Volume 1 photovoltaic solar energy 1 29 – intermediate band solar cells

Volume 1 photovoltaic solar energy 1 29 – intermediate band solar cells Volume 1 photovoltaic solar energy 1 29 – intermediate band solar cells Volume 1 photovoltaic solar energy 1 29 – intermediate band solar cells Volume 1 photovoltaic solar energy 1 29 – intermediate band solar cells Volume 1 photovoltaic solar energy 1 29 – intermediate band solar cells Volume 1 photovoltaic solar energy 1 29 – intermediate band solar cells

1.29 Intermediate Band Solar Cells E Antolín, A Martí, and A Luque, Universidad Politécnica de Madrid, Madrid, Spain © 2012 Elsevier Ltd All rights reserved 1.29.1 Introduction 1.29.2 Theoretical Model of the Intermediate Band Solar Cell 1.29.3 The Impurity-Based Approach or ‘Bulk IBSC’ 1.29.4 The QD-IBSC 1.29.4.1 The Use of QDs for Implementing an IBSC 1.29.4.2 QD-IBSC Prototypes 1.29.4.3 Proof of the Concept 1.29.4.4 Strategies to Boost the Efficiency of the QD-IBSC 1.29.4.4.1 Improved InAs/GaAs QDs 1.29.4.4.2 Non-Stranski–Krastanov QDs 1.29.5 Summary Acknowledgments References 619 619 624 628 628 630 631 632 633 635 635 637 637 1.29.1 Introduction The efficiency of solar cells has experienced a notable increase in the past decades The conventional photovoltaic (PV) technology, based on single-gap semiconductor devices, has achieved record conversion efficiencies of 29% in operation under concentrated sunlight [1] However, the room for improvement of this technology is limited The fundamental principles of photoconversion applied in single-gap cells are subject to an absolute efficiency limit, the Shockley–Queisser (SQ) limit, of 40.7% (calculated for an ideal single-gap cell under maximum sunlight concentration [2, 3]) If it is desired to achieve a substantial increase in the efficiency of PV energy conversion, novel devices not subject to the SQ limit are required Such alternative technologies are usually known as ‘third-generation solar cells’ and some researchers have proposed that their implementation could prompt a breakthrough in PV electricity cost reduction and be the seed for a massive solar energy production [4–7] The most developed third-generation approach at the moment is the multijunction solar cell (MJSC) A MJSC is a device that combines several single-gap cells of different semiconductor materials Using the MJSC technology, it has become recently possible to fabricate devices that exceed in practice the SQ limit (the current record is 43.5% for a triple-junction GaInP/GaAs/GaInNAs cell operated at 400 sunlight concentration) [1] Other alternatives have been proposed with the aim of achieving similar or even higher efficiencies, accompanied by potential advantages such as a more compact design, lower manufacture cost, higher tolerance toward changes in the solar spectrum, and so on One of these proposals is the subject of the present review: the intermediate band solar cell (IBSC) [8] It has an ideal efficiency limit of 63.2%, the same that of the current-matched triple-junction solar cell A few years ago, it was just a theoretical concept Now, several research groups around the world aim to materialize the concept on real devices To understand the potential of the IBSC concept, it is useful to discuss first the intrinsic limitation of conventional solar cells The efficiency of single-gap solar cells is fundamentally limited by the fact that they only harness a portion of the solar spectrum A conventional solar cell is made of a semiconductor material, characterized by a bandgap of forbidden energies of width EG In principle, the optical energy of a solar photon can be absorbed by an electron at the valence band (VB), which will use that energy to promote to the conduction band (CB), creating an electron–hole pair However, not all photons from the solar spectrum are suitable for that process A photon of energy equal to EG can generate a VB → CB electronic transition, but a photon of lower energy cannot, and it will not be absorbed in the semiconductor A photon of energy greater than EG can be absorbed in an electronic transition, but its excess energy with respect to EG will be lost Since the electronic states within the bands form a continuum, the produced carriers will easily migrate to lower energy states, transferring the energy excess to the lattice in the form of heat (phonon emission) In any conventional semiconductor, carriers will relax by this ‘thermalization’ process to the bandgap edges in sub-picoseconds time and the remaining collectable energy from a photon of energy greater than EG will be the same as in the case of a photon of energy equal to EG We face then a trade-off: if we choose a semiconductor of high EG, such as GaAs, few photons will be absorbed, whereas if a low-bandgap material as Ge is chosen, we will absorb more photons, but a greater part of their energy will be lost to heat 1.29.2 Theoretical Model of the Intermediate Band Solar Cell The IBSC concept is based on the use of an absorbing material characterized by the existence of an isolated electronic band, the so-called intermediate band (IB), between the CB and VB [8] As depicted in Figure 1, the IB divides the main bandgap (EG) into two sub-bandgaps, referred to as EL, the smallest one, and EH, the largest one An electron–hole pair can be generated in this material by two mechanisms: absorption of one photon in a conventional VB → CB transition (labeled (3) in Figure 1) or absorption of two Comprehensive Renewable Energy, Volume doi:10.1016/B978-0-08-087872-0.00127-X 619 620 Technology CB EL (2) IB Sunlight spectrum (3) EG EH (1) VB Figure Simplified band diagram of an IB material showing the three possible optical transitions that allow a better exploitation of the solar spectrum in the case of a single-gap solar cell sub-bandgap photons through the IB-mediated transitions labeled (1) and (2) We have represented the IB in the upper half of EG (EL is identified with the IB–CB gap) This arrangement will be maintained throughout our description, but it is an arbitrary choice Conceptually, it would make no difference to presume that the IB is located in the lower half of EG In this respect, it can be only anticipated that in the general case, the IB should not coincide with EG’s midpoint so that three distinct absorption thresholds are produced The potential of the IBSC relays on the production of extra photocurrent by the simultaneous absorption of photons in the two sub-bandgap transitions In order to surpass the single-gap efficiency limit, it is necessary that the increase in photocurrent is not counteracted by a reduction of the output voltage This can be achieved if the electronic populations associated with the IB, the CB, and the VB are each described by the respective quasi-Fermi levels εFIB, εFe, and εFh, to be defined below In addition, two layers of conventional semiconductor of opposite doping, usually called p-emitter and n-emitter, have to be attached on either side of the IB material to block the direct flow of carriers from the IB to the metal contacts For simplification, we shall assume in the following description that the emitters have a zero width and not absorb light Figure shows the band diagram of an ideal IB material in two situations Under equilibrium (Figure 2(a)), the electronic population in all bands is described by a Fermi-level εF When the semiconductor is illuminated (Figure 2(b)) with photons of suitable energy, electrons are excited from the VB to the CB, from the VB to the IB, and from the IB to the CB, at a rate gVC, gVI, and gIC, respectively The system will tend to recover equilibrium and the excited carriers will recombine at the respective rates rCV, rIV, and rCI, which will depend on the generation rates, as well as on the boundary constraints of the system (e.g., on the amount of each