Direct measurement of strain in a Ge island on Si(001)

Article abstract of DOI:10.1063/1.124272

We report on a direct measurement of the strain in a single Ge quantum dot island grown on Si by chemical vapor deposition. This transmission electron microscopy method is reliable: without the need for detailed modeling of the strain field, it measures the maximum in-plane displacement. Good agreement is found between the experimental value of 0.86±0.17% average strain and finite element simulations assuming pure Ge. Thus no evidence of significant alloying with Si is observed.

Full text of DOI:10.1063/1.124272

Direct measurement of strain in a Ge island on Si(001)
Peter D. Miller, Chuan-Pu Liu, William L. Henstrom, J. Murray Gibson, Y. Huang, P. Zhang, T. I. Kamins, D. P.
Basile, and R. Stanley Williams
Citation: Applied Physics Letters 75, 46 (1999); doi: 10.1063/1.124272
View online: http://dx.doi.org/10.1063/1.124272
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/75/1?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Atomic scale stresses and strains in Ge ∕ Si ( 001 ) nanopixels: An atomistic simulation study
J. Appl. Phys. 96, 4429 (2004); 10.1063/1.1792811
Photoluminescence of strained and relaxed multilayered Ge islands on Si(001)
Appl. Phys. Lett. 81, 1186 (2002); 10.1063/1.1500776
The effect of strain field seeding on the epitaxial growth of Ge islands on Si(001)
Appl. Phys. Lett. 78, 1658 (2001); 10.1063/1.1352660
Strain and composition of capped Ge/Si self-assembled quantum dots grown by chemical vapor deposition
Appl. Phys. Lett. 77, 370 (2000); 10.1063/1.126979
Strain relaxation of faceted Ge islands on Si(113)
Appl. Phys. Lett. 75, 2395 (1999); 10.1063/1.125025
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
136.165.238.131 On: Fri, 19 Dec 2014 03:14:40

APPLIED PHYSICS LETTERS
VOLUME 75, NUMBER 1
5 JULY 1999
Direct measurement of strain in a Ge island on Si„001…
Peter D. Miller, Chuan-Pu Liu, William L. Henstrom, and J. Murray Gibson
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Y. Huang and P. Zhang
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign,
Urbana, Illinois 61801
T. I. Kamins, D. P. Basile, and R. Stanley Williams
Hewlett-Packard Laboratories, 3500 Deer Creek Road, Palo Alto, California 94304-1392
͑Received 21 December 1998; accepted for publication 12 May 1999͒
We report on a direct measurement of the strain in a single Ge ‘‘quantum dot’’ island grown on Si
by chemical vapor deposition. This transmission electron microscopy method is reliable: without the
need for detailed modeling of the strain field, it measures the maximum in-plane displacement.
Good agreement is found between the experimental value of 0.86Ϯ0.17% average strain and finite
element simulations assuming pure Ge. Thus no evidence of significant alloying with Si is observed.
© 1999 American Institute of Physics. ͓S0003-6951͑99͒01927-0͔
In recent years, researchers have shown considerable in-
terest in Ge–Si heteroepitaxy due to the system’s potential
technological importance and to basic questions regarding
the system’s morphological evolution. The observation that
Ge forms uniformly sized, nondislocated, well-ordered ar-
contrast due to strain in the Si substrate.9 Images ͑Fig. 1͒
were acquired with Ge islands on the top ͑the electron beam
entry surface͒ at a location where the substrate thickness was
550 nm,10 thick enough to make image contrast relatively
insensitive to small changes in thickness or deviation param-
eter. A thick specimen also reduces to a negligible level the
effects of relaxation at the bottom surface. In determining the
strain, line profiles parallel to g across individual islands
were analyzed and compared to simulations. As we will
show, the interpretation of image line profiles ͑Fig. 1͒ is
quite straightforward.
rays of islands when deposited under appropriate conditions
1–3
onto Si͑001͒
has led to the hope that this simple system
will find applications in novel electronic and optical devices.
Alternatively, several aspects of this system’s morphological
evolution have led to differing theories regarding the mecha-
nism of evolution, including the basic question of whether
the different morphologies arise kinetically or thermo-
dynamically.4–6 Since the lattice parameter of Ge is 4.2%
larger than that of Si, strain is an important feature of the
system and plays a key role in the system’s behavior, both
electronically and morphologically.
Transmission electron microscopy ͑TEM͒ has long been
recognized as a valuable tool for measuring strain;7,8 the
challenge is finding a simple way to model complicated
strain fields. Below, we show that a universal strain model
can be used to measure strain due to Ge quantum dots and
many related systems.
The islands analyzed were deposited by chemical vapor
deposition on Si͑001͒ wafers. After baking at 1150 °C in a
H2 ambient and depositing a Si buffer layer at 1080 °C, Ge
was deposited at 600 °C and a pressure of 10 Torr using
GeH4 in a H2 carrier gas. The amount of Ge deposited was
equivalent to 11 ML (1 MLϭ6.27ϫ1014 Ge atoms cmϪ2).
The heating power was turned off shortly after the GeH4
flow stopped, and the sample was not intentionally annealed.
Further details of the growth can be found elsewhere.3 We
prepared TEM specimens by mechanical dimpling followed
by wet chemical thinning in a 1:10 HF:HNO3 solution. Wax
which was applied to protect the Ge-coated surface from the
acids was removed using a series of organic solvents.
Digital images were acquired using a Gatan 1024
ϫ1024 slow-scan charge coupled device ͑CCD͒ camera in a
Philips CM-12 TEM operating at 120 kV. We acquired dark
field images at the exact two-beam condition for gϭ(220)
and gϭ(400), conditions for which the islands show strong
FIG. 1. ͑a͒ Strain caused by coherent Ge islands results in strong TEM dark
field image contrast. In ͑b͒, a line profile across an island reveals detailed
structure. Extrema which lie inside the island radius are arrowed.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
0003-6951/99/75(1)/46/3/$15.00 46 © 1999 American Institute of Physics
136.165.238.131 On: Fri, 19 Dec 2014 03:14:40

