Coalescence of islands

The presented results distinctively show the coalescence of islands during the initial growth stage of the antimonide layer. The current notion supposes the creation of TDs due to a mismatch of MFD networks in different islands. The discovered number and distribution of TDs suggests mechanisms to connect networks without the emergence of dislocations.

Models of island coalescence found in literature are summed up in the following paragraphs.

Afterwards the implications of the experimental results are regarded with respect to existing and extended models.

Coalescence without the formation of threading dislocations

Figure 4.21 is dedicated to the matching of MFD networks without the emission of a TD. The initial state before coalescence occurs, is illustrated in figure 4.21(a). The island perimeters are illustrated as grey rims. One set of MFDs with the equilibrium distanced₁is represented by black dashed lines. The orthogonal set is omitted for simplicity. The model for the MFD formation is described by Rocher and Snoeck [190]. It is based on the inclusion of perfect 90^◦ dislocations at the lateral growth front i.e. along the [110] and the [¯110] direction. The

Burgers vector of these Lomer dislocations~b90^◦lies in the (001) interface plane together with the orthogonal line direction. Consequently, the dislocation does not belong to a common glide system of bulk sphalerite structure. These glide systems are bound to the {111} planes outlined by the Thompson tetrahedron (see figure 2.3). Perfect dislocations of a common glide system are denoted 60^◦ dislocations although they only form an angle of 60^◦ in case of a respective line direction. This convention is convenient to distinguish the sessile Lomer and the glissile dislocations. ~b90^◦ = ¹₂[110] is assigned to the sketched dislocation lines without loss of generality for the following considerations. In general, the parallel sets of MFDs in the two islands are shifted with respect to each other. Hence, the question arises how dislocation lines connect to each other without gliding when islands merge.

d₁

Island coalcesence without threading dislocation generation

Figure 4.21.The schemes depict the island perimeter (grey rim) in the (001) interface plane. One set of the MFD network is represented by dashed lines with a equilibrium distanced1and the Burgers vectorb₉₀^◦ of a perfect dislocation. (a) In general MFD networks of two islands are not in phase. (b) - (d) Different models for the behaviour of MFD networks during island coalescence have been proposed [194, 196, 197].

(Details are described in the text.)

Figure 4.21(b) represents a proposal of Zhu and Carter [196] who investigated the case of GaAs on Si(001). They actually studied the reaction of a 60^◦ dislocation gliding to the interface and reacting with the 90^◦ MFDs. Later Kanget al. [194] considered the insertion of 60^◦dislocation segments with~b⁰₆₀^◦and~b⁰⁰₆₀^◦as mechanism to link the shifted sets of MFDs in two islands for the case of GaSb epitaxy on GaAs(001) substrates. The Burgers vectors must satisfy one of the following equations at the nodes.

1

The zigzag structure is dedicated to an energetically favourable configuration but requires a glide within the (001) plane as outlined by Zhu and Carter [196]. It is omitted by Kang et al.[194] keeping the glissile dislocation character of the 60^◦segments. The natural origin of an initial 60^◦ dislocation at the coalescence line is considered below. Moreover, the authors distinguish between large MFD network shifts of approximately ^d₂¹ and small ones.

In the latter situation, they assume the direct connection of MFDs with a slight bending as presented in figure 4.21(c). A different explanation for the observed shifts of ^d₂¹ is given by Komninouet al.[197] who dwell on the problem of GaAs growth on Si(001) substrate. The integration of polar GaAs on non-polar Si entails the formation of APBs. It is argued that the interaction of an APB with the MFD network requires the shift for symmetrical reasons.

As a result, the connection is realized by short screw components placed within the APB at the interface between layer and substrate [197]. This situation is illustrated in figure 4.21(d).

The ideal linkage of MFD networks without the emission of TDs is considered because the density of threading defects is much lower than the density of coalescence sites. The finally established MFD network appears less disturbed in the presented heterostructure of GaSb on vicinal Si(001) compared to the case of GaAs on Si(001) (cf. micrographs in [196, 197]). The obvious difference is the shorter MFD spacingd1in the heterostructure with the higher lattice mismatch. To account for this perfection, mechanisms to align the MFD over long distances are regarded in addition to the models presented in figure 4.21. Bourret and Fuoss [198] studied the GaSb/GaAs system and introduced the idea of a "generalized Stranski-Krastanov mechanism". They observed a periodic interface corrugation that might be initiated by a thin alloyed layer of Ga(As,Sb) at the early growth stage before the island formation would start. A much simpler notion comprises the movement of MFDs within the (001) interface plane. This consideration violates the common idea of the sessile Lomer dislocations. The usual slip system in bulk fcc crystals requires the Burgers vector and the dislocation line to lie on a {111} lattice plane [62]. Rare examples for dislocation motion on {001} planes are presented, for instance, in [62, p.273] and in [199] for bulk fcc metals.

The model introduced by Zhu and Carter [196] actually demands the (001) glide plane, too.