type of carrier that is allowed to exit the IB material) The balance populations of electrons at the CB, holes at the VB and IB carriers in the IB material are now described by the respective quasi-Fermi levels εFIB, εFe, and εFh In the IBSC model, the (quasi-)Fermi level concept maintains the two-fold physical meaning, thermodynamical and statistical, that it has in common semiconductor science From a quantum-statistical point of view, it is the energy at which the probability of occupation by the carriers of an electronic gas is ½ States of higher (lower) energy will have an occupation probability lower (higher) than ½, following the Fermi–Dirac distribution In this context, it is important to recall that in the IBSC model, the creation of an electron–hole pair from the absorption of sub-bandgap photons does not imply the simultaneous absorption of two photons by a single electron in the VB, a rather unlikely three particle collision mechanism The generation is produced by the confluence of a VB → IB and an IB → CB transitions Therefore, it is preferred that εFIB crosses the IB in order to maximize sub-bandgap absorption: if the IB is semi-filled, it has enough electrons to promote to the CB and enough unoccupied states to receive electrons from the VB In principle, the position of εFIB can be adjusted by the generation and recombination rates But to make it independent of the operation conditions, the ideal model assumes that εF is pinned to the IB under equilibrium (using n- or p-doping if necessary) and that the IB has a sufficient density of states so that εFIB remains clamped to it under illumination, as depicted in Figure (a) (b) CB IB CB εFe glC rCl IB εF gVC rCV gVI rIV VB εFIB εFh VB Figure Simplified band diagrams of an IB material: (a) under equilibrium and (b) under illumination with photons of appropriate energy to generate electronic transitions between any pair of bands Intermediate Band Solar Cells 621 From the point of view of thermodynamics, the (quasi-)Fermi level is the electrochemical potential of the carrier ensemble, that is, the amount of free energy that is gained or lost by the system when a carrier is added to or removed from it We refer here to the ‘Gibbs free energy’, the thermodynamic potential that measures the ‘useful’ energy (which can be entirely transformed into work) obtainable from a system at a constant temperature and pressure In our context, to define the electrochemical potential, it is assumed that the carrier ensemble is in thermal equilibrium with the semiconductor lattice, or in other words, that carriers with an excess of kinetic energy have thermalized instantaneously The definition of three quasi-Fermi levels in the IB material has important implications This means that each band contains an electronic gas and carrier relaxation between any pair of bands (recombination) is a much slower process than carrier relaxation within the bands (thermalization) In addition, when three quasi-Fermi levels are defined, the promotion of electrons, for example, from the IB to the CB at a rate gIC, implies that the free energy of the system increases at a rate gIC  (εFe – εFIB) As it is well known, the laws of thermodynamics restrict the ways by which the useful energy of a system can be increased For instance, it can be demonstrated [9, 10] that the thermal energy of the lattice is used to promote a carrier from the IB to the CB, augmenting the total free energy of the system, violates the second law of thermodynamics Thermal IB → CB generation can of course take place, but to comply with thermodynamics, the electrochemical potential of CB electrons thermally promoted from the IB has to be set to εFe ≤ εFIB and there is no possible net gain in free energy but even loss That is not the case when IB → CB transitions take place because photons from a source hotter than the cell are absorbed The later consideration, which might appear rather abstract in the way it has been expounded, is indeed the cornerstone of the prediction of a high voltage, and hence a high efficiency, for the ideal IBSC For simplification, we shall assume that the quasi-Fermi levels are constant through the IB material The following quasi-Fermi splits can be defined, which according to our argumentation, should be nonzero in an IB material under certain illumination conditions and boundary constrains of the carrier ensembles μCV ≡ εFe − εFh μCI ≡ εFe − εFIB μIV ≡ εFIB Fh ẵ1 CV ẳ CI ỵ IV ẵ2 They are related by the equation The emitters play an important role in the way carriers and useful energy are extracted from the IBSC Figure illustrates the complete structure of an IBSC including the emitters and the corresponding band diagram under equilibrium, as well as when the cell is illuminated and connected to an external load As the emitters are located between the IB material and the metal contacts, they define the boundary constrains of the carrier ensembles in the IB material They act as selective contacts: the n-emitter only allows the transport of electrons, setting their quasi-Fermi level εFe to match that of electrons at the adjacent metal contact (εFn) and the p-emitter only allows the transport of holes, setting their quasi-Fermi level εFh to match that of electrons at the adjacent metal contact (εFp) When the IBSC is under operation, electrons from the CB leave the solar cell through the n-contact, their free energy is used at the external load, and they return to the cell as low-energy carriers through the p-contact (in other words, VB holes leave the cell through the p-contact) The power (P) that the cell delivers by means of the electron flux can be expressed as _ Fe Fh ị ẳ n _ CV ẵ3 P ẳ n_ Fn Fp ¼ nðε where n_ is the rate at which carriers are transferred This power, P, has to equal the electrical power consumed at the external load, which can be expressed as P ẳ JV ẵ4 _ q being the electron where V is the voltage drop generated at the load and J is the photocurrent delivered by the cell, that is, J = qn, charge From eqns [3] and [4], it is deduced that V ẳ CV=q ẳ CI ỵ μIV e ½5Š We shall denote the net generation rates between the bands of the IB material as n_ CV ðμCV Þ ≡ gVC − rCV ðμCV Þ n_ IC ðμCI Þ ≡ gIC − rCI ðμCI Þ n_ VI IV ị gVI rIV IV ị ẵ6 As the emitters prevent that carriers are extracted directly from the IB, the net generation across both sub-bandgap transitions must be equal n_ IC CI ị ẳ n_ VI IV ị Therefore, the total current extracted from the device can be expressed as ½7Š 622 Technology nemitter pemitter IB material CB IB εF VB Under equilibrium εFn μ IV J εFe μ CI εFIB μ CV εFp εFh V – + Under operating conditions Figure Structure of an IBSC (top) and corresponding band diagrams under equilibrium (middle) and under illumination and positive bias (bottom) J ẳ qẵn_ VC CV ị ỵ n_ IV IV ị ẵ8 Equations [5] and [8], together with conditions [2] and [7], determine the current–voltage characteristic of an ideal IBSC Based on those expressions, we can compare now the potential of the ideal IBSC to the potential of the ideal single-gap solar cell Let us take as an example a single-gap cell and an IBSC with the same EG The band diagram of the single-gap cell would be as depicted in Figure 3, without IB (and without εFIB) The J–V characteristic would be given by sg À sg Á Jsg ¼ qn_ VC CV sg V sg ẳ CV e ẵ9 sg sg We have used the symbols n_ VC and μCV to remark that those magnitudes cannot be directly identified with the magnitudes n_ VC and μCV of the IBSC (even in the case that only photons with energy ≥EG reach both cells) But some absolute limits can be defined for the two cells In both cases, the maximum V (the open-circuit voltage (VOC) is limited by EG If the cells were operated at a voltage exceeding EG, then their electronic populations would be inverted (the electron occupation in the lower CB