phys. stat. sol. (a) 171, 239 (1999)

Subject classification: 68.55.Ln; 61.72.Lk; S5.11; S7.13

Misfit Dislocations in Epitaxial Heterostructures:Mechanisms of Generation and Multiplication

V. I. Vdovin

Institute for Chemical Problems of Microelectronics, B. Tolmachevsky per. 5,109017 Moscow, Russiae-mail: icpm@mail.girmet.ru

(Received October 12, 1998)

In this paper, the regularities of dislocation pattern formation in single layer heterostructures withlow lattice mismatch (f < 1%) are reviewed. The main attention is focused on the recently sug-gested mechanisms of dislocation nucleation and multiplication. An evolution of dislocation patternfrom regular flat misfit dislocation network to the dense three-dimensional one was found to pro-ceed during the epitaxial growth. Experimentally found regularities of dislocation structure forma-tion are treated in terms of the influence of the nature of materials contacting at the interfaceupon the dislocation behavior. Special emphasis is given to the role of microsegregations and self-point defects in the alloy matrix in dislocation generation, propagation and multiplication.

1. Introduction

Over the last decade, numerous studies performed on different hetorostructures, fromtraditional single layer structures with constant alloy composition to multilayer struc-tures with a complex profile of distribution of misfit strains, including superlattices,markedly enriched the general knowledge about the dislocation behavior in epitaxialheterostructures. The variety of materials studied was also wide enough, from elementalsemiconductors to III±V quaternary alloys. The attention was paid to the effect of plas-tic deformation of the substrate during epitaxial growth. Appropriate dislocation pat-terns (hereafter called three-dimensional misfit dislocation (MD) networks) were ob-served, for example, in InGaAs/GaAs [1, 2], SiGe/Si [3, 4] and SiGe/Ge [5]heterostructures. The formation of such 3D-MD networks was attributed to the MDmultiplication and/or dislocation interaction.

Some previously proposed mechanisms of MD generation were criticized or re-viewed. In particular, more sophisticated calculations have shown that high minimummismatch strain level (about 2%) is needed for surface nucleation of dislocation half-loops to operate [6]. That result required new mechanisms to be proposed to explainthe generation of dislocation half-loops in low misfit (f < 1%) heterostructures [7, 8].In InGaAs/GaAs [1] and SiGe/Si [9] heterostructures, it has been found that tips ofdislocation angles, formed at the crossing points of MDs with identical Burgers vec-tor, turned down into the substrate rather than into the layer. It leads to the conclu-sion that the Hagen-Strunk mechanism [10] is not valid for at least these heterostruc-tures.

In general, one can expect different behavior of one or another dislocation genera-tion mechanism in different heterosystems, taking into account that strain relaxation in

V. I. Vdovin: Misfit Dislocations in Epitaxial Heterostructures 239

SiGe/Si systems proceeds in different ways in dependence on Ge content in the alloy[11]. Thus, it seems to be important to find a layer/substrate material effect on thedislocation pattern formation and to evaluate the suggested models.

2. Evolution of Dislocation Patterns in Heterostructures duringthe Epitaxial Growth

2.1 SiGe/Si

In the Si1±±xGex/Si system, it has been previously found by transmission electron micro-scopy (TEM) that dislocation pattern in the heterostructures progressively evolves pas-sing through at least two distinctive stages [12]. Dislocation networks appropriate tothese stages are shown in Fig. 1 for heterostructures with an alloy composition of 4 at%Ge. At the initial stage of misfit strain relaxation, MDs generate from sources of pri-mary generation (dislocations propagating from the substrate into the layer [13], preci-pitates [14] or oxide particles [15] remaining at the substrate surface etc.) and a regularMD network forms (Fig. 1a, b). Regular MD networks are flat and lie strictly at theinterface. The V tips turning down into the substrate are only observed near the cross-ing points of perpendicular MDs, where dislocation reactions occur followed by a splitof dislocation nodes or the formation of dislocation junctions [16]. The particular dislo-cation configurations described by Hagen and Strunk [10] are commonly observed insuch networks (Fig. 1b).

