Misfit dislocations and antiphase domain boundaries in GaAs/Si interface

Misfit dislocations and antiphase domain boundaries in GaAs/Si interface Ph. Komninou, J. Stoemenos, G. P. Dimitrakopulos, and Th. Karakostas Department of‘ Phyks, Section of Soiid State 313-1, Aristotle Unbersity of Thessaloniki, MO 06 Thessaloniki, Greece

(Received 11 June 1993; accepted for publication 16 September 1993)

The interaction of the antiphase boundaries that are formed at the early stage of growth with the interfacial misfit dislocations is studied by transmission electron microscopy using contrast criteria. Experimental analysis has shown that the shifting of the misfit dislocation families, by half of their periodicity, is due to their intersection with antiphase boundaries emanating from demisteps on the Si substrate. The observed discontinuity of dislocation lines is attributed to dynamical contrast conditions. The antiphase boundaries do not interrupt the continuity of the network of dislocations. The dichromatic theory of interfacial defects is applied in order to illustrate the geometrical features of the pattern. The disymmetrization mechanism of the pattern obeys the principle of symmetry compensation. A symmetry analysis of the GaAs/Si interface justifies the agreement of the observations with the structural model.

I. INTRODUCTION

The epitaxial growth of III-V semiconductors on Si has attracted the interest of many research studies in the previous years.’ One of the fundamental problems con- nected with the epitaxy of polar semiconductors on (001) nonpolar semiconductor substrates is the formation of antiphase domains (APDs) surrounded by antiphase boundaries CAPBs). APBs in GaAs are strongly electrically ac- tive. They could be avoided by the proper occupation of each GaAs sublattice in the early stage of growth.” GaAs grown on Si is a system of specific importance and signif- icant progress has been already done for the understanding of its properties.” However, prablems such as the interaction of the misfit dislocations with the APDs and their APBs at the early stage of growth need further investigation.“”

In this work the interaction of the APBs, which are formed at the early stage of growth due to the presence of demisteps on the Si substrate,’ with the interfacial misfit dislocations is studied by transmission electron microscopy (TEM). The APDs are revealed in dark-field (DF) images by the difference in the background intensity when they are viewed using the symmetrical hlk and &t?i superlattice reflections.” The dichromatic theory of interfacial defects is applied in order to illustrate the geometrical features of the pattern. A symmetry analysis of the GaAs/Si interface justifies the agreement of the observations with the structural model.

II. EXPERIMENT

GaAs was deposited on Si in a molecular-beam-epitaxy QMBE) system using the migration-enhanced epitaxy tech- nique. The films were grown on vicinal silicon (001) mis- oriented q towards [l lo]. The surface of the substrate was subjected to an irz sitrc laser desorption before deposition.” The deposition conditions have been outlined in Ref. 10.

Disks of 3 mm diameter were cut and used for the observat.ions. The disks were initially thinned from the Si substrate back side and then progressively from the front GaAs overlayer so that a thin layer at the GaAs/Si interface was left. A JEM 120CX and a JEM 2OOOFX electron microscope were used.

Ill. RESULTS

Under ideal conditions, the most efficient mechanism to relieve the 4% lattice mismatch between Si substrate and GaAs overgrow is the generation of a network of Lamer dislocations with Burgers vector a/2(110) on the (001) interface. If all the misfit is relieved by such type of defect, a cross grid of parallel dislocations with lines along the [l lo] and [ilO] directions and a spacing of 0~9.2 nm is anticipated; however, the network of the misfit dislocations is generally distorted due to the three-dimensional formation of GaAs islands at the early stage of growth.” This is observable in the cross-section and plane-view TEM micrographs of Figs. 1 (a) and l(b) that depict the GaAs/Si interface grown under standard MBE conditions. The distortion of the network of misfit dislocations is attributed to the small misorientation of GaAs nuclei that result in the generation of additional 60” glissible dislocations of i( 101) type. These are introduced during the co- alescence of the islands. Defects and local st.rain variations result also in fringe irregularities of the moirt pattern as it is seen in Fig. 1 (b).

