UNITED STATES


 


 


 


ARC
PHOTOVOLTAICS CENTRE OF EXCELLENCE 2010/11 ANNUAL

REPORT, pp 61-99

ARC PHOTOVOLTAICSCENTRE OF EXCELLENCE ANNUAL REPORT,

2012, pp 169-224


 


 


 


Article referenced as support for the following
sections:


Page 8 & 9: Figure and Text on Tandem Solar Cells













4.5 THIRD GENERATION STRAND -ADVANCED CONCEPTS


	
  

 	
  

 
	
 University
 Staff:

 
	
 •

 	
 A/Prof.
 Gavin Conibeer (group leader)

 
	
 •

 	
 Dr
 Richard Corkish

 
	
 •

 	
 Prof.
 Martin Green

 
	
  

 	
  

 
	
 Senior
 Research Fellows:

 
	
 •

 	
 Dr.
 DirkKÖnig

 
	
  

 	
  

 
	
 Research
 Fellows:

 
	
 •

 	
 Dr
 Shujuan Huang

 
	
 •

 	
 Dr.
 Ivan Perez-Wurfl

 
	
  

 	
  

 
	
 Lecturers:

 
	
 •

 	
 Dr
 Santosh Shrestha

 
	
  

 	
  

 
	
 Postdoctoral
 Fellows:

 
	
 •

 	
 Dr
 Supriya Pillai (part time)

 
	
 •

 	
 Dr
 Xiaojing Jeana” Hao

 
	
 •

 	
 Dr
 Sangwook Park (to Apr 2010)

 
	
  

 	
  

 
	
 Professional
 officers:

 
	
 •

 	
 DrTom
 Puzzer (part time)

 
	
 •

 	
 Dr
 Patrick Campbell (shared with Thin Film)

 
	
 •

 	
 Mark
 Griffin (shared with Thin Film)

 
	
  

 	
  

 
	
 Research
 Associates:

 
	
 •

 	
 Dr
 DidierDebuf (adjunct fellow)

 
	
 •

 	
 Yidan
 Huang

 
	
 •

 	
 Lei
 “Adrian” Shi (from Sept 2009)

 
	
  

 	
  

 
	
 Higher
 Degree Students:

 
	
 •

 	
 LaraTreiber

 
	
 •

 	
 Pasquale
 Aliberti

 
	
 •

 	
 Yong-Heng
 So

 
	
 •

 	
 Robert
 Patterson

 
	
 •

 	
 Binesh
 Puthen Veettil

 
	
 •

 	
 Chao-Yang
 “Jeff” Tsao

 
	
 •

 	
 Bo
 Zhang

 
	
 •

 	
 Andy
 Hsieh

 
	
 •

 	
 DaweiDi

 
	
 •

 	
 Zhenyu “Wayne” Wan

 
	
 •

 	
 Craig
 Johnson

 
	
 •

 	
 Sammy
 Lee

 
	
 •

 	
 Haixiang
 Zhang

 
	
  

 	
  

 
	
 Casual
 Staff:

 
	
 James Rudd (part time)

 
	
  

 
	
 Visiting
 Researchers:

 
	
 •

 	
 Dr.Yukiko
 Kamikawa (AIST, Tsukuba, Japan, June 2009 – Dec 2012)

 
	
 •

 	
 Prof.
 Bingqing Zhou (Inner Mongolia Normal University, China, Sept 2009 – Aug 2010)

 
	
 •

 	
 Dr.
 Mallar Ray (Bengal Eng. and Sci. University, May 2010)

 
	
  

 	
  

 
	
 Undergraduate
 Students:

 
	
  

 
	
 4th
 Year Thesis Projects:

 
	
 •

 	
 Yu
 Feng

 
	
 •

 	
 Tao
 Zhan

 
	
 •

 	
 Chen
 Pan

 
	
 •

 	
 Xi Li

 
	
 •

 	
 YaoYao

 
	
 •

 	
 Linzhi
 Ma

 
	
 •

 	
 Lin
 Dong

 
	
  

 	
  

 
	
 Masters
 Project:

 
	
