Crystallographic Polarity of ZnO Crystals
A. N. Mariano and R. E. Hanneman
Citation: J. Appl. Phys. 34, 384 (1963); doi: 10.1063/1.1702617
View online: http://dx.doi.org/10.1063/1.1702617
View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v34/i2
Published by the American Institute of Physics.
Additional information on J. Appl. Phys.
Journal Homepage: http://jap.aip.org/
Journal Information: http://jap.aip.org/about/about_the_journal
Top downloads: http://jap.aip.org/features/most_downloaded
Information for Authors: http://jap.aip.org/authors
Downloaded 05 Oct 2012 to 152.14.136.96. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
JOURNAL OF APPLIED
PHYSICS
VOLtiME
34.
NUMBER
i
FEBR1JARY
1963
Crystallographic Polarity of ZnO Crystals
A. N. MARIANO AND R. E. HANNEMAN
Lincoln Laboratory,* Massachusetts Institute of Technology, Lexington 73, Massachusetts
(Received 30 July 1962)
The crystallographic polarity of the noncentrosymmetric material zincite (ZnO) has been determined by
a rapid x-ray absorption edge method. The polarity results have been correlated to marked differences in
etching behavior and crystal morphology in opposite polar directions of ZnO crystals. These differences are
shown to be consistent with the proposed surface bonding model for AII-Bv! compounds. Crystal morphology
is shown to be a useful criterion to indicate crystallographic polarity in well-formed wurtzite-type crystals.
I. INTRODUCTION
II. X-RAY THEORY AND TECHNIQUE
ONSIDERABLE interest in recent years has
focused on crystallographic polarity and consequent property differences on opposite polar surfaces
of various materials having noncentrosymmetric structures. Particular emphasis has been placed on materials
of significance in solid-state electronics of the ArnBv
type and, to a more limited degree, the ArrBvI type.
In the course of some of this recent work a model was
conceived/,2 based on the surface bonding characteristics of the A and B surface atoms, to account for the
marked differences in some physical and chemical properties of the opposite polar surfaces of these crystals.
It is of considerable interest to investigate the applicability of the proposed surface bonding model to noncentrosymmetric materials which are oxides and those
with larger electronegative differences (and greater
ionicity) than heretofore examined. The present paper
treats this region of interest by studying the crystallographic polarity of ZnO and its relationship to certain
property differences on A and B polar surfaces, including etching behavior and crystal morphology. Recently,
Cole3 and Stemple3 presented a lucid description of the
effect of crystal perfection and polarity on x-ray absorption edges seen in Bragg diffraction by noncentrosymmetric crystals. The present work describes in some detail a modification of that x-ray method for rapid absolute polarity determination, with specific application to
wurtzite-type materials.
The crystal habit of many well-formed noncentrosymmetric crystals is distinctly different in the opposite
polar directions of such materials. This study attempts
to show that crystal morphology of euhedral ZnO crystals is consistent with the surface bonding model and
that morphology can be used to determine crystallographic polarity in many cases. This criterion should be
particularly useful for polarity identification in compounds not amenable to x-ray or piezoelectric studies.
The spatial arrangement of atoms in the unit cell of
a crystal and the differential scattering power of the
individual types of atoms determine the modulus of the
geometric scattering factor of such a crystal. James 4
and Cole3 have presented theoretical treatments relating the geometric scattering factor F to the intensity
of x rays diffracted from perfect and mosaic crystals.
If a crystal scatters as an ideally mosaic crystal the intensity is proportional to 1 F 1 2, whereas, in the case of
strong reflections from a perfect crystal the diffracted
intensity is proportional to 1F I. The geometric scattering factor of a general (hkl) reflection is given by
C
F(hkl) = Lj(fo+~1'+i~f")j
X exp[27ri(hxj+kYj+lzj)],
(1)
where 10 is the atomic scattering factor, ~1' and ~1"
are anomalous dispersion corrections,4.5 and (XjYjZj)
are the spatial coordinates of each of the j atoms in the
unit cell.
