Influence of strain on semiconductor thin film epitaxy - Fitzgerald ...

<strong>Influence</strong> <strong>of</strong> <strong>strain</strong> on semiconductor thin film epitaxy
E. A. Fitzgerald, a) S. B. Samavedam, Y. H. Xie, b) and L. M. Giovane
Department <strong>of</strong> Materials Science and Engineering, MIT, Cambridge, Massachusetts 02139
Received 2 October 1996; accepted 24 March 1997
Under typical growth conditions, <strong>strain</strong> levels greater than or equal to 10 4 are shown to influence
thin film surface morphology and <strong>strain</strong> relaxation pathways. Misfit and threading dislocations in
relaxed heterostructures produce long wavelength undulations on the surface and shallow
depressions, respectively. Threading dislocation densities greater than 10 5 –10 6 cm 2 in relaxed
heterostructures must be due to increased impediments to dislocation motion, which in turn
originate from the effect <strong>of</strong> the misfit dislocations on the surface morphology. Under typical growth
conditions, the origin <strong>of</strong> <strong>strain</strong>-induced surface features can be identified by recognizing the length
scale at which the features occur. © 1997 American Vacuum Society. S0734-21019711403-8
I. INTRODUCTION
The ability to employ different semiconductor materials
on a common substrate for many applications is limited by
the wide variety <strong>of</strong> lattice constants that these semiconductors
possess. When the lattice constant differs by only 10 4
between the substrate and thin film, the <strong>strain</strong> introduced in
the thin film can have pronounced effects on the properties
<strong>of</strong> device layers. In this article, we review the influence <strong>of</strong>
defect <strong>strain</strong>s and lattice <strong>strain</strong>s on semiconductor thin films,
and also show that deleterious interactions can occur between
these two <strong>strain</strong>s.
II. THE SIGNIFICANCE OF THE GeSi SYSTEM
The GeSi alloy system is a completely miscible alloy system,
ideal for decreasing the band gap <strong>of</strong> Si, which is useful
in fabricating heterojunction bipolar transistors 1 and extending
the long wavelength limit <strong>of</strong> Si-based photodetectors. 2 In
these applications, slight lattice mismatches can be accommodated
between the film and substrate by keeping the GeSi
film thickness below the critical thickness for dislocation
formation. 3,4 For many applications such as III–V integration
on Si the goal is to create high quality, relaxed semiconductor
layers. Complete relaxation requires the introduction
<strong>of</strong> a large number <strong>of</strong> dislocations.
The relaxation pathways for mismatched films are schematically
drawn in Fig. 1. One method shown in the figure is
the direct growth <strong>of</strong> a highly mismatched material on a substrate.
The most widely investigated system using this
method is the GaAs/Si system, 5 in which 4% <strong>strain</strong> is accommodated
across a single interface. Such a high mismatch
creates uncontrolled pathways to lattice relaxation, such as
three-dimensional growth and the introduction <strong>of</strong> a large
number <strong>of</strong> immobile edge dislocations and threading dislocations.
After the film forms a continuous layer, some
threading dislocations annihilate due to the extremely large
number generated at the interface, so dislocation interaction
is probable. However, the remaining density is near
a Electronic mail: eafitz@mit.edu
b Present address: Lucent Technologies, Murray Hill, NJ 07974.
10 8 cm 2 or higher for practical thickness. Many methods
have been applied to reduce this threading dislocation density,
such as thermal cycling <strong>of</strong> the substrate 6 and <strong>strain</strong>edlayer
superlattices. 7 However, these techniques do not reduce
the threading dislocation below 10 8 cm 2 . The <strong>strain</strong>ed layer
superlattice, proposed to eliminate all dislocations by moving
the threading dislocations to the edge <strong>of</strong> the wafer, cannot
achieve the goal <strong>of</strong> removing a significant number <strong>of</strong>
threading dislocations due to the limited <strong>strain</strong> available on a
large substrate. 8
Figure 1 also shows the typical defect morphology for a
low mismatched system 1.5% for most common growth
conditions. In this case, the dislocations introduced are predominately
mobile 60° dislocations, the misfit dislocation
lengths are very long, and the threading dislocation density is
very low. However, due to the very low mismatch, it is difficult
to drive the system to complete relaxation. Thus, even
though the dislocation morphology is more attractive, the
small jump in lattice constant is not a practical solution. Figure
1 shows a distinct difference between relaxation pathways
in small and large mismatched heteroepitaxy. The relaxation
pathway depends on the degree <strong>of</strong> lattice mismatch
and the temperature <strong>of</strong> growth. For many semiconductor materials,
1.5%–2% mismatch <strong>strain</strong> is the transition point between
the two pathways at typical growth conditions. At
mismatch <strong>strain</strong>s near 1.5%–2% <strong>strain</strong>, a transitional morphology
occurs in which the epitaxial layer is continuous,
but develops a ripple on the surface. 9 These ripples have
been shown to nucleate misfit dislocations when the layer
begins to relax. 10 In the case <strong>of</strong> liquid phase epitaxial growth
<strong>of</strong> GeSi on Si, the growth temperatures are extremely high,
and even at relatively low lattice mismatch, one can develop
surface ripples. 11
GeSi alloys <strong>of</strong>fer the perfect solution to the problem <strong>of</strong>
lattice relaxation for many applications. For both GeSi devices
on relaxed GeSi/Si Ref. 12 and for III–V integration
on Si, GeSi alloys can span the desired lattice constants. For
this reason, GeSi relaxation was studied as a model system,
and indeed it was found that relaxed alloys on Si could be
produced by employing graded-composition layers grown at
high temperatures 13 900 °C compared to conventional GeSi
1048 J. Vac. Sci. Technol. A 15(3), May/Jun 1997 0734-2101/97/15(3)/1048/9/$10.00 ©1997 American Vacuum Society 1048

1049 Fitzgerald et al.: <strong>Influence</strong> <strong>of</strong> <strong>strain</strong> on semiconductor thin film epitaxy 1049
FIG. 1. Schematic showing typical defect morphology in low mismatched
and high mismatched heteroepitaxy. In the low mismatch case the epilayer
relaxes typically by nucleating long 60° misfit dislocations. Under a high
lattice mismatch the epilayer will tend to nucleate in form <strong>of</strong> 3-D islands,
which subsequently coalesce. The relaxation is predominantly by formation
<strong>of</strong> edge dislocations.