Evidence for the movement of Lomer dislocations in the (001) interface plane is given by Qianet al.[200] who have investigated the growth of GaSb on GaAs(001). They observed that MFD nucleate at the island growth front with a spacing greater thand₁and move inward during continued lateral island expansion to reach the equilibrium distance. On the other hand, the character of bonding at the heterostructure interface is assumed to be similar to the bulk layer and substrate material because both III-V and Si exhibit a covalent bonding.

Hence, the origin of the stress to conservatively move a MFD or even a set of MFDs on the (001) plane is questioned.

Formation of threading dislocations during coalescence

A survey of proposed mechanisms for the generation of TDs is given in figures 4.22 and 4.23.

The first case is a consequence of a different MFD spacing in networks. The equilibrium distanced_idepends on the height of an island [194]. Thus, two islands withd₁ andd₂ have to be connected as shown in figure 4.22(a). Kang et al. [194] investigated the growth of GaSb on GaAs(001). They have observed the termination of two half lines in Moiré patterns of plan view samples (cf. equation 4.8). Thus they have concluded that 90^◦ dislocations

move out of the interface as depicted in the right part of figure 4.22(a). It is remarked that the pure edge character will be preserved if the dislocation line is kept as short as possible during subsequent growth.

d₁ d₂

b_90°

b_90°

d₁ d₃ d₁ d₁ d₁

b_60°

b_90°

b_90° b_90° b_90°

b_90°

(a)

(b)

d₁ d₂

[110]

[110]

d₁ d₁

b_60°

b_90°

d₁

b_60°

b_90°

b_90°

(c)

d₁ Formation of threading dislocations by island coalcesence

d₄

Figure 4.22.The schemes depict the island perimeter (grey rim) in the (001) interface plane. One set of the MFD network is represented by dashed lines equilibrium distanced₁ and the Burgers vectorb₉₀^◦ of a perfect dislocation. (a) An island height dependent equilibrium distanced₂ is added according to [194].

(b)+(c) The insertion of a perfect 60^◦dislocation and subsequent implications are illustrated.

Except for this example, mixed type dislocations are usually observed to emanate from the interface. Three possible origins are discussed which are based on reports in literature.

The first one is mentioned by Rocher and Snoeck [190] and illustrated in figure 4.22(b).

If the distance between two islands d₃ is very small and if MFDs are just nucleated at the island edge, the remaining lateral stress σk will not suffice to form a further perfect edge dislocation. The spacing of the last two MFDs fulfilsd₃ <2d₁. The right scheme illustrates the insertion of a 60^◦ dislocation at the interface passing through the coalesced island in-stead. This train of thought has to be completed because, so far, this does not give rise to a threading dislocation. Figure 4.22(c) describes the circumstance at a triple point during the coalescence with a third island. Here, the 60^◦ dislocation cannot match one of the MFDs.

Hence, it moves out of the interface plane as illustrated or has to react with one MFD where-upon a third line segment with a different Burgers vector is emitted into the layer. At this point, it is worth to consider the orthogonal set of MFDs and the model presented in figure 4.21(b). The mechanism to create a 60^◦ dislocation according to figure 4.22(b) inherently

SF AlS

Figure 4.23.(a) The simplified scheme illustrates the interaction of a SF that randomly nucleates on the (111) growth front, and the MFD network. (b) The sketch depicts the extension of the island along x_k. The diagrams schematically describe the development of the in-planeσ_kand out-of-planeσ_⊥stress.

provides a dislocation to link the shifted orthogonal MFD networks. To be precise, the idea must be extended because alternating 60^◦ segments (~b⁰₆₀^◦and~b⁰⁰₆₀^◦) are required.

The next two cases regard further sources fot the formation of 60^◦ dislocations before is-land coalescence. Indirectly, they lead to TDs according to figure 4.22(c). Ernst and Pirouz [195] report on an unexpectedly high SF density in several heterostructures on Si(001) which start growing in a 3D mode. Later, islands coalesce to a closed film and 2D growth follows.

The authors explain this phenomenon by the random inclusion of SFs on {111} side facets during initial island growth. They assume that layers at the growth front that nucleate in wrong positions on {111} planes, result in SFs which cover the complete side facet. Alter-natively, the formation of SFs or twins is caused by impurities at the substrate surface as recently outlined by Madiomananaet al.[201]. These mechanisms are independent of the island coalescence. In fact, Qianet al.[200] state that the dislocation density in GaSb lay-ers grown on GaAs(001) does not increase during island coalescence. Vajargahet al.[165]

show SFs within AlSb islands deposited on Si(001). TDs are already formed during the ini-tial 3D growth mode. At this stage, the SF only forms a dislocation line with the interface to the substrate. Again this idea must be further elaborated with regard to island coalescence.