 Chandraprasad Ramachandran

 
	
  

 
	
 Visiting
 Practicum students:

 
	
 •

 	
 Stephan
 Michard (RWTH Aachen, Germany, Aug 2009 – Feb 2010)

 
	
 •

 	
 DolfTimmerman
 (Amsterdam University, Oct – Dec 2010)

 



20 nm


abstract


There
has been approximately equal work on the two major projects in Third Generation in 2010. These are the
Group IV nanostructure tandem cells project - the “all-Si” tandem cell - and the Hot Carrier
solar cell project, with its continuing funding from GCEP (Global Climate and Energy
Project). There has also been further work on Up-conversion and on Plasmonics.


The Si
nanostructure work has seen increased understanding of the mechanisms for transport and quantum
confinement. More sophisticated modelling of both has been tied more directly to improved interpretation of experimental results. This has led to establishment of a predictive ‘equivalent circuit modeller’ which will allow optimisation of Si QD device parameters to maximise transport and
performance in the photovoltaic devices. Improved models for the understanding of doping effects in these materials have also been established. Work on alternate matrices for Si quantum dots, in both silicon
nitride and carbide, has seen development of composite structures which have improved transport in the growth
direction, whilst maintaining quantum confinement in the plane, but which also increase the uniformity of QD sizes. Work on Ge nanostructures has also improved with high electrical p-type conductivity established for Ge quantum dots and
excellent pseudo single crystalline growth quality for Ge quantum wells in a nitride
matrix. Heterojunction photovoltaic devices
combining the advantages of two of these different material types are now being
investigated.


Hot
Carrier cells have seen very significant improvement in demonstrated resonance in energy selective
contacts using Si nanostructure layers, as well as a development of 2 and 3D modelling of
transport in these structures. Modelling of Hot Carrier efficiencies continues to get more
sophisticated with application to real material systems such as III-nitrides and
inclusion of Auger processes which become significant at high carrier concentrations. Work on
absorbers has allowed
modelling of the phononic properties of a range of bulk materials, in
conjunction with
time resolved photoluminescence measurement of carrier cooling in some of these materials. Also
modelling of coherent nanoparticle nanostructures, which emulate the phononic properties
required, has developed into direct application to structures grown directly. These
structures include the


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Loss processes in a standard
solar cell: (1) non-absorption of below band gap photons; (2) lattice
thermalisation loss; (3) and (4) junction and contact voltage losses; (5)
recombination loss.


FIGURE 4.5.1


colloidal
dispersion of Si nanoparticles, which has seen coherent arrays successfully grown, and growth of III-V
quantum dot structures with collaborators, with modelling and characterisation indicating their
usefulness as absorbers. The parameters needed for a real hot carrier solar
cell are now
better defined, and candidates for its structure are now being modelled in more
detail. This
will feed into fabrication and characterisation of some candidate structures in
the near future.


The
up-conversion project in 2009 reported the approach of use of
porous-Si as a host material for an Erbium upconverter. This has the advantage of much greater
versatility in fabrication and electrochemical doping with Er, compared to other host phosphors.
Work in 2010 has further demonstrated up-conversion of below band gap photons. The ease of
control of porous-Si growth at different refractive indices has also been exploited to create fully
integrated multiple Distributed Bragg Reflectors. These allow a tuning of the forbidden photonic band such that
regions just outside the bandgap (which have enhanced density of photonic
states) lie at the 1500nm absorption window of Er. This effectively concentrates light into this absorbance
window and boosts up-conversion quadratically. Enhancements of up to 80 are possible with
multiple levels, with a consequent narrowing of the wavelength range enhanced. Enhancements of
40 are very practical. This represents a big potential improvement for up-conversion efficiency.


Plasmonics
has previously been applied to both frst generation and second generation Si
cells with very significant enhancements in absorbance of near band gap photons.
Work in 2010 has applied plasmonic silver nanoparticles to nanostructured Si QD layers. Again
significant enhancements of photoluminescence (reciprocal with absorption) have been absorbed, up
to 16x for wavelengths just shorter than the effective band gap. Also application to the rear
of the layer is seen to be better than the front because the reflection of the silver particles
themselves is beneficial rather than parasitic. Just as with thin film second
generation cells,
light trapping by these non-texturing methods is very important for third generation devices,
which consist of very thin layers
of material.


