G. Costantini, C. Manzano, R. Songmuang, O.G. Schmidt, and K. Kern Self-organized semiconductor quantum dots
(QDs) produced by lattice-mismatched het-eroepitaxy are considered a promising system for many novel electronic technologies and de-vices such as nanoelectronics, low-threshold lasers, memory storage, testing paradigms for quantum computers, etc. A precise control over dimension and shape of the QDs is of crucial importance since these morphological
charac-teristics influence the quantum confinement of the charge carriers and therefore set the opto-electronic properties. But the determination of the morphology of free-standing QDs alone is not sufficient, since the process of capping the QDs with a larger bandgap material is essential for any device application and can dramatically change their shape and size. Even by limiting only to the most studied system, namely InAs
QDs grown on GaAs(001), a number of dif-ferent and sometimes contradictory results have been reported in literature for the QD shapes:
lenses, full or truncated pyramids and a vari-ety of multi-facetted structures. Moreover the oversimplified assumption that the QDs remain structurally unchanged during overgrowth is of-ten considered. Therefore we decided to inves-tigate the InAs/GaAs(001) system by means of in situ scanning tunneling microscopy (STM) and to use its ultimate spatial resolution in or-der to clarify some of the open questions.
InAs was deposited by molecular beam epi-taxy at an extremely low flux (0.008 mono-layers per second [ML/s]) and high substrate temperature (500ÆC) in order to be as close as possible to thermodynamic equilibrium condi-tions. As a matter of fact, being less sensitive to small variations in the experimental parameters, these conditions allow a higher degree of repro-ducibility and transferability of the achieved re-sults. Moreover ‘large’ QDs are produced that are characterized by light emission wavelengths close to the technologically relevant 1.3 µm.
The deposition of 1.8 ML InAs results in two coexisting types of QDs: ‘small’ (height 1.80.6 nm, density 71010cm2) and ‘large’
(height 14.40.7 nm, density 3109cm2) ones. The former show large variations in heights and widths and completely disappear after a 30 s annealing at 500ÆC [Kiravittaya et al., Physica E 13, 224 (2002)], thus demon-strating that they are not equilibrium structures.
Conversely, the larger QDs remain almost un-changed after the annealing and are character-ized by an extremely narrow size distribution.
Despite of their large dimension, these dots are dislocation-free, as confirmed by good photo-luminescence properties and transmission elec-tron microscopy measurements. Figure 49(a) is a typical high resolution STM topography of a large QD and shows a truncated-pyramid shape with an octagonal base elongated along110. A closer inspection of such images reveals that the sides of the QDs are composed of only two type of facets with rectangular
symme-(111) (Fig. 49(d)) orientations. Moreover the evaluation of their lattice parameters allows even the identification of the surface reconstruc-tions which turn out to be (11) for (110) and (22) for (111).
Figure 49: (a) 5050 nm2 STM topography of a large QD. (b) Theoretical equilibrium shape of an InAs QD. High resolution views of (c) the (110) facet (1212 mm2) and (d) the (111) facet (44 nm2) of the same island.
The accurate experimental determination of the morphology of QDs allowed for the first time a meaningful comparison with recent theoret-ical predictions for the equilibrium shape of InAs/GaAs(001) QDs [Pehlke et al., Applied Physics A 65, 525 (1997)]. M. Scheffler and col-laborators have developed an hybrid approach in which the surface energies are calculated ab initio by density-functional theory, while the long-range strain relaxation are determined by continuum elasticity theory. The striking agree-ment between experiagree-ment and theory can be verified by comparing Figs. 49(a) and (b). This agreement extends also to the surface recon-structions of the island facets and, since the the-ory essentially relies on the hypothesis of ther-modynamic equilibrium, it represents a test on how close the chosen experimental parameters
Figure 50: (a)–(c) STM images of the QD capping at increasing GaAs coverages. (d) typical1¯10scans through the QD center.
The QDs were overgrown by depositing GaAs at a flux of 0.08 ML/s and a substrate tem-perature of 460ÆC. The initial stages of cap-ping (Fig. 50) already demonstrate that crucial changes in the morphology of the dots take place. The QDs quickly transform into elon-gated structures with a principal axis parallel to
1¯10and their height is considerably reduced (see Fig. 50(c)).
A quantitative analysis of these transformations reveals two different regimes (black squares in Fig. 51): an initial rapid dissolution of the QDs followed by a slower real capping of the remain-ing structures with a transition that, for the cho-sen deposition parameters, takes place at around 4 ML.
Figure 51: QD height during the GaAs capping pro-cess. Together with the STM data (black squares) the results of a second capping series done at higher flux and analyzed by atomic force microscopy are presented (red triangles). Inset: model evolution, see text (GaAs yellow, InAs red).
These phenomena can be at least qualitatively understood by supposing that the following atomic processes take place at the QD surface:
the outmost In atoms first interchange with the incoming Ga atoms (a highly probable process, [Muraki et al., Applied Physics Letters 61, 557 (1992)] and then both In and Ga atoms prefer-entially diffuse out of the dot region because of energetic reasons (high mismatch with the sur-rounding environment). The iteration of such processes, whose net result is the removal of the outmost InAs layer and the exposing of the next InAs layer, is clearly a continuous dissolution of the QD. Moreover the dissolution will be ac-companied by the deposition of an InxGa1xAs alloy in the region close to the QD and, be-cause of the anisotropic diffusion directions of the GaAs(001) surface, this will preferentially happen along1¯10. A ‘critical’ thickness can naturally be defined in this model when the de-creasing front of the top of the dot meets the raising front of the lateral shoulders (insets of Fig. 51). After this thickness is reached, the number of free In sites at which the intermix-ing can take place becomes extremely small so that the dissolution of the InAs core continues only for a limited time. The removed material is still accumulated close to the dot center, but now at a higher position so that shallow ridges form (e.g. Fig. 50(b)). Thereafter the deposited Ga atoms do not find any free In site and sim-ply bind with As ones starting a true capping process.
A simple one-dimensional quantitative model for the QD dissolution can be developed based on this atomic-level picture. By direct com-parison of the linescans in Fig. 50(d), it turns out that the 1¯10 lineshape of the QDs (or of their remaining parts) can be approximated by a parabola, i.e., the QD can be described by y =αx2+ ct where the function c(t) corre-sponds to the QD height. If we suppose that each incoming Ga atom removes one In atom, the number of removed In atoms in the time interval dt will be equal to the number of de-posited Ga atoms during the same time, i.e.
the InAs unit cell. As a consequence, the height decay of the QD obeys to the simple differen-tial equation ct=Φ Ωand therefore is de-scribed by the function ct= c0–Φ Ωt that is
linearly dependent on the amount of deposited material Φt. Despite it simplicity, this model captures the essential features of the QD dis-solution process as can be verified by compar-ing the two curves in Fig. 51. For both of the capping experiments (GaAs flux of 0.08 ML/s black squares, GaAs flux of 0.6 ML/s red trian-gles) the QD height shows a linear decay and the decay rate is identical, i.e., it depends only on the amount of deposited material.
The fact that a model that essentially is based on atomic-scale intermixing and diffusion pro-cesses nicely describes the experimental data is a strong sign that kinetic effects play the deter-mining role during the overgrowth of QDs. This can be used for steering the final optoelectronic properties of embedded QDs but it represents also an indication that the use of sole thermo-dynamic arguments in the description of the QD capping process, as is often found in literature, is not appropriate.