Oxygen and carbon transfer during solidification of semiconductor grade silicon in different processes

Journal of Crystal Growth 210 (2000) 541}553

Oxygen and carbon transfer during solidi"cation of semiconductor grade silicon in di!erent processes P.J. Ribeyron, F. Durand* INP Grenoble and CNRS, EPM-Madylam, ENSHMG, BP 95, 38402 St Martin d'Heres, France Received 1 September 1999; accepted 6 December 1999 Communicated by M.E. Glicksman

Abstract A model is established for comparing the solute distribution resulting from four solidi"cation processes currently applied to semiconductor grade silicon: Czochralski pulling (CZ), #oating zone (FZ), 1D solidi"cation and electromagnetic continuous pulling (EMCP). This model takes into account solid}liquid interface exchange, evaporation to or contamination by the gas phase, container dissolution, during steady-state solidi"cation, and in the preliminary preparation of the melt. For simplicity, the transfers are treated in the crude approximation of perfectly mixed liquid and boundary layers. As a consequence, only the axial (z) distribution can be represented. Published data on oxygen and carbon transfer give a set of acceptable values for the thickness of the boundary layers. In the FZ and EMCP processes, oxygen evaporation can change the asymptotic behaviour of the reference Pfann law. In CZ and in 1D-solidi"cation, a large variety of solute pro"le curves can be obtained, because they are very sensitive to the balance between crucible dissolution and evaporation. The CZ process clearly brings supplementary degrees of freedom via the geometry of the crucible, important for the dissolution phenomena, and via the rotation rate of the crystal and of the crucible, important for acting on transfer kinetics. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: Crystalline silicon; Solidi"cation; Crystal pulling; Oxygen; Carbon

1. Solidi5cation processes, solute distribution in the product Silicon is presently the basic material for the electronics industry, mostly because of its suitability in the manufacture of integrated circuits by surface treatment on thin crystal wafers, cut from massive silicon blocks called `ingotsa. The quality criteria concerning the as-grown material refer to

* Corresponding author. Tel.: #33-4-7682-5213; fax: #334-7682-5249. E-mail address: [email protected] (F. Durand)

impurity contents (typically oxygen and carbon in the ppma level, and metallic impurities in the ppba level) and to extended crystal defects [1}5]. In particular, it is admitted that metallic atoms are shared between oxide precipitates, preferentially. The rest could form agglomerates with point defects, mainly silicon self-interstitial or vacancies. Therefore, the space distribution of electrical defects seems to be dependent on the distribution of oxygen and carbon. The rapid expansion of the market for silicon products, integrated circuits and also photovoltaic cells, has stimulated several projects to create new industrial lines for producing massive silicon, single

0022-0248/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 9 ) 0 0 8 7 8 - 7

542

P.J. Ribeyron, F. Durand / Journal of Crystal Growth 210 (2000) 541}553

Nomenclature A 1 A} ab R ,R C3 1 ¸ ¸ 0 C a U} ab < L v Z CH, CH L S C F C 0 C 00 D L d} ab k} ab

area of the cross section of the product area of exchange between a and b phases radius of the crucible, of the cross section of the product length of the product ingot length corresponding to the initial melt volume volume concentration of the solute in the a phase #ow rate of exchange between a and b phases volume of the liquid zone solidi"cation rate length of the solidi"ed zone value of the solute concentration at the interface position feedstock concentration initial concentration of the liquid zone initial solid concentration di!usion coe$cient of the solute in the liquid phase thickness of the boundary layer at the a/b interface mass #ow coe$cient at the a/b interface

crystal or multicrystalline. The present paper aims to compare four solidi"cation processes in terms of solute transfer and distribution in the crystal. Silicon single crystals made with the #oating zone technique (referred to as FZ) are known to have the lowest impurity content (approximately 0.2 ppma O and 0.2 ppma C [4}6]). Most silicon single crystals are produced by Czochralski pulling (CZ), which gives a higher level of oxygen (20}30 ppma [4,5]), with carbon remaining low (0.2 ppma [4]). A large number of photovoltaic cells are made from multicrystalline silicon obtained by unidirectional solidi"cation (1D-Soldn) [7}9]. In the same "eld of application, the electromagnetic continuous pulling process (EMCP) is presently in the industrial development stage [10}12]. In this recent process, multicrystalline billets are continuously pulled down from a molten zone heated by induction in a cold crucible, which is fed with raw silicon in granular form. This process o!ers the advantages of cleanliness, lower costs, and continuous processing. These four processes will be compared with respect to the distribution of impurities in the solidi"ed products. The distribution of oxygen in CZ products is a well-documented subject. Di!erent steps are to be

