Size

Unfortunately, it is necessary to start this section by pointing out that the word "size," as used in much of the QD literature, has an imprecise meaning. Sometimes it is used to mean volume (in which case, the better word would be volume), but at other times it is used to mean width. In this latter case, two QDs of equal size (width) can be of different volume as, for example, for a pyramid and a dome. This is an important point where objects of different shape are to be compared (e.g., dome to pyramid). Because of this imprecision in the literature, and because it is not always possible to determine which is meant, we use the word size in the ambiguous sense where ambiguity exists. Of course, where shape remains fixed, volume scales with size; however size is interpreted.

Daruka and Barabasi [161] showed that in the S-K mode, when the island growth starts, the equilibrium island size does not increase continuously but jumps discontinuously from zero to a value that depends upon the lattice mismatch and the wetting layer thickness. Spencer and Tersoff [162] also suggested that island formation starts from a fixed width (a minimum island size). Very narrow island size distributions at the early stages of island growth have been observed [103, 163-168] in various material systems and have been attributed to specific models of self-limiting growth [107, 169-171]. When the thickness of deposited materials reaches a certain value, Ostwald ripening occurs [161, 172] and the above narrow size distribution no longer exists. Bimodal size distribution has also been reported [93, 95] and has been discussed in Section 2.1.

In a study of InAs/GaAs QDs grown at different temperatures, Saito et al. [76] showed that QD size depends greatly on growth temperature. They found that with increasing growth temperature, the island density decreases while island size increases and the island size distribution becomes more uniform. The same effect was found in the Ge/Si system [173]. Kinetic Monte Carlo simulations suggest that the QD size distribution immediately after deposition is kinetically controlled, giving smaller islands for lower temperatures and larger islands for higher temperatures [174]. Allowing for variations of the island density, the stability of the combination of larger islands with a lower island density implies the action of Ostwald ripening [175].

Quantum dot size also depends on the orientation of the substrate surface. It has been reported that QDs grown on some high-index surfaces are smaller, more uniform in size, and of a higher density than QDs grown on (001). For example, under the same deposition conditions, SiGeC QDs grown on Si(311) [75], InP QDs grown on GaInP/GaAs(311)A [74], and InGaAs QDs grown on GaAs(311)B [176] are smaller than their counterparts grown on (001).

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