Modeling Electronic and Optical Properties of InAs/InP Quantum Dots

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors present a detailed review of electronic and optical properties of InAs/InP QDs. The topic is relevant because InAs/InP QDs can emit in the important telecom C-band, but their properties have not been fully understood in terms of the effect of GaAs/GaP sublayers, polarization of QDs and especially two-state lasing. Similar reviews have not been found in the databases of scientific papers. The review is aimed to realistic objects - QDs which would be formed after a double-capping procedure - and has numerous practical applications, including two-state lasing. It is noteworthy that the authors' model takes into account non-uniform strain distribution in the QD system and resonant electronic coupling. However, I have several comments and questions concerning the paper:

 

1. Considering that this is a review, it may be possible that there is repetition of data previously published in other articles. However, for example, Figure 4b in the presented review is exactly the same as Figure 4 in the paper with DOI: 10.1063/1.5082722, and there are several overlaps between Figures with the paper with DOI: 10.1063/1.5132965. The need to exclude borrowing of already published figures is left to the discretion of the authors and editors.

 

2. Specific models for certain subsections of the review are not described in detail, but the authors give references. The need for more detailed descriptions of models within subsections is also left to the discretion of the authors and editors.

 

3. For equations (1)-(17) (especially 6-17), no references are given. For some equations, it can be understood from the text where they came from, but even in this case it's worth putting the references in addition, especially since this is a review.

 

4. Lines 173-174: "...due to the mixing and exchange of As/P flux". If QDs are covered by the InGaAsP layer, why is In/Ga mixing not considered as well? Ga atoms may easily incorporate into QDs because of their smaller size than that of In atoms and impact electronic and optical properties of QDs. The authors should clarify this aspect in the manuscript.

 

5. Lines 174-175: "Once the system stabilizes...". How was the stabilization time estimated? 

 

6. The authors should mention in the manuscript what the dagger mark † in Eqs. 11 and 14 denotes.

 

7. Table 1 contains complicated expressions of material parameters dependent on the composition of the capping layer. However, the derivation of these expressions is not obvious. How were they obtained?

 

8. In the caption to Table 1, RT/LT abbreviations should be disclosed due to their first mention in the text. The same applies to STM abbreviation on line 314, ML in Figure 6 and line 480. Re-introduction of abbreviations ("quantum dot (QD)" in line 330, "longitudinal optical (LO)" on line 504, 509, 514 etc.) is not necessary.

 

9. The authors should mention in Section 2.1.2 which version of COMSOL was used for the calculations.

 

10. Lines 263-264: "The 3D models were built based on the fabricated QDs in those reported experimental works [8,22,74–76]." There are no TEM or X-STM images in the mentioned papers to judge about the 3D shape of QDs. Are there any confirmations that QDs have exactly the shape of a truncated pyramid and not lens, for instance. Line 333: "For this simulation, QD parameters are based on measurements reported in Refs. [8,63]". However, the experimental shape of capped QDs cannot be understood from these papers too.

 

11. What is the density of experimental QDs for which the modeling is carried out? For a plausible estimate that takes into account many details, the area of the modeled region in the lateral slice should be equal to the area per one QD. It appears that this area in the model is smaller than in the experiments. Can the authors estimate how much this difference affects the modeling result? Have you evaluated the difference in results for different lateral modeling areas?

 

12. If I understand correctly, the left and right graphics of Figure 4a should be swapped on lines 302-303 because the spacer is thicker on the left graphic.

 

13. Lines 345-346: "These deviations broaden with increasing average dot height or barrier material thicnkess". Where are the deviations with increasing dot height shown?

 

14. Lines 347-348: "... suggesting average dot base diameters of approximately 30 and 40 nm". Please explain where this conclusion follows from.

 

15. Line 457: "GaAs has a smaller lattice mismatch to InAs QD material." Actually, GaAs has a larger lattice mismatch with InAs, doesn't it?

 

16. For Figures 10 and 12, a comparison with the experimental PL spectra is recommended.

 

17. Line 660: Which experiments were used to set a standard deviation of 30 meV?

 

18. A 3-layer QD stack has been analyzed to study polarization of QDs. Why exactly 3 layers and was a different number of QD layers studied?

 

19. The text should be proofread for typos and language aspects. For example, "messured", "band structure of (a? the?) QD", "properties of (a?) QD-based laser", "oscillate strength" ("oscillator"), "Hamilton" ("Hamiltonian"?), "more nearest" ("nearer"?), "strian", double "and" in Line 262, "many attentions" ("much attention"?), "did not observed" ("was not observed"), etc. Furthermore, I'd say that it is better to use "optical" throughout the text instead of "optic".