At the second stage, the dislocation patterns evolve from a regular flat MD networkto a dense three-dimensional one (Fig. 1c, d) as the layer thickness increases. As a

240 V. I. Vdovin

Fig. 1. Evolution of dislocation pattern in Si1±±xGex/Si (x = 0.04) heterostructures with layer thick-nesses a), b) 0.6 and c), d) 1.5 mm. a), c) TEM cross-sectional micrographs; b), d) TEM plan-viewmicrographs of misfit dislocation networks at the interface

result, a dense multilevel MD network is formed near the interface and dislocationhalf-loops spread predominantly downwards the substrate. The multilevel part of the3D-MD network encompassing some parts of both the layer and substrate, and itswidth is usually about 0.1 to 0.2 mm (Fig. 1c). On TEM plan-view micrographs 3D-MDnetworks look like dense irregular networks (Fig. 1d). The formation of such networkshas been attributed to a MD multiplication near the interface through modified Frank-Read mechanism [17, 18].

For the SiGe/Si system, such evolution of dislocation patterns is valid for alloy com-positions up to 20 at% Ge. However, the density of threading dislocations in the layerand dislocations in the substrate as well as the depth of dislocation propagation into thesubstrate depends on the alloy composition and layer thickness. Practically the sametendency in dislocation pattern evolution was found in the GeSi/Ge system for similarSi alloy composition [5, 12].

2.2 GaAlAsSb/GaSb

In LPE Ga1±±xAlxAsySb1±±y/GaSb heterostructures grown under the same conditions(Tgr = 510 �C, h = 2 mm), we observed different stages of dislocation pattern formationfor different alloy compositions. Plan-view micrographs of MD networks are shown inFig. 2 for heterostructures with alloy compositions of 20 and 6 at% Al. In the formercase, a regular MD network was formed in the heterostructure (Fig. 2a), whereas in thelatter case, a dense 3D-MD network was formed (Fig. 2b). The fact that for xAl = 0.2the dislocation pattern was developed to a smaller extent was attributed to a largerlayer strengthening [8]. As seen in Fig. 2a, the Hagen-Strunk dislocation configurationsare formed in the regular MD networks in this heterosystem. It is noteworthy that wealso observed similar images with the Hagen-Strunk dislocation configurations in theregular MD networks in the InGaAsP/InP heterosystem [8].

From a comparison of the present results, it follows that dislocation pattern forma-tion in different heterostructures passes through the same stages. However, the finalstate of the MD network depends on the alloy composition. It should be noted thatMD multiplication, accompanied by the formation of Hagen-Strunk dislocation config-urations, occurs at the stage of formation of regular flat MD network and operatesbefore activation of multiplication through the Frank-Read mechanism.

Misfit Dislocations in Epitaxial Heterostructures 241

Fig. 2. Misfit dislocation networks formed in LPE Ga1±±xAlxAsySb1±±y/GaSb (Tgr = 510 �C,h = 2 mm) heterostructures with different Al contents in the alloy (at. share): a) x = 0.2, b) 0.06

3. Mechanisms of Initial Misfit Dislocation Generation

The mechanisms proposed to explain dislocation generation in low misfit heterostruc-tures are displayed in Table 1. A part of these mechanisms is concerned with heteroge-neous dislocation nucleation at some particles (b-SiC precipitates [14] or oxide particles[15]) remaining at the substrate surface or so-called diamond defects [19]. We will notconsider these mechanisms in detail. In the following, we will be concerned with othermechanisms the behavior of which can be affected by the nature of the materials com-prising a heteropair.