In situ thermal desorption assisted by excimer laser greatly improves the quality of the GaAs film at the early stage of growth.” In Fig. 2(a), a bright-field (BF) plane- view micrograph with the 220 reflection in two-beam condition, moirC fringes of the displacement type parallel to the [ilO] direction reveal the quality of the interface. The superposition of the GaAs and Si lattices normally results in the formation of satellite spots due to double diffraction. The perfection of this interface is also manifested by the

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a

FIG. I. GaAs film grown on (001) Si substrate under standard MHE conditions. (al Cross-sectional micrograph showing the overall structure. (b) Plane-view micrograph from the GaAn/Si interface. The misfit dislocations and moirk fringes parallel to the [IlO] direction are visible. Notice the irregularities of the moirk fringes due to defects and local strain variations.

presence of forbidden satellite spots in the diffraction pattern of Fig. 2(b). Thus, extra satellite spots, in addition to the double diffraction spots, appear due to the periodic modulation of strain introduced by the net of the misfit dislocations that acts as a two-dimensional grating. Natu- ral grating of dislocations that results in the formation of satellite spots has been observed in grain boundaries.‘““3 The periodicity of the extra satellite spots is half of the periodicity of the double-diffraction spots corresponding to a lattice modulation in real space -9.4 nm, in agreement

with the periodicity of misfit dislocations; these are indicated by arrows in the inset of Fig. 2(b). The spacing of the misfit dislocations is double the spacing of the 220 moirP pattern.‘” The set of misfit dislocations can be dis- tinguished from the moir& pattern, since the moir& contrast is rapidly fading as the deviation from the exact Bragg condition increases.15 Therefore, at certain deviations from the exact Bragg condition the image due to dislocations is stronger than the contrast from the moire pattern. For the same reason it is possible to image the two sets of the misfit dislocations, when the multiple diffraction condition is sat- isfied, by using simultaneously the 220, 520, and 040 reflections,” as is shown in Fig. 2(c). In the same micrograph the perfection of the cross grid of misfit dislocations is also apparent. To our knowledge, for the first time an artificially grown system gives such a perfect grating of dislocations.

However, in some areas a shift of the misfit dislocations for half of their periodicity occurs along both the ( 110) directions, as is indicated by arrows in Fig. 2(c). The high-magnification micrograph of Fig. 3 shows the characteristics of the observed shifting that are the follow-k. ing.

(i) When both families of misfit dislocations are in contrast, the boundaries bet.ween adjacent domains separate cross grids of dislocations, shifted by half of their periodicity. This is indicated by the dashed line.

(ii) The domains can have any shape; however, their boundaries consist of segments that follow low-index crystallographic directions, mainly ( 110) and ( 100) type.

(iii) The boundaries with traces along the (110) directions intersect only the family of the misfit dislocations that is perpendicular to them while they disturb the periodicity of the family that is parallel to them, as in A and B areas.

(iv) The boundaries with traces along the ( 100) directions intersect with both families, as for example in the area denoted by the letter C.

Shifting of the misfit dislocations in the GaAs/Si system was reported in the literature’7-‘0 and was attributed: (i) to the interaction of a 60” dislocation with the network of the Lomer misfit dislocations;‘7-‘9 (ii) to the presence of monoatomic surface steps or demisteps at the interface.”

In order to conclude whether a possible interaction of 60” dislocations with the misfit dislocations is the reason accounting for the shifting in our case, tilting experiments were performed.

An interac.tion of a 60” dislocation with one set of misfit dislocations at the GaAs/Si interface could result in the formation of a new 60” dislocation according to the reaction b+bsa=b’, as is schematically given in Fig. 4. In an array of misfit dislocations with b = $ilO], a 60” interfacial dislocation, having a line along the [I lo] direction, should have one of the following Burgers vectors: bhO,i=f[Oil]r i[Oii], $lOi], $1011, where i=1-4 Table I gives the possible dislocation reactions bf, between b and bbo,? Table II gives the corresponding g*beO,+ and g-b; values for the reflections that were used for the observations. It is deduced that for g=220 the two segments of the disloca-