 

20. Check the references list for formatting, in particular, 18 and 72.

Comments on the Quality of English Language

The text should be proofread for typos and language aspects. For example, "messured", "band structure of (a? the?) QD", "properties of (a?) QD-based laser", "oscillate strength" ("oscillator"), "Hamilton" ("Hamiltonian"?), "more nearest" ("nearer"?), "strian", double "and" in Line 262, "many attentions" ("much attention"?), "did not observed" ("was not observed"), etc. Furthermore, I'd say that it is better to use "optical" throughout the text instead of "optic".

Author Response

Response to reviewers

Reviewer 1

1. Considering that this is a review, it may be possible that there is repetition of data previously published in other articles. However, for example, Figure 4b in the presented review is exactly the same as Figure 4 in the paper with DOI: 10.1063/1.5082722, and there are several overlaps between Figures with the paper with DOI: 10.1063/1.5132965. The need to exclude borrowing of already published figures is left to the discretion of the authors and editors.

Response:

Thank you for your observation. The figures used in this review paper are intended to better present the works from our group. To avoid any potential copyright issues, we have obtained all the necessary copyright permissions from the respective publishers.

2. Specific models for certain subsections of the review are not described in detail, but the authors give references. The need for more detailed descriptions of models within subsections is also left to the discretion of the authors and editors.

Response:

Thank you for your suggestion. Since most of the works presented in this review paper are theoretical research, a clear description of the theoretical calculation models is crucial. The main contribution from our group is combining multi-step strain analysis with the 8-band k·p model, which enhances the calculation precision. Therefore, we have detailed this method in Section 2, “Theoretical Models and Methods.” For parts that are similar to conventional models, we have provided references. We believe this approach helps to highlight our original contribution. Otherwise, the manuscript would be too long and also including the previous model descriptions are degradable to readability.

3. For equations (1)-(17) (especially 6-17), no references are given. For some equations, it can be understood from the text where they came from, but even in this case it's worth putting the references in addition, especially since this is a review.

Response:

Thank you for your suggestion. We have added a declaration before introducing equations (1)-(17) in the manuscript, providing the necessary references. This will help readers easily find the sources for more detailed information.

4. Lines 173-174: "...due to the mixing and exchange of As/P flux". If QDs are covered by the InGaAsP layer, why is In/Ga mixing not considered as well? Ga atoms may easily incorporate into QDs because of their smaller size than that of In atoms and impact electronic and optical properties of QDs. The authors should clarify this aspect in the manuscript.

Response:

This is a very good question. The diffusion of components during the epitaxial growth process does indeed impact the optical properties of quantum dots, and both experimental and theoretical studies on this issue have been published. We specifically mention “the mixing and exchange of As/P flux” as it is considered the primary reason for the height reduction of QDs self-assembled by double capping procedures. In our calculation model, component diffusion is not considered; the QD is assumed to be pure InAs, and the components in the InGaAsP capping layer are assumed to remain unchanged. Only the height reduction and corresponding strain changes are considered in our model. We have added a detailed description to clarify this aspect in the manuscript.

5. Lines 174-175: "Once the system stabilizes...". How was the stabilization time estimated?

Response:

Thank you for raising this question. "The system stabilizes" refers to the termination of the pause periods in the double capping procedures. In these procedures, a very thin first capping layer is grown, followed by a short growth interruption. During this pause, diffusion of components, height reduction, and strain relaxation occur. Once the pause ends, the material system is considered stable. Therefore, the stabilization time corresponds to the growth interruption time, which is around 30 seconds.

6. The authors should mention in the manuscript what the dagger mark † in Eqs. 11 and 14 denotes.

Response:

Thank you for raising this question. The dagger mark (†) in Eqs. 11 and 14 denotes conjugation. We have added an explanation in the manuscript to clarify this.

7. Table 1 contains complicated expressions of material parameters dependent on the composition of the capping layer. However, the derivation of these expressions is not obvious. How were they obtained?

Response:

Thank you for raising this question. We have added the references from which we obtained the material parameters in Table 1.

8. In the caption to Table 1, RT/LT abbreviations should be disclosed due to their first mention in the text. The same applies to STM abbreviation on line 314, ML in Figure 6 and line 480. Re-introduction of abbreviations ("quantum dot (QD)" in line 330, "longitudinal optical (LO)" on line 504, 509, 514 etc.) is not necessary.