growth 550 °C. Essentially by creating a series <strong>of</strong> low mismatched
interfaces at high temperature, it is possible to encourage
dislocation propagation and minimize dislocation
nucleation, resulting in complete relaxation <strong>of</strong> GeSi alloys on
Si with threading dislocation densities on the order <strong>of</strong>
10 5 –10 6 cm 2 . 14 Thus, the surface during the graded layer
growth is always in the low mismatch regime discussed
above, allowing long misfit lengths in the relaxed graded
layer.
The remaining portion <strong>of</strong> this article concentrates on the
effect <strong>of</strong> defect <strong>strain</strong> in these graded relaxed buffer layers
and the effect <strong>of</strong> <strong>strain</strong> on layers grown on these buffers.
Graded buffers <strong>of</strong>fer the best pathway to high quality, relaxed
layers with significant lattice mismatch, and the effects
<strong>of</strong> <strong>strain</strong> in these structures is critical in evaluating their potential
for different applications. We begin by discussing the
effect <strong>of</strong> <strong>strain</strong> from the defects in the relaxed layers, and
then discuss the effect <strong>of</strong> mismatch <strong>strain</strong> on device layers
grown on these relaxed buffers.
A. Defect <strong>strain</strong>
In relaxed graded structures grown under low mismatch
<strong>strain</strong> conditions, it has long been known that a cross-hatch
surface morphology Fig. 2 occurs when growth is performed
on 001 oriented substrates. Although the presence
<strong>of</strong> the cross-hatch pattern has been associated with dislocation
lines at the mismatch interface, the exact correlation
between the dislocation lines and surface morphology is usually
absent. It has been shown that the cross-hatch pattern in
low-mismatch, heavily relaxed layers correlates with misfit
FIG. 2. An AFM image <strong>of</strong> a relaxed graded GeSi structure grown on Si001
showing the cross-hatch surface morphology.
dislocation groups at the heterointerface 15 and that the crosshatch
pattern is a response <strong>of</strong> the epitaxial surface to the
<strong>strain</strong> fields originating from the buried misfit dislocations. 14
In graded layers, the distance <strong>of</strong> the surface from the buried
misfit dislocations is controlled by the grading rate, i.e., the
amount <strong>of</strong> mismatch introduced per thickness. A larger grading
rate reduces the thickness <strong>of</strong> the <strong>strain</strong>ed layer which is
present at the surface throughout graded layer growth, bringing
the surface closer to the buried misfit dislocations. Thus,
if the total relaxation is equal, a comparison <strong>of</strong> the surface <strong>of</strong>
relaxed graded GeSi layers with different grading rates will
reveal the effect <strong>of</strong> the buried misfit dislocation <strong>strain</strong> fields.
Indeed, the surface morphology degrades and the root-meansquared
rms roughness increases.
To connect the effect <strong>of</strong> dislocation <strong>strain</strong> fields to the
surface morphology, two models are needed: a model which
determines the magnitude <strong>of</strong> the defect <strong>strain</strong> fields at the
surface, and a model which describes the response <strong>of</strong> that
surface to the <strong>strain</strong> fields. The first can be accomplished by
using continuum elastic theory and known expressions for
dislocation stress fields, and the latter can be achieved with
an equilibrium calculation which balances <strong>strain</strong> energy with
surface energy.
The stress fields from a 60° also called a mixed dislocation
can be thought <strong>of</strong> as a mix between the stress fields <strong>of</strong>
two edge dislocations and those <strong>of</strong> a screw dislocation. Thus,
a mixed dislocation produces a completely nonzero stress
tensor at every point in the material around the dislocation:
Dy3x 2 y 2
Dxx 2 y 2
b s y
4s
Dxx 2 y 2
Dyx 2 y 2
b s x
4s
b s y
4s
b s x
4s
2Gb s y
21sDy3x 2 y 2 Dxx 2 y 2 0
Dxx 2 y 2 Dyx 2 y 2 0
2Gb s y
0 0
21s,
JVST A - Vacuum, Surfaces, and Films

1050 Fitzgerald et al.: <strong>Influence</strong> <strong>of</strong> <strong>strain</strong> on semiconductor thin film epitaxy 1050
D Gb
e
, s x 2 y 2 ,
s 2
where G is the shear modulus, b e is the magnitude <strong>of</strong> the
edge component <strong>of</strong> the Burgers vector in the plane <strong>of</strong> the
mismatch interface <strong>strain</strong> relief component, b e is the magnitude
<strong>of</strong> the edge component <strong>of</strong> the Burgers vector in the
plane perpendicular to the interface tilt component, b s is
the magnitude <strong>of</strong> the screw component <strong>of</strong> the Burgers vector
along the z direction, and the dislocation is assumed to be
lying along the z axis. The stress tensor on the right-hand
side is in a coordinate system that is rotated 90° with respect
to the stress tensor on the left-hand side. The x and z directions
are along the misfit interface, whereas the y direction is
perpendicular to the interface in the case <strong>of</strong> the left-hand
expression.
