The high efficiency limit of the intermediate band solar cell (IBSC) corresponds to the case of using as intermediate band (IB) host material a semiconductor with gap in the range of 2 eV. Traditional photovoltaic materials, such as Si and GaAs, are not appropriate to produce IB devices because their gaps are too narrow. To overcome this problem, we propose the implementation of a multi-junction device consisting of an IBSC combined with a single gap cell. We calculate the efficiency limits using the detailed balance model and conclude that they are very high (> 60% under maximum concentration) for any fundamental bandgap from 0.7 to 3.6 eV in the IBSC inserted in the tandem. In particular, the two-terminal tandem of a GaAs-based IBSC current matched to an optimized AlGaAs top cell has an efficiency limit as high as 64%

Antolín Fernández, Elisa

García-Linares Fontes, Pablo

Hernández Martín, Estela

Luque López, Antonio

Martí Vega, Antonio

Ramiro Gonzalez, Iñigo

English

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

RAISING THE EFFICIENCY LIMIT OF THE GaAs -BASED INTERMEDIATE BAND SOLAR CELL 
THROUGH THE IMPLEMENTATION OF A MONOLITHIC TANDEM WITH AN AlGaAs TOP CELL 
 
 
E. Antolín*, A. Martí, P. G. Linares, I. Ramiro, E. Hernández, and A. Luque 
Instituto de Energía Solar–UPM, ETSIT de Madrid, Ciudad Universitaria sn, 28040 Madrid, Spain 
*Phone: +34 914533549; FAX: +34 915446341; email: elisa@ies-def.upm.es 
 
 
ABSTRACT: The high efficiency limit of the intermediate band solar cell (IBSC) corresponds to the case of using as 
intermediate band (IB) host material a semiconductor with gap in the range of 2 eV. Traditional photovoltaic 
materials, such as Si and GaAs, are not appropriate to produce IB devices because their gaps are too narrow. To 
overcome this problem, we propose the implementation of a multi-junction device consisting of an IBSC combined 
with a single gap cell. We calculate the efficiency limits using the detailed balance model and conclude that they are 
very high (> 60% under maximum concentration) for any fundamental bandgap from 0.7 to 3.6 eV in the IBSC 
inserted in the tandem. In particular, the two-terminal tandem of a GaAs-based IBSC current matched to an optimized 
AlGaAs top cell has an efficiency limit as high as 64%.  
 
Keywords: Fundamentals, Detailed Balance, Intermediate Band, Multi-junction. 
 
 
1 INTRODUCTION 
 
The efficiency limit of the Intermediate Band Solar 
Cell (IBSC) is 63.2%[1] according to detailed balance 
calculations under the 6000K black-body spectrum and 
maximum sunlight concentration. Such a high efficiency 
limit has prompted an intensive research on practical 
ways to implement this novel photovoltaic concept. A 
great part of the research has been focused on GaAs-
based devices, such as the InAs/GaAs quantum dot (QD) 
IBSC [2, 3]. The development of GaAs IBSCs through 
the insertion of deep level impurities at high densities is 
also under study [4].  
The choice of GaAs as IB host material to fabricate 
the first IBSC prototypes is justified by sound practical 
reasons: it can be synthesized with excellent quality and 
exhibits dominant radiative recombination, and it is one 
of the materials that have rendered the most successful 
results in high concentration PV applications. Also, the 
InAs/GaAs QD material technology is one of the most 
developed nanotechnologies to date, mainly because of 
its application in the production of lasers and LEDs.  
However, the gap of GaAs (1.42 eV) is far from 
being optimum for the implementation of the IBSC 
concept. The GaAs approach has been regarded as a 
means to test the operation principles of the IBSC 
concept (with notable results [2, 5-8]) rather than as a 
definitive candidate for the fabrication of high-efficiency 
IBSCs. In this work we will evaluate the potential of 
implementing a double junction cell (2J) composed of an 
IBSC and a single gap cell (SGC). The efficiency limit of 
the SGC/IBSC tandem for any IBSC host semiconductor 
gap will be presented. This novel IBSC device can allow 
us to exploit the GaAs-based IBSC technology with the 
potential to attain really high efficiencies. Therefore, it 
may constitute a convenient alternative to the use of less 
known wide-gap materials in a single IBSC, which is also 
being researched by our group in parallel to this work.  
 
