San Jose State University
From the SelectedWorks of David W. Parent
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X-ray rocking curve analysis of tetragonally distorted ternary
semiconductors on mismatched „001… substrates
X. G. Zhang, D. W. Parent, P. Li, A. Rodriguez, G. Zhao, J. E. Ayers,
a)
and F. C. Jain
Electrical and Computer Engineering Department, University of Connecticut, Storrs,
Connecticut 06269-2157
共Received 30 July 1999; accepted 28 February 2000兲
For ternary heteroepitaxial layers, the independent determination of the composition and state of
strain requires x-ray rocking curve measurements for at least two different hkl reflections because
the relaxed lattice constant is a function of the composition. The usual approach involves the use of
one symmetric reflection and one asymmetric reflection. Two rocking curves are measured at
opposing azimuths for each hkl reflection. Thus, it is possible to account for tilting of the hkl planes
in the epitaxial layer with respect to the hkl planes in the substrate, by averaging the peak
separations obtained at the opposing azimuths. This procedure presents a practical problem in the
case of asymmetric reflections, for which the tilting can only be canceled if the rocking curve for
one azimuth is obtained using
⫺
incidence. A preferable approach, which provides sharper,
more intense rocking curves and greater experimental accuracy, is to measure both asymmetric
rocking curves at
⫹
incidence. This approach requires that the data be corrected for the tilting
of the asymmetric planes introduced by tetragonal distortion. Here we have presented a new analytic
procedure that incorporates the tilting of asymmetric diffracting planes due to tetragonal distortion.
The new procedure allows the measurement of all rocking curves at
⫹
incidence. We have
applied this new method to the case of ZnS
y
Se
1⫺ y
grown heteroepitaxially on GaAs 共001兲, using
004 and 044 x-ray rocking curves. We have shown that neglect of the tilting in asymmetric planes
results in gross errors in the calculated values of composition 共as much as 35 times兲 and in-plane
strain 共as much as 2.6 times兲 for this material. © 2000 American Vacuum Society.
关S0734-211X共00兲06403-9兴
I. INTRODUCTION
Ternary and quaternary alloys of zincblende semiconduc-
tors are important for the fabrication of high-performance
transistors, such as heterojunction bipolar transistors and
high electron mobility field effect transistors, as well as op-
toelectronic devices, including laser diodes, modulators, and
detectors. The composition and state of strain in an alloy
semiconductor greatly affect device performance. Therefore,
much effort has been devoted to the characterization of these
materials by x-ray diffraction and photoluminescence.
In the case of a ternary heteroepitaxial layer, the indepen-
dent determination of the relaxed lattice constant 共and there-
fore the composition兲 and state of strain requires at least two
x-ray rocking curve measurements. This is because the re-
laxed lattice constant is a function of the composition. Some-
times the analysis is simplified with the assumption that the
heteroepitaxial layer has grown coherently on the
substrate.
1–3
With this ‘‘pseudomorphic’’assumption, the in-
plane lattice constant is assumed to be equal to the substrate
lattice constant. Then a single rocking curve measurement,
using a symmetric reflection, is sufficient for the estimation
of the composition and state of strain in a ternary layer. This
simplified approach has been extended to quaternary semi-
conductors, for which a single x-ray measurement is com-
bined with a photoluminescence measurement to determine
the relaxed lattice constant and band gap for the material.
Such a simplified approach is suitable for a heteroepitaxial
system such as AlGaAs/GaAs, for which the lattice mis-
match is small over the entire range of aluminum composi-
tion. In other heteroepitaxial systems, the possibility of par-
tial lattice relaxation mandates the use of at least two
different x-ray rocking curve measurements.
Typically, for heteroepitaxy on a 共001兲 substrate, rocking
curves are obtained for one symmetric reflection such as the
004 and one asymmetric reflection such as the 115 or 044.
Then, with the assumption that the strained alloy layer is
distorted tetragonally, the in-plane and out-of-plane lattice
constants 共a and c, respectively兲 may be determined. A com-
plication that arises in this procedure is the tilting of the
asymmetric diffracting planes, which is caused by the tetrag-
onal distortion.