Appl. Phys. Lett., Vol. 75, No. 1, 5 July 1999
Miller et al.
47
FIG. 2. In the abrupt displacement approximation, the continuous bending
of lattice planes is approximated as a step function.
To do this, image simulations were performed by inte-
grating the two-beam Howie–Whelan equations7,9 using the
MATHEMATICA software package. These are a system of
coupled first-order ordinary differential equations that can be
used to simulate contrast due to strained crystalline speci-
mens if a strain model is available.
FIG. 3. Simulated image contrast can be used to improve the accuracy of
strain measurements. As the slope of ␣(r)ϭ␣maxr/r0 increases, the extrema
move closer to the center of the island. Here, ␣max/(␲/2) varies from 5
͑lightest͒ to 6 ͑darkest͒. By analyzing the positions of the extrema in experi-
mental images, accurate strain measurements are possible.
Unfortunately, no simple analytical model exists for the
strain field due to isolated Ge islands on Si͑001͒. Other re-
searchers have shown that image simulations using finite el-
ement ͑FE͒ strain fields yield contrast that is qualitatively
similar to experimental images,11,12 however such simula-
tions have not been used for quantitative measurements. It is
difficult to measure sample properties such as strain using FE
simulations since it is difficult to adjust simulation param-
eters: one FE simulation is needed to generate each image
simulation.
Surprisingly, results can be well explained by using a
greatly simplified strain model. We find that when the dis-
placement field decays rapidly compared with the length
scale relevant to imaging, i.e., the electron extinction dis-
tance ͑typically ϳ100 nm͒, qualitative features can be pre-
dicted using a very simple approximation which we call the
abrupt displacement approximation ͑ADA͒. In this approxi-
mation, the continuous displacement field is replaced by a
step function a short distance into the substrate ͑Fig. 2͒. The
size of the step increases linearly from the center to the edge
of the island.
In other words, provided that the displacement field de-
cays rapidly enough—within 10–20 nm of the strain
source—the ADA allows us to replace any continuous dis-
placement field with a stacking fault-like9 abrupt displace-
ment which is at a fixed depth and has a variable magnitude.
This approximation is useful since TEM image contrast due
to stacking faults is well understood. Comparison of this
model with image simulations using full strain fields shows
that the ADA works well.
Properties of image contrast depend on the scalar prod-
uct of the diffraction vector used for imaging, g, and the
displacement field, u, via the quantity ␣ϭ2␲ g.u. If u in-
creases linearly parallel to g, then ␣ϭ2␲g(⑀r), for rϽr0
where r is parallel to g, r0 is the radius of the island, and ⑀
ϭ⑀rr , the radial strain in the substrate. Using these assump-
tions with the ADA, we find that image contrast is periodic
with ␣, nearly following a sinusoid. By counting extrema
that lie inside the radius of the island the maximum value of
the phase ␣max can be bounded. If n is the number of extrema
between the center of the island and the island’s edge, then
More precise measurements are made by analyzing the posi-
tions of intensity extrema inside the island’s radius.
Line profiles across islands imaged with a gϭ(400) dif-
fraction vector show three extrema, allowing us to place
bounds on ␣max. Analyzing the positions of extrema closest
to the particle edges improves the measurement. The average
position of the outermost extrema for three islands was found
to be 0.887 r0 , which, when compared with a contrast table
͑Fig. 3͒, leads to a value ␣m(4a0x0)ϭ8.98 (ϭ5.72␲/2). By
simple algebra, the maximum lattice plane displacement is
⑀r0ϭ0.19 nm and using a weak-beam TEM measurement of
the average island radius, we find that ⑀ϭ0.19 nm/22.5 nm
ϭ0.84Ϯ0.17%. We expect that by improving experimental
procedures, measurement error less than 10% will be readily
achievable.
Our measurement agrees well with FE simulations and
with other measurements of the strain. FE results show a
maximum displacement ⑀r0ϭ0.216 nm. Converting our
strain measurement to a stress ͑using 170 GPa for the Si
Young’s modulus and 0.262 for the Poisson ratio͒, we find
␴rrϭ1.6 GPa, a value which lies at the upper end of a re-
cently measured range of stress values for pure Ge on
Si͑001͒ during the ‘‘nucleation and growth’’ phase of evolu-
tion, prior to dislocation introduction.13 A combined x-ray
scanning tunneling microscopy ͑STM͒ measurement of
strain in an earlier growth phase, when the presence of
‘‘huts’’ or ‘‘pyramids’’ dominates, led to a strain measure-
ment at the edge of the island equal to 0.5%.14 Strain has also
been measured in islands composed of dilute SiGe alloys on
Si͑001͒, and values similar to those measured here have been
predicted and measured.6,15
We offer the following observations about the measured
strain value: first, since the measured maximum displace-
ment matches the results of FE simulations for pure Ge, this
suggests that Si has not diffused into the Ge to relax strain.
This stands in contrast to electron diffraction strain measure-
ments of pure Ge islands deposited and capped with Si at a
much higher temperature ͑750 °C͒. In this case the islands
were observed to incorporate nearly 40% Si into the Ge.16
Second, we note that the maximum displacement of lat-
tice planes, 0.19 nm, is equal to the Burgers vector for an
␲
␲
2nϪ1͒ Ͻ␣maxϽ 2nϩ1͒
.
This article ͑is copyrighted as indica͑ted in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
2
2
edge dislocation in Si. Displacement of lattice planes greater
136.165.238.131 On: Fri, 19 Dec 2014 03:14:40