 
2 THE GaAs-BASED IBSC 
 
Let us first review shortly the IBSC theoretical model 
and state some nomenclature. Figure 1 (a) shows the 
band diagram of an ideal IBSC under operation. In the IB 
material we can define three gaps: the fundamental gap 
or host material gap (EG), between the valence band 
(VB) and conduction band (CB), and two sub-bandgaps 
between the IB and CB, and between the VB and IB. The 
sub-gaps are usually labeled as EL (the smallest one) and 
EH (the largest one). In our calculations we will assume 
that the IB has a zero width, that is, EG = EH + EL. 
The high theoretical efficiency limit of this cell relays 
on its capability of producing extra photocurrent with 
respect to a single gap solar cell of the same EG, while 
preserving a similar output voltage. The first is achieved 
because sub-bandgap photons can contribute to the 
photocurrent through a two-step absorption process 
mediated by the IB (transitions labeled 1 and 2 in Figure 
1). The voltage preservation is enabled by the existence 
of three distinct electronic gasses within the IB material 
(described by three quasi-Fermi levels) and because the 
IB material is sandwiched between two emitters that pin 
the quasi-Fermi levels of holes and electrons at the metal 
contacts.  
It has to be noticed that to attain a high efficiency the 
spectral splitting among transitions 1, 2 and 3 needs to be 
optimized. Using a circuital expression, transitions 1 and 
2 are series connected (their generation has to be equal 
for optimal performance) and their generation is parallel 
connected to that of transition 1. In Fig. 2 we have plotted 
the limiting efficiency of the IBSC depending on the 
value of EG. The absolute limit of 63.2% is achieved for 
EG = 1.94 eV. For lower gaps the efficiency sinks 
because too much light is absorbed in transition 1 and we 
do not really exploit efficiently the absorption through 
the IB. These calculations have being made using the 
original detailed balance model from [1], which assumes 
the following conditions and idealities: maximum 
concentration, the solar spectrum modeled as a 6000K 
black-body, cell temperature set to 300K, non non-
radiative recombination or resistive losses, absorptivity = 
1, full selectivity between absorption coefficients. The 
same conditions are maintained for all the calculations 
presented in the paper.  
Coming back to the GaAs case, we see from this plot 
that the efficiency limit for a 1.4 eV gap is 59%. In fact, 
the practical situation can be worse, because it is possible 
that the implementation of an IB in a host material 
reduces its effective bandgap. In the particular case of the 
InAs/GaAs QD-IBSC it has been pointed out [9] that the 
effective gap is reduced to about 1.2 eV. The reason can 
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65
be seen in Figure 1(b). In this QD material system we 
have confinement for both electrons and holes. While the 
electron confined levels are used as the IB, the hole 
confined levels are nor useful. Since there is almost a 
continuum of hole states, they can be regarded as an 
extension of the VB to higher energies. For EG = 1.2 eV 
the IBSC efficiency limit 56%. 
 
 
 
(a) 
(b) 
Figure 1. (a) Band diagram of an ideal IBSC under 
operation conditions, showing the three quasi-Fermi 
levels (εFe, εFh and εFIB) and the corresponding quasi-
Fermi level splits (μCI, μIV and μCV). (b) Simplified band 
diagram of InAs/GaAs QD material, illustrating how 
the existence of confined hole levels reduces the 
effective VB-CB gap. 
 
 
 
Figure 2. Detailed balance efficiency limit of a single 
IBSC with optimized IB position, as a function of the 
fundamental gap EG. 
 
 
 
3 DETAILED BALANCE MODEL FOR THE 
MULTI-JUNCTION IBSC 
 
We have already presented a detailed balance model 
for calculating the efficiency limit of a double-junction 
IBSC (2J-IBSC) [10]. Figure 3 shows a schematic of that 
device. In principle, the structure is that of a conventional 
two junction cell where both sub-cells are IBSCs. The 
bandgaps are labeled following the nomenclature stated 
before and adding “top” and “bot” for the top and bottom 
IBSCs, respectively. Besides the conditions listed above, 
we consider here that a perfect selective reflector is 
placed between subcells. This is usually included in the 
detailed balance model of the multijunction solar cell 
(MJC) (see, for instance, [11]). It means that all photons 
with energy greater than EL,TOP are reflected back to the 
top cell, where they can be more efficiently used, while 
all photons of lower energy pass through to the bottom 
cell.  
 
