Effect of an Electrical Field Applied During Czochraslki Crystal Growth – Applications to Growth of Oxides Materials (LiNbO3:Cr+3) and Silicon-

Germanium Alloys

Octaviano, E.S.*, Alves, L.M**. and Andreeta, J.P.

Grupo de Crescimento de CristaisInstituto de Física de São Carlos

Universidade de São PauloC.P. 369, 13560-970 – São Carlos – SP – Brazil

*Permanent AddressAcademia da Força Aérea

Divisão de EnsinoCampo Fontenelle – Pirassununga – 13630-000 - SP – Brazil

**Permanent AddressUniversidade Estadual de Ponta Grossa

Departamento de Engenharia de MateriaisAv. Gal. Carlos Cavalcanti, 4748, UvaranasCEP - 84030-000 Ponta Grossa-PR-Brazil

ABSTRACT

Electrical fields can produce change in the effective segregation coefficient during the growth process. These phenomena is explain to the growth process of LiNbO 3:Cr+3, and Silicon-Germanium alloys (Si80Ge20), using theoretical and experimental results. The crystals obtained are analyzed by chemical etching, Atomic Absorption Spectroscopy (AAS), and Energy's Dispersive X-Ray (EDX).

Keywords: crystal growth, electric field, segregation, lithium niobate, Silicon, Germanium

1. Introduction

The most usual description of the effective segregation coefficient is based on the theory of Burton, Prim and Slichter [1] (the BPS theory), where only the normal crystal parameter dependence is considered. In some reports [2-7] it has been observed that the effective segregation coefficient is also a function of the applied electric field in the crystal growth process or of the electric field that appears in the crystal-melt interface, due to the great thermal gradient, as in the single crystal fibers growth of oxide materials [8-12]. One of the reasons for which this electric field is applied in crystal growth is the possibility of obtaining single domain ferroelectric crystals directly from the experiment [13-14]. In some cases the influence of an electric field in dopant incorporation is explained by a growth rate change due to the Peltier effect and constitutional supercooling [2,4,15]. In another case [8-12,16] the phenomena that explain the dopant incorporation rate changes are related to electrochemical processes and ion electromigration in the boundary layer, and Seebeck effect, with a change in the growth rate. All these effects normally modify the crystal growth rate due to the dopant concentration profile changes that again bringing about new modifications in the dopant distribution. The first studies were done by Angus et al. [17], Pfann and Wagner [18], Hay and Scala [19] and Verhoeven [20]. The result of these works led to a modification in the expression for the effective segregation coefficient obtained by BPS [1], and to a new expression of keff. However, such a new expression, according to the authors themselves, was only good for a qualitative evaluation of the phenomenon, due to the fact that it is impossible to determine the terms involved in a real growth process. Therefore it became a limit to this kind of analysis.

Tiller and Uda [8,9] and Uda et al [10-12], developed an excellent formulation for the variation of the effective segregation coefficient and of the growth velocity due to a electric field in the growth interface, mainly applied in the single crystal fiber growth in oxide materials through laser-heated pedestal growth (LHPG) and micro-pulling (µ-PD) techniques. Garendet [21] report an expression for the keff due to changes in growth velocity, mainly applied in the case of semiconductors materials, where the applied electric field causes a cooling in the interface through Peltier effect.

2 – Effect of the Electric Field in Dopant Segregation

In previous works [22,23] we built a model in order to explain the changes that took place in the keff, for the case of oxide materials (e.g. LiNbO3), as well as in semiconductor materials, grown through the Czochralski’s method with an electric field applied. The equation for the keff was found:

(1)

where is the crystal growth rate modification that must be obtained as a laboratory parameter, f is the growth velocity and ko is the equilibrium segregation coefficient.