The wurtzite structure contains 4 atoms per unit cell,
two of the A species (i.e., Zn) at the positions (000) and
(Ht) and the B species (i.e., 0) at (OOl) and (Hi).
Substituting these values into Eq. (1) and regrouping:
F(hkl) = [(fA'+i~fA")+ (f B'+it.fB")e!!ril]
X {1 exp[27ri (ih+~k+tl)],
+
(2)
where 1'= (fo+~f'). Multiplying by the complex conjugate of F(hkl) and simplifying, the following expression is obtained for the modulus of the geometric scattering factor:
1
* Operated with support from the U. S. Army, Navy, and Air
Force.
.,
1 H. C. Gatos and M. C. Lavine, J. Electrochem. Soc. 107, 427
(1960).
2 E. P. Warekois, M. C. Lavine, A. N. Mariano, and H. C.
Gatos, J. App!. Phys. 33, 690 (1962).
8 H. Cole and N. R. Stemple, J. App!. Phys. 33, 2227 (1962).
FF*(hkl) 1 = {2+2 cos27r(ih+~k+tl)}
X {[jA' + fB' cOS!7rl- t.fB" sih!7rl]2
+[t.fA"+~fB" cos!7rl+ fB' sinhl]2}.
(3)
This equation is a general expression for any (hkl) reflection in any material with a wurtzite structure.
For the determination of absolute configuration, or
polarity, in noncentrosymmetric crystals in the wurtzite class, such as ZnO, the {OO ·l} family of reflections
must be considered, as they are normal to the polar
axis. Referring to Eq. (3), if lis odd, FF*{OO·I} is equal
4 R. W. James, Optical Principles of the Diffraction of X-rays
(G. Bell and Sons, Ltd., London, 1958).
6 C. H. Dauben and D. H. Templeton, Acta Cryst. 8, 841 (1955).
384
Downloaded 05 Oct 2012 to 152.14.136.96. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
CRYSTALLOGRAPHIC
to zero; if 1= 4n, where n is zero or an integer, F F* {OO ,1)
is equal to FF*(oo·l). However, for ±1=4n-2(i.e.,
002, or 002), FF*(OOl);;Z!FF*(OOl), and therefore the
diffracted intensity of these reflections should be different on the A and B sides of the wurtzite crystal. (The
A and B sides are defined as those opposite surfaces,
which are parallel to {OO ·l} planes and they terminate
with only A and B atoms, respectively.2) Using Eq. (3)
this intensity ratio, which is used to identify ZnO
crystal polarity in this paper, is given by:
1(00·2)
FF*(OO·2)
1(00·2)
FF*(00·2)
385
POLARITY OF ZnO CRYSTALS
A-
80
o
Zn
SURFACE
(00'2)
SURFACE
(00·2 )
>-
!:: 60
II)
z
UJ
>.., •
1.263A
>"K"
>"2"
1.303 A
1.283A
~
~
40
20
IBACKGROUND\
{[jA'+LlfB"]2+[LlfA"- fs']2}
O~__~~~~~~__~~~~~~~b~l~'_~~__~
(4)
28
{[fA' -Llfs"]2+[LlfA"+ fB']2} '
where I (00·2)/1 (00,2) is the calculated intensity ratio
for ideally mosaic crystals. (The ZnO crystals used were
found to behave as almost ideally mosaic crystals from
intensity measurements of several {hkl} planes.)
Since the dispersion corrections, in effect, represent
a differential absorption of incident radiation by the
scattering atoms, the maximum effect will be noted at
the short wavelength side of the absorption edge of one
of the elements. The anomalous dispersion effect becomes quite small immediately adjacent to the long
wavelength side of the edge. All other variables cancel
in the calculated intensity ratios except FF* (00 ·1)/
FF*(OO·l). Thus a comparison of experimental and calculated l(OO·I)/l(Oo·i) near both sides of the absorption edge provides a highly sensitive and convenient
method for unambiguous determination of crystallographic polarity. There are no higher-order {OO ·/} reflections superimposed on the {OO· 2} reflections near
the corresponding K edge of interest because the x-ray
tube is operated at sufficiently low voltage that:
I\(Kedge»I\SWL>tl\(Kedge). I\SWL is the short wavelength limit of the continuous spectrum source corresponding to the operating voltage.
