Metastability of Ultradense Arrays of Quantum Dots

Shchukin, V. A.; Bimberg, D.; Munt, Timothy P; Jesson, D. E.

doi:10.1103/physrevlett.90.076102

Cited by 37 publications

(25 citation statements)

References 17 publications

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“…5 It is important to note that while the optoelectronic properties of lowdimensional semiconductors have been investigated widely 6,7 this is one of the few studies on dense ensembles of QDs or QDSs. 8,9 A major problem with isolated semiconductor nanoparticles is that they often have surface electronic states within the highest occupied molecular orbital/lowest unoccupied molecular orbital ͑HOMO-LUMO͒ gap that provide nonradiative decay channels and lead to a severe degradation in optoelectronic properties. This problem has been addressed by "capping" the semiconductor nanoparticle with a thin layer of a higher band gap material.…”

Section: Introductionmentioning

confidence: 99%

Photoluminescence enhancement in nanocomposite thin films of CdS–ZnO

Ayyub

Vasa

Taneja

et al. 2005

Journal of Applied Physics

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We show that the photoluminescence emitted from a dense, two-component quantum dot ensemble on a thin film is significantly higher and decays much faster than that from quantum dots of either of the two pure systems ͑CdS and ZnO͒. The semiconductor nanocomposite, in which the characteristic grain size of each species was 2 -3 nm, was deposited directly on Si wafers by high-pressure magnetron sputtering, and exhibits a single, relatively sharp optical absorption edge.

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Section: Introductionmentioning

confidence: 99%

Photoluminescence enhancement in nanocomposite thin films of CdS–ZnO

Ayyub

Vasa

Taneja

et al. 2005

Journal of Applied Physics

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“…3, in which the boundary between metastable and unstable regions is plotted as a function of surface coverage q s and island size b / b cr where b cr = ␤ ͑1+I + ␤g͒ 2 / w d ␤g 2 is a critical radius. The solution of Shchukin et al 15 ͑for small slopes, small interactions, and similar materials͒ is the same as Fig. 2 in that reference.…”

Section: ͑7͒mentioning

confidence: 54%

“…Note that this reproduces the energy expression of Shchukin et al 15 if we take E s = E d and s = d ͑similar materials͒ and linearize the strain energy term such that it is the sum of a self-relaxation energy and an interaction energy, such that ͑1+I͒ / ͑1+I + ␤g͒ −1Ϸ −␤g / ͑1+I͒Ϸ−␤g + ␤gI, where the first step assumes ␤g Ӷ 1 ͑small slopes͒ and the second assumes I Ӷ 1 ͑small interactions͒.…”

Section: ͑7͒mentioning

confidence: 81%

Enhanced elastic interactions between conical quantum dots

Gill

2006

Applied Physics Letters

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An analytical model for the elastic energy of a system of conical heteroepitaxial quantum dots of finite slope is presented. An expression for the surface tractions at the dot-substrate interface is proposed. This includes a singularity in the stress field at the perimeter of the dot. The strength of this singularity increases as the slope of the dot increases. This dramatically enhances the elastic interaction between dots and the metastability of a quantum dot array. This could help explain the stability of bimodal island size distributions observed in some quantum dot systems. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.2390651͔The elastic strain energy of a system of heteroepitaxial quantum dots is critical in determining their ability to selforganize and achieve a metastable state.1,2 A number of authors have investigated the rich behavior of such systems using analytic expressions for the strain energy of the combined multidot system. [3][4][5][6][7][8] These models represent the effect of the dots' presence on the substrate by a distribution of point forces on an elastic half-space. This is a small slope approximation based on the assumption that the energy change in the island-substrate system due to the relaxation of the mismatch strain is small compared to the energy of the unrelaxed island. 9 In this case, the tractions are simply proportional to the slope of the surface profile. This is a valid approximation for small slopes if the tractions on the halfspace are continuous. 10,11 For the case of quantum dots this is not the case, as there is a discontinuity in the dot profile at the edge of the dot. This generates a singularity in the stress field of the dot at its outer perimeter. These singularities are expected to interact strongly over relatively large distances. These singularities have not been treated explicitly in previous analyses, although fitted models for the interaction energy between dots based on finite element calculations have been proposed. 12 The surface tractions in Fig. 1 are singular at the dot perimeter. 13 The radial surface traction at the dot-substrate interface is fitted towhere ␣ is the strength of the singularity at the island edge and the second term ensures that f r ͑0͒ = 0. The two exponents are well fitted by ␣ = 1 2 tanh͑1.41͒ and ␦ = 0.114␣ −1 + 0.638 for E s = E d and s = d = 0.3. The magnitude of the surface traction, c, is that which minimizes the elastic strain energy ͑see below͒. In the small slope limit ͑ → 0͒, ͑2͒ is equivalent to ͑1͒. Figure 1 shows that ͑2͒ is a good representation of the numerical results.Shchukin et al. 5 analyzed the change in strain energy of an elastic half-space ͑substrate͒ due to radial surface tractions distributed over a number of circular patches p of radius b p . Their result is for the constant radial surface traction model ͑1͒, but their elegant derivation is applicable for any radial surface traction model. To first order, the change in strain energy is given bywhere ⌬E pp is the self-relaxation energy of patch p and...

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“…Here, we can neglect the effects of surface stress and assume that total energy change from 2D growth to 3D island growth is the sum of changes in surface and strain energy, i.e. DE total ¼ DE surf +DE elast [23]. It should be noted that DE surf > 0 and DE elast o0: Thus, if 9DE surf 9o9DE elast 9; we can see clearly that DE total o0; which indicates that 3D island growth is the favorable state in the system.…”

Section: Methodsmentioning

confidence: 99%