Growth and Defect Structures

151 Pages·1984·6.571 MB·English

by  Yu. M. Tairov, V. F. Tsvetkov (auth.), Prof. Dr. H. C. Freyhardt, Georg Müller (eds.)

10 Crystals
Growth, Properties, and Applications
Managing Editor: H. C. Freyhardt
Editors: T. Arizumi, W. Bardsley, H. Bethge
A. A. Chernov, H. C. Freyhardt, J. Grabmaier
S. Haussiihl, R. Hoppe, R. Kern, R. A. Laudise
R. Nitsche, A. Rabenau, W. B. White
A. F. Witt, F. W. Young, Jr.
Growth
and Defect Structures
With Contributions by
V. V. Osiko V. I. J>olezhaev A. A. Sobol
Y. Tairov V. Tsvetkov Y. K. V oron'ko
Springer-Verlag
Berlin Heidelberg New York Tokyo 1984
Managing Editor
Prof. Dr. H. C. Freyhardt, Kristall-Labor der Physikalischen Institute,
Lotzestr. 16-18, D-3400 Gottingen
and Institut flir Metallphysik der Universitat Gottingen, Hospitalstr. 12,
D-3400 Gottingen
Editorial Board
Prof. T. Arizumi, Department of Electronics, Nagoya University, Furo-cho Chikusa-Ku,
Nagoya 464, Japan
Dr. W. Bardsley, Royal Radar Establishment, Great Malvern, England
Prof. H. Bethge, Institut fUr Festkorperphysik und Elektronenmikroskopie, Weinberg, 4010 Halle/
Saale, DDR .
Prof. A. A. Chernov, Institute of Cristallography, Academy of Sciences, Leninsky Prospekt 59,
Moscow B -117333, USSR
Dr. I. Grabmaier, Siemens AG, Forschungslaboratorien, Postfach 80 1709, 8000 Miinchen 83,
Germany
Prof. S. Haussuhl, Institut fUr Kristallographie der Universitiit KOln, Ziilpicherstr. 49,5000 Koln,
Germany
Prof. R. Hoppe, Institut fUr Anorganische und Analytische Chemie der Justus-Liebig-Universitiit,
Heinrich-Buff-Ring 58, 6300 GieSen, Germany
Prof. R. Kern, Universite Aix-Marseille ill, Faculte des Sciences de St. Jerome, 13397 Marseille
Cedex 4, France
Dr. R. A. Laudise, Bell Laboratories, Murray Hill, NJ 07974, U.S.A.
Prof. R. Nitsche, Krlstallographisches Institut der Universitiit Freiburg, HebelstraBe 25,
7800 Freiburg, Germany
Prof. A. Rabenau, Max-Planck-Institut fUr Festkorperforschung, Heisenbergstr. 1,7000 Stutt
gart 80, Germany
Prof. W. B. White, Materials Research Laboratory, The Pennsylvania State University, University
Park, PA 16802, U.S.A.
Prof. A. F. Witt, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.
Dr. F. W. Young, Jr., Solid State Division, Oak Ridge National Laboratory, P.O. BOX X,
Oak Ridge, TN 37830. U.S.A.
Guest Editor
Prof. Dr. H. Muller-Krumbhaar, Institut fUr Festkorperforschung, KFA Jiilich, Postfach 1913,
5170 Jillich, Germany
ISBN-13: 978-3-642-69868-2 e-ISBN: 978-3-642-69866-8
DOl: 10.1007/978-3-642-69866-8
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Table of Contents
Growth of Polytypic Crystals
Y. Tairov and V. Tsvetkov 1
Spectroscopic Investigations of Defect Structures and Structural Transformations
in Ionic Crystals
V. V. Osiko, Y. K. Voron'ko and A. A. Sobol . . . . . . . . . . . . . . . .. 37
Hydrodynamics, Heat and Mass Transfer During Crystal Growth
V. 1. Polezhaev . . . . . . 87
Author Index Volumes 1-10 .................... . 149
Growth of Polytypic Crystals
Yu. M. Tairov and V. F. Tsvetkov
Electrical Engineering Institute, 5 Prof. Popor Street, Leningrad 197022, USSR
The present state of the investigations ofg rowth processes, structural and thermodynamic properties of
poly typic crystals of different substances, the nature ofp olytypism and the physics ofp hase transitions
between poly typic structures is considered in this review. The main thermodynamic and kinetic princi
ples of polyt ype-crystal synthesis are discussed as well as the major problems in the field of their
controlled growth.
