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Quantum Dot Solar Cells
A. Jackson, M. Pathak, D. Gomez
Abstract:
Current literature on quantum dots in solar cells (QDSC) was analyzed. It involved a general
review on the physics of quantum dots and the exciton excitation spectrum focusing on their
ability to enhance solar cell properties. An in depth view on the high carrier lifetime within in
solar cells was done, focusing on the suppression of common relaxation mechanisms
commonly found in solar cells. A review of the different manufacturing processes of QDSCs
was conducted to determine the expected time until economic QDSCs will reach the market.
Introduction:
The current search for an environmentally and economically sustainable energy source has put
increase pressure on the development of inexpensive and efficient renewable energy sources to
replace the existing, heavily polluting, energy production methods. This has caused a rapid rise in
funding directed into advanced research aimed at lowering the cost per W of solar cells. Standard
bulk solar cells are limited by the excitation energy of the materials used, which is determined by the
band gap of the semiconductors used in the cell. Existing, silicon-based bulk photovoltaics have a
peak theoretical efficiency of 32% [2]. Cells of this type have been manufactured to have a
maximum effective efficiency of 25%. Recently scientists have developed novel ways to increase the
theoretical efficiency by generating solar cells doped with quantum dots and even cells completely
made out of quantum dots. These provide the ability to control the excitation energy in order to
maximize the quantum efficiency of the solar cell. The following page contains an article along with
a vast amount of related information on the topic of quantum dot solar cells, the physics behind
them, and the corresponding production techniques.
Energy of Excitons:
When electrons are optically excited within a quantum dot they are confined to within the quantum
dot. This results in an increased probability of the electron interacting with its associated hole,
orbiting around each other called an exciton. The excitons have a different energy structure then the
bulk conduction electrons, and this energy structure is a function of the confinement from the
quantum dot. By controlling the quantum dots shape and material the exciton energy levels can be
engineered to optimize optical collection, which greatly increases the materials use as a photovoltaic
solar cell [3].
This engineering control is a result that higher confined systems result in higher energy gaps, thus as
the radius of a spherical quantum dot decreases, the energy of the exciton increases. This effect also
allows control of the energy required for creating mobile energy charged carriers and induced
electrical conductivity. Other then the shape, the material used also changes the strength of
confinement as the energy levels are related to the effective masses of both the electrons and the
holes[1] (see inset). This is very useful as by controlling the material and shape of the quantum dot,
we can engineer its properties to meet the goals of the product.
Schrodingers Equation for Quantum Dot [1]:
To first understand these effects the energy of the excitons needs to
be explored. To describe the energy of the exciton, the hamitonian
for a spherical quantum dot of radius R can be used as a starting
point. This uses a single wavefunction to describe both the electron
and the hole, and tracks their radial separation.
(1)
The first two terms in equation (1) describe the kinetic energy
operators for the electron and hole. The last term describes the
potential energy of the electron hole interaction located at position
re and rh from the center.
(2)
The potential energy can be written as seen in equation (2). Epsilon
(ε) is the permittivity of the medium. This equation only takes into
account the Coulomb attraction between the hole and electron. This
is assuming that the quantum dot is a sphere, but it has been shown
experimentally that most quantum dot exciton systems can be
modeled as either a sphere with asphyerical perturbations or a disk
with perturbations. This is also ignoring the effect of polarization of
the medium caused from the electrons and holes. If we solve
Schrödinger’s equation we can solve for equation (3), for the lowest
excited exciton state.
By adjusting the shape and material properties
the higher order exciton energy levels can be
engineered to have equal spacing. This is
beneficial for solar cell application because it
allows for charge multiplication, the main
benefit of quantum dot solar cells because it
allows for quantum efficiencies higher then
100%. Because the energy gaps are equal, an
exciton in the second excited state can relax to
the first excited state through exciting a
ground state electron into the first excited
state, referred to as the reverse auger effect
[7]. Thus the single high energy photon
generated two conduction band electrons.
Non-radiative mechanisms result in the
relaxation of the charge carriers decreasing
the quantum efficiency.
Mechanisms for Relaxation:
For solar cell applications this is not true as
the charged carriers need to be collected. The
intrinsic electric field from the dopants in the
substrate causes the excitons to leave the
confinement of the quantum dot and move
towards the anode and cathode. Within the
quantum dot, the excitons have a lifetime that
is highly dependant on the strength of the
confinement, the stronger the confinement the
(3)
longer the lifetime. This long lifetime is
characteristic of the excitons undergoing
radiative relaxation, in which it self-annihilates releasing a photon. This process has been
explained theoretically which has led to the conclusion of a size dependency on the exciton
lifetime, concept that has been confirmed experimentally Note that at higher energetic exciton
states the lifetime of the exciton decreases because its probability of being found outside of the
quantum dot is higher, in which it is more susceptible to non-radiative relaxation [4].