In this article, we describe a procedure for the determina-
tion of a self-consistent set of values for the in-plane lattice
constant, the out-of-plane lattice constant, and the tilting of
the asymmetric diffracting planes, using measurements of
asymmetric rocking curves with only
⫹
incidence. We
have also demonstrated the procedure by applying it to the
case of heteroepitaxial ZnS
y
Se
1⫺ y
grown on GaAs 共001兲
substrates, using 004 and 044 x-ray rocking curves. We show
that gross errors result if the composition and strain in the
ternary layer are calculated by neglecting the tilting of the
044 planes due to tetragonal distortion.
a兲
Author to whom all correspondence should be addressed; present address:
University of Connecticut, 260 Glenbrook Road, Storrs, CT 06269-2157;
electronic mail: jayers@engr.uconn.edu
1375 1375J. Vac. Sci. Technol. B 18„3…, MayÕJun 2000 0734-211XÕ2000Õ18„3…Õ1375Õ6Õ$17.00 ©2000 American Vacuum Society
II. THEORY
When using symmetric x-ray rocking curves for het-
eroepitaxial layers 关for example, the 004 reflection for the
共001兲 heteroepitaxial samples兴 it is necessary to measure the
peak separation ⌬
at a minimum of two azimuths in order
to determine the difference in Bragg angles ⌬
B
.
4
This is
because there is, in general, a tilting of the heteroepitaxial
layer with respect to the substrate.
5–12
Thus, the 关001兴 axes
of the two are not parallel. The rocking curve peak separa-
tion is then
13
⌬
⫽ ⌬
B
⫹ ⌬
0
cos
共
⫺
0
兲
, 共1兲
where ⌬
is the rocking curve peak separation measured at
an azimuth
, ⌬
B
is the Bragg angle difference between
the heteroepitaxial layer and the substrate, ⌬
0
is the tilt
between the 关001兴 axes of the substrate and the epitaxial
layer, and
0
specifies the direction of the tilt. Thus, the
effect of ⌬
0
on the measured peak separations can be
eliminated by recording the rocking curves at opposing azi-
muths 共i.e.,
⫽ 0° and
⫽ 180°).
An additional complication arises if one attempts to use
the above approach with an asymmetric reflection 关for ex-
ample, the 044 reflection for 共001兲 heteroepitaxial samples兴.
In such cases there is an additional tilt component ⌬
tet
if
the heteroepitaxial layer is tetragonally distorted:
⌬
⫽ ⌬
B
⫹ ⌬
0
cos
共
⫺
0
兲
⫹ ⌬
tet
. 共2兲
As before, the measurement of the asymmetric rocking
curves at opposing azimuths, for the same set of planes, al-
lows elimination of the tilt component ⌬
tet
. That approach
has been described in detail previously.
14–16
However, the
disadvantage of that approach is that it requires measuring
the rocking curve for one azimuth using
⫺
incidence.
This leads to a relatively weak rocking curve peak and re-
quires longer scanning time compared to using
⫹
inci-
dence 共Fig. 1 shows the
⫹
and
⫺
geometries as used
in this approach兲. The reflected intensity ratio for the two
geometries can be estimated as
17
I
共
⫹
兲
I
共
⫺
兲
⫽
sin
2
共
⫹
兲
sin
2
共
⫺
兲
, 共3兲
where I(
⫹
) and I(
⫺
) are the reflected intensities for
the cases of
⫹
and
⫺
incidence, respectively. For
example, in the case of the 044 reflection from 共001兲 GaAs,
the ratio is 112. This means that the reflected intensity for the
⫺
incidence may be insufficient for the purpose of an
accurate measurement in that case. Thus, it is generally de-
sirable to measure both asymmetric rocking curves 共at the
two opposing azimuths兲 with only
⫹
incidence 共as shown
in Fig. 2兲, to obtain rocking curve peaks with optimum in-
tensity and full width at half maximum. This minimizes the
experimental uncertainty in the measured peak separation.
