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PROGRESS ON HOT CARRIER CELLS
Gavin Conibeer1, Nicholas Ekins-Daukes1, Jean-François Guillemoles2, Dirk KĘnig1,
Eun-Chel Cho1, Santosh Shrestha1, Martin Green1
1ARC Photovoltaics Centre of Excellence, AUSTRALIA, 2IRDEP: joint CNRS-EDF-ENSCP, France
Corresponding e-mail: g.conibeer@unsw.edu.au
ABSTRACT
Hot Carrier cells aim to tackle the carrier thermalisation
loss after absorption of above band-gap photons by
separating and collecting carriers before they
thermalise. This requires slowed carrier cooling in an
absorber material and collection through narrow
selective energy contacts. Previous work has proved
the concept of these selective energy contacts using
resonant tunneling in Si QD double barrier structures.
Further experimental work on electrical and optical
excitation of these structures will be re presented.
Previous modeling work has demonstrated the
possibility of slowing the rate of carrier cooling by
modifying the phonon dispersion in QD superlattices.
Developments in this modeling which indicate the
critical importance of the interface are also presented.
1. INTRODUCTION
The concept underlying the hot carrier solar cell is
to slow the rate of photoexcited carrier cooling to allow
time for the carriers to be collected whilst they are still
at elevated energies (“hot”), and thus allowing higher
voltages to be achieved from the cell [1,2]. Significant
reduction in cooling has been observed at very high
illumination intensities via a ‘phonon bottleneck’
mechanism [3] which has been demonstrated to be
enhanced in QW nanostructures [4,5]. In order to
reduce the illumination intensities at which this
mechanism gives significantly slower cooling towards
one sun intensities, it is necessary to block the decay of
optical phonons into acoustic phonons.
EG
Es
Hot carrier
distribution
small Eg
Ef
(
n
)
Ef
(p)
TA
TH
TA
e- selective
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E
f
Es
qV
A
μ '
Fig. 1 Band diagram of an ideal hot carrier solar cell.
The absorber has a hot carrier distribution at temp TH .
Carriers cool isoentropically in the mono-energetic
contacts to TA .
In addition to an absorber material that slows the
rate of carrier relaxation, a hot carrier cell must allow
extraction of carriers from the device through contacts
which accept only a very narrow range of energies
(energy selective contacts or ESC). This is necessary so
that cold carriers in the contact do not cool the hot
carriers, i.e. the increase in entropy on carrier extraction
is minimised. This paper discusses experimental work
which is currently focussed on energy selective contacts
using resonant tunnelling structures using a single layer
of Si quantum dots as resonant centres.
2. ENERGY SELECTIVE CONTACTS
The operation of the ESCs is best understood by
considering the hot carrier distribution in the absorber
as being comprised of three components:
1. Those carriers at the energy of the ESC: - these are
collected at the optimal energy and hence
electrochemical potential of the appropriate
contact.
2. A distribution of carrier energies below the ESC
energy: - these must be prevented from being
collected by the lower band edge of the contact or
they would decrease the average energy and hence
electrochemical potential of collected carriers.
3. A distribution of carrier energies above the ESC
energy: - this is more subtle - collection of these
carriers would indeed increase current (as occurs in
a thermoelectric cell) but the excess energy of each
carrier above the ESC energy would be lost in
thermalisation in the external contact. A more
efficient “hot carrier cell” is achieved if these
carriers are reflected back into the absorber by an
upper energy cut-off in the contact. A further
requirement is that carriers in the absorber with
energy higher and lower than the ESC are then able
to re-normalise their energy through carrier-carrier
scattering so as to re-populate the ESC level.
An alternative description of such an ESC, in
thermodynamic terms, is that the carriers are thus
collected with a very small increase in entropy. Ideally
this collection would be isoentropic using mono-
energetic contacts [2,6]. It can be shown that the
entropy generation is in the first order proportional to
the energy width of the ESC and negligible as long as
this width is much less than kT [7].