Optical Properties dependent on Size of
Quantum Dot:
The energy bands of quantum dots are dependant on the size
of the particles. Thus when an aqueous solution of quantum
dots is thermally excited its emission spectrum is dependant
on the radius of the particle. This figure from the
Department of Immunology from the University of Toronto,
shows vials with high concentrations of specific quantum dot
sizes. All the dots are made out of Cadmium Selenide.
Periodicity of Quantum Dots [9][10][11]:
Recent research has developed a method of reducing
these surface effects by using periodic self assembled
quantum dots. By generating layers of self-assembled
quantum dots with 5 nm layers of substrate between
them results in self assembled periodicity. The
quantum dots form into a square lattice within the
plane and begin to align in the vertical direction, thus
resulting in a rectangular lattice. This ordering is
caused by the strain field induced within the substrate
from the initial quantum dots. This effect results in
the vertical alignment. As the quantum dots are
created the atoms attempt to minimize energy, which
results in the spreading out of nucleation sites,
resulting in the in-plane periodicity. It was seen that
after 10 layers of quantum dots, the strains from each
layer add up with the in-plane periodicity resulting in
the self-assembled rectangular lattice.
Non-radiative relaxation mechanisms (NRRM) [5][6]:
NRRM are much quicker and dominate bulk semiconductor carrier lifetimes, but these
mechanisms are suppressed within quantum dots due to the break in periodicity of
the lattice. There are three main sources of non-radiative relaxation of excitons,
phonon interaction, surface reflection, and non-uniform confinement potentials.
Phonon relaxation occurs with quantum dots through some of the same
mechanisms as they do for the bulk, but at decreased rate. This decreased rate
leads to a longer exciton lifetime, which is the primary reason for the enhanced
collection efficiencies of quantum dots. The main methods of relaxation in bulk
semiconductors are the Frohlich interaction, deformation potential interactions,
and the piezoelectric interaction. These are all present for quantum dots as well,
but have much different characteristics, and have been found to be highly
dependant on the size of the quantum dot.
 Frohlich (Piezoelectric) interaction: Excitons interact with temporary
dipoles caused from LO (LA) phonons
 Deformation potential interaction: Small shifts in atomic placement act as
defects scattering excitons
 Surface interactions: Mismatched lattice constants at QD interface cause
electron reflections
 Non-uniformity interactions: discontinuities in the QD construction
result in anisotropic exciton distributions
The first two effects are reduced due to the phonon bottlenecking that
occurs. This occurs because for the relaxation to occur the exciton requires
a specific energy thus it only couples to certain phonons. Thus if all the
QDs the same then the phonons will be absorbed faster then they are
generated resulting in a lack of correct energy phonons.
Periodic Quantum Dots, within 25 layers
This periodicity was shown to greatly reduce the
surface scattering due to the quantum dots, thus
improving the overall quantum efficiency. The
periodicity reduces the scattering by generating an
intrinsic electrical field around the quantum dots
reducing the probability of surface scattering. This
effect is energy dependant and has been measured to
increase the quantum efficiency of the lower energetic
photons. This is because the surface scattering can be
modeled as a small perturbation in the conduction
band, which would affect the lower energetic carriers
most.
The NRRM can be reduced for certain quantum dot
giving adequate time for the excitons to relax through the
reverse-auger effect causing charge multiplication [7].
There is currently a debate on whether or not the reverse
auger effect is the primary mechanism for charge
multiplication within quantum dots. Experiments have
shown that the multiplication occurs nearly instantaneous
(order of ps), which is too fast to be explained by the
reverse auger effect [8]. They explain the instantaneous
carrier multiplication as the result of a quantum effect.
When the photon interacts with the electron cloud wave
function it causes an excited wave function that has
electrons in the superposition of both multi-exciton and
single exciton states. This is possible because an excited
single exciton in a high energy state has close to the same energy of multiple excitons at lower
levels, thus allowing for mixing states. This would result in the peak theoretical efficiency of
quantum dots to be limited by the mixing ratio of these two states. This mixing ratio is
difficult to measure as it appears to be highly responsive to materials and the confinement
potential. It is also hard to predict theoretically because of the probability of generating more
than two excitons. Either way, by ensuring the band structure has equal spacing between levels
QDs can be used in solar cells to increase the quantum efficiency above 100%.
Effects of Quantum Dots on Nanotubes [3] :
Nanoparticle Absorbance
Two cases were looked at in terms of how the quantum
dots were placed on a substrate. The substrate was made of
TiO2 and the nanoparticles and tubes were made of CdSe.
The first case the nanoparticles were placed substrate and
in the second case nanotubes were placed on the substrate.
