Multijunction solar cells
The multijunction solar cells can be found in two configurations (see the figure below): in
parallel (left) or in series/tandem (right). As for thin-film solar cells with heterojunctions, for
enhanced performances all layers should have similar crystalline structures/lattice constants.
Otherwise, the discontinuities in the lattice constants lead to defects or dislocations at the
interface, which are preferred recombination sites.
In the parallel configuration, called also multi-terminal tandem, each solar cell can be
independently optimized, but the whole system is more complicated. Therefore, the series/
tandem solar cells are mostly used; they consist of different p-n junction solar cells placed one
after another, each utilizing a part of the solar spectrum and allowing the passage through of
the other part. The solar cells at the top (the first illuminated) have a larger bandgap, this
parameter decreasing progressively in the following cells (see the figure below).
In tandem solar cells the output current is limited by the smallest current generated in
the individual junctions, and the voltages produced by the individual cells are added. Therefore, the solar cell must be designed such that all junctions generate the same photocurrent.
2
The conversion efficiency increases with the number of cells. In the figure above,
which presents two solar cells with p-n junctions in materials with E g = 1.6 eV, and 0.9 eV,
respectively, the conversion efficiency calculated with the Shockley-Queisser theory is of
45%. This is the maximum efficiency that can be obtained with a two-junction tandem solar
cell. The maximum efficiency for a three-junction tandem solar cell is 51%, and is obtained in
materials with bandgaps of 1.8 eV, 1.2 eV and 0.7 eV, the efficiency increasing up to 54% for
four-junction tandem solar cell and to 66% for an infinite number of junctions that cover the
whole solar spectrum. Obviously, the efficiency of solar cells increases if light concentrators
are employed. For example, if the light intensity is 100 times more powerful, the efficiency of
a single junction increases at 40%, and that of an infinite number of junctions reaches 86%.
Multijunction solar cells in tandem configuration are fabricated from a-Si/μ-Si
(amorphous Si/microcrystalline Si), and organic or inorganic semiconductors, for example IIIV compounds. The highest efficiency in two-junction solar cells has been obtained in III-V
compounds. For instance, in the tandem configuration a conversion efficiency of 30.3% at
AM1.5G and 1 sun has been obtained in the In0.49Ga0.51P/GaAs structure, in which both
materials have a lattice constant of 5.64 Å, and an efficiency of 32.6% at AM1.5D and 1000
suns (30% at 500 suns) was observed for the GaInP2/GaAs structure. In the four-terminal
parallel configuration, the highest efficiency for two-junction solar cells, of 32.6% at AM1.5D
and 100 suns, was obtained for the GaAs/GaSb structure.
The figures below illustrate the quantum efficiency of materials used in three-junction
tandem solar cells; note the optimum use of solar radiation. The experimental maximum
conversion efficiency in a GaInP2/GaAs/Ge structure is 32% for 1 sun and 40.7% for 135
suns, the average efficiency for the same structure at 1 sun being of 28%. Such a structure
produced 375 kW in space (on the orbit). Experimentally, the number of junctions reaches 6,
the epitaxial growth of heterostructures being costly and slow.
3
As already mentioned, the tandem solar cell must be designed such that the photocurrent
generated by the individual solar cells is the same. The photocurrent depends on the number
of photons with energies higher than E g and on the absorption coefficient (on the layer
thickness, respectively). In the three-junction GaInP2/GaAs/Ge structure, for example, this
requirement imposes that the Ge layer is thicker than the other layers because its absorption
coefficient is smaller. The layer thicknesses for terrestrial applications can be different from
the thicknesses required by spatial applications (the solar spectrum differs)!
Observation: The photocurrent in a tandem multijunction cell is generally smaller that that
obtained in a solar cell with a single junction because the available photons are collected by
several junctions.
Presently, efforts are made to obtain conversion efficiencies higher than 35% in
multijunction tandem cells, eventually using concentrators. For example, the maximum
efficiency of the InGaP2/(In)GaAs/Ge structure is 37.3% at 175 suns. The Ge substrate is
flexible if thinner than 100 μm. At the moment, research is focused towards finding
semiconductor materials with E g = 1 eV or 1.25 eV, because Ge in the GaInP2/GaAs/Ge
structure absorbs a higher fraction of photons in the solar cell than in the ideal case, that of
current equality in the three layers (see the figure below). If the GaAs layer would be replaced
with a material with E g = 1.25 eV, for instance, the second layer would generate a higher
photocurrent, allowing less photons to pass in Ge. In this case, the first layer could be thicker
in order to generate a higher current/power.
