**3.1. AlGaAs/GaAs multiple quantum well and superlattice solar cell**

As a test of our model, we compare the QE calculated with the experimental values of G951 QWSC sample (*Al*0.33*Ga*0.67*As*/*GaAs*) from the Quantum Photovoltaics Group at Imperial College London [26]. Table 1 displays the pertinent features of several solar cells that were used to compare our model with experimental parameters. The absorption coefficient of *AlxGa*1−*xAs* bulk solar cell was determined from the GaAs spectrum *<sup>α</sup>*(*λ*), using the same nonlinear shift of the energy axis reported by M. Paxman et al. [5].

The expressions for the generation of the bulk absorption coefficient and the values of AlGaAs parameters used in the calculation are obtained from reference [15]. The internal quantum efficiency for G951 QWSC is calculated as function of energy and is compared to experimental curve shown in Figure 3, where is shown a good agreement between experimental and modeled spectra. In the calculations only the QWSC growth and material parameters were used, without any fitting parameter. The deconvolved spectra in Figure 3 clearly show that the absorption edge of the QWSC is shifted to lower energies due to the existence of quantum wells in the intrinsic region, and increases the QE values in the short wavelength region and consequently the short-circuit current will increase.


**Table 1.** Details of cells structures

Good fit between modeled and experimental QE spectra was also observed for all solar cells reported in Table 1. The photocurrent calculated by equation (7) is compared with the experimental values in Table 2 and also show good agreement as the difference between theoretical and experimental values did not exceed 10%.

**Figure 3.** Experimental and modeled IQE for G9551 QWSC. The contributions from p, i, and n layers are separated.

We also compared the calculated open-circuit voltages with experimental shown in table 3 for four QWSCs, showing a good agreement between experimental and calculated values.

used to compare our model with experimental parameters. The absorption coefficient of *AlxGa*1−*xAs* bulk solar cell was determined from the GaAs spectrum *<sup>α</sup>*(*λ*), using the same

The expressions for the generation of the bulk absorption coefficient and the values of AlGaAs parameters used in the calculation are obtained from reference [15]. The internal quantum efficiency for G951 QWSC is calculated as function of energy and is compared to experimental curve shown in Figure 3, where is shown a good agreement between experimental and modeled spectra. In the calculations only the QWSC growth and material parameters were used, without any fitting parameter. The deconvolved spectra in Figure 3 clearly show that the absorption edge of the QWSC is shifted to lower energies due to the existence of quantum wells in the intrinsic region, and increases the QE values in the short

Cell Cap p layer p doping n layer n doping i layer well well width (*µm*) (*µm*) (*cm*−3) (*µm*) (*cm*−3) (*µm*) number (*µm*)

G946 0.017 0.15 1.3 <sup>×</sup> <sup>10</sup><sup>18</sup> 0.46 1.3 <sup>×</sup> 1018 0.51 50 8.5 QT76 0.02 0.3 7.0 <sup>×</sup> <sup>10</sup><sup>17</sup> 0.6 3.0 <sup>×</sup> 1017 0.48 30 8.7 G951 0.02 0.15 1.3 <sup>×</sup> <sup>10</sup><sup>18</sup> 0.46 1.3 <sup>×</sup> 1018 0.81 50 8.5 QT468A 0.04 0.15 9.0 <sup>×</sup> <sup>10</sup><sup>17</sup> 0.6 2.5 <sup>×</sup> 1017 0.48 30 8.4 QT229 0.045 0.5 2.0 <sup>×</sup> <sup>10</sup><sup>18</sup> 0.5 6.0 <sup>×</sup> 1018 0.80 50 10.0 QT468B 0.02 0.15 9.0 <sup>×</sup> <sup>10</sup><sup>17</sup> 0.6 2.5 <sup>×</sup> 1017 0.48 0 0 CB501 0.02 0.15 9.0 <sup>×</sup> <sup>10</sup><sup>17</sup> 0.6 9.0 <sup>×</sup> 1017 0.31 1 5.0

Good fit between modeled and experimental QE spectra was also observed for all solar cells reported in Table 1. The photocurrent calculated by equation (7) is compared with the experimental values in Table 2 and also show good agreement as the difference between

> Sample G951 Model p−zone Model i−zone Model n−zone Model Total Experimental

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2

Energy (eV)

**Figure 3.** Experimental and modeled IQE for G9551 QWSC. The contributions from p, i, and n layers are separated.

nonlinear shift of the energy axis reported by M. Paxman et al. [5].

wavelength region and consequently the short-circuit current will increase.

