been obtained with Co in Si [22]. Due to the fact that 57Co is a radioactive isotope . suitable for tracer experiments and for Mossbauer spectroscopy, PDG of Co has been studied experimentally in some detail [23]. Preliminary estimates of the segregation [24] indicate that at 9201C the gettering efficiency exceeds segregation by a factor 10–100, which would imply the operation of a further new gettering mechanism. We have recently extended the computer model of PDG to Co in Si, assuming segregation as the dominant gettering mechanism, and compared the results with the experimental data. The results confirm that segregation is not the dominant gettering mechanism (see Section 3.2.2). However, the extension of our computer model to PDG of 3d-elements requires also to consider the mobilisation problem again, i.e. the transfer of metallic impurity (M) to its mobile species. For Au the initial state in the bulk is Aus, the mobile one is Aui, and PD establishes the supersaturation ½I=½IðeqÞ ; which controls the reaction between the two species. Due to their high diffusivity, some of the 3d-elements will not or only partly stay in solution during cooling from high temperatures and may then respond to PDG with a slow mobilisation rate. The latter can be affected by the supersaturation of self-interstitials in the bulk resulting from P-diffusion (see Section 2.2). A simple estimate can be derived from the volume change DV associated with the precipitation of interstitially dissolved metallic impurities, Mi ; as the silicide Mx Siy : (see Table 1). Assuming that the volume change is entirely accommodated by the emission or absorption of self-interstitials, the number a of self-interstitials produced (a > 0) per precipitated metal atom can be calculated (Table 1, last row) which finally allows to evaluate the driving force Dfa ¼ a kT lnð½I=½IðeqÞ Þ which add to the driving force Df ¼ kT lnð½Mi =½Mi ðeqÞ Þ for precipitate dissolution. Taking e.g. for T¼ 8001C; ½I=½IðeqÞ E100 one obtains for Fe Dfa E  0:05 eV/Featom indicating a slight stabilisation of FeSi2-precipitates, whereas for Cu Dfa E0:23 eV/Cu-atom=2.5 kT, i.e. Cu3Si precipitate dissolution in the bulk may be enhanced by the I-supersaturation resulting from P-diffusion. Inspection of Table 1 shows that such interaction of silicide precipitates and self-interstitials are weak for all 3d-elements except for Cu. Please note, that mobilisation and gettering are two different phenomena. In the case of Au in Si, the PDG-induced I-supersaturation in the bulk mobilises Aus by the kick-out reaction. The increase of the gettering efficiency above segregation by one

Table 1 Volume change associated with the formation of silicide precipitates Mx Siy from interstitially dissolved metallic impurities, Mi

Silicide DV =V (%) a

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

TiSi2 6.9 0.138

VSi2 3.85 0.077

CrSi2 9.75 0.195

MnSi2 5.3 0.106

a-FeSi2 5.85 0.117

CoSi2 3.45 0.07

NiSi2 1.2 0.024

Cu3Si 150 0.55

DV =V denotes the relative volume expansion (DV > 0) or contraction (DV o0). a is the number of I emitted (a > 0) or absorbed (ao0) per precipitated metal atom. The disilicides from V to Ni show small volume contractions, whereas TiSi2 and in particular Cu3Si leads to a volume expansion.