The simplest equation to represent as a function of the electric current density, we could write as follows (this case occurs when an increase in the current density causes a decrease in keff):

= aJ (2)

where a is a constant to be experimentally determined and J is the applied electrical current density. Combining Equations 1 and 2 we obtain

(3)

For [J] = [mA cm-2] and [] = [cm s-1], dimensional analysis requires that [a] = [cm3

mA-1 s-1].There is still the possibility (depending on the polarization of the crucible-melt system)

that an increase in the current density causes a decrease in the rejection of the dopant in the solid phase, and consequently an increase in keff. We can express this variation as inversely proportional to the current density, i.e.

= b/J (4)

where b is the constant to be experimentally determined. Combining eq. 1 and 4 we obtain;

(5)

In this case the dimensional analysis requires that [b] = [mA cm-1 s-1].

4. Experimental Procedures and Results

The LiNbO3 is used in many electro-optic and acusto-optic devices due to its non-linear properties, has been extensively studied [5,6,8,16,22,23].

The Si:Ge alloys (single or polycrystalline) in the atomic composition of 80% of Si and 20% of Ge have very extensive technological applications [Kürten and Schilz(24), Kadokura and Takano (25), Abrosimov et al. (26) and Abrosimov et al. (27)], like, for example, in the generation of electrical energy for satellites, nuclear batteries for a wide range of applications, RTG calls, radioisotope thermoelectrical generators, in electronics and, also, for applied research in several areas.

4.1 - Growth of LiNbO3:Cr+3

The raw materials was Nb2O5 (Puratronic, 99,9985%), Li2CO3 (Merk, Optipur), and Cr2O3 (Johnson Matthey, 99,9999%) powders. They were weighed according to congruently ratio Li2CO3 (48.6 mol%):Nb2O5 (51.4 mol%) powders, and heated 900C 8hrs. Cr2O3 is added in the quantity of 0.066 mol%. LiNbO3:Cr+3 crystals were grown by the Czochralski method, where f = growth velocity = 1.81 10-4 cm/s (6.5mm/h), = rotation rate = 34 rpm. An electrical field of 2/2.5 mA/cm2 is applied during the growth, where the crystal is negatively polarized in relation to the melt. There will then be a tendency to increase the dopant adsorption in the crystal [22,23]. The concentration in solid is obtained by Atomic Absorption Spectroscopy (AAS).

4.1.1 - Applications to Growth of Oxides Materials (LiNbO3:Cr+3)

Using experimental results obtained by Raüber and Feisst [5] for the effective segregation coefficient of Cr3+ in LiNb03 (Fig. 1), where f = 1.81 10-4 cm/s (6.5mm/h), = 34 rpm, and ko = 5, it was possible to calculate the a and b constant values for this results;

a1 = 0.248 [cm3/mA s]a2 = -0.910 [cm3/mA s]b1 = -3.10 10-6 [ mA /cm s]

These suppositions were analyzed in detail in Octaviano et al [22,23], due to the value of the equilibrium segregation coefficient ko to the convention of polarization of the crystal-melt system and the interface shapes [5,27-29]. Fig. 1 shows the new behavior of k eff as a function of the electric current density in three different regions after the introduction of the correction term (Equations 3 and 5), the Raüber and Feisst [5] results and our experimental results. One must observe that the constant a1 is predicted in figure 6c, constant a2 in figure 6d and the constant b1

through figure 6f.

Figure 1

4.2 - Applications to Growth Silicon-Germanium Alloys

The raw materials was Si ( Wacker, 99,99%), and Ge ( Aldrich, 99,9999% ). They were weighed according to the atomic composition of Si 80% and Ge 20%. Si:Ge crystals were grown by the Czochralski method, using a Kokusai DP-1300 A system of growing for semiconductors. The limitations of the equipment make the obtained crystals with reduced dimensions. The growth parameters are f = 1.0-0.3 mm/min and the rotation rates were 10 rpm (crystal, CW), and 10 rpm (crucible, CCW). An electrical field of 0.5/3 A/cm2 is applied during the growth, where the melt is negatively polarized in relation to the crystal. The atmosphere in the growing chamber was Ar (10/min), and the seed orientation was [111]. The concentration in solid is obtained by Energy's Dispersive X-Ray (EDX).

