On the development of misfit dislocation distributions in strained epitaxial layer interfaces

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Pergamon

etbt&dia, Vol. 33. No. I, pp. 123-128, 1995 cowright 1995ElsavierSci~Ltd Pri&dintheUSAAllri$&-cd 0956-716x/95 $9.50 + .@I

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ON THE DEVELOPMENT OF MISFIT DISLOCATION DISTRIBUTIONS IN STRAINED EPITAXIAL LAYER INTERFACES G. MacPherson, R. Beanland and P.J. Goodhew Department of Materials Science and Engineering University of Liverpool Liverpool, L69 3BX (Received December 15,1994) (Revised February 2 1,1995) Jntroductioq

Electronic devices such as lasers with performance characteristics that are unique may be constructed by the growth of a thin layer of semiconductor epitaxially on a substrate. Since the materials are otlen selected for reasons other than a perfect match of lattice constants, the mismatch between the two layers produces strain in the epitaxial layer that has to be accommodated in some way. The two possibilities are Grstly, that the layer is in perfect register with the substrate leaving a strain in the layer, or secondly, the strain can be partially relieved in the layer by an array of misfit dislocations in the substrate-epilayer interface. Which of these possibilities will occur depends on energy considerations and leads to the existence of a ‘critical’thickness for the presence of misfit dislocations. The ex&ence of a critical thickness was first predicted in 1949 by Frank and Van der Merwe[ l] and has become of increasing importance with the advent of heteroepitaxial semiconductor devices. If the layer is less than a critical thickness (hJ it is not energetically favonrable for a threading dislocation to glide into the layer driven by the misfit stress, leaving a misfit dislocation at the substrate-epilayer interface. When the layer exceeds h, the reverse is true and the threading dislocation can move, which relieves misfit. It has been recognised by many workers[2-61 that misfit dislocations in thin layers (i.e. during the initial stages of relaxation) appear to be formed from substrate threading dislocations bending over. This process has a low activation energy because no new dislocation needs to be nucleated since the misfit segment is the only part of the dislocation that need be created. For a threading dislocation to be glissile it must lie on a glide plane (i.e, { 111)) in the layer and EBIC studies have shown that dislocations from the substrate do indeed produce mistit dislocations in the interface[6]. When the strain in the mismatch layer is of sufiicient magnitude these threading dislocations ‘bend over’ in the strain field and produce 60” dislocations in the interface as shown in fig. 1. The generation of misfit dislocations by multiplication and other such processes need only be considered at thicknesses well beyond 4. Recent work has put this thickness at approximately 4hJ7]. Numerous observations have revealed that the dislocations in the interface are not regularly spaced [8,9], but reseat& into the distribution of dislocation spacings appears to be very limited and usually consists of no more than a few hundred measnrements[ IO]. This paper is the first report of a detailed study of the evolution of the distributions involving statistically sign&ant measurements.

123

124

Vol. 33, No. 1

MISF’ITDISLOCATION DISTRJBUTIONS

I I

Misfit

dislocation

SUBSTRATE Figure 1. Formation of a misfit dislocation at the substrak-qitaxial

layer interface due to an advancing threading dislocations

We show that, far tiom being a regularly spaced array in both orthogonal directions, the misfit dislocations have a distribution of spacings which depends on the extent of strain relaxation. Just above 4, when the dislocation density is low, a single-peaked,broad distribution of spacings is present. As 4 is further exceeded and the dislocation density increases, the distribution becomes bimodal and a simple model involving the interaction of 600 dislocations is proposed to account for the second peak.

Six IqGa,&aAs strained layer samples were examined and are described in Table 1. Their thicknesses are described in terms of the Matthews and Blakeslee critical thickness, 4, for the turning over of a threading dislocation in a single interface[ 111. This is the geometry appropriate to the relaxation of single layers and it is now widely accepted that the Matthews and Blakeslee value of h, best fits the majority of experimental data. Samples a and e were grown by metal organic molecular beam epitaxy(MOMBE) at a temperature of SOO”C, samples b, c and d by molecular beam epitaxy (MBE) at a temperature of 500 “C, and sample f by atomic layer molecular beam epitaxy (ALMBE) at a temperature of 350°C. Thicknesses were measured by cleaved edge TEM imaging with the gO02 reflection[ 121 and all compositions were determined by double crystal X-ray difI?action@CXRD). Plan view TBM samples were

TABLE 1 Details of the In,Ga,.JGaAs Layers

a,

Mean Dislocation Density (x lO%m~‘)

Composition (x)

Thickness (nm)

Method

10

0.22 f 0.05

0.03

396 f 5.0

MOMBE

16

1.30 f 0.03

0.20

62 f 3.0

MBE

49

1.37 f 0.03

0.11

375 f 2.5

MBE

d

89

1.53 f 0.04

0.105

730 f 5.0

MBE

t-

e

197

1.93 f 0.05

0.124

1325 f 15.0

MOMBE

I

f

47

2.52 f 0.06

h Sample

GrOWth

Vol.