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to two orders of magnitude has its origin in the I-current to the surface. In the case of Cu in Si, the PDG-induced I-supersaturation in the bulk assists the dissolution of precipitates, but I does not couple to Cui, the predominant dissolved species, so that for ½CuðinitÞ p½CuðeqÞ the I-current to the surface does not establish a gettering mechanism. 3.1. Redistribution of 3d-elements during cooling from high temperatures 3.1.1. Quenching from diffusion temperature We begin with a brief outline of possible distributions of M during cooling in a process step preceding PD. The 3d transition elements in silicon, when compared to shallow dopants, are characterised by deep levels, low solubilities, and high diffusivities (D(10001C) from about 109 to 104 cm2/s) with low migration enthalpies (from about 2 eV for Ti to 0.18 eV for Cu) [25]. Because of their small atomic volume, 3d-atoms fit rather well into the interstitial sites of the silicon lattice. The solubility of M in Si decreases exponentially with decreasing temperature and is negligibly small at room temperature. While Fe and the early elements in the 3d-row can be quenched-in on interstitial sites in FZ-Si, Co, Ni, and Cu even after fast quenching are found in pairs with shallow dopants, segregated at extended defects or precipitated in silicide particles [26]. When M in Si becomes supersaturated, large driving forces for precipitation are established with decreasing temperature and easily lead to formation of metastable precipitates [27]. Many industrial processes have as integrated part an anneal treatment followed by cooling with a rate b ¼ dT=dt: A useful parameter to estimate the distribution of 3d-atoms after cooling, is the diffusional range RðdiffÞ M ; defined as the mean distance an impurity moves from its initial position during cooling [26]. It is given by ! Z T ðsupÞ M QðmiÞ ðdiffÞ M b1 dT1=2 ; RM ¼ ½6 D0 exp  ð1Þ k T B T0 ðsupÞ where T0 and TM are the temperature to which the specimen is cooled, and the one at which the specimen enters into supersaturation with respect to the metallic impurity, respectively, D0 and QðmiÞ M are the pre-exponential factor and the migration barrier of the metallic impurity. In Table 2 we give in the last two rows values of the diffusional range for the 3dðsupÞ elements, assuming TM ¼ 8001C: Large quenching rates have to be applied if one wants to study Ti, V, Cr, Mn, and Fe as interstitial species and the early stages of precipitation, especially of Co, Ni, and Cu. For cooling rates of several K min1, applied also in industrial processing, still Ti and V will probably not precipitate, but might decorate extended defects like dislocation, if these have densities >107 and 106 cm2, respectively. For Cr, Mn, Fe etc. one expects to find precipitates that have undergone internal and also Ostwald ripening. However, whether for the small cooling rates the same metastable precipitates nucleate and grow, which are found after rapid quenching, or an alternative path evolves from the beginning, is an open

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Table 2 Pre-factor D0 and activation energy QðmiÞ for the interstitial (index: i) species of the 3d-elements in silicon Tii 2

D0 ðcm =sÞ QðmiÞ ðeVÞ RðdiffÞ ðmmÞ M b ¼ 103 Ks1 b ¼ 6 K min1

0.12 2.05

Vi 9  10 1.55

Cri 3

Mni 3

2.6  10 0.81

0.027 (+) 0.13(+) 5.0 2.7 13 500

Fei 4

Coi 3

Nii 4

Cui 3

6.9  10 0.63

1.3  10 0.68

9.7  10 0.37

2  10 0.47

7.5(+) 750

7.6 760

44.6 (+) 4500

34(+) 3400

3  104 0.18 88.1 8800

has been calculated for an anneal treatment at 8001C and Using Eq. (1) the diffusional range RðdiffÞ M subsequent quenching with rates b ¼ 103 K s1 and b ¼ 6 K min1 to room temperature. In some cases the diffusion data had to be extrapolated (+).

question. At the moment, there are only two experimental results that indicate the first alternative to hold under many conditions. Co, Ni, and Cu precipitate as CoSi2, NiSi2, and Cu3Si, respectively. It has been shown that for rapid quenching they form metastable platelets [27], which in the case of NiSi2 are of 0.63 nm thickness. Each platelet empties a sphere of a radius R much smaller than the diffusional range RðdiffÞ M : The difference between the two radii may be explained by the assumption that nucleation of the silicide-platelets demands a significant supersaturation of M yielding a driving force [26] ! ðsupÞ ½MðT Þ M Dfchem ¼ kB T ðnuclÞ ln : ð2Þ ½Meq ðT ðnuclÞ Þ ðsupÞ has the meaning described for Eq. (1). ½Meq denotes the equilibrium TM concentration of M: The temperature T ðnuclÞ ; at which the platelets nucleate, may be estimated from the assumption that after nucleation a diffusional range of M of ðnuclÞ just R is needed: RðdiffÞ Þ ¼ R : Using Eq. (1) yields T ðnuclÞ and using Eq. (2) M ðT and the extrapolated solubility data for M; one may calculate Dfchem : For the system Si/Ni Dfchem E1:0 eV/Ni-atom has been obtained. This is an exceptionally large driving force compared to those realised in metallic systems. It has been shown that a stacking fault lowers the driving force necessary to nucleate the NiSi2-precipitate to about 0.8 eV/Ni-atom [28].