To apply an electric field during the growth of Si:Ge was made used a contact with a silicon electrode, introduced through an auxiliary opening in the edge of a alumina rod. This electrode is connected to a DC source and the crystals is linked to another polarity of the source through the cold finger and a mobile contact.

Was obtained a polycrystal of approximately 17mm by 10mm of diameter which was cut in three parts for the compositions analysis.

4.3. Metalographic Analysis of Polycrystalline Si:Ge Alloy

The metalographic and chemical analysis of the crystal grown was made through Energy's Dispersive X-Ray (EDX).

Figure 2With Scanning Electronic Microscopy and the EDX chemical analysis, it was possible

to detect differences between the phases, differences in the chemical compositions, and the solute

concentration over all the samples. However, in these samples where the electric field was applied, a decrease in the germanium segregation was observed. Typical micrographs of the regions where

the chemical analysis were made, with a contrast enhancement to differentiate the slightly different chemical compositions phases are shown in Figures 2 to 5.

Figure 3Figure 4

4.3.1. Regional Chemical Analysis

The first chemical analysis was made in the large areas ( 4.5 mm x 4.5 mm) of the grown alloy using the conventional electronic microscope to find an average composition. The results found in three different regions (at beginning, at the middle and the end of the grown alloy) analyzed are shown in table 1.

Table 1 Chemical Analysis in Si:Ge

Area Si(%atomic) Ge(%atomic)Initial 93.5 0.3 6.5 0.1

Central 93.3 0.3 6.7 0.2Final 92.9 0.3 7.1 0.2

The chemical analysis results shown in Table 1 show a good homogeneity in the whole crystal in relation to previous techniques. The micrographies of these areas were made using detection of electrons backscattering (Figure 5), differentiating the chemical phases that posses different densities. The lighter areas correspond to germanium and the darker ones correspond to silicon. The percentage for each one of these elements can only be measured in each of these micro-areas, through a spot chemical analysis.

4.3.2. Spot Chemical Analysis

We observed in each one of the three analyzed areas basically three different micro-areas: a light area, a grey one, and a dark one, as shown in Figure 5. The Table 2 shows a spot chemical analysis in each of these micro-areas.

Table 2Spot Chemical Analysis of the Si:Ge - Initial Area

Micro-Area Si(%atomic) Ge(%atomic)Light 92.0 0.3 8.0 0.2Grey 93.4 0.3 6.6 0.2Dark 94.5 0.3 5.5 0.2

Table 3 Spot Chemical Analysis of the Si:Ge - Central Area

Micro-Area Si(%atomic) Ge(%atomic)Light 92.0 0.3 8.0 0.2Grey 92.1 0.3 7.9 0.2

Table 4 Spot Chemical Analysis of the Si:Ge - Final Area

Micro-Area Si(%atomic) Ge(%atomic)Light 88.5 0.3 11.2 0.2Grey 92.2 0.3 7.8 0.2Dark 94.3 0.3 5.7 0.2

These results provide the existence of larger germanium concentration in the grey tonality of the samples. The darker area contains less germanium than the grey ones and these less than the light area, and for the silicon the relation is inverse.

Figure 5

The effect of the electric field over the growth favored the alloy's homogenization as show in Figures 2 to 5, because the alloys obtained through ECZ show a decrease of the germanium segregation in all the material. Therefore, it showed a better distribution of said germanium in relation to those obtained through the same Czochralski's technique without applied an electric field (CZ), or through simple techniques of fusion.

The efficiency in the homogenization through electric field application can be attributed to a change in the velocity of solidification occurs in an efficient way, produced through Peltier Effect (cooling or heating of the solid/liquid interface ) during the growth, which led the molten to an imprisonment ( incorporation ) of the germanium in the silicon's crystalline structure. This change produces convection that stirred the liquid after the solid/liquid interface, destroying the effects of concentration and thermal gradients of the constitutional supercooling , leading the liquid close to the interface to solidify in a more homogeneous way. We observe that the micrographies show cooling fronts which move from the crystal to the liquid showing the germanium's rejection by silicon. This phenomenon is typical of a segregation coefficient k < 1. We can still get a better homogeneity with this technique, adjusting the crystal growth's parameters, such as pulling velocity, rotation rate and the electric field value.

