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Strain analysis for the prediction of the preferential nucleation sites of stacked quantum dots by combination of FEM and APT.

Hernández-Saz J, Herrera M, Duguay S, Molina SI - Nanoscale Res Lett (2013)

Bottom Line: It has been used for the prediction of the nucleation sites of stacked quantum dots (QDs), but often using either simulated data of the atom positions or two-dimensional experimental data, in such a way that it is difficult to assess the validity of the predictions.This also allows us to compare the simulation results with the one obtained experimentally.Our analysis demonstrates that FEM and APT constitute a good combination to resolve strain-stress problems of epitaxial semiconductor structures.

View Article: PubMed Central - HTML - PubMed

Affiliation: INNANOMAT Group, Departamento de Ciencia de los Materiales e I,M, y Q,I,, Facultad de Ciencias, Universidad de Cádiz, Campus Río San Pedro, s/n, Puerto Real, Cádiz 11510, Spain. jesus.hernandez@uca.es.

ABSTRACT
The finite elements method (FEM) is a useful tool for the analysis of the strain state of semiconductor heterostructures. It has been used for the prediction of the nucleation sites of stacked quantum dots (QDs), but often using either simulated data of the atom positions or two-dimensional experimental data, in such a way that it is difficult to assess the validity of the predictions. In this work, we assess the validity of the FEM method for the prediction of stacked QD nucleation sites using three-dimensional experimental data obtained by atom probe tomography (APT). This also allows us to compare the simulation results with the one obtained experimentally. Our analysis demonstrates that FEM and APT constitute a good combination to resolve strain-stress problems of epitaxial semiconductor structures.

No MeSH data available.


Related in: MedlinePlus

Strain and SED maps in the growth plane of the upper QD. (a) ϵxx, (b) ϵyy, (c) ϵzz and (d) normalized SED calculated in the surface of the barrier layer. Superimposed to each map, we have included the APT data corresponding to the upper layer of QDs in the form of In concentration isolines, ranging from 25% In (dark blue) to 45% In (red), in steps of 5%. In (d), we have included an inset showing a complete map of the APT data for clarity.
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Figure 3: Strain and SED maps in the growth plane of the upper QD. (a) ϵxx, (b) ϵyy, (c) ϵzz and (d) normalized SED calculated in the surface of the barrier layer. Superimposed to each map, we have included the APT data corresponding to the upper layer of QDs in the form of In concentration isolines, ranging from 25% In (dark blue) to 45% In (red), in steps of 5%. In (d), we have included an inset showing a complete map of the APT data for clarity.

Mentions: Figure 3 shows 2D views of the strain maps calculated in the growth plane, at the surface of the barrier layer: (a) and (b) shows the strain in x and y directions (ϵxx and ϵyy), which are two perpendicular axes contained in the growth plane, (c) shows ϵzz, and (d) shows the normalized SED. In order to compare the predictions calculated by FEM with the experimental results obtained by APT, superimposed to these strain maps, we have included the APT data corresponding to the upper layer of QDs in the form of In concentration isolines, ranging from 25% In (dark blue) to 45% In (red), in steps of 5%. Also, in (d), we have included an inset showing a complete map of the APT data for clarity. As it can be observed in Figure 3a,b,c, there is a relatively wide area of similar strain where the QD would be favoured to grow, and the real QD is actually included in this area according to the APT data. Figure 3d shows the distribution of the normalized SED, which represents a compendium of strain–stress in all directions ij as explained earlier, and which maximum value determines the most favoured localization of the QD[29]. In this map, the area favoured for the growth of the QD has a reduced size, but the actual QD is still included in this area according to the APT experimental data[14,19]. This result shows that FEM using APT experimental data is an accurate tool for the prediction of stacked QD nucleation sites for structures where the strain component has a major effect in the chemical potential during growth. It should be mentioned that the eventual nucleation of the quantum dot is governed by a flux that drives surface adatoms from locations of higher to lower potential and the strain energy density critical value (minimum or maximum depending on the sign convention of SED[30]) is therefore the preferential site for nucleation. A more refined model would include additional parameters that typically affect the growth process, such as the surface energy[31] or kinetic effects[32]. These parameters are essential in the prediction of the nucleation sites of some semiconductor systems. For example, in InAs QWires, it has been reported that the stacking pattern is determined by the combined effect of strain and surface morphology on the growth front of the spacer layers[33]. In the structure considered in the present work, our results have shown that a simplified approximation of the chemical potential considering only the strain component is valid for obtaining accurate results.