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MISFIT DISLOCATION DISTRIBUTIONS

12.5

prepared by back-thinning to 100~ and etching from the substrate side to perforation using chlorine in methanol. Cross sections were prepared by mechanical thinning to SOum and argon ion milling at liquid N, temperature to perforation with an accelerating voltage of 5kV and glaucing augle of 12”. The plan view specimens were examined in a JEOL 2000FX operating at 200kV and the cross sections in a JEOL 12OOFX operating at 120kV. ExDerimentd Results

Dislocation spacings were determined from plan view EM micrographs taken using the g220 reflection. Measurements of only one of the two perpendicular sets were taken. Only one of the g220 reflections could be used in this situation, since it was desired to measure the spacings of all the dislocations with this line direction One of the g220 reflections renders invisible the edge dislocations in this set, aud at all tunes it was necessary to ensure that this invisibility criterion was not being thltilled for the dislocation sets being measured. Fig. 2(a)-(d) show histograms describing the distribution of dislocations in samples b, c, d and f respectively. The minimum number of measumments on these samples was 1500 (with a maximum of 2000), which is sufbcient to give sta&icz~Lerrors of approximately 10% in the magnitude of each histogram bar around the peaks.Enwrangesaremarkedoneachofthehistogrambars.Insampleb,asinglepeakisseen,withamodal spacing of approximately 25nm. The next three samples (with increasing dislocation density) show the possible appearance of a second peak in sample c, and the de&rite appearance of a second peak corresponding 0.10 c

0.08

2

0.06

E 0.08 =i z 0.06

3 f!j 0.04 f?

2

0.02 0.00

0

42

21

2

0.04

a

0.02 0.00

63 84 105 126 147 SPACING(nm)

0

80

120

160

200

SPACING(nm)

(a) 0.12 (

40

(W

r

0.10

!$ 0.06

!: 0.08 =i “m 0.06

E fs 0.04

s 0

E 0.08 =j

E

0.02

0.04 0.02 0.00

SPACING(nm) (c)

60 80 SPACING(nm) (d)

Figure 2. Histogramsshowing the distributionof dislocationspacingsfor samples b, c, d, and f.

100

240

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MISFIT

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DISLOCATIONDISTR.IBU’I’IONS

to 1.5 times the first modal peak spacing in sample d. In the last of these histograms (sample f) this second peak has shifted to 2.0 times the first modal peak. In all histograms an extended tail is observed and values of ten times the first modal peak were not uncommon in all the samples. Effect of haee

Width on the Awearance

of Histoerams

Since the dislocation images have a fmite width, dislocations which have spacings smaller than the width of the images cannot be resolved. This proved to a&& the appearance of the histograms. The tirst five samples had spacings measured Corn micrographs taken with bright field imaging conditions, while sample f micrographs were taken in weak beam g(3g) imaging conditions.For bright field imaging conditions the image width was typically S-lOnm, and for weak beam imaging conditions this value could be reduced to approximately 4nm. Another advantageof the weak beam technique is the reduction in the intensity of moirA fringes. This is due to the fact that for a deviation parameter s, the intensity of moire tiinges is proportional to s-*[ 131, while the intensity of a dislocation image is proportional to s-l. Therefore, in the histograms, dislocations spaced less than the image width will not be resolved and the probability of resolving pairs of dislocations will tend to zero as the spacing approaches the image width. Discussion

The principal result of our measurements is that the distribution of spacings begins as a broad unimodal distribution which becomes bimodal as misfit relief progresses, i.e. as the mean spacing decreases. We now consider a mechanism which will infhxnce the distribution of spacings, which is the formation of edge dislocations by the reaction of 600 dislocations. Observations have shown that two 60 ’ dislocations, with Burgers vectors of the correct orientation can, by the process of glide along {111} planes, form a sessile edge dislocation lying above the interface, as shown in fig. 3. It has also been found that glide in the opposite direction can occur, with edge dislocations being formed in the substrate[ 14,151. In our samples, analysis by cross sectional TEM showed that the majority of edge dislocations were formed in or below the interface (in the substrate). This is consistent with previous work carried out with similar compositions of indium[ 141. Not all pairs of 60” dislocationsin the interface can glide to form an edge dislocation. Their line directions must be parahel, and their Burgers vectors must be inclined to each other at an angle of 60”. When this is the situation, some of the dislocations may attract each other and combine to form an edge dislocation. This process may be snf3icientto describe the appearance of the observed distributions. It should be noted that the growth of all the samples involved in this study is two-dimensional, and the edge dislocations do not form at island edges as is the case in GaAs grown on Si[ 161. Recently it has been shown that the interaction energy between two dislocations becomes negligible when the spacing of the dislocations in the interface becomes greater than the thickness of the epilayer[l7]

A .G Glide

-

Resultant dislocation

edge

P\ planes \

SUBSTRATE Figure 3. Formation of an edge dislocation above the iaterfkce due to the glide of two comctly oriented 60” dislocations. The two glide planes being opposite { 111) planes.

