Facet-Affected Czochralski Growth of SrLaAlO4 Crystals
CRYSTAL GROWTH & DESIGN 2001 VOL. 1, NO. 4 321-325
D. Klimm,* P. Reiche, R. Uecker, and S. Ganschow Institute of Crystal Growth, Max-Born-Strasse 2, 12489 Berlin, Germany Received February 21, 2001
ABSTRACT: SrLaAlO4 (SLA) crystals have been grown by the Czochralski method on a [100] seed. One common problem during SLA growth is a distinct tendency for the formation of stacking faults and of polycrystalline material on facets and edges. It could be observed that the polycrystalline growth results from the highly different wetting of neighboring facets that are forming the habit of the SLA crystal. The different degrees of wetting can be estimated on the basis of a relative Coulomb interaction energy. This interaction energy is proportional to the sum of Coulomb charge densities of the different ions that are present in the crystal surface. Introduction Some ABCO4 (A ) Ca, Sr; B ) Y, rare-earth element; C ) Al, Ga) compounds have become objects of theoretical and crystal growth studies, as they are known to be suitable substrates for high-Tc superconductors. Some peculiarities of the crystal growth connected with strong faceting were discussed on the basis of the HartmanPerdok theory.1,2 Theoretical growth forms were constructed from attachment energies Ehkl, which were assumed to be directly proportional to the growth rate of F faces. According to these considerations, for CaYAlO4 as a model substance for the K2NiF4 structure type, the F faces {002}, {101}, {103}, {110}, {112} {200}, {211}, and {213} should be expected as the most prominent growth forms. Indeed, this claim could be proved by the Czochralski growth of different K2NiF4 type single crystals as SrLaGaO4, SrPrGaO4, and SrLaAlO4. The present paper is initiated by some problems connected with the facets that are well-developed at Czochralski-grown SrLaAlO4 (SLA) crystals. Some problems that are connected with the oxygen partial pressure of the growth atmosphere leading to different colorations of the crystals were discussed elsewhere.3,4 It was ascertained that the color of the crystals originates from oxygen point defects. The concentration of these defects was found to be reduced by the application of active afterheaters during the crystal growth process, leading to a considerable reduction of the axial temperature gradient. However, the growth of defect-free SLA crystals remains difficult: the growth process tends to be unstable due to different wettings of the lateral (cylinder) facets by the melt. Eventually, this inhomogeneous wetting can lead to fluctuations of the mass signal which is used for the automatic diameter control. It will be shown in the following that inhomogeneous wetting can result also in spontaneous solidification onto cold facets and, hence, in the formation of stacking faults and of polycrystals. Structural Aspects As for other ABCO4 family compounds, SrLaAlO4 crystallizes tetragonally with space group symmetry I4/ * To whom correspondence should be addressed. Phone: (+49) 30 6392 3024. Fax: (+49) 30 6392 3003. E-mail:
[email protected].
mmm (No. 139, K2NiF4 structure type, lattice constants a0 ) 0.37564 nm, c0 ) 1.26357 nm). In this structure, Al3+ is coordinated octahedrally by four O1 atoms (in the AlO2 layer, bond length 0.1878 nm) and two O2 atoms at the apexes (bond length 0.2053 nm). Sr2+/La3+ is coordinated 9-fold by four O1 atoms in the neighboring AlO2 layer (bond length 0.2590 nm) and (4 + 1) O2 atoms (bond lengths 0.2670 and 0.2482 nm, respectively) in the (Sr, La)O double layer. No ordering of the Sr2+ and La3+ is reported on this position. Both the position of Sr/La [[00z1]] (z1 ) 0.358 85) and of O2 [[00z2]] (z2 ) 0.1625) have one degree of freedom. The crystal structure data with isotropic temperature factors were published elsewhere.5 The crystal structure is shown in Figure 1. It is obvious, that the low-indexed lattice planes {001} and {100} exhibit high packing density of ions. Such surfaces are known to have low specific free energy and are often dominant, as they show low growth rates. Other low-energy surfaces have already been found by Woensdregt2 and are given above in the text. From Figure 1 it furthermore becomes obvious why the comparably high indexed {103} faces are present: {103} almost cuts the positions of Sr/La, of Al, and of O1, thus showing a comparably high packing density. Crystal Growth and Wetting of Facets SLA crystals were grown by the Czochralski technique from nearly stoichiometric mixtures (composition SrLa1.03Al0.97O4) of the pure (5N) oxides from [010] seeds within flowing nitrogen. An rf-heated iridium crucible had to be used due to the high melting point of the material (1650 °C). An appropriately designed active afterheater allowed the adjustment of temperature gradients to an acceptable level of 10 K/cm. The threephase solid/liquid/gas junction of the growing crystal could be observed using a video camera and a monitor screen. More details of the growth technique have been described elsewhere.3 Figure 2 shows the typical habit of a [100]-grown SLA crystal. {001} (in front) is dominating, and the prism {101} is the second form. These two forms were found to build up the cylindrical part of the Czochralski crystal. Other well-developed cylinder facets could not be observed. It can be seen from Figure 2 that {001}
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Figure 3. Growth facets of a 〈100〉-grown SLA crystal. [010] is equivalent to [100].