[3] . The in both cases the diameter was changed and the
wavelengths were plotted against absorbance to see the
effect. This comparison between particle and nanotube
shapes electron transport behaviour shows the dependence
of photoconversion efficiencies with shape of quantum
dots. The results show that decreasing the particle size
causes a better absorption of lower wavelengths.
These wavelengths match the 1S transition. These results
were similar for both cases. This allows the possibility to
selectively harvest various incident light wavelengths.
Nanotube Absorbance
Hot Carrier Collection:
Manufacturing:
To collect the current from the quantum dots, intrinsic
electrical fields are generated through dopants in the
substrate. Because quantum dots have a reduced size
compared to the bulk systems, at the metal-QD junctions
there is no band bending due to mismatched Fermi levels.
When the metal surface comes into contact with a bulk
semiconductor, the semiconductor undergoes Fermi energy
equilibrium. This bending rectifies the flow of the charged
carriers produced from the photogeneration to produce the
photocurrent in the photovoltaic cell. Within the QD, after
equilibrium has been achieved, the conduction and valance
bands remain flat. This intrinsic electric field can be
engineered to modulate the charge transfer across
particles[2]. This then drives the energetic electrons to
desired energy levels to start the change injection thus
allowing for electrons of high and low energy into the
conduction band of the metal. This is known as hot carrier
collection [6], which results in a higher power output of the
quantum dot solar cell.
The level to which quantum dot solar cell (QDSC)
technology will impact the future of renewable
energy and the positive effect it has on our
overall quality of life fully depends on the ability
to make QDSC a commercially viable product. In
order to achieve this, proper economic and upscalable manufacturing techniques have to be
developed and implemented.
Several methods exist to produce quantum dots
and
to
perform
the
corresponding
implementation onto solar cells. Molecular Beam
Epitaxy is one of the earliest methods developed
to produce quantum dots and it continues to be
used by some researchers to create more
efficient solar cell [12]. Molecular Beam Epitaxy
is a single crystal deposition method developed
in the late 60's by Bell Laboratories which
exploits the use of high vacuum, up to 10-8 Pa,
and slow deposition rates, about 1000 nm per
hour, to achieve epitaxially grown films of
layered materials that allow electron confinement
in space [13]. The intrinsic characteristics of this
process such as the slow deposition rate and the
high vacuum requirements currently make this
process unviable as a mass production method
for quantum dot solar cells.
Other methods, such as Colloidal Synthesis, have
also been used to produce nanocrystals and
Semiconductor Bandgap [2]
nanocrystal superlattices. This technique yields nanocrystals of controlled composition,
size, shape and internal structure through high temperature (100-300°C) solution-based
synthesis. The uniformity in the size of the nanocrystals produced by this technique allows
for self-assembly of closed-packed, ordered nanocrystal superlattices (colloidal crystals)
[14]. Quantum dots of about 2 to 10 nm in diameter can be created using colloidal
synthesis, which is currently considered an inexpensive and relatively safe method for
creating quantum dots [18].
The power behind the quantum dot solar cell technology, however, lies on the product's
market competence. The manufacturing techniques used in the production of QDSC have
to be economical and efficient. Recent breakthroughs obtained from the research at Rice
University's Centre for Biological and Environmental Nanotechnology has provided the
necessary groundwork to develop such manufacturing processes. The breakthrough comes
from the chemical-based method developed to create four-legged Cadmium Selenide
quantum dots (CdSe tetrapods). Dr. Wong and his team improved on the previously used
tetrapod production methods, a schematic of this new synthesis method and the tetrapods
it produces is shown below in Figure 1 [15]. These QDs are investigated because of ideal
energy absorption range for solar power conversion, good electron acceptance for
conjugated polymers, and easily achievable shape control [20].
Figure 1: Schematic of New Synthesis Method for CdSe tetrapods [16]
Even though the use of CdSe nanoparticles in photovoltaic devices is not a new concept,
the combination of a less expensive production method for the quantum dots and an
innovative screen printing fabrication method for solar cells has strengthened the case for
this particular kind of nanoparticle-based solar cell. Screen printing methods can be used
very effectively to produce organic-based bulk heterojunction solar cells with layers of the
order of tens of nanometres. A schematic of the screen printing technique investigated by
a team at the University of Arizona is shown below in 2.
Figure 2: Schematic of Screen Printing Technique [17]
As it can be seen from the schematic in Figure 2, a screen, placed a few millimetres above
the surface of the substrate, is covered with the coating solution and subsequently
pressed by a 'squeegee' which sweeps across the surface of the screen. The momentary
contact between the screen and the substrate allows for the flow of the solution onto the
substrate which then dries to a continuous film soon after the squeegee has passed and
the screen separates from the substrate [17]. Screen printing methods for the
implementation of quantum dots offer a level of versatility and control that can take
optimization of inexpensive photovoltaic devices to a new level. A schematic of the
placement of the quantum dots with respect to the substrate is shown below in Figure 3.