states would exceed the electron occupation in the upper VB states) In this case, the semiconductors would be unable to absorb photons; on the contrary, stimulated photon emission would be released On the other hand, the current that each device can produce is Intermediate Band Solar Cells 623 Ideal J-V curves and efficiencies (detailed balance model) Maximum concentration, 6000K black-body solar spectrum (power density 159.6 mW cm–2) Current density J/X (mA cm–2) 100 Optimum IBSC EG = 1.95 eV, EL = 0.71 eV, EH = 1.24 eV η = 63.2% 80 High voltage single gap cell EG = 1.95 eV η = 29.7% 60 High current single gap cell EG = 0.71 eV η = 36.1% 40 Optimum single gap cell EG = 1.11 eV η = 40.7% 20 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 Voltage (V) Figure Ideal current–voltage characteristics (under maximum sunlight concentration) The current density is expressed as current per unit of concentrator area (i.e., current per exploited solar flux area) The bandgap configuration and ideal efficiency (η) for each curve are given in the legend The solid black curve corresponds to an IBSC of optimized bandgaps EG, EH, and EL It is compared with a single-gap cell with gap equal to the lowest gap of the optimized IBSC (0.71 eV, red curve) and a single-gap cell with gap equal to the highest gap of the optimized IBSC (1.95 eV, blue curve) The dashed black curve corresponds to the optimized single-gap cell (EG = 1.11 eV) limited by the number of photons that it absorbs For the single-gap cell to achieve a current as high as that produced by the IBSC, it would be necessary to reduce EG But in that case, its voltage would be decreased This trade-off between current and voltage for the single-gap cell is indeed another way of seeing the trade-off between absorption and thermalization that we had already mentioned above We see that the IBSC design breaks the trade-off between current and voltage of the single-gap cell: an IBSC can deliver a high current by exploiting sub-bandgap absorption, while it preserves a high output voltage not limited by the sub-bandgap absorption thresholds This is illustrated in Figure The plot shows the current–voltage curve of an ideal IBSC with bandgaps EG = 1.95, EH = 1.24, and EL = 0.71 eV under maximum concentration (X = 46 050 suns; the solar spectrum is approximated by the black-body spectrum at 6000 K) It is compared with the curves of three ideal single-gap cells, with EG of 0.71, 1.95, and 1.11 eV, under the same conditions The curves have been calculated using the detailed balance model [2, 3, 8] and the legend gives the corresponding efficiency The bandgap values chosen for the IBSC are optimized; they give the absolute efficiency limit of the IBSC under maximal concentration, 63.2% In the case of the single-gap cell, EG = 1.11 eV is the optimal gap under the same conditions Its choice results in the SQ efficiency limit of 40.7% So far, we have summarized the fundamental principles of the IBSC theoretical model We will now briefly discuss some properties that are required in an IBSC prototype in order to achieve proper IBSC operation References are given where these aspects have been discussed in detail • The preservation of a high output voltage is possible only if both µCI and µIV are positive under illumination, that is, if the IBSC absorbs photons in VB → IB transitions and in IB → CB transitions If there is absorption only in, say, VB → IB transitions, then µCI ≤ and VOC is limited by EH (the cell is subjected to the single-gap efficiency limit for EH [9, 10]) As we have said before, thermal generation from the IB to the CB cannot help in this respect • To maximize sub-bandgap absorption, εFIB has to be pinned to the IB The minimum IB density of states required depends on the illumination conditions for which the IBSC prototype is designed (in particular, the concentration level) For example, it has been calculated that if the IBSC is implemented using quantum dots (QDs), a dot density of 1017 cm−3 provides a clamping of εFIB at the IB within kT when the cell is operated up to 1000 suns [12] • To make consistent our argumentation regarding voltage preservation, the fact that εFIB crosses the IB must not prompt stimulated photon emission If the upper and lower energy levels of the IB are designated by EIBH and EIBL, then we have µCI < EC – EIBH and µIV < EIBL – EV, where EC and EV are the CB minimum and VB maximum energy levels [13] Therefore, there is a limitation to the quasi-Fermi level splits that can be tolerated in relation to the IB bandwidth For the example studied in Reference 13, it was estimated that the IB width can be ≤ 700 meV for one-sun operation and ≤ 100 meV for 624 Technology { High efficiency Lossing energy Figure In an IB material, photons of certain energy range could in principle be absorbed in different electronic transitions The diagram on the left shows the case where photons are absorbed over the largest bandgap with energy smaller than the photon energy The diagram on the right corresponds to the less favorable case where photons are absorbed over bandgaps of energy lower as possible and a greater part of the photon energy is lost by thermalization operation under maximum concentration On the other hand, the mobility of IB carriers will typically have a positive dependence on the IB width (the carrier effective mass is proportional to the inverse of the band curvature at its extremes), and therefore, an IBSC with a relatively wide IB can homogenize better its carrier population in case illumination is too inhomogeneous throughout the device [14] (very high mobilities in the IB are not required because this band is not connected to the external contacts) • According to thermodynamics, the work delivered in an energy conversion process is maximized when the process is reversible In this case, the highest degree of reversibility in the optical–electrochemical energy conversion corresponds to the case where carriers in any band can only recombine by emitting a photon (exactly the same case in a single-gap solar cell) The ideal curves plotted in Figure have been calculated assuming that there are no nonradiative recombination mechanisms, such as Auger or Shockley–Read–Hall (SRH) recombination The relative strength and spectral dependence of the three transitions within the IB material are a sensitive aspect of the IBSC design It is quite intuitive that the efficiency of the device would sink if part of the energy of the photons gets lost because they are absorbed in a transition of energy lower than possible (e.g., if photons with energy enough to be absorbed in an VB → CB transition are absorbed in an VB → IB transition; see Figure 5) The most certain way to achieve optimal performance in an IBSC (at least when the bandgaps are optimized) would be to ensure the selectivity of the absorption coefficients (αVC, αVI, and αIC) associated, respectively, to the VB → CB, VB → IB, and IB → CB transitions This means that αIC should be zero in the range where αVI is nonzero (photon energies ≥EH) and αVI should behave analogously with respect to αVC (Note that also from a thermo­ dynamic point of view this condition should lead to the highest efficiencies, since it maximizes the reversibility of the process When a photon is absorbed in a high energy transition, it can be re-emitted and recycled inside the material using the same transition [15]) (see Figure 6) Absolute selectivity of the absorption coefficients has been assumed to compute the ideal IBSC J–V curve of Figure But it seems difficult to achieve such a complete selectivity in a real IB material A probably more feasible approach is to engineer an IB material with αIC n1) and under low injection (n0 >> Δn), τ equals the minority carrier lifetime τp0 For a sufficiently high injection, τ = τp0 + τn0 in any sample (Δn >> n0, n1, p0, p1) It has been commonly assumed that the capture cross-section of the traps is independent of their concentration and, conse­ quently, that the lifetimes given by eqn [11] decrease linearly with increasing Nt Within this context, the model of the delocalization transition introduces the novelty of considering a concentration dependent σn,p(Nt) and, in particular, that the capture cross-sections will decrease if a sufficiently high Nt is reached Therefore, it is expected to observe an increase of the SRH lifetime as the impurity concentration reaches the critical value ~1020 cm−3 The lifetime raise at the transition point is expected to be quite abrupt (in homogenously doped samples) because the assumption of constant σn,p has proven to be extremely accurate in the DL concentration range usually explored The solubility of deep level impurities (e.g., transition metals) is low in common semiconductors and samples contaminated with DLs, unintentionally or even intentionally, rarely are able to reach 1018 cm−3 without forming clusters However, it is difficult to extract conclusions about the actual lifetime related to impurity assisted recombination In the context ultrafast electronic device devel­ opment, semiconductor samples are often implanted with DL at very high doses, but the damage produced to the crystalline lattice impacts and even determines the final carrier lifetime (see, e.g., [33]) One of the main challenges of the current work on the bulk IBSC is to achieve an ultrahigh DL concentration while keeping a crystalline quality high enough as to allow and make observable the predicted delocalization transition or, in other words, the formation of an IB A first experimental observation of a partial lifetime recovery in a bulk IBSC material has recently been obtained in Si samples that were heavily doped with Ti The samples were prepared [34] by heavy ion implantation (with densities above 1021 cm−3) followed by a pulsed laser melting process that restores crystal quality Ti produces deep levels in silicon and leads to strong recombination [35–37] and is thus known to be a minority carrier lifetime killer The effective lifetime has been measured by the quasi-steady photoconductance technique and longer lifetimes have been found for the samples with the higher Ti doses [38] However, in this first study, the lifetime recovery is still small and much more research needs to be done Apart from the problem of NRR, it is also important to study which combinations of impurities and host materials can lead to the most suitable band diagrams for IBSc implementation Ab initio quantum mechanical calculations have been performed by Tablero, Wahnón, Palacios, and others, to assess whether the substitution of certain host semiconductor atoms by certain impurity atoms would give rise to an isolated IB or, to the contrary, the states introduced by the impurities would overlap with the CB and the VB In this respect, it has been found, for example, that Ti-substituted GaAs or GaP could be suitable IB material candidates [39–41], in addition to Sc-, V-, or Cr-substituted GaP [42], Ti-substituted CuGaS2 [43], or Cr-substituted ZnS [44] The insertion of V as impurity in In-thiospinels has also been theoretically proposed [45] In this case, V-substituted In2S3 with high V concentration (V2In14S24) could be prepared by solvo-thermal synthesis and experimental evidence of sub-bandgap absorption has been reported [46] (see Figure 8(a)) Following a different approach, Yu et al have synthesized II-VI oxide semiconductors [48] and GaNAsP quaternary alloys [49] Those materials belong to the so-called highly mismatched alloys (HMAs) and they are expected to exhibit an IB due to the interaction of localized impurity states with CB continuum states by 12 11 10 0.5 (b) T = 300k V: In2S3 In2S3 1.0 1.5 2.0 E/eV 2.5 3.0 3.5 Response (Arb.Units) KM function (a) ZnTe ZnTe:O 1.0 1.5 2.0 Energy (eV) 2.5 3.0 Figure Plot (a) shows the K-M function (absorption) measurements versus photon energy for V2In14S24 and In2S3 materials fabricated by solvothermal synthesis The red circle is associated with transitions from the IB to the CB, the green one to transitions from the VB to the IB, and the blue one to transitions from the VB to the CB Extracted from Lucena R, Aguilera I, Palacios P, et al (2008) Synthesis and spectral properties of Nanocrystalline V-substituted In2S3, a novel material for more efficient use of solar radiation Chemistry of Materials 20: 5125–5127 [46] Plot (b) shows the photoresponse of a ZnTe:O based IBSC compared with a ZnTe reference cell Extracted from Wang W, Lin AS, and Phillips JD (2009) Intermediate-band photovoltaic solar cell based on ZnTe:O Applied Physics Letters 95: 011103 [47] 628 Technology the band anticrossing effect [50] In this case, it has also been possible for the authors to show the existence of an IB through optical characterization (photoreflectance measurements) Finally, Phillips et al have also shown promising results with ZnTe:O material [47] (see Figure 8(b)) 1.29.4 The QD-IBSC 1.29.4.1 The Use of QDs for Implementing an IBSC The use of QDs arrays for the implementation of IB materials was proposed in Reference 51 As it is well known, QDs are semiconductor crystals of such a reduced size (typically in the order of nanometers) that their electronic properties resemble those of single atoms, that is, they exhibit discrete energy levels instead of the continuous bands that characterize bulk crystals [52–54] If they are embedded in a material (host or barrier material) of wider bandgap, three-dimensional (3D) confining potentials are created for electrons, for holes, or for both carriers, depending on the respective electronic affinities of QD and barrier materials The number and energy of the discrete energy levels that appear in the confining potential is determined by the QD size and the carrier-effective masses In the simplest case of an infinite band-offset between barrier and dot and assuming a QD with the shape of a rectangular box, the energy of the confined levels is given by ! nz2 nx2 ny ỵ ỵ ẵ12 Enx ; ny ; nz ¼ Lz 2mà Lx2 L2y where ħ is the reduced Plank’s constant; m* is the carrier effective mass; Lx, Ly, and Lz are the box lengths; and nx,y,z = 1, 2, … are the quantum numbers In principle, confining potentials in the CB are preferred for the implementation of a QD-IBSC, because the effective mass of electrons is typically smaller than that of holes, and therefore, the number of excited levels that appear is lower As depicted in Figure 9(b), the IB is formed in this case by the ground states of electrons in the QDs To fabricate the QD-IBSC, the QD array has to be sandwiched between an n-emitter and a p-emitter (see Figure 9(a)) When the IB material is implemented with QDs, the Fermi level can be located at the IB using δ-doping [55] This means that a shallow dopant species is introduced in a concentration equal to the density of dots, resulting in the semi-occupation of the ground states (these states can host two electrons due to spin degeneracy) Figure 9(c) shows the simplified band diagram of a QD-IBSC under (a) Quantum dots: (c) n doping P+ emitter Rear contact p n Front contact n+ emitter QD-IB material Emptied dots Barrier material CB (b) Quantum dot Donor impurity e– Filled dots EF IB CB IB E∗ VB G EG ΔEV VB Figure (a) Elements of a quantum-dot intermediate band solar cell (b) Formation of an intermediate band from the confined electronic states in an array of quantum dots (c) Simplified energy band diagram of a QD-IBSC in equilibrium Intermediate Band Solar Cells (a) 629 (b) 0.2 0.4 0.6 0.8 μm 0.2 0.4 0.6 0.8 μm Figure 10 AFM images of two InAs/GaAs QD layers grown by MBE The growth conditions applied in sample (a) have allowed the achievement of high size uniformity, contrarily to the