Formation of pores in GaSb epilayers

The discussion of the pore formation requires an idea of their localization within the het-erostructure stack and a proof that they have not accidentally occurred in the investigated sample. In fact, their presence is unexpected for the intended layer-by-layer grown het-erostructure. The following paragraphs address the localization, an idea for a formation mechanism and the implications of the morphological analysis. The experimental findings are discussed according to the publication of the results in [163]. The significance for future growth experiments and the device performance is discussed at the end of section 4.3.

Localization of pores

The occurrence of a pore in the III-Sb heterostructure on vicinal Si(001) which has been recorded in a tilt series (figure 4.2), is not an exemption. All samples listed in table A.1 except for sample F show the emergence of pores. Figure 4.7 presents ADF STEM images of sample cross-sections. Samples A and D have been grown on nominal Si(001) and Si(111) substrates, respectively. The other heterostructures are deposited on vicinal Si(001) wafers.

The thickness of the GaSb buffer layer is different for samples A and B and samples C and D, respectively. Sample E presents a different sequence of III-Sb layers. The attention is drawn only to the initial superlattice of AlSb and GaSb layers. All samples presented in figure 4.7 have the presence of an AlSb layer in common. The lateral distribution of pores appears heterogeneous. Their distances among each other vary between less than 100 nm up to the order of 1 µm. On the other hand, their position along the growth direction is common to all samples presented in figure 4.7. Pores occur below the AlSb barrier layer independent of the substrate choice and the GaSb buffer layer thickness. As a consequence, the formation during the coalescence of the initial 3D growth (cf., for instance, [165]) is excluded.

Pores are not observed in sample F which does not exhibit an AlSb layer. Furthermore, the observation of a heterostructure with the same design like samples A, B and C but grown on GaSb(001) does not show pores either in spite of the AlSb layer presence. An additional distinctive feature in the images of figure 4.7 is highlighted for the following discussion.

The collection angle of the ADF STEM image of sample C is smaller than in the other cases. The remaining diffraction contrast resulting under the applied imaging conditions (cf.

section 3.2.3) reveals microstructural features that are attributed to dislocation lines.

The remarkably rough interfaces and surface of sample D originate from the presence of twins. Twinning is characteristic for the growth of III-Sb on Si(111). Steps at interfaces and the surface of the other three samples are addressed later on in section 4.3.2.1.

Si(111) 500 nm

200 nm 200 nm 400 nm

sample A sample B sample C

sample D

4° off Si(001)

Si(001) 6° off Si(001)

GaSb AlSb

sample E

200 nm 100 nm

GaSb

GaSb AlSb...

GaSb AlSb

4° off Si(001)

Figure 4.7.HAADF STEM images are captured in order to determine the location of pores in heteroepitaxial III-Sb multilayers. They are grown on nominal Si (001) (sample A) and on vicinal Si(001) with 4^◦(sample B) and 6^◦ miscut (sample C) toward the [110] direction as well as on Si(111) substrates (sample D).

In contrast to the overview images, only the AlSb-GaSb superlattice near the interface to the 4^◦ miscut Si(001) substrate are shown for sample F in the lower row of images. Black arrows mark the pores. The image contrast settings exclusively shows the III-Sb layers while the Si substrate and the protective carbon layers appear in black.

Origin of pores

It is assumed that a significant number of point defects is incorporated into the GaSb layer under the applied Sb-rich MBE growth conditions. Following hypothesis is suggested start-ing from this assumption. It is schematically depicted in figure 4.8. There is an excess of vacancies that exceed the thermodynamically stable concentration. Hence, there is a driving force that moves the vacancies toward the sample surface in order to annihilate. The dif-fusion of vacancies precedes slower than the advance of the growth front. The deposition of the AlSb layer presents an obstacle to the vacancy migration toward the surface. Instead of annihilating at the surface, the vacancies accumulate below the AlSb barrier and,

eventu-v_vac

GaSb v_growth AlSb

planar defect dislocation vacancy

t₁ t_end

Figure 4.8.The schematics describe a model of pore formation. During GaSb buffer growth (t) excess vacan-cies are introduced in the epitaxial layer. The vacanvacan-cies annihilate at the surface in order to establish an equilibrium concentration. The growth front moves faster than the vacancies (vvac< vgrowth). The insertion of an AlSb layer presents an obstacle for vacancies and stops their motion (tend). The vacancies cluster and create voids. the right scheme extends the idea by nucleation sites defined by dislocations and planar defects.

ally, condensate in pores. This final situation is exclusively observed in samples exhibiting an AlSb barrier layer (figure 4.7). Samples with a composition gradient from GaSb to the (Al,Ga)(Sb,As) cladding layer appear free of pores. The disability to pass the AlSb thin film is suggested to have an electrostatic reason. Murarka and Peckerar [166] and Tahini et al.

[167] have considered charged point defects in semiconductors. A repulsive electrostatic field has to be created. It is speculated that accumulated charges at the AlSb layer which owns the highest band gap of 1.61 eV [55] in the layer stack, are the origin of such a field.

The range into the GaSb buffer defines the distance of the pore toward the barrier. The func-tion of the AlSb as barrier to point defects might be beneficial in order to suppress defect motion during operation of the finalized laser device.

