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Cryst. Res. Technol. 35 (2000) 541-548
P. MÖCK1 and G.W. SMITH 2
1 Department of Materials, University of Oxford,
2 Defence Evaluation and Research Agency
How to avoid plastic deformation in GaAs wafers during molecular beam
epitaxial growth
Plastic deformation in two-inch diameter GaAs wafers resulted from standard thermal treatments which
accompanied epitaxial growth in molecular beam epitaxy (MBE) machines of three different makes.
Synchrotron based X-ray transmission topography was used to distinguish between thermal treatment induced
dislocation bundles and misfit dislocations. Eradication of the wafer slip related dislocation bundles has been
achieved by modifications to the sample holder of a user built MBE machine. These modifications are
discussed, the extent of the problem is briefly outlined, and an extrapolation of the susceptibility of GaAs
wafers of higher diameters to this type of plastic deformation is given.
1. Introduction
It is well known that heat treatment induced plastic deformation of GaAs wafers is a key factor that reduces
the yield of electronic devices in manufacturing processes on an industrial scale [YAMADA et al.,
KAWASE et al., TATSUMI et al., KIYAMA et al., SAWADA et al. (1996)]. Our recent X-ray transmission
topography survey demonstrated that a quite common, radiatively heated, non In-bonded sample holder design
of a molecular beam epitaxy (MBE) machine can cause severe plastic deformation when standard thermal
treatments that accompany epitaxial growth are applied [MÖCK et al., MÖCK]. A series of papers which
compared plastic deformation in thermally processed GaAs wafers with and without epitaxial layers shows
clearly that it is not the epitaxial growth process which causes the plastic deformation, but the thermal
treatments that are accompanying it [YAMADA et al., KAWASE et al., TATSUMI et al.].
In the near future, six-inch diameter GaAs wafers are expected to take over the market of four-inch
diameter GaAs wafers as far as industrial applications are concerned [SAWADA et al. (1995)]. Since bulk
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crystal growth induced residual strain and plastic deformation are more difficult to avoid in the former case
[FLADE et al.], and because further thermal processing of already dislocated wafers leads to more plastic
deformation [KAWASE et al., TATSUMI et al.], the lesson from our successful eradication of heat treatment
induced plastic deformation in two-inch diameter GaAs wafers can be learned and applied to higher diameter
wafers.
The main aim of this paper is to describe modifications to a standard MBE sample holder that led to the
eradication of thermally induced plastic deformation. We will briefly highlight the extent of the plastic
deformation problem and point out that the true extend is often grossly underestimated.
In order to set the scene, we will distinguishing between different types of thermal treatment induced
dislocation bundles in the bulk of the GaAs wafer. Subsequently we will distinguish between these
dislocation bundles and misfit dislocations in the interface between the epitaxial structure and the substrate.
Both destinctions will be made on the basis of contrasts in X-ray transmission topograms taken under
conditions of low anomalous absorption. Finally, extrapolations of the susceptibility of GaAs wafers of
higher diameters to heat treatment induced plastic deformation will be given.
2. Experimental details
Sixteen low misfit III-V compound semiconductor structures were grown in MBE machines of three different
makes. While the first of these MBE machines was a purpose built piece of equipment for in-situ X-ray
imaging of relaxation processes in strained epitaxial layers [WHITEHOUSE et al.], the second was a
commercial Varian GEN II. The third MBE machine was a commercial VG Semicon machine. The sample
holders of these three MBE machines are all of the radiatively heated non In-bonding type.
Undoped as well as Si doped, two-inch diameter, (001) vertical gradient freeze Bridgman (VGFB) GaAs
wafers were used as substrates. The epitaxial samples possessed a wide variety of structural parameters and
were either fully elastically strained, partly relaxed, or almost completely relaxed. Before the growth of the
epitaxial structures commenced, buffer layers of up to 0.5 µm were grown at temperatures of typically about
600 °C, preceded by surface oxide desorption at up to 650 °C.