To determine the effect <strong>of</strong> a randomly located array <strong>of</strong>
misfit dislocations, we need to calculate the total stress tensor
at a point by summing the stress fields from all the dislocations
acting on that point. Although translating the tensors
into correct coordinate systems is tedious, the effect <strong>of</strong>
each <strong>of</strong> these dislocations on a point in the material can be
determined. The total stress tensor then can be rotated into
the coordinate system <strong>of</strong> the elastic constants, C ij , and the
<strong>strain</strong> fields can be solved using i C ij j . Thus, we can
establish a picture <strong>of</strong> the <strong>strain</strong>s in the material by solving the
equation at each point in the material, in our case the material
above the buried misfit array. Figure 3 is a contour plot
<strong>of</strong> the <strong>strain</strong> fields above a low-mismatched graded layer, in
which the dislocations are randomly placed in the first 0.1
m cross-section view. The contours are separated by
10 4 <strong>strain</strong>, and the <strong>strain</strong> in the 001 direction is plotted
( 33 ). Although we chose this particular part <strong>of</strong> the <strong>strain</strong>
tensor, it should be remembered that all other elements are
nonzero as well. Even at 2 m from the surface, there are
still varying <strong>strain</strong> fields on the order <strong>of</strong> 10 4 over distances
<strong>of</strong> microns. This calculation is encouraging since this wavelength
is approximately what we expect for the cross-hatch
pattern.
In the calculation for Fig. 3, it is important to mention that
the effects <strong>of</strong> a surface are not considered, i.e., the <strong>strain</strong> and
stress fields are assumed to be in an infinite solid. To be
more precise, the zero-stress boundary condition at the surface
must be included. This correction leads to a more rapid
decay <strong>of</strong> the stress towards the surface. However, the ‘‘no
surface’’ approximation is valid to the degree that we consider
structures in which the surface is far from the dislocations,
because the <strong>strain</strong> pr<strong>of</strong>iles will not change significantly
for such low values <strong>of</strong> stress.
As mentioned above, the second required model is the
response <strong>of</strong> the surface to the dislocation <strong>strain</strong> fields. For
simplicity, we modeled the problem as shown in Fig. 4. The
<strong>strain</strong> fields will tend to have an oscillatory behavior as
shown in Fig. 3, therefore the <strong>strain</strong> field is modeled as a
periodic wave across the sample with a wavelength <strong>of</strong> 1 m.
Since the dislocation <strong>strain</strong> fields increase closer to the dislocations,
we have allowed the magnitude <strong>of</strong> this wave to
increase as l/h, the distance to the interface. We then assume
that the system will be driven to remove material from the
high <strong>strain</strong> regions, and place that material in low <strong>strain</strong> regions.
Thus, we have also let a surface wave develop at a
wavelength () which is half the wavelength <strong>of</strong> the <strong>strain</strong>
field. To determine the equilibrium morphology, we balance
the <strong>strain</strong> energy reduction formed by the surface wave with
the increase in energy due to an increase in surface area
created by the surface wave.
Figure 5 is a plot <strong>of</strong> the total energy change surface
energy–<strong>strain</strong> energy for the formation <strong>of</strong> this surface wave.
The different lines on the graph represent the different magnitudes
<strong>of</strong> the elastic <strong>strain</strong> wave. The magnitudes <strong>of</strong> <strong>strain</strong>
were based on the magnitudes expected from the previous
calculation Fig. 3 about 1–2 m from the interface. The
curve minimums occur at a greater depth from the surface as
the <strong>strain</strong> increases, showing that the greater the un-
FIG. 3. A contour plot <strong>of</strong> the <strong>strain</strong> fields in the 001 direction ( 33 ) above
a 0.1 m graded layer in which dislocations have been randomly placed.
The contours are separated by 10 4 <strong>strain</strong>. It is seen that there are varying
<strong>strain</strong> fields on the order <strong>of</strong> 10 4 –10 5 even at 2 m away from the graded
region.
FIG. 4. Schematic illustrating the <strong>strain</strong> field model used to explain the
formation <strong>of</strong> cross-hatch morphology. The solid line on the surface is the
sinosoidally varying <strong>strain</strong> field <strong>of</strong> wavelength whose magnitude changes
as l/h as one approaches the interface. The dotted line is the surface response
to the varying <strong>strain</strong> field. Since material will redistribute from regions
<strong>of</strong> high <strong>strain</strong> to regions <strong>of</strong> low <strong>strain</strong>, the surface will approximately
vary as which is equal to 0.5.
J. Vac. Sci. Technol. A, Vol. 15, No. 3, May/Jun 1997

1051 Fitzgerald et al.: <strong>Influence</strong> <strong>of</strong> <strong>strain</strong> on semiconductor thin film epitaxy 1051
FIG. 5. Plot <strong>of</strong> total energy change for the formation <strong>of</strong> the surface wave.
The <strong>strain</strong> increase from the surface is an order <strong>of</strong> magnitude higher for case
a than case b. It is seen that the depth change at the surface is greater for
a greater increase in <strong>strain</strong> a.
dulating <strong>strain</strong> magnitude, the greater the depth <strong>of</strong> the crosshatch
pattern.
Another variable in the calculation is the rate at which the
magnitude <strong>of</strong> <strong>strain</strong> increases away from the surface. For the
calculation in Fig. 5a, the derivative <strong>of</strong> <strong>strain</strong> with distance
into the material is an order <strong>of</strong> magnitude greater than the
calculation in Fig. 5b. As expected, the surface roughness
is greater for the material with a larger <strong>strain</strong> gradient Fig.
