**1. Introduction**

High-efficiency solar cells are of interest to further decrease the cost of solar energy. Conventional solar cells are based on single junction semiconductor structures and its efficiency limit is constrained by the Shockley-Queisser limit [1] to 31%. Among the several concepts for ultra-high-efficiency photovoltaic cells, in this chapter will be presented two: quantum well solar cell and superlattice solar cells.

These approaches consist of a p-i-n solar cell of wider bandgap semiconductor (called barrier or host material) with several very thin layers of another semiconductor of lower bandgap inserted into the intrinsic region, which constitutes multiple quantum well or superlattice system. The photon absorption is then enhanced to lower energies than the bandgap of the host material, adressing one of the fundamental losses of single-junction solar cells, improving the spectral response of the solar cell in the energy region below the absorption edge of host material.

This idea was pioneered by Barnham and Duggan in 1990 [2] when they proposed the quantum well solar cell (QWSC). The superlattice solar cell (SLSC) is a more recent proposal [3], which extends the QWSC concept to the case when tunneling probability of photogenerated carriers of adjacent wells is greatly increased, and the carriers are no longer localized in individual wells. Both approaches are based on the use of nanotechnology, by the exploiting of the quantum effects of the nanostructures presented, therefore the proper understanding and calculation of the quantum effects on the solar cell operation parameters is of crucial importance.

Improving the spectral response of the cell by absorbing low energy photons from the solar spectrum is important in order to obtain extra photocurrent and therefore an increment in the short-circuit current. Nevertheless, a drop in open circuit voltage (*VOC*) of the device has been observed, due to carrier losses caused by inclusion of lower bandgap material and the interfaces, but this voltage loss could be overcompensated by the increased short-circuit current (*ISC*) from the quantum wells as has benn demonstrated by Nelson et al[4].

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In the quantum well solar cell, as the quantum wells are inserted in the intrinsic region, the built-in electric field of the depletion layer drives to an efficient collection of carriers photo-generated in the wells. Quantum efficiency (QE) modeling showed that escape efficiency from the wells is practically unity[5], leading to an enhanced photo-current. In the case of SLSC, as the spuperlattice is obtained by tuning the quantum well width in order to maximise the tunnel probability between adjacent wells, the carriers are spreaded out through the whole superlattice via continuous minibands [6] and as a consequence obtain high conductivity and delocalisation of photogenerated carriers in the minibands decreasing the recombination. QWSC or SLSC can also be tuned, playing with material structure and compositions, in order to diminish the mistmatch between the incident spectrum and the spectral absorption properties of the device.

GaAs solar cells currently hold the world efficiency record for single-junction solar cells [7], hence the improvement of GaAs based solar cell could be important to enhance solar cell performance. The use of GaAs as host material for the design of a QWSC or SLSC would be, then, the best option. However, lattice mismatch issues place an upper limit on the quantity of quantum wells that can be contained in the intrinsic region before strain relaxation takes place, compromising the open circuit voltage. The first attempts included strained GaAs/InGaAs QWSCs, but they shown not enough quantum well absorption to increase the short-circuit current in order to overcome the loss in the Voc resulting from dislocations [8].

As a solution to the lattice mismatch problem was the insertion of strain-balanced GaAsP/InGaAs quantum wells and barriers into the intrinsic region [9]. The GaAsP/InGaAs strain-balanced quantum well solar cell (SB-QWSC) has shown an impressive performance, achieving 27% conversion efficiency at 320 suns concentration [10]. Furthermore, the SB-QWSC can offer some other advantages if used in a tandem, in the substitution of the current-limited GaAs cell in the design of high-concentration triple-junction cells which potentially could exceed the performance over the conventional metamorphic approach. These include: the absence of dislocations, dark-current dominated by radiative recombination at high incident light concentration, and so the possibility of using radiative recycling to enhance efficiency and the ability to optimize the middle cell absorption edge of the tandem for different spectral conditions.