Figure 1. Crystal structure of SrLaAlO4. [AlO6] octahedra build up layers parallel to (001). (Sr, La) positions are represented by filled circles.
Figure 2. Initial stage of SrLaAlO4 growth with one large {001} facet in front and two smaller {101} facets on both sides.
extends to an altitude that is about 1 mm higher than the neighboring {101} facets. Observation of the crystal during growth shows that the higher altitude of {001} is connected with a higher wetting of these facets. The origin of the wetting anisotropy will be discussed later in this article. Two reasons can be given for problems that are connected with this anisotropic wetting of facets. (1) The axial thermal gradient near the interface in the present setup is close to 30 K/cm.6 As the meniscus height on {101} and {001} has a difference of ∼1 mm, the melt on the higher wetted {001} facet is exposed to a supercooling that is 3 K stronger than on {101}. The stronger supercooling can result in rapid crystallization and in the formation of planar defects that are parallel to this facet. Indeed, the initial shape of the seed {001} faces is often marked within the later grown crystal by a defective region containing stacking faults. Frequently the defect concentration is so high that a nebulous region can be seen with the naked eye. (2) The different wetting results in a strong bent of the melt surface close to the crystal. The different equilibrium wetting heights of neighboring facets can
lead to instability, if the crystal rotates with a different rate than the surrounding melt volume. The {001} defect formation mentioned in the preceding paragraph is forced by this hydrodynamic instability. Moreover, defects can be formed at the edges between neighboring facets. A schematic top view of a SLA crystal is shown in Figure 3. Apart from the dominant cylinder forms {001} and {101} that were already shown in Figure 2, {103} and {100} are considered in this figure and in the following discussion as well. The occurrence of {103} at SLG (but not at SLA) crystals was found to be related to the weaker Ga-O bonds as compared to the Al-O bonds.7 {103} is an F form,2 and {100} is very low indexed. {013} that is present at the conical part of the crystal is equivalent to {103}. The two crystal faces that are marked as “ridged” in Figure 3 are not flat. They consist of almost perpendicular (with respect to the paper plane) {101} or {103} steps, respectively, and almost flat (010) parts. Even in the seed region, stacking faults can be observed quite often. Frequently it was even impossible to obtain crack-free crystals. The cracking can be partially attributed to the anisotropic thermal expansion of the materialsthe coefficient of linear thermal expansion in the b c direction is about twice as high as compared to the b a direction (R11 ) R22 ) 8.8 × 10-6 K-1; R33 ) 16.9 × 10-6 K-1 at room temperature).8 As both directions lie within the growth plane {010}, high thermal stresses can occur due to nonlinear temperature fields. This is especially true for the peripheral part of the crystal.9 Video observation of the growth process allowed the revealing of another phenomenon that can lead to the formation of defects. It turned out that the different facets forming the cylindrical part of the growing crystal are wetted by the melt in a highly different manner. Obviously, the capillary forces that attract the liquid phase to the crystal depend substantially on the orientation of the surface for SLA. Because of friction and hydrodynamic forces inside the melt, the rotation rate of the crystal is different from the flow rate of the surrounding melt. Therefore, one volume element of the melt is in contact with different faces of the rotating crystal successively. Problems arise if the capillary forces between neighboring facets are too different, as the meniscus height is thus different on these facets. For too high rotation rates it may
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Figure 5. {100} surface of SLA: (black circles) Sr2+/La3+; (gray circles) Al3+; (empty circles) O2-. Figure 4. {110} surface of SLA in a projection close to {001} (exactly {11 h 33}): (black circles) Sr2+/La3+; (gray circles) Al3+; (empty circles) O2-.