case of sample (b) The vertical dimension is overestimated in the pictures (the dot’s height is actually smaller than the base) When the QDs are buried with a GaAs layer, their morphology typically changes These pictures are a courtesy of the University of Glasgow equilibrium Using δ-doping, it is, in principle, possible that most QDs are semi-filled with electrons, except those located at the extremes of the IB material, which are embedded in the space charge region (SCR) Most of the QD-IBSCs that have been fabricated to the moment use InAs as dot material and GaAs as host material [56–64] InAs and GaAs present a relatively large difference in lattice constant When an InAs layer is epitaxially deposited on a GaAs layer QDs form spontaneously (self-assemble) because islanding allows some elastic relaxation of the strain induced by lattice mismatch [65] In particular, the growth takes place in the Stranski–Krastanov mode [66], which means that a part of the InAs material forms a thin layer (the so-called ‘wetting layer’ (WL)) and the 3D islands grow on top of it Figure 10 shows atomic force microscope (AFM) images of uncapped InAs QDs grown on GaAs by this method using molecular beam epitaxy (MBE) The successive deposition of In(Ga)As and GaAs layers has been widely used since the middle 1990s to fabricate QD arrays It has been shown that the islands can be coherently strained (i.e., no dislocations) and pretty uniform in size [67] The fabrication of In(Ga)As/GaAs QD arrays is now widely used to implement infrared (IR) detectors [68] and lasers [69, 70] Of course, there are limitations to the size and morphology of QDs that can be grown, as we will discuss later in Section 1.29.4.4 The InAs/GaAs QD material system is not optimal for the implementation of an IBSC The gap of GaAs is 1.42 eV, much lower than the IBSC optimum according to the ideal models Furthermore, the effective gap (EG*) of the QD material is reduced by the offset between the VB maxima of InAs and GaAs (see Figure 9(b)) This material system has been chosen for the implementation of the first QD-IBSC prototypes mainly because there is a wide previous experience in its fabrication It is interesting to review why QDs, not quantum wells (QW), are proposed to implement IBSCs A QW is a thin layer of material where confinement only takes place in the growth dimension It is easier to fabricate, since strain fields to not play such a relevant role as for QDs It is known that in both cases band-to-band recombination (of confined electrons with confined holes, also called ‘excitonic’ recombination) is of dominant radiative nature But in the case of a QD, the density of states is δ-like, as illustrated by eqn [12], while in a QW the lack of confinement in the transversal dimensions leads to the formation of continuous sub-bands In a QD there are gaps with zero density of states that separate the levels from each other and also from the continuous states of the bulk semiconductor bands (see Figure 11) If these gaps are larger than the energy of optical phonons, carrier relaxation from one state to a lower state by interaction with a single phonon is ruled out due to energy non-conservation Therefore, the relaxation times for excited carriers to the fall to the ground-state should be much larger than in the case of QWs (see Figure 11) This phenomenon, usually called phonon-bottleneck effect (PBE) [71–73], can be used to prevent fast thermalization of carriers from the CB to the IB as required in the IBSC context In the case of self-assembled InGaAs/GaAs QDs relaxation times ranging from ns to 10 ps have been reported [74] However, several works (see [75] for a literature review) point out that in real QDs at room temperature some mechanisms can appear that introduce paths for fast relaxation, such as inelastic multi-phonon and second-order electron-phonon processes [76, 77], coupling to defect states [78], coupling to the 2D states of the WL [79], electron–electron scattering [80, 81], and very importantly, electron–hole scattering [82, 83] In fact, the results obtained in InAs/GaAs QD-IBSCs that we will discuss later in this Chapter show that the relaxation/escape of carriers between CB and IB are too strong to achieve proper IBSC behavior at room temperature With respect to the absorption properties of QDs, it has been shown that QDs enable the absorption of photons both in excitonic and intra-band transitions (see Figure 11) It is of particular importance for photovoltaic applications that in the case of 630 Energy Energy Technology Intraband photon absorption Interband (excitonic) photon absorption Intraband relaxation Interband photon emission Interband photon absorption Quantum dot DOS Interband photon emission Quantum well DOS Figure 11 Density of states (DOS) and band structure of a QD (left) and a QW (right) Some of the numerous possible transitions are shown It is remarked the fact that optical intraband transitions under normal incidence are allowed for electrons confined in the QD, but not for electrons confined in the QW, and also that fast relaxation of confined electrons has a higher probability in the QW electronic intra-band transitions light can be also absorbed in normal incidence [84–86], and not only when it propagates parallel to the growth plane, as it is the case of QWs [87] However, it must be taken into account that the density of dots is rather low when compared to the atomic density of bulk semiconductors (in current In(Ga)As/GaAs QD arrays it is typically ≤ 1017 cm−3) Then, the resulting volumetric absorption coefficient in the transitions only allowed inside the dots can be low and selective light trapping techniques may be required for the implementation of IBSCs of really high efficiency 1.29.4.2 QD-IBSC Prototypes Figure 12 shows some examples of QD-IBSC structured designed and fabricated by University of Glasgow/IES-Universidad Politécnica de Madrid [63, 64, 88–95] The structure depicted in Figure 12(a) is an older one, which includes a GaAs n-emitter, a GaAs p-emitter, and Si δ-doping for half-filling the QDs as explained above It contains a QD stack of 10 layers Attempts to grow more layers failed due to strain build-up and emitter degradation [90] Another problem observed while the structure shown in Figure 12(a) was studied was that the whole QD stack was immersed in the SCR of the junction [88] Under these circumstances, only the QDs of a few layers will be semi-filled with electrons (the ones for which the Fermi level crosses the electron ground states), while the rest will be either completely full or empty According to the ideal IBSC theory, full QDs are ineffective for VB–IB photon absorption processes and the empty ones are ineffective for photon absorptions that should cause transitions from the IB to the CB In addition, tunneling of carriers from the QD confined states to the CB is possible in this structure, which makes voltage preservation impossible (this will be further discussed in the next section) These problems can be solved by inserting a thin, conventional n-layer adjacent to the p-emitter and a thin p-layer next to the n-emitter to sustain the built-in field [12] This kind of layers are called ‘field damping layers’ (FDLs) and the way to optimize their design for a certain QD-IBSC structure has been expounded in detail in Reference 96 The structure in Figure 12(b) includes FDLs Finally, the third possibility shown in Figure 12(c) has thicker GaAs spacers between the QD layers (84 vs 10 nm) This possibility constitutes an alternative solution to the tunneling problem [94] A second motivation for the insertion of thick spacers in the QD-IBSC structure is to allow the dilution of the strain produced by the deposition of a QD layer before the next layer is grown This is expected to avoid the formation of defects by