1 Introduction . . . . . . . . . . . . . . . . . . . . . 3
2 Polytypism and Polytypic Structures . . . . . . . . . 4
3 Chemical Bond and Structure of AnBS-n Compounds. 6
4 Thermodynamic Properties, Parameters of Crystal Lattices and Polytypic
Crystal Composition . . . . . . . . . . . . . 12
5 Phase Transformations in Polytypic Crystals . 16
6 Formation and Growth of Polytypic Crystals . 21
6.1 Process Temperature . . . . . . . 22
6.2 Growth Rate . . . . . . . . . . . 23
6.3 Non-Stoichiometry and Impurities 24
6.4 Substrate Surface . . . . . . . . . 25
6.5 Controlled Formation of Growth Centres . 28
7 Conclusions 31
8 References. . . . . . . . . . . . . . . . . . . 32
Crystals 10
@ Springer-Verlag Berlin Heidelberg 1984
Growth of Polytypic Crystals
1 Introduction
Polytypic crystals of semiconductors, dielectrics and magnetic materials attract an
increasing attention in science and technology. On one hand, the phenomenon of polyty
pism is one of the fundamental problems of solid-state physics; its solution would make it
possible to elucidate-the problem of the interconnection of different structures and
intraatomic forces acting in crystals. On the other hand, the polytypic difference in
crystals is most strongly expressed in electro-physical properties, which makes their
application promising, mainly in semiconductor electronics. Thus, the difficulties of pro
ducing modulated structures in polytypic crystals can be overcome since these crystals
form a class of one-dimensional natural superlattices.
At present it has become clear that polytypism in crystals and compounds is the rule
rather than an exception and it is determined by the conditions of their synthesis. This
phenomenon seems to be rather widespread in nature and fundamental for crystal forma
tion. H polytypism was recently thought to be but a specific structural feature of a few
substances such as SiC, ZnS, CdI2, etc., by now this phenomenon has been discovered in
an increasing range of crystalline substances, for example, in silicon, diamond, AIIIBv,
AIIBVI, AIBVII compounds, in ternary semiconducting compounds, metals, silicates,
perovskites, mica, organic crystals. The more accurately the structural studies are per
formed, the greater is the number of crystals of various substances found to exhibit the
phenomenon of polytypism.
Recently, excellent surveys have systematized our knowledge of polytypism. Among
them the book by Verma and Krishna!) should be mentioned first, wherein both theoreti
cal and experimental investigations up to 1966 are systematized. This book is very well
supplemented by Trigunayar), Dubef), Prasad4), Baronnef), who mainly deal with the
structural aspects.
The present work describes the modem studies of composition, thermodynamic prop
erties of polytypic crystals, the nature of polytypism and the physics of phase transitions
between polytypic structures. The kinetic aspects of the synthesis of polytypic crystals as
well as the main problems of their controlled production are considered. The analysis is
=
carried out mainly for crystals of the class of AnBS-n compounds (where n 1,2,3,4);
they are the best studied ones at present.
The analysis of thermodynamic properties of polytype crystals leads to the conclusion
that the nature of polytypism in crystals is kinetic.
The generalized diagram of the crystalline state is constructed from an electronegativ
ity quantum scale. The average s-p hybridization of electron wave functions is plotted on
one of the diagram axes, and the total electronegativity of the atoms on the other one. In
these coordinates. the crystals of elements and binary compounds AnBS-n are subdivided
into four groups of substances with a different stable crystalline structure: graphite, rock
salt, wurtzite and sphalerite. The main advantage of the coordinate system is that it
separates substances with wurtzite and sphalerite structures differing in atomic arrange
ment beginning with the third coordination sphere.
The compounds in which the polytypism is most easily manifested (SiC, ZnS, ZnSe,
ZnTe and CdTe) lie at the boundary between the sphalerite and wurtzite structures. Thus
the relation between the electron structure of crystals and the polytypism is traced. The
experimental data known on the nucleation and growth of polytypic crystals reveal that in
3
Y. Tairov and V. Tsvetkov
all the diverse substances polytypic structure is manifested when in the nucleation stage
or in the crystal growth conditions are created allowing the formation of a metastable
structure. In subsequent growth stages, a phase transition is accompanied by the genera
tion of stacking faults and their exposure on the growing surface, as well as their partici
pation in crystal growth. Impurities as well as deviations from the stoichiometry of the
principal components in the parent medium greatly affect these processes resulting in the
stabilization of a polytypic structure.
The validity of the ideas presented on the nature of polytypism is confirmed by the
polytypism control in crystals based on their nucleation stage, considered in this work.