However, ⌬
tet
has the same sign for both measurements
and cannot be eliminated by taking the average value of the
peak separation as before. Nonetheless, ⌬
tet
can be calcu-
lated from knowledge of the strained lattice constants in the
heteroepitaxial layer. For the common case of 共001兲 het-
eroepitaxy, strain in the grown layer results in tetragonal
distortion. Then for the hkl reflection, ⌬
tet
is given by
⌬
tet
⫽ cos
⫺ 1
冉
l/c
冑
共
h/a
兲
2
⫹
共
k/a
兲
2
⫹
共
l/c
兲
2
冊
⫺ cos
⫺ 1
冉
1
冑
h
2
⫹ k
2
⫹ l
2
冊
, 共4兲
FIG. 1. Asymmetric 044 reflections at opposing azimuths using the same set
of diffraction planes. 共a兲
⫽ 0° with
⫹
incidence and 共b兲
⫽ 180° with
⫺
incidence. The
axis is parallel to the 关001兴 direction and perpen-
dicular to the sample surface. The
⫽ 180° rocking curve must be obtained
with the
⫺
incidence in this case.
FIG. 2. Asymmetric 044 reflection at opposing azimuths using two different
sets of planes. 共a兲
⫽ 0° and 共b兲
⫽ 180°. Both rocking curves may be
obtained with the
⫹
incidence in this case.
1376 Zhang
et al.
: X-ray rocking curve analysis 1376
J. Vac. Sci. Technol. B, Vol. 18, No. 3, MayÕJun 2000
where a and c are the in-plane and out-of plane lattice con-
stants for the heteroepitaxial layer, respectively, and the sub-
strate has been assumed to be unstrained. Thus, for measure-
ments with
⫹
incidence, biaxial compression causes
⌬
tet
to be positive while biaxial tension causes ⌬
tet
to be
negative.
For the rocking curve analysis of a ternary heteroepitaxial
layer on a 共001兲 substrate, the ideal procedure is as follows:
First, a symmetric 00m reflection is measured at two oppos-
ing azimuths and the out-of-plane lattice constant is deter-
mined from the average peak separation ⌬
ave
. Using the
00m reflection,
c⫽
m
2 sin
共
B00m,substrate
⫹ ⌬
ave,00m
兲
, 共5兲
where is the x-ray wavelength. Next, an asymmetric hkl
reflection is measured with
⫹
incidence at two opposing
azimuths. The spacing for the hkl planes can be determined
as
d
hkl
⫽
2 sin
共
Bhkl,substrate
⫹ ⌬
ave,hkl
⫺ ⌬
tet
兲
, 共6兲
where ⌬
ave,hkl
is the average peak separation for the hkl
reflection. Then the in-plane lattice constant may be deter-
mined from
a⫽
冉
h
2
⫹ k
2
l
2
/c
2
⫺ 1/d
hkl
2
冊
⫺ 1/2
. 共7兲
If Eqs. 共6兲, 共7兲, and 共4兲 are solved iteratively, starting with
any particular value of ⌬
tet
, then the end result will be a
consistent set of values for c, a, and ⌬
tet
. Then the relaxed
lattice constant a
0
and state of strain
⑀
may be determined
for the heteroepitaxial layer using
a
0
⫽
c⫹
冉
2
1⫺
冊
a
1⫹
冉
2
1⫺
冊
, 共8兲
in-plane
⫽
a⫺ a
0
a
0
, 共9兲
and
out-of-plane
⫽
c⫺ a
0
a
0
, 共10兲
where
is the Poisson ratio of the heteroepitaxial layer
which is defined as the negative of the ratio between lateral
and longitudinal strains under uniaxial longitudinal stress
and is related to the elastic stiffness constants C
11
and C
12
as
关
001
兴
⫽
C
12
共
C
11
⫹ C
12
兲
共11兲
for the 关001兴 orientation.
