On the Potential of Silicon Intermediate Band Solar Cells

Round 1

Reviewer 1 Report

This paper reports an interesting physical model study on the efficiency of Si intermediate band (IB) solar cell. However, before its publication, the following questions need to be addressed.

1)The details about how the results of figures 3 & 4 are derived should be given. 

2) Since sub-bandgap photons can be untilized in the case of IB solar cell, the additional photo-current contributed by the sub-bandgap absorption should increase the efficiency. But this is not the case as shown by figure 3. The result needs to be explained.     

3) The huge increase in efficiency at 100 suns and more as shown in figure 4 needs a more comprehensive explanation. Is it only due to the increase in photon flux? or other factors also take effect?

4) Experimental studies on IB solar cell have made no sigificant advances since the report of Luque in 1997. One of the main difficulties is the low absorption of VI and IC. How the authors set the values of these absorptivities when calculating equation 1.  

5) IB in silicon is introduced by impurities. However, impurities are known as bulk recombination centers, and would cause photovoltaic loss. How will the authors treat this problem in their model?

6) In line 42, "whether" or "where"? In line 103 "Where" or "where"? In line 86, "being alpha xy" or "alpha xy being"?

Author Response

Please find our response to your comments, point-by-point, marked in green color below (they can also be found in the attachment):

 

This paper reports an interesting physical model study on the efficiency of Si intermediate band (IB) solar cell. However, before its publication, the following questions need to be addressed.

1)The details about how the results of figures 3 & 4 are derived should be given. 

Thank you for pointing out that those details are missing. They are now emphasized in lines (152-162).

2) Since sub-bandgap photons can be untilized in the case of IB solar cell, the additional photo-current contributed by the sub-bandgap absorption should increase the efficiency. But this is not the case as shown by figure 3. The result needs to be explained.     

This is now explained in lines (251-254) and illustrated in a new figure (Figure 5) to facilitate the explanation.

3) The huge increase in efficiency at 100 suns and more as shown in figure 4 needs a more comprehensive explanation. Is it only due to the increase in photon flux? or other factors also take effect?

Indeed, the increase in efficiency under concentration (100 and 46050 suns) is mainly due to an increase in voltage, which approaches the voltage of a conventional cell without IB. This is now explained in lines (254-258) and illustrated in a new figure (Figure 5) to facilitate the explanation.

4) Experimental studies on IB solar cell have made no sigificant advances since the report of Luque in 1997. One of the main difficulties is the low absorption of VI and IC. How the authors set the values of these absorptivities when calculating equation 1.  

We completely agree regarding that one of the main challenges of practical IBSCs is the low absorption of transitions involving the IB. This has been found, especially, in IBSC based on quantum dots. However, IBSC based on inserting a high concentration of impurity, as the ones considered in this work, can lead to a volumetric absorption coefficients higher than the volumetric absorption coefficients resulting from the QD approach because of impurity densities can be rather higher than QD densities. Indeed in "Intermediate Band to Conduction Band Optical Absorption in ZnTeO" published by E.Antolín et al in IEEE Journal of Photovoltaics (2014) was found that semiconductor layers of ZnTe with a high concentration of oxigen impurities provide a absorption coefficient up to 700 cm-1 associated to sub-bandgap transitions. Higher sub-bandgap absorption coefficients of 2E4 cm-1 are reported in " Demonstration of ZnTe 1- x O x Intermediate Band Solar Cell ", published by T. Tooru et al in Japanese Journal of Applied Physics (2011). Those references are not included because they correspond to different materials to the one studied in this work.

In this work we use detail balance to derive the limiting efficiency of silicon-IBSCs (this is emphasized in line 97). This model assumes absorptivity equal to 1 (regardless if in real devices this would be consequence of a high absorption coefficients or a thick absorber layers), which means that all the incoming photons are absorbed (Fabs). In this work, because the absorption coefficients can overlap, Fabs is multiplied by factors Me and Mh (derived from reference [21]), which can be considered as equivalent absorptivities for electrons and holes. As it is derived from equation (4) and (5), those factors depends on the degree of the absorption coefficient overlap in a given energy range, taking values between 0 and 1.

5) IB in silicon is introduced by impurities. However, impurities are known as bulk recombination centers, and would cause photovoltaic loss. How will the authors treat this problem in their model?

We assume that the impurity-host interaction can result in the emergence of deep-levels (DLs) with a delocalized wave function if the concentration of these impurities is high enough. This is known as Mott transition (lines55-56). Under these circumstances the non-radiative recombination introduced by the DLs can be reduced (references [16] and [18]), so radiative recombination can dominate the transitions involving the DLs that form the IB. In the model we assume two cases: radiative limit (line 137) and presence of Auger recombination (line 143)

6) In line 42, "whether" or "where"? In line 103 "Where" or "where"? In line 86, "being alpha xy" or "alpha xy being"?

Thank you for the corrections. They are now included in the revised version of the manuscript.