Alternatively, if the first two layers in a three-junction structure are (Al)InGaP and
GaAs, the optimum E g for the bottom cell is 1 eV (see the figure below). For example, in the
AlInGaP(1.9 eV)/GaAs(1.4 eV)/1.0 eV structure the maximum conversion efficiency is 55%
4
at 1000 suns, and only 50.1% if the last layer is Ge. GaInNAs is one material with the same
lattice constant as GaAs and with E g = 1 eV.
A further improvement in the conversion efficiency can be obtained introducing a
material with E g = 1 eV between GaAs and Ge layers, such that a four-junction structure is
formed (see the figures above). The conversion efficiency in this case would be of 60.9% at
1000 suns (47.7% at 1 sun, AM1.5G).
The solar spectrum can be optimally covered by progressively increasing the number
of junctions, as in the example above. Every time a layer is replaced by two layers the
photocurrent in the individual solar cells decreases (the number of photons absorbed in each
layer is smaller), but Voc increases, such that the conversion efficiency of the tandem
structure is improved. The external quantum efficiencies of the tandem structures with 3 and 5
junctions above are represented in the figures below left and right, respectively.
5
As can be seen from the figure below, left, good tunnel junctions are required for a
series connection of solar cells. A tunnel junction is junction in which electrons tunnel
through the potential barrier formed at the interface between two layers, i.e. electrons pass
through a narrow barrier having a fixed energy, which is smaller than the potential barrier; see
the figure below, right). In such junctions, the transfer of charge carriers from one solar cell to
another occurs rapidly (in a very small time interval).
V2
V1
V3
x=0
x=L
In a tandem configuration, if the individual solar cells do not have the same
photocurrent, the structure works far from the operating point corresponding to the maximum
power and has large losses. Because the multijunction tandem cells have a higher spectral
sensibility, losses caused by inequalities of currents in individual solar cells can occur due to
natural changes in the solar spectrum (seasons, hours in a day), which modify the relative
absorption in the subcells.
6
An example of an optimized two-junction tandem cell from thin layers of amorphous
Si (a-Si) and microcrystalline Si (μ-Si) is illustrated in the figure below, left, the absorption
spectrum of the individual cells and of the tandem structure being represented in the figure
below, right.
In this example, light trapping is achieved by growing the tandem cell on a structured
substrate, which scatters light and thus increases the effective light pathlength in the
absorbing film. In the case above, light trapping must occur between 600 nm and 750 nm for
the top amorphous cell, and between 800 nm and 1100 nm for the bottom microcrystalline
cell. For amorphous Si, light trapping has another role: sunlight degradation can be minimized
in thinner layers, whereas in microcrystalline Si, the trapping enhances light absorption (the
material has indirect energy bands). Structured surfaces can also be the electrodes, in p-i-n or
n-i-p type configurations; the structure above is n-i-p/n-i-p. For amorphous Si cells, the
corrugation height must be between 50 nm and 90 nm and its lateral dimension between 300
nm and 500 nm. For microcrystalline Si cells, the lateral dimension of the corrugation is
between 1000 nm and 1400 nm and its height must be comparable to that in amorphous Si. In
the tandem structure, in order to optimize the structuring of the substrate for both cells, a ZnO
intermediate asymmetric reflector layer is introduced between the two cells. This reflector,
denoted by AIR (asymmetric intermediate reflector) in the figure above, enhances light
trapping in the top amorphous solar cell and so improves the external quantum efficiency of
the amorphous Si cell. The tandem structure in the figure above was frown on a flexible
polyethylene layer, which is periodically structured before deposition of the Si layers. In n-i-p
type configurations the i layer must be thinner than 2.5 μm in the μ-Si layer to avoid
recombination losses, and thinner than 300 nm in the a-Si layer to limit the sunlight
degradation.
7
A three-junction tandem structure from non-crystalline Si is illustrated in the figure
below, left, the absorption spectrum of the three layers being represented at right. Note the use
of a metallic reflector layer, which reflects the light that passes through the structure and thus
enhances the photon pathlength and the light absorption. The conversion efficiency in this
case is 7−10%.
Emergent configurations of solar cells
The solar cells studied so far, although not easy to manufacture or cheap, do not pose serious
technological problems. The emergent configurations of solar cells are based on
semiconductor structures with nanometer dimensions in which the electron energy levels are
discrete rather than continuous, as in crystals, or on plasmons.
