21st European Photovoltaic Solar Energy Conference, 4-8 September 2006, Dresden, Germany
PROGRESS IN QUANTUM-DOT INTERMEDIATE BAND SOLAR CELL RESEARCH
A. Martí, E. Antolín, E. Cánovas, N. López and A. Luque
Instituto de Energía Solar–UPM, ETSIT de Madrid, Ciudad Universitaria sn, 28040 Madrid, Spain
Phone: +34 915495700; FAX:+34 915446341; email:amarti@etsit.upm.es
C. R. Stanley, C. D. Farmer and P. Díaz
Department of Electronics and Electrical Engineering, University of Glasgow,
Glasgow G12 8QQ, United Kingdom
Ph:+44(0)1413304798; Fax:+44(0)1413304907; email:crsmbe1@elec.gla.ac.uk
C. Christofides and M. Burhan
Department of Physics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
Ph: +357 22892824; Fax: +357 22892821; email: ccc@ucy.ac.cy
ABSTRACT: The intermediate band solar cell concept can be implemented in practice by means of quantum dots
(QDs), but a number of challenges must be solved in order to make progress. This paper describes some of them:
a) the problem of having the quantum dots embedded in the space charge region, b) the identification of the energy
levels involved in the QD system and c) the weak absorption provided by the dots. Regarding the first, the inclusion
of semiconductor dumping field layers sandwiching the region containing the stack of QDs is suggested as a way to
drive the QDs into a flat band potential region. Concerning “b”, the intermediate band is found to be separated from
the conduction band by only 0.2 eV, far from the optimum value. Finally, the weak light absorption provided by the
dots is discussed as a factor, together with the low intermediate band to conduction band bandgap that prevents a
significant quasi-Fermi level split between the IB and the CB under normal illumination conditions.
Keywords: Fundamentals, Devices, Modeling.
1
INTRODUCTION
The intermediate band solar cell (IBSC) concept has
been proposed [1] as a means to take advantage of below
bandgap energy photons and thus increase the efficiency
of solar cells beyond the Shockley and Queisser
efficiency limit [2,3]. The interested reader is directed to
Refs. [47] for further details, since the description of the
fundamentals will be restricted here to the minimum
necessary to make the paper self-consistent.
Fig. 1 shows the basic band structure of an IBSC.
Vertical arrows “1” to “3” identify the three possible
photon absorption mechanisms. A cornerstone of the
IBSC concept is that two below bandgap energy photons
provoke transitions “1” and “2” via the intermediate band
(IB) to generate one electronhole (eh) pair in the
conduction and valence bands (CB and VB). This eh
pair adds to the ones that are generated conventionally in
a single step by photons that possess an energy above the
bandgap EG (transition “3”). Note that the IB has to be
half-filled with electrons to provide both empty states to
receive electrons from the VB and to supply them to the
CB. For this reason, the IB is often referred to as a
“metallic” intermediate band.
A further condition for operation is that each band is
described by its own quasi-Fermi level (EFC, EFI and EFV
for the CB, IB and VB respectively). This is a
consequence of the assumption that the lifetimes
associated with the carrier recombination processes
between bands (i.e. from the CB to the IB...) are much
larger than carrier relaxation times within bands.
Although it can be demonstrated with rigour [1], it is
evident from the plot in Fig. 1 that the output voltage of
the cell, related to the quasi-Fermi level split by
eV E FC E FV , is still limited by the high bandgap
EG and not by either of the two lower sub-bandgaps into
which it is divided by the IB (i.e., EL or EH).
Figure 1. Schematic band diagram describing the basic
operation of an intermediate band solar cell.
Independently of the IBSC concept, understanding
the physical reasons that can lead an energy level within
the semiconductor bandgap to behave either radiatively
or non-radiatively, and mastering the technology that can
render it one type or the other, is of the outmost
importance. We have provided a detailed discussion in
[8] on this phenomenon providing arguments to prevent
non-radiative recombination. In essence, the key physical
aspect is the delocalization of the wave-function of the
electrons in the IB. Hence, when this wave-function is
delocalized and a recombination between the CB and the
IB takes place, the electron charge density is distributed
through many atoms (delocalized) both in the initial and
the final state. When a transition from the CB to the IB
takes place, no significant redistribution of charge
density is involved and therefore, the transition does not
require an interaction of the electron through an electric
field with the impurities that caused the appearance of
the intermediate levels. Since this interaction is inhibited,
the possibility of the electron giving its energy to the
impurity, along with non-radiative recombination, is also
inhibited. In [8], it is suggested that this delocalization
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21st European Photovoltaic Solar Energy Conference, 4-8 September 2006, Dresden, Germany
could be achieved by increasing the density of the centres
responsible for the intermediate levels beyond the Mott
transition [9] value.