happen that the melt overruns from one facet with high meniscus to the subsequent one with substantially lower meniscus. As the initially nonwetted surface of this second facet is expected to be colder than the melt, the overrunning melt becomes supercooled quickly. Polycrystalline solidification may be initiated by such quick supercooling. Estimation of Wetting Anisotropy Anisotropy of capillary wetting results from the geometrical shape of facets (Laplace equation) as well as from different surface structures. The first aspect is discussed elsewhere10 and will not be considered here in detail. As the main result of these considerations of the shape influence, the two limit cases
h)
{x
x12R for small R 2σ for large R 2 Fg
(1)
for the height h of the meniscus can be obtained for a small and for a large radius R of the growing crystal (σ - surface tension). Accordingly, h reaches a minimum value at sharp edges of the growing crystal that correspond to a small R. Therefore, the meniscus height is small on the tiny (and usually even not observed) {100} and {103} facets. In the central parts of the facets (R f ∞) the meniscus height h rises to the limit value 2x2σ/Fg that depends, however, on the surface tension of the corresponding facet. According to our observations, typical values for h are a few tenths of a millimeter to a few millimeters. Unfortunately, numerical values for σhkl for different crystal faces {hkl} are often not available. Common techniques for its measurement rely on the determination of the wetting (contact) angles of liquids with known surface tension, but the measurement of wetting angles at as high temperatures as the melting point of SLA is not easy. An estimation for σhkl is given here. Because of the high difference of the electronegativities (Pauling) between the cations (Sr, 0.95; La, 1.10; Al, 1.61) and the anion (O, 3.44), the interactions between the solid surface and the melt are assumed to be mainly electrostatic. The wetting of the solid surface is driven by attractive forces between cations within the surface and O2- within the melt and vice versa. Figure 4 shows as an example the ideal {110} surface of one SLA unit cell. The surface is built up from Al-O-Sr/
La-Sr/La-O-Al rows along [001]. The distance between neighboring rows is 1/2x2a0 ) 0.2656 nm. The relative strength of first-nearest-neighbor bonds between ions in the surface layer and free ions in the melt can corresponds to the Coulomb interaction energies q1q2/r. These interaction energies are scaled by the reciprocal value of the dielectric constant of the matter between the two pointlike charges. It is discussed by Bennema11 that only for nearest-neighbor interaction does ) 0 hold. For distances inside the crystals (e.g., the six oxide ions in the second layer below the {110} surface in Figure 4) the larger value ) 0r must be used. The value of r at the melting temperature is not known, but a room-temperature value of r ) 21-22 is given in the literature.12 This high dielectric constant, together with the larger distances, reduces the influence of ions in the interior to a negligible measure. Hence, only the distribution of charges in the outermost surface layer of the crystal has to be considered in the following. The wetting of the surface, represented by the meniscus height h, can assumed to be proportional to the relative Coulomb interaction energy
Φ{hkl} ) rel
Φ{hkl}
) A{hkl} {hkl} + 2 × 3 × n{hkl} + 8/3 × 2 × n{hkl} 2 × 5/2 × nSr/La Al O A{hkl}
(2)
where A is the area of the SLA unit cell in the {hkl} corresponding projection and the nelement values are numbers of atoms of the corresponding element at the is given here in units of a reciprocal area surface. Φ{hkl} rel and describes the relative bond strength per area. Atoms at the edges have to be counted only half and atoms at the corner only to one-fourth. The two factors before {hkl} nelement are the charges of the interacting ions of the opposite charge and of the element itself, respectively. For oxygen the average charge of cations in the almost stoichiometric melt (2 + 3 × 1.03 + 3 × 0.97)/3 ) 8/3 was chosen as the opposite charge. Equation 2 will be calculated for the cylinder facets shown in Figure 3 in the following. {100}. The {100} surface (Figure 5) consists of rectangular c0 × a0 meshes. 1/4 Al3+ occupies each corner (n{100} ) 1). 4 × 1/2 Sr2+/La3+ occupy the long edges of Al 1 2- occupy the elementary mesh (n{100} Sr/La ) 2). 6 × /2 O the 4 edges, and 1 O2- occupies the center of the mesh (n{100} ) 4). The area of the mesh is c0 × a0 ) 0.47465 O nm2. With (2) one obtains Φ{100} ) (10 + 6 + 21.333)/ rel 0.4765 nm2 = 79 nm-2.