The intensity of (00·2) and (00·2) reflections from
ZnO are obtained as a function of A from the continuous
spectrum of a copper tube in a Norelco x-ray unit. The
sample is placed on the diffractometer specimen holder
with {00·2} planes satisfying the Bragg relation; a
Geiger counter is used to record intensity as a function
of 28 (and hence A). Measurements are arbitrarily made
at a convenient position very close to either side of the
absorption edge of interest. In this case measurements
and calculation of intensity were made at ±0.02 A from
the Zn Kedge (i.e., approximately ±O.So 28 on either
side of Zn Kedge). Background intensity is subtracted
before calculating the experimental 1(00·2)/1(00·2)
ratio.
29
28
29
28·FIG. 1. Continuous spectrum diffraction contours across the
zinc K-absorptiop edge wavelength, from ZnO single crystal with
(00·2) and (00·2) planes satisfying the Bragg condition.
III. RESULTS AND DISCUSSION
A. X-Ray Diffraction
The diffraction contours from the continuous spectrum produced by the (00· 2) and (00· 2) planes of ZnO
are shown in Fig. 1 with their differential absorption
edge effect due to anomalous dispersion. The background
x-ray level is indicated below the scans of both sides in
Fig. 1. Referring to Table I, the calculated intensity
ratio [FF*(00·2)/FF*(00·2)]c~lc at A=1.303 A is very
close to unity (i.e., 1.01 to 1). Experimentally this condition is effected by slight adjustment to the tube current before the x-ray scan of either side of the crystal
such that the [I(00·2)/1(00·2)]exptl at A=1.303 A is
equal to unity as seen in Fig. 1. The 1(00·2)/1(00·2)
at A= 1.263 A, however, is then observed to be appreciably less than unity as predicted by theory and consistent with [FF*(00·2)/FF*(00·2nalc in Table I. The
deviations of calculated and observed differences of
1(00·2)/1(00·2) at A= 1.263 A are due to: (1) the fact
that the crystals are really not ideally mosaic, and thus
the intensity does not exactly have /F /2 dependence for
strong reflections, (2) approximately a one percent error
inherent in the calculated ratio by not including the
Debye-Waller temperature factor in the atomic scattering factors, and (3) the degree of crystal perfection
TABLE
r. Calculated and observed values of 1(00·2)/1(00·2)
for ZnO on either side of Zn Kedge.
ExperiCalculated mental
FF*(00'2) 1(00·2)
X(A)
1.263
1.303
10(Zn) 10(0)
22.8
22.8
5.75
5.75
!llzn'
!llo'
-4.06
-4.37
+0.04
+0.04
---- ---
!llzn" tl/o" FF*(00·2) 1(00·2)
3.41
0
0.03
0.03
0.82
1.01
Downloaded 05 Oct 2012 to 152.14.136.96. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
0.7
1.0
386
A.
N.
MARIANO
AND
which can vary from Zn to 0 surfaces. Nevertheless
the agreement between calculated and experimental
values is good and the polarity determination is unambiguous with Zn occupying the (00·1) surface, which
had the lower intensity in Fig. 1 for t.. < 1.283 A, and the
R.
E.
HANNEMAN
t
Zo<OO'l>
FIG. 3. Photomicrograph (16X) of euhedral ZnO crystal
etched with a 6:6: 1 solution (by volume) of fuming HNO.,
glacial acetic add, and H 20. Distinctly polar etch figures are
evident on the (lOiO) prism faces.
o atoms occupying the (00· i) surface. The relationship
Ca) Zn(OOol)
of these x-ray results is correlated to crystal morphology
and etching behavior in the following section. (The experimental values shown in Fig. 1 and listed in Table I
are for the natural ZnO used, but the other grades of
zincite crystals used in the experiment gave almost identical results.) In the course of this work new accurate
lattice constants were determined by powder methods
for pure ZnO. These are: a= 3. 2499± 0.0001 A and
c= S.206±O.001 A.