**Table 1.** Details of cells structures

164 Solar Cells - New Approaches and Reviews

theoretical and experimental values did not exceed 10%.

0

0.1

0.2

0.3

Quantum Eciency

0.4

0.5

0.6

The influence of the quantum well width and the barrier band gap energy upon the normalized efficiency *η*∗ is shown in Figure 4. We define the *η*∗ as the ratio between *AlxGa*1−*xAs*/*GAs* QWSC efficiency and baseline p-i-n solar cell efficiency. The best values for *η*∗ are obtained for shallow and wider wells with an efficiency enhancement of about 15%. Increasing the quantum well thickness also increases the normalized efficiency until saturation. For high barrier Al concentration the normalized efficiency grows more quickly with the increase of *LW*. The *η*<sup>∗</sup> have a maximum value for 15 wells of 15 nm width using *Al*0.1*Ga*0.9*As*/*GaAs* QWSC, with and approximately 20% of efficiency enhancement between the QWSC and its equivalent baseline cell. On the other hand, the increase of Al composition in the barrier, that means deeper wells, is detrimental for *η*∗.

**Figure 4.** AlGaAs/GaAs QWSC normalized efficiency as a function of the quantum well width and the barrier band gap energy for *NW* = 20.

On the other hand, the expected high efficiency of the SLSC not only depends on the material and structure quality, ensuring minimum non-radiative recombination losses at the bulk and the interfaces, but it also depends on the escape rate of photogenerated carriers out of the clusters into the n and p-regions having minimum radiative losses within minibands.

We looked for recombination mechanisms in an SLSC and compared them with the same mechanisms in an QWSC. Using Equations (2)-(3) , we calculated radiative enhancement ratio, non-radiative enhancement ratio, and the interface recombination current for the SLSC (Figure 2(b)). These coefficients are function of the effective density of states and the absorption coefficient, which depend on the electron miniband width. Similar calculations were carried out for an QWSC with 15-nm well width and 24 wells in the intrinsic region (Figure 2(a)) where the efficiency reaches a maximum, which is always higher to the corresponding homogeneous p-i-n cell without quantum wells, as it was shown in a previous study [3].


**Table 2.** Experimental and calculated photocurrent of AlGaAs QWSCs.

**Figure 5.** (*Jsc* − *Jsc*0)/*Jsc*<sup>0</sup> and (*Voc*<sup>0</sup> − *Voc*)/*Voc*<sup>0</sup> as a function of electron miniband width. *Jsc*<sup>0</sup> and *Voc*<sup>0</sup> were calculated for Γ*e* = 1 meV.

In the case of the AlGaAs/GaAs SLSC, the effective density of states and the absorption coefficient were calculated using the AlGaAs parameters reported in Table 2 of reference [15]. The short-circuit current density *JSC* and the open-circuit voltage *VOC* were determined using Equation (1) and showed in Figure 5, as a function of the miniband width *Γe*. In this figure, *Jsc*<sup>0</sup> and *Voc*<sup>0</sup> were calculated at *Γ<sup>e</sup>* = 1*meV* and it can be observed that an increment in the electron miniband width causes a light increase in the *Jsc*<sup>0</sup> and the *Voc*<sup>0</sup> does not decrease significantly. This result suggests that changing the width of the miniband does not influence


**Table 3.** Experimental and calculated open-circuit voltage for three AlGaAs QWSCs.

too much the photon absorption, which could be because solar photon density in that spectral region is not high. The linear dependence of *JSC* is a confirmation of this assumption. The very small decrease in *VOC* is a consequence of the weak increment of the interface recombination current with the miniband width.

corresponding homogeneous p-i-n cell without quantum wells, as it was shown in a previous

Sample Photocurrent (*A*/*m*2)

**Figure 5.** (*Jsc* − *Jsc*0)/*Jsc*<sup>0</sup> and (*Voc*<sup>0</sup> − *Voc*)/*Voc*<sup>0</sup> as a function of electron miniband width. *Jsc*<sup>0</sup> and *Voc*<sup>0</sup> were