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Figure 6. {101} surface of SLA. Symbols as in Figure 4. Figure 8. {001} surface of SLA: (left) flat AlO2 layer; (right) rugged (Sr, La)O layer.
Figure 7. (left) {103} surface of SLA. (right) view in the direction [010].
{101}. The {101} surface (Figure 6) consists of xc20+a20 × a0 meshes. Al3+ occupies positions at the corners and in the center (n{101} ) 2). O2- occupies the centers of all Al {101} edges (nO ) 2). No Sr2+/La3+ is found in the surface
2 2 layer (n{100} Sr/La ) 0). The area of the mesh is xc0+a0 × a0 {101} ) 0.495 18 nm2. With (2) one obtains Φrel ) (0 + 12 + 10.667)/0.49518 nm2 = 46 nm-2. {103}. The following ions span up one plane: Sr/La1 [[1,0,0.35885]], Sr/La1 [[1,1,0.35885]], Sr/La1 [[0,0,0.64115]], Sr/La1 [[0,1,0.64115]], Al1 [[1/2,1/2,1/2]], O1 [[1/2,0,1/2]], O1 [[1/2,1,1/2]] (Figure 7). The difference vector between the first Sr/La1 ions is b ν1 ) [0,1,0]. For the difference between the third and the first Sr/La1 ions one obtains b ν2 ) [1 h ,0,0.2823]. Miller indices of the plane that is spanned by the two vectors can easily be obtained by the vector product
|
|
i j k b ν1 × b ν2 ) 0 1 0 ) (0.2823,0,1) ≈ (1,0,3.54) 1 h 0 0.2823 (3) The angle φ between the plane (h1k1l1) ) (1,0,3.54) that is spanned by the ions and the lattice plane (h2k2l2) ) (1,0,3) can be calculated using the relation
cos φ )
a2 h1h2 + k1k2 + l1l2 2 c
x
h21
+
k21
+
a2 l21 2 c
x
h22
+
k22
(4) +
a2 l22 2 c
which is valid for tetragonal lattices. With the lattice
constants given above, one finds the angle φ ) 4.75° between both planes. This means that the morphological planes {103} are in close correspondence to the plane that is spanned by these ions. The relative Coulomb interaction energy estimates are as follows: 1 Al3+ in the center of the mesh (n{103} Al ) 1), 4 × 1/4 Sr2+/La3+ at the corners (n{103} Sr/La ) 1), and 2 × 1/2 O2- at the edges (n{103} ) 1). The area of the mesh O is 0.518 nm × a0 ) 0.19458 nm2. (2) gives Φ{103} ) (5 + rel 6 + 5.333)/0.19458 nm2 = 84 nm-2. {001}. The structure of the {001} plane depends on the height where the cut through the elementary cell in Figure 1 is performed. The structure on the left-hand side of Figure 8 is obtained if the cut is performed in the height z ) 0 or z ) 1/2 through the AlO6 octahedra. The structure on the right-hand side is not flat, as the ions are in slightly different heights (zSr ) 0.14115, zO ) 0.16250), resulting in a vertical difference of 0.027 nm. The mesh size is always a20 ) 0.14111 nm2. This type of (Sr, La)O layer exists twice as often as the AlO2 layers on the left-hand side of Figure 8. The relative interaction energy can be calculated for both cases. ) 1; n{001},a ) 0; n{001},a ) 2. AlO2 layer: n{001},a Al Sr/La O {001},a Φrel ) (0 + 6 + 10.667)/0.14111 nm2 = 118 nm-2. {001},b ) 0; n{001},b ) 2. (Sr,La)O layer: n{001},b Al Sr/La ) 0; nO {001},b 2 Φrel ) (5 + 0 + 5.333)/0.14111 nm = 73 nm-2. Discussion has a minimum for the {101} It turns out that Φ{hkl} rel planes of {010}-grown SLA crystals. Thus, the low wetting of the cylinder facets that can indeed be observed during crystal growth can be explained by eq 2. No decision can be made as to whether Φ{001} ) 73 rel -2. The first value would apply nm-2 or Φ{001} ) 118 nm rel to a