Author Response File: Author Response.docx

Reviewer 2 Report

In the manuscript under review, Lopez et al investigate the limiting efficiency of IBSCs with silicon as bulk material. They specifically investigate the difference between non-overlapping and overlapping absorption coefficients. They find that an IBSC in Silicon can work better with overlapping than non-overlapping absorption coefficients. They claim this as the main novelty that has “never been pointed out before”. This statement is false. In the paper “Increasing efficiency in intermediate band solar cells with overlapping absorptions” published in 2016 in the Journal of Optics, Volume 18, Krishna and Krich looked at the influence of overlapping absorption coefficients in IBSCs and investigated a whole range of band gap combinations (see Figure 5 therein), including the band gap for Silicon and found the same result. This leaves the inclusion of Auger recombination as the only novelty in the present manuscript.

 

Lopez et al. also claim that Silicon cannot be improved by the inclusion of an IBSC at 1 Sun. This is a result of the overly restrictive condition for the absorption edges. Symmetry-forbidden transitions allow the possibility to have absorption edges whose value adds up to more than the band gap (the case of “maximally overlapping absorption coefficients“ discussed in the work by Krishna and Krich, equivalent to the photon ratchet put forward by Yoshida et al in “Photon ratchet intermediate band solar cells” published in 2012 in Applied Physics Letters, Volume 100, pages 263902). As pointed out by Pusch and Ekins-Daukes in “Voltage matching, etendue and ratchets in advanced concept solar cells” (published in 2019  in Physical Review Applied, Volume 12, page 044055) this allows for a matching of voltages between the bulk and IBSC transitions, which enables efficiency gains even for non-ideal situations like Silicon at 1 Sun. Macdonald et al. proposed an approach for such a Silicon based device in “Electronically-coupled up-conversion: An alternative approach to impurity photovoltaics in crystalline silicon”, published in 2007 in Semiconductor Science and Technology, Volume 23, pages 015001.

 

Additionally, the statement that voltage preservation occurs for the ideal IBSC mention explicitly that this is only true at high concentration. As explained in the afore mentioned paper by Pusch and Ekins-Daukes, voltage preservation at low concentration is not possible if the IB absorption edges add up to the band gap energy. Also, The efficacy of the Mott transition at slowing non-radiative recombination seems to have been disproven by Krich et al in “Nonradiative lifetimes in intermediate band photovoltaics—Absence of lifetime recovery” published in 2012 in the Journal of Applied Physics, Volume 112, pages 013707. The authors should acknowledge this work and if they insist that lifetime recovery does - nonetheless - occur, they should provide reasons for their belief.

 

Because the work presented in this manuscript has not been put into the proper context with the recent literature and the main claim of novelty is false, I cannot recommend publication of this manuscript in its present form.

The authors should put the work into proper context and rescind the claim of novelty for the overlapping absorption result. The inclusion of Auger recombination combined with a proper discussion of the additional points raised above would still lead to sufficient novelty in this manuscript to warrant publication.

 

Author Response

Please find our response to your comments, point-by-point, marked in green color below (they can also be found in the attachment):

 

In the manuscript under review, Lopez et al investigate the limiting efficiency of IBSCs with silicon as bulk material. They specifically investigate the difference between non-overlapping and overlapping absorption coefficients. They find that an IBSC in Silicon can work better with overlapping than non-overlapping absorption coefficients. They claim this as the main novelty that has “never been pointed out before”. This statement is false. In the paper “Increasing efficiency in intermediate band solar cells with overlapping absorptions” published in 2016 in the Journal of Optics, Volume 18, Krishna and Krich looked at the influence of overlapping absorption coefficients in IBSCs and investigated a whole range of band gap combinations (see Figure 5 therein), including the band gap for Silicon and found the same result. This leaves the inclusion of Auger recombination as the only novelty in the present manuscript.

Thanks for the update, we agree with your comments. However, we want to inform you of an unfortunate paradox. As we expressed in our disclaimer, part of the content of our work was submitted to the 2014 IEEE 40th Photovoltaics Specialist Conference under the title “Limiting Efficiency of silicon intermediate band solar cells”. This is actually the work cited in “Increasing efficiency in intermediate band solar cells with overlapping absorptions” as Ref [15]. The problem is that the interested readers will not be able to find this work because, due to technical problems, beyond our responsibility, that we do not understand and that we have tried to solve for more than 2 years, the paper is not accessible. What we claimed about the novelty of this study was true when the work was done but this is not true anymore since, as you mentioned, there is a paper from Krishna and Krich where the influence of overlapping absorption coefficients in IBSCs is already investigated (this work is properly referenced in the manuscript by Krishna and Krich). For this reason we have rescinded that claim of novelty. However, we consider that Auger recombination is not the only novelty of the manuscript, since the results obtained are not really the same than the ones reported previously (emphasized in lines 203-206). We think that reporting these different results and discussing why they differ from Krishna and Krich's paper is worth. So now, thanks to the opportunity given by Energies in their special issue we see the opportunity of letting the readers to find in the literature the work presented in “Limiting Efficiency of silicon intermediate band solar cells”, updated with a deeper analysis about the influence of Auger recombination as well as the results obtained with restrictive condition for the absorption edges (not graphically illustrated in Krishna and Krich paper, probably because it was already credited to [15]). We do not want to confuse to much the readers with this situation, which is probably not to much of their interest, but we also would like that readers looking now, for example for Ref [15] in Krishna and Krich paper can find it and follow the arguments. We think this necessity, as well as the requirements by the reviewer, can be now clarified by a few paragraphs added to the previous disclaimer, and in this respect we have written