2 IMPLEMENTING THE INTERMEDIATE BAND
SOLAR CELL WITH QUANTUM DOTS
(a)
(b)
(modulation doping), a few QD layers are sacrificed to
sustain the electric field at the junctions with the
emitters, but nevertheless a sufficient number of layers
remain half-filled with electrons. In this approach, the
QD layers close to the p-emitter are sacrificed because
they are empty and whilst those close to the n-emitter are
sacrificed because they are full. Note that no electron
transport through the IB is required in this ideal case.
However, when the number of QD layers is limited
by the growth technology (either because of the
appearance of defects or simply because of the time
involved in their production), there is a risk that most of
the QD layers are sacrificed just in sustaining the
junction field (see Fig. 2(b)) without leaving a sufficient
number suitable for the absorption of two sub-bandgap
photons. This is believed to be the case in some of our
experimental samples manufactured in the past [13].
To prevent this effect, an n-type semiconductor layer
can be inserted next to the p-emitter and just before the
stack of QD layers (Fig. 2(c)). Carefully designed, this nlayer can sustain the junction electric field and drive the
dots into a flatband potential region. Similarly, an
undoped layer can be inserted between the stack of QDs
and the n-emitter to contribute to the same effect but also
to prevent electrons from the emitter conduction band
tunnelling into the IB.
Our aim of locating the QDs in a flat-band potential
region might appear contradictory to the belief that the
electric field is the driving force of the photovoltaic
effect by separating electrons from the holes. It must be
remembered that it is the feasibility of manufacturing
selective contacts (p- and n-emitters in the case of the
semiconductors) to a material that is sensitive to light
[14] that gives rise to the photovoltaic effect.
Further, if carrier transport through the IB is be
allowed (in our case, this would imply that electrons
could move from their confined electron state in one dot
to another), electrons from the VB could be absorbed in
the dot region that is closer to the p-emitter and thus
empty of electrons, be transported through the IB to QD
region close to the n-emitter and from there, be pumped
to the CB by a second photon as outlined in Fig. 2(d).
3 IDENTIFICATION OF THE ENERGY LEVELS
AND GAPS INVOLVED IN THE OPERATION OF
THE QD-IBSC
(c)
(d)
Figure 2. (a) Ideal case with an unlimited number of QDs
layers available. (b) Real situation in which only a
limited number of QD layers can be realistically grown
(c) Insertion of conventional semiconductor structures to
regain the flat band condition and with it, half-filling of
the IB with electrons. (d) Illustration to show an electronhole pair can be still be created even when the dots are
not located in a flat band potential region by allowing
transport through the IB.
The use of quantum dots was proposed as a practical
means of implementing the IBSC concept [10,11]. Fig. 2
shows a plot of a simplified band gap diagram for a QDIBSC under several conditions. Fig. 2(a) represents the
ideal case in which the number of QD layers that can be
grown is not limited by the technology. Under these
circumstances, although the QD region in our structures
is doped to half-fill the IB with electrons [12]
100
We have carried out quantum efficiency and
electroluminescence measurements in the past whose
spectral peaks have allowed us to draw a picture of the
main energy levels involved in the operation of the QDIBSCs [13]. Fig. 3 shows the simplified energy band gap
diagram which best fits our implementation of the IBSC
with InAs/GaAs quantum dots.
Level marked “WL”, close to the CB, arises from the
wetting layer when the QDs are grown in the
StranskyKrastanov mode [15]. In reality, the wetting
layer is a quantum well and, therefore, there is no a true
zero density of states between this level and the CB. The
consequence for the IBSC is that the edge of the CB is
lowered to the level “WL”. On the other hand, level(s)
“QL” are introduced specifically by the QDs and are
separated from WL levels by a null density of states.
The separation between “QL” and “WL” determines
the gaps EL|0.2 eV and EH|1.1 eV of the IBSC. These
21st European Photovoltaic Solar Energy Conference, 4-8 September 2006, Dresden, Germany
are far from the optimum ones for photovoltaic energy
conversion which are given by EL=0.71 eV and EH=1.24
eV [4]. Actually, the limiting efficiency at maximum
concentration of an IBSC characterised by these nonoptimum gaps is “only” 47.8 %, compared with the
63.2 % limiting efficiency of the optimised structured.
Therefore, our QD-IBSC structures are more test benches
to prove the principles of operation of the IBSC rather
than devices capable of delivering the highest
efficiencies.
possible to inject current densities into the device which
are higher than this thermal escape value, allowing
experimental evidence for the existence of this quasiFermi level split to be found [20,21].