Another novel material system proposed is the dilute nitride (GaIn)(NAs) lattice matched to GaAs. This compound is obtaining growing interest in recent years due to its very unique physical properties and a wide range of possible device applications. The band gap of GaAs decreases rapidly with the addition of small atomic fractions of nitrogen [11], besides the addition of In to GaNAs does not only provide a lattice matched material to GaAs and also decreases the band gap. A approach, using GaInNAs subcells, has been formulated to enhance the efficiency of existing triple and quadruple junction solar cells [12]. Nonetheless, so far, the poor minority carrier properties and doping issues specific to bulk dilute nitrides have frustrated the success of this approach. A different strategy has been published by Freundlich et al [13], where multiple quantum wells of GaNAs are growth inside the intrinsic region of conventional GaAs p-i-n solar cells. The authors showed a short-circuit current about 25 *A*/*m*<sup>2</sup> without anti-reflection coating (ARC) and open circuit voltages approximately 0.6 V, although much smaller than those reported for conventional GaAs solar cells, certainly due to high interface recombination as consequence of the lattice mismatch between GaAs and GaNAs layers.

In this chapter, we examine a general theoretical model for QWSC, which is applied to p-i(QW)-n QWSC of different material systems. Firstly we will apply it to an AlGaAs/GaAs QWSC, and will show that conversion efficiencies are significantly enhanced when compared with the corresponding AlGaAs baseline solar cell. Open circuit voltage, current densities, I-V curves and conversion efficiencies are calculated as function of the well and barrier band gaps, the width and depth of the wells, the number of the wells in the intrinsic region. We will take into account the light absorption by the energy levels in the quantum wells, and we show that for certain values of the studied parameters, the conversion efficiencies of the quantum well solar cell are higher than that of the corresponding homogenous p-i-n solar cell.

In the quantum well solar cell, as the quantum wells are inserted in the intrinsic region, the built-in electric field of the depletion layer drives to an efficient collection of carriers photo-generated in the wells. Quantum efficiency (QE) modeling showed that escape efficiency from the wells is practically unity[5], leading to an enhanced photo-current. In the case of SLSC, as the spuperlattice is obtained by tuning the quantum well width in order to maximise the tunnel probability between adjacent wells, the carriers are spreaded out through the whole superlattice via continuous minibands [6] and as a consequence obtain high conductivity and delocalisation of photogenerated carriers in the minibands decreasing the recombination. QWSC or SLSC can also be tuned, playing with material structure and compositions, in order to diminish the mistmatch between the incident spectrum and the

GaAs solar cells currently hold the world efficiency record for single-junction solar cells [7], hence the improvement of GaAs based solar cell could be important to enhance solar cell performance. The use of GaAs as host material for the design of a QWSC or SLSC would be, then, the best option. However, lattice mismatch issues place an upper limit on the quantity of quantum wells that can be contained in the intrinsic region before strain relaxation takes place, compromising the open circuit voltage. The first attempts included strained GaAs/InGaAs QWSCs, but they shown not enough quantum well absorption to increase the short-circuit current in order to overcome the loss in the Voc resulting from dislocations [8]. As a solution to the lattice mismatch problem was the insertion of strain-balanced GaAsP/InGaAs quantum wells and barriers into the intrinsic region [9]. The GaAsP/InGaAs strain-balanced quantum well solar cell (SB-QWSC) has shown an impressive performance, achieving 27% conversion efficiency at 320 suns concentration [10]. Furthermore, the SB-QWSC can offer some other advantages if used in a tandem, in the substitution of the current-limited GaAs cell in the design of high-concentration triple-junction cells which potentially could exceed the performance over the conventional metamorphic approach. These include: the absence of dislocations, dark-current dominated by radiative recombination at high incident light concentration, and so the possibility of using radiative recycling to enhance efficiency and the ability to optimize the middle cell absorption edge of