“The results presented in this paper in sections 3.1 and 3.2 were presented at the the 2014 IEEE 40th Photovoltaics Specialist Conference under the title “Limiting Efficiency of silicon intermediate band solar cells”. However, due to technical problems beyond the responsibility of the authors, they are not accessible and have included for completitude. The study about the impact of overlapping absorption coefficients in intermediate band solar cells working in the radiative limit is notably expanded by Krishna and Krich in “Increasing efficiency in intermediate band solar cells with overlapping absorptions” published in 2016 in the Journal of Optics, Volume 18, where many other materials than silicon are studied".  

Lopez et al. also claim that Silicon cannot be improved by the inclusion of an IBSC at 1 Sun. This is a result of the overly restrictive condition for the absorption edges. Symmetry-forbidden transitions allow the possibility to have absorption edges whose value adds up to more than the band gap (the case of “maximally overlapping absorption coefficients“ discussed in the work by Krishna and Krich, equivalent to the photon ratchet put forward by Yoshida et al in “Photon ratchet intermediate band solar cells” published in 2012 in Applied Physics Letters, Volume 100, pages 263902). As pointed out by Pusch and Ekins-Daukes in “Voltage matching, etendue and ratchets in advanced concept solar cells” (published in 2019  in Physical Review Applied, Volume 12, page 044055) this allows for a matching of voltages between the bulk and IBSC transitions, which enables efficiency gains even for non-ideal situations like Silicon at 1 Sun. Macdonald et al. proposed an approach for such a Silicon based device in “Electronically-coupled up-conversion: An alternative approach to impurity photovoltaics in crystalline silicon”, published in 2007 in Semiconductor Science and Technology, Volume 23, pages 015001.

You are also right pointing out that we cannot claim that including an IB in silicon cells does not enable an efficiency gain at 1 sun, since under the specific conditions that you mention (absorption edges whose value adds up to more than the band gap or energy band diagrams including a ratchet step) an efficiency gain is possible. Those possibilities are now mentioned in the manuscript in lines (182-184). We have made now clear, following the context of the discussion to the previous point, that the efficiency increase is not possible under the traditional IBSC formulation by which the absorption edges add up to the value of the gap.

Additionally, the statement that voltage preservation occurs for the ideal IBSC mention explicitly that this is only true at high concentration. As explained in the afore mentioned paper by Pusch and Ekins-Daukes, voltage preservation at low concentration is not possible if the IB absorption edges add up to the band gap energy. Also, The efficacy of the Mott transition at slowing non-radiative recombination seems to have been disproven by Krich et al in “Nonradiative lifetimes in intermediate band photovoltaics—Absence of lifetime recovery” published in 2012 in the Journal of Applied Physics, Volume 112, pages 013707. The authors should acknowledge this work and if they insist that lifetime recovery does - nonetheless - occur, they should provide reasons for their belief.

We agree than in order to put this work in a proper context we should reference the paper “Nonradiative lifetimes in intermediate band photovoltaics—Absence of lifetime recovery” published by Krich et al. in 2012, where the slowing of non-radiative recombinantion is questioned (this reference is now included as [8] in line 59). However, we cannot conclude that slowing non-radiative recombination is impossible, since other theoretical works based on ab initio methods (more sophisticated than the Born-Oppenheimer approximation with classical treatment for the motion of the lattice used by Krich et al.) have reported that it is possible. Those theoretical works (included now in the manuscript) are:

- C. Tablero, “Effects of the impurity–host interactions on the nonradiative processes in ZnS:Cr,” Journal of Applied Physics, vol. 108, no. 9, p. 093114, Nov. 2010, doi: 10.1063/1.3506705.

- C. Tablero, “Effects of the impurity–impurity and impurity–host interactions on the charge density and the related processes,” Physica B: Condensed Matter, vol. 404, no. 21, pp. 4023–4028, Nov. 2009, doi: 10.1016/j.physb.2009.07.148.

In addition, there are experimental works (references [16] and [18]) where a lifetime recovery is obtained by increasing impurity concentration in silicon.

Because the work presented in this manuscript has not been put into the proper context with the recent literature and the main claim of novelty is false, I cannot recommend publication of this manuscript in its present form.

The authors should put the work into proper context and rescind the claim of novelty for the overlapping absorption result. The inclusion of Auger recombination combined with a proper discussion of the additional points raised above would still lead to sufficient novelty in this manuscript to warrant publication.

We would like to thank you for pointing us all the aspects raised above to put the work in a proper context with the recent literature and we hope you find the revised version improved with the additional discussion.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

publish as it is now

Reviewer 2 Report

The changes made and the reasons given for the previous claims of novelty are satisfactory. I am happy to recommend publication of the manuscript.