Response:

Thank you for raising this issue. We have corrected the incorrect acronyms and provided explanations for abbreviations upon their first mention in the manuscript. Additionally, we have removed unnecessary re-introductions of abbreviations.

9. The authors should mention in Section 2.1.2 which version of COMSOL was used for the calculations.

Response:

Thank you for raising this issue. The versions of COMSOL used in our calculations are COMSOL 5.4 and COMSOL 5.6. We have added this information in Section 2.1.2 of the manuscript.

10. Lines 263-264: "The 3D models were built based on the fabricated QDs in those reported experimental works [8,22,74–76]." There are no TEM or X-STM images in the mentioned papers to judge about the 3D shape of QDs. Are there any confirmations that QDs have exactly the shape of a truncated pyramid and not lens, for instance. Line 333: "For this simulation, QD parameters are based on measurements reported in Refs. [8,63]". However, the experimental shape of capped QDs cannot be understood from these papers too.

Response:

Fig1. The X-STM images of self-assembly QDs[1]

Thank you for raising this question. We constructed the 3D models based on the observations from the experimental work cited in Ref. [1] (DOI 10.1088/0957-4484/15/12/001), which includes X-STM images showing the shapes of the self-assembled QDs. We intended to include these images for a more intuitive comparison but were unable to obtain copyright authorization. We have now added this reference to our manuscript to clarify the basis for the QD geometries used in our simulations.

11. What is the density of experimental QDs for which the modeling is carried out? For a plausible estimate that takes into account many details, the area of the modeled region in the lateral slice should be equal to the area per one QD. It appears that this area in the model is smaller than in the experiments. Can the authors estimate how much this difference affects the modeling result? Have you evaluated the difference in results for different lateral modeling areas?

Response:

For the typical InAs/InGaAsP QD, the surface density is 3×10¹⁰ ~ 5×10¹⁰ cm^-2. The geometry settings in our calculation are changed based on the experimental observations. In the most case, we assume the surface density is 4×10¹⁰ cm^-2, corresponding to the outer length of the 50 nm and the QD base length of the 30 nm. The surface density affects the in plane coupling strength, which has been observed by some experiment works. Also, our group published theoretical investigation on this issue.[2]

12. If I understand correctly, the left and right graphics of Figure 4a should be swapped on lines 302-303 because the spacer is thicker on the left graphic.

Response:

Thank you for pointing out this error. We have corrected them in manuscript.

13. Lines 345-346: "These deviations broaden with increasing average dot height or barrier material thickness". Where are the deviations with increasing dot height shown?

Response:

Thank you for raising this question. In the sentence, "deviations broaden with increasing average dot height or barrier material thickness," the term "barrier thickness" refers to the thickness of the first capping layer (FCL) in the double capping procedure. During the growth interruption, the QD height reduces due to component diffusion, and the average dot height approaches the FCL thickness. Therefore, in this context, the average dot height and barrier material thickness (FCL thickness) represent the same parameter. We realize that this expression may have caused confusion, so we have revised it in the manuscript for clarity.

14. Lines 347-348: "... suggesting average dot base diameters of approximately 30 and 40 nm". Please explain where this conclusion follows from.

Response:

Thank you for your question. The full sentence in question is: "Obviously, the measured data align closely with the lower and upper margins of the tunable range in Figures 5(a) and 5(b), respectively, suggesting average dot base diameters of approximately 30 and 40 nm, consistent with descriptions in Refs." This sentence aims to convey that the geometry settings in our calculation model correspond to the experimental observations of dot base diameters of approximately 30 and 40 nm. Additionally, the optical properties calculated using this model are consistent with experimental results, demonstrating the model's accuracy. We recognize that the original expression may have been unclear, so we have revised the sentence in the manuscript to clarify this point.

15. Line 457: "GaAs has a smaller lattice mismatch to InAs QD material." Actually, GaAs has a larger lattice mismatch with InAs, doesn't it?

Response:

Thank you for pointing out this error. The full sentence is: "We compare the QDs with GaAs and GaP sublayers, and GaAs has a smaller lattice mismatch to InAs QD material." To clarify, we intended to convey that GaAs has a smaller lattice mismatch to InAs compared to GaP. We have corrected this in the manuscript to accurately reflect the lattice mismatch between the materials.

16. For Figures 10 and 12, a comparison with the experimental PL spectra is recommended.

Response:

Thank you for your suggestion. The PL spectra presented in Figure 10 are based on our calculations for the proposed five-layer chirped QD structures, and unfortunately, there are no experimental results available for comparison. For Figure 12, our calculated PL spectra are consistent with experimental observations (Ref. [3], DOI 10.1143/JJAP.45.6544). However, we were unable to obtain copyright authorization to include these experimental figures in the manuscript. We have provided a reference to this work in the manuscript to support our results.