Strain analysis for the prediction of the preferential nucleation sites of stacked quantum dots by combination of FEM and APT.

Hernández-Saz J, Herrera M, Duguay S, Molina SI - Nanoscale Res Lett (2013)

Strain and SED maps in the growth plane of the upper QD. (a) ϵxx, (b) ϵyy, (c) ϵzz and (d) normalized SED calculated in the surface of the barrier layer. Superimposed to each map, we have included the APT data corresponding to the upper layer of QDs in the form of In concentration isolines, ranging from 25% In (dark blue) to 45% In (red), in steps of 5%. In (d), we have included an inset showing a complete map of the APT data for clarity.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4234348&req=5

Figure 3: Strain and SED maps in the growth plane of the upper QD. (a) ϵxx, (b) ϵyy, (c) ϵzz and (d) normalized SED calculated in the surface of the barrier layer. Superimposed to each map, we have included the APT data corresponding to the upper layer of QDs in the form of In concentration isolines, ranging from 25% In (dark blue) to 45% In (red), in steps of 5%. In (d), we have included an inset showing a complete map of the APT data for clarity.
Mentions: Figure 3 shows 2D views of the strain maps calculated in the growth plane, at the surface of the barrier layer: (a) and (b) shows the strain in x and y directions (ϵxx and ϵyy), which are two perpendicular axes contained in the growth plane, (c) shows ϵzz, and (d) shows the normalized SED. In order to compare the predictions calculated by FEM with the experimental results obtained by APT, superimposed to these strain maps, we have included the APT data corresponding to the upper layer of QDs in the form of In concentration isolines, ranging from 25% In (dark blue) to 45% In (red), in steps of 5%. Also, in (d), we have included an inset showing a complete map of the APT data for clarity. As it can be observed in Figure 3a,b,c, there is a relatively wide area of similar strain where the QD would be favoured to grow, and the real QD is actually included in this area according to the APT data. Figure 3d shows the distribution of the normalized SED, which represents a compendium of strain–stress in all directions ij as explained earlier, and which maximum value determines the most favoured localization of the QD[29]. In this map, the area favoured for the growth of the QD has a reduced size, but the actual QD is still included in this area according to the APT experimental data[14,19]. This result shows that FEM using APT experimental data is an accurate tool for the prediction of stacked QD nucleation sites for structures where the strain component has a major effect in the chemical potential during growth. It should be mentioned that the eventual nucleation of the quantum dot is governed by a flux that drives surface adatoms from locations of higher to lower potential and the strain energy density critical value (minimum or maximum depending on the sign convention of SED[30]) is therefore the preferential site for nucleation. A more refined model would include additional parameters that typically affect the growth process, such as the surface energy[31] or kinetic effects[32]. These parameters are essential in the prediction of the nucleation sites of some semiconductor systems. For example, in InAs QWires, it has been reported that the stacking pattern is determined by the combined effect of strain and surface morphology on the growth front of the spacer layers[33]. In the structure considered in the present work, our results have shown that a simplified approximation of the chemical potential considering only the strain component is valid for obtaining accurate results.

Bottom Line: It has been used for the prediction of the nucleation sites of stacked quantum dots (QDs), but often using either simulated data of the atom positions or two-dimensional experimental data, in such a way that it is difficult to assess the validity of the predictions.This also allows us to compare the simulation results with the one obtained experimentally.Our analysis demonstrates that FEM and APT constitute a good combination to resolve strain-stress problems of epitaxial semiconductor structures.

View Article: PubMed Central - HTML - PubMed

Affiliation: INNANOMAT Group, Departamento de Ciencia de los Materiales e I,M, y Q,I,, Facultad de Ciencias, Universidad de Cádiz, Campus Río San Pedro, s/n, Puerto Real, Cádiz 11510, Spain. jesus.hernandez@uca.es.

ABSTRACT
The finite elements method (FEM) is a useful tool for the analysis of the strain state of semiconductor heterostructures. It has been used for the prediction of the nucleation sites of stacked quantum dots (QDs), but often using either simulated data of the atom positions or two-dimensional experimental data, in such a way that it is difficult to assess the validity of the predictions. In this work, we assess the validity of the FEM method for the prediction of stacked QD nucleation sites using three-dimensional experimental data obtained by atom probe tomography (APT). This also allows us to compare the simulation results with the one obtained experimentally. Our analysis demonstrates that FEM and APT constitute a good combination to resolve strain-stress problems of epitaxial semiconductor structures.

No MeSH data available.


Related in: MedlinePlus