 
 
 
 
(a) 
 
 
 
(b) 
Figure 3. (a) Stack consisting of two IBSCs. (b) two-
terminal monolithic stack of two IBSCs connected in 
series through a tunnel junction. 
 
 The absolute efficiency limit of the 2J-IBSC concept 
is 73.2% when no interconnection between sub-cells is 
considered (unconstrained case) and 72.7% if series-
interconnection (current-matching) is imposed [12]. This 
limit is comparable to that of a six junction MJC 
(unconstrained 74.4% and series connected 73.4% [11]). 
As illustrated in Figure 3 (b), one of the advantages of the 
2J-IBSC is that it is possible to implement a two terminal 
monolithic device using just one tunnel junction instead 
of the five junctions required for the 6J cell. We consider 
that this is a promising concept for future applications. 
However, in the short term, a tandem combining only one 
IBSC and a SGC is a more feasible device. The results 
that we present here for this device have being calculated 
using the same model that in [10, 12], also including the 
condition of no optical coupling (selective reflector) 
between sub-cells.  
 
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4 EFFICIENCY LIMIT OF THE TANDEM SGC / 
IBSC AND APPLICATION TO THE GaAs-BASED 
IBSC 
 
 The mixed tandems SGC/IBSC have four different 
energy thresholds and, thus, should have, in principle, an 
absolute efficiency limit approaching the absolute 
efficiency limit of the unconstrained 4J cells. We have 
evaluated the two possible implementations: with the 
IBSC as bottom cell and with the IBSC as top cell. The 
results are shown in Figure 4, red and blue lines 
respectively. The absolute efficiency limits of these 
devices are compiled in Table I.  
 
 
Figure 4. Efficiency limit of the tandem SGC/IBSC 
considering that the IBSC is the bottom cell (red lines) 
or that the IBSC is the top cell (blue lines). Dashed 
repressents the unconstrained and solid the constrained 
case. The effciency limit of the single IBSC is 
included for comparison (black line) 
 
 
Table I. Absolute efficiency limit (η) of different 
SGC/IBSC and MJC configurations. All gap figures are 
given in eV. 
 
Tandem top SGC / bottom IBSC, independently 
connected (this work) 
EG,TOP EG,BOT EL,BOT   η (%) 
2.39 1.59 0.55    68.6 
Tandem top SGC / bottom IBSC, series connected (this 
work) 
EG,TOP EG,BOT EL,BOT   η (%) 
1.65 1.39 0.47    64.6 
Tandem top IBSC / bottom SGC, independently 
connected (this work) 
EG,TOP EL,TOP EG,BOT    η (%) 
2.48 0.96 0.49    68.5 
Tandem top IBSC / bottom SGC, series connected (this 
work) 
EG,TOP EL,TOP EG,BOT    η (%) 
2.83 1.13 0.52    67.9 
4 junctions tandem, independently connected [11] 
EG,1 EG,2 EG,3 EG,4   η (%) 
2.41 1.61 1.03 0.52   68.7 
4 junctions tandem, series connected [11] 
EG,1 EG,2 EG,3 EG,4   η (%) 
2.02 1.39 0.94 0.51   67.9 
 The absolute limits of both mixed tandems are very 
close to the efficiency ceiling of a 4 gap system when 
they are independently connected, being the 
configuration with top IBSC marginally better. Both 
outdo the efficiency of the two-terminal current-matched 
4JC. When the sub-cells are series-connected the absolute 
limit of the tandem with bottom IBSC drops 0.6 points, 
equaling the current-matched 4JC. But for the top single 
cell/bottom IBSC system, the series connection produces 
an efficiency fall of 4 points. The most interesting 
conclusion from this calculation is that we can have a 
very high efficiency limit for any fundamental gap of the 
IBSC from 0.7 to 3.6 eV, even if we impose current 
matching. Figure 5 shows the optimized EG,TOP and 
EL,BOT values for the tandem with the IBSC as bottom 
cell.  
 