5a. Thus, a structure with a dislocation array closer to the
surface Fig. 5a will have a deeper cross-hatch pattern than
one in which the dislocations are much more remote from
the interface Fig. 5b. This behavior is in agreement with
experimental data for graded GeSi layers grown with different
grading rates. 14,16 Note that in both parts <strong>of</strong> Fig. 5, <strong>strain</strong>
values in the 10 4 range are sufficient to create a surface
undulation. Thus, at sufficiently high growth temperatures,
adatoms have a large enough surface mobility to create the
equilibrium surface, and the cross-hatch pattern will form in
almost any lattice mismatched system within the lowmismatch
growth regime.
If the surface responds to these <strong>strain</strong> values, we expect
almost any crystalline defect to create a perturbation at the
surface in epitaxial growth. In graded GeSi buffer layers, if
the grading rate is on the order <strong>of</strong> 10% Ge/m and the
growth temperature is high, complete relaxation occurs in the
graded buffer layer via the introduction <strong>of</strong> many misfit dislocations,
but there are few threading dislocations protruding
up to the surface region. When the occasional threading dislocation
does terminate at the surface, we expect a strong
effect in the surface morphology since the <strong>strain</strong> values near
the threading dislocation center approach extremely high values
(10 4 ). We expect that circular dishes would appear
where the threading dislocation reaches the surface, since in
equilibrium, material will be removed from the high-<strong>strain</strong>
core region. As a crude estimate, we can approximate the
<strong>strain</strong> field <strong>of</strong> a threading screw as b/r, where b is the
magnitude <strong>of</strong> the Burgers vector and r is the distance from
the dislocation core. If we use b410 8 cm for a typical
semiconductor material, we find that decays to about
10 4 at distances near 4 m. Atomic force microscopy
AFM analysis <strong>of</strong> threading dislocations at GeSi surfaces
reveals circular dishes approximately 200 Å deep and approximately
0.5–1 m wide. 16,17 Thus, within the uncertainty
<strong>of</strong> our crude calculation, we do indeed see the effect <strong>of</strong>
the threading dislocation <strong>strain</strong> field on the sample surface.
However, growth kinetics are an additional factor which
adds to the discrepancy. The AFM data also show that a rim
<strong>of</strong> increased thickness can be found at the circumference <strong>of</strong>
these dishes. Thus, atoms are preferentially being removed
from the high energy core area and being deposited in the
surrounding area, creating the thicker rim. This kinetic effect
is in agreement with the expected migration distance <strong>of</strong> adatoms
on the semiconductor surface during growth, and indicates
that the dish pr<strong>of</strong>ile is determined by the equilibrium
pr<strong>of</strong>ile and distorted by the kinetics <strong>of</strong> surface diffusion.
Understanding the effect <strong>of</strong> misfit dislocations and threading
dislocations on surface morphology can explain gross
surface morphologies seen in heteroepitaxy. After depositing
high lattice-mismatched systems such as GaAs on Si, Ge on
Si, it is possible to produce smooth films, whereas deposition
<strong>of</strong> low mismatched films leads to a rough surface due to
the generation <strong>of</strong> the cross-hatch pattern. Ironically, the
cross-hatch film morphology indicates a lower threading dislocation
density at the surface than the optically smooth surface
morphology. In the low-mismatch case, the misfit dislocations
are long, few threading dislocations are present,
and the long misfit dislocations dominate the <strong>strain</strong> fields in
the growing layer, producing a cross-hatch pattern with periodicity
that can scatter visible light. In the high-mismatch
JVST A - Vacuum, Surfaces, and Films

1052 Fitzgerald et al.: <strong>Influence</strong> <strong>of</strong> <strong>strain</strong> on semiconductor thin film epitaxy 1052
film case, the threading dislocations are approximately 1 m
apart at the surface. Neighboring threading dislocation <strong>strain</strong>
fields overlap creating a surface that appears optically flat.
Strain fields affect a large number <strong>of</strong> experimental techniques.
Another example is x-ray diffraction. In very high
mismatched systems, an empirical relationship has been established
between rocking curve full width at half-maximum
FWHM and threading dislocation density. 18 The larger the
FWHM, the higher the threading dislocation density. However,
graded layers introduce a large number <strong>of</strong> misfit dislocations
in the graded region, as well as wafer curvature.
Dislocations 19 and wafer curvature can contribute to quite a
large mosaic spread. Thus, even though the graded layers can
have a large FWHM, the threading density can be quite low.
By carefully studying the FWHM, it is possible to separate
out the contribution from the misfits in the graded buffer and
estimate the threading dislocation density. 19
B. Bulk <strong>strain</strong> effect
Defects can contribute to a change in surface morphology,
and we have explained the driving force as a reduction in
<strong>strain</strong> energy, and the resisting force as the increase in surface
energy. In this section, the discussion focuses on <strong>strain</strong>
in the layer itself which can drive this morphological change.
The sign <strong>of</strong> the <strong>strain</strong> compressive or tensile is important in
determining the expected morphology.
As we have mentioned above, Fig. 1 represents the main
growth modes as they depend on the magnitude <strong>of</strong> the mismatch
<strong>strain</strong>. In between the high and low mismatch cases,
there exists a mode which is a continuous film, but which has
a rippling developing on the surface. 9 This mode is inconvenient
in most cases, since many applications require the incorporation
<strong>of</strong> 1%–2% <strong>strain</strong> in a flat, unrelaxed layer. The
rippling surface morphology lowers the nucleation energy
for dislocations, thus creating a defective layer. 10 The impetus
for rippling is the decrease in <strong>strain</strong> energy at the expense
<strong>of</strong> the increase in surface energy, as we have discussed for
the defect <strong>strain</strong> fields.