The generation of MD from dislocations pre-existing in the substrate (bending mech-anism [13]) easily operates in any heterostructure because there is no energy barrier fordislocation nucleation. The identification of this mechanism by TEM is hampered bythe fact that MDs are often very long, which excludes the possibility of observing boththreading segments. We have ascertained the MD generation through the bending mech-

242 V. I. Vdovin

Ta b l e 1Mechanisms of initial misfit dislocation generation

anism in InGaAsP/InP heterostructures after analysis of the dependence of linear MDdensity upon growth conditions [8]. We obtained a relatively weak dependence uponlattice mismatch and, in contrast, a distinctive dependence upon the initial substratedislocation density.

The mechanism of dislocation half-loop generation at the layer surface [20] can bereadily identified due to the peculiar form of half-loops, if they have no time to spreadout for a long distance. Dislocation half-loops we observed in GaInAsSb/GaSb hetero-structures, in which long MDs are never formed regardless of the value of lattice mis-match or layer thickness [8]. The same half-loops were also observed in GaAlAsSb/GaSb heterostructures with relatively thin layers. In heterostructures with thickerlayers, well-developed MD networks covering the entire interface were observed. Insuch heterostructures, the linear MD density did not markedly depend on the initialsubstrate dislocation density. In contrast, it abruptly increased with lattice mismatch [8].However, homogeneous nucleation of dislocation half-loops at a perfect layer surfacedoes not seem to operate in the mentioned heterostructures without high misfit strains[6]. Let us review these results using a mechanism recently proposed by Perovic andHoughton [7].

A mechanism of heterogeneous nucleation of dislocation half-loops at interstitial per-turbations localized at the strained layer interface has been proposed for the SiGe/Sisystem [7]. The model involves the nucleation of small (� 1.5 nm) prismatic dislocationloops of vacancy type at Ge-rich platelets (microsegregations) due to strain-inducedsurface segregation during epitaxial growth. Small prismatic loops can expand towardsthe layer surface on {111} planes to form stable 60 half-loops. Thus, the existence ofinterstitial perturbations and high vacancy concentration in the epilayer are necessaryfor this mechanism to operate. Unfortunately, the authors did not indicate possiblesources of high vacancy concentration in SiGe layers. We suppose that the well-knowneffect of reduction of vacancy generation enthalpy in compressed materials is responsi-ble for the high vacancy concentration in these layers. As for III±V quaternary alloys,microsegregations arising as a consequence of alloy spinodal decomposition characteris-tic of these materials can be the centers of heterogeneous nucleation of dislocationloops. The residual vacancy concentration in GaSb substrates is very high and signifi-cantly exceeds that in InP substrates. This leads to an intensive vacancy migration fromthe substrate into the epilayer in LPE heterostructures grown on GaSb substrates.Thus, sufficient conditions are present in GaAlAsSb/GaSb and GaInAsSb/GaSb hetero-structures for this mechanism to operate. In line with this assumption, the mechanismdoes not operate in InGaAsP/InP heterostructures because of insufficient vacancy con-centration in epilayers.

4. Mechanisms of Secondary Generation (Multiplication)of Misfit Dislocations

As pointed out above, MD multiplication in epitaxial heterostructures varies in the typeof dislocation patterns formed, namely, regular flat or irregular three-dimensional MDnetworks. A number of mechanisms has been proposed to account for such networks.The list of mechanisms displayed in Table 2 is not complete but sufficient to evaluate apossibility to account for adequate dislocation processes occurring in real materials. Allmechanisms displayed, but the Hagen-Strunk mechanism, are based on the cross slip of

Misfit Dislocations in Epitaxial Heterostructures 243

a screw segment of inclined dislocations followed by the operation of Frank-Read spiralsource with one or two pinning points.