48
Appl. Phys. Lett., Vol. 75, No. 1, 5 July 1999
Miller et al.
than this amount would be unlikely since introduction of a
dislocation would be energetically more favorable.
In conclusion, we have presented a universal strain mea-
surement technique that does not rely on detailed knowledge
of the form of the strain field, and we have used it to measure
the in-plane strain in individual coherent Ge islands on
Si͑001͒. The measurement agrees well with previous mea-
surements using different techniques, and it suggests that Si
diffusion into pure Ge islands does not contribute signifi-
cantly to stress relaxation in unannealed Ge islands deposited
under the present conditions.
Note added in proof. While the measurements presented
here are correct, subsequent measurements have shown that
specimen preparation may affect the strain. We refer the
reader to future publications for more extensive measure-
ments of strain in this system.
4 L. B. Freund, ZAMP 46, S185 ͑1995͒.
5 G. Medeiros-Ribiero, A. M. Bratkovski, T. I. Kamins, D. A. A. Ohlberg,
and R. S. Williams, Science 279, 353 ͑1998͒.
6 J. A. Floro, E. Chason, R. D. Twesten, R. Q. Hwang, and L. B. Freund,
Phys. Rev. Lett. 79, 3946 ͑1997͒.
7 M. F. Ashby and L. M. Brown, Philos. Mag. 8, 1083 ͑1963͒.
8 O. V. Kolosov, M. R. Castell, C. D. Marsh, G. A. D. Briggs, T. I. Kamins,
and R. S. Williams, Phys. Rev. Lett. 81, 1046 ͑1998͒.
9 P. Hirsch, A. Howie, R. Nicholson, D. W. Pashley, and M. W. Whelan,
Electron Microscopy of Thin Crystals ͑Butterworths, London, 1967͒.
10 S. M. Allen, Philos. Mag. A 43, 325 ͑1981͒.
11 Y. Androussi, A. Lefebvre, B. Courboules, N. Grandjean, J. Massies, T.
´
Bouhacina, and J. P. Aime, Appl. Phys. Lett. 65, 1162 ͑1994͒.
12 T. Benabbas, P. Franc¸ois, Y. Androussi, and A. Lefevbre, J. Appl. Phys.
80, 2763 ͑1996͒.
13 G. Wedler, J. Walz, T. Hesjedal, E. Chilla, and R. Koch, Phys. Rev. Lett.
80, 2382 ͑1998͒.
14 A. J. Steinfort, P. M. L. O. Scholte, A. Ettema, F. Tuinstra, M. Nielsen, E.
Landemark, D.-M. Smilgies, R. Feidenhand’l, G. Falkenberg, L. Seehofer,
and R. L. Johnson, Phys. Rev. Lett. 77, 2009 ͑1996͒.
15 S. Christiansen, M. Albrecht, H. P. Strunk, and H. J. Maier, Appl. Phys.
1 D. J. Eaglesham and M. Cerullo, Phys. Rev. Lett. 64, 1943 ͑1990͒.
2 Y.-W. Mo, D. E. Savage, B. S. Swartzentruber, and M. G. Lagally, Phys.
Rev. Lett. 65, 1020 ͑1990͒.
Lett. 64, 3617 ͑1994͒.
D. Cherns, A. Hovsepian, and W. Jager, J. Electron Microsc. 47, 211
16
3 T. I. Kamins, G. Medeiros-Ribeiro, D. A. A. Ohlberg, and R. S. Williams,
J. Appl. Phys. 85, 1159 ͑1999͒.
¨
͑1998͒.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
136.165.238.131 On: Fri, 19 Dec 2014 03:14:40