3.1.2. Quenching with a given impurity content When a specimen containing a certain concentration of a metallic impurity, say ½M0 ¼ 1013 cm3, is cooled or quenched from high temperatures, the temperature, at ðsupÞ which the specimen enters into supersaturation, TM ; and at which nucleation of the silicide precipitates may start, T ðnuclÞ ; depend on the solubility and its temperature dependence. The solubilities of the 3d-elements in silicon reach maximum values at high temperatures, which range from 1015 cm3 for Ti to 1018 cm3 for Ni and Cu, and below the eutectic temperature decrease exponentially with activation energies lying

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between 2.8 and 3.0 eV for Ti, V, Cr, Mn, Fe, and Co, and decrease to 1.68 eV for Ni and to 1.49 eV for Cu [26]. Due to their small solubility, Fe and Co come into supersaturation at higher temperatures than Ni and Cu. Therefore the RðdiffÞ M -values of Fe and Ni are now comparable, and one might wonder, why interstitial Nii cannot be quenched-in as isolated species, whereas interstitial Fei can. The answer is indicated in the last but one row of Table 3, where the diffusional range at room temperature during 1 h is given. Since the extrapolated solubility of all 3d-atoms comes to very small values of the order of a few atoms per cm3 at room temperature, the driving force is sufficiently high for silicide nucleation. However, interstitial Ni and also Co and Cu have a sufficient diffusivity to respond to it, while interstitial Fe and the 3d-elementes on the left to it have not. The last row gives the mean displacement of the interstitial 3d-elements during an anneal treatment at 8001C for 30 min. As one sees, there is hardly any chance to remove Tii and Vi from a wafer by PDG or by Al-gettering. This implies that utmost care should be taken to avoid the incorporation of Ti and V during growth of crystalline silicon for solar cells. For Cr, Mn, and Fe, PDG has to be carefully designed if purification of the whole wafer is needed. 3.2. Computer modelling of PDG of Co in FZ-Si 3.2.1. Estimates of the segregation coefficient Values for the segregation effect have been derived by extrapolation of solubility data obtained for P-doped silicon (½P ¼ 1  1020 cm3 at T¼ 7001C and 8001C) [31]. A solubility enhancement from 1  1014 Co-atoms/cm3 at 9201C in the wafer to about 1016 Co-atoms/cm3 in the highly P-doped region (½P ¼ 3  1020 cm3) is expected by the Fermi level effect and the presence of P as a second solute, which corresponds to a segregation coefficient of SðsurfÞ E102 : This increase of the total cobalt concentration has been attributed to substitutional cobalt, Cos with at least one acceptor level, and to CosP-pairs [31]. Table 3 ðsupÞ ; at which the equilibrium For silicon containing 1013 cm3 of a 3d-element M the temperature TM ðsupÞ 3 eq 13 concentration is equal to this value, i.e. ½M ðTM Þ ¼ 10 cm (row 1) the range RðdiffÞ M ; which the ðsupÞ metallic impurity M diffuses during quenching with rate b ¼ 1000 K s1 from TM to room temperature (row 2), and the root of the mean square displacement of M for 1 h at room temperature (row 3) and for 30 min at 8001C (last row) are given Tii

Vi

Cri

Mni

Fei

ðsupÞ TM (1C) 1054 1134 920 828 845 RðdiffÞ quench (mm) 0.32 1.2 8.5 8.4 9.2 M

Coi 825 47.6

Nii 491 9.0

Cui 426 36.8

ð2DtÞ1=2 (mm) and (number of M-atoms within this range) 201C, 1 h 0.083 (o1) 29.0 (1 0 6) 6.0 (9050) 638 (1.1  1010) 8001C, 30 min 3.2 13.0 383 522 547 2530 2110 3930