144 J. Appl. Phys., Vol. 75, No. 1, 1 January 1994 Komninou et a/.


a b c

FIG. 2. C<aAs film grrwrt on vicinrtl [OnI ) Si substrate that was subjected to an irr situ thermal dewrption before deposition by eximer laser. (a) RF plane-view microgrJph taken with the = 220 retleotion; the perfect sequence of moir& fringes, parallel to the [ilO] direction, is characteristic of the quality of the interface. i b) Diffraction pattern of the [Ool] zone axis from the GaAs/Si interface; the coexistence of both GaAs and Si ditfractioa spots and the sharp extra satellite spots that are pointed by the arrows in the inset, indicate the perfection of the misfit dislocation network. The spots near the 2t~l positions are matrix spots from G;IAY. C,c) BF plane-view micrograph from the CiaAs;?ji interface with the beam slightly deviating from the exact [Ool] dir&on. .A shifting of the misfit dislocations by half of their periodicitg along both (1 IO) directions is visible.

tions with Burgers vector I.+’ or b,o,i should be in contrast., which is not the case of our observations. This is illustrated in the weak-beam micrograph of Fig. 5 !a). The figure shows that the misfit dislocations a-e abruptly shifted for half of their period without splitting and no segments of dislocations with Burgers vector bf or bs,~,i are observed. However, the experiment is not sufficient to exclude a reaction with hO” dislocations since gjzo* b( = 1 and f&o l bGO,;= - 1. If s>O, as in the weak-beam case, the dis-

FIG, 3. Detailed view of the cross grid of misfit dklacations. The bound- atier het\wen adjaci:Cnt d~.unains separate shifted cross grids of mistit dislocations by h&of their prriodicity. The boundaries with traces along the $1 IO) dire&ions intersect the one family of the misfit dislocations while &se along < IW,! directions inter$rst both. This is indicated by the letters A, 13, and C, respectively.

d; Appl, Phys., Vol. 75, No. 1, 1 January 1994

locations might be invisible for gab= f 1. Observation with the 220 reflection in the two-beam condition is im- possible due to the strong contrast of the moire pattern.

The best condition to avoid ambiguity is to work with the 222 and the 322 superlattice reflections. These exclude the formation of rnoir.6 pattern and give, with bf, vector dot products with values of 2 or 0. Figure S(b) is a DF image, from the same area presented in Fig. 5(a), using the g=I22 superlattice reflection. A bending of the dislocations at the boundaries is observed, denoted by the letter B. If the shifting of the net occurs due to the reaction with a 60” dislocation, the operation of the 322 superlattice reflection will result in an interchange of the invisibility criteria, according to Table IT. The other segment of the dislocation will be visible and the dislocations will look bent in the opposite sense of the boundary. However, experiments performed with the 222 and 222 reflections at the same area show that no reverse bending of the dislocations occurs at the boundaries, which means the displacement of the misfit dislocations is not attributed, in this case, to a 60” dislocation reaction.

The interaction of the 60” dislocations with the Lamer

b -

b

FIG. 5. Schematic illustration of the interaction between the one set of misfit dislocations b with an interfacial 50” dislocation b,,.

Komninou ef al. 145


TABLE I. Dislocation reactions between misfit dislocations b and 60’ interfacial dislocations b60,i on GaAsiSi interface; b; =b + bbO,,, i= 14.

b,i goi l] +[Oii] Qpoi] ;[lol]

b=i[ilO] bi= f{iOl] b+ @oil b;= $[oii] b;= 3011]

misfit dislocations was also studied in an area of the spec- imen where interfacial 60” dislocations coexist with the Lomer dislocations. The two 60” dislocations, denoted by the letters A and B in Fig. 6, lie along the {l lo] direction. .The set of Lomer misfit dislocations along the [ilO] direction crosses these dislocations without shifting. However, they are shifted by half of their periodicity at the boundaries of the exist.ing domains. One of these domains crossing the 60” dislocation (B) is depicted by a dashed line in the 220 weak-beam micrograph of Fig. 6(a). A misfit dislocation is shifted by half of its periodicity when it crosses a 60” dislocation at the intersection with a domain boundary, as in the area denoted by the letter C. Both the above- mentioned 60” dislocations have b=a/2[0li], as deduced from the tilted micrographs of Figs. 6(b) and 6[c) where the 111 and 111 reflections are operating, respectively. Thus, in our experiments the shift of the misfit dislocation network is not attributed to an interaction with 60” dislocations.