2 Polytypism and Polytypic Structures
The phenomenon of polytypism represents the ability of solid materials to crystallize in
more than one structural modification having strictly similar chemical composition (if the
deviation from stoichiometry due to natural defects is neglected; see below) and differing
in number, nature and arrangement of layers in the crystal unit cell. The layers may be of
a complicated composition, but they all are identical and are superimposed on each other
on closely packed crystal surfaces. Due to the structural identity of layers, the polytypic
crystals have similar cell parameters in the layer plane and different cell parameters in the
normal direction. The value of the cell size normal to the layers or the height of the cell in
the same substance may vary from a few to several thousands of Angstroms. Due to the
identity of elemental layers the height of the unit cell is equal to the product of elemental
layer height and their number in the cell. More accurate recent investigations (see below)
indicate that elemental layers in different polytypic structures of the same substance are
not quite identical, their parameters both in the layer plane and normal to it may rather
differ from one polytype to another within a thousandth of an Angstrom.
We shall mention the principal methods of describing the polytypic structures used in
our further discussion.
For describing three-dimensional closely-packed crystalline structures a classical
ABC scheme is widely used by which the alternation sequence of two-dimensional layers
is shown. The three positions of layers in the most closely-packed arrangement of hard
sphere atoms are denoted as A, Band C (Fig. 1). Each subsequent identical layer of
spheres, if closely packed on layer A, can occupy positions of either B or C type.
Similarly, a layer either in position C or A can be placed on layer B, or else a layer in
Fig. 1. The densest packing of similar hard
spheres. Three possible layer positions, A, B and C,
are characterized by the arrangement of spheres
within the (1120) crystal plane
4
Growth of Polytypic Crystals
position A or B on layer C. Hence, any sequence of letters A, B and C, in which no letter
is immediately followed by the same one characterizes the most closely-packed arrange
ment. The height or the parameter C of a unit cell in the most closely-packed arrange
ment depends on the number of layers after which the packing sequence is repeated. This
number, n, defines the identity period and varies from 2 up to infinity for different
closely-packed arrangements. The mutual arrangement of atoms in layers is clearly seen
from the structure of the crystallographic plane (1120) (Fig. 2 for two silicon carbide
structures). The structure of a wurtzite type is represented by the sequence [AB]AB ...
with a repetition· of two layers; that of a sphalerite type, by the sequence of [ABC]
ABCABC ... with a repetition of three layers. The six-layer structure is represented by
the sequence of [ABCACB]ABCACB ... etc.
Such a notation becomes too bulky for long-period structures. More conveniently,
polytypic structures are described with Zhdanov symbols6). The symbol consists of num
bers of which the first one indicates the number of successive cyclic (A ~
B ~ C ~ A ...) packing arrangements, whereas the second one - that of anticyclic
(A ~ C ~ B ~ A ...) packings. The same numbers characterize the sequence of zig
zags formed by atoms in the plane of (1120) (Fig. 2). H a preceding and a succeeding
layer have a similar orientation the intermediate one is designated with the letter h for
hexagonal; whereas the layer on both sides of which the adjacent layers have a different
orientation is denoted with the letter K (for cubic). Consequently the hexagonality
D = nt!(nh + nO, where nh and nk are the number of layers in hexagonal and cubic
positions, respectively, is more convenient.
Since a layer having a hexagonal position in a cubic lattice represents a stacking fault,
such a configuration in polytypic crystals is often termed a microtwin.
Ramsdel's notation7 ) includes the number of layers in a unit cell, which is followed by
a Latin letter indicating the crystallographic system to which the given structure belongs.
It is recommended to use letters C, Th 0, H, R, M and Tc to denote the cubic, tetra
gonal, orthorhombic, hexagonal, rhombohedral, monoclinic and triclinic crystallographic
ASCA'CA'CA8CASC'
!J
Fig. 2a, b. Arrangement of Si and C atoms in tbe (1120) crystal plane of polytypic silicon carbides
6H (a) and 15R (b). Large circles represent silicon atoms, small black ones - carbon atoms
5
Y. Tairov and V. Tsvetkov
systems, respectively. For instance, a sii-Iayer hexagonal and a fifteen-layer rhombohe
dral polytype with layer-packing sequences of ABCACB and ABCBACABACBCACB
or hkkhkk and hkhkkhkhkkhkhkk, respectively, are represented as [33] and [32b with
Zhdanov symbols and as 6 H and 15 R with Ramsdell symbols. Polytypes having similar
dimensions of the unit cell but different sequences of packing arrangements of ABC are
distinguished by subscripts, e.g. nHb nH2, etc.
These designations are applicable to polytypic structures of both elements and chemi
cal compounds. In this case the elemental layers of the structure A, Band C will no
longer be monoatomic, but polyatomic, and the letters, A, B, and C characterize the
positions of atoms of one kind in the elemental layer , whereas the positions of the other
atoms in these layers are determined relative to those mentioned above. For example, in
SiC the elemental layer of the structure consists of closely packed Si atoms; and above
each of them one C atom is located at a distance of 0,189 nm (Fig. 2).