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The gettering efficiency of PDG for Co in Si has been found to depend sensitively on the boundary conditions of P-indiffusion. Using a gas mixture of N2, O2, and POCl3, the relation between the gas composition and the ratio Q=Qel of the total amount of phosphorus Q; brought into the silicon specimen, to the electrically active part of it, Qel has been systematically investigated and is available in the literature [29]. Appropriate choice of the gas composition allows to adjust ½PðsurfÞ ¼ ½PðeqÞ with Q=Qel ¼ 1 without a PGS-layer growing on the silicon surface. Under this condition ½CoðsurfÞ ¼ 1:5  1017 cm3 after 108 min of PDG at 9201C has been found. For Q=Qel > 1 a phosphorus glass layer (PGS) grows on top of silicon. The profile of the electrically active phosphorus, ½Pel ðzÞ; as determined by resistivity measurements, has been observed to exhibit a plateau at the level ½Pel E½PðeqÞ : For Q=Qel ¼ 2:3 the cobalt concentration at the Si/PGS interface increases to ½CoðsurfÞ E1:4  1018 cm3. While in the case of Q=Qel E1 the concentration profile of cobalt follows that of phosphorus, the cobalt concentration for Q=Qel E2:3 was found to decrease rapidly within the plateau region. These results show that for PDG of Co with Q=Qel E2:3 at 9201C the gettering efficiency surmounts the estimated segregation coefficient by about two orders of magnitude. It also surmounts the value of G measured for Q=Qel E1 by more than one order of magnitude. Comparison of the values of the gettering efficiency G for Q=Qel E1 and for Q=Qel E2:3 strongly hints to an important role of the inactive phosphorus or of processes related to it for the gettering mechanism responsible for effective gettering beyond segregation. However, strong gettering with ½CoðsurfÞ X1018 cm3. has been also observed for Q=Qel E1; if at the same time oxidising conditions induce the growth of a PGS-layer on top of the silicon surface. We have treated this case by computer modelling of PDG as described in the next section. 3.2.2. Computer modelling of segregation of Co during PDG We have applied our computer model, which has been developed for PD and for segregation of Au under PDG, to Co in Si. We make use of the fact that the number of acceptor levels for Cos and the pairing reaction between phosphorus and Cos have been studied experimentally and theoretically. These data are needed as input for computer modelling of segregation. Measured data have been taken from Kuhnapfel . et al. [30], who state that they have adjusted the activity of oxygen and phosphorus so that all phosphorus becomes dissolved, which is a basic presupposition for the application of our computer modelling of PD (see Fig. 1). They have also measured . Mossbauer spectra of the gettered Co-species, which will be used to critically check the results of our computer modelling. As has been outlined in Section 3.1.1, Co cannot be quenched-in as a solute, but precipitates during or after quenching. The dissolution of the precipitate is then the first step of PDG and is followed by diffusion of Coi. The final step is the transition into the segregated state. If the gettering layer is established quickly, like e.g. for AlG, one of those steps will determine the time development of gettering. There is some evidence that the dissolution of precipitates might become rate-limiting, especially for silicon containing extended defects. However, it was shown by Kveder et al. [7] that for FZ-Si PD is the slowest compared to all steps, in which Coi takes part.

Concentration [cm-3]

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21

10

20

10

19

309

PS

18

10

(P2 Co)

17

10

16

10

CoS

15

10

14

10

13

10

Co I

12

10

0.0

0.2

0.4 Depth [µm]

0.6

Fig. 1. Comparison between measured phosphorus (’) and cobalt profiles ( ) with the results of computer modelling of segregation (F) (see text). Initial cobalt concentration ½CoðiniÞ ¼ 4  1014 cm3, PDG: gas mixture: 99.59 vol%+N2+0.13 vol% POCl3+0.28 vol% O2, Q=Qel ¼ 1 (TEM: no SiPprecipitates), thickness of phosphorus glass layer: B60 nm, T¼ 9201C; t ¼ 54 min, rapid quenching in ethylene glycole, autoradiographic imaging shows homogeneous distribution of 57Co parallel to the Si/ . PSG interface, Mossbauer spectroscopy of gettered Co shows a SL (isomer shift: 0.51 mm/s) and a QD (isomer shift: 0.19 mm/s, splitting: 0.55 mm/s).