Figure 6 shows cross-section transmission electron microscope
TEM micrographs <strong>of</strong> two <strong>strain</strong>ed layers grown on
top <strong>of</strong> relaxed buffers. In the GeSi system, <strong>strain</strong>ed layers <strong>of</strong>
Si or Ge on relaxed, graded GeSi layers on Si have demonstrated
very high electron and hole mobilities, 20–22 making
such layers attractive for integration into a field effect transistor
structure. 23,24 In Fig. 6a, we show a <strong>strain</strong>ed Si layer
on relaxed Ge 0.30 Si 0.70 suitable for electron channels and in
Fig. 6b, we show a cross section <strong>of</strong> a Ge layer grown on
relaxed Ge 0.60 Si 0.40 suitable for hole channels. Note that the
compressive <strong>strain</strong>ed system, the Ge layer, develops a ripple
at the top surface, whereas the tensile system Si layer remains
completely flat. Both layers experience a greater than
1% mismatch <strong>strain</strong>, yet the tensile layers produces a relatively
flat surface.
To confirm this observation, a more controlled set <strong>of</strong> experiments
was accomplished utilizing the flexibility <strong>of</strong> relaxed
buffers in the GeSi system. To remove any influence
from the material composition, Ge 0.50 Si 0.50 layers were
FIG. 6. Cross-section TEM images <strong>of</strong> a a tensile <strong>strain</strong>ed Si layer suitable
for electron channels in field effect transistors, b compressively <strong>strain</strong>ed
Ge layer suitable for hole channels. Note that the compressively <strong>strain</strong>ed Ge
layer develops a ripple at the top surface whereas the tensile <strong>strain</strong>ed Si
layer is flat.
grown on relaxed buffers <strong>of</strong> Ge x Si 1x . 25 By varying x, different
<strong>strain</strong>s were applied to the 50% layer. These experiments
confirmed that the tensile systems retain a flat surface
morphology up to 2% mismatch Ge 0.50 Si 0.50 on Ge,
whereas rippling was occurring in the compressive layers
even at 1% mismatch, indicating that the sign <strong>of</strong> the <strong>strain</strong> is
important as well as the magnitude.
This rippling affects many applications such as the field
effect transistor application described above. Another example
can be found in the growth <strong>of</strong> <strong>strain</strong>ed layer superlattices
in the GeSi system. GeSi alloys have reduced band gaps
as compared to Si, creating the possibility <strong>of</strong> inexpensive
infrared detectors on Si which would be sensitive to 1.3 and
1.55 m wavelengths. Such detectors could readily be integrated
with Si complementary metal–oxide–semiconductor
CMOS circuits on a common Si substrate. However, the
detectors are plagued by the fact that GeSi materials have
indirect band gaps, requiring long absorption path lengths.
This problem can be overcome by decreasing the band gap
much more than needed for the particular absorption. The
J. Vac. Sci. Technol. A, Vol. 15, No. 3, May/Jun 1997

1053 Fitzgerald et al.: <strong>Influence</strong> <strong>of</strong> <strong>strain</strong> on semiconductor thin film epitaxy 1053
FIG. 7. Schematic <strong>of</strong> a <strong>strain</strong>-balanced superlattice structure SLS consisting
<strong>of</strong> alternating compressive Ge and tensile (Ge 0.5 Si 0.5 ) grown on a
relaxed buffer (Ge 0.75 Si 0.25 ).
critical thickness limitation <strong>of</strong> GeSi alloys on Si prevents the
incorporation <strong>of</strong> high concentrations <strong>of</strong> Ge.
The advent <strong>of</strong> high quality relaxed buffers on Si <strong>of</strong>fers a
potential solution, since high-Ge content alloys can be grown
on Si. For example, Ge detectors on Si can absorb 1.3 and
1.55 m light efficiently, so that normal-incidence detectors
could be fabricated. Unfortunately, as we discuss below,
graded layers with a final composition <strong>of</strong> pure Ge do not
have as low threading dislocation density as layers graded to
50% or 70% Ge.
A possible solution is to incorporate a <strong>strain</strong>-balanced superlattice
structure on relaxed 75% GeSi buffers. This structure
is schematically shown in Fig. 7. Because the layers in
the superlattice alternate about the 75% GeSi lattice constant,
and because the layers are below the critical thickness, there
should be no dislocation introduction into the superlattice.
Figure 8a shows a cross-section TEM micrograph <strong>of</strong> the
superlattice structure grown at 650 °C. Despite the <strong>strain</strong>balanced
superlattice, a large number <strong>of</strong> dislocations are introduced.
Closer examination <strong>of</strong> the micrographs from this
sample reveal that rippling is occurring in the compressive<strong>strain</strong>ed
layers in the superlattice. Despite the tensile layers
which follow, the compressive layers communicate elastically
across the tensile layers, encouraging the ripples to
propagate through the superlattice structure. At 650 °C, this
behavior quickly ripples the surface to a degree where dislocation
nucleation occurs. Such nucleation is extremely deleterious,
since there is no long-range <strong>strain</strong> to be relieved
since the superlattice is <strong>strain</strong>-balanced to the relaxed GeSi
buffer. Thus, local rippling results in the local nucleation <strong>of</strong>
dislocations, yet the dislocations do not propagate into neighboring
areas. Dislocation nucleation events are not efficiently
used, and an extremely large threading dislocation density
results.
Currently, we have applied a kinetic solution to the problem.