considered [4,13}15]: (a) Feeding from the raw material, continuous or batch. (b) Incorporation in the solidi"ed product via the solid}liquid interface. (c) Possible evaporation via the free surface. (d) Possible contamination from the container. Carlberg "rst [13] published a model based on phenomenological solute balances incorporating the above four steps. Kim and Langlois [14,15] established a numerical model for #uid #ow and mass transfer, more particularly oriented towards the e!ect of a static magnetic "eld. Concerning the kinetics of silica dissolution, Chaney and Varker [16] measured the diameter reduction of a silica rod dipped into a silicon melt. They concluded on a dissolution #ow rate of 1.0]1020 at m~2 s~1. Zulehner and Huber [17] mentioned an e!ect of the gas pressure in CZ conditions. From their measurements, we will take a dissolution #ow rate of 1.11]1020 at m~2 s~1. Moreover, silica crucibles used in 1D-solidi"cation can receive a protective coating (Si N or other) 3 4 which strongly reduces the dissolution. The information is much scarcer concerning carbon. This element exists in the raw material source

P.J. Ribeyron, F. Durand / Journal of Crystal Growth 210 (2000) 541}553

at a low level (0.2 ppm [18]), mainly from the ethylchlorosilanes which are common impurities in silanes [19]. A further important source of C may also be the graphite parts of the heating apparatus. In the 1960s, it was mentioned that C in the gas phase can be transported to molten silicon, resulting in tiny SiC crystallites coating the surface of the crystal [5]. This can make twinning and polycrystalline growth near the end of the ingot [3]. However, improvements in the pulling equipment using a well-de"ned stream of inert gas have led to reduction in the level of the carbon contamination to a value approaching 0.2 ppma or less [5]. Concerning the relevant phase equilibria, there is a general agreement on the solubility in solid silicon of oxygen [2] and of carbon [5], but the results on their solubility in liquid silicon are somewhat dispersed. We have adopted the values given in Table 1. This present paper deals with the space distribution of oxygen and carbon resulting from four solidi"cation processes, FZ, EMCP, CZ and 1Dsolidi"cation. The objective is to establish the minimum set of parameters that are necessary for representing the solute transfer involving the liquid phase. These transfers are indicated schematically in Figs. 1}4. Each solute is treated separately. A balance taking into account the di!erent transfer phenomena is established and integrated to predict the axial distribution.

543

Fig. 1. Czochralski pulling (CZ).

Fig. 2. 1D-ingot solidi"cation (1D-soldn). Table 1 Physico-chemical data

2. Analysis of the solidi5cation process Oxygen [O] F [O]%2 S [O]%2 L kO9 %2 DO9

5 ppma 44 ppma 63 ppma 0.698 3.3]10~8 m2 s~1

[17] [2] [20] [20] [21]

Carbon [C] F [O]%2 S [O]%2 L kC %2 D#

0.80 ppma 9 ppma 261 ppma 0.034 2]10~8 m2 s~1

[17] [5] [22] [22] [21]

2.1. Solute balance of the liquid zone For each solute species, an overall balance of the transfers between the liquid zone and its neighbouring phases is established. This balance is expressed in a di!erential equation which is integrated, taking into account the peculiarities of the di!erent processes. In all the considered cases, the product is a block of solid silicon (index S), in the form of a cylinder with a constant cross section (area A , radius R , 1 1 length ¸).

544

P.J. Ribeyron, F. Durand / Journal of Crystal Growth 210 (2000) 541}553

The solid is produced from a liquid (index L), which can be fed from a feed stock (index F) in the form of a rod for FZ, and in the form of granules for EMCP. The liquid can be in contact with a container (index Cr, crucible, in CZ and in 1D Ingot), and with a gas phase (index G). The composition is represented by volume concentration of the solute in the phase C (a"L, S, G). a The transfer from phase a to phase b involves the exchange area A } , and the solute #ow rate ab / } per unit surface. The overall solute balance of ab the liquid (volume < ) is expressed as follows: L d (< C )"A } / } #A } / } C3 L C3 L FL FL dt L L

Fig. 3. Floating zone (FZ).