This
progress in all the main Third Generation project areas is improving understanding and allowing optimisation of
modelling, structures and devices. Developments to come in the next year will see significant
advancement in these areas, with excellent prospects for good demonstration devices.


4.5.1 third generation Photovoltaics


The
“Third Generation” photovoltaic approach is to achieve high
efficiency whilst still using “thin flm” second generation deposition methods.
The concept
is to do this with only a small increase in areal costs and to use abundant and
non-toxic materials
and hence reduce the cost per Watt peak [4.5.1]. Thus these “third generation”
technologies will
be compatible with large scale implementation of photovoltaics. The aim is to decrease costs to
well below US$0.50/W, towards US$0.20/W or better, by dramatically increasing
efficiencies but maintaining the economic and environmental cost advantages of
thin film deposition techniques (see Fig. 4.1.3 showing the three PV generations) [4.5.1, 4.5.2].
To achieve such efficiency improvements such devices aim to circumvent the
Shockley-Queisser limit for single band gap devices that limits efficiencies to
the
“Present limit” indicated in Fig. 4.1.3 of either 31% or 41% (depending on
concentration ratio). This requires multiple energy threshold devices such as
the tandem or multi-colour solar cell. The Third Generation Strand is
investigating several approaches to achieve such multiple energy threshold device [4.5.1, 4.5.3].


The two
most important power loss mechanisms in single-band gap cells are the inability to
absorb photons with energy less than the band gap (1 in Fig. 4.5.1), and
thermalisation of photon energy exceeding the band gap, (2 in Fig. 4.5.1). These two mechanisms alone
amount to the loss of about half of the incident solar energy in solar cell conversion to
electricity. Multiple energy threshold


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A tandem photovoltaic cell
using quantum confined QDs or QWs to engineer the band gap of the top cell and
potentially also the lower cells. Short wavelength light is absorbed in the top
cell and longer wavelengths in lower cells, thus boosting the overall voltage
generated and hence efficiency.


FIGURE 4.5.2


approaches
can utilise some of this lost energy. Such approaches do not in fact disprove
the validity of the Shockley-Queisser limit, rather they avoid it by the exploitation
of more than one energy level for which the limit does not apply. The limit
which does apply is the thermodynamic limit shown in Fig. 4.1.3, of 68.2% or
86.8% (again depending on
concentration).


In the
Third Generation Strand, we aim to introduce multiple energy levels by
fabricating a tandem cell based on silicon and its oxides, nitrides and carbides using reduced dimension
silicon nanostructures to engineer the band gap of an upper cell material. We
are aiming to collect photo-generated carriers before they thermalise in the “Hot Carrier” solar
cell. Also
we are investigating absorption of two below bandgap photons to produce an
electron-hole pair
in the cell by up-conversion in a layer behind the Si cell using erbium doped
host materials. In order to optimise the requisite properties, all these structures are
likely to be thin hence maximising absorption of light in thin structures
through light trapping is very important. Hence we are also investigating
localised surface plasmon enhanced coupling of light into these Third Generation devices.


4.5.2 Si nanostructure solar cells


4.5.2.1 the ‘‘all-Si’’ tandem cell


Researchers:


Shujuan
Huang, Ivan Perez-Wurfl, DirkKÖnig, Tom Puzzer, Xiaojing Hao, Sangwook Park, Bo Zhang, Dawei Di,
Yong-Heng So, Zhenyu Wan, Sammy Lee, Yidan Huang, Gavin Conibeer, Martin Green


We are
developing a material based on Si (or other group IV) quantum dot
(QD) or quantum well (QW) nanostructures, from which we can engineer a wider band gap material
to be used in tandem photovoltaic cell element(s) positioned above a thin flm bulk Si cell, see Fig. 4.5.2.