B. Etching Behavior and Crystal Morphology
The A and B surfaces of ZnO crystals show marked
differences in their response to chemical etching. This
is in agreement with earlier studies of other materials
with the wurtzite structure.2 ,6,7 Specific etchants used
for revealing differences in chemical reactivity on polar
surfaces are listed in Figs. 2 and 3, and their effects are
illustrated therein. From the etching experiments it was
found that the (0001) surface (i.e., oxygen surface as
identified by x rays) etched more rapidly in the oxidizing etchants used than did the Zn surface. In impure
crystals etching action on the A (or Zn) face is primarily
located where dislocations intersect that surface [see
Fig. 2(a)]. This preferential etching effect is particularly noticeable in such ZnO crystals.8 The rapidly attacked B surface (oxygen surface) in these crystals,
(b) O(oo.i)
FIG. 2. Photomicrographs of ZnO 100· t I showing Zn and a surfaces
after etching 90 sec in 20% HNO a solution (180X).
(\ D. C. Reynolds and S. J. Czyzak, J. Appl. Phys. 31, 94 (1960).
7 R. Zare, W. R. Cook, Jr., and L. R. Shiozawa, Nature 189,
217 (1961).
S Crystals used in these studies included: (1) laboratory pure
vapor grown crystals and (2) cinderbank crystals from furnace
residues; both from the New Jersey Zinc Company. These crystals
had sufficiently well-developed external forms to correlate crystal
morphology with x-ray polarity results. Other crystals used include ZnO grown in a PbF2 flux and the naturally occurring
mineral zincite from Sterling Hill, Franklin, New Jersey.
Downloaded 05 Oct 2012 to 152.14.136.96. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
CRYSTALLOGRAPHIC
POLARITY OF ZnO CRYSTALS
however, is etched with more uniformly distributed etch
figures (hillocks). Since the formation of intermediate
surface products does not appear to interfere with
etching these factors are consistent with a surface bonding model proposed by Gatos and Lavine for III-V
compoundsl and modified for II-VI compounds by
Gatos et al. 2 As shown in Fig. 4 which illustrates this
model, the surface atoms are triply bonded, and the
bulk atoms are tetrahedrally bonded. The A atoms have
no electron dangling bonds at the surface whereas the
B atoms have a dangling bond with two electrons at the
surface. As a result the A atom bonds are more severely
distorted from tetrahedral Sp3 symmetry than the B
atom bonds. Of the three bonds joining each surface
atom to the crystal, two are considered largely covalent,
and the third bond is considered coordinate, with resonance between each bond.
Since the Zn and 0 atoms show a significant difference
in electronegativity, an appreciable part of the so-called
covalent bonds possess a partial ionic character which
indicates that the zinc atoms tend to transfer some of
their electrons to the oxygen atoms. In this case the
layer of zinc surface atoms tends to have a positive
charge and the layer of oxygen surface atoms a negative
charge, in addition to the two dangling electrons per
oxygen atom. A net surface dipole moment prevails
which has recently been discussed by Gatos.9
The dangling electrons on the B surface account for
the high etching rate on the B surface because of their
susceptibility to reaction with electron-seeking agents
in the etchant. The relatively uniform attack observed
on the oxygen surface in Fig. 2 (b) is also consistent with
the idea that dangling electrons largely control the surface etching action in certain kinds of etchants where the
formation of intermediate products is not controlling.
The slower over-all etching rate of the A surface is in
accord with the absence of any dangling electrons on
the A surface. Dislocation etch pits probably occur at
t<OOO/)
BULK
"A" SURFACE
o
A
A
f
\2100
B
,,'0..--' ,,
,, ,,
: 0:
'(.\
/\::.;\
','
~ 0i
A
A
l
1
BULK
BULK
o
"B" SURFACE
1<tIoo i>
FIG. 4. Scehmatic of surface bonding mode of
Au - BVI wurtzite compounds.