Since the rippling is a function <strong>of</strong> growth temperature, a
decrease in growth temperature <strong>of</strong> the superlattice to 450 °C
suppresses the formation <strong>of</strong> the equilibrium surface <strong>of</strong> the
compressive layer. The result is shown in Fig. 8b. Despite
this very low growth temperature, slight ripples form in
FIG. 8. Cross-sectional TEM picture <strong>of</strong> a Ge/Ge 0.5 Si 0.5 <strong>strain</strong>-balanced superlattice
grown on a Ge 0.75 Si 0.25 relaxed buffer substrate: a superlattice
grown at 650 °C exhibits rippling <strong>of</strong> the <strong>strain</strong>ed layers which create stressconcentrations
leading to the nucleation <strong>of</strong> dislocations, b superlattice
grown at 450 °C, shows suppression <strong>of</strong> rippling due to decreased mobility <strong>of</strong>
surface atoms at the lower temperature.
some <strong>of</strong> the layers. However, dislocation nucleation was prevented
and the superlattice possesses only remnant threading
dislocations from the relaxed buffer.
C. Characterization <strong>of</strong> <strong>strain</strong> effects by length scale
Strain levels at magnitudes <strong>of</strong> 10 4 or higher influence
semiconductor growth and surfaces at typical growth temperatures.
Under these conditions, we can separate the origin
<strong>of</strong> the surface topology based on the length scale <strong>of</strong> the surface
perturbation. At the shortest length scales, bulk <strong>strain</strong>
from lattice mismatch occurs, typically with wavelengths at
about a few hundred angstroms, and height changes <strong>of</strong> a few
monolayers, as shown in Fig. 6. At larger dimensions
(0.1 m), defect <strong>strain</strong> from threading dislocations or
misfit dislocations close to the surface will be the source.
Finally, at the longest dimensions 1–10 m, <strong>strain</strong> fields
from remote misfit dislocations will be the source <strong>of</strong> the
surface topography.
An interesting example <strong>of</strong> the effects <strong>of</strong> different sources
<strong>of</strong> <strong>strain</strong> on epitaxial growth can be seen in Fig. 9. Figure 9
JVST A - Vacuum, Surfaces, and Films

1054 Fitzgerald et al.: <strong>Influence</strong> <strong>of</strong> <strong>strain</strong> on semiconductor thin film epitaxy 1054
case, the bulk mismatch <strong>strain</strong> is interacting with the <strong>strain</strong>
fields from the buried misfit dislocation. Below, we discuss
an important deleterious interaction between the misfit <strong>strain</strong>
fields, surface morphology, and threading dislocations.
FIG. 9. AFM image <strong>of</strong> Ge x Si 1x graded layer with linear grading rate 10%/
m to x0.3 and a subsequent fast grade rate to x1.0. Ge islands on the
surface have oriented themselves along the misfit dislocations from the
steeply graded part <strong>of</strong> the structure. The weak, longer wavelength contrast
seen is the cross-hatch pattern from the initial 10%/m grade.
shows AFM images <strong>of</strong> a GeSi graded layer surface, in which
the pr<strong>of</strong>ile <strong>of</strong> Ge concentration was linear, than increased
sharply towards the surface to pure Ge. The result was a
structure in which there is a buried misfit dislocation array
as in a conventional graded heterostructure, a misfit array
located closer to the surface, and island growth at the top
surface. Note that the long wavelength surface features from
the relaxed buffer can be seen in the image, as well as the
island growth from the high mismatched growth at the end <strong>of</strong>
the run. We also observe an interaction between the island
growth or rippling and the misfit dislocations that are located
close to the surface. The islands tend to form along the misfit
dislocation lines due to the tensile <strong>strain</strong> field areas from the
misfit dislocations. Thus, the islands can lower their energy
by aligning with the misfit dislocation <strong>strain</strong> field. Recent
work suggests that such a phenomenon might be used to
engineer Ge island structures. 26
Figure 9 is an example <strong>of</strong> how <strong>strain</strong> fields introduced
from different sources can interact with each other. In this
D. Interaction between surface morphology
and <strong>strain</strong> relief
Except for the case <strong>of</strong> Fig. 9, we have been discussing the
sources <strong>of</strong> <strong>strain</strong> which can influence epitaxy separately;
however, it can be expected that the sources <strong>of</strong> <strong>strain</strong> may
influence each other, and possibly alter <strong>strain</strong> relaxation
pathways through this interaction.
During graded layer growth, if the grading rate is slow
and the temperature high, threading dislocation densities on
the order <strong>of</strong> 10 5 –10 6 cm 2 are sufficient to relax the layer
continuously, i.e., such that elastic <strong>strain</strong> does not build as
the graded layer growth continues. 14 This constant relief <strong>of</strong>
mismatch <strong>strain</strong> allows the layer to relax, yet without a building
<strong>of</strong> <strong>strain</strong>, and dislocation nucleation is discouraged. Thus,
one would expect that the final threading dislocation density
is independent <strong>of</strong> the final composition <strong>of</strong> the graded layer.
However, this is not the case. Consider Fig. 10, which is a
plot <strong>of</strong> typical threading dislocation densities <strong>of</strong> GeSi graded
layers grown with a grading rate <strong>of</strong> 10% Ge/m versus the
final Ge concentration. Unlike the expected result <strong>of</strong> a constant
threading dislocation density, we see that the threading
dislocation density increases with final Ge concentration.
This effect can only be described by a net decrease in misfit
dislocation length in the buffer layer. 13 A decrease in the
average misfit dislocation length can only occur through the
increased blocking <strong>of</strong> threading dislocations, or through increased
dislocation nucleation. Due to the slow grading rates,
the surface morphology even up to 50%–70% Ge is relatively
flat compared to the surface angles acquired in rippling
which can nucleate dislocations. Thus, the gradual increase
in threading dislocation density with final Ge concentration
must be due to an infrequent blocking <strong>of</strong> threading dislocation
motion.