Another novel material system proposed is the dilute nitride (GaIn)(NAs) lattice matched to GaAs. This compound is obtaining growing interest in recent years due to its very unique physical properties and a wide range of possible device applications. The band gap of GaAs decreases rapidly with the addition of small atomic fractions of nitrogen [11], besides the addition of In to GaNAs does not only provide a lattice matched material to GaAs and also decreases the band gap. A approach, using GaInNAs subcells, has been formulated to enhance the efficiency of existing triple and quadruple junction solar cells [12]. Nonetheless, so far, the poor minority carrier properties and doping issues specific to bulk dilute nitrides have frustrated the success of this approach. A different strategy has been published by Freundlich et al [13], where multiple quantum wells of GaNAs are growth inside the intrinsic region of conventional GaAs p-i-n solar cells. The authors showed a short-circuit current about 25 *A*/*m*<sup>2</sup> without anti-reflection coating (ARC) and open circuit voltages approximately 0.6 V, although much smaller than those reported for conventional GaAs solar cells, certainly due to high interface recombination as consequence of the lattice

spectral absorption properties of the device.

152 Solar Cells - New Approaches and Reviews

the tandem for different spectral conditions.

mismatch between GaAs and GaNAs layers.

This theoretical model when applied to the study of AlGaAs/GaAs SLSC, also allows the determination of performance parameters (short-circuit current density, open-circuit voltage, and conversion efficiency) behavior as a function of absorption and recombination mechanisms. We present a comparative study between AlGaAs/GaAs SLSC and QWSC, which could predict the possible advantages for the use of the SLSC. A variably spaced semiconductor super-lattice was optimized to enhance the resonant tunneling between adjacent wells following the method reported by Reyes-Gómez et al. [14]. A discussion about the conditions where the SLSC performance overcomes that of QWSC is addressed. Our approach will be focused on examining the viability of the SLSC for its possible use and to clarify if they present advantages over QWSC.

Following, the model is then applied to a GaAsP/InGaAs/GaAs SB-QWSC, demostrating that high efficiency devices are feasible. Our model takes into account the influence of the strain over the energy bands of the material. The impact of tensile and compressive strain on the band structure for both conduction band and valence band are calculated in order determine the electron and hole dispersion relation *E*(**kB**). Similarly, the optical transitions in quantum well and barriers as a function of tensile and compressive strain are evaluated to calculate the quantum efficiency, dark current and photo-current and compared with experimental data. The broken degeneracy of the valence band due to the effect of the strain is also studied, which causes the suppression of a transition that contributes to photon emission from the edge of the quantum wells. We study both, the emission light polarized in the plane perpendicular (TM) to the quantum well which couples exclusively to the light hole transition and the emission polarized in the plane of the quantum wells (TE) which couples mainly to the heavy hole transition. It is found that the spontaneous emission rates TM and TE increase when the quantum wells are deeper. The addition of a distributed Bragg reflector can substantially increase the photocurrent while decreasing the radiative recombination current. We examine the impact of the photon recycling effect on SB-QWSC performance. Then, GaAsP/InGaAs/GaAs solar cell is optimized to reach the maximum performance by evaluating the current-voltage curves under illumination. Our model was used to determine the highest efficiencies for cells containing quantum wells under varying degrees of strain, but it could also allow the optimization of the photocurrent or the open circuit voltage in a triple-junction concentrator cell based on a SB-QWSC middle cell.

Another approach, where GaAs/GaInNAs multiple quantum wells and superlattice are added within the intrinsic region of conventional GaAs p-i-n solar cells is also presented. First, the model is applied to GaAs/GaInNAs QWSC in order to study the conversion efficiency as a function of nanostructure parameters as wells width and depth. On the other hand, a variably spaced superlattice structure was designed to enhance the resonant tunneling between adjacent wells after the method reported [3, 14] and J-V characteristic for this devices is obtained. The effect of the superlattice characteristics on the conversion efficiency is discussed. The SLSC conversion efficiency is compared with the maximum conversion efficiency obtained for the QWSC. Finally, we present GaAs/ GaInNAs SLSC conversion efficiency as a function of solar concentration, showing an clear increment in its performance.