5. Configurations of the keff under the Effect of an Electric Field

The following analysis both describes and predicts a great quantity of experimental results. They built a series of curves, shows in figure 1, with all the possible keff configuration due to the value of constants a and b, of ko, and of the possible polarization of crystal-melt interface.

In this analysis we used some typical values for the growth of LiNbO3:Cr3+ : a = 0,25 cm3/mA s, b = 3.10-6 mA/cm s, ko = 5.0, f = 1.81 10-4 cm/s (6.5 mm/h), = 0.198.()-1/2 cm [27], = 34 rpm, D = 5.10-5 cm2/s, is the diffusion coefficient, and keff

t refers to the effective segregation coefficient’s value predicted by BPS [1].

In the figure 6 the curves a, b, g and h show a behavior of the k eff for a 0, J 0 and values of f and k0 variables.

In the curves c, d, e and f of figure 1 we find a situation of keff < 0. The behavior of the curve that anticipates keff < 0 is just part of a mathematical solution. It has no physical meaning in spite of the fact that Uda [10] considers the possibility of keff < 0, as in a situation in which there is a diffusion of the dopant of the crystal to the melt.

The curves i and j show a variation of the keff with the current density, which would be as expected if the electrochemical and electromigration process in the growth were simple, that is, the adsorption is simply due to the valence of the dopants atoms and the polarization of the crystal-melt interface.

The curves k and l show a variation of the keff with a current density, with a behavior that opposes the figures i and j, that is, a situation in which the electrochemical and electromigration process are complex, for in these figures we find a great variation in the behavior of keff to the value expected for J = 0 (keff

t ) when the applied current's density is slightly varied.

Figure. 6

6 - Conclusions

Through this model new elements are derived for the effective segregation coefficient of materials, obtained with the application of an electric field. The application of Equations 3 and 5 is general, and is subject to the same limitations as that of the BPS equation. For each material, nevertheless, there must be different values (or more than one for the same material, as for the LiNb03:Cr3+ case) for the a and b constants. However, once these constants’ value is found, we’ll proved to anticipate the next growths, situation in which the curves described in this work would be of fundamental importance.

We must also take into consideration the existence of materials with more complex electrochemical process, which would evidently have relations for different from the ones shown in this work and the materials who don't have, obligatorily, changes in the interface due to the application of an electric field.

We could see that the idea of using the electric field to avoid the germanium segregation through Peltier Effect was good and the results obtained so far were promising. However, it is necessary to modify the electrode's geometry for the effect to be homogeneous over the whole material.

7 - Acknowledgements

The authors would like to thank Elderson Cássio Dominicucci, for technical assistance and Professor Antonio Carlos Hernandez for the extending the use of the furnaces and crystal growth apparatus.

We thank FAPESP, FINEP, CAPES, and CNPq for the financial support.

8 - References

1 - Burton, J. A., Prim, R.C. and Slicther, W. P. - J. Chem. Phys, vol. 21, 11(1953)1987.2 - Lawrence, D. J. and Eastman, L.F. - J. Crystal Growth, 30(1975)267.3 - Rauber, A. - Mat. Res. Bull., 11(1976)497.4 - Daniele, J.J. - App. Phys. Letters, 27(1975)373.5 - Raüber, A. and Feisst, A. - J. Crystal Growth, 63(1983)337.6 - Raüber, A. - Chemistry and Physics of LiNbO3 - Current Topics in Materials Science, North-

Holland, 1978.7 - Reiche, P. et al. - J. Crystal Growth, 108(1991)759.8 - Uda, S. and Tiller, W. A. - J. Crystal Growth, 121(1992)93.9 - Uda, S. and Tiller, W. A. - J. Crystal Growth, 126(1993)396.