3 Chemical Bond and Structure of An B8-n Compounds
The structure and physical properties of crystals are determined by the nature of the
chemical bond which in tum depends on the electron structure of atoms involved. At
present there is no quantitative theory describing the changes in crystals depending on
the changes in the chemical bond. Therefore, the empirical approach is very important,
i.e. the establishment of correlations between atom character and the crystal structure.
The quantum coordinates are most suitable for distinguishing characteristic proper
ties of the chemical bond. In this case the coordinates must be able to characterize the
atoms of the substances in the bound state, already. The Pearson-Mooser diagram8) is the
first attempt to use quantum coordinates. When constructing this diagram, two factors of
structure stability are utilized for AnBB-n compounds: first, the charge transport to the
anion (ionicity) described by the electro negativity X, and second, the dehybridization
(metallization) of directional s-p bonds by d and f states. The weakest metallization is
observed in compounds with components belonging to the second row in the periodic
system; this is caused by the high energy of transition from 2 s, 2 p states into 3 d, 4 f ones.
The metallization is increased with increasing main quantum number n; therefore an
average quantum number ii = (nA + nB)/2 can be used as a measure of metallization.
Such a simple approach gives only 8 errors out of more than 100 predictions of the
coordinate number in the crystalline structure of ADBB-n and similar compounds. On the
one hand, this is due to the electronegativity difference AX being not an exact measure of
the ionicity of the bond, since the shielding in the crystal is not accounted for. On the
other hand, ii does not describe the bond dehybridization in the best way. The substances
with sphalerite and wurtzite structures and polytypic substances are not isolated into
independent groups in this coordinate system.
Phillips and Van-Vechten have perfected the Pearson-Mooser coordinate system on
the basis of their dielectric theory9). The optical spectra for a large number of tetrahe
drally coordinated A DBB-D semiconductors together with pseudo-potential calculations
showed that solid-state properties depend directly on two variables: the bond length and
the value of ionicity of the covalent bond. This resulted from the spectroscopic determi
nation of electronegativity, the values of which for tetrahedral bonds with Sp3 hybridiza-
6
Growth of Polytypic Crystals
tion are much more accurate than Pauling's data. The ionicity according to Phillips9), fj, is
determined as
where Eg is the energy gap between bonding and antibonding states in the two-zone
isotropic dielectric model of a solid body. This value is expressed as
where Eh is the homopolar (covalent) part of the energy gap to which a symmetrical part
of the crystal potential corresponds; C is the heteropolar (ionic) part of it corresponding
to the antisymmetric part of the crystal potential. Plotting Eb and C along the coordinate
axes, Phillips and Van Vechten constructed a diagram to predict the coordination
number of A DB&-n compounds without any errors10). According to the diagram the ionic
ity is a determining factor of the crystalline structure. For fj < fim' = 0.785 ± 0.010 the
coordination number is 4, and for fj > fim' it is 6.
The relationship established is easily and satisfactorily explained by the deflection of
the bond charge toward the anion when the ionicity fj is increased. The phase transition
or the transition from one coordination to another occurs when the bond charge enters,
so to say, the ion core. Since the interaction of only the nearest neighbours is considered
in the Phillips-Van Vechten dielectric theory, the sphalerite and wurtzite structures
cannot be differentiated in the diagram plotted. It is even more impossible to isolate in
this diagram a group of polytypic substances (ZnS, SiC, ZnSe, ZnTe, CdTe) whose
structures differ in the third coordination sphere only.
The John-Bloch model of electron shellsll) is much more successful, since it permits to
find the stability boundaries for structures of graphite, sphalerite, wurtzite, NaCI and
CsCI (Fig. 3). To plot this diagram John and Bloch suggest to use the orbital coordinates
of 0-and n-bonds. When the chemical bond is formed, the density of valence electrons
entering the atom combination is redistributed. The extent of electron density redistribu
tion is determined by the interaction of valence electrons with the charge Z of ion core.
Hydrogen-like atoms (i, e, Li, Be+, B+2, C+3 etc.) can serve as a convenient model for
studying this interaction. Therefore Simons and Bloch have calculated orbital radii rl for
orbital quantum numbers I
1(1 + 1)
rl = Z .
where 1i s a non-integer to be chosen in such a way that 0nl = (1 - 1) should represent an
experimentally observed quantum defect. It should be pointed out that rl is determined
by the ratio of the Coulomb attraction force and the Pauli repulsion force between the
core electrons and valence electrons. On the other hand, it is known that the fractions of
the lattice energy corresponding to the attraction raise the stability of more-ionic crys
talline structures, while the fractions corresponding to the repulsion en~rgy, contribute to
the formation of covalent structures.
Orbital radii Ra and R,. are determined as a linear combination rio and may serve as a
measure for the electron charge transfer from cations to anions (Ra) and the bond charge
7