Quantum dots, wires and wells. Superlattices
Up to now we have encountered semiconductor structures with discrete electronic levels,
more exactly quantum dots, when dealing with TiO2 nanoparticles in the dye-sensitized solar
cells. We have then mentioned that in a nanocrystalline particle with dimensions Lx , L y and
L z , the electron is localized in the region with the minimum potential energy/in the
nanoparticle, and its energy spectrum is no longer formed from allowed and forbidden bands,
as in crystals, but from discrete levels (see the figure below), given by
8
D0D
z
y
x
E112
E111
h2
E (k x , k y , k z ) = Ec +
2m n
2
⎛ pπ ⎞
h2
⎜⎜
⎟⎟ +
2m n
⎝ Lx ⎠
⎛ qπ
⎜
⎜L
⎝ y
E113
2
⎞
h2
⎟ +
⎟
2m n
⎠
E
⎛ rπ
⎜⎜
⎝ Lz
2
⎞
⎟⎟ = E pqr
⎠
where p, q, r are integer numbers. These discrete levels result from the Schrödinger equation
satisfied by the electrons in the material (see part I of the course). A discrete energy spectrum
is similar to that in atoms or molecules. A nanoparticle is called quantum dot if the discrete
energy levels can be observed, i.e. if the difference between adjacent discrete energy levels is
higher than the thermal vibration energy, k B T . This implies h 2π 2 / 2mn L2x , h 2π 2 / 2m n L2y ,
h 2π 2 / 2mn L2z > k B T , or Lx , L y , L z < h 2π 2 / 2mn k B T .
In a quantum dot the electron is not free to move/it is localized in the dot. There are
also structures in which electron movement is allowed along a single direction (quantum
wires) or in one plane (quantum wells). Unlike these structures, in a bulk crystalline material
the electron can move freely along all three spatial directions, and the energy dependence on
the wavevectors k in the first Brillouin zone (see part I of the course) is given by
E ( k ) = E c + h 2 k 2 / 2m n = E c + h 2 ( k x2 + k y2 + k z2 ) / 2m n
where Ec is the bottom edge of the conduction band and mn is the effective electron mass. In
a quantum wire as that in the figure below, left, with dimensions L y , L z along the
confinement directions, the conduction electrons can move freely only along the x direction
and the dispersion relation is expressed as
2
h 2 ⎛ pπ ⎞
h 2 ⎛ qπ ⎞
h 2 k x2
h 2 k x2
⎜
⎟ +
E ( k x , k y , k z ) = Ec +
E
+
=
+
⎜
⎟
,
s
pq
2m ⎜⎝ L y ⎟⎠
2m ⎝ Lz ⎠
2m
2m
2
9
with p, q integer numbers. As in a quantum dot, in a quantum wire the difference between
adjacent discrete electron levels must be higher than k B T , i.e. L y , L z < h 2π 2 / 2mn k B T .
D2D
D1D
z
z
x
Es,11
Es,12
Es,13
y
y
E
x
Ec Es,1
Es,2
Es,3
E
Analogously, in a quantum well as that in the figure above, right, the electrons are free
to move along the x and y directions and the dispersion relation is
2
h 2 ⎛ pπ ⎞
h2 2
h2 2
E ( k x , k y , k z ) = Ec +
(k x + k y2 ) = E s , p +
(k x + k y2 )
⎜
⎟ +
2m ⎝ Lz ⎠
2m
2m
with p integer. These discrete energy levels can be observed if the width of the quantum well
satisfies the relation L z < h 2π 2 / 2mn k B T . In the figures above the red lines represent the
densities of states in the quantum dot (in which the electron cannot move along any direction),
quantum wire (in which the electron movement is one-dimensional), and quantum well (in
which electrons are free to move in two dimensions). The green line in the figure above, right,
represents the density of states in a crystalline lattice in which electrons move freely in three
dimensions, given by D3 D ( E ) = D( E ) = [(2mn )1 / 2 / 4π 2 h 3 ]( E − E c )1 / 2 (see the first part of the
course).
In quantum wells, wires or dots, the region in which the electron motion is allowed is
called potential well, and the region in which this motion is forbidden is referred to as
potential barrier. Note that, in a quantum structure (well, wire or dot), there is also a similar
discretization of the energy levels of holes in the valence band, and the excitation of an
electron from the valence in the conduction band as a result of photon absorption is possible
only for photon energies E higher than E g in the material that contains the quantum well, this
minimum photon energy depending also on the width of the well and the height of the
potential barrier (see the figure below, right). More precisely, the electron transition from the
10
valence band, with upper edge Ev , in the conduction band with bottom edge Ec occurs
between the corresponding discrete levels in the potential well. In bulk crystals the similar
electron excitation occurs if the incident photon energy E is equal to E g (see the figure
below, left). The quantum wells, wires and dots are generically called mesoscopic structures
since they have nanometer-size dimensions, between the dimensions of the microscopic
structures (molecules) and macroscopic materials.
Ec
Ec
E
E
Eg
Eg
Ev
Ev
potential
barrier
potential
well
potential
barrier
The table/figure below illustrates the dependence of the minimum energy of absorbed
photons (denoted by E g )/absorption on the dimensions of CdSe nanoparticles. In the table
below τ is the carrier lifetime. It can be seen that, as the particle dimension decreases, the
absorption shifts toward smaller wavelengths (higher energies) and photons from the visible
spectrum range are less absorbed.