2.1 Silicon quantum dots for ESCs
A double barrier resonant tunneling structure is
used for experimental ESC measurements. This uses a
method of self-organised Si quantum dot growth
developed at UNSW over the last few years [8,9]. The
structure consists of 5nm barriers of sputtered SiO2
between which is sputtered a 4nm layer of Si rich
silicon oxide. The whole structure is deposited on
degenerate n-Si wafer and capped with a heavily doped
layer of sputtered n-Si. On annealing, Si nanocrystals
precipitate from the Si rich layer, limited in size by the
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thickness of the layer, as determined by TEM. The
small size of these nanocrystals is such that discrete
quantum confined energy levels develop (as suggested
by photoluminescence) such that they can be regarded
as true quantum dots. Mesas of area 1/16cm2 were
prepared lithographically and Al contacts evaporated to
front and back by shadow masking. For the growth and
anneal conditions used, each mesa of this size contains
about 1010 Si QDs [10].
A significant proof of concept has been achieved,
as shown in Fig. 2 with negative differential resistance
observed at room temperature for a double barrier
quantum dot structure [10]. The NDR resonance does
not appear to be strong but nonetheless such a result at
room temperature is very encouraging as evidence for
1D energy selection.
Fig. 2 I-V data at 300K for the double barrier resonant
tunneling structure, showing NDR (indicative of
resonant tunneling) for two different devices.
Further work on the modelling of the 1D resonant
tunnelling has been carried out with a model developed
for perturbations in the position of a defect in an oxide
barrier [11].
2.2 Conductive atomic force microscopy
Further characterisation of the resonant tunnelling
structures has been carried out using conductive atomic
force microscopy (CAFM), through a collaboration with
Dr Chris Pakes at Melbourne University. A bias is
applied to the conductive probe tip and the current-
voltage characteristics of the single layer of Si quantum
dots is mapped with a spatial resolution of a few
nanometres [12].
Fig. 3 CAFM on a double oxide resonant tunnelling
structure. a) Current map obtained at 10V (white dots at
up to 800 pA); b) The current profile across two spots
in a) indicated by the circle.
Results from CAFM of a sample similar to that used
for the data in Fig. 2 but without contacts or Si capping
layer and with a thicker front oxide layer of about
20nm, are shown in Fig. 3. These indicate that CAFM
is useful for verifying the location and density of
quantum dots non-destructively. Further data on a
single Si QD layer sandwiched between layers of silicon
nitride are reported in [13].
Optically assisted I-V
An alternative technique for measurement of
selective energy contacts uses a high intensity optical
excitation [14]. If hot carriers can be generated near the
barrier, a hot carrier like distribution of level
occupancies is created at the ESC. This also requires
that the optical generation rate within the semiconductor
is high enough and/or that the current is measured
within a few picoseconds of the massive generation of
hot carriers.
Work is progressing on this technique with
excitation using pairs of filters on a xenon beam source
to give a variable narrow range of optical energies.
Initial experiments without the filters show an increase
in current on illumination, apparently due to a non-
equilibrium hot carrier population, which does not
appear to be due to purely thermal affects. Future
measurement down to LN2 temperatures should show
more detailed features of the IV behaviour.
3. SLOWED CARRIER COOLING
Previous work [15-18] has investigated the critical
role in the decay of hot optical phonons predominantly
by scattering with optical phonons. (Scattering with
acoustic phonons also occurs but all phonons emitted
are close to zone centre, very little energy is lost by
acoustic phonon scattering.) This emission of optical
phonons builds up a hot non-equilibrium population.
This hot optical phonon population re-heats the electron
population, thus slowing carrier cooling. Thus the
critical feature in the overall carrier cooling is the rate
of decay of the hot optical phonons. It has been
identified by other workers that the principal
mechanism for this in most semiconductors is the decay
of an optical phonon into two longitudinal acoustic
(LA) phonons of energy half that of the optical phonon
and of equal and opposite momenta, known as the
anharmonicity or Klemen’s mechanism in which optical
phonons decay only into two longitudinal acoustic
phonons of half the energy and of equal and opposite
momenta: Oĺ2LA(only) [19,20]. Interruption of this
mechanism maintains a hot optical phonon population
which reheats the carrier population.
In some bulk semiconductors, with a large
difference in their anion and cation masses, there can be
a large gap between the highest acoustic phonon energy
and the lowest optical phonon energy. This can be
termed a “phononic band gap” referring to the
disallowed phonon energies caused by a periodic
modulation of atomic force constants [16]. [This is
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analogous to the “photonic band gap” which arises from
the disallowed photon energies caused by a periodic
modulation of refractive indices.] In a few cases – e.g.
InN, GaN, BiN, AlSb & SnO – this gap is larger than
the highest acoustic phonon energy and hence prevents
operation of the optical decay mechanism described
above. (In a few others – e.g. InP – the gap is almost
this large.) A comparison of the normalised phononic
band gaps to the acoustic phonon energy is shown in
Fig. 4 as calculated by simple force constant
calculations.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
BiN
InN
SnO
GaN
AlSb
InP
SiC
AlN
BN
AlP
0%
20%
40%
60%
80%
100%
Fig. 4 Ratios of phononic band gap energy values for
various binary compounds, based on simple elemental
mass calculations: Ŷenergy gap between acoustic and
optical modes normalised to acoustic frequency; Ÿ
energy dispersion of optical modes. The dashed line
indicates the max. acoustic phonon energy to which the
other data are normalised.
It can be seen in Fig. 4 that the largest gap for a
simple III-V zinc-blende or wurtzite material occurs in
InN with a normalised ratio of optical to acoustic
phonon energies of 1.8. Such a phononic band gap is
confirmed in measured and calculated data on a full InN
dispersion [21]. This is more than enough to prevent
operation of the Klemens mechanism as the acoustic
phonon energies are forbidden. The largest gap in
Fig. 4 is that for BiN, with a normalised ratio of 2.8.
Carrier cooling data for InN are very limited in the
literature [22], but do indicate reduced carrier cooling
rates as compared to GaAs [4,5]. This thus supports the
idea that the Klemens mechanism is suppressed in these
materials with a wide phononic band gap. However, a
further important consideration is that a hot carrier
absorber must have a narrow electronic band gap to
maximise photon absorption. Of the materials
discussed, only InN has a band gap less than 1eV
(0.7eV) with InP and AlSb both at about 1.6eV. All the
others are too large for a wide range of solar photon
absorption.
3.1 Reduced Dimension Phononic Structures
The current work, is in modelling a similar
prevention of the Klemens optical phonon decay
mechanism in less exotic materials (possibly based on
elemental semiconductors), by exploiting the Bragg
reflection that occurs at the mini-Brillouin zone
boundaries of nanostructure superlattices. This
reflection opens up mini-gaps in the phonon dispersion
for those acoustic phonon energies which satisfy the
Bragg condition. Fig. 5(a) shows the acoustic phonon
dispersion modelled using a linear chain force constant
model similar to that for Fig. 4. Fig. 5(b) shows a
psedo-3D phonon density of states, assuming the gaps
are as calculated for 1-D in Fig. 5(a) [17,18]. [A full
calculation of the true 3-D DOS is a rather complex and
beyond the scope of this paper.] The important property
in this context is a poor transmission of lattice
vibrations (or phonons) across the interface between the
QW or QD and its matrix, rather than the more usual
modulation of the electronic properties in such
superlattices.
In Fig. 5 the dispersion is shown in both a folded
zone and extended zone representation. These are
equivalent but do serve to emphasise different points.
The folded zone branches are seen to have energy at
zone centre. Hence they are often termed ‘optical-like’.
However they are indistinguishable from optical modes
and indeed optical modes in a bulk material are purely
standing waves set-up with just the same way, except
that reflection is from the Brillouin zone boundary
rather than the mini-zone. Hence all the branches in
Fig. 5, above the very bottom purely acoustic branch,
are the optical modes of the superlattice system. Hence
we can represent Klemens decay of an optical phonon
by the dotted arrow shown in Fig. 5(a). It can be seen
that this can indeed decay to two allowed energies for
phonons at half the energy and equal momenta but that
these decay modes are other lower energy optical modes.
This particular structure then seems not to be very
useful in blocking Klemens decay.
Fig. 5 a) Acoustic phonon dispersion calculated using a
linear chain force constant model. b) pseudo-3D
calculation of the DOS. c) Force constants as for a) but
including soft interface modes. [Superlattice period, l1
= l2= 2a, a = 0.23nm; ratio of force constants, T1/T2 = 2;
ratio of masses, M/m = 10 for (a); = 7 for (c).] Also
shown is the supression of the Klemems mechanism.
In Fig. 5 the mass ratio used is 10 , which is rather
large but comparable to that of Bi:N and In:N. The
gaps are sufficient to block decay of the highest phonon
energy by Klemens decay. Hence, if the superlattice
structure is engineered correctly, the mini-gaps can in
principle be arranged such that they prevent the decay
of optical phonons by Klemens and enhance the phonon
6 8 10 12 14
m-
1
x 10
9
0.01
0.02
0.03
0.04
0.05
a) Wave vector,
402
1e
b) DOS, au
Energy (eV)
E n e r g y [ e v ]
024
0
c) wave vector
E n e r g y [ e v ]
Eoptical í Eacoustic
Eacoustic
Eoptical (Max - Min)
Eacoustic
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bottleneck effect and hence slow carrier cooling.
However, to achieve such effects in practice, the
structure would need to be finely tuned. Indeed the
peaks in the DOS around the gaps in Fig. 5(b) indicate
that a very slight variation will lead to many more states
being available for the decay mechanism.
The wider range of phonon modes which are
optically active due to mini-zone folding, will scatter
with hot electrons in addition to the originally optically
active top branch of the dispersion. These occupied
phonon modes will then be able to decay by the
Klemens mechanism down to the purely acoustic
branch, as shown by the lower two arrows in Fig. 5(a).
Thus providing a route for optical phonon decay and
hence for electron cooling.
Although consideration of the lower energies of
these branches and a default to the bulk situation would
mitigate the effectiveness of this route it would
nonetheless seem advantageous to engineer a
superlattice such that Klemens decay of phonons in the
lower branches is blocked as well.
2.2 Interface Modes
Consideration of the interface as a region with
discrete phonon properties can modulate the dispersion
further. Some initial work was done along these lines in
[17,18] and showed an increase in the size of the
dispersion gaps. Fig. 5(c) shows an extension of this
work for an interface layer which is modelled with a
stiffness 20% of the QD or matrix layers. The mass
ratio is now chosen as 7:1 (the same as that for In:N).
These soft interfaces result in widening of the gaps
because it is more difficult for phonons to propagate
between the QD and the matrix material. For the
paramaters chosen, it can be seen that the gaps are now
sufficient to block Klemens decay from all the optically
active branches. This then should, in principle, should
be a structure capable of blocking all Klemens decay –
but still only modelled in one dimension.
4. CONCLUSIONS
Hot carrier cells require two difficult
implementations: (A) slowing of the rate of carrier
cooling and (B) collection of carriers through energy
selective contacts of a narrow width. Proof of concept
of (B) has been demonstrated with a double barrier Si
QD resonant tunnelling structure and further work on
characterisation is improving the data. Theoretical
modelling work on (B) is attempting to emulate the
phononic gaps observed in bulk semiconductors with
large elemental mass ratios, with the mini-Brillouin
zone folding of phonon dispersions in QD superlattices.
That these should block the dominant mechanism for
optical to acoustic phonon decay, has been
demonstrated, but that full blocking for all folded
optical modes requires consideration of an interface
between QDs and matrix of a material with very
different spring constant. This may be achieved in a
core-shell QD superlattice nanostructure.
ACKNOWLEDGEMENTS
The authors acknowledge the support of the
Australian Research Council for the Photovoltaics
Centre of Excellence and the CAFM work of Dr Chris
Pakes at Melbourne University.
REFERENCES
[1] P. Würfel, Sol. Energy Mats. and Sol. Cells. 46
(1997) 43.
[2] M.A. Green, Third Generation Photovoltaics
(Springer-Verlag, 2003).
[3] A.J. Nozik, C.A. Parsons, D.J. Dunlary, B.M.
Keyes, R.K. Ahrenkiel, Solid State Comm. 75
(1990) 247.
[4] Y. Rosenwaks et al, Phys Rev B, 48 (1993) 14675.
[5] W.S. Perlouch et al, Phys Rev B, 45 (1992) 1450.
[6] G.J. Conibeer, C-W. Jiang, M.A. Green, N. Harder,
A. Straub, Proc. 3rd World Conf. on Photovoltaic
Solar Energy Conversion (Osaka, 2003).
[7] J-F. Guillemoles, G.J. Conibeer, M.A. Green, Proc.
21st Euro PV SEC (Dresden, Germany, 2006) 234.
[8] E-C. Cho, Y.H. Cho, R. Corkish, J. Xia, M.A.
Green, D.S. Moon, Asia-Pacific Nanotechnology
forum (Cairns, 2003).
[9] E-C. Cho, Y.H. Cho, T. Trupke, R. Corkish, G.
Conibeer, M.A. Green, Proc. 19th European
Photovoltaic Solar Energy Conference (Paris,
2004) 235.
[10] C-W. Jiang, E-C. Cho, G. Conibeer, M.A. Green,
Proc. 19th European Photovoltaic Solar Energy
Conference (Paris, 2004) 80-83.
[11] C-W. Jiang, M.A. Green, E-C. Cho, G. Conibeer, J
Appl Phys, 96 (2004) 5006.
[12] C.I. Pakes, S. Ramelow, S. Prawer, D.N. Jamieson,
Appl. Phys. Lett. 84 (2004) 3142.
[13] E-C. Cho, M.A. Cho, Green, G. Conibeer, Y.H.
Cho, D. Song, G. Scardera, S. Huang, S. Park, X.J.
Hao, Y. Huang, Advances in Optoelectronics,
accepted.
[14] D. König, C-W. Jiang, G. Conibeer, Y. Takeda, T.
Ito, T. Motohiro, T. Nagashima, 21st European
Photovoltaic Solar Energy Conf. (Dresden, 2006)
124.
[15] G. Conibeer et al, in Proceeding of 21st Euro PV
SEC (Dresden, Germany, 2006) 47.
[16] G.J. Conibeer & M.A. Green, Proc. 19th Euro. PV
Conf. (Paris, 2004) 270.
[17] G.J. Conibeer, J-F. Guillemoles & M.A. Green,
Proc. 20th Euro. PV Conf. (Barcelona, 2005) 35.
[18] J-F. Guillemoles, G.J. Conibeer & M.A. Green,
Proc. 15th PV SEC (Shanghai, 2005) in press.
[19] P.G. Klemens, Phys. Rev. 148 (1966) 845.
[20] C. Colvard, T.A. Gant, M.V. Klein, Phys Rev B, 31
(1985) 2080.
[21] V. Davydov, V. Emtsev, I. Goncharuk, A. Smirnov,
V. Petrikov, V. Mamutin, V. Vekshin, S. Ivanov,
Appl Phys Lett, 75 (1999) 3297.
[22] F. Chen, A.N. Cartwright, Appl Phys Lett, 83
(2003) 4984.
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