Quantum Calculations for Nanostructured Solar Cells

Quantum dots (QDs) and quantum wells (QWs) in semiconductors have a typical size in the range of 2-20 nm to be compared to the 0.5-0.6 nm of the atomic unit cells. Attempts of applying ab initio calculation, which is deemed the most accurate, usually requires calculation cells including 10000 atoms or more, which is in the limit of what is feasible even with big computers.   

The mesoscopic nature of the nanostructures allows applying the integral factorization rule that states that any 3D-integral comprising the product of a periodic function times a function that varies slowly with respect to the period can be separated into two factors: the integral of the periodic function over the unit cell, times the integral of the slowly varying function.

In the k·p methods the one-electron Hamiltonian of the nanostructured system is developed in an orthonormal basis formed by the Bloch functions —which are the solutions of a non-structured semiconductor— calculated at the semiconductor G-point (k=0) for a certain band, multiplied by a plane wave of arbitrary wavevector k [1]. The basis considered in this work comprises the conduction band (cb) and three valence bands —the light holes (lh), the heavy holes (hh) and the spin-orbit (so) band— all spin double-degenerated. This leads to a matrix Hamiltonian of dimension four whose terms are function of k. In zincblende materials —such as those used in high efficiency cells (GaAs, GaP, InAs, and alloys, among many others) — this matrix is quite easy. However, in this easy form it does not include the spin-orbit interaction or the strain effects due to the inclusion of the nanostructure.  We call it the (H0) matrix. We have proposed [2, 3] a Hamiltonian whose eigenvalues are the parabolic dispersion functions characterized by the experimental band edges and effective masses. The use of these experimental dispersion functions, obviously, takes into accounts the spin-orbit interaction, the strain effects, and any other forgotten effect should have been taken into consideration. This is why we call it the empiric k·p Hamiltonian (EKPH) and its matrix (HEKP).  The non diagonalized form of this Hamiltonian may be approximately calculated by using the diagonalization matrix for the initial Hamiltonian, without spin-orbit interaction or strain. This matrix is formed with the eigenvectors of (H0). In summary the model based on the EKPH assumes as eigenvalues the empiric ones but as eigenvectors those of (H0).

The introduction of the nanostructures produces offsets in the band edges. We assume them to be square. This is not real but is an acceptable approximation. The shape of the QDs is debatable but we consider it a squat parallelepiped. These two approximations, together with the analytic diagonalization matrix used, lead to a very strong simplification of the calculations (around 106 times faster than the established and more accurate Luttinger-Kahn-Pikus-Bir (LKPB) calculations), and thus to a deep, we think unprecedented, progress in the modeling and interpretation of the solar cells comprising nanostructures. It also leads to a simple labeling of the wavefunctions appearing in the solar cell.

In particular, in the case of QDs, the full spectrum in all the four bands —including bound and extended states— can be calculated. The EKPH model helps interpreting the origin of the peaks found in the solar cell measured quantum efficiency and the calculated spectrum allows to determine the QD size, that coincides with the one observed by TEM.

It also allows determining the eigenfunctions, which are linear combinations of the products of the G-Bloch functions in all the four bands, multiplied by functions that vary in the range of the nanostructure dimensions, called envelope functions. This is necessary to calculate the absorption coefficients in QD intermediate band solar cells and in the QW-tuned bandgap solar cells. They both are in semi-quantitative agreement with the observed quantum efficiency.  This method may also be applied to non-structured semiconductors, such as GaAs, leading also to a semi quantitative agreement with the measured absorption coefficient. In all the cases the calculations do not require a full knowledge of the G-Bloch functions but only of the envelope functions and of some symmetry properties of the G-Bloch functions. Thus the absorption coefficients depend mainly on the nanostructure characteristics, although they keep relation with the semiconductor material through its symmetry properties and the effective masses imposed by it to the different bands.

The approximate knowledge of the absorption coefficient for each one of the transitions involved, confirmed also by the quantitative interpretation of the experimental variation of the sub-bandgap quantum efficiency with the temperature [4],  allows for a realistic detailed balance treatment and therefore it allows predicting the behavior of nanostructured solar cells in its radiative limit, that, we remind, is almost achieved in the high efficiency multijunction cells of today, and so allows orienting the technological research.