terminating AlO2 layer. The second value would be a crude estimation for a terminating (Sr, La)O layers a crude estimation, because the rugged surface of such a layer cannot be considered exactly by the present calculations. In any case, the equilibrium meniscus height is correctly predicted to be considerably lower on the {101} facets with respect to all other facets. for Table 1 compares the calculated values Φ{hkl} rel SLA with the corresponding values for SrLaGaO4 (SLG). This substance is an isotype of SLA but does not show the critical high wetting anisotropy. The c0/a0 ratio for SLG is less than for SLA, but the small difference does result only in a marginal reduction of the high Φ{hkl} rel anisotropy. The (Sr, La)O-terminated {001} face of SLG,
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Crystal Growth & Design, Vol. 1, No. 4, 2001 325
Table 1. Comparison of Relative Coulomb Interaction Energies for SLA with the Isotype SLG and with the Cubic BGO Φrel (nm-2) cryst SrLaAlO4 SrLaGaO4 Bi12GeO20
c0/a0 3.364 3.301 1.000
{100} 79 77 31
{101} 46 44 45
{103} 84 81
{001}
{112}
73/118a 70/113a 31 (Φ{100} rel )
∼46b
a Values are given for the flat Al(Ga)O and for the rugged (Sr, 2 La)O layer. b Only an approximate value is available, as most positions have free parameters.
which is even more rugged than the corresponding face of SLA, could be responsible for the different behaviors. The vertical difference of both positions is 0.027 nm for SLA. From zSr ) 0.141 33 and zO ) 0.167 30, one obtains a vertical difference of 0.033 nm for SLG. The increased “ruggedness” is expected to reduce Φ{001} for this face. rel Recently, Pajaczkowska et al.4 reported that the oxygen partial pressure of the growth atmosphere has a remarkable influence on the morphology of [001]grown SLG but not on SLA. On [001] SLG crystals, the size of {110} facets increases and {100} decreases with increasing oxygen content. The oxygen concentration in the atmosphere was found to be related to the coloration and to the concentration of oxygen vacancies in the crystal. It is not yet clear whether Φ{hkl} can be influrel enced by the different effective charge of the Ga ion that is due to the variation of the oxygen vacancy concentration, but this point should be the subject of further investigation. As another example, Φ{hkl} values for Bi12GeO20 rel (BGO) are given in Table 1. This substance crystallizes in space symmetry group I23 (No. 197, lattice constant a0 ) 1.0153 nm). All bismuth and most oxygen ions are on an arbitrary position 24f [[x,y,z]], and therefore, most crystal faces are more or less rugged. This applies especially to higher indexed lattice planes. Nevertheless, Table 1 gives an overview of the relative Coulomb interaction energies, considering only ions that are completely (for {100} and {101}) or almost (for {112}) “in plane”. In contrast to SLA, this highly faceted cubic crystal is wetted almost isotropically and can be grown easily without stacking faults. The appearance of facets depends on the growth direction and was discussed by Piekarczyk et al.13 Conclusions A semiquantitative description of the wetting height for different cylinder facets occurring during the Czochralski growth of crystals with ionic bonding can be given on the basis of relative Coulomb interaction energies Φ{hkl} that depend on the density of ion rel charges in the crystal surface {hkl}. For the calculation it is assumed that each cation in the surface interacts with the corresponding free anion in the melt (for oxides O2-). Each anion in the surface is assumed to interact