Let us consider case (ii). APBs of GaAs that are formed on monoatomic steps or demisteps of Si surface should be responsible for the shift. Figure 7 shows an APB introduced by a demistep of the Si surface. In the noncen- trosymmetric crystals of the III-V group, such as GaAs, the APDs are generated by the combination of an inversion operation and a latt.ice displacement R = a/4( 1 1 1 > . Due to the violation of Friedel’s law,8,2*-24 an inversion operation results in differences of the contrast of the APDs when they are viewed in DF by symmetrical hkl and zasuper- lattice reflections. Figure 8 contains two DF plane-view micrographs with the 222 and 223 superlattice reflections, under nearly two-beam conditions. Dark and bright. domains are visible and the corresponding areas have reversed contrast in the two images. Only the one set of the misfit dislocations is visible since the other satisfies the condition g l b=O and consequently is out of contrast. The same area was observed in BF with the 220, 220, and 040 reflections under multiple-beam conditions, Fig. 3, where the network of misfit dislocations is shifted by half of its

TABLE Il. gsbf and g-b,,,i values.

g b;= fpol] b+ $ioi] b;= $[oli] b;= $0111

b61J,1=~[0ill I -- bmaI=q[Ol l] b,,,=f[lOi] bsoc=f[lOl]

220 g-b;= 1 g-b;= 1 g-b;=1 g-b;= 1 rbo,r= - 1 g*b,o,z= ~ 1 g*b6U,3- -- 1 g.bso,r=-l

522 g-b;=2 g* b;=O g-b;=0 g-b;=2 g*bwvI=O x*$oQz= -2 g*bGoJ= -2 g- bail=0

522 g-b;=0 g-b;=2 g-b;=2 g-b;=0 x-b,,,= -2 g.b,u,z==O g.b,g,=O g*baa,d=-2

periodicity as the dislocations cross the boundaries of the domains. Therefore, the shifting of the cross grid of misfit dislocations is attributed to their interaction with the APBs emanating from the interface.

IV. DISCUSSION

A. Shifting of the misfit dislocations

Demisteps with a height 1 a/4[001] 1 are formed easily on the (001) Si surface. Scanning tunneling microscopy observations display that Si surfaces on the exact (001) orientation introduce demisteps with a mean distance of 4 nm. ” Their densi 7 is reduced in case of vicinal (00 1) Si,

a

b FIG. 5. (a) Weak-beam plane-view micrograph of the GaAs/Si interface using the ‘20 reflection. (b) DF plane-view micrograph, with the 222 superlattice reflection, showing the bending of the misfit dislocations crossing the boundaries of adjacent domains.



a

b

FIG b Plane-view micrographs of a GaAslSi interface where two inter- * . facial t&Y dislocations, A and R, coexist with the mistit dislocations: (a) weak-beam image, taken with the 220 retlection, showing the set of misfit dislocations aiong the [ilO] direction and the A and B dislocations; (b) DF image taken with the I1 1 reflection where the A and B dislocations are out of contrast; (c) DF image taken with the 117 reflection where both A and I3 dislocations togther with the [ilO] misfit dislocations are visible.

tilted J? toward ( 1 lo>, since t.h$y are roplwed by complete steps with height 1 ui2[001] 1; however, demisteps are still numerous since at the kinks the complete steps have the tendency to break up into kinked demisteps.2s Conse-

FIG. 7. [I 101 projection of a GaAs film grown on [OOl] Si substrate. The Si surface contains a demistep which introduces an APB, indicated by the dashed line, in the GaAs epilayer. Notice the difference in the bond lengths between like atoms.

quently, in agreement with our observations, the formation of APBs in high density is inevitable in the early stage of growth (Fig. 8). Most of the APBs that are formed at the GaAs/Si interface are annihilated by the development of inclined APBs as the growth proceeds. This amlihilation mechanism was also reported by other researchers.2h,27

A possible explanation for the shifting of the net of misfit dislocations can be related with elastic stress relaxation that results from the local bond distortion at the APBs.“s In the simplest case of { 1 lO}-type APBs, where an equal number of wrong Cam -Ga and As-As bonds are involved, a high strain energy concentration is expected due to the difference in bond strength between like atoms. The estimated bond strength of the As-As bonds is about three times stronger than that of the Ga-Ga bonds, as is schematically shown in Fig. 7 with the difference in the bond lengths between like atoms. Lattice displacement R, due to the lattice distortion at the APBs, was also observed.2”-“”

The Lomer misfit dislocations are kinked at the APB and become screwlike in character, running parallel to the APB for a distance equal to half of their periodicity. Half of the periodicity is the optimum segment of the dislocation in order to retain equilibrium between the dislocations with the same Burgers vector. At this point the dislocations turn by 90” crossing the APB and continue as a Lomer misfit dislocations in the adjacent APD. For a (1109 APB, a screw dislocation running parallel to the APB results in a partial relaxation of the lattice by shifting the Ga-@a and As- -As bonds apart. The proposed stress-relief mechanism for the dislocations at their intersection with the APBs explains their abrupt shifting that is visible in Figs. 3 and 5 (a).