inelastic strain relaxation, improving the general material quality, and preventing the emitter degradation found in our previous batches Hence, it seems that it is possible to grow a high number of QD layers using this new approach, without the need of implementing strain compensation growth techniques Some QD-IBSC designs reported in the literature implement strain compensation strategies in order to avoid strain built-up effects They consist in using as spacer material GaNAs [59] or GaAsP [57, 58, 60] The lattice constant of the alloy is smaller than that of InAs, so that the averaged lattice constant of the InAs QD layer + spacer system is similar to the GaAs substrate lattice constant [97] Although the application of strain compensation methods has been very useful in some cases to increase the VB–IB sub-bandgap absorption, it may compromise other aspects of the QD-IBSC performance, in particular the always problematic split between IB and CB The use of GaNAs reduces the EL gap [59] In Reference 60, it is noted that the conditions needed to achieve strict strain-balance using GaAsP in thin spacers (< 20 nm) also leads to a narrower EL gap Intermediate Band Solar Cells (a) Cap nm un-GaAs Window layer ARC 631 Front metal grid 50 nm p+ - GaAs 100 nm p-emitter 200 nm InAs QD (2.7 ML) 10 X QD stack 110 nm Si δ-doping × 1010 cm–2 Spacer 5+5 nm Wetting layer 300 nm n-emitter Buffer layer 100 nm Substrate Rear metal (c) (b) Cap nm un-GaAs ARC front metal grid 19 –3 p - GaAs (Be × 10 cm ) contact layer Window layer 40 nm p-emitter Cap nm ARC front p-GaAs metal grid Window layer 900 nm FDL p-emitter InAs QD (3.2 ML) Si δ-doping 104 nm × 1010 cm–2 Spacer + 3.5 nm Wetting layer 2.5 ML InAs + 8.5 nm spacer 100 nm + seed FDL 3100 nm n-emitter BSF Buffer layer 30 x QD stack p++ - GaAs (Be 2.5 × 1019 cm–3) contact layer 30 nm 900 nm InAs QD (2.4 ML) + nm In0.20Al0.20Ga0.60As 170 nm 10 X QD stack Rear metal ++ GaAs 2655 nm high T Spacer 75 nm low T Spacer 4.5 + 4.5 nm Si δ-doping × 1010 cm–2 BSF 200 nm Buffer layer 500 nm Rear metal Substrate 200 nm 500 nm Substrate Figure 12 Evolution during the last years of the InAs/GaAs QD-IBSC prototypes fabricated by University of Glasgow/IES – Universidad Politécnica de Madrid The first sample in (a) has a simple structure with 10 QD layers separated by thin spacers In (b), field dumping layers were introduced to put the QD stack in a flat band region Another possibility is to use thicker GaAs spacers as shown in (c) In this last structure, the number of layers could be increased to 30 because the thicker spacer dilutes the strain 1.29.4.3 Proof of the Concept The quantum efficiency (QE) of the very early QD-IBSC devices already showed the production of photocurrent for below bandgap energy photons (Figure 13) However, this result does not necessarily mean that they are behaving according to the IBSC model It is possible that the monochromatic photons used in the QE measurement are only absorbed in one sub-bandgap transition, and that the photocurrent is extracted because carriers escape (thermally or by tunnel) to the other band instead of undergoing a second photon absorption In particular, in the case of InAs/GaAs QDs it was expected that the IB-CB optical transition could be supplanted by thermal escape, since the EL gap is so small in this structures (more details about this problem are given in the next section) As discussed when presenting the IBSC model, under that situation the principle of voltage preservation cannot be achieved, which states that the output voltage of an IBSC is limited by the wider bandgap EG, and not by the sub-bandgaps EL or EH The QD-IBSC prototype behaves then just as a solar cell with tailored bandgap and is subjected to the Shockley-Queisser limit 632 Technology Absolute external quantum efficiency QD-IBSC GaAs reference 0,1 300 K 0,01 1E-3 1E-4 1E-5 1E-6 1E-7 400 600 800 1000 1200 Wavelength λ (nm) 1400 1600 Figure 13 Example comparing the quantum efficiency of a quantum dot InAs/GaAs solar cell and a GaAs single-gap control cell Extracted from Antolín E, Martí A, Stanley CR, et al (2008) Low temperature characterization of the photocurrent produced by two-photon transitions in a quantum dot intermediate band solar cell Thin Solid Films 516: 6919–6923 [92] It was necessary to define and perform two proof-of-concept experiments to clarify whether InAs/GaAs QDs have the potential to fulfill the IBSC principles Both were conducted at low temperatures and showed a positive result after optimization of the QD stack and QD-IBSC design Now the goal is to improve the quality of IB materials to achieve similar properties at room temperature The first experiment aimed to proof unambiguously that the QD-IBSC is capable to produce photocurrent due to “two sub­ bandgap photon absorption”, that is, electron–hole pairs generated by the confluence of the absorption of one sub-bandgap photon in a VB → IB transition and the absorption of another sub-bandgap photon in an IB → CB transition In the demonstrative experiment the QD-IBSC prototype was illuminated with two light sources: one of them (the primary source) with variable photon energies between EH and EG, the other (the secondary source) with fixed photon energies between EL and EH To distinguish the photocurrent produced by any of them or by their confluence, the secondary source was frequency modulated while the primary (see Figure 14) Also, the photocurrent was extracted under short-circuit conditions to discard photoconductive effects A repre­ sentative result of this experiment is given in Figure 14 Further details can be found in References [89, 91, 92] The second experiment showed that properly designed QD-IBSCs are capable of achieving an open-circuit voltage (VOC) that surpasses the energy (divided by the electron charge) of the sub-bandgap photons that it absorbs This constitutes a measurable confirmation of the voltage preservation principle of the IBSC model Figure 15 shows results of this experiment when applied to two different QD-IBSC prototypes (from [95]): plot Figure 15(b) corresponds to the prototype depicted in Figure 12(a) and plot Figure 15(c) corresponds to Figure 12(c) Finally, Figure 15(a) shows the behavior of a GaAs reference cell In the case of the reference cell, the VOC (black circles) increases as the temperature is lowered, approaching EG (solid black line) The QD-IBSC in Figure 15(b) shows proper IBSC voltage preservation, since its VOC also approaches EG although EH is much lower (red line) The values of EH have been extracted from QE measurements and they are not plotted for lower temperatures because the sub-bandgap QE is suppressed This fact is in itself a demonstration that thermal escape from the IB to the CB has been suppressed The QD-IBSC prototype in Figure 15(c) does not behave as a proper IBSC even at the lowest temperatures, since its VOC is limited by the position of the IB This problem has been explained by the existence of tunneling mechanisms that let carrier escape from the IB to the CB independently of the temperature 1.29.4.4 Strategies to Boost the Efficiency of the QD-IBSC In this section, we will review the limitations found in the InAs/GaAs QD system for implementation of a QD-IBSC We will also review the strategies that are being explored in order to achieve a QD-IBSC capable of operating with high efficiency at room temperature First, the gap of GaAs, 1.4 eV, is too low to fabricate a very efficient IBSC A gap of about eV would be required But this is not the only limiting factor Most of the problems of the InAs/GaAs-based IBSC are strain related The QD synthesis is based on the Stranski–Krastanov (S-K) growth mode, in which nano-islands nucleate on top of a thin WL with certain critical thickness [65] This process is triggered by the elastic relaxation of the strain