with the average of the charge of free cations within the melt, depending on the melt stoichiometry. For strontium lanthanum aluminate (SLA) it turnes {101} is highly different (with Φ{001} > out that Φ{hkl} rel rel /Φrel 2) for the two main facets {001} and {101} of a crystal grown in [010] (equivalent to the b a axis). This result is in agreement with the visual observation that the meniscus on {001} facets is higher than on {101} facets. The formation of defects as stacking faults or even polycrystalline growth can be initiated by rapid crystallization in the strongly supercooled region of the highly wetted {001} facet or if melt from the high meniscus of a well-wetted {001} facet overruns to a neighboring {101} facet with low meniscus. Faceting itself (without high anisotropy of wetting on neighboring facets) is not found to be critical. Therefore, two ways can be proposed to reduce the formation of defects in critical cases: (1) If possible, a growth direction should be selected that suppresses the formation of cylinder facets. n-fold rotation axes (n ) 3, 4, 6) show this property often. If the formation of facets cannot be avoided, Φ{hkl} should rel be checked for maximum isotropy. (2) Even in the case of highly different Φ{hkl} values rel on neighboring facets the hydrodynamic instability due to different wetting heights can be reduced, if a small rotation rate is applied to allow melt adjustment to the subsequent facet wetting height. Acknowledgment. We are indebted to A. Pajaczkowska, Warsaw, Poland, for discussion and hints. References (1) Woensdregt, C. F. Acta Phys. Pol. A 1997, 92, 35-46. (2) Woensdregt, C. F.; Janssen, H. W. M.; Gloubokov, A.; Pajaczkowska, A. J. Cryst. Growth 1997, 171, 392-400. (3) Gloubokov, A.; Jablonski, R.; Ryba-Romanowski, W.; Sass, J.; Pajaczkowska, A.; Uecker, R.; Reiche, P. J. Cryst. Growth 1995, 147, 123-129. (4) Pajaczkowska, A.; Klos, A.; Kasprowicz, D.; Drozdowski, M. J. Cryst. Growth 1999, 198/199, 440-443. (5) Shannon, R. D.; Oswald, R. A.; Parise, J. B.; Chai, B. H. T.; Byszewski, P.; Pajaczkowska, A.; Sobolewski, R. J. Solid State Chem. 1992, 98, 90-98. (6) Baumann, I. Lithiumniobat fu¨ r optische Anwendungen. Ph.D. Thesis, Humboldt University, Berlin, 1993 (in German). (7) Pajaczkowska, A.; Gloubokov, A.; Klos, A.; Woensdregt, C. F. J. Cryst. Growth 1997, 171, 387-391. (8) Byszewski, P.; Domagala, J.; Fink-Finowicki, J.; Pajaczkowska, A. Mater. Res. Bull. 1992, 27, 483-490. (9) Galazka, Z. J. Cryst. Growth 1997, 178, 345-349. (10) Rudolph, P. Profilzu¨ chtung von Einkristallen; AkademieVerlag: Berlin, 1982. (11) Bennema, P. Growth and Morphology of Crystals: Integration of Theories of Roughening and Hartman-Perdok Theory. In: Handbook of Crystal Growth; Hurle, D. T. J., Ed.; Elsevier: Amsterdam, 1993; Vol. 1A, pp 477-581. (12) Brown, R.; Pendrick, V.; Kalokitis, D.; Chai, B. H. T. Appl. Phys. Lett. 1990, 57, 1351-1353. (13) Piekarczyk, W.; SÄ wirkowicz, M.; Gazda, S. Mater. Res. Bull. 1978, 13, 889-894.
CG015507F