All of these samples were assessed by means of synchrotron based single-crystal X-ray transmission
topography under conditions of low anomalous absorption employing the experimental facilities at Daresbury
Laboratory (U.K.). At least one {202} topogram was taken from each of the samples at a wavelength of 0.13
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nm, where the product of the linear absorption coefficient and the sample thickness (≈ 450 µm) is about
eleven.
3. Results and Discussion
3.1. Distinction between different types of dislocations
The X-ray transmission topograms in Figs. 1a,b, show thermal treatment induced plastic deformation in a
two-inch diameter GaAs wafer. There is an epitaxial structure on one side of this wafer, but this structure is
fully elastically strained. Hence, there are no images of misfit dislocations visible in these two topograms.
The cellular dislocation structure that is visible in Figs. 1a,b was typical for the batch of undoped VGFB
grown wafers we used for our experiments. As both topograms show, the plastic deformation up to about 98
% is realised by bundles of dislocations which start at the sample edges around the four <100> peripheral
areas. These dislocation bundles glide into the bulk of the wafer following <110> and <1-10> line directions,
and form a pseudo-symmetric, four-fold set in undoped GaAs. This sort of dislocation bundle is named
majority type dislocation bundle.
Since the contrast in both topographs is rather similar regardless of the fact that opposite surfaces of the
sample have been exposed first to the incoming X-ray beam, we can safely conclude that the thermal treatment
induced dislocation bundles are distributed through the whole thickness of the wafer, but are definitively not
confined to the interface between the epitaxial structure and the substrate. Since the Borrmann shadows of the
dislocation bundles seem to be similarly blurred in Figs. 1a,b, the related Borrmann fans must be of about
equal size for both cases [MÖCK].
In addition to majority type dislocation bundles, there can be dislocation bundles of various minority types
with a spatial distribution that is centred at and around <110> peripheral regions (Figs. 1a,b). As demonstrated
conclusively by MÖCK et al. and MÖCK, it is only these minority type dislocation bundles (i.e. only a few
percent of all dislocations) that can be detected by commonly applied surface inspection techniques such as
standard Nomarski microscopy or Makyoh (Magic Mirror) topography, since only they form slip line bunches
of sufficient height at the free wafer surface. We found that minority type dislocation bundles can be detected
on severely plastically deformed wafers under a wide range of illumination conditions by the unaided human
eye if the slip line heights are larger than about 150 nm [MÖCK et al.]. So if one can see slip line bunches by
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means of any commonly applied surface inspection technique (including the unaided human eye), one should
be aware that the extent of plastic deformation can be much larger than what meets the eye directly.
The X-ray transmission topogram in Fig. 2 shows thermal treatment induced plastic deformation in another
two inch-diameter substrate with a partially relaxed epitaxial structure. In this figure, misfit dislocations,
which are due to the partial relaxation of the epitaxial structure, are visible in addition to the thermal treatment
induced majority and minority type dislocation bundles and the cellular in-grown dislocation structure. Since
the bare back side of the wafer, i.e. the side opposite to the epitaxial structure, was exposed first to the
incoming X-ray beam, the misfit dislocations appear much sharper than the thermally induced majority and
minority type dislocation bundles in the bulk of the wafer. This is because the misfit dislocations are located
very close to the exit surface of the X-ray beam and therefore their Borrmann fans are insignificantly small in
comparison to the Borrmann fans of the thermal treatment induced majority and minority type dislocation
bundles [MÖCK].
3.2. Modifications to the sample holder of a user built MBE machine that led to the eradication of
majority and minority type dislocation bundles
The wafers that are shown in Figs. 1a,b and 2 were processed in a Varian Gen II MBE machine. This MBE
machine was taken as a model for the construction of a user built MBE machine for in situ X-ray imaging of
relaxation processes in strained semiconductor systems [WHITEHOUSE et al.]. Since the same sample
holder design, as described below, was originally used, thermal treatment induced dislocation bundles were
observed initially in wafers that were processed in that MBE machine as well.
The modifications that are described in the following, however, led to a complete eradication of these
dislocations bundles. The appearance of Kossel lines in X-ray transmission topograms (Fig. 3) can be
regarded as a proof of a superior crystalline quality of thermally processed wafers after the eradication of
majority and minority type dislocation bundles has been achieved. (As Fig. 3 also illustrates, misfit
dislocations can not be eradicated by modifications to the sample holder.)
The standard Varian/Epi two-inch wafer holder has the wafer resting on a thin annular tantalum ledge all
round its circumference. The wafer is held in place with molybdenum springs, which push on the back of the
wafer. The employed modification was to remove the annular ledge and replace it with three "U-shaped"
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pieces of molybdenum wire which were spot welded to the holder so that the open end of the "U" was facing
in towards the centre of the holder.
This had (at least) four effects:
1. The contact area between the wafer and the mount was reduced, thus increasing the thermal resistance
between the two.
2. The thermal environment was made more uniform because the edge of the wafer was no longer hidden
behind the annular ledge.
3. Growth could now occur right up to the edge of the wafer.
4. A reduction in sample rocking, as a three-point mount was now established.
The motivation for the modification was that we expect that the molybdenum wafer block will be at a
significantly different temperature to the wafer. This is because it has very different emisivity and absorption
coefficients to GaAs wafers of the commonly used thickness. Therefore if there is good thermal contact
between the wafer and the block we would expect to find that the edge of the wafer would be hotter than the
centre, which is predominantly radiatively heated by the heater that sits about one cm behind it, due to
conductive heat flow.
The ideal condition for temperature uniformity would be a free floating wafer in front of a semi-infinite
heater. This is difficult to achieve in practice, but the modifications made were intended to move us in that
direction.
We note that our modifications are supported by the reasoning that is given by SAWADA et al. (1996). We
would, however, like to stress that these modifications have been made independently before that study was
published. SAWADA and co-workers suggest two approaches to reduce thermal treatment induced plastic
deformation during MBE: to reduce the contact area between the wafer and the ledge of the sample holder
area or to make the thermal resistance of the contact layer large by inserting a thermal buffer between the two
of them.
While we employed the former approach successfully to the point of the complete eradication of thermal
treatment induced dislocation bundles, the second approach has been used by some MBE equipment
manufacturers such as the Vacuum Generators Ltd. [ROBERTS]. As our X-ray topography survey showed
[MÖCK], the second approach was, however, only successful in 3 out of 4 cases.
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3.3. Estimations of the susceptibility of GaAs wafers of higher diameters to thermal treatment induced
plastic deformation
Using a combination of quantitative scanning infrared polariscopy, high-resolution X-ray diffractometry and
synchrotron based X-ray transmission topography, we estimated there to be approximately 105 additional
dislocations due to the plastic deformation in the whole two-inch diameter GaAs wafers we studied and
threading dislocation densities of about 104 cm-2 in the affected one third of the wafer area (or about 5 103
dislocations per cm2 averaged over the whole wafer [MÖCK et al.]). KIYAMA et al. and SAWADA et al.,
on the other hand, derived experimentally the stationary critical temperature difference between the centre and
wafer periphery for the onset of plastic deformation in four-inch diameter GaAs wafers. This difference is
about 13 K at a temperature background of 650 °C and for a temperature field that is assumed to be
stationary, possesses rotationally symmetry with the [001] direction of the GaAs wafer and is parabolic with
the radius. Such a temperature field leads to circular isotherms.
According to the macroscopic theory of dislocation formation during various thermal treatments of crystals
[INDENBOM], the total Burgers vector of the thermally induced dislocations that intersect the isothermal
surfaces must be zero (and all grown-in dislocations have to be neglected for the calculation of the total
Burgers vector). One way to satisfy this condition is to have equal numbers of dislocations in all of the eight
active slip systems of the majority type dislocation bundles [MÖCK]. Judging from Figs. 1a,b and 2 this
seems to be the case, taking into account the extinct dislocation bundles in the particular reflections. We are,
thus, justified to assume, that the same kind of temperature field persisted during the plastic deformation of
our wafers as the one that was experimentally set up by KIYAMA et al. and SAWADA et al.
Since the temperature background was in both cases about 650 °C as well, we can quite confidently
extrapolate both the content of additional dislocations and the threshold values of the average stationary
radial temperature gradients that cause the onset of plastic deformation in circular GaAs wafers of varying
diameters on the basis of both sets of data.
For an identical temperature profile, one would obtain for a wafer that is linearly scaled in all dimensions
an identical thermal stress [VÖLKL], which would lead to an identical dislocation density. Linear scaling in
all wafer dimensions leads to an increase in the volume that is equal to the third power of the scaling factor.
The dependency of the amount of plastic deformation on the wafer diameter, thus, follows under these
conditions a “proportional to the third power of the scaling factor” rule. Extrapolating from the observed 105
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additional dislocations in two-inch diameter wafers [MÖCK et al., MÖCK], for a four-inch diameter wafer
one has to expect under these conditions an additional dislocation content of about 8 105. Correspondingly, a
six-inch diameter wafer is expected to possess about 2.7 106 dislocations in addition to any grown-in
dislocations.
Extrapolating from the data given by KIYAMA et al. and SAWADA et al., we obtain average stationary
radial temperature gradients of about 5.1 K cm-1 for two-inch, 2.6 K cm-1 for four-inch, and 1.7 K cm-1 for
six-inch diameter wafers as threshold values for the onset of plastic deformation, i.e. an inversely linear
scaling of the average stationary critical temperature gradient with the wafer radius. It should be noted that
strictly linear temperature gradients would not cause plastic deformation [VÖLKL]. Another matter, for
which we do not have data are transient temperature fields and gradients.
For the dependency of the thermal stresses on the rates of heating or cooling [BRICE] beyond the relevant
critical rates that mark the onset of plastic deformation in either case, on the other hand, an “inversely
proportional to the square of the radius” rule is expected. Again an identical thermal stress is expected to
result in an increase of the number of additional dislocations that correspond to the increase in the volume.
Thus for linear scaling in all dimensions, the dependency of the number of dislocations on the wafer diameter
may follow for transient temperature gradients a “proportional to the sixth power of the scaling factor” rule.
This highlights the fact that transient temperature gradients may cause much more plastic deformation than
stationary temperature gradients.
The conditions under which these rules would apply are, however, very difficult to achieve in cases of
practical interest. Extrapolating from JORDAN et al., FLADE et al., and von AMMON et al., who made
efforts to avoid increases of thermal stresses with increasing crystal sizes, each inch increase in the crystal
radius leads in practical applications to an increase in the thermal stresses by a factor somewhere between
about 1.1 to 2. The above formulated rules of thumb can, thus, only be regarded as rough approximations of
the lower bound values and may actually underestimate plastic deformation effects by some 10 to 100%. As
higher diameter wafers are more susceptible to sample holder induced plastic deformation, it will be
especially beneficial to modify the design of the sample holders used for their thermal treatments.
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4. Summary and Conclusions
We have highlighted the extent of plastic deformation in two-inch diameter GaAs wafers that resulted from
standard thermal processing which accompanied epitaxial growth by means of molecular beam epitaxy. We
described the modifications of a particular MBE sample holder that led to the eradication of the wafer slip
related dislocation bundles. Finally, extrapolations of the susceptibility of GaAs wafers of higher diameters
to thermal treatment induced plastic deformation were made. The conclusions of this paper are that the
proposed modifications to a quite common, radiatively heated, non In-bonded sample holder are not only
easily done, but also quite effective in removing thermal treatment induced plastic deformation in GaAs
wafers.
9
↑ →
g
a)
↑→
g
b)
Figure 1: Single-crystal X-ray transmission topograms of a fully elastically strained (In,Ga)As double
heterostructure on an undoped GaAs wafer; a) (0-22) reflection, b) (-20-2) reflection. As in all topograms
below, the major diameter of the ellipse equals about 4.8 cm.
Since conditions of low anomalous absorption were employed, the thermal treatment induced majority and
minority dislocation bundles show up as pronounced Borrmann shadows. The contrast of the dislocations is
rather similar in both topograms despite the fact that opposite surfaces of the sample have been exposed first
10
to the incoming X-ray beam. This indicates that the Borrmann fans of the dislocation bundles are of about
equal size and that the dislocation bundles must be distributed through the thickness of the substrate, but are
definitively not confined to the interface between the substrate and the epitaxial structure. The cellular
dislocation structure was typical for the batch of undoped VGFB wafers we used for this study.
11
↑ →
g
Figure 2: Single-crystal X-ray transmission topogram of a partially relaxed (In,Ga)As double
heterostructure on an undoped GaAs wafer, (0-22) reflection.
Since the bare back side of the wafer was exposed first to the incoming X-ray beam, the images of the
misfit dislocations appear much sharper than the images of the thermal treatment induced majority and
minority type dislocation bundles. This is because the Borrmann fans of the misfit dislocations are
insignificantly small in comparison to the Borrmann fans of the majority and minority type dislocation
bundles, (compare Fig. 3 where the opposite side of an almost completely relaxed epitaxial sample was
exposed first to the incoming X-ray beam).
12
↑ →
g
Figure 3: Single-crystal X-ray transmission topogram of an almost completely relaxed single (In,Ga)As
heterostructure on a Si doped GaAs wafer, (-20-2) reflection.
Due to the Si doping, no cellular dislocation structure was present in the batch of wafers we used for this
study. Since this sample is curved, the minor axis of the ellipse appears to be slightly compressed in relation
to Figs. 1a,b and 2. The curvature of the sample introduces sufficient divergence for a Kossel line, which is
prove of a superior crystalline perfection, to appear. (This Kossel line has probably originated from the
diffraction of characteristic radiation that emerged from the In atoms in the 2.7 µm thick In0.066Ga0.934As
epilayer of this sample and could therefore be referred to as pseudo-Kossel line since the diffraction took
place in the GaAs wafer.)
The faint cross hatch pattern is due to a high density of misfit dislocations in the epilayer / wafer interface.
Since the epitaxial layer side of the sample was exposed first to the incoming X-ray beam, the misfit
dislocations appear blurred as a result of their wide Bormann fans, (compare Fig. 2 where the opposite side
of a partially relaxed epitaxial sample was exposed first to the incoming X-ray beam). The footprints of the
six pins of the new sample holder design that held this wafer in the MBE growth chamber are clearly revealed
as bright areas of enhanced X-ray intensity.
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Acknowledgements
Previous experimental collaboration with Prof. B.K. Tanner (Department of Physics, Durham University)
and Dr. D. Laundy (Daresbury Laboratory) is gratefully acknowledged. The experimental work at the U.K.
Synchrotron Radiation Source, Daresbury Laboratory, was financially supported by the Engineering and
Physical Research Council as “Direct Access” projects (No.: 30047 and 31098).
14
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Dr. Peter Möck
Department of Materials
University of Oxford
Parks Road
Oxford OX1 3PH
England, U.K.
now at: Department of Physics (M/C 273), University of Illinois at Chicago, 845 West Taylor Street,
Chicago, IL 60607-7059, U.S.A.
Dr. Gilbert W. Smith
Defence Evaluation and Research Agency
St Andrews Road
Great Malvern
Worcestershire WR14 3PS
England, U.K.
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