For computer modelling of the segregation of Co during PDG, we have taken, following conclusions drawn from experimental results [31], three acceptor levels to be associated with Cos. We have assumed that their positions are at Ec 20:43 eV, Ec 20:37 eV, and Ec 20:12 eV. Their sum determines ½Cos ðeqÞ and has been chosen to adjust to the value of ½Cos ðeqÞ ; which has been measured for ½Ps E1020 cm3 [32]. To agree with the measured prefactor of the pairing reaction, we have to assume (P(+))2Co(3) as the dominant pair. Please note that the concentration of these pairs s is related to the phosphorus concentration by a power law ð½PÞ5 : Fig. 1 presents measured concentration profiles of electrically active phosphorus ½Pel ðzÞ (data points) and of associated profiles of the total cobalt concentration [Co](z). The results of our computer model for the PD andFadjusted to the dataFfor the segregation of cobalt are shown as full lines. Using the computer generated P-profiles, the measured concentration profiles of Co are approximately reproduced by our model. The value obtained by us for the total cobalt concentration at the Si/PGS interface differs from the experimental value by about a factor 2.5.

4. M.ossbauer spectra of gettered Co-species The large segregation coefficient in our model is mainly caused by (P2Co)-pairs, whose concentration, being of the order of [Cos] for ½PE1020 cm3, is expected

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to grow fast with increasing phosphorus concentration according to . ½P2 Cos =½Cos B½Pel 2 : The gettered Co-species have been studied by Mossbauer spectroscopy, using 57Co as a radioactive isotope, which decays into an excited state 57 . of the Mossbauer-isotope Fe with half-life of 270 days. Cobalt in cubic surrounding is expected to exhibit a single line (SL), cobalt–phosphorus pairs a quadrupole doublet (QD). Kuhnapfel . et al. [30] have measured for the specimen, whose data have been used . by us for computer modelling, Mossbauer spectra up to a depth of about 200 nm, i.e. in the range of the P-plateau (B170 nm). They measured spectra before and after removal of a layer of thickness 35 nm and subtracted them from each other to obtain the first points. Deeper lying points represent the mean taken over a larger thickness. The resulting spectra have been fitted simultaneously to one QD (isomer shift: 0.19 mm/s, splitting: 0.55 mm/s) and one SL (isomer shift: 0.51 mm/s). If one associates the QD with (CosP2)-pairs and the SL with Cos, one finds the ratio [CosP2]/[Cos]E2 for the first 35 nm and a decreasing value to about 0.5 at 200 nm. We note that Kuhnapfel . et al. [30] have adjusted the boundary conditions by appropriate choice of the gas mixture (see caption of Fig. 1) to ½PðsurfÞ p½PðeqÞ ; so that Q=Qel E1; and to the growth of PSG on top of Si. They mention that associated to PSG-growth they find a plateau of ½Pel -profile at (2–3) 1020 P-atoms/cm3 and claim that PSG-growth as well as the formation of the plateau are necessary conditions for effective gettering with ½CoðsurfÞ X1018 cm3. Using transmission electron microscopy they have checked that no SiP-growth has occurred. They also have performed PDG of Co under ½PðsurfÞ > ½PðeqÞ ; i.e. Q=Qel > 1 and with SiP . growing inward from the Si/PSG-interface. They have observed the same Mossbauer lines as for the specimen without SiP-growth and find as the main difference that now the intensity of the QD is much larger than that of the SL. In addition they have observed two SLs within the first 35 nm to the interface which represent about 30% of the total gettered Co-amount. Kuhnapfel . et al. [30] have already noted that the quadrupole splitting measured in Si doped with 1020 P-atoms/cm3 by Gilles et al. who associated it with Co-P pairs, is about 50% larger than the value they found for Co after PDG. Two years later, Utzig [32] has given an alternative interpretation of the QD. He has studied Cz–Si and FZ-Si with phosphorus doping levels between 1  1015 and 2  1018 P-atoms/cm3, into which Co had been diffused at around 11001C and which had been quenched with a rate of about 103 K s1 to room temperature. . The Mossbauer spectra of these specimens showed a SL, whose position is different from that observed by Kuhnapfel . et al. [30], and a QD, which agrees in all parameters with that observed by Kuhnapfel . et al. Utzig [32] showed by annealing experiments and comparison with high-resolution electron microscopic data for Si/Ni that the QD, which he measured, and which is identical to that observed by Kuhnapfel . et al. [30], is caused by Co in the Si/CoSi2 interface of thin CoSi2platelets, and the SL by Co inside the platelets. This identification is based on the observation of an irreversible transformation of the QD into the SL on annealing between 2001C and 6001C (see Fig. 3a), while Gilles