III. EXPERIMENT
For this study, ZnS
y
Se
1⫺ y
heterostructures were grown on
semi-insulating GaAs 共001兲 ⫾ 0.5° substrates supplied by
Atomergic Chemetals. Prior to epitaxy, the substrates were
cleaned sequentially in boiling trichloroethylene, acetone,
and methanol. After rinsing in deionized water, the sub-
strates were etched for 3 min in Caro’s etch of a 5:1:1
H
2
SO
4
:H
2
O
2
:H
2
O composition, at a temperature of 60 °C.
After a second rinse in deionized water, the substrates were
treated for one minute in 1:1 HC1:H
2
O to remove the native
oxide. Finally, substrates were rinsed in deionized water,
then boiling isopropanol, and loaded into the reaction cham-
ber.
A vertical, stainless steel EMCORE reactor with a rotat-
ing, resistively heated molybdenum susceptor was used. All
growth runs were carried out at 250 Torr with 350 rpm sus-
ceptor rotation, and with 14.25 slm of palladium-diffused
hydrogen as the carrier gas. The photoirradiation was
achieved using an Oriel Hg arc lamp operated at 150 W
electrical power. The ultraviolet 共UV兲 irradiation was
brought into the reaction chamber using a mirror and a
quartz window, resulting in normal incidence on the sample.
Neutral density filters were used to adjust the irradiation in-
tensity. All irradiation intensities reported were measured us-
ing an intensity meter 共manufactured by HTG兲 outside of the
reaction chamber.
Prior to growth, the substrates were held at 610°C for 2
min in pure hydrogen to remove oxygen and carbon contami-
nation. Growth was always initiated or restarted on Se-
stabilized surfaces 共the DMSe flow was started 1 min before
the DMZn flow兲. The growth was interrupted for tem-
FIG. 3. 004 rocking curves for sample 744. Top: The azimuth was 180°.
Bottom: the azimuth was 0°.
1377 Zhang
et al.
: X-ray rocking curve analysis 1377
JVSTB-MicroelectronicsandNanometer Structures
perature ramps and changes in ultraviolet intensity.
A high-temperature ZnSe buffer layer was always grown
first, at 595 °C and without UV irritation, because photoas-
sisted metalorganic vapor phase epitaxy growth cannot be
initiated directly on the bare GaAs surface. The reactant
mole fractions were 10
⫺ 4
共DMZn兲 and 2⫻ 10
⫺ 4
共DMSe兲 for
the high-temperature buffer. The total thickness of the two
ZnSe buffer layers was 130 nm.
ZnS
y
Se
1⫺ y
was grown on top of the ZnSe buffer layers at
360 °C and with the incident irradiation intensity adjusted to
36 m W/cm
2
, with a growth time of 45 min. The reactant
mole fractions were 10
⫺ 4
共DMZn兲,2⫻ 10
⫺ 4
共DMSe兲 and 0
to 2.5⫻ 10
⫺ 4
共DES兲.
The heteroepitaxial samples were characterized by high-
resolution x-ray diffraction using a Bartels five-crystal x-ray
diffractometer described previously.
18,19
The Philips fixed-
anode Cu x-ray source was operated at 40 kV and 20 mA.
The line-focused beam was slit limited to 5 mm length nor-
mal to the plane of the diffractometer and 0.5 mm width in
the plane of the diffractometer by pairs of slits placed on
either side of the monochromator. The spacing between the
slits was 210 mm. A four-crystal Bartels-type monochro-
mator was employed using four Ge 022 reflections from Ge
共011兲 crystals arranged in the 共⫹, ⫺, ⫺, ⫹兲 geometry and
tuned to the Cu K
␣
1
lined (⫽ 1.540 594 Å兲. 004 and 044
rocking curves were measured at 293 K using the 共⫹, ⫺, ⫺,
⫹, ⫺兲 and 共⫹, ⫺, ⫺, ⫹, ⫹兲 geometry. For each rocking
curve measurement, the specimen tilt was adjusted to bring
the specimen diffraction vector into the plane of the diffrac-
tometer. Tilt optimization was performed by adjusting the tilt
for maximum peak reflected intensity and with a precision of
⫾ 0.5°.