Previously
we have demonstrated the ability to fabricate materials which exhibit a blue shift in
the effective
band gap as the QD or QW size is reduced, using photouminescence [4.5.4] and absorption
[4.5.5] data [4.5.6]. A thin film deposition of a self-organised QD
nanostructure is achieved through a sputtered multi-layer of alternating Si rich
material and stoichiometric dielectric [4.5.4]. On annealing the excess Si
precipitates into small nanocrystals which are limited in size by the layer thickness,
thus giving reasonable size uniformity, as first demonstrated by Zacharias
[4.5.7]. Demonstration of doping of these layers with both phosphorus and boron to create a
rectifying p-n junction has resulted in devices with a photovoltaic open circuit voltage of 490mV [4.5.6, 4.5.7, 4.5.8].


Formation
of Si (or Ge or Sn) QDs through layered thin film deposition of Si rich material which crystallises into
uniform sized QDs on annealing.


A cell
based entirely of Si, or other group IV elements, and their dielectric compounds with other abundant elements
(i.e. silicon oxide, nitride or carbide) fabricated with thin film techniques, is advantageous in terms of
potential for large scale manufacturability and in long term availability of its
constituents. Such thin film implementation implies low temperature deposition without melt processing, it hence also involves imperfect crystallisation with high defect densities. Hence
devices must be thin to limit recombination due to their short diffusion lengths, which in turn
means they must have high absorption
coefficients.


For
photovoltaic applications, nanocrystal materials may allow the fabrication
of higher band gap solar cells that can be used as tandem cell elements on top of normal Si cells
[4.5.11, 4.5.12]. For an AM1.5 solar spectrum the optimal band gap of the top cell required to
maximize conversion efficiency is 1.7 to 1.8eV for a 2-cell tandem with a Si
bottom cell
[4.5.13]. To date, considerable work has been completed on the growth and characterization of Si
nanocrystals
embedded in oxide [4.5.7, 4.5.14] and nitride [4.5.15, 4.5.16] dielectric
matrices. However, little has been reported on the experimental


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FMG scheme employed for
finding electronic states and the confined energy.


FIGURE 4.5.5





Multilayer deposition of
alternating Si rich dielectric and stoichimetric dielectric in layers of a few
nm. On annealing the Si precipitates out to form small nanocrystals of a size
determined by the layer thickness. Nanocrystal or quantum dot size is therefore
uniform.


FIGURE 4.5.3





Bulk band alignments between
silicon and its carbide, nitride and oxide. Tunnelling probability between QDs
separated by d depends
exponentially on the square root of the barrier height (ΔE1/2)
multiplied by d (e.g. [4.5.19]
p244).


FIGURE 4.5.4


properties
of Si nanocrystals embedded in SiC matrix [4,5,17]. These are of particular interest for
application in photovoltaic devices because of an expected significant increase in carrier transport due to a
decrease in the barrier height between adjacent nanocrystals [4.5.18]. As a result,
sufficient carrier mobility can be obtained to satisfy device fabrication requirements.


4.5.2.2 Fabrication of Si QD nanostructures


Thin
film techniques are used for nanostructure fabrication. These
include sputtering and plasma enhanced chemical vapour deposition (PECVD). The deposition is a
variation of the multi-layer alternating ‘stoichiometric dielectric / Si rich dielectric’ process,
shown in Fig. 4.5.3, followed by an anneal during which Si nanocrystals precipitate limited in
size by the Si rich layer thickness [4.5.12, 4.5.7]. The most successful and hence most
commonly used
technique is sputtering, because of its large amount of control over deposition material,
deposition rate and abruptness of layers. A multi-target remote plasma sputtering machine with two independent RF power
supplies as well
as dditional DC power supplies is used
in this work.


RF
magnetron sputtering is used to deposit alternating layers of SiO2 and SRO of thicknesses down
to 2nm. [SRO refers
to Si rich oxide, formed by co-sputtering Si and SiO2 .] Deposition of multi-layers,
consisting typically
of 20 to 50 bi-layers, is followed by an anneal in N2 from 1050 to 11500C. During
the anneal the
excess silicon in the SRO layer precipitates to form Si nanocrystals between the stoichiometric oxide layers.


For Si
QDs in SiO2 the precipitation occurs according to the following:





Precipitation
of excess Si from Si rich dielectrics in SiNx and SiC follows a similar
crystallisation reaction as Si precipitates from the amorphous matrix. The
techniques has also been applied to growth of Sn and Ge QDs in SiNx in SiO2.
Ge quantum dots can be precipitated at substantially lower temperature, as discussed below.


4.5.2.2.1 carrier tunnelling transport in Si QD superlattices


Transport
properties are expected to depend on the matrix in which the silicon quantum dots are embedded. As shown in
Fig. 4.5.4 different matrices produce different transport barriers between the Si dot
and the matrix, with tunnelling probability heavily dependent on the height of this barrier. Si3N4
and SiC give lower barriers than SiO2 allowing larger dot spacing for a
given tunnelling current.





The
results suggest that dots in a SiO2 matrix would have to be separated by
no more than 1-2 nm of matrix, while they could be separated by more than 4 nm of SiC. Fluctuations
in spacing and size of the dots can be investigated using similar calculations. It is also found that the
calculated Bloch mobilities do not depend strongly on variations in the dot spacing but do depend
strongly on dot size within the QD material [4.5.18]. Hence, transport between dots can be
significantly increased by using alternative matrices with a lower barrier height, ∆E. For the same tunnelling current
the spacing of QDs can increase for oxide to nitride to carbide matrix.


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4.5.2.2.2 modelling of quantum confinement and tunnelling
transport


Researchers:


Binesh Puthen-Veettil, Robert
Patterson, Dirk KÖnig


Band gap engineering for
these Si nanostructure materials requires a large number of almost identical
quantum dots (QDs), evenly distributed in a dielectric layer. As the proximity
of dots increases, confined wavefunctions in the QDs interact with one another
to form mini-bands. It is also seen that higher Si content in the Si rich layer
gives rise to bigger QDs, due to the tendency of QDs to merge together and form
bigger dots during annealing [4.5.12, 4.5.20]. If the dielectric layer is a
good diffusion barrier for Si (such as the nitride layer in Si/Si3N4
or Si3N4 interlayer samples, see sections 4.5.2.3.1 and
4.5.2.3.2), this effect is strongly reduced. For relatively thick layers in
which diffusion is not constrained, the shapes of these QDs can differ greatly
from an ideal spherical shape. Calculation of confined energy in QD structures
is of interest since their electronic and optical properties can be determined
by determining the confined energy levels in the structure.


Since these calculations are
extremely difficult to perform using ab-initio methods due to the large memory
and computation time requirements, we have developed a model to quantitatively
analyse electronic states and their interactions in a QD array, in the
framework of the effective mass approximation (EMA) calibrated by ab-initio DFT
calculations. This model is realized by solving the three dimensional time
independent discretized SchrÖdinger’s equation in the EMA, employing a modified
Full Multi Grid method (FMG) [4.5.21] to overcome the difficulty of
computational intensity. By using exact solution methods to solve the Eigen
equation for the coarsest grid, the non convergence problems [4.5.22] arising
from oscillatory eigenvalues are eliminated. Since initial guesses of the
solution are very close to the approximate solution, this method proves to be
much faster than other iterative methods. The flow diagram for this process is
shown in Fig. 4.5.5.


In order to demonstrate the
conformity of results from this model with experimental results, we compared it
with experimental results for Silicon QDs in SiO2 dielectric grown
using sputtering methods and characterized using photoluminescence (PL)
[4.5.20]. Figure 4.5.6 shows the dependency of confined energy on the size of
QDs for Si/SiO2 QD structures. Confined energy increases
exponentially as QD size decreases. Comparison shows that for larger QDs
experimental and theoretical values are similar, but for smaller dots the
experimental results for the confined energy shows a lower degree of
confinement than the theoretical result. This difference can be attributed to
interface defects between Si and SiO2 and to defects within the SiO2
matrix but near the interface. For QDs below a diameter of about 4 nm these
interface effects have a larger influence on the confined energy level. This is
because the ground state electron density, which is concentrated at the centre
of the QD, is closer to these interface defects for the smaller QDs and hence more
strongly influenced.


As an extreme example of
irregularly shaped QD, we have investigated electronic states in aribitrarily
shaped QDs. Here we have used the “horseshoe” morphology [4.5.24], formed by
lateral growth of Si QD inside SiO2 dielectric shown in Figure 4.5.7
(left). These states are found to be very different from the expected
electronic energy levels that are associated with spherical QDs as shown in
Fig. 4.5.7 (right). The degeneracy in spherical QDs (3 in first excited level
and 5 in second excited level) is lost due to the asymmetric shape. The
deviation from the expected confinement level becomes significant at higher
confined levels.


This thus indicates the
importance of knowing the regime of QD growth relevant for the material
conditions. As shown in the TEM tomography of Section 4.5.2.2.3, under
appropriate conditions of Si density and annealing, a spherical morphology can
be maintained and QD merging avoided, thus giving greater control over the
confined energy levels.





Simulation results -
multigrid method and Density Functional Theory (DFT) calculations [4.5.23]
compared with the experimental results for Silicon QDs in SiO2
dielectric.


FIGURE 4.5.6





First three modes of
electronic wave-functions in a “horseshoe” shaped QD with high surface to
volume ratio (far left). The ground state is located near the centre of the dot
and is approximately in a spherical shape with zero nodes. The number of nodes
increases with the increase in the energy level. Energy levels associated with
a horseshoe shaped QD compared with that of a 6nm diameter spherical QD (left).
The two morphologies give energies which are most similar for their ground
states, with the horseshoe shape giving significantly lower energies than
spherical for higher confined levels. The degeneracy in energy levels is lost
in the horseshoe shaped dot.


FIGURE 4.5.7


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Energy filtered TEM
tomography images of Si QDs in a SiO2 matrix formed as multilayers
(left), and top view of one Si QD layer (right).


FIGURE 4.5.8





The spectra fittings of the R and T
data. The inset shows the corresponding employed optical model in
the fitting of a 20 bilayer structure composted of 5 nm SRN / 3 nm Si3N4.


FIGURE 4.5.9





Real (ε1) and imaginary
(ε2) parts of the complex dielectric function of Si QDs samples with
various sizes obtained from spectral fittings.


FIGURE 4.5.10


4.5.2.2.3 3D Ef-tEm tomography on Si QDs embedded in oxide
matrix formed as multilayers (collaboration with cornell university)


Researchers:


Xiaojing
Hao, Shujuan Huang, Lena Fitting Kourkoutis (Cornell University), Ivan Perez-Wurfl, Tom Puzzer


A
significant challenge to the design of nano-scale materials and devices arises
from the difficulty of characterising complex three-dimensional structures on small
length scales, which is nonetheless critical in understanding the material performance. Whilst a number of techniques,
such as
conventional transmission electron
microscopy, provide sufficient two-dimensional (2-D) resolution, they have insufficient depth sensitivity to obtain internal three-dimensional (3-D) structure. Electron tomography can be applied to obtain such information by using high-angle dark-feld scanning transmission electron microscopic (STEM) tomography and energy filtered transmission electron microscopy (EFTEM) tomography. We have applied this EFTEM tomography to investigate Si QDs
embedded in an oxide matrix formed
as multilayers, in order to better
understand the dot size, shape and
distribution for further optimization of
Si QD device performance. Fig. 4.5.8 illustrates the ability of electron tomography to reconstruct the morphology and internal structure of a Si QD nanostructure. Fig. 4.5.8 (left) shows the aligned
“on-axis” reconstructed EFTEM tomography,
and Fig. 4.5.8 (right) shows a top-view of the Si QD size and shape
distribution in one Si QD layer. With such information, we can confirm that inside the Si QD layer, most of the Si QDs are reasonably
spherical and well separated from
each other. This indicates that
individual QDs have not merged to form larger particles under these conditions. This is important in designing the optimum concentrations to give minimum QD spacing whilst maintaining individual
QDs.


4.5.2.3. Different materials for QD nanostructures


As
described in section 4.5.2.2.1, different matrices are useful to modify
both the tunnelling probability between adjacent quantum dots and the energy levels in the quantum
dots themselves. This approach has been carried out for both Si QDs in SiNx and in
SiC. It is also possible to have asymmetric superstructures in which quantum confinement and hence enhanced band
gap is maintained in the plane, but in which tunnelling probability is maximised in the
direction normal to the plane such that transport of carriers to contacts is maximised. Interlayers use for such
asymmetric structures can also act as diffusion barriers enhancing size uniformity of QDs.


Alternative
group IV materials such as Ge offer the possibility of lower temperature precipitation of nanostructures and the potential for band gaps lower than that of silicon should these be
required for tandem cell elements
under a silicon cell. We have
investigated both QDs and QWs of Ge in either SiO2 or SiNx
matrices.


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(a) Normalized PL spectra of
Si QDs samples (S3-S5) with various sizes. (b) Comparison of band gap expansion
(ΔEg) of Si QD as a function of QD size.


FIGURE 4.5.11


4.5.2.3.1 Silicon QDs embedded in silicon nitride matrix


Researchers:


Yong-Heng
So, Shujuan Huang


 (i) Size-dependent optical properties of Si QDs in Si-rich
nitride/Si3N4 superlattice


An
approach similar to spectroscopic ellipsometry analysis has been
proposed to determine the size dependent optical properties of silicon quantum dots (Si QDs) in Si-rich
nitride/silicon nitride superlattice structure (SRN/Si3N4-SL)
[4.5.26]. The optical
properties of Si QDs are modelled using the Tauc-Lorentz (TL) model and Bruggeman effective medium
approximation that can yield the energy bandgap of the Si QDs based on spectral ftting of the reflection
(R) and transmission (T ) of characterized samples, as shown in Fig. 4.5.9. A
four-phase
optical model as shown in the inset of Fig. 4.5.9 was employed for the spectral fitting.


Figure
4.5.10 shows that the dielectric functions of Si QDs are strongly
size dependent. Sample S3, S4 and S5 correspond to SRN/Si3N4
thicknesses of 3/3 nm, 4/3 nm and 5/3 nm, respectively. The suppressed imaginary
dielectric function of Si QDs exhibit a broad peak centred between transition energies E1
and E2 of bulk crystalline Si and which blue shift towards E2
as the QD size reduces.


Figure
4.5.11(b) shows that the band gap expansion indicated by the TL model when the size of Si QD reduces is
in good agreement with PL measurements (Fig. 4.5.11(a)). The bandgap expansion with the
reduction of Si QD size is well supported by the ab-initio calculations of confined energy levels from [4.5.25].


 (ii) n-type conductivity of nanostructured thin film composed
of antimony-doped Si nanocrystals in silicon nitride matrix


Highly
conductive thin films composed of antimony (Sb)-doped Si
nanocrystals (Si-NCs) embedded in Si3N4 matrix were prepared by a
co-sputtering technique.
Results from structural characterizations suggest that doping with Sb concentration of 0.54 at. % has negligible
affect on the crystallization properties of Si-rich nitride (SRN) films. The X-ray Photoelectron (XPS) data
of Fig. 4.5.12(a) and (b) show the Si 2p and
Sb 3d3/2 spectra of
the undoped and Sb-doped SRN films. The slight asymmetric Sb 3d3/2 peak was analyzed using a
curve-fitting routine and could be decomposed into two components, δ1
(537.0 eV) and δ2 (537.8 eV) as shown in Fig. 4.5.12(c). The two
components δ1 and δ2 (0.8 eV apart) can be assigned to
neutral Sb and positively charged
donors, respectively.


Thus,
the appearance of δ2 suggests the presence of Sb-Si bonds which
implies that Sb stoms were either incorporated within the Si-NCs or located at the interface between the
NCs and Si3N4. matrix.





XPS spectra of (a) Si 2p and (b) Sb 3d3/2 for the undoped and 0.54 at.% Sb-doped
Si-NC. (c) Fitting of Sb 3d3/2
spectrum by two peaks separated by 0.8 eV in energy (δ1 and
δ2).