4.1 Misfit dislocation multiplication with formation of regular networks

MD multiplication through Hagen-Strunk mechanism is based on the formation of tworight-angle dislocations as a result of interaction of perpendicular MDs with identicalBurgers vector. The tip of one of these angle dislocations bends upwards from the inter-face to reach the layer surface and produce two free threading segments. Subsequentgliding of these segments leads to the formation of bunch of parallel MDs with thesame Burgers vector and closely spaced to each other. We have observed particular

244 V. I. Vdovin

Ta b l e 2Mechanisms of misfit dislocation multiplication

Hagen-Strunk dislocation configurations (Fig. 1b and 2a) in different heterostructures(Ge/GaAs, SiGe/Si, GeSi/Ge, InGaAsP/InP, GaAlAsP/GaAs, GaAlAsSb/GaSb) withlattice mismatch less than 1%. Recently this mechanism has reasonably been subjectedto question. Some authors suppose that the appropriate dislocation configurations couldarise as a result of any intersection of clusters of 60 dislocations having the same Bur-gers vector [19]. One can allow the formation of a cluster of two or three the sameMDs (typical clusters for SiGe/Si heterostructures) arising from separate sources on theassumption that the MD nucleation sources are randomly distributed over the hetero-structure. However, it is hard to agree that a cluster consisting of a larger number ofMDs is formed in this way. We observed the typical dislocation configurations with alarge number of the same parallel MDs in GaAlAsSb/GaSb heterostructures (Fig. 3).Thus, in general, the Hagen-Strunk dislocation configurations should be considered as aresult of MD multiplication. For evaluating the responsible mechanism, it is noteworthyto emphasize the major features of such configurations, which are as follows: (i) newMDs arrange strictly at the interface; (ii) arbitrary distances between adjacent parallelMDs.

Recently an interesting mechanism has been proposed [21] to account for dislocationpatterns arising in compositionally graded SiGe buffer layers. One model is based onthe assumption that the threading segment of a gliding dislocation can be pinned at adefect in its middle part. If the top element of this threading segment is of screw type itcan cross slip onto another {111} plane. Simultaneously, the resolved shear stress cancause the lower lying part of the original branch to underpass the pinning point anddevelop a loop towards the surface. Once the loop has reached the surface, it separatesinto two threading segments. As a result, two unpinned dislocation half-loops areformed to produce MDs in orthogonal h110i directions, an initial one and a new half-loop located in the middle part of the layer. If we extend this mechanism to the layerswith constant alloy composition, we can imagine the following scenario. Once formed,the new half-loop glides towards the interface and crosses the initial MD to form right-angle dislocations at a crossing point. Such multiplication events can occur repeatedlyduring further movement of the initial MD. Hence this process can lead to the forma-tion of a typical Hagen-Strunk dislocation configuration. Moreover, the mechanism en-tirely satisfies both major features of such configurations. In this case, no matter whatdirection, upwards or downwards, the tips of right-angle dislocations turn out from theinterface because this is unrelated to the multiplication process. Thus this mechanism canbe a candidate to account for a dislocation multiplication in flat regular MD networks.

Misfit Dislocations in Epitaxial Heterostructures 245

Fig. 3. Numerous multiplication of misfit dislocations in Ga1±±xAlxAsySb1±±y/GaSb (x = 0.2) hetero-structure

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4.2 Misfit dislocation multiplication with formationof three-dimensional networks

Three-dimensional MD networks (Fig. 1c, d) have been studied in detail in SiGe/Si[3, 4] and InGaAs/GaAs [1, 2] heterostructures. The major features of such networksare as follows: (i) multilevel MD network at the interface; (ii) misfit dislocation pile-upsspreading deeply into the substrate; (iii) low density of threading dislocations in thelayer. Two modified Frank-Read mechanisms [17, 18] have been proposed to accountfor such dislocation patterns. In both models, the angle dislocation tips turning downinto the substrate are treated as sources for multiplication.