10 - Uda, S. et al. - J. Crystal Growth, 179(1997)567.11 - Uda, S. et al. - J. Crystal Growth, 182(1997)403.12 - Uda, S. et al. - J. Crystal Growth, 155(1995)22913 - Nassau, K. , Levinstein, H.J. and Loiacono, G. M. - J. Phys. Chem. Solids, 270(1966)989.14 - Octaviano, E. S. and Andreeta, J.P. - Revista de Física Aplicada e Instrumentação, vol. 3,

1(1988)30.15 - Corre, S. et al. – J. Crystal Growth, 180(1997)60416 – Uda, S and Tiller, W. A - J. Crystal Growth, 121(1992)155.17 - Angus, J. et al. - Physical Chemistry of Process Metallurgy, Part II, Interscience, N. York,

(1961)833.18 - Pfann, W.G. and Wagner, R. S. - Trans AIME, 224(1962)1139.19 - Hay, D. R. and Scala, E. - Trans AIME, 223(1965)1153.20 - Verhoeven, J. D. - Trans AIME, 223(1965)1156.21 - Garandet, J.P. – J. Crystal Growth, 131(1993)431.22 - Andreeta, J.P. , Octaviano, E.S. and Gallo, N.J.H. - Journal of Mat. Science, 28(1993)65.23 - Octaviano, E. S – Ph. D Thesis, Instituto de Física e Química de São Carlos, USP,1991.24 - Kürten, M. and Schilz, J. - J. Crystal Growth, 139(1994)1.25 - Kadokura, K. and Takano, Y. - J. Crystal Growth, 171(1997)56.26 - Abrosimov, N.V. et all. - J. Crystal Growth, 166(1996)657.27 – Hartman, P. (Editor) - Crystal Growth: An Introduction. North-Holland Pub. Comp. - 1973,

pg. 232.28 – Wilcox, W.R. (Editor). - Fractional Solidification. Ann Arbor, vol. 1, 1967.29 – Hwang, C. et al. – J. Crystal Growth, 165(1996)147

Figure Captions

Figure 1 - keff against J : ( ) theoretical curve, () experimental data of Raüber and Feistt [5], () our results [22], () value predicted by BPS theory. The a1 constant is used in the positive J region, a2 for - 6 mA/cm2 < J < 0, and b1 for J < - 6 mA/cm2.

Figure 2 - Crystal's micrography - Image obtained through electrons backscattering - Increase 50 X - Area 1- beginning alloy regions .

Figure 3 - Crystal's micrography - Image obtained through electrons backscattering -Increase 50 X - Area 2 –middle alloy regions.

Figure 4 - Crystal's micrography - Image obtained through electrons backscattering - Increase 50 X - Area 3- end alloy regions.

Figure 5 - Typical micrography of the micro-area where the chemical analysis were made, with a contrast highlighting, to differentiate the chemical composition stages that are slightly different.

Figure 6 – Effect of electrical field on the effective segregation coefficient in systems with different crystal growth parameters. a) = aJ, a > 0, J 0 ko > 1 and different values of f; (b) = aJ, a > 0, J 0 f > 0 and different values of k0 ; (c) = aJ, a > 0, ko > 1; (d) ) = aJ, a < 0, ko > 1; (e) = b/J, b > 0, ko > 1; (f) = b/J, b < 0, ko > 1; (g) = aJ, a > 0, J 0 ko 1 and different values of f ; (h) = aJ, a > 0, J 0, f > 0 and different values of k0; (I) = aJ, a > 0, ko < 1; (j) = aJ, a < 0, ko < 1; (k) = b/J, b > 0, ko < 1; (l) = b/J, b < ), ko < 1.

Fig, 1 - Octaviano

Octaviano – Figure 2

Octaviano – Figure 3

Octaviano – Figure 4

Fig. 5 - Octaviano

Fig. 6 - Octaviano