11
The absorption spectrum depends on the nanoparticle diameter due to the relations above
between electron energy and the dimensions of the potential well. The colors of the solutions
that contain nanoparticles with different diameters are also different.
Observation: Because of the spatial overlap of electrons and holes confined a quantum well,
the electrostatic Coulomb interaction is enhanced and absorption of a photon generates, in
general, excitons and not free/unbound electron-hole pairs.
When several quantum wells, wires or dots are separated by small distances, the
electrons can jump from one structure to another if their (thermal) energy is high enough to
overcome the potential barrier. A structure consisting of several neighboring quantum wells,
for example, is called MQW (multiple quantum well) if the quantum wells do not influence
one another. When the distance between adjacent quantum wells is very small, so that the
electron movement in one well is influenced by the presence/potential energy of the other
well, and the quantum wells are arranged periodically, the resulting structure is a superlattice.
In this case, the electron passes from one quantum well to another through tunneling, i.e. the
(quantum) penetration of a potential barrier by an electron with a smaller energy than that of
the barrier, phenomenon that is forbidden for a classical particle. In such coupled identical
quantum wells, the conduction electrons feel a periodic potential with a periodicity which is
no longer at the atomic scale, of few Angstrom, but at nanometer scale. The periodicity of
potential energy imposes (as in bulk materials, where the periodicity is that of the lattice) the
formation of allowed and forbidden energy bands (see part I of the course), with positions and
widths depending on the form of the periodic potential and that can be controlled by the width
and height of the potential barrier. The superlattice is an artificial crystal.
The figures below represent the difference between electron and hole in MQW and
superlattices, the indices w and b referring to potential wells and barriers, respectively. In
superlattices, the well and barrier layers have widths of 10-50 nm.
12
Conventional solar cells with mesoscopic structures
The mesoscopic structures can enhance the performances of conventional solar cells (those
referred to up to now) or can inspire specific solar cells. In this section we focus on the first
case, the second one being treated in the following sections.
A typical example of increasing the conversion efficiency of solar cells by using
quantum wells as absorbant in GaAs/AlGaAs cells is presented in the figure below, left. Note
the significant (few times) increase of the photocurrent, while the corresponding decrease of
the open-circuit voltage is only moderate. The figure below, right, illustrates the absorption
increase in the organic material CuPc deposited as a thin film, by the introduction of Ag
nanoparticles.
The CdSe quantum dots, which have the advantage of a tunable E g , are also used in
sensitized solar cells instead of the dyes based on Ru. The figure below, left, presents the
absorption spectrum of quantum dots with different diameters, while the right figure
compares the I − V characteristic at 1 sun of a TiO2 nanostructured electrode sensitized with
13
CdSe quantum dots with a diameter of 2.8 nm, by using different molecule links between
CdSe and TiO2: MPA (mercaptopropionic acid) and cysteine.
The scheme of the transitions induced by light absorption in a solar cell sensitized with InP
quantum dots is presented in the figure below. Note that the energy gap in quantum dots can
be varied in a large interval by controlling their diameter.
In order to enhance and tune light absorption in solar cells, the quantum dots can also
be dispersed in matrices of organic semiconducting polymers. For example, the CdSe
quantum dots can be introduced in the hole conductor polymer MEH-PPV (poly(2methoxy,5-(2’-ethyl)-hexyloxy-p-phenylenevinylene). The carrier photoexcitation occurs in
the quantum dots, the holes being then injected in MEH-PPV and collected by electrical
contacts in the polymeric phase MEH-PPV. The electrons remain in the quantum dots and are
collected by diffusion and percolation in the nanocrystalline phase at an electrical contact in
14
the network of quantum dots. Alternatives of these solar cells include the use of
polycrystalline TiO2 layer as the electron conducting phase and MEH-PPV as hole conductor,
the electrons and holes being injected in the respective layers after photoexcitation, or (see the
figure below) the quantum dots can be dispersed in a mixture of polymers that conduct
electrons and holes. Each polymer type has a selective contact that extracts the corresponding
charge carriers. The problem in this solar cell is to avoid electron-hole recombination at the
interfaces between the polymers in the mixture. The figure below illustrates also that (we will
detail latter) the quantum efficiency in quantum dots can be enhanced by impact ionization,
which generates several electron-hole pairs after absorption of a single photon.
The spectral response of the mesoscopic structures depends not only on their diameter
but also on their length. An example in this sense is presented in the figure below and refers
to a hybrid polymer-semiconductor nanowire solar cell based on P3HT and CdSe. By
controlling the length of the nanowires one can change the distance traveled by electrons in
the solar cell, while a control of the energy gap (through the nanowire radius) can be used to
optimize the overlap between the absorption spectrum of the solar cell and the solar spectrum.