In the (100) APBs both sets of misfit dislocations are shifted, as is indicated in Fig. 3 by the letter C. This is consistent with high-resolution observations of APBs which show that APBs are composed by small facets of { 1101 boundaries.“’ The faceting of any arbitrary APB in segmented { 110) boundaries is attributed to the process of interfacial energy minimization since the { 110) APBs are considered to have the lowest interfacial energy.32p”3 An-

J. Appl. Phys,, Vol. 75, No. 1, 1 January 1994 Komninou et al. 147


TABLE III. Layer groups of the various APB types.

Orieatation Symmetry

a

b

FIG, 8, DF plane-view micrographs of a GaAs/Si interface, taken with the symmetrical 222 and 2% superlattice reflections. Bright and dark areas separate domains with reversed contrast.

other important reason for the faceting of the APBs is to avoid deviation from stoichiometry and to ensure charge neutrality. Thus, in an APB, the ratio of the number of Ga--Ga and As-As bonds varies with the crystallographic plane. Only the { 110) and { 112) APBs are self- compensated and from them only the { 110) have the lowest index plane and the lowest formation energy.““,“”

The visibility of the segments of dislocations at the APBs using the hhh reflections and their invisibility using the hh0 reflections can be attributed to their interaction with the APB. High-resolution images reveal a strain field at the APBs that results in a bending of the lattice planes.3’

I 10’2 {1W Clll> t.hkOl (hll}, h > I {hhl}, h > I {h/d)

pmmg’ p2’/m p3’m pit

p2’/m p2 ‘/m

pi*

B. Crystallographic analysis

The dichromatic theory of interfacial defects”” is applied in order to analyze crystallographically the interaction of the misfit dislocation network with the APBs. It is essential to recognize that diamond can be regarded as a parent phase of sphalerite where, in the latter, all nonsym- morphic symmetry operations are broken (due to its non- holosymmetric nature), thus reducing the symmetry from Pd%z to .Fz33ne. Epitaxial interfaces can be considered as the “welding” of two complementary surfaces of the two materials. Diamond { 100) surfaces have symmetry pmm2, and there are always symmetry elements (the perpendicular fourfold screw and two diamond planes) which, while leaving the surface orientation invariant, relocate the surface by the introduction of a demistep of height a/4, and a consequent change of the fee sublattice.‘” These operations are termed sublattice exchange operations.” Sphalerite { 100) surfaces again have symmetry pmm2 but, in this case, the sublattice exchange operations of the parent structure introduce a reversal of the polarity of surface atoms, i.e., in the case of GaAs from As to Ga or vice versa. Surface polarity is preserved only if an APB emanates from the demistep, thus introducing antisite occupation of the atoms in the lattice: however, the APB orientation camtot be predicted crystallographically. When t.wo complementary surfaces are brought together in parallel orientation, the layer group symmetry of the interface is the intersection of their symmetries, i.e., in this case, orthodigonal pmm2.“8 The {loo} interface can be demistepped and the demistep is invariably related to an APB emanating from it into the sphalerite crystal.36

Two antisite domains, separated by an APB, are interrelated by the anti-inversion operation [I’ ] i/4( 11 l)], in Seitz notation.“’ The anti-inversion center is located at po- sition l/8,1/8,1/8. The APB symmetry is given in Table III for all APB orientations. Since the APB is considered as always passing through anti-inversion centers, it always exhibits at least anti-inversion symmetry. Hence, the orientation of an APB emanating from the interface must be governed by energy minimization rules. The APB symmetry analysis shows that the dichromatic pattern symmetry is FdTml’ and the dichromatic complex symmetry is Fd’Fm.38 Thus, there are two complex variants corresponding to reverse occupation of the fee sublattices of both components. They are interrelated by the exchange operations, as well as by the antisymmett-y operations of FdTm 1’ which have a zero translation part; hence, we in-



Q /.-, @j (--., .-.