Previous analysis <strong>of</strong> graded GeSi layers grown at different
grading rates have shown that there is an increase in threading
dislocation density with increased grading rate due to an
increase in the density <strong>of</strong> dislocation pileups within the
graded structure. 27 At 10% Ge/m grading rates, there are
nearly zero pileups in layers graded to 30% Ge. For layers
grown on 001 wafers, an increase in pileup density with
final Ge concentration occurs for a constant grading rate. In
addition, in layers graded to pure Ge, the pileup regions can
form long faceted grooves along the 110 that are visible to
the eye. A dislocation blocking phenomenon is occurring
which is rare, but which also contributes to further degradation
in surface morphology. In mismatched interfaces, it is
possible that perpendicular dislocations can block the glide
<strong>of</strong> threading dislocations. 28 However, our calculations show
that at 10% Ge/m grading rates, perpendicular dislocations
are very ineffective at blocking the glide <strong>of</strong> the threading
dislocations in these graded structures. This behavior is expected,
since one <strong>of</strong> the advantages <strong>of</strong> the graded layer is that
J. Vac. Sci. Technol. A, Vol. 15, No. 3, May/Jun 1997

1055 Fitzgerald et al.: <strong>Influence</strong> <strong>of</strong> <strong>strain</strong> on semiconductor thin film epitaxy 1055
FIG. 10. Plot <strong>of</strong> average threading dislocation density observed in the top
uniform cap layer grown on relaxed GeSi layers graded to different final Ge
concentrations. The grading rate is constant at 10% Ge/m for all samples.
FIG. 11. A schematic showing threading dislocation interacting with the
stress fields <strong>of</strong> existing orthogonal misfit dislocations and getting blocked at
trench side walls.
dislocation interaction is reduced, thus allowing the more
efficient use <strong>of</strong> each dislocation nucleation event by promoting
dislocation glide.
An explanation <strong>of</strong> the increased formation <strong>of</strong> pileups with
final Ge composition can be found in the inhomogeneous
distribution <strong>of</strong> misfit dislocations in relaxed mismatched
heterostructures. 15 The <strong>strain</strong> fields from groups <strong>of</strong> misfit dislocations
create infrequent deep troughs in the cross-hatch
pattern. Gliding threading dislocations then have a decreased
glide channel above the dislocation group, not only because
<strong>of</strong> an additive effect <strong>of</strong> the misfit dislocation <strong>strain</strong> fields, but
also because there is decreased thickness above this <strong>strain</strong>ed
area. The combined effect is to block threading dislocations,
as schematically shown in Fig. 11. On nearly exactly oriented
001 substrates, these blocking troughs can extend for
long lengths along the 110. Once threading dislocations
become blocked, they create the dislocation pileup and contribute
to blocking additional dislocations. With the added
condition that threading dislocations also affect surface morphology,
the growth rate above the pileup is effectively decreased,
increasing the depth <strong>of</strong> the trough with further
growth. In chemical vapor deposition CVD growth, yet another
deleterious factor is that the growth rate slows as the
growth surface rotates from the 001; thus, as the reduced
growth rate above the pileup occurs, the nearby 001 areas
continue to increase in thickness, rotating the local plane
near the pileup, decreasing the growth rate even more. Eventually
a facet occurs, as observed in samples graded to
pure Ge.
One way to decrease the formation <strong>of</strong> the pileups is to
prevent the groups <strong>of</strong> dislocations from creating a large
stress disturbance in the structure, thus avoiding long lengths
<strong>of</strong> deep cross-hatch. This can be accomplished by growing
on <strong>of</strong>f-axis 001 wafers. 30 In particular, we have grown relaxed
graded GeSi structures, graded to pure Ge, on <strong>of</strong>f-axis
wafers cut 6° towards the 110. Indeed, there is a marked
reduction in both surface roughness and dislocation pileup
density. The statistics comparing growth on 001 wafers and
<strong>of</strong>f-cut wafers are shown in Fig. 12. On each wafer, we have
calculated the density <strong>of</strong> pileups and the rms roughness <strong>of</strong>
the layer in the two 110 directions in the 001 surface. One
can see a drastic reduction in both surface morphology and
pileup density. This behavior can be explained by the crystallographic
effect <strong>of</strong> the substrate <strong>of</strong>f-cut. On an <strong>of</strong>f-cut wafer,
the misfit dislocations lying in the 001 plane in one <strong>of</strong>
the 110 directions are not parallel to each other. 29 Therefore,
dislocations from a common nucleation source are not
likely to be parallel to each other, and long troughs which
can lead to pileups cannot form. The fact that the pileup
density decreases on the <strong>of</strong>f-cut wafer sample as well verifies
that the pileups are created by, and contribute to, the roughness
observed in the on-axis wafers.
FIG. 12. A bar graph showing the effect <strong>of</strong> substrate <strong>of</strong>f-cut on the surface
roughness and dislocation pileup densities. 0D refers to the on-axis 001Si
substrate, 6D refers to the samples grown on miscut 001Si substrates. It is
seen that there is a drastic reduction in surface roughness and pileup density
on the <strong>of</strong>f-cut wafers.
JVST A - Vacuum, Surfaces, and Films

1056 Fitzgerald et al.: <strong>Influence</strong> <strong>of</strong> <strong>strain</strong> on semiconductor thin film epitaxy 1056
III. CONCLUSIONS
The effect <strong>of</strong> <strong>strain</strong> on semiconductor epitaxy produces a
variety <strong>of</strong> changes to the surface morphology. Defect <strong>strain</strong>
fields from misfit dislocations and threading dislocations in
purposely relaxed heterostructures modulate the film thickness,
producing cross-hatch patterns and shallow pits, respectively.
Compressive and tensile <strong>strain</strong> have different effects
on film morphology, the former having a much greater
tendency for creating surface roughness. With the variety <strong>of</strong>
morphologies that are possible with different growth techniques
and temperatures, we unify the effect <strong>of</strong> <strong>strain</strong> by the
length scale at which they operate under typical growth conditions.