The purpose of the work in this Mega-Grant consists on comparing the calculation with more available experimental data experiments in order to further support the appropriateness of the EPKH, and some additional results have already been achieved within the Mega-Grant: for instance its use has permitted a rather correct calculation of the band to band absorption in GaAs, as compared to classical experimental data (work submitted to publication). It has been used to predict the size of the QDs form sub-bandgap quantum efficiency measurements in InAs/GaS and InAs/GaAlAs QD/host materials (work submitted to publication). It has also been used to suggest the interest of using Type II QDs in the VB in order to prevent a reduction of the voltage (work already published [5]) so giving birth to a new experimental research on Type II QDs under way in this Mega-Grant. Additional work is under way in refining the EKPH method and substantial work is also under way in the comparison of the EKPH method with the more widely used LKPB method in order to compare their respective stresses and wqaeaknesses.  




[1]           S. Datta, Quantum Phenomena (Addison Wesley, Reading (Mass), 1989).

[2]           A. Luque et al., Solar Energy Materials & Solar Cells 95, 2095 (2011).

[3]           A. Luque et al., Solar Energy Materials and Solar Cells 103, 171 (2012).

[4]           A. Mellor et al., Advanced Functional Materials 24, 339 (2014).

[5]           A. Luque et al., Applied Physics Letters 103, 123901 (2013).

The background work of this group is described by the abstracts of papers published in relation to the subject of the Mega-Grant

Luque, A., Martí, A.: Increasing the efficiency of ideal solar cells by photon induced transitions at intermediate levels. Physical Review Letters 78(26), 5014–5017 (1997).


Recent attempts have been made to increase the efficiency of solar cells by introducing an impurity level in the semiconductor band gap. We present an analysis of such a structure under ideal conditions. We prove that its efficiency can exceed not only the Shockley and Queisser efficiency for ideal solar cells but also that for ideal two-terminal tandem cells which use two semiconductors, as well as that predicted for ideal cells with quantum efficiency above one but less than two. © 1997 The American Physical Society


Luque, A., Martí, A.: A metallic intermediate band high efficiency solar cell. Progress in Photovoltaics: Res. Appl. 9(2), 73–86 (2001).


This paper describes how to partially fill the intermediate band formed by the confined states of quantum dots with electrons. Efficiencies of up to 63.2% have been calculated in ideal cases for solar cells with this intermediate band. In order to achieve this, the barrier region is n-doped so that the electrons delivered by the donors fall into the otherwise empty intermediate band states.

This method produces a fully space-charged structure whose electrostatic properties are studied in this paper, thus confirming the feasibility of the proposed method. Partial filling of the intermediate band is necessary to provide strong absorption in transitions from it to both the valence and the conduction bands.


 Luque, A., Marti, A., Antolin, E., Garcia-Linares, P.: Intraband Absorption for Normal Illumination in Quantum Dot Intermediate Band Solar Cells. Solar Energy Materials & Solar Cells 94, 2032–2035 (2010).


In the current intermediate band solar cells made with InAs quantum dots (QDs) in GaAs, the transitions by absorption of photons between the intermediate band and the conduction band for illumination normal to the cell surface is very weak or, more often, undetectable. We model the QD as a parallelepiped potential well and calculate the envelope function of the electron wavefunctions. By obtaining the dipolar matrix elements we find that, with the present shapes, this absorption is forbidden or very weak. Deeper QDs with smaller base dimensions should be made to permit this absorption. Copyright © 2001 John Wiley & Sons, Ltd.


Luque, A., Martí, A., Stanley, C., López, N., Cuadra, L., Zhou, D., Mc-Kee, A.: General equivalent circuit for intermediate band devices: potentials, currents and electroluminescence. Journal of Applied Physics 96(1), 903–909 (2004).

Abstract :

A general model to describe the operation of intermediate band solar cells (IBSCs), incorporating a significant number of physical effects such as radiative coupling between bands, and impact ionization and Auger recombination mechanisms, is presented in equivalent circuit form. The model

is applied to IBSC prototypes fabricated from InAs quantum dots structures to determine the value of the circuit elements involved. The analysis shows evidence of splitting between the conduction and intermediate band quasi-Fermi levels, one of the fundamental working hypotheses on which operation of the IBSC depends. The model is also used to discuss the limitations and potential of this type of cell. © 2004 American Institute of Physics.


Luque, A., Marti, A., Lopez, N., Antolin, E., Canovas, E., Stanley, C., Farmer, C., Caballero, L.J., Cuadra, L., Balenzategui, J.L.: Experimental analysis of the quasi-Fermi level split in quantum dot intermediate-band solar cells. Applied Physics Letters 87(8), 083505-083503 (2005).


The intermediate-band solar cell _IBSC_ has been proposed as a device whose conversion efficiency can exceed the 40.7% limiting value of single-gap cells. It utilizes the so-called intermediate-band material, characterized by the existence of a band that splits an otherwise conventional semiconductor bandgap into two sub-bandgaps. Two important criteria for its operation are that the carrier populations in the conduction, valence, and intermediate-bands are each described by their own quasi-Fermi levels, and that photocurrent is produced when the cell is illuminated with below-bandgap-energy photons. IBSC prototypes have been manufactured from InAs quantum dot structures and analyzed by electroluminescence and quantum efficiency measurements. We present evidence to show that the two main operating principles required of the IBSC are fulfilled. © 2005 American Institute of Physics

DOI: 10.1063/1.2034090


Luque, A., Martí, A., Antolín, E., C.Tablero: Intermediate bands versus levels in non-radiative recombination. Physica B 382, 320-327 (2006).


There is a practical interest in developing semiconductors with levels situated within their band gap while preventing the non-radiative recombination that these levels promote. In this paper, the physical causes of this non-radiative recombination are analyzed and the increase in the density of the impurities responsible for the mid-gap levels to the point of forming bands is suggested as the means of suppressing the recombination. Simple models supporting this recommendation and helping in its quantification are presented. © 2006 Elsevier B.V. All rights reserved.


Luque, A., Martí, A., López, N., Antolín, E., Cánovas, E., Stanley, C.R., Farmer, C., Díaz, P.: Operation of the intermediate band solar cell under nonideal space charge region conditions and half filling of the intermediate band. Journal of Applied Physics 99(1), 094503 (2006). doi:10.1063/1.2193063


A photovoltaic device based on an intermediate electronic band located within the otherwise conventional band gap of a semiconductor, the so-called intermediate band solar cell (IBSC), has been proposed for a better utilization of the solar spectrum. Experimental IBSC devices have been engineered using quantum dot technology, but their practical implementation results in a departure of key underpinning theoretical principles, assumed to describe the operation of the IBSC, away from the ideal. Two principles which are only partially fulfilled are that (i) the intermediate band should be half filled with electrons and (ii) the region containing the quantum dots should not be located fully within the junction depletion region. A model to describe the operation of the devices under these nonidealized conditions is presented and is used to interpret experimental results for IBSCs with ten layers of quantum dots. Values for the electron and hole lifetimes, associated with recombination from the conduction band to the intermediate band and from the intermediate band

to the valence band (0.5 and 40 ps, respectively) are thus obtained. © 2006 American Institute of Physics. (DOI: 10.1063/1.2193063)


Luque, A., Marti, A., Nozik, A.J.: Solar cells based on quantum dots: Multiple exciton generation and intermediate bands. Mrs Bulletin 32(3), 236-241 (2007).


Semiconductor quantum dots may be used in so-called third-generation solar cells that have the potential to greatly increase the photon conversion efficiency via two effects: (1) the production of multiple excitons from a single photon of sufficient energy and (2) the formation of intermediate bands in the bandgap that use sub-bandgap photons to form separable electron–hole pairs. This is possible because quantization of energy levels in quantum dots produces the following effects: enhanced Auger processes and Coulomb coupling between charge carriers; elimination of the requirement to conserve crystal momentum; slowed hot electron–hole pair (exciton) cooling; multiple exciton generation; and formation of minibands (delocalized electronic states) in quantum dot arrays. For exciton multiplication, very high quantum yields of 300–700% for exciton

formation in PbSe, PbS, PbTe, and CdSe quantum dots have been reported at photon energies about 4–8 times the HOMO–LUMO transition energy (quantum dot bandgap), respectively, indicating the formation of 3–7 excitons/photon, depending upon the photon energy. For intermediate-band solar cells, quantum dots are used to create the intermediate bands from the confined electron states in the conduction band. By means of the intermediate band, it is possible to absorb below-bandgap energy photons. This is predicted to produce solar cells with enhanced photocurrent without voltage degradation.


Luque, A., Marti, A., Mendes, M.J., Tobias, I.: Light absorption in the near field around surface plasmon polaritons. Journal of Applied Physics 104(11), 113118 (2008). doi:10.1063/1.3014035


A semiclassical method is developed to calculate the energy absorption of an electronic system located in the near field of a metal nanoparticle sustaining surface plasmons. The results are found to be similar to those of photon absorption from ordinary transversal radiation. However, they are affected by a geometrical factor that can increase the absorption by several orders of magnitude. As example, we investigate ellipsoidal-shaped metal nanoparticles which, under favorable conditions, may provide near field absorption enhancements almost as large as 10^4, and in many cases above 10.

© 2008 American Institute of Physics.  DOI: 10.1063/1.3014035


Marti, A., Antolin, E., Canovas, E., Lopez, N., Linares, P.G., Luque, A., Stanley, C.R., Farmer, C.D.: Elements of the design and analysis band solar of quantum-dot intermediate cells. Thin Solid Films 516(20), 6716-6722 (2008). doi:10.1016/j.tsf.2007.12.064


We have demonstrated recently that two below bandgap energy photons can lead to the creation of one electron–hole pair in a quantum-dot intermediate band solar cell (QD-IBSC). To be effective, the devices used in the experiments were designed to a) half-fill the intermediate band with electrons; b) to allocate the quantum dots in a flat-band potential region, and c) to prevent tunnelling from the n emitter into the intermediate band. QD-IBSCs have also shown degradation in their open-circuit voltage when compared with their counterparts without quantum dots. This loss is due to the presence of the intermediate band (IB) together with the incapacity of the quantum dots to absorb sufficient below bandgap light as to contribute significantly to the photogenerated current. It is predicted, nevertheless, that this voltage loss will diminish if concentration light is used leading to devices with efficiency higher than single gap solar cells. A circuit model that includes additional recombination levels to the ones introduced by the IB is described to support this discussion.

© 2007 Elsevier B.V. All rights reserved.



Luque, A., Marti, A.: The intermediate band solar cell: progress towards the realization of an attractive concept. Adv. Mater. 22, 160-174 (2009).


The intermediate band (IB) solar cell has been proposed to increase the current of solar cells while at the same time preserving the output voltage in order to produce an efficiency that ideally is above the limit established by Shockley and Queisser in 1961. The concept is described and the present realizations and acquired understanding are explained. Quantum dots are used to make the cells but the efficiencies that have been achieved so far are not yet satisfactory. Possible ways to overcome the issues involved are depicted. Alternatively, and against early predictions, IB alloys have been prepared and cells that undoubtedly display the IB behavior have been fabricated, although their efficiency is still low. Full development of this concept is not trivial but it is expected that once the development of IB solar cells is fully mastered, IB solar cells should be able to operate in tandem in concentrators with very high efficiencies or as thin cells at low cost with efficiencies above the present ones.  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.


Antolin, E., Marti, A., Olea, J., Pastor, D., Gonzalez-Diaz, G., Martil, I., Luque, A.: Lifetime recovery in ultrahighly titanium-doped silicon for the implementation of an intermediate band material. Applied Physics Letters 94(4), 042115 (2009).


The doping of conventional semiconductors with deep level (DL) centers has been proposed to synthesize intermediate band materials. A recent fundamental study of the nonradiative recombination (NRR) mechanisms predicts the suppression of the NRR for ultrahigh DL dilutions as a result of the delocalization of the impurity electron wave functions. Carrier lifetime measurements on Si wafers doped with Ti in the 10^20–10^21 cm−3 concentration range show an increase in the lifetime, in agreement with the NRR suppression predicted and contrary to the classic understanding of DL action. © 2009 American Institute of Physics. (DOI: 10.1063/1.3077202)


Antolín, E., Marti, A., Farmer, C.D., Linares, P.G., Hernández, E., Sánchez, A.M., Ben, T., Molina, S.I., Stanley, C.R., Luque, A.: Reducing carrier escape in the InAs/GaAs quantum dot intermediate band solar cell. Journal of Applied Physics 108(6), 064513 (2010).


Intermediate band solar cells (IBSCs) fabricated to date from In(Ga)As/GaAs quantum dot arrays (QD-IBSC) exhibit a quantum efficiency (QE) that extends to below bandgap energies. However, the production of sub-bandgap photocurrent relies often on the thermal and/or tunneling escape of carriers from the QDs, which is incompatible with preservation of the output voltage. In this work, we test the effectiveness of introducing a thick GaAs spacer in addition to an InAlGaAs strain relief layer (SRL) over the QDs to reduce carrier escape. From an analysis of the QE at different temperatures, it is concluded that escape via tunneling can be completely blocked under short-circuit conditions, and that carriers confined in QDs with an InAlGaAs SRL exhibit a thermal escape activation energy over 100 meV larger than in the case of InAs QDs capped only with GaAs. © 2010 American Institute of Physics. (doi:10.1063/1.3468520)



Luque, A., Marti, A., Antolín, E., Linares, P.G., Tobias, I., Ramiro, I.: Radiative thermal escape in intermediate band solar cells. AIP Advances 1, 022125 (2011).


To achieve high efficiency, the intermediate band (IB) solar cell must generate photocurrent from sub-bandgap photons at a voltage higher than that of a single contributing sub-bandgap photon. To achieve the latter, it is necessary that the IB levels be properly isolated from the valence and conduction bands.We prove that this is not the case for IB cells formed with the confined levels of InAs quantum dots (QDs) in GaAs grown so far due to the strong density of internal thermal photons at the transition energies involved. To counteract this, the QD must be smaller. © 2011 Author(s). This article is distributed under a Creative Commons Attribution Non-Commercial Share Alike 3.0 Unported License. [doi:10.1063/1.3597326].


Luque, A., Marti, A., Antolín, E., Linares, P.G., Tobías, I., Ramiro, I., Hernandez, E.: New Hamiltonian for a better understanding of the Quantum Dot Intermediate Band Solar Cells. Solar Energy Materials & Solar Cells 95, 2095-2101 (2011). doi:10.1016/j.solmat.2011.02.028


The quantum dot intermediate band solar cell has the potential for very high conversion efficiency. However, the cells manufactured so far show efficiencies below the expectations mainly because the sub-bandgap photocurrent associated to the quantum dots is too low and because of a substantial reduction of the voltage. We present a new Hamiltonian for the use with the k·p method with low computing power demands. With it, we show here the fundamentals that explain the low light absorption coefficient and, consequently, the low photocurrent observed. We also prove that the bandgap of the host material, GaAs in our case, is reduced by the introduction of the quantum dots, which also explains the voltage reduction. The model is justified by the agreement with internal quantum efficiency measurements. It opens the path for improvement and suggests changes for increasing the photocurrent and for the compensation of the voltage reduction. & 2011 Elsevier B.V. All rights reserved.


1. Tobías, I., Luque, A., Martí, A.: Numerical modeling of intermediate band solar cells. Semicond. Sci. Technol. 26, 014031 (2011).


The performance of intermediate band solar cells under concentrated sunlight is analyzed by means of computer simulation. The continuity equations for electrons and holes and the Poisson equation are numerically solved in one dimension under steady-state conditions. Two situations are considered for a given density of intermediate band centers and optical cross sections. In the first situation, the intermediate band is undoped and a large capture coefficient links conduction and intermediate bands; a large short circuit current enhancement with respect to a conventional cell is obtained, but at the price of strong voltage and efficiency degradation. In the second, the intermediate band is partially filled by doping and there is little thermal contact with the semiconductor bands. The potential of the intermediate band concept is then realized with significant efficiency improvement under highly concentrated illumination. The analysis also reveals that the approximation of flat quasi-Fermi levels is not appropriate. © 2011 IOP Publishing Ltd.


Luque, A., Marti, A., Stanley, C.: Understanding intermediate-band solar cells. Nature Photonics 6(3), 146-152 (2012). doi:10.1038/nphoton.2012.1


The intermediate-band solar cell is designed to provide a large photogenerated current while maintaining a high output voltage. To make this possible, these cells incorporate an energy band that is partially filled with electrons within the forbidden bandgap of a semiconductor. Photons with insufficient energy to pump electrons from the valence band to the conduction band can use this intermediate band as a stepping stone to generate an electron–hole pair. Nanostructured materials and certain alloys have been employed in the practical implementation of intermediate-band solar cells, although challenges still remain for realizing practical devices. Here we offer our present understanding of intermediate-band solar cells, as well as a review of the different approaches pursed for their practical implementation. We also discuss how best to resolve the remaining technical issues. © 2012 Macmillan Publishers Limited. All rights reserved.


Luque, A., Linares, P.G., Antolín, E., Ramiro, I., Farmer, C.D., Hernández, E., Tobías, I., Stanley, C.R., Martí, A.: Understanding the operation of quantum dot intermediate band solar cells. Journal of Applied Physics 111, 044502 (2012). doi: [doi:10.1063/1.3684968]


In this paper, a model for intermediate band solar cells is built based on the generally understood physical concepts ruling semiconductor device operation, with special emphasis on the behavior at low temperature. The model is compared to JL-VOC measurements at concentrations up to about 1000 suns and at temperatures down to 20 K, as well as measurements of the radiative recombination obtained from electroluminescence. The agreement is reasonable. It is found that the main reason for the reduction of open circuit voltage is an operational reduction of the bandgap, but this effect disappears at high concentrations or at low temperatures. © 2012 American Institute of Physics.


Marti, A., Antolin, E., Linares, P.G., Luque, A.: Understanding experimental characterization of intermediate band solar cells. Journal of Materials Chemistry 22(43), 22832-22839 (2012). doi:10.1039/c2jm33757f


An intermediate band solar cell is a novel photovoltaic device with the potential to exceed the efficiency of single gap solar cells. In the last few years, several prototypes of these cells, based on different technologies, have been reported. Since these devices do not yet perform ideally, it is sometimes difficult to determine to what extent they operate as actual intermediate band solar cells. In this article we provide the essential guidelines to interpret conventional experimental results (current–voltage plots, quantum efficiency, etc.) associated with their characterization. A correct interpretation of these results is essential in order not to mislead the research efforts directed towards the improvement of the efficiency of these devices. © (2012) The Royal Society of Chemistry 2012.


Luque, A., Mellor, A., Antolin, E., Linares, P.G., Ramiro, I., Tobias, I., Marti, A.: Symmetry considerations in the empirical k.p Hamiltonian for the study of intermediate band solar cells. Solar Energy Materials and Solar Cells 103(0), 171-183 (2012).


With the purpose of assessing the absorption coefficients of quantum dot solar cells, symmetry considerations are introduced into a Hamiltonian whose eigenvalues are empirical. In this way, the proper transformation from the Hamiltonian’s diagonalized form to the form that relates it with G-point exact solutions through the k.p envelope functions is built accounting for symmetry. Forbidden transitions are thus determined reducing the calculation burden and permitting a thoughtful discussion of the possible options for this transformation. The agreement of this model with the measured external quantum efficiency of a prototype solar cell is found to be excellent. © 2012 Elsevier B.V. All rights reserved.


Mellor, A., Luque, A., Tobias, I., Marti, A.: The influence of quantum dot size on the sub-bandgap intraband photocurrent in intermediate band solar cells. Applied Physics Letters 101, 133909 (2012). doi:10.1063/1.4755782


The effect of quantum dot (QD) size on the performance of quantum dot intermediate band solar cells is investigated. A numerical model is used to calculate the bound state energy levels and the absorption coefficient of transitions from the ground state to all other states in the conduction band. Comparing with the current state of the art, strong absorption enhancements are found for smaller quantum dots, as well as a better positioning of the energy levels, which is expected to reduce thermal carrier escape. It is concluded that reducing the quantum dot size can increase sub-bandgap photocurrent and improve voltage preservation. © 2012 American Institute of Physics.


Tobías, I., Luque, A., Antolín, E., Linares, P.G., Ramiro, I., Hernández, E., Martí, A.: Realistic Performance Prediction in Nanostructured Solar Cells. Journal of Applied Physics 112, 24518 (2012). doi: 10.1063/1.4770464


The behavior of quantum dot, quantum wire, and quantum well InAs/GaAs solar cells is studied with a very simplified model based on experimental results in order to assess their performance as a function of the low bandgap material volume fraction fLOW. The efficiency of structured devices is found to exceed the efficiency of a non-structured GaAs cell, in particular under concentration,

when fLOW is high; this condition is easier to achieve with quantum wells. If three different quasi Fermi levels appear with quantum dots the efficiency can be much higher. © 2012 American Institute of Physics.


1. Linares, P.G., Martí, A., Antolín, E., Ramiro, I., López, E., Farmer, C.D., Stanley, C.R., Luque, A.: Low-Temperature Concentrated Light Characterization Applied to Intermediate Band Solar Cells. IEEE J. Photovolt. 3(2), 753-761 (2013). doi:10.1109/jphotov.2013.2241395


 In this paper, we describe a novel low-temperature concentrated light characterization technique, and we apply it to the study of the so-called intermediate band solar cell (IBSC). This type of cell is characterized by hosting an intermediate band (IB) that is capable of providing both high current and high voltage. In most of its practical implementations, which are carried out by means of quantum dot (QD) structures, the energy band-diagram shows additional confined energy levels. These extra levels are responsible for an increase in the thermalization rate between the IBand the conduction band, which produces the degradation of the open-circuit voltage VOC. The original implementation of a setup that combines concentrated light and low temperature conditions is discussed in this paper. In this context, photogenerated current (IL)−VOC characteristics that are measured on QD-IBSC are presented in order to study their recombination, as well as their

VOC recovery. © 2013 IEEE.


Luque, A., Antolín, E., Linares, P.G., Ramiro, I., Mellor, A., Tobías, I., Martí, A.: Interband optical absorption in quantum well solar cells. Solar Energy Materials & Solar Cells 112, 20-26 (2013). DOI: 10.1016/j.solmat.2012.12.045


The eigenfunctions and the interband photon absorption of a solar quantum well solar cell are calculated using the k.p Empirical Hamiltonian developed for quantum dot solar cells. The calculations are compared with the measured quantum efficiency in a prototype quantum well solar cell. The agreement is reasonably good. The absorption with quantum wells is found to be much greater than with quantum dots. This is due, besides the higher number of states, to the partially extended nature of quantum well wavefunctions that leads to photon matrix elements which are substantially different to those applicable to quantum dots. © 2013ElsevierB.V. all rights reserved.


Luque, A., Marti, A., Mellor, A., Marron, D.F., Tobias, I., Antolín, E.: Absorption Coefficient for the Intraband Transitions in Quantum Dot Materials. Progress in Photovoltaics 21, 658-667 (2013). DOI: 10.1002/pip.1250


In this paper, we present calculations of the absorption coefficient for transitions between the bound states of quantum dots grown within a semiconductor and the extended states of the conduction band. For completeness, transitions among bound states are also presented. In the separation of variables, single band k·p model is used in which most elements may be expressed analytically. The analytical formulae are collected in the appendix of this paper. It is concluded that the transitions are strong enough to provide a quick path to the conduction band for electrons pumped from the valence to the intermediate band. Copyright © 2012 John Wiley & Sons, Ltd.


Luque, A., Mellor, A., Ramiro, I., Antolín, E., Tobías, I., Martí, A.: Interband absorption of photons by extended states in intermediate band solar cells. Solar Energy Materials & Solar Cells 115, 138-144 (2013).


This paper considers sub-bandgap photon absorption in an InAs/GaAs quantum dot matrix. Absorption coefficients are calculated for transitions from the extended states in the valence band to confined states in the conduction band. This completes a previous body of work in which transitions between bound states were calculated. The calculations are based on the empirical k·p Hamiltonian considering the quantum dots as parallelepipeds. The extended states may be only partially extended—in one or two dimensions—or extended in all three dimensions. It is found that extended-to-bound transitions are, in general, weaker than bound-to-bound transitions, and that the former are weaker when the initial state is extended in more coordinates. This study is of direct application to the research of intermediate band solar cells and other semiconductor devices based on light absorption in semiconductors nanostructured with quantum dots. © 2013 Elsevier B.V. All rights reserved.


Luque, A., Mellor, A., Tobías, I., Antolín, E., Linares, P.G., Ramiro, I., Martí, A.: Virtual-bound, filamentary and layered states in a box-shaped quantum dot of square potential form the exact numerical solution of the effective mass Schrödinger equation. Physica B 413, 73-81 (2013). DOI: 10.1016/j.physb.2012.12.047


The effective mass Schroedinger equation of a QD of parallelepipedic shape with a square potential well is solved by diagonalizing the exact Hamiltonian matrix developed in a basis of separation-of-variables wavefunctions. The expected below bandgap bound states are found not to differ very much from the former approximate calculations. In addition, the presence of bound states within the conduction band is confirmed. Furthermore, filamentary states bounded in two dimensions and extended in one dimension and layered states with only one dimension bounded, all within the conduction band—which are similar to those originated in quantum wires and quantum wells—coexist with the ordinary continuum spectrum of plane waves. All these subtleties are absent in spherically shaped quantum dots, often used for modeling. © 2013 Elsevier B.V. All rights reserved.


Mellor, A., Luque, A., Tobias, I., Marti, A.: A numerical study into the influence of quantum dot size on the sub-bandgap interband photocurrent in intermediate band solar cells. AIP Advances 3, 022116 (2013).


A numerical study is presented of the sub-bandgap interband photon absorption in quantum dot intermediate band solar cells. Absorption coefficients and photocurrent densities are calculated for the valence band to intermediate band transitions using a four-band k·p method. It is found that reducing the quantum dot width in the plane perpendicular to the growth direction increases the photocurrent from the valence band to the intermediate-band ground state if the fractional surface coverage of quantum dots is conserved. This provides a path to increase the sub-bandgap photocurrent in intermediate band solar cells. Copyright 2013 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License.


Mendes, M.J., Hernandez, E., Lopez, E., Garcıa-Linares, P., Ramiro, I., Artacho, I., Antolın, E., Tobıas, I., Martı, A., Luque, A.: Self-organized colloidal quantum dots and metal nanoparticles for plasmon-enhanced intermediate-band solar cells. Nanotechnology 24, 345402 (2013).


A colloidal deposition technique is presented to construct long-range ordered hybrid arrays of self-assembled quantum dots and metal nanoparticles. Quantum dots are promising for novel mopto-electronic devices but, in most cases, their optical transitions of interest lack sufficient light absorption to provide a significant impact in their implementation. A potential solution is to couple the dots with localized plasmons in metal nanoparticles. The extreme confinement of light in the near-field produced by the nanoparticles can potentially boost the absorption in the quantum dots by up to two orders of magnitude.

In this work, light extinction measurements are employed to probe the plasmon resonance of spherical gold nanoparticles in lead sulfide colloidal quantum dots and amorphous silicon thin-films. Mie theory computations are used to analyze the experimental results and determine the absorption enhancement that can be generated by the highly intense near-field produced in the vicinity of the gold nanoparticles at their surface plasmon resonance


The results presented here are of interest for the development of plasmon-enhanced colloidal nanostructured photovoltaic materials, such as colloidal quantum dot intermediate-band solar cells.

© 2013 IOP Publishing Ltd.


Mellor, A., Luque, A., Tobías, I., Martí, A.: Realistic detailed balance study of the quantum efficiency of quantum dot solar cells. Advanced Functional Materials 24(3), 339-345 (2014). doi:10.1002/adfm.201301513


An attractive but challenging technology for high effi ciency solar energy conversion is the intermediate band solar cell (IBSC), whose theoretical efficiency limit is 63%, yet which has so far failed to yield high efficiencies in practice. The most advanced IBSC technology is that based on quantum dots (QDs): the QD-IBSC. In this paper, k·p calculations of photon absorption in the QDs are combined with a multi-level detailed balance model. The model has been used to reproduce the measured quantum effi ciency of a real QD-IBSC and its temperature dependence. This allows the analysis of individual sub-bandgap transition currents, which has as yet not been possible experimentally, yielding a deeper understanding of the failure of current QD-IBSCs. Based on the agreement with experimental data, the model is believed to be realistic enough to evaluate future QD-IBSC proposals. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Luque, A., Linares, P.G., Mellor, A., Andreev, V., Marti, A.: Some advantages of intermediate band solar cells based on type II quantum dots. Applied Physics Letters 103, 123901 (2013). doi:10.1063/1.4821580


Unlike Type I, Type II quantum dots do not have hole bound states. This precludes that they invade the host semiconductor bandgap and prevents the reduction of voltage in intermediate band solar cells. It is proven here that the optical transition between the hole extended states and the intermediate bound states within the host bandgap is much stronger than in Type I quantum dots, increasing the current and making this structure attractive for manufacturing these cells. © 2013 AIP Publishing LLC.

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