17. Line 660: Which experiments were used to set a standard deviation of 30 meV?

Response:

The standard deviation of 30 meV in our model is a fitting parameter used to match the experimental results from Ref. [3] (DOI 10.1143/JJAP.45.6544). This value was chosen as it best fits the experimental data, representing the inhomogeneous broadening effect of the quantum dots.

18. A 3-layer QD stack has been analyzed to study polarization of QDs. Why exactly 3 layers and was a different number of QD layers studied?

Response:

The choice of a 3-layer QD stack was based on the experimental setup described in Ref. [3] (DOI 10.1143/JJAP.45.6544), where a 3-layer QD sample was fabricated and measured. We selected this configuration to directly align our study with the experimental conditions.

19. The text should be proofread for typos and language aspects. For example, "messured", "band structure of (a? the?) QD", "properties of (a?) QD-based laser", "oscillate strength" ("oscillator"), "Hamilton" ("Hamiltonian"?), "more nearest" ("nearer"?), "strian", double "and" in Line 262, "many attentions" ("much attention"?), "did not observed" ("was not observed"), etc. Furthermore, I'd say that it is better to use "optical" throughout the text instead of "optic".

20. Response:

    Thank you for pointing out these errors. We have carefully proofread the manuscript and corrected the typos and language issues, including those you mentioned.

    20. Check the references list for formatting, in particular, 18 and 72.

    Response:

    Thank you for pointing out these formatting issues. We have corrected the formatting problems in the references list, including references 18 and 72.

The figures cannot be copied and pasted. Please see the attachment. 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This paper presents a detailed study on the electronic and optical properties of InAs/InP QDs using an two-step strain-based approach and showed that it can achieve better accuracy compared to conventional method. It also discussed the carrier dynamics of QDs and studied the effect of different parameters that can be changed in fabrication on the optical properties of the QDs. In general, this paper provided a well-rounded analysis of the dynamics of QDs and is well written, with adequate references. There is some minor grammar usages and errors that needs to be addressed as follows:

 

1.      Some grammar errors:

a.      Line 32: “many attentions” should be “much attention”

b.     Line 575: I am not sure why the author put a “Since,” here in the sentence, it should connect a dependent clause, but there is no such. The author should modify this sentence to make it make sense.

2.      Line 78-80, this sentence needs proper paper reference to support.

3.      Line 142, the author should clarify strain impacts on confinement of “what”.

4.      Line 185, “PZT” is a piezoelectric material, stands for lead zicronite titante. It does not equal to or replace the concept of “piezoelectric effect” in the context. The author should remove ALL “PZT” and replace it with piezoelectricity or equivalent concepts.

 

5.      For table 1, where are all these material parameters from? The author should give proper references if they are from other sources.

Comments on the Quality of English Language

minor grammar errors, see above

Author Response

1. Some grammar errors:
2. Line 32: “many attentions” should be “much attention”
3. Line 575: I am not sure why the author put a “Since,” here in the sentence, it should connect a dependent clause, but there is no such. The author should modify this sentence to make it make sense.

Response:

Thank you for pointing out these errors. We have corrected “many attentions” to “much attention” and revised the sentence on line 575 to ensure it makes sense and properly conveys the intended meaning.

2. Line 78-80, this sentence needs proper paper reference to support.

Response:

Thank you for your suggestion. We have added the appropriate references to support the sentence on lines 78-80.

3. Line 142, the author should clarify strain impacts on confinement of “what”.

Response:

Thank you for your suggestion. We intended to express that strain impacts the electrical confinement. We have revised this section to clarify this point and make the context clearer.

4. Line 185, “PZT” is a piezoelectric material, stands for lead zicronite titante. It does not equal to or replace the concept of “piezoelectric effect” in the context. The author should remove ALL “PZT” and replace it with piezoelectricity or equivalent concepts.

Response:

Thank you for pointing out this issue. We have replaced all instances of "PZT" with "piezoelectricity" or equivalent concepts in the manuscript to accurately reflect the intended meaning.

5. For table 1, where are all these material parameters from? The author should give proper references if they are from other sources.

Response:

Thank you for your suggestion. We have added the appropriate references to Table 1 to indicate the sources of the material parameters.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have thoroughly revised the manuscript so that it is now better grounded and more readable. All comments have been addressed properly. I believe the paper can now be accepted in present form.