that appears between the two materials, which have a large lattice mismatch However, as depicted in Figure 16, the band diagram is severely affected by the presence of strain The InAs gap is blue-shifted from 0.36 to $0.7 eV, and the sub-gaps become extremely asymmetric: EH is typically over eV, while EL is in the range of 0.2 eV This makes that the electron populations of CB and IB (i.e., εFe and εFIB) cannot be split at room temperature The situation is worsened because the Intermediate Band Solar Cells (a) Chopper IR source GaSb filter 633 Halogen lamp Filter wheel To preamp and lock-in Sample (inside cryostat) Monochromator (primary source) (b) 10–4 EG EL Photocurrent (Acm–2) 10–5 10–6 Response to primary (Curve 1) EH 10–7 IR on (Curve 3) 10–8 Noise background (IR off-Curve 2) 10–9 10–10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Primary beam energy (eV) Figure 14 (a) Modified quantum efficiency setup suitable to demonstrate the production of photocurrent from the absorption of two below bandgap energy photons (b) Results of the measurement showing the photocurrent produced in the QD-IBSC samples as a function of the energy of the photons of the primary light source Curve (response to primary) represents the photocurrent produced when pumping with the chopped primary source only (cell biased at –1.5 V, T = 4.2K) Curve (noise background) is the photocurrent measured when the IR source is off while the chopper, located in front the of the IR source, is kept spinning (cell biased at V, T = 36K) Curve (IR on) is the photo-generated current when the IR source is turned on and chopped (cell biased at V, T = 36K) Extracted from Martí A, Antolin E, Stanley CR, et al (2006) Production of photocurrent due to intermediate-to-conduction­ band transitions: A demonstration of a key operating principle of the intermediate-band solar cell Physical Review Letters 97: 247701–247704 [89] strain also induces a degradation of the shape of the dots, which tend to have a very wide base and small height This shape results in a high number of extra confined states for electrons We have identified that this situation reduces the absorption in intraband (IB → CB) transitions [98] and enhances the thermal connection between IB and CB [99, 100] Besides, the existence of a WL also degrades the QD material properties because it contributes to a fast nonradiative relaxation of carriers from the CB to the IB [99] The fact that the quasi-Fermi levels εFe and εFIB cannot be split at room temperature is a fundamental drawback of present QD-IBSC prototypes It explains why voltage preservation could be realized only for the moment at low temperatures [95] With these considerations in mind, there are two possible strategies for the development of the QD-IBSC One is to continue using the III-V S-K approach, but with introducing important variations in the QD material system To maintain the S-K approach means most likely to keep fighting the effects of strain with techniques as reported in References 57–60 The second strategy is to move away from the InAs/GaAs QD family toward a completely different set of materials We will give some examples of these two approaches in the following two subsections 1.29.4.4.1 Improved InAs/GaAs QDs One possibility to enlarge the IB–CB gap in order to reduce thermal escape and improve optical absorption is the capping of the InAs QDs with a thin InAlGaAs strain relief layer [94] It has been demonstrated in the context of QD lasers and LEDs that the use of InGaAs or InAlGaAs SRLs is an effective method to red-shift EH [101–105] It has been proposed that this red-shift is produced by an increase in the effective height/size of the QDs in the presence of an SRL [102–104] and also that the reduction of the local strain in the QDs may avoid, to some extent, the blue-shifting of the InAs bandgap energy [101, 105] However, for the QD-IBSC application, the red-shift of EH alone is not a solution if EL is not increased at the same time For example, if an InGaAs SRL was applied, the SRL would form a QW adjacent to the dots The EH gap would be reduced due to strain relief, but the effective value of EL would not be as much increased, since the presence of the InGaAs QW would lower the effective CB minimum To avoid this possibility, in the samples it is necessary to produce a quaternary SRL where the Inx(AlyGa1 – y)1 – xAs composition has been tuned to achieve a negligible CB offset with respect to GaAs [106] Technology (b) 1.6 1.4 1.4 1.2 1.2 Energy (eV) (a) 1.6 Energy (eV) 634 1.0 0.8 QD-IBSC S1 e V oc (HI) e V oc (MI) e V oc (LI) GaAs gap QD ground state transition QD 1st excited state transition 0.8 0.6 0.6 GaAs ref GaAs gap e V oc 0.4 0.2 1.0 0.4 0.2 50 100 150 200 Temperature (K) (c) 250 300 50 100 150 200 Temperature (K) 250 300 1.6 1.4 Energy (eV) 1.2 1.0 0.8 0.6 Sample GaAs gap e V oc QD ground state transition 0.4 0.2 50 100 150 200 Temperature (K) 250 300 Figure 15 Comparison between open-circuit voltage (filled black dots) and location of the intermediate band energy levels (blue and red lines) at different temperatures for: (a) a GaAs reference cell, (b) QD-IBSC in which thermal and tunnel escape from the IB to the CB is not effectively suppressed and (c) QD-IBSC in which thermal and tunnel escape from the IB to the CB is effectively suppressed The GaAs bandgap connected line is shown for reference Thermal escape Effective CB minimum IB EL ~ 0.2 eV EG [GaAs] 1.42 eV WL Effective EG ~ 1.2 eV EH ~ 1.0 eV EG [strained InAs] ~ 0.7 eV EG [InAs] 0.36 eV Effective VB maximum Figure 16 Simplified InAs/GaAs QD band diagram including the effects of strain and the WL On the left are shown the corresponding effective bandgaps of an IBSC fabricated with that QD material system On the right is included the band diagram of bulk (unstrained) InAs for comparison Intermediate Band Solar Cells 635 In Reference 94, QD-IBSCs have been fabricated using this capping technique and it was possible to estimate the thermal escape activation energy, EA, from the thermal dependence of sub-bandgap QE An enhancement of EA indicates that the thermal carrier escape is weaker It was found that EA = 224 meV in samples with InAlGaAs capping, to be compared with 115 meV for the samples where QDs are directly buried in GaAs The increase of more than 100 meV in EA was related to the following observed changes in the electronic configuration: (1) the red-shift of the VB–IB gap, (2) the augmentation of the energy difference between the QD ground-state transition and the first transition involving excited states, and (3) the blue-shift of the WL absorption edge (due to the substitution of In atoms in the WL by Al atoms) The values for (1) and (2) are 0.974 eV and 101 meV in the samples with SRLs Although these results are encouraging from the point of view of the electrical problem, it is doubtful that the InAlGaAs capping can introduce notable room of improvement with respect to the optical problem, that is, the weak absorption between IB and CB Figure 17 presents high magnification TEM images of the InAlGaAs-capped QDs compared to QDs directly capped with GaAs The dimensions of a significant number of QDs were measured on those images, leading to the histograms and the average values for width and height that can be seen at the bottom of the figure The conclusion is that the aspect ratio has been improved because the height has been increased, but the base has not been reduced According to theoretical modeling [98], the intraband transitions in these QDs are stronger between adjacent confined levels Therefore, it would be boosted if we could split more confined levels, which would require a reduction of the base Further experiments are needed in order to see whether a lower InAs content could lead to smaller dots with a similar aspect ratio Other