In the solar cell below (see first line, right) P3HT is a hole acceptor, CdSe is an electron
acceptor, CdSe and P3HT having complementary absorption spectra. The solar cell absorbs
between 300 nm and 720 nm, the CdSe nanowires with a length of 60 nm starting to absorb at
650 nm if their diameter is 3 nm, and at 720 nm for diameters of 7 nm. If the photon is
absorbed by P3HT the electrons excited in the nanocrystal reach directly the electrode, the
PEDOT:PSS polymer leading the holes at the opposite electrode. The external efficiency of
such a cell is 54% at AM1.5, the power conversion efficiency, however, being of only 1.7%
15
( Voc = 0.7 V, FF = 0.4). The open-circuit voltage Voc is determined by the difference in the
workfunctions of the electrodes (PEDOT:PSS and Al) and by the difference between the
lowest free level in the CdSe nanowire and the HOMO in P3HT. In addition, in nanocrystals
the absorption coefficient is higher than in the bulk material and therefore thinner devices can
be fabricated, with lower recombination losses.
As can be seen from the figure above, left, the external quantum efficiency is higher in
nanowires than in quantum dots, since the pathlengths for electrical transport are longer in
nanowires (the potential barriers at the nanowire/polymer interface decrease in number and
hence the collecting efficiency of electrons increases). The external quantum efficiency is
defined as the number of collected electrons per incident photon (without accounting for
corrections due to reflection losses). In networks from shorter nanowires/nanoparticles, the
electrons are transported by hopping, while in longer nanowires band conduction dominates.
An example of solar cell containing a superlattice is the tandem multijunction cell in
the figure below, which consists from a succession of three junctions in amorphous Si in
which the different bandgaps form between allowed levels in the valence and conduction
bands in three regions containing superlattices with different periods and heights of the
potential barriers.
16
Schottky solar cells in nanocrystalline colloidal films
We have seen that in organic solar cells it is possible (although inefficient) to convert the
solar energy in electricity in a single polymer layer placed between asymmetric contacts/with
different workfunctions. Such a simple, metal/nanocrystals/metal configuration, can be
implemented in colloidal nanocrystals (PbSe nanocrystals in the figure below), which have,
however, a much higher external quantum efficiency.
17
The large photocurrent in the solar cell above (of 24.5 mA/cm2) is due to the Schottky
junction at the negatively polarized electrode that separates the photogenerated carriers. The
external quantum efficiency is 55-65% in the visible range and 25% in infrared at AM1.5G,
the power conversion efficiency being of 2.1% for Voc = 239 mV and FF = 0.41. Voc depends
linearly on the height of the potential barrier eφ B = E g − e(φ m − χ ) , where φ m is the
workfunction of the metal and χ is the electronic affinity of the semiconductor, and decreases
as the metal workfunction increases. Moreover, the open-circuit voltage is smaller in thicker
devices because the recombination processes increase in number. In thicker device the blue
photons, which are absorbed at the front of the cell have a smaller contribution to the
photocurrent as the red photons, which penetrate deeper, close to the active region. The active
region is thin since the exciton diffusion length is small, of 100 nm. In thick solar cells the
series resistance increases because the transport distance is enhanced and the surfaces are less
smooth, but the shunt resistance does not vary significantly with the thickness (it increases
only slightly). The figure below shows an example of the open-circuit voltage dependence on
the diameter of colloidal nanocrystals (left) and metal workfunction (right).
Solar cells with intermediate band
The intermediate band solar cell is based on a succession of (coupled or not) potential wells,
such that the intermediate band positioned between the valence and conduction bands of a
semiconductor increases the absorption of low-energy photons (of photons with energies
equal to the difference between the conduction and, respectively, valence bands and the
18
intermediate band, i.e. the red and green photons in the figure below) without reducing the
energy gap, and hence the photovoltaic voltage of the device. The electrons can be excited in
the conduction band by a single absorption process (in which an electron in the valence band
absorbs a violet photon in the figure below), or by a combination of two processes, which
imply the absorption of two lower-energy photons (red and green) the electron performing
first a transition from the valence in the intermediate band, and then from the intermediate to
the valence band.
conduction band
intermediate band
valence band
The intermediate band solar cell is similar in principle to the tandem multijunction solar cell
(both split the solar spectrum and convert it in electricity utilizing several forbidden bands)
and has the same estimated maximum conversion efficiency, of 86%.
In an intermediate band solar cell the quantum wells form a superlattice or a MQW
type structure (a succession of uncoupled quantum wells). In the last case (see the figure
above, in a p-i-n configuration), the charge carriers or the excitons generate by the absorption
19
of a photon with energy Ea or Eγ , both smaller than E g , can be thermally injected in the
conduction band (for electrons) and valence band (for holes) where they are no longer
localized (become free to move in the whole structure and are no longer confined in the
quantum well) and contribute to photocurrent. In this solar cell, Voc is controlled by
recombination in the bulk material (in barriers), and there is additional absorption in the
quantum wells. The open-circuit voltage is the same as in a p-n junction in the barrier
material, but the short-circuit current, and thus the efficiency, increases. In a GaAs structure
with MQW from InGaAs/GaAs, the estimated maximum efficiency is 63% at 46000 suns.
Alternatively, quantum wells can form in a single band (the conduction band in the
figure above), the electrons being excited in the highest energy band either in a single process
(process 1), or by a combination of two processes, which imply the absorption of two lowerenergy photons (processes 2 and 3). The practical implementation of such structures is
difficult, the carrier mobility is small, and the undesirable recombination processes are
frequent. For these reasons, the experimentally obtained conversion efficiency is still small.
Solar cells with hot charge carriers
The solar cells with hot charge carriers collect the non-thermalized carriers (with energies
higher than E g ) before they collide with phonons and thus lead to a temperature increase in
the device. The estimated conversion efficiency of these solar cells is η = 85.4% (the
maximum theoretical efficiency is 86.8%).
Hot carriers form by absorption of a photon with an energy E much higher than the
bandgap, E >> E g . The excess energy, or kinetic energy E − E g , can heat the solar cell and
thus reduce its efficiency. The charge carriers with excess energy are called hot electrons and
holes if their excess kinetic energy is higher than the edges of conduction and valence bands
20
with at least k B T , and can be understood as having an effective temperature higher than that
of the crystalline lattice. The effective temperature of hot carriers can reach 3000 K even for
crystalline lattice temperatures of only 300 K.
After photoexcitation, the hot carriers interact first with themselves and with the cold
carrier population (the electrons and holes that exist previously in the conduction and valence
bands, at the crystalline lattice temperature) through carrier-carrier collisions and scattering
processes. The collision rate (the number of collisions per unit time) is different for electrons
and holes. Therefore, the separate distributions form, and separate temperatures can be
assigned to electrons and holes. After about 100 fs, the separate electron and hole populations
reach equilibrium, but are not in equilibrium with the crystalline lattice. To reach equilibrium
with the crystalline lattice, carrier-phonon interactions must occur, which can be distinct for
each carrier type, or Auger processes must take place, in which the excess energy of a carrier
type is first transferred to the other carrier type that interacts subsequently with phonons. As a
result of these processes the lattice temperature becomes equal to that of charge carriers
(increases from the initial values); this phenomenon is called thermalization. After
thermalization, the electrons and holes recombine in radiative or non-radiative processes. The
hot electrons and holes relax/thermalize with different rates due to their different effective
masses. In general, the effective electron mass is smaller than that of holes, so that electrons
cool slower.
There are two methods to use efficiently the hot carriers: for generating a higher
photovoltage or a higher photocurrent. In the first case, the carriers are extracted from the
active region before thermalization/before cooling, while in the second case the hot carriers
generate a second (or several) electron-hole pair(s) by impact ionization. In the first case the
separation, transport and transfer rates of photogenerated carriers at the interface between the
two semiconductors must be smaller than their cooling rate, whereas in the second case the
rate of impact ionization must be higher than the cooling rate. These rates can be tuned to
desired values in quantum structures (in quantum dots, wires or wells). In particular, the
cooling rate of hot carriers can be reduced dramatically and the rate of impact ionization can
become similar to that of cooling rate of charge carriers.
The charge carriers (electrons and holes) can be extracted from the absorbing material
before thermalization by tunneling contacts (see the figure below). In this situation the hot
carriers are extracted rapidly and at fixed energy (the energy of the discrete level in the thin
layer/quantum well introduced between the absorbing material and contacts).
21
The photovoltaic elements in which several pairs of charge carriers are generated per
absorbed photon have an internal quantum efficiency higher than 1. The process in which
more than one electron-hole pair (or excitons) is produced for each absorbed photon is called
impact ionization. In this nonlinear process, the excess energy of electrons, which would
otherwise dissipate as heat, leads to the formation of another electron-hole pair. These solar
cells are based only on hot electrons, which (as explained previously) thermalize slower than
holes. An electron excited in a high-energy state can generate another electron-hole pair as a
result of the desexcitation process.
In bulk materials this ionization mechanism is inefficient because the charge carriers have a
higher recombination rate than the impact ionization rate and because the total momentum
must be conserved in the crystal. This phenomenon is observed in bulk semiconductors only
for photon energies E several times higher than the energy bandgap E g . For example, in Si
22
the efficiency of impact ionization is 5% (so, the total quantum efficiency is 105%) for
E = 3.6 E g = 4 eV, and 25% at E = 4.4 E g = 4.8 eV. The theory predicts that in a single p-n
junction in which up to 8 electron-hole pairs can be generated per photon, the efficiency is
58% for 1000 suns (39% for 1 sun), compared to 38% (31%), if more than one pair is excited.
In this respect, the generation of several electron-hole pairs could become interesting even in
bulk materials, if solar concentrators are used.
On the contrary, the impact ionization is favored in quantum dots due to an enhanced
Coulomb interaction in excitons and because the requirement of momentum conservation is
relaxed in confined structures. In quantum dots the impact ionization has as result the
generation of more excitons. For example, in PbSe quantum dots up to 7 excitons can be
generated per absorbed photon: two excitons form at E = 3E g , and the impact ionization
efficiency becomes 118% (more than two excitons form) at E = 3.8 E g . At E = 4 E g the
efficiency of impact ionization is higher than 200% (so, the internal quantum efficiency is
higher than 300% and more than three excitons form per absorbed photon) in PbSe quantum
dots with a diameter of 3.9 nm. Multi-excitonic generation has been evidenced also in
quantum dots of CdSe, InAs, or Si.
The figure above illustrates the dependence of the internal quantum efficiency on the
energy of incident photons normalized at E g for quantum dots in several materials. The PbS
and PbTe quantum dots have diameters of 5.5 nm, and 4.2 nm, respectively, the E g being
indicated in the figure, whereas the three E g values for PbSe correspond to quantum dots
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with different diameters: 5.7 nm ( E g = 0.71 eV), 4.7 nm ( E g = 0.82 eV), and 3.9 nm ( E g =
0.91 eV).
To control both photon absorption and the cooling rate of hot carriers one can use
superlattices, usually in p-i-n configurations. In this case, the fraction of absorbed photons in
the solar spectrum increases due to the intermediate (mini)bands of the superlattice. At the
same time, the superlattice minibands slow the cooling of the hot electron distribution and
allow the rapid transport and collection of electrons with high excess kinetic energy, so that a
higher open-circuit voltage Voc is produced. Impact ionization processes can occur also in
these structures, resulting in an increase in photocurrent, but usually the generation of several
excitons per absorbed photon and the efficient transport/collection of hot carriers do not occur
simultaneously.
Solar spectrum modification
An alternative to using several layers to convert the solar energy (as in multi-junction solar
cells) is the modification of the solar spectrum before photons reach the photovoltaic element.
The principle of this method is illustrated in the figures below and is based on the fact that the
maximum conversion efficiency of a solar cell with a single junction can be obtained in
semiconductors with an E g between 1.25 eV and 1.45 eV, while the solar spectrum is much
wider: between 0.5 eV and 3.5 eV. If a single p-n junction can convert at most 31% of the
incident solar power (33% in the Shockley-Queisser theory) because some photons cannot be
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absorbed because their energy is smaller than E g and are thus transmitted through the solar
cell, while others have an excess energy that is lost through thermalization (see the figure
below, left), the conversion efficiency could increases if the solar spectrum could be modified
such that it overlaps the spectrum of absorbed photons in a single-junction solar cell (see the
figure below, right).
This spectral transformation can be achieved by two processes: up-conversion and downconversion of the energy of incident photons. In the up-conversion process (see figure (a)
below), two (or several) photons with lower energy generates a single photon with higher
energy, which can be absorbed.
(a)
(b)
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On the contrary, in the down-conversion process (see figure (b) above) a high-energy photon
(in the ultraviolet region of the solar spectrum) transforms in two or several lower-energy
photons that can be absorbed in the cell. The up- and down-conversion of the photon energy
are nonlinear processes, which occur with relatively small efficiency in, generally, lanthanide
ions.
For example, the down-conversion can take place if the emission of two low-energy
photons can be induced in a material with an impurity level in the energy bandgap, such as
LiGdF4 doped with Eu3+, in which two photons in the visible range are emitted for each
absorbed photon in ultraviolet through an energy transfer from excited Gd3+ to Eu3+. The
same effect has been observed in Si quantum dots with Er3+ ions in a SiO2 matrix, other
potential materials for down-conversion being AlAs and GaP.
The up-conversion of photon energy has been demonstrated in a GaAs solar cell doped
with rare earths (Er3+ and Yb3+), in the configuration presented in the figure above. The
(estimated) efficiency of the solar cell is 48% for 1 sun, and 63% for 46200 suns. Infrared
photogeneration has been evidenced also in up-conversion Si solar cells with Er3+ ions, the
external quantum efficiency being of only 2%.
Plasmon solar cells
Plasmons are collective oscillations of the electron gas in metals or semiconductors and are
associated with a strong amplification of the electromagnetic field at the interface between a
metal and a dielectric/isolator (see the figure below). In particular, surface plasmons form in
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metallic nanoparticles, which enhance light absorption due to the coupling of incident photons
with the collective oscillations of free electrons at the metal surface.
Moreover, the electromagnetic energy can be guided without significant losses along a
periodic chain of metallic nanoparticles (even around 90-degrees corners) which convert the
optical mode in non-radiative surface plasmons. For example, it has been observed that Ag
nanoparticles with a diameter of 30 nm guide the electromagnetic energy along several
hundreds of nm via interactions between particles in the near field. Such nanoparticles act as
antenna on the solar cell surface, which collect the incident light around the resonance of the
surface plasmons and then scatter it in a wide angular range, such that the optical pathlength
in the absorbing layer increases (see the figure below, left). In another configuration, light
couples to the surface plasmons that propagate at the semiconductor/metal interface (the metal
being placed under the semiconductor, as in the figure below, right) through corrugations with
a periodicity much smaller than the light wavelength. In this way, the energy flux direction
changes from perpendicular to lateral with respect to the photovoltaic layer.
27
The figure below represents a tandem solar cell that uses surface plasmon polaritons to
enhance light absorption via scattering on metallic nanoparticles around the plasmonic
resonance frequency. Such solar cells can use very thin layers of different materials.
In plasmonic solar cells, the photocurrent can increase 18 times (for a light wavelength
of 800 nm) if Ag nanoparticles are placed on the surface of a crystalline Si photovoltaic
element with a thickness of 165 nm deposited on a SiO2 substrate. In the same type of solar
cell with Au nanoparticles, the photocurrent increases with 80% at λ = 500 nm, which
corresponds to 8% increase in the conversion efficiency.
Other solutions to increases the conversion efficiency of solar cells
Other solutions to increase the conversion efficiency of solar cells and/or reduce their costs
include the use of new materials and of new configurations of solar cells. For example, it was
found that carbon compounds such as camphor K = C10H16O, can be used to fabricate solar
cells. The conversion efficiency of the n-K/p-K/p-Si structure is 2.3%.
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graphene
ITO
FTO
The figure above illustrates a solar cell with graphene electrodes. Graphene (see the
figure above, left) is a single layer of carbon atoms arranged in a periodic hexagonal lattice (it
is thus a mesoscopic structure). The advantage is that (as can be seen from the figure above,
right) its transmission coefficient is higher than that of other compounds usually used as
transparent oxides, such as ITO (indium tin oxide) and FTO (fluorine tin oxide), in the highwavelength (low-energy) region of incident photons.
The solar cell configurations have also evolved in order to reduce the losses due to the
“shadow” of grid electrodes, for instance. A succession of such improvements is presented in
the figures below, the solar cell configurations evolving from the traditional one (in figure
(a)), to the MWT (metallisation wrap-through) type in figure (b), in which the metallization
wraps the structure, followed by the EWT (emitter wrap-through) configuration in figure (c),
in which the emitter wraps the structure, and finally the back-junction configuration in figure
(d). In the figures below the grid consists from parallel thin fingers that transport current to
busbars, which are wide central electrodes that connect the solar cells to external circuits.
(a)
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(b)
(c)
(d)
In the configuration in figure (b), a part of the top metallic grid is moved backwards (the
busbar moves), and the remaining part at the surface is connected to the back part by
extending it through a number of holes in the wafer. In figure (c), the upper surface has no
metallization, but the emitter is still connected to it. The base, interdigitated contact, is
interdigitated with the emitter contact (placed backwards), and the up-down contact is realized
with the help of the emitter, which extends through the holes in the substrate. In the backjunction solar cell, both the metallization and the emitter are placed backwards, which allows
the increase of density and interconnectivity of solar cells, reducing at the same time the
losses due to electrode shadow and grid resistivity. This configuration, in which the electronhole pairs are generated in the bulk region with a long lifetime, have small surface
recombination and can work at high radiation fluxes/in concentrators.
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Conclusions
Estimations show that, in 2050, an energy of 30 TW/year not produced based on carbon/fossil
fuel would be necessary to satisfy the needs of a population of 10-11 billion humans if the
increase rate of global economy would be 2% per year. This value is calculated based on the
quantity of atmospheric CO2 that can be tolerated without a major impact on global climate
change. Presently, this quantity is 275 ppm (increasing from 175 ppm CO2 before the
industrial revolution), and could stabilize at 400 ppm in 2050. Currently, the annual
consumption of 6 billion humans is of 13 TW/year. A large part of this energy could be
generated by solar cells. Solar cells could be used not only in panels placed on houses or in
solar production facilities, but also in (see the figures below) solar planes, photovoltaic
clothing, or solar cars. All these applications are in the prototype phase. The knowledge
accumulated at this course (and at others during your master studies) helps you to contribute
actively/be part of this technological revolution.