Within the same defect-engineered sample, it is possible
to see the effect <strong>of</strong> different sources <strong>of</strong> <strong>strain</strong> at different
length scales. The effect <strong>of</strong> <strong>strain</strong> fields on surface
morphology can also interact with subsequent <strong>strain</strong> relief,
creating dislocation pileups and increased roughness in
slowly graded GeSi structures. By growing on <strong>of</strong>f-cut substrates,
the interaction can be minimized, leading to smooth
surfaces and lower defect densities.
1 S. S. Iyer, G. L. Patton, J. M. C. Stork, B. S. Meyerson, and D. L.
Harame, IEEE Trans. Electron Devices 36, 2043 1989.
2 R. People, IEEE J. Quantum Electron. QE-22, 1696 1986, and references
therein.
3 J. W. Matthews, A. E. Blakeslee, and S. Mader, Thin Solid Films 33, 253
1976.
4 For a review, see E. A. Fitzgerald, Mater. Sci. Rep. 7, 871991.
5 S. F. Fang, K. Adomi, S. Iyer, H. Morkoc, H. Zabel, C. Choi, and N.
Otsuka, J. Appl. Phys. 68, R31 1990.
6 M. Yamaguchi, M. Tachikawa, Y. Itoh, M. Sugo, and S. Kondo, J. Appl.
Phys. 69, 4518 1990.
7 J. W. Matthews and A. E. Blakeslee, J. Vac. Sci. Technol. 14, 989 1977.
8 E. A. Fitzgerald, J. Metals 41, 201989; J. Vac. Sci. Technol. B 7, 782
1989.
9 A. G. Cullis, D. J. Robbins, S. J. Barnett, and A. J. Pidduck, J. Vac. Sci.
Technol. A 12, 1924 1994.
10 D. E. Jesson, S. J. Pennycook, J.-M. Baribeau, and D. C. Houghton,
Scanning Microscopy 8, 849 1994.
11 S. Christiansen, M. Albrecht, H. P. Strunk, P. O. Hansson, and E. Bauser,
Appl. Phys. Lett. 66, 574 1995.
12 Y. H. Xie, E. A. Fitzgerald, D. Monroe, P. J. Silverman, and G. P. Watson,
J. Appl. Phys. 73, 8364 1993.
13 E. A. Fitzgerald, Y.-H. Xie, M. L. Green, D. Brasen, A. R. Kortan, J.
Michel, Y.-J. Mii, and B. E. Weir, Appl. Phys. Lett. 59, 811 1991.
14 E. A. Fitzgerald, Y.-H. Xie, D. Monroe, P. J. Silverman, J.-M. Kuo, A. R.
Kortan, F. A. Thiel, B. E. Weir, and L. C. Feldman, J. Vac. Sci. Technol.
B 10, 1807 1992.
15 E. A. Fitzgerald, P. D. Kirchner, G. D. Pettit, J. M. Woodall, and D. G.
Ast, J. Appl. Phys. 63, 693 1988.
16 J. W. P. Hsu, E. A. Fitzgerald, Y. H. Xie, P. J. Silverman, and M. J.
Cardillo, Proc. SPIE 1855, 118 1993.
17 J. W. P. Hsu, E. A. Fitzgerald, Y. H. Xie, P. J. Silverman, and M. J.
Cardillo, Appl. Phys. Lett. 61, 1293 1992.
18 A. T. Macrander, R. D. Dupuis, J. C. Bean, and J. M. Brown, Semiconductor
Based Heterostructures: Interface Structure and Stability TMS,
Warrendale, PH, 1986, p.80.
19 E. Koppensteiner, A. Shuh, G. Bauer, V. Holy, G. P. Watson, and E. A.
Fitzgerald, J. Phys. D 28, A114 1995.
20 Y. J. Mii, Y. H. Xie, E. A. Fitzgerald, D. Monroe, F. A. Thiel, B. E. Weir,
and L. C. Feldman, Appl. Phys. Lett. 59, 1611 1991.
21 F. Schaffler, D. Tobben, H. J. Herzog, G. Albstreiter, and B. Hollander,
Semicond. Sci. Technol. 7, 260 1992.
22 Y. H. Xie, D. Monroe, E. A. Fitzgerald, P. J. Silverman, F. A. Thiel, and
G. P. Watson, Appl. Phys. Lett. 63, 2263 1993.
23 U. Konig, A. J. Boers, F. Schaffler, and E. Kasper, Electron. Lett. 28, 160
1992.
24 K. Ismail, B. S. Meyerson, S. Rishton, J. Chu, and S. Nelson, IEEE
Electron Device Lett. 13, 229 1992.
25 Y. H. Xie, G. H. Gilmer, C. Roland, P. J. Silverman, S. K. Buratto, J. Y.
Cheng, E. A. Fitzgerald, A. R. Kortan, S. Schuppler, M. A. Marcus, and
P. H. Citrin, Phys. Rev. Lett. 73, 3006 1994.
26 S. Y. Shiryaev, F. Jensen, J. L. Hansen, J. W. Petersen, and A. N. Larsen,
Phys. Rev. Lett. 78, 503 1997.
27 G. P. Watson, E. A. Fitzgerald, B. Jalali, Y.-H. Xie, and B. E. Weir, J.
Appl. Phys. 75, 263 1994.
28 L. B. Freund, J. Appl. Phys. 68, 2073 1990.
29 P. Kightley, P. J. Goodhew, R. R. Bradley, and P. D. Augustus, J. Cryst.
Growth 112, 359 1991.
30 S. B. Samavedam and E. A. Fitzgerald, J. Appl. Phys. 81, 3108 1997.
J. Vac. Sci. Technol. A, Vol. 15, No. 3, May/Jun 1997