&a $3 lcj -. l ‘-., ~ Jai i@

_-% ~ ~~~ l .,-.

@ c-j @ (-::,

~ y . i@ yJ@ &..-i@ @

i @ ,y,

0 Q . $3 l -- @ @ (1.’ @ fz.j @ (,y-.j @ i-’

63 l @ Q * l .-)

-3 - Si atom at height 0 8 - Si atom at height l/4 @ - Si atom at height l/2 0 - As atom at height l/4 0 - Ga atom at height l/2 l - As atom at height l/2

0 - Ga atom at height 3/4

FIG. 9. Schematic illustration (planar view) of a (001) interface demistepped along two crystallographically equivalent in-plane (1 IO) directions I dashed lines). Two C-&As atomic layers and two Si layers are shown. The lowermost GaAs atomic layer is constrained to be composed of As atoms. The ctkt of the fourfold screw axis on the rotation of the atomic planes can be seen. An APB emanates from each dsmistep in order to preserve GaAs polarity.

elude the latter opwations under the term exchange operations. The antisymmetry exchange operations correspond to a polarity reversal due to a transition from one crystal component to the other. According to the above, the introduction of an APB to preserve the sphalerite surface polarity can be better esplained. For example, the fourfold screw axis normal to {loo) introduces a change of both atom type and sublattice. In order to preserve surface polarity, a transition to the corresponding sublattice of the second donlain is necessary. Such a transition is brought about by the anti-identity operation. The two operations, taken successively, I~;r,:~~~I$WOl Ih’.h

are equivalent to the operation w IC is one of the possible APB descrip-

tions.

In addition, an analysis similar to that for sphalerite surfaces can be applied to show that any API3 of type {lOO}, {l lo}, or {MO) can be crossed by another APB. Also, any APB not belonging to one of the above forms should be crossed by another APB only when it facets to a crystallographically equivalent orientation belonging to the second complex variant (i.e., { 111) to { lli}, {hll) to {h?o, {hhl) to {1&j, and {hki) to {1&Q) if the APB polarity is to remain the same. This symmetry prediction could account for some of the complex APB structures observed in epitaxial &As.”

The dichromatic theory can also provide us with the geometrically permissible interfacial dislocations in an APB. Thus, perfect crystal dislocations can be incorpo-

J. Appl. Phys., Voi. 75, No. I, 1 January 1994 Komninou et a/. 149


FIG. 10. Magnified part of the image presented in Fig. 3. In the area denoted by B one family of misfit dislocations is shifted, while in the area denoted by A both families are shifted by half of their periodicity, following the tetragonal symmetry of their pattern.

rated in the APB with the subsequent introduction of a step of height h=$* b where n is the APB unit normal. For example, if b=$l lo] and the dislocation is incorpo- rated in a (100) APB, then h=a/4, i.e., equal to a demistep. If a perfect crystal dislocation crosses the APB, then a complete step of height h =n* b is created.“5 Class 1 dislocations (broken translation symmetry) cannot exist since all translation symmetry is conserved. Class 2 dislocations (frustrated symmetry) cannot exist since all non- symmorphic symmetry is conserved in Fd% 1 I. However, there could exist class 3 dislocations [broken symmetry/ broken antisymmetry) since an APB rigid-body translation has been observed and measured in the APBs of epitaxial G~As.*“‘~~~’ In addition, there exists a class 2 disloc.ation character at the junction of the APB with the interface, i.e., at the demistep. 36 The reason is that, due to the misfit, all translation symmetry is broken at the interface. Then, if we use the structure matrix Yt = [kl (01, where k is the ratio of the lat.tice constants (k =aG,A4/Usi) and substitute, for example, the demistep introducing operation I4(,,) 1 a< 11 l}] for lV(A)i and W(p)j into the well-known expression3*

g,= w(A)jRct’(p)~‘iH--1, (11 we obtain a Burgers vector bz 1/96.5[1 11].“6 The predicted demistep height is I2= 1.385 A, i.e., it is equal to the average of the demistep heights of the two materials. The effect of this result on the APB rigid-body translation and on other APB defects remains to be investigated. The predicted demistep dislocation is a coherency dislocation. As