In the case of the AlGaAs/GaAs SLSC, the effective density of states and the absorption coefficient were calculated using the AlGaAs parameters reported in Table 2 of reference [15]. The short-circuit current density *JSC* and the open-circuit voltage *VOC* were determined using Equation (1) and showed in Figure 5, as a function of the miniband width *Γe*. In this figure, *Jsc*<sup>0</sup> and *Voc*<sup>0</sup> were calculated at *Γ<sup>e</sup>* = 1*meV* and it can be observed that an increment in the electron miniband width causes a light increase in the *Jsc*<sup>0</sup> and the *Voc*<sup>0</sup> does not decrease significantly. This result suggests that changing the width of the miniband does not influence Sample *VOC*(*V*) *VOC*(*V*) experiment theory

> QT468A 0.99 0.99 QT229 1.02 0.97 CB501 1.10 1.16 QT468B 1.18 1.28

**Table 3.** Experimental and calculated open-circuit voltage for three AlGaAs QWSCs.

G946 87.8 82.2 QT76 76.0 81.5 G951 112.0 132.8 QT468A 76.8 77.0 QT229 18.9 20.6

**Table 2.** Experimental and calculated photocurrent of AlGaAs QWSCs.

calculated experimental

study [3].

166 Solar Cells - New Approaches and Reviews

calculated for Γ*e* = 1 meV.

**Figure 6.** The normalized efficiency versus cluster number (a) and Al composition (b). The normalized efficiency is defined as the ratio between SLCS efficiency and its equivalent QWSC efficiency

If we increase the electric field in the intrinsic region, the number of quantum wells in the superlattice period should be smaller in order to obtain the resonant tunneling conditions. Therefore, a larger amount of cluster should be inserted to enhance the absorption, but then the interfaces and non-radiative recombination will increase. Great reduction of the electric field is not good in the p-i-n solar cells because it requires a low doping level in the p- and n-regions or an increase of the intrinsic region width.

After aplying the model proposed to the case of AlGaAs/GaAs SLSC, it was obtained that the three studied recombination mechanisms show independence with electron miniband width, remaining constant the heavy and light-hole miniband width, 35 and 15 meV, respectively. This is a significant result because the photocurrent could be improved in SLSC, and open-circuit voltage does not change. The values of the SLSC radiative recombination are almost smaller by two orders of magnitude than those obtained for the QWSC.

This result suggests that photogenerated carriers can escape out of the clusters more efficiently in SL structures because transport of carriers is enhanced via tunneling through thin potential barriers. In fact, the electrons in the minibands have high probability of tunneling assisted by electric field, through thin barriers and are recollected in n-AlGaAs region. An advantage of an SL barrier over a bulk barrier is the elimination of deep-level recombination between single and double heterojunctions, therefore, a non-radiative recombination reduction is expected in SLSC. This assumption is supported by our calculations, which show a drop in the non-radiative recombination value. The interface recombination current is greater for SLSC as a consequence that there are more interfaces, in particular, when 10 clusters of superlattices are inserted in the intrinsic region. Therefore, this mechanism becomes the most relevant for SLSC.

We researched the AlGaAs/GaAs SLSC efficiency, which was compared with the AlGaAs/GaAs QWSC efficiency. Figure 6 illustrates the normalized efficiency versus Aluminium composition and cluster number in the QWSC. The normalized efficiency in this figure is defined as the ratio between the efficiencies of SLSC and its corresponding QWSC for the graph versus Aluminium concentration. In the case of the graph in function of the cluster number the QWSC efficiency in the ratio is the highest. The SLSC efficiency is better than the highest QWSC efficiency for five or more clusters of superlattices in the intrinsic region which meas that under these conditions the photocarrier generation in the SLSC overcome the recombination. However, the best SLSC efficiency is just 4% better than the QWSC efficiency because the increase of SLSC photocurrent does not increase enough. This suggest that the miniband absorption and the absorption of wide quantum wells are comparable. On the other hand, normalized efficiency was plotted versus Al concentration in the QWSC, for 10 clusters in the SLSC intrinsic region, 15 nm well width, and 24 wells in the QWSC intrinsic region and in this case Figure 6 exhibits that SLSC efficiency is always higher than the QWSC efficiency, and become larger as the well barrier height increases. Because of the results that our model predictions are neither compared nor confirmed experimentally, it would be interesting to see if future experiments will corroborate our findings.