modifications of the classical InAs/GaAs QDs are also being considered to improve the band diagram enlarging the separation between IB and CB One example is to add N to the dot and substitute the GaAs host by a wider gap material (GaInP or AlGaAs) as proposed in Reference 107 1.29.4.4.2 Non-Stranski–Krastanov QDs In this section, we will present a different family of epitaxial QD materials, the lead salt QD materials, which are synthesized by a completely different technique than the S-K method In this case, the QD and host materials have closely matched lattice parameters Both have the same face-centered cubic symmetry, but the bonding configuration is different: lead salts crystallize in the sixfold coordinated rocksalt lattice and the host materials in the fourfold coordinated zincblende lattice This lattice-type mismatch results in a large miscibility gap, that is, for a range of synthesis temperatures, lead salt QDs precipitate in the host zincblende material The most studied IV-VI/II-VI QD material system is PbTe/CdTe The QDs are typically synthesized in a two-step method: first, a PbTe/CdTe multilayer stack is epitaxially grown, and second, the material is annealed to make the QDs precipitate [108] In this approach the size of the dots is determined by the thickness of the PbTe layers grown Diameters as small as nm and areal densities over 1011 cm−2 can be achieved from a nm PbTe epitaxial layer [109] It has been demonstrated that PbTe/CdTe QDs are WL-free and can have highly centrosymmetric shapes (almost spherical) [108], they have atomically sharp interfaces [110] and they are strongly luminescent up to over 400K [110–112] Figure 18 illustrates how a QD-IBSC would be produced using this method The main advantage of this system is that the lack of strain between the QD and the host eliminates the problems illustrated in Figure 16 for the InAs/GaAs QD system Thus, the QD material gap is not blue-shifted This, together with the possibility of growing small, centrosymmetric QDs (aspect ratio $ 1) [108, 110–112], is expected to provide an advanta­ geous band diagram for IBSC implementation: EH and EL can be maximized, while the number of undesired extra confined states can be minimized In a more optimized design, it has been proposed that PbTe QDs could be embedded in a Cd1−xMgxTe alloy to fabricate a high efficiency IBSC [113] It has been calculated an efficiency limit of 60.7% for Cd0.7Mg0.3Te as host material under maximum concentration The reason to add Mg to the host material is twofold On the one hand, it increases the host gap, making it approach eV, which increases the detailed balance efficiency limit of the IBSC On the other hand, it improves the lattice-matching between QD and host (see Figure 19) Other possibilities include embedding PbSe dots in a CdSe or ZnTe matrix, or embedding PbS QDs in a CdS1−xSex or ZnSe1−xTex host The three families are marked by the red boxes on Figure 19 1.29.5 Summary The operation of the IBSC is first reviewed in this chapter The principles of two-photon sub-bandgap photocurrent and voltage preservation are explained, showing how they lead to the theoretical efficiency limit of 63.2% The two possible implementations of the IBSC, using impurity doping and QDs, are presented In both cases, multiple references are given for different theoretical and experimental works where IB materials and devices have been tested It is explained how it is expected to mitigate nonradiative recombination in impurity-doped IB materials by increasing the impurity density With regard to the QD implementation, the design and properties of to-date fabricated prototypes are described, as well as the proof-of-concept experiments that have allowed the demonstration of the principles of two-photon sub-bandgap photocurrent and voltage preservation at low temperatures The reasons why those experiments are not successful at room temperature using InAs/GaAs QDs have been analyzed and some alternative QD materials have been proposed 636 Technology 20 nm 20 nm InAs QDs burried directly with GaAs spacer InAs QDs capped with a nm InAlGaAs SRL 20 20 15 15 10 10 5 0 10 15 20 25 30 10 35 15 20 Base length (nm) 25 30 35 40 Base length (nm) 18 14 16 12 14 10 12 10 8 6 4 2 0 Height (nm) 6 Height (nm) Average values: Width = 20 ± nm Height = 4.0 ± 0.7 nm Average values: Width = 21 ± nm Height = 6.5 ± 1.0 nm Figure 17 Comparison between the morphology of InAs QDs capped only with GaAs (on the left) and InAs QDs capped with a thin InAlGaAs layer before depositing the GaAs spacer (on the right) In both cases, the QDs are formed by depositing 2.4 ML of InAs under the same conditions The top images have been obtained by high angular annular dark field scanning transmission electron microscopy (HAADF-TEM), a technique which is suitable for extracting reasonably accurate QD dimensions The histograms show the occurrence of QDs dimensions in nm for the two samples and the corresponding average values and standard deviations are given below The images and morphological data are a courtesy of Tersa Ben and Sergio I Molina, University of Cádiz p CdTe p CdTe CdTe barriers PbTe/ CdTe QDs CdTe PbTe n CdTe Annealing n CdTe Buffer Buffer n GaAs or GaSb substrate n GaAs or GaSb substrate Figure 18 Example of a lead salt QD-IBSC structure using PbTe/CdTe QDs as IB material, and CdTe p- and n-emitters Intermediate Band Solar Cells 4.5 Direct gap 637 Indirect gap MgSe 4.0 ZnS MgTe Bandgap energy (eV) 3.5 3.0 ZnSe CdS AlP GaP 2.5 ZnTe AlAs 2.0 CdSe AlSb GaAs 1.5 CdTe InP Si 1.0 GaSb Ge PbS* 0.5 InAs PbSe* PbTe* InSb 0.0 0.54 0.56 0.58 0.60 0.62 0.64 0.66 Lattice parameter (nm) Figure 19 Bandgap vs lattice parameter map, including most used binary compounds of the III-V, II-VI, and VI-VI families, and the diamond-like semiconductors Si-Ge All values correspond to the zincblende structure, except those marked with *, which correspond to the rocksalt crystal structure Acknowledgments This work was funded by the European Commission under the project Ibpower (Contract 211640) The authors are indebted to collaborators in their research group for assistance and fruitful discussion: P G Linares, I Ramiro, E López, E Hernández, I Artacho, C Tablero, D Fuertes-Marrón, M J Méndes, A Mellor, and I Tobías C R Stanley and C D Farmer (University of Glasgow, UK) are acknowledged for the growth and processing of many samples discussed here, and S I Molina and T Ben (Universidad de Cádiz, Spain) for TEM characterization E A is grateful to Prof J Phillips and the University of Michigan for hosting her during part of the duration of this work References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] Green MA, Emery K, Hishikawa Y, et al (2011) Solar cell efficiency tables (version 38) Progress in Photovoltaics: Research and Applications 19: 565–572 Shockley W and Queisser HJ (1961) Detailed balance limit of efficiency of p-n junction solar cells Journal of Applied Physics 32: 510–519 Arẳjo GL and Martí A (1994) Absolute limiting efficiencies for photovoltaic energy conversion Solar Energy Materials & Solar Cells 33: 213–240 Luque A and Martí A (2008) Ultra-high efficiency solar cells: The path for 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(Acm–2) 10 –5 10 –6 Response to primary (Curve 1) EH 10 –7 IR on (Curve 3) 10 –8 Noise background (IR off-Curve 2) 10 –9 10 10 0.0 0.5 1. 0 1. 5 2.0 2.5 3.0 3.5 Primary beam energy (eV) Figure 14 (a)... QDs capped with a nm InAlGaAs SRL 20 20 15 15 10 10 5 0 10 15 20 25 30 10 35 15 20 Base length (nm) 25 30 35 40 Base length (nm) 18 14 16 12 14 10 12 10 8 6 4 2 0 Height (nm) 6 Height (nm) Average... [1] [2] [3] [4] [5] [6] [7] [8] [9] [10 ] [11 ] [12 ] [13 ] [14 ] [15 ] [16 ] [17 ] [18 ] [19 ] [20] Green MA, Emery K, Hishikawa Y, et al (2 011 ) Solar cell efficiency tables (version 38) Progress in Photovoltaics: