1

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).

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↑ →

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).

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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.