4
LIGHT ABSORPTION IN THE QUANTUM DOTS
QDs in densities that can usually be grown
(~4u1010 cm-2) absorb light weakly. This is the case for
transitions from the VB to the IB but more so for
transitions from the IB to the CB. In spite of this, the
contribution of the former to the photocurrent can be
detected easily and studied in quantum efficiency
measurements [22].
(a)
(c)
Figure 3. Approximate energy levels involved in the
operation of an intermediate band solar cell implemented
with InAs quantum dots in GaAs.
It is perhaps surprising that the low value of the
energy separating the conduction band from the confined
energy states of the electrons in the QDs is often
sufficient to explain the “phonon bottleneck” effect [16].
This phenomenon, very much unwanted in the context of
the QD laser, makes it difficult to explain how an
electron “recombines” from the CB to the IB because
there is no element to which the electron can transfer this
energy. Simultaneous collisions with several phonons,
each with an energy in the range of a few tens of meV,
are considered unlikely. However, to our knowledge, no
one has put forward this argument (with the exception of
[8]) as a possible mechanism preventing recombination
from the CB to the VB through mid-gap energy levels i.e. ShockleyReadHall recombination [17, 18] that
are even more separated in energy (0.5-0.7 eV) from the
CB of conventional semiconductors, than is the case for
the confined electrons in the QDs. Therefore, while the
“phonon bottleneck” effect is a phenomenon to be
avoided when manufacturing QD lasers because it
inhibits radiative recombination, conversely it is a
desirable phenomenon when manufacturing a QD-IBSC
where rapid nonradiative recombination to the QD
energy level must be avoided.
On the other hand, associated with the low value of
the gap EL, is an equivalent minimum thermal escape
current density from the IB to the CB given by
9 mA cm2 [19]. This high value also makes it difficult to
achieve a significant quasi-Fermi level split between the
IB and the CB (EFC EFI) when the absorption of photons
from an external illumination source that are capable of
exciting transitions from the IB to the CB is weak. The
cause of this weak absorption will be discussed in the
next section. Conversely, under dark conditions, it is
(b)
Figure 4. (a) Conventional, isolated quantum dot: the
wave-function of the electron in the dot is localised but
mostly delocalised in the CB. (b) Delocalization of the
electron wave-function in the IB by increasing the dot
regularity (c) Localization of the electron wave-function
at the CB by inserting a semiconductor with a high
conduction band offset between the dot and barrier
regions.
Optical absorption by IB to CB transitions is the
weakest process [23], although to have this absorption
stronger than the optical absorption related to VB to IB
transitions would be detrimental to the cell performance
[24]. The absorption from the IB to the CB is believed to
be weak because the wave-function of the electrons in
the QDs is confined (Fig. 4(a)) while the wave-functions
of the electrons in the CB are delocalised [11] so that
little overlap exists between the two (maybe with the
exception of those states close to the CB edge). The
overlap might be increased by enhancing the regularity
of the QD size and their distribution because in this way,
the wave-functions of the confined electrons also
delocalise (Fig. 4(b)) [11]. It might also be possible,
however, that a mere increment in the dot density will
produce the same effect as a consequence of a process
similar to the Mott transition. However, a third option
might be to increase the confinement of the wavefunction of the electrons in the CB by inserting a
semiconductor of high conduction band offset between
the QD and the barrier material as illustrated in Fig. 4(c).
The layer should be sufficiently thin to allow electron
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21st European Photovoltaic Solar Energy Conference, 4-8 September 2006, Dresden, Germany
transport through it by tunnelling.
5
SUMMARY
Intermediate band solar cells are being researched by
our groups through implementation with quantum dots.
Functional devices have been manufactured whose
operation is largely determined by the underlying
physical principles of the IBSC, in particular, the
extraction of photocurrent for below bandgap energy
photons and the existence of a quasi-Fermi level split
between the CB and the IB under strong excitation in
dark conditions [20].
To progress the research, the issue of maintaining the
QDs in a region with flat-band potential has been
addressed, and a way of achieving this goal has also been
discussed.
Previous work has also established ways to map the
energy levels involved in the operation of an InAs/GaAs
QD-IBSC. Further, it has been pointed out that the low
value of the gap EL (0.2 eV) together with the weak
absorption associated with the IB to CB transition will
make it difficult to obtain a split between the CB and IB
quasi-Fermi levels, EFC and EFI, under normal conditions
of illumination.
ACKNOWLDGMENTS
This work has been supported by the project
FULLSPECTRUM,
funded
by
the
European
Commission under Contract No. SES6-CT-2003-502620,
the Spanish Plan for R&D (TIC2003-02281), Consolider2010 Program GENESISFV (CSD2006-00004) and the
Comunidad de Madrid (S-0505/ENE/000310). E.C.
acknowledges a “Plan Nacional de Formación de
Personal Investigador” research grant.
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