9
H. C. Gatos,
J.
App!. Phys. 32, 1232 (1961).
387
both surfaces due to etchant attack along the dislocations, but they are readily apparent only on the A (Zn)
surface where their effect is not masked by the rapid
etching action which prevails everywhere on the B
surface.
Etching behavior on the (lOiO) natural prism planes,
shown in Fig. 3, also provides a means of unambiguous
identification of polarity in ZnO. The apex of the large
etch pits (which are depressed from the surface level)
point toward the Zn surface. Conversely the small etch
hillocks (which are elevated above the prism plane level)
point toward the 0 surface. These effects are observed
in both pure and impure ZnO.
Another physical property, abrasion resistance, was
found to be different on the Zn and 0 surfaces. While
polishing with 600 grit garnet abrasive it was observed
that one of the basal surfaces liberated a yellow ZnO
residue much more rapidly than the other side. The
side which abraded most rapidly was identified by x-ray
results to be the (B) oxygen surface. This is in agreement with earlier findings on III-V compounds. lO
Noncentrosymmetry in the polar direction is immediately revealed by the crystal morphology of ZnO, as is
illustrated in Fig. 3. The crystals are characterized by
a flat base at one end and by steep pyramidal forms at
the opposite end. X-ray absorption edge data established
that the large flat base is the B surface, or oxygen
layer, and that the steeply terminated end is the A surface, or zinc layer. This crystal morphology can be explained with the bonding model described above. According to that model the A surface atom bonds are
more severely strained than the B surface atom bondsl l
and thus the effective surface energy should be higher on
the Zn surface. Since a fast growing plane generally
tends to disappear (leaving behind the slower growing
forms with lower surface energy),12 the steeply inclined
pyramidal faces should form on the fast growing, or Zn,
end of euhedral (well-formed) ZnO crystals.
There are a number of wurtzite-type Au-Bv! compounds which occur as natural or synthetic euhedral
crystals with analogous crystal morphology to ZnO.13
In some of these materials it would be very difficult to
determine crystallographic polarity by any x-ray
method. In such an instance, Newkirkl4 and coworkers have identified the polarity of BeO by piezoelectric methods and found that the differences in crystal morphology and etching behavior are in agreement
10 E. P. Warekois, M. C. Lavine, and H. C. Gatos, J. App!.
Phys. 31, 1302 (1960).
11 Recent experimental evidence on spontaneous bending of
thin wafers of the Am-Bv material, InSb, supports this theory.
R. E. Hanneman, M. C. Finn, and H. C. Gatos, J. Phys. Chern.
Solids 23, 1553 (1926.)
12 F. C. Frank in Growth and Perfection of Crystals, edited by R.
H. Doremus, B. W. Roberts, and D. Turnbull (John Wiley &
Sons, Inc., New York, 1958), p. 4.
13 C. Palache, H. Berman, and C. Fronde1, The System of Mineralogy (Dana) (John Wiley & Sons, Inc., New York, 1955), 7th
ed., Vo!' I.
14 H. Newkirk, D. Smith, and J. Kahn (private communication).
Downloaded 05 Oct 2012 to 152.14.136.96. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
388
A.
N.
MARIANO
AND
with the ZnO results reported above. In similar cases,
especially if unambiguous piezoelectric polarity data
are not attainable, crystal morphology may be especially
useful as a rapid indication of the crystal polarity.
R.
E.
HANNEMAN
posite polar directions are entirely consistent with this
model.
(3) Crystal morphology can serve as a means of
identification of polarity in well-formed crystals of any
wurtzite-type materials.
IV. CONCLUSIONS
(1) The absolute crystallographic polarity of ZnO
has been determined by a useful, rapid x-ray method
and the results have been correlated to etching figures
and crystal morphology.
(2) The surface bonding model for An-Bv! compounds has been extended to a noncentrosymmetric
material of the oxide type and with a larger electronegativity than previously investigated. Etching behavior and crystal morphology of ZnO crystals in op-
JOURNAL
OF
APPLIED
PHYSICS
ACKNOWLEDGMENTS
Appreciation is extended to T. B. Reed of Lincoln
Laboratory and C. R. Bieling of New Jersey Zinc
Company for supplying the ZnO crystals used in this
work. The authors are grateful to E. P. Warekois and
H. C. Gatos for valuable discussions. They wish particularly to thank H. Cole and H. Newkirk for furnishing results regarding the x-ray method and the BeO
polarity, respectively, prior to publication.
VOLUME
34.
NUMBER
2
FEBRUARY
1963
Growth of Ferrous-Free Cobalt Ferrite Single Crystals
A. FERRETTI, W. KUNNMANN, AND A. WOLD
Lincoln Laboratory,* Massachusetts Institute of Technology, Lexington 73, Massachusetts
(Received 21 May 1962)
Single crystals of cobalt ferrite were grown from a melt having the composition 95% CoFe 20. - 5% NaFe02
by weight, under an oxygen pressure of 1650 psig and a temperature of 1590°C. Chemical analysis indicated
that the crystals contained no Fe2+ and 3 parts per 10 000 sodium.
INTRODUCTION
been difficult to grow pure ferrite crystals from
I Tthehasmelt
because they dissociate at high temperatures with the loss of oxygen. Pure magnetite single crystals have been grown by a Bridgman method! and the
ferrite region of the phase diagram Fe-Co-O has also
been investigated. 2 Cobalt ferrite single crystals, which
contained 1.3% Fe2+, were grown from melts by Ferretti,
Arnott, Delaney, and Wold. a Ferrous-free cobalt ferrite
single crystals have been grown from sodium ferrite
flux by Kunnmann, Banks, and Wold. 4
It was believed that pure cobalt ferrite crystals could
, also be grown from melts if sufficient oxygen pressure
(ca. 1600 psig) was maintained to prevent decomposition of the ferrite. However, under these conditions
stoichiometric cobalt ferrite melted at a much higher
temperature than reported previously and platinum
crucibles could no longer be used. Both iridium and
platinum-rhodium crucibles were used and found to be
unsatisfactory. The lack of suitable crucible materials
* Operated with support from the U. S. Army, Navy, and Air
Force.
1 J. Smiltens, J. Chern. Phys. 20, 990 (1952).
2 J. Smiitens, J. Am. Chern. Soc. 79, 4881 (1957).
3 A. Ferretti, R. J. Arnott, E. Delaney, and A. Wold, J. App!.
Phys. 32, 905 (1961).
• W. Kunnmann, E. Banks, and A. Wold, J. App!. Phys. 33,
1364 (1962).
necessitated the development of a modified Bridgman
technique in which crystals were grown from a melt,
having the composition 95% CoFe 204-5% NaFe02 by
weight, under an oxygen pressure of 1650 psig and a
temperature of 1590°C.
EXPERIMENTAL
Preparation of Starting Materials
The cobalt ferrite used in these investigations was prepared by the thermal decomposition of a cobalt pyridinate "precursor" COaFe6(CHaC02)170aOH·12C5H5N.5
The ferrite obtained was free from any impurities which
would be introduced by ball-milling or other ceramic
technique. A ratio of Fe/Co of 1.99±0.01 was computed
from values obtained for total iron and cobalt. Cobalt
ferrite prepared by this procedure did not melt at
1600°C and 1650 psig oxygen pressure, whereas the
ferrite obtained by ball-milling and firing cobalt carbonate and iron oxide mixtures did melt under these
conditions.
The sodium ferrite was formed by the fusion of sodium
carbonate with an equimolar mixture of ferric oxide.
X-ray examination of the product showed the presence
of several weak lines which indexed as sodium ferrate,
6 D. G. Wickham, E. R. Whipple, and E. G. Larson,
Nuel. Chern. 14, 217 (1960).
Downloaded 05 Oct 2012 to 152.14.136.96. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
J.
Inorg.