!A } / } !A } / } . (1) LS LS LG LG This solute balance will be applied only to the steady-state regime, then the solidi"cation rate l is constant. The progress of the solidi"cation process is measured by the solidi"ed length Z. Therefore, the time increment dt is replaced by: dZ dt" . v

(2)

This balance will be applied to the four solidi"cation processes (CZ, 1D Ingot, FZ and EMCP) with the following remarks: (a) FZ and EMCP are continuous processes. In steady-state regime, < is constant. L (b) CZ and 1D-soldn are batch processes during which < and also A } decrease regularly. L C3 L (c) There is no crucible contamination in FZ and in EMCP. 2.2. Transfer at the solid}liquid interface This is a reactive interface moving with respect to the material at the pulling rate l. The liquid layer of composition CH is transformed into a liquid layer L of composition CH. Here we recall in some detail S the arguments leading to the e!ective distribution coe$cient k [23]. First the di!usion into the %&& solid is neglected (assumption H1). Therefore, the interfacial concentration is frozen in as the local solid concentration C , which is the reference variS able: Fig. 4. Electromagnetic continuous pulling (EMCP).

CH"C . S S

(3)

P.J. Ribeyron, F. Durand / Journal of Crystal Growth 210 (2000) 541}553

The considered system is the liquid zone. The solid is extracted from the liquid with the velocity !l, resulting in a solute transport #ux (per unit surface): / } "vC . (4) LS S Assumption H2 is that the compositions of the solid and liquid layers at the interface are related by the equilibrium distribution coe$cient:

2.4. Transfer at the container wall In this section, we consider the solute transfer from the container to the liquid resulting from dissolution. Here the dissolution rate is not a controlled parameter. This is usually formulated through a mass transfer coe$cient de"ned as follows: / } "k } (C !C ). (10) C3 L C3 L C3 L / } can be interpreted in terms of boundary layer C3 L thickness related to the convective #ow conditions:

(5) CH"k CH. S %2 L This relation gives the concentration of the interfacial liquid. Assumption H3: the bulk liquid is perfectly mixed (mean concentration C ), except a boundary L layer of thickness d } , through which the solute is SL submitted to steady-state di!usion from CH to C . L L For

D k } " L . C3 L d } C3 L

z"d } , C"C . (6) SL L k , the e!ective partition coe$cient, is de"ned by %&& CH k " S. (7) %&& C L It is related to the solidi"cation conditions by [23]:

Si(L)#O(L)NSiO(G).

A

B A

B

1 1 !ld } SL . "1# !1 exp (8) D k k L %&& %2 k will take a value in the range from k to 1 %&& %2 according to the value of the monomial ld } /D . SL L For oxygen, this range is relatively narrow (from 0.698 to 1). It is larger for carbon (from 0.034 to 1). 2.3. Transfer at the feeding interface in FZ and in EMCP At this interface, the material is submitted to melting and dilution. What is controlled is the mass #ow rate and the feed-stock concentration C . We F make assumption (H4) that the melting interface has the same area A as the solidi"cation interface. 1 The solute transport #ux from feedstock to liquid, per unit area, is / } "vC . FL F

(9)

545

(11)

2.5. Transfer from liquid to gas phase 2.5.1. Case of oxygen transfer The transfer to gas phase is performed in the form of SiO molecules. This involves an interface reaction

We can consider that the step of evaporation at the free surface is rapid compared to the step of di!usion through the free surface boundary layer (thickness d } ), which is determining the rate. LG Therefore, we use a mass transfer coe$cient k } , in LG the same approximation as in Section 2.4 above: / } "k } (C !C } ) LG L LG LG with

(12)

D k } " L . (13) LG d } LG In our applications, we consider d } and LG C } as parameters. LG 2.5.2. Case of carbon transfer in a carbon-lean atmosphere Here again an interface reaction is needed: C(L)#O(L)NCO(G). Referring to a crude application of the reaction rate theory, the evaporation rate of the carbon

546

P.J. Ribeyron, F. Durand / Journal of Crystal Growth 210 (2000) 541}553

species should be of the order of (XL )/(XL ) smaller S* C than the evaporation rate of oxygen. Consequently it will be considered as negligible. 2.5.3. Case of carbon from a carbon-rich atmosphere As mentioned above, in the absence of a welldesigned argon gas circulation system, SiC particles can be observed on the surface of Si products solidi"ed in the presence of graphite components. In this case, Eq. (12) will be used with C } corresponding LG to saturation with respect to SiC, i.e. C } " LG 261 ppma (Table 1).

3. Solute balance for a molten zone of constant volume In this section, we consider a liquid zone of constant volume, which is representative of the FZ or EMCP processes in steady-state pulling conditions. We assume that its height H is constant: < "A H. (14) L 1 There is no contamination from the crucible (EMCP), or there is no crucible at all (FZ): / } "0. (15) C3 L The overall solute balance of the liquid zone is given by Eq. (1), taking into account Eq. (2) for steady state, and Eq. (14) for constant volume. The interfacial #ow rates are given by Eqs. (4), (9) and (12). C is expressed as a function of C L S using Eqs. (7) and (3). The solute balance for the liquid zone of constant volume is expressed as follows: dC k S " %&& dZ C !bC H ! S with k } A } b,1# L G L G k l A %&& P and A } k } C "C # L G L G C } . ! F LG A l 1

(16)

The liquid zone can have an initial composition C di!erent from C . Therefore Eqs. (16a) and 0 F (16b) is integrated from (Z"0, C "k C ) to S %&& 0 (Z, C ): S C !bC bk Z ! S "exp ! %&& . (18) C !bk C H ! %&& 0 For the particular case in which the initial liquid is noncontaminated (C "C ) and has no ex0 F changes with the gas phase (A } "0 or k } "0), LG LG by integrating Eqs. (16a) and (16b) from (Z"0, C "k C ) to the situation (Z, C ), Eq. (18) comes S %&& 0 S to the classical Pfann law for zone melting [24]:

A

A

(16b)

B

C k Z S "1!(1!k ) exp ! %&& . (19) %&& C H F The general solution Eq. (18) has the same exponential form as the Pfann law. Nevertheless, the characteristic length is modi"ed by the coe$cient b which represents the evaporation e!ect.

4. Solute balance for a batch solidi5cation process (CZ, 1D solidi5cation) The liquid volume decreases when solidi"cation proceeds: < "A (¸ !Z). (20) L 1 0 Moreover, the contact area between liquid and container also decreases: Z A } "A !2A . (21) C3 L 0 1R C3 There is no feeding (/ } "0). As in the precedFL ing case, C is expressed as a function of C . So the L S solute balance of the liquid zone (Eq. (1)) in steadystate solidi"cation (Eq. (2)) is expressed as follows:

A

(16a)

B

A

B

A } / } A } k } dC " C3 L C3 L k # (1!k )! L G L G S %&& A v %&& A v P P dz A } k } ]C # L G L G k C } . (22) S A v %&& L G (¸ !z) P 0 In the general case, Eq. (22) is integrated numerically because A } is a function of Z. C3 L Limit case: No evaporation (k } "0), no disLG solution phenomena (k } "0). Eq. (22) can be C3 L

B

P.J. Ribeyron, F. Durand / Journal of Crystal Growth 210 (2000) 541}553

integrated in the form of the Gulliver}Scheil equation [25,26], using k as partition coe$cient: %&& C Z S "!(1!k ) ln 1! ln (23) %&& C ¸ 00 with C "k C , C concentration of the initial 00 %&& 0 0 melt.

A B

A

B

5. Calculation of the initial melt concentration

d } ). The concentration at the graphite}liquid LS interface is the saturation concentration CH" L 261 ppma (Table 1). The solute balance of the liquid is expressed as follows: D L (CH!C ) dt"H dC . (27) L L d } L LS This equation is integrated from (t"0, C " L C ) to (t , C ): F 1 0 CH!C D L 0 "exp ! L t . (28) CH!C Hd } 1 L F LS

A

5.1. Oxygen dissolution in the initial CZ melt The initial melt concentration C is not equal to 0 C because even during the melting of silicon, siliF con reacts with the crucible material made of vitreous silica. The solute balance (Eq. (1)) is applied to the melting step (l"0):

547

B

6. Application to published data 6.1. Choice of the geometrical and hydrodynamic parameters

(26)

The above model is applied to make a comparison between the four processes (EMCP, FZ, CZ, 1D-soldn). The solidi"cation product is represented by a cylinder of length ¸ (1000 mm for EMCP or FZ, 500 mm for CZ [17,21], 250 mm for 1D-soldn. The section of the cylinder is usually circular in FZ and in CZ, preferably square in 1D-soldn and in EMCP, but the calculations are made for a circular geometry. For FZ or EMCP, the signi"cant geometrical parameters are H and A } /A only. H is LG 1 usually larger in the EMCP than in the FZ process (Table 2). In the CZ process, application of Eqs. (20)}(22) requires values for ¸ , A , R , A } / 0 0 C3 C3 L A , A } /A . They were derived from Fig. 1 from 1 LG 1 Ref. [17] and from Tables 2 and 3 from Ref. [21]. Concerning the mass transfer parameters, in the CZ and FZ processes, d } depends on the rotation LS rate u according to the theoretical law of a disk rotating in a semi-in"nite liquid [23]:

In the EMCP process operated in the P3 procedure [12], the initial liquid zone is formed by melting feedstock granules (C ) in contact with a graphite F base. Carbon is assumed to contaminate the liquid by transfer through a boundary layer (thickness

(29) d } "1.6 D1@3l1@6u~1@2. L LS l is the kinematic viscosity of liquid silicon (1.06]10~6 m2 s~1 [27]), and D the di!usion coL e$cient of the solute (Table 1). Considering the transfer of oxygen from the silica crucible to the liquid, we will take / } " C3 L 1.11]1020 at m~2 s~1 [17]. The presence of a coating will be represented by an arbitrary reduction of the total #ow rate.

d < (C )"A } / } !A } k } (C !C } ). L dt L C3 L C3 L LG LG L LG (24) This equation is integrated from (t"0, C " L C ) to the current time (t, C ). The solution is F L analytical and has the classical exponential form:

A

B

/ } C3 L k } LG A } / } # C !C } ! C3 L C3 L F LG A } k } LG LG k } A } ]exp ! L G L G t . < L C is the following asymptotic value: 0 A } / } C "C } # C3 L C3 L . 0 LG A } k } LG LG A } C " C } # C3 L L LG A } LG

A

A

B

B

(25)

5.2. Carbon contamination of the initial EMCP liquid zone

548

P.J. Ribeyron, F. Durand / Journal of Crystal Growth 210 (2000) 541}553

Table 2 Parameters used for the calculations (value by default, in absence of ad hoc speci"ed values)

v R 1 ¸ H ¸ 0 A 1 A } LG A } C3 L A } /A C3 L 1 A } /A LG 1

Identi"cation

Unit

EMCP

FZ

CZ

1D-soldn

Casting rate Product size Product length Liquid zone height Initial liquid height

mm/min mm mm mm mm (cm)2 (cm)2 (cm)2

1 60 1000 120

1 60 1000 50 * 113 188 0 0 1.67

1 100 500 * 765 28.27 226.2 738 26.12 8.00

0.1 300!300 250 * 250 900 900 2100 2.33 1

414! 304! 120"

23 850"

352!

23 850"

Oxygen transfer

d } LS d } LG

113 452 0 0 4

lm

500"

lm

306"

lm

500"

430" 509" 309"

1700"

Carbon transfer

d } LS !Theoretical, Eq. (29). "Adjusted, see text.

In the other cases, d will be treated as a parameter, to be "tted on the experimental measurement when available. 6.2. Carbon distribution in FZ experiments Kolbesen and MuK hlbauer [19] give welldocumented data. There is no evaporation, gas contamination is neglected, then the authors apply the plain Pfann equation (Eq. (19)). For v" 2 mm/min, a linear "t of the measured points gives k "0.11. Moreover, the authors determine %&& k "0.058 from measurements on k at three %2 %&& di!erent solidi"cation rates extrapolated to zero. The seed crystal is rotating at 10 rpm, and application of Eq. (29) for d } , and of Eq. (8) gives LS DL "2]10~8 m2 s~1 and d } "430 lm. C LS Concerning k , this method is quite unsafe, be%2 cause any error on C creates an error on F k which is ampli"ed in the extrapolation. We %&& prefer to use the solubility data issued from simpler measurements (k "0.034, Table 1). This gives %2 smaller values for DL and for d } , but the order of C LS magnitude is the same.

6.3. Carbon distribution in carbon-lean CZ process This case is also very simple. There is no carbon dissolution. The transfer to the gas phase is negligible. Then the carbon distribution follows the classical Gulliver}Scheil law (Eq. (23)). The `typical curvea for carbon distribution given by Zulehner and Huber [17] in their Fig. 41 can be reproduced using k "7.45]10~2. Assuming a rotation rate %&& of 15 rpm, d } "350 lm (Eq. (29)). With k " LS %2 0.034 (Table 1), Eq. (8) leads to v"47 lm s~1, in agreement with usual pulling rates [21]. The calculated distribution, as well as the original curve, shows that practically 90% of the crystal has a carbon content which is lower than the content of the feedstock (C "0.8 ppma, [17]), F a direct result of the very low partition coe$cient of carbon. 6.4. Oxygen distribution in CZ pulling, xxed conditions Zulehner [17], in his Fig. 32, gives two typical curves of oxygen axial distribution. The di!erence

P.J. Ribeyron, F. Durand / Journal of Crystal Growth 210 (2000) 541}553

in the initial value (C "22 or 18 ppma) can be 00 attributed to di!erent conditions for melt preparation (Eq. (26)). Besides, the curves have two di!erent, constant and negative slopes. This shows that evaporation dominates the enrichment resulting from both crucible dissolution and interface rejection (see Fig. 5). In our model, we use the geometrical parameters from Table 2. The product length (¸"500 mm), lower than ¸ , the length corresponding to the 0 initial melt volume, is not given. d } is calculated LS from Eq. (29) for 15 rpm (d } "414 lm), LS v"17 lm s~1, then k "0.74. C is taken from %&& 00 the experimental "gure. / } is kept constant C3 L (/ } "1.11]1020 at m~2 s~1 [17]), but the disC3 L solution area which is not given is adjusted through ¸ . k } is treated as an adjustable parameter. The 0 LG calculated curve has a very short initial transient part, corresponding to the adjustment of the initial concentration to the dynamical balance of evaporation versus (dissolution#rejection), a transient part which practically disappears for the proper choice of parameters:

¸ "765 mm, 0

d } "110 lm. LG

(30)

549

6.5. CZ pulling, ewect of crucible rotation Wen Lin [4], in his Fig. 12 reproduced here in Fig. 6, comments on the control of oxygen level by acting on the crucible rotation rate. We try to represent this e!ect through modi"cation of the dissolution rate / } , resulting from possible C3 L modi"cation of d } . Our procedure is the followC3 L ing. The experimental rotation rate of the crystal is 28 rpm, which "xes d } at 304 lm (Eq. (29)), and LS k "0.71. k } is kept as in par 6.4 (d } " %&& LG LG 110 lm). C is taken from the experimental "gure, 00 then the distribution curve is calculated as above, this time using / } as parameter. Fig. 6 and Table C3 L 3 give the best "t. An increase in the crucible rotation rate results in a higher content of the initial melt (exp.), which we represent by a (slightly) higher dissolution rate (adjusted). The overall oxygen content is higher (observed on exp. and calc. curves). The evaporation rate is higher (higher calc. slope), because the oxygen content is higher. This e!ect overcomes the higher dissolution rate. As shown in Zulehner's Fig. 32, manufacturers today commonly produce CZ crystals with a quasi constant oxygen concentration, owing to proper

Fig. 5. CZ pulling, oxygen concentration as a function of the relative crystal length. Dotted line, typical axial distribution ([17], Fig. 32 Curve 1), solid lines calculated from Eq. (22). (a) E!ect of ¸ , (b) e!ect of d } . 0 LG

550

P.J. Ribeyron, F. Durand / Journal of Crystal Growth 210 (2000) 541}553

Fig. 6. CZ pulling, e!ect of dissolution rate on oxygen pro"le. (a) Solid curves according to Wen Lin [4]. (b) Dotted lines calculated for adjusted dissolution rates / } , the unit is C3 L 1]1020 at m~2 s~1.

Fig. 7. Carbon pro"le in Solarex ingots, square dots according to Brenneman [7], curve by Eq. (23) with k "0.205. %&&

Table 3 E!ect of crucible rotation rate on crucible dissolution Rot. rate Cs(0) exp Calc / } C3 L

r.p.m. ppma 1]1020 m~2 s~1

5 18 1.11

15 22 1.32

20 26 1.62

25 28 1.78

k "0.205. Then for v"1.7 mm s~1: %&& d } "23850 lm. SL

(31)

6.7. Oxygen segregation in Solarex ingots

programming of melt preparation and crucible rotation rate. 6.6. Carbon segregation in Solarex ingots Brenneman [7] gives some experimental results on carbon and oxygen concentrations along a Solarex ingot made with 1D solidi"cation. These data will be used in order to obtain informations on the model parameters. Evaporation is neglected, so the plain Gulliver}Scheil Eq. (23) is applied to the set of experimental points. Fig. 7 shows that an excellent agreement with experimental results obtained for

Solarex ingots are solidi"ed in a silica crucible. Then the oxygen pro"le results from the competition of three mechanisms: dissolution, evaporation and solidi"cation rejection. Brenneman indicates two kinds of ceramics. The "rst one is a plain silica crucible. The second one, improved, in which the crucible is coated with Si N . In the 3 4 absence of dissolution data for this latter case, we assume that the dissolution rate is divided by a factor of 10. Fig. 8 shows that the experimental measurements can be explained using the same d } "23 850 lm LS as in Section 6.6, combined with the reduced dissolution rate, and with d } "1.7 mm. This means LG that the proposed model is able to re#ect the

P.J. Ribeyron, F. Durand / Journal of Crystal Growth 210 (2000) 541}553

551

Fig. 8. Oxygen pro"le in a Solarex ingot. The square dots are from Brenneman [7]. Curve from Eqs. (20)}(22), with / } " C3 L 0.11]1020 at m~2 s~1, d } "1.7 mm, d } "23 850 lm. Other LS LG parameters from Table 2. Fig. 9. Carbon distribution in the EMCP product. SIMS measurements [28] represented by circles.

experimental tendencies using a limited number of physically simple parameters. 6.8. Carbon distribution in the EMCP process In the P3 procedure described by Gilles Dour et al. [12], the initial liquid zone is formed by feedstock granules accumulating and melting in contact with the graphite base of the pulling system. Then the initial concentration of the solidi"cation process, C , is calculated from Eq. (28), with t "1 h, 0 1 and CH"261 ppma (Table 1). There is no evaL poration, nor contamination via the gas phase (k } "0). Then the pro"le is given by Eq. (19). LG d } is both in Eq. (19) and in Eq. (28). Therefore, we LS have treated it as a parameter to be adjusted, taking discrete values (d } "0.1, 0.2, 0.5, 1.0, 2.0, 3.0 mm, LS Fig. 9). There are only three experimental measurements by SIMS [28], corresponding to only two distan-

ces. Nevertheless, values of d } equal to or higher LS than 1 mm give an unrealistic negative high value to the slope, and they are rejected. The best "t is obtained for d } "500 lm, which we choose as LS our reference value for the EMCP process. According to the corresponding curve in Fig. 9, in the P3 procedure the "rst 60% of the silicon billet should have a total carbon content which is above the solubility limit (9 ppma, Table 1), then a few ppm of SiC precipitates should be found in the product. Fortunately at this low level, they are considered electrically nonactive. 6.9. Oxygen evaporation in FZ and in EMCP According to Yatsurugi et al. [29], the FZ process exerts a strong puri"cation on oxygen. FZ}Si usually ranges from 0.10 to 0.40 ppma oxygen,

552

P.J. Ribeyron, F. Durand / Journal of Crystal Growth 210 (2000) 541}553

much lower than the range of the raw poly-Si (1.6}6 ppma). This puri"cation e!ect was con"rmed more recently by Wen Lin [4]: the solidi"cation segregation is not su$cient to explain this e!ect, because k "0.698 is not su$ciently low. %2 An asymptotic value of the oxygen content is given by Eqs. (16b) and (18), taking C } "0 to LG simplify A } k } C L G L G " F !1. (32) A vk C= P %&& S According to Nozaki [18], the ratio C /C= is of F S the order of 15. We take a rotation rate of 10 rpm, then Eq. (29) gives d } "509 lm, v"17 lm s~1, LS other data from Table 1 or 2. Then k "0.75. This %&& gives an order of magnitude of the evaporation mass transfer coe$cient k } , and of d } : LG LG (33) k } "1.07]10~4 ms~1, d } "309 lm. LG LG An intense evaporation of SiO also occurs in the EMCP process. We measured the weight of the

Fig. 10. Oxygen pro"les for di!erent processes: (a) CZ, data from Zulehner [17], "xed conditions, (b) 1D-solidi"cation, data from Brenneman [7], (c) FZ, data from Yatsurugi [29], (d) EMCP data from Table 2.

powder deposited on the crucible surface. Taking into account deposits on other container walls, we conclude that the same order of magnitude can be applied to d } in the EMCP process. LG 7. Comparison of the oxygen pro5les Fig. 10 presents together the oxygen pro"les of the four cases treated above. Two groups are clearly distinguished: (a) In the noncontact processes (FZ and EMCP), the pro"le is dominated by evaporation, the solid}liquid exchange is completely hidden. (b) In the batch processes (CZ and 1D-solidi"cation), the pro"le is governed by the formation of the initial melt.

8. Conclusion A model is proposed for treating solute transfer in solidi"cation processing of electronic grade silicon. This model takes into account the solute exchange at the di!erent interfaces of the liquid, solid}liquid interface exchange, evaporation to or contamination by the gas phase, and container dissolution. For the sake of simplicity, the transfer between the liquid and the contacting media were treated in the crude approximation of a boundary layer and a perfectly mixed liquid. As a consequence, only the axial (z) distribution can be represented. The application to published data on the four processes currently used, i.e. CZ, FZ, 1D soldn and EMCP, gives a set of acceptable values for the thickness of the boundary layers. Conversely, this model is a valuable tool for estimating the relative importance of the di!erent exchanges, possible dissolution of the crucible, and moreover exchange (evaporation or incorporation) with the gas phase. The processes are separated into two groups: (a) Processes in which the liquid volume is kept constant (FZ and EMCP). The reference is the Pfann law. The solute distribution can be strongly modi"ed by exchange with the gas phase.

P.J. Ribeyron, F. Durand / Journal of Crystal Growth 210 (2000) 541}553

(b) Processes involving a decreasing liquid volume (CZ and 1D-soldn). Here the reference is the Gulliver}Scheil law. A large variety of solute pro"le curves can be obtained, because they are very sensitive to the balance between crucible dissolution and evaporation. In comparison, the CZ process clearly needs a special mention, because it has supplementary degrees of freedom via the geometry of the crucible, important for the dissolution phenomena, and via the rotation rate of the crystal and of the crucible, important for acting on transfer kinetics. Acknowledgements The authors gratefully acknowledge the "nancial support of the French Government via the ADEME and CNRS-ECODEV programs since 1990, and of the European Community in the JOULE program since 1996. References [1] B. Leroy, Rev. Phys. Appl. 21 (1986) 467. [2] A. Borghesi, B. Pivac, A. Sassella, A. Stella, J. Appl. Phys. (Appl. Phys. Rev.) 77 (1995) 4169. [3] W.C. O'Mara, Oxygen, carbon and nitrogen in silicon, in: O'Mara et al. (Eds.), Handbook of Semiconductor Silicon Technology, Noyes Publ., 1990, pp. 451}549. [4] Wen Lin (AT and T Bell labs), The incorporation of oxygen into silicon crystals, Semiconductors and SemiMetals, Vol. 42, Academic Press, New York, 1994, pp. 9}52. [5] G. Davies, R.C. Newman, Carbon in monocrystalline silicon, in: S. Mahajan (Ed.), Handbook of semiconductors, Vol. 3, Elsevier Science, Amsterdam, 1994, pp. 1557}1635. [6] W. Dietze, W. Keller, A. MuK hlbauer (UniversitaK t Hannover (D)), Float-Zone grown silicon, in: Crystals, Growth, Properties and Applications, Vol. 5, Springer Berlin, 1981, pp. 1}42.

553

[7] R.K. Brenneman, High performance CDS polycrystalline silicon: challenges and opportunities, Technical Digest of the Int. PVSEC-5, Kyoto, Japan, 1990, pp. 197}199. [8] J. Fally, E. Fabre, B. Chabot, Rev. Phys. Appl. 22 (1987) 529. [9] F. Lasnier, T.G. Ang, Photovoltaic Engineering Handbook, Adam Hilger, Bristol, 1987. [10] T.F. Ciszek, J. Electrochem. Soc. Solid State Sci. Technol. 132 (4) (1985) 963. [11] K. Kaneko, R. Kawamura, T. Misawa, Present status and future prospects of electromagnetic casting for silicon solar cells, Conference of the PV Proceedings, Hawaii, December 1994, pp. 30}33. [12] G. Dour, E. Ehret, A. Laugier, D. Sarti, M. Garnier, F. Durand, J. Crystal Growth 193 (1998) 230. [13] T. Carlberg, T.B. King, A.F. Witt, J. Electrochem. Soc. (1982) 189. [14] K.M. Kim, W.E. Langlois, J. Electrochem. Soc. 138 (1991) 81. [15] W.E. Langlois, K.M. Kim, J.S. Walker, J. Crystal Growth 126 (1993) 352. [16] R. Chaney, C.J. Varker, J. Crystal Growth 33 (1976) 188. [17] W. Zulehner, D. Huber, Czochralski-grown silicon, in: Crystals, Growth, Properties and Applications, Vol. 8, Springer, Berlin, 1982, pp. 1}144. [18] T. Nozaki, Y. Yatsurugi, N. Akiyama, J. Electrochem. Soc. 117 (1970) 1566. [19] B.O. Kolbesen, A. MuK hlbauer, Solid-State Electron. 8 (25) (1982) 759. [20] B. Hallstedt, Calphad 16 (1992) 53. [21] W. Zulehner, in: Semiconductors, Czochralski growth of Si and Ge, Landolt}BoK rnstein Series, Vol. 3, 17c, Springer, Berlin, 1984, pp. 28}39. [22] F. Durand, J.C. Duby, J. Phase Equilibria 20 (1999) 61. [23] J.A. Burton, R.C. Prim, W.P. Slichter, J. Chem. Phys. 21 (11) (1953) 1987. [24] W.G. Pfann, Trans. AIME 194 (1952) 747. [25] G.H. Gulliver, Metallic Alloys, Their Structure and Constitution (Appendix p. 397), Gri$n, London, 1922. [26] E. Scheil, Z. Metall. 34 (1942) 70. [27] A. MuK hlbauer, in: Semiconductors, Si and Ge, technological data, Landolt}BoK rnstein Series, Vol. 3, 17c, Springer, Berlin, 1984, pp. 12}20. [28] D. Ballutaud, Y. Marfaing, Internal Report of the JOULE-Menhir Programme, 1997. [29] Y. Yatsurugi, N. Akiyama, Y. Endo, T. Nozaki, J. Electrochem. Soc. (1973) 975.