Figure 4.23(a) outlines that the SF is bound by TDs after the adjacent islands merged with the faulted one. In this case, a partial dislocationbp is formed at the interface. Of course, a reaction with a MFD is thinkable, too. In addition, the nucleation of dislocation half-loops and their glide toward the interface [68] has to be considered as source for TDs after the closure of the epitaxial film. The driving force could originate from residual, accumulated strain similar to the case of figure 4.22(b). This option is discussed in section 4.3.2.1.

So far, the origin of TDs is discussed regardless of the Si(001) substrate miscut. The up-per part of figure 4.23(b) describes the above discussed notion in terms of in-plane stress σk. The island expands in the lateral directionxk whileσk increases to a critical value. The nucleation of a MFD at the intersection of interface and growth front relieves the stress.

This procedure is periodically continued until islands coalesce. The application of a wafer miscut necessitates the consideration of an out-of-plane stress σ⊥. Every time the growth front crosses a surface stepσ⊥increases. Finally, the accumulated stress has to be plastically

relaxed by a dislocation. The Lomer MFD do not contribute to this relaxation. A dislocation with a Burgers vector component along the [001] direction is required which is most effi-ciently realized by 60^◦ dislocations

~b∈₁

2[101],¹₂[011],¹₂[0¯11],¹₂[¯101]

. This situation is depicted in figure 4.23(b). Assuming ideal Si double steps and a terrace width of 3.9 nm, every 9 steps or after approximately 35 nm such a dislocation has to be included in case of the listed 60^◦ dislocations. The alternating sign in the component along the [001] direction in equations 4.9 and 4.10 implies that the configuration proposed in figure 4.21(b) does not relief the out-of-plane strain due to the stepped substrate surface. Partial dislocations would be less effective but could contribute as well. On the other hand, they trigger the formation of a SF. Hence, there is a general need for dislocations at the interface in addition to the 90^◦ MFD.

Comparison to experimental results

Eventually, a comparison of discussed models and the experimental facts is provided in the following. The analysis of the Moiré pattern according to figure 4.16 does not reveal TDs with a Burgers vector parallel to the (001) interface plane in the investigated specimen. As a consequence, the height distribution of the present islands does not account for different equilibrium distancesd_i of MFDs which has been discussed with respect to figure 4.23(b).

On the other hand, the height dependence of d_i could be saturated for the prevailing island heights. In addition to the Moiré analysis, a result from section 4.3 is anticipated. Dis-locations with~b = ¹₂[110] are rarely observed in subsequently grown layers although the investigated volume is much larger. Beyond, the detected dislocations are formed apart from the interface in dislocation reactions.

The presence of perfect 60^◦ or partial dislocations at the interface is a necessary conse-quence of the deduced TDs. The determination of their segments within the (001) plane is inaccessible due to the unique sample holder tilt axis limiting possible imaging conditions.

Nevertheless, they are excluded as cause for the observed half period shifts in MFD net-works which are outlined in figure 4.18(a). On the one hand, those segments are expected to run along the intersection lines of {111} glide planes with the interface. The irregular courses would imply a non-conservative motion parallel to the (001) planes before meet-ing the interface. The motion within the interface plane is hindered by the presence of the MFDs. On the other hand, the presented results clearly suggest the interaction of the MFD network with APBs (cf. figures 4.18 and 4.19). Therefore, the coalescence model according to figure 4.21(d) (cf. [197]) is regarded as explanation for the observed shifts.

The predominant detection of TDs at the edges of AlSb islands is unexpected. The coales-cence of islands during GaSb overgrowth is assumed to occur midway between two initial AlSb islands. Two scenarios are considered. Either TDs are formed where they are observed, or they move toward these sites. The motion needs to answer the question for the driving force again. The residual stress is regarded as too small in order to extend the dislocation line within the heterostructure interface. The proximity to the presence of APBs (cf. figure 4.19) is emphasized with respect to the first scenario. On the contrary to the assumption on the site of coalescence, a monoatomic step hinders the lateral expansion of the island because the insertion of an APB is required. Hence, the interspace is filled by only one expanding

island and the coalescence occurs at the edge of the AlSb island where the APB must be formed during the closure of the epitaxial film. At this site, a perfect 60^◦ dislocation like in figure 4.22(b) or (c) is forced to bend upwards. The interaction of the dislocation with the APB is treated in chapter 4.3.

The lateral bending of the Lomer dislocations in order to connect MFD of different is-lands is apparently easier in the high mismatched GaSb/Si system than in, e.g., GaAs on Si because the maximal shift accounts for only 4 GaSb(110) lattice planes. This allows the linkage according to figure 4.21(c). The shift between the networks is smaller than 1 nm in 66 % of the cases. Therefore, the perfection of the MFD network is facilitated by the large mismatch and the small equilibrium MFD distance. Whether the MFD are straightened to minimize the line energy, is difficult to judge from the presented investigation. In fact, this confirmation would give another hint to the mobility of Lomer dislocations at the interface -be it conservative or non-conservative.

4.2.2.3. Technical aspects of the measurements and results

Im Dokument Electron tomography and microscopy on semiconductor heterostructures (Seite 93-99)