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i.e, greater than a spacing of h. For 60” dislocations with some opposite Burgers vector component this interaction energy leads to an attractive force between the two dislocations, and when the spacing is sufficiently small this force can be large enough to allow the two 60” dislocations to glide on { 111) planes to form an edge dislocation. In thin layers the&&e, when d&cations are on average widely spaced and have narrow strain fields, edge dislocations are unlikely to form and will constitute only a small portion of the array. However, as the layer thickens, edge diskxxtion formation will become more likely because: a) the lateral extent of the dislocation fields, and hence the number of candidates for edge dislocation formation, increases; and b) dislocations become on average more closely spd increasing the strength of the interaction forces. We may thus expect the proportion of edge dislocations to increase as the layer thickens and misfit relief progresses. Part of the array of 60 Qdislocations becomes converted into an array of edge dislocations. An explanation why the second peak should be found between 1.5 and 2.0 times the first modal peak is described in fig. 4(a) and (b). The situation has been simplified so that the 60” dislocations are evenly spaced in the interface. Fig. 4(a) shows all the 60” dislocations spaced by a distance p and fig. 4(b) shows the situation when 60” dislocations of the correct orientation have reacted to form edge dislocations in the substrate. It should be noted that edge dislocation formation above or below the interface does not affect the measurement of dislocation spacings,which are seen in projection. Fig. 4(a) shows that for the case of adjacent 60” d&cations reacting to fnm an edge dislocation, the resultant spacings that will be measured around this edge diskution will be 1.5~ rather than p. For the case of non-adjacent 60” dislocations reacting to form an edge dislocation the spacing increases to 2p. The&ore, it can be envisaged that as misfit relief progresses and the mean spacing decreases, a situation EPILAYER [OOI]

[ilo

h+

[I 101 k’.

-*

*

y

!’

,.‘.**-”

!y!!?--

..,, T”,

EDGE DISLOCATION

EDGE DiSLOCATlON

SUBSTRATE (4

EPILAYER

LOOll It+ [ilo] [I 101 A

TT

i F’

\

EDGE DlSLOCATlON

i

A

P 2p

T

EDFEDISLOCATION

SUBSTRATE (4

Figmu 4. Si situ&m of60” dislocationsinitiallyevenly spaced by a dktance p giving rise to spacings of 1.Sp and 2p due to the reaction of correctly oriented 60” dislocationsforming edge dislocations.

MISFITDISLOCATIONDISTRIBUTIONS

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will be reached where it is only energetically possible for adjacent 60 o dislocations of the correct orientation form an edge dislocation. 60 ’ dislocations of the correct orientation that are not adjacent would be at a greater spacing and would be less likely to react. In this situation it would be expected that any second peak in the distributionwould be associatedwith edge dislocations being formed from the reaction of adjacent 60” d&xx&ions only, leading to a peak at 1.5~. As misfit relief progresses still further, the mean dislocation spacing decreases to such an extent that there are a large number of 60” dislocations that are candidates for the formation of an edge dislocation. The energy restrictions that were the case for greater mean spacings are greatly ieduced and there is a much greater likelihood of 60 Ddislocations that are not adjacent reacting. The net et%& of this is that the second peak in the distribution should shift to a spacing corresponding to 2p and increase in magnitude as the dislocation spacing further decreases. Ibis is an important result since it has been recently calculated that whilst keeping the mean spacing constant, the total energy of a system containingirregular spacings increases above that expected from a regularly spaced array[lS]. to react to

Conclusions

It has been shown that the distribution of dislocation spacings in samples with a dislocation density less than approximately 2 x 1O4cm-’ has a broad distribution, with a single peak and an extended tail. A second peak forms in the distribution as the dislocation density increases to approximately 1.5 x 10’ cm-‘. This peak is found initially at 1.5 times the first modal peak, and as the dislocation density increases further, the second peak increases in magnitude and shifls to 2 times the first modal peak. This second peak occurs when the dislocation density reaches approximately2.5 x 105cni’. We have provided an explanation for why this should occur, suggesting that it is due to the formation of edge dislocations by the interaction of gliding 60” dislocations. Acknowledeements

We acknowledge valuable discussions on statistics with Dr. J. Hutton. Funding for this work was provided by ESPRIT project No. 6854(BIES). The cross-sectionalwork was performed in the Department of Inorganic Chemistry and Materials Science at the University of CYtdiz,Spain. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12. 13. 14. 15. 16.

17. 18.

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