FIG. 11. Computed line pattern composed of two superimposed cross grids kaving a common origin and parameters related by a 4% mismatrh. In the upper right-hand-side quarter of the figure, one cross grid has been shifted by half of its periodicity stimulating the structural conditions of Fig. 9.

has been pointed out by Hirth and Balufi,” misfit dislocations can be regarded as “anticoherency” dislocations, introduced to cancel the stresses due to a continuous array of infinitesimal virtual dislocations (coherency dislocations) in the interface. However, when the slightly mismatched crystals are forced into coherency along the demistep, the long-range stresses are not cancelled by misfit dislocations,“3 and thus such an isolated morphological feature possesses virtual dislocation character. The same dislocation character should be eshibited by any interfacial defect associated with a step, in addition to its normal dislocation character. However, the Burgers vector of such a dislocation is very small since the matching strains are small.

The disymmetrization mechanism that the epitaxially grown GaAs on Si follows obeys the principle of symmetry compensationScl according to which, when symmetry is broken at one structural level, it arises and is preserved at another; i.e., in periodic interfaces, the defects arise to compensate for any symmetry elements lost by the introduction of the interface. The consequences of this principle are illustrated in Fig. 9 where an unrelaxed atomic model of two epitaxial API% separated by crystallographically equivaient demisteps along the two in-plane (110) directions can be seen. Two atomic layers from each crystal component are drawn. The 90” rotation of the atomic planes due to the broken fourfold screw axis introduces each demistep plus an APB emanating from it. Figure 10 is a magnified part of Fig. 3. In the area shown by arrow A the demistep trace is along an in-plane (100) direction, and in the area shown by arrow B along an in-plane ( 110) direction. When a demistep runs along an in-plane (100)

150 J. Appl. Phys., Vol. 75, No. 1, 1 January 1994 Komninou et al.


direction, the shift of both sets of misfit dislocations is evident. However, when the demistep is along ( 1 IO), only one set can be seen to shift. This is beause for the misfit dislocations parallel to the demistep, the m-plane shift component is normal to the demistep. Then an a posteriori analysis leads to the following conclusions. The pattern of the misfit dislocations has tetragonal symmetry @mm, i.e., greater than the interfacial layer symmetry (pmm2) and in agreement with the fully compensated layer symmetry. Due to the existence of an APB emanating from the de- n&&p, the misfit distort.ion is rotated by 90” when passing from one domain to another, followed by a $( 111) translation. In order to establish the effect of broken symmetry on the geometry of the network of misfit dislocations, a line pattern following t.he translational periodicities of both lattices has been constructed (Fig. 11). E.ach line corresponds to an atomic plane normal to the iuterface. The pattern is composed of two superimposed cross grids having a common origin and with parameters related by a 4% mismatch. Thus, a moire pattern is created having a periodic- it\: equal to that of the misfit dislocations. In the upper right-hand-side quarter of the figure, one cross grid has been shifted by half of its periodicity simulating the structural conditions of Fig. 9. This introduces a shift of the fringes by half of their periodicity as well. Therefore, we conclude that, when passing from one APD to another, the totragonal pattern of misfit dislocations is forced to comply with the requirement for compensation of the broken !( 11 I) translation. In order to preserve the continuity of the pattern, the misfit dislocations turn by 90” crossing the APB and then continue in the second APD translated by half of their periodicity. Figure 11 is in full agreement with Fig. 10.

These conclusions support the argument that. the observed shifting of the dislocation lines in our experiments is due to the interaction between APBs, emanating from interfacial demisteps and misfit dislocations.

V. CONCLUSIONS

The misfit dislocations are the dominant interfacial defects in GaAs/Si interface. Experimental analysis, using transmission electron microscopy, has shown that the shifting of the misfit dislocation families, by half of their periodicity, is due to their intersection with antiphase boundaries emanating from dcmisteps on the Si substrate. The interaction of 4PBs with the mistit dislocations has been studied based on contrast criteria. The observed discontinuity of dislocation lines is attributed to dynamical contrast conditions. The APBs do not interrupt the continuity of the network of dislocations. The disymmetrization mechanism of the pattern obeys the principle of symmetry compensation

ACKNOWLEDGMENTS

The authors would like to acknowledge Professor A. Christou for useful discussions and Dr. A. Georgakilas for providing the specimens.

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Misfit dislocations and antiphase domain boundaries in GaAs/Si interface

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