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. Fig. 2. (a) Mossbauer spectra of 57Co in Si+1020 P-atoms/cm3 show a SL (isomer shift: 0.45 mm/s) and a QD (isomer shift: 0.11 mm/s, splitting: 0.79 mm/s) [31]. From the resonance area the concentration CSL and CQD of the associated Co-species are obtained. On annealing a reversible transformation between two species has been observed, yielding: CQD =CSL ¼ 4:2  107 expð1:5 eV=kTÞ: (b) The two species, represented by the SL and by the QD in Fig. 2a, have been identified by Gilles et al. [31] as substitutional cobalt Cos (SL) and cobalt–phosphorus pairs CosPn (n: number of P-atoms in the pair). For comparison, the concentration of Co(0) i , as given by the solubility of Co in intrinsic Si, is also shown (Courtesy of Gilles et al. [31]). These values and their variation with P-concentration significantly disagree with the results of our computer modelling of segregation, which yield [CosP2]/[Cos]b1 near the Si/PSG interface and also at a depth of 200 nm.

et al. have observed a reversible transformation between the two Co-species associated with their lines (see Fig. 2a). Co and Ni in Si, both precipitate during cooling from high temperature into MSi2platelets (M=Ni, Co), having the CaF2 structure with a misfit of their lattice constant to that of Si by less than 1.2% (see Table 1). After rapid quenching (X500 K s1) the platelets consist of only two (1 1 1)-planes, coherently embedded into the Si-matrix, and therefore are metastable. As has been investigated in some detail for the system Si/Ni, on annealing these thin platelets undergo an internal ripening, whereby they become more compact without changes in their density. The irreversible transformation found by Utzig [32] exhibits all features known of internal ripening (see Fig. 3).

5. Summary Summarising, we have used computer modelling to calculate the segregation of Co by PDG. Taking measured P-profiles as input we have reproduced satisfactorily measured Co-profiles. Our model predicts cobalt–phosphorus pairs to be the predominant gettered Co-species. However, this result is inconsistent with . Mossbauer spectra, measured for the same specimen. They show that two Cospecies, one giving rise to a SL, one to a QD have comparable concentration near to

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. Fig. 3. (a) Mossbauer spectra 57Co in FZ-silicon, as obtained by quenching the sample after in-diffusion of Co at 11001C, show one SL (isomer shift: 0.015 mm/s) and a QD (isomer shift: 0.18 mm/s, splitting 0.55 mm/s) [32]. After quenching the Co-species, associated with QD1, represents about 99% of the total cobalt concentration. Annealing at temperatures between 2001C and 6001C leads to an irreversible transformation of a part of this species to that associated with the SL. (b) Utzig [32] has identified the Cospecies, yielding QD1, with Co in the Si/CoSi2 interface of the thin platelets, and that, yielding SL, with Co inside the CoSi2-platelets. The irreversible transformation has been also observed in the system Si/Ni by high-resolution electron microscopy and has been called internal ripening. Thin platelets become thicker, thereby reducing their self-energy (courtesy of Utzig [32]).

the Si/PGS interface. The QD, associated by the authors tentatively with CoPn-pairs (n remained undetermined), has later been shown to have its origin in thin CoSi2platelets. The PD induced silicide formation has been indeed observed by high-resolution electron microscopy for Ni, Fe, and Pt under the condition of SiP-growth ð½PðsurfÞ > ½PðeqÞ Þ: It occurs at the Si/PSG interface near to the SiP-precipitates. As a possible mechanism local I-currents and their coupling to Ms have been discussed. From the comparison of computer modelling with experimental data it follows that this gettering mechanism is very effective and also works without electrically inactive phosphorus ð½PðsurfÞ o½PðeqÞ Þ under the condition that a PSG-layer grows on top of the silicon. Quantitative modelling of PDG in this regime has to incorporate the PSG-layer growth and in a further step the case of high phosphorus concentration ð½PðsurfÞ > ½PðeqÞ Þ; which is a field of actual theoretical and experimental research [33,34].

Acknowledgements We gratefully acknowledge financial support by the BMBF under contract No. 0329743C and the BMWi under contract No. 0329858B/1.

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