Figure 3: Schematic of Substrate Covered With a Layer Quantum Dots [19]
Conclusion:
This report is a summary of a literature review of quantum dot solar cells, the full report is a
wiki page, http://wiki.phy.queensu.ca/shughes/index.php/Team_1. A brief summary of
quantum dot physics was done to briefly explain the fundamental nanoscale physics that occurs
within quantum dots. A discussion on how the quantum dots have been adapted for solar
voltaic cell uses, through different substrates and size optimization. An overview on the
different methods of producing solar cells was done, focusing primary on the implementation
of CdSe particles and the new methods of mass-producing quantum dot solar cells. In
conclusion, quantum dot solar cells offer a form of engineering control on the nanoscale with
the potential of solving some big challenges. The question doesn’t seem to be whether or not
quantum dots are the solution to the energy crisis, but if the nano-scientists are up for the
challenge of making them the solution.
References:
[1] Atkin's Physical Chemistry - Atkins, P. and Paula, J. W.H. Freeman and Company: New
York (2006)
[2] Kamat, P.V. - Quantum Dot Solar Cells: Semiconductor Nanocrystals as Light Harversters
[3] Quantum Dot Solar Cells. Tuning Photoresponse through Size and Shape Control of
CdSe−TiO2 Architecture
[4] Takagahara, Takeda, ‘Theory of the quantum confinement effect on excitons in quantum
dots of indirect-gap materials’ Physical Review B V46 N 23, 1992
[5] X B Zhang, T Taliercio, S Kolliakos and P Lefebvre, ‘Influence of electron–phonon
interaction on the optical properties of III nitride semiconductors’ J. Phys.: Condens. Matter
13 (2001) 7053–7074
[6] Ryan R. Cooney, Samuel L. Sewall, Kevin E. H. Anderson, Eva A. Dias, and Patanjali
Kambhampati, ‘Breaking the Phonon Bottleneck for Holes in Semiconductor Quantum Dots’
PRL 98, 177403 (2007) 27 APRIL 2007
[7] A. R. Beattie and P. T. Landsberg, ‘Auger Effect in Semiconductors’ Series A, Mathematical and
Physical Sciences, Vol. 249, No. 1256 (Jan. 1, 1959), pp. 16-29
[8] R. Schaller, V. Agranovich, and V. Klimov, ‘High-efficiency carrier multiplication through
direct photogeneration of multi-excitons via virtual single-exciton states nature physics’, VOL
1 December 2005 www.nature.com/naturephysics
[9] Arnold Alguno, Noritaka Usami, Toru Ujihara, Kozo Fujiwara, Gen Sazaki, and Kazuo
Nakajima, ‘Enhanced quantum efficiency of solar cells with self-assembled Ge dots stacked in
multilayer structure’ Appl. Phys. Lett Vol 83, No 6 11 AUGUST 2003
[10] A. A. Darhuber, V. Holy,a) J. Stangl, and G. Bauer, A. Krost, F. Heinrichsdorff, M.
Grundmann, and D. Bimberg, V. M. Ustinov and P. S. Kop’ev, A. O. Kosogov and P. Werner
,‘Lateral and vertical ordering in multilayered self-organized InGaAs quantum dots studied by
high resolution x-ray diffraction’ Appl. Phys. Lett., Vol. 70, No. 8, 24 February 1997
[11] A. E. Romanov,a) P. M. Petroff, and J. S. Speckb, Lateral ordering of quantum dots by
periodic subsurface stressors Applied Physics Letters, Vol. 74, No. 16 19 APRIL 1999
[12] http://physicsworld.com/cws/article/news/38046
[13] http://en.wikipedia.org/wiki/Molecular_beam_epitaxy
[14] http://www.research.ibm.com/journal/rd/451/murray.html
[15] http://www.sciencedaily.com/releases/2007/05/070502143631.htm
[16] http://www.ruf.rice.edu/~wonglab/full%20research%20article.html
[17] http://www.solterrasolarcells.com/downloads/screenprintingsolar.pdf
[18] http://en.wikipedia.org/wiki/Quantum_dot#Colloidal_synthesis
[19] http://physicsworld.com/cws/article/news/38046
[20]
http://books.google.com/books?id=PqgYXOBKJagC&pg=PA185&lpg=PA185&dq=CdSe+tet
rapod+manufacturing&source=bl&ots=eKiTZaG6_g&sig=VI2aZyufL8m3ZjBM_TOUMXvaaF
0&hl=en&ei=BNuSZu3M5TcMcj_qaAN&sa=X&oi=book_result&resnum=1&ct=result#PPA181,M1