A further aspect in the nucleation location of pores is the lateral position. The determina-tion of nucleadetermina-tion sites by dislocadetermina-tions or planar defects is taken into consideradetermina-tion. The left scheme in figure 4.8 presents the respectively extended model. Anticipating the correlation of the step revealed by the tomographic data (figure 4.6) with a planar defect (cf. section 4.3), there is a hint to the coincidence of a pore with a planar defect. The image of sample C in figure 4.7 gives a further hint to the coincidence of pores with dislocations. The absence of pores below the AlSb layer deposited on a homoepitaxially grown GaSb buffer layer which appears widely free of defects, is in agreement with this notion of nucleation sites.

So far, a shortcoming of the presented model has to be pointed out. The consideration of vacancy condensation neglects the fact that the compound semiconductor GaSb consists of two different atom species. Consequently, there are two types of vacancies: V_Ga and V_Sb. The growth under Sb-rich conditions suggests that the assumed excess vacancies belong to only one type. The nucleation of these point defects belonging to only one fcc sublattice in the sphalerite structure implies the excess of atoms from the other fcc sublattice. These have to remain as precipitate within the pore or have to be emitted as interstitials into the crystal lattice. Several nanometre sized precipitates are experimentally ruled out (cf. section 4.1.1.1) whereas a small remaining wetting layer on the pore bounding surfaces might be undetected in the case of the experimental sensitivity. Regarding the stay of resulting inter-stitials, the publication of Vardya and Mahajan [168] provides an interesting option beside the simple movement toward the surface. The authors describe a mechanism of dislocation climb which is based on the absorption of point defects (interstitials or vacancies) at the dis-location core. The mechanism is based on the inherent function of a disdis-location as sink and source for point defects. Moreover, the authors underline that pairs of vacancies or

intersti-tials have to be accumulated at once because a single absorbed point defect is energetically highly unfavourable. In order to have a concrete example, Sb interstitials Sb_i and V_Ga are assumed. That is, V_Gahave to be emitted into the GaSb buffer layer if dislocations climb by absorption of Sbi. In this example, further vacancies are provided for the growth of pores and an interaction mechanism of pores and dislocations is implied.

Final pore morphology

The detailed analysis of the pore morphology provides insights into the energetics of a stable crystal form. The dominance of {100} and {110} facets is deduced from the tomographic evaluation of the tilt series. In contrast, pores bound by {111} planes in sphalerite struc-tured materials have been reported by Huanget al. [169] and Jäger and Jäger [170]. The former work describes tetrahedral etch pits in GaSb that are overgrown subsequent to the etching step with arsenic. The latter work deals with voids in GaP that form in annealing experiments of dopant diffusion. Considerations of energetically stable habits of sphalerite structures belong to a long lasting discussion. Cahn and Hannemann [171] argued that the surfaces with the lowest density of dangling bonds are energetically favourable. Sectioning the bulk GaAs crystal parallel to {111} is the simplest realization of this proposal. This is in accordance with the findings of the afore mentioned publications [169, 170]. A further aspect is introduced by the polar character of the {111} surfaces. Harrison [172] addresses this problem and finds the perfect cleavage planes {110} in GaAs as energetically favourable surface. The strong ionic bonding contribution in III-V compound semiconductors necessi-tates an equivalent presence of group III and group V elements in the surface plane [173].

This argument agrees with the revealed {110} facets of the pore but contradicts the presence of {100} surfaces. Ideas of energetically favoured surfaces must be extended by possibil-ities of surface reconstructions. These include the reduction of dangling bonds, the local rearrangements of surface and near surface atoms as well as the incorporation of adatoms.

It is assumed that foreign adatoms are negligible under the MBE growth conditions. But excess Sb atoms may be responsible for the formation of a stable reconstruction of a {100}

surface of GaSb [174] which explains the presence of respective pore facets.

Qualitatively, the presence of {100} and {110} facets conveys the notion of a form that approximates a sphere (see figure 4.9). The dimensionless sphericityΨallows to quantita-tively compare the similarity of 3D objects to a sphere. The surfaceAof the object is related to its volumeV by

Ψ = π¹³(6V)²³

A . (4.5)

The smallest ratio of volumeV and 3D object surfaceAis realized by a sphere and results in Ψ = 1 which corresponds to the minimization of the surface tension of the 3D object.

Figure 4.9 shows different habits and their sphericity. Pure crystal forms like the octahedron (Ψ = 0.67), the cube (Ψ = 0.81) and the rhombic dodecahedron (Ψ = 0.90) which are formed by {111}, {100} and {110} facets, respectively, are less similar to a sphere than the habit with mixed forms. The example with {100} and {110} bounding planes of equal distance to the centre of gravity accounts for a sphericity ofΨ = 0.94. This consideration suggests a tendency to approximate a sphere. In contrast, the quantitative determination of the pore sphericity from the experimental data results in the significantly smaller value

{111}

{110}

Ψ = 0.94 {110}

+ {100}

Ψ = 0.67 Ψ = 0.90

[010]

[100]

[001]

{100}

Ψ = 0.81

Ψ = 1.00 sphere

Figure 4.9.The notion about the pore morphology is supported by the visualization of different cubic crystal habits. The sphericity quantifies the similarity to a sphere.

of Ψ = 0.85. This contradiction is solved by the consideration of concavities in the pore morphology (arrows in figure 4.5). The coalescence of two pores is supposed which leaves these recesses in the surface. Hence, this fine detail has to be emphasized as valuable hint for the understanding of the pore shape.

The treatment of the pore as 3D body is convenient but the general difference between a usual, convex crystal form and a pore has to be mentioned. The concave surface of the crystal matrix surrounding the pore is the substantial matter. The approach is assumed to be valid as long as the bounding facets dominate over the impact of edges comparing a crystal and the pore. This limitation implies a possible size effect, i.e the size dependent change of the pore morphology.