Both models account for the formation of dislocation pile-ups in the substrate withdue regard for the symmetrical and asymmetrical glide of dislocations in SiGe/Si andInGaAs/GaAs heterostructures, respectively. However, a spatial arrangement of MDs inmultilevel network is treated differently by different authors. The model of LeGoueset al. [18], for the SiGe/Si system, implies that newly formed MDs arrange at the inter-face and in the near-interface layer region. The model of Lefebvre et al. [17], for theInGaAs/GaAs system, implies that multiplication proceeds in the substrate and ex-cludes the generation of MDs in the near-interface layer region. Our results obtainedon SiGe/Si and GeSi/Ge heterostructures indicate that, at the initial stages of multiplica-tion, long dislocation half-loops propagate under the interface in substrate. Wherease,in heterostructures with well-developed dislocation pattern (more layer thickness), themultilevel network fills the near-interface regions of both the substrate and layer.

Of particular importance is the low threading dislocation density in the layers. InSiGe/Si heterostructures with thick (� 1 mm) single layers, we have found that the dis-location density in substrates is one to two orders of magnitude higher than the thread-ing dislocation density in the layers, and the difference depends on the alloy composi-tion (for detail, see Fig. 6). However, we observed the absence of threading dislocationsin strained layer heterostructures (Tgr = 500 �C, xGe = 0.11, h = 0.3 mm) in which misfitstrain relaxation occurred during thermal annealing (Fig. 4). In the same heterosystem,a relative low density of threading dislocations was observed in heterostructures withgraded layers [18]. The authors explained this effect as a result of their disappearanceat the edges of the wafer or annihilation. However, a present scheme of dislocationgliding rather excludes than accounts for the possibility of threading dislocations toannihilate. A more plausible explanation of this effect has been proposed by Shiryaev[25]. Since the sources are obviously arranged along one initial MD and gliding of dis-location half-loops occurs on one and the same {111} slip plane, threading segments

246 V. I. Vdovin

Fig. 4. Cross-sectional micrograph of MBESi1±±xGex/Si (Tgr = 500 �C, x = 0.11,h = 0.3 mm) heterostructure after misfitstrain relaxation during thermal annealingat 800 �C for 15 min

with antiparallel Burgers vector from neighboring half-loops are to annihilate at theirmeeting. Unfortunately, the author did not indicate clearly enough the source of MDmultiplication. It is interesting to note that in one set of samples (single layers withconstant alloy composition), we observed a generation of bunches of threading disloca-tions (Fig. 5) unusual for this heterosystem. As seen from Fig. 5, the threading disloca-tion bunches are obviously linked with dislocation pile-ups. Very high growth tempera-ture (900 �C) is a distinctive feature of these heterostructures. For reasons unknown inthis case an annihilation of threading dislocations did not occur or dislocation nuclea-tion rate was very high.

The other mechanisms displayed in Table 2 slightly differ from each other and de-scribe somewhat different variants of the formation of dislocation pile-ups in the layer.They do not give an explanation of the entire three-dimensional dislocation patternbecause they exclude the formation of dislocation half-loops deep in the substrate.Nevertheless, these mechanisms appear to merit attention because appropriate disloca-tion configurations have been experimentally observed in SiGe/Si heterostructures andthe authors concentrate on more reasonable (energetically speaking) Frank-Read-typesources located in the epilayer. Hence, one should bear in mind that these mechanismsalong with the other mechanisms can contribute to the formation of three-dimensionaldislocation patterns.

5. Effect of Alloy Composition on the Formationof Dislocation Patterns in SiGe/Si Heterosystem

Formerly we have found in single layer SiGe/Si heterostructures that dislocation patternformation depends significantly upon alloy composition [4, 5]. This conclusion has beenclearly demonstrated by the compositional curves for threading dislocations (ND) in thelayer, dislocations in the substrate (NS) and MDs (NL) at the interface (Fig. 6a). Thedislocation density values displayed in these graphs were determined from etch pits(NS, ND) and from TEM plan-view micrographs (NL). Fig. 6b shows the plan-viewimages of dislocation patterns in the near-interface substrate region of heterostructureswith sharply different dislocation features. As can be seen from Fig. 6a, the dislocationpattern in the near-interface substrate region, which we attribute to the multiplicationthrough Frank-Read-type mechanism, changes nonmonotonically passing through amaximum at alloy composition of 10 at% Ge. At lower Ge content (< 5%), separatelong misfit dislocations are formed in the substrates (image 1). The misfit dislocation

Misfit Dislocations in Epitaxial Heterostructures 247

Fig. 5. Cross-sectional micrograph of MBESi1±±xGex/Si (Tgr = 900 �C, x = 0.11,h = 1.8 mm) heterostructure. Threading dis-locations grouped in dense bunches arelinked with dislocation pile-ups

17*

pile-ups with high dislocation density are formed (image 2) in heterostructures corre-sponding to the maximum in the ND(x) graph (x � 0.01). At a Ge content largerthan 15%, a radically different dislocation pattern is formed in the substrates (image3). High density of very short dislocation segments is observed on plan-view TEMimages. The study of cross-sectional TEM images shows that the propagation depthof small half-loops is less than 0.1 mm. Obviously, etch pits are not revealed in thesubstrate at such dislocation half-loops. In the latter composition region, the disloca-tion nucleation from other sources increases and this leads to the reduction of dislo-cation multiplication. It is possible that, in such heterostructures, the generation ofdislocation half-loops at Ge-rich microsegregations located at the interface (Perovic-Houghton mechanism) provides high MD density at the initial stages of misfit strainrelaxation.

The complex form of the compositional dependencies of dislocation density in differ-ent regions of the heterostructures implies that the SiGe layer plasticity changes non-monotonically with Ge content. It may be possible that fluctuations in local Ge contantare responsible. We can suggest that sizes and density of such microsegregations in-

248 V. I. Vdovin

Fig. 6. Dependence of dislocation pattern on alloy composition for SiGe/Si heterostructures.a) Composition dependence of dislocation density for threading dislocations (ND) in the layer, dis-locations in the substrate (NS) and misfit dislocations (NL) at the interface. b) TEM plan-viewmicrographs of dislocation patterns in the near-interface substrate region (depth of dislocation pro-pagation into the substrate: (1) 0.2, (2) 2.5, (3) < 0.1 mm)

crease as the Ge content in the alloy increases. Depending on the size, microsegrega-tion can act as effective stopper on gliding dislocations (small microsegregations) or asa center of heterogeneous dislocation nucleation (large microsegregations). This ap-proach accounts for qualitatively a gradual layer strengthening leading to high substrateplastic deformation followed by subsequent layer disstrengthening as the density oflarge microsegregations in the layer increases.

6. Conclusions

The dislocation pattern in epitaxial heterostructures evolves from a regular flat MDnetwork, arising at the initial stages of misfit strain relaxation, to a dense three-dimen-sional one as the layer thickness increases. Regular MD networks lie strictly at theinterface. Three-dimensional networks consist of a multilevel MD part formed at theinterface and dislocation half-loops spreading downwards into the substrate. The Hagen-Strunk dislocation configurations are formed at the initial stages of misfit strain relaxationdue to a misfit dislocation multiplication. In general, the mechanism proposed by Hoh-nisch et al. [21] can describe the formation of such dislocation configurations. The for-mation of three-dimensional MD networks is a result of dislocation multiplication nearthe interface. The known models based on the operation of Frank-Read-type mecha-nism do not entirely describe dislocation patterns in SiGe/Si heterostructures.

Alloy inhomogeneity at the nanometer scale, intrinsic point defects in the epilayerand substrate markedly affect the dislocation generation, propagation and multiplica-tion.

Acknowledgements The author is grateful to Prof. M. G. Milvidskii and Dr. T. G. Yu-gova for their significant contribution to the results presented in this paper.

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