 
Figure 5. Detailed balance calculations for a 2J-IBSC 
consisting of a top IBSC and a bottom SGC, in the 
independently connected case (red lines) and the 
series-connected case (blue lines). The upper plot 
represents the maximal efficiency that can be achieved 
for different values of the fundamental gap EG of the 
IBSC. The central and lower plots represent the 
optimized values of the single gap cell’s EG and the 
IBSC’s EL (the smaller of the sub-bandgaps) that lead 
to the efficiencies given in the upper plot. The white 
(black) star marks the GaAs case with (without) 
reduction of the effective gap. 
 
 
 The stars in Figure 5 mark the EG,BOT value of GaAs 
with (white) and without (black) effective gap reduction. 
In the first case the efficiency limit for the series-
connected case is the highest possible (64.6%). With 
effective gap reduction (EG = 1.2 eV) the efficiency limit 
is marginally lower (64.2%). The optimized EG,TOP and 
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67
EL,BOT values required for these tandems are indicated in 
Figure 6. The tandems could be implemented using for 
the top cell an AlxGa1-xAs alloy with x = 0.19 and 0.12, 
respectively. With such a low Al content, the gap of 
AlGaAs is direct and the lattice mismatch to GaAs is 
negligible. The fabrication of a monolithic AlGaAs/GaAs 
two-terminal 2JCs is currently a standard technology. 
 
 
 
 
 
(a) 
 
 
(b) 
Figure 6. Structure of the monolithic series-
interconnected AlGaAs/GaAs IBSC tandems proposed in 
this work: (a) assumes that the GaAs fundamental gap is 
unaltered by the implentation of the IB, (b) includes a 
reduction of the GaAs effective gap. 
 
 
5 CONCLUSIONS 
 
 It has been calculated the efficiency limit of a double 
junction device combining a single gap solar cell and an 
IBSC. It has been found that it is comparable to that of a 
four-junction cell (68%) both when the IBSC is used as 
the top cell or as the bottom cell. This implementation in 
tandem has an efficiency limit over 60% for any IBSC 
fundamental gap between 0.7 to 3.6 eV, even under the 
constraint of current-matching. 
 An important application of this concept can be the 
implementation of high efficiency devices using IBSCs 
of low fundamental gap, such as those based in common 
photovoltaic materials. In particular it has been found that 
a GaAs based IBSC can be combined monolithically with 
an AlGaAs top cell, resulting in an efficiency limit of 
64% under current-matching.  
  
 
ACKNOWLEDGMENTS 
 
 This work has been supported by the IBPOWER 
project funded by the European Commission (Grant 
Agreement No. 211640), by the Regional Government of 
Madrid within the project NUMANCIA2 (S2009/ENE-
1477), by the Spanish National Research Program within 
the project Consolider GENESIS-FV (CSD2006-0004) 
and by MICINN (project NANOGEFES ENE2009-
14481-C02-02). 
 
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5th World Conference on Photovoltaic Energy Conversion, 6-10 September 2010, Valencia, Spain
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Raising the Efficiency Limit of the GaAs-based Intermediate Band Solar Cell Through the Implementation of a Mololithic Tandem with an AlGaAs top Cell.

Archivo Digital UPM

Advances in quantum dot intermediate band solar cells,&quot;

AlGaAs/GaAs photovoltaic cells with InGaAs quantum dot arrays,&quot;

Detailed balance limit for the series constrained two terminal tandem solar cell,&quot;

Energy conversion efficiency limit of series connected intermediate band solar cells,&quot;

Experimental analysis of the quasi-Fermi level split in quantum dot intermediate-band solar cells,&quot;

H u b b a r d , C . G . B a i l e y , C . D . C r e s s , e t a l . , &quot;Short circuit current enhancement of GaAs solar cells using strain compensated InAs quantum dots &quot;

IBPOWER: Intermediate band materials and solar cells for photovoltaics with high efficiency and reduced cost,&quot;

Increasing the efficiency of ideal solar cells by photon induced transitions at intermediate levels,&quot;

Intermediate Band Solar Cells,&quot; in Next Generation Photovoltaics: High Efficiency through Full Spectrum Utilization,

Production of Photocurrent due to Intermediate-to-Conduction-Band Transitions: A Demonstration of a Key Operating Principle of the Intermediate-Band Solar Cell,&quot;

Quantum dot intermediate band solar cell,&quot;

Thesis, Insituto de Energía Solar, UPM,

Raising the Efficiency Limit of the GaAs-based Intermediate Band Solar Cell Through the Implementation of a Mololithic Tandem with an AlGaAs top Cell.

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