Two symmetric 004 reflections and two asymmetric 044
reflections have been measured at two opposing azimuths
from each sample. Figure 3 shows the 004 rocking curves for
sample 744 for
⫽ 0°, 180°,
being the azimuth. Two
diffraction peaks are observed, one for the GaAs and one for
the ZnS
y
Se
1⫺ y
. The peak of the pseudomorphic ZnSe buffer
layer, which is observed from other samples, is merged in
the left tail of the ZnS
y
Se
1⫺ y
peak. Typical intensities mea-
sured with a Bicron scintillation counter were 3000 counts
s
⫺ 1
for the GaAs 004, 300 counts s
⫺ 1
for the ZnSe 004, and
1500 counts s
⫺ 1
for the ZnS
y
Se
1⫺ y
004. The measured 004
rocking curve peak separation between the GaAs and the
ZnSe is about 780 arc sec for the analyzed samples. Figure 4
shows the 044 rocking curves for sample 744 for
⫽ 45°
and 225° both at
⫹
incidence. While there was sufficient
x-ray intensity to clearly resolve the ZnS
y
Se
1⫺ y
peak, the
peak of the ZnSe buffer layer was too weak to be resolved.
The summary of measured 004 and 044 rocking curve
data and the calculated results for all of the analyzed samples
is reported in Tables I and II, respectively. To determine the
peak separation accurately, the 004 and 044 rocking curve
profiles for the GaAs, ZnSe, and ZnS
y
Se
1⫺ y
were extracted
by least squares fitting to Lorentzian profiles 共GaAs兲 and
Gaussian profiles 共ZnSe and ZnS
y
Se
1⫺ y
). The peak separa-
tions could be evaluated with an accuracy of ⫾ 1.5 arc sec.
The procedure for the determination of a self-consistent set
of values for the out-of-plane lattice constant c, the in-plane
lattice constant a, and the relaxed lattice constant a
0
for the
ZnS
y
Se
1⫺ y
epitaxial layers are as the follows: 共1兲 Determine
the out-of-plane lattice constant from the 004 measurement.
FIG. 4. 044 rocking curves for sample 744 both at
⫹
incidence. Top: the
azimuth was 45°. Bottom: The azimuth was 225°.
TABLE I. Summary of measured 004 and 044 rocking curve data for the
different samples investigated. ⌬
is the peak separation between the
ZnS
y
Se
1⫺ y
and the GaAs.
is the azimuth.
⌬
004
共arc sec兲⌬
004
共arc sec兲⌬
044
共arc sec兲⌬
044
共arc sec兲
Sample (
⫽ 0°) (
⫽ 180°) (
⫽ 45°) (
⫽ 225°
743 ⫺441 ⫺425 ⫺420 ⫺340
744 ⫺350 ⫺325 ⫺320 ⫺320
745 ⫺180 ⫺190 ⫺90 ⫺90
751 ⫺90 ⫺70 ⫺90 ⫺120
746 110 125 ⫺130 ⫺120
748 340 340 ⫺120 ⫺90
749 570 520 150 120
TABLE II. Summary of the calculated results for the different samples inves-
tigated. c, a, and a
0
are the out-of-plane, the in-plane and the relaxed lattice
constants of the ZnS
y
Se
1⫺ y
epitaxial layer, respectively. y is the solid phase
composition. a, a
0
, and y have been calculated by correcting the tilting of
the 044 planes, ⌬
tet
.
Sample c 共Å兲 a 共Å兲
a
0
共Å兲
y 共%兲
743 5.6716 5.6660 5.6685 0.08
744 5.6677 5.6600 5.6635 2.0
745 5.6611 5.6547 5.6576 4.3
751 5.6567 5.6556 5.6561 4.9
746 5.6483 5.6571 5.6531 6.04
748 5.6391 5.6573 5.6490 7.6
749 5.6305 5.6526 5.6426 10.1
1378 Zhang
et al.
: X-ray rocking curve analysis 1378
J. Vac. Sci. Technol. B, Vol. 18, No. 3, MayÕJun 2000