FIGURE 4.5.12


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(a) Conductivities measured
throughout the entire voltage range. (b) ln(σ) vs 1/T1/2 plot
from 120 to 220 K, for the 0.54 at.% Sb-doped sample. The solid line is least
square fit to the data. (c) Temperature-dependent conductivities for the
undoped and 0.54 at.% Sb-doped samples.


FIGURE 4.5.13


The
temperature dependent conductivity data of Fig. 4.5.13(a) indicate that the conductivity of
0.54 at.%
Sb-doped SRN film (2.8X10-2 S/cm) is six orders of magnitude higher than that for undoped material (7.3X10-8
S/cm), which could be attributed to an increase in carrier concentration. Furthermore, n-type
electrical behaviour with carrier concentration of 2.4X1016 cm-3
and mobility of
2.94 cm2/V s in the doped films as observed from Hall measurements was
attributed to free carrier generation due to the effective Sb doping.


The
temperature-dependent conductivities of both undoped and Sb-doped samples are shown in Fig. 4.5.13(b). As
can be seen, doping of the Si-NCs strongly influences the electronic transport properties of the films.
Arrhenius-like temperature dependence is observed in the T range between 220 and 320 K,
attributable to thermally activated conduction. From the slope of the Arrhenius
plot, we
found that the activation energy EA
decreases to 0.182
eV for the Sb-doped Si-NCs film, suggesting effective n-type doping of the
Si-NCs. Nevertheless, the extracted EA
is much larger than that of bulk Si with the same dopant. One possible explanation for
the large EA observed would be the deeper
donor level
expected in Si-NCs. Also, it is possible that the number of free carriers
available for conduction may be limited due to a trap density distributed within the bandgap that
is comparable to the doping
density.


Interestingly,
the conductivity for the Sb-doped sample at T < 220 K deviates from Arrhenius behavior and is best
described by the expression, σ = σ0 exp [-(T0/T)1/2] as illustrated in Fig. 4.5.13(c). The charge transport
mechanism can be explained well by
a percolation-hopping model.


4.5.2.3.2 Si QDs in SiO2/Si3N4 hybrid
matrix


Reserachers:


Dawei
Di, Ivan Perez-Wurfl, Gavin Conibeer


To
improve the current transport properties in the vertical direction and to
obtain better size control of Si quantum dots, we proposed a new design based on Si QDs embedded in a
SiO2/Si3N4 hybrid matrix [4.5.27, 4.5.28]. By
replacing the SiO2 tunnel barriers with the Si3N4 layers, the
new material manages to constrain the growth of doped Si quantum dots effectively and
enhances the apparent band gap. Also electrical characterisation on Si QD/c-Si hetero-interface test
structures indicates the new material possesses improved vertical carrier transport properties.


Doped
and undoped samples with different barrier dielectrics (SiO2 and Si3N4)
are compared. Samples were fabricated using the co-sputtering multilayer technique with
layers containing excess Si consisting of SRO for both materials, with an SRO thickness of 4 nm.
Samples were either undoped or co-sputtered with either P2O5 or B
for n- and p-type doping respectively. After annealing at 11000C the crystalline
properties were characterised by X-ray diffraction (XRD), as shown in Fig. 4.5.14. For samples with Si3N4
barriers, the measured Si NC sizes are 4.3 nm when undoped, 3.5 nm when B doped and 5.0 nm when P2O5
doped. For samples with SiO2 barriers, grain sizes are 7.7 nm when undoped, 7.2 nm when B
doped, and 15 nm when P2O5 doped. The Si NC sizes vary significantly
although all samples have the same silicon-to-oxygen ratio in the SRO layers and the same as-deposited layer thickness.


It can
be observed from the experiment that samples with Si3N4
barriers contain generally smaller Si QDs than samples with SiO2
barriers. This
is because Si3N4 a denser and stiffer material than SiO2,
acts as a better diffusion barrier than SiO2 [4.5.27]. It could also be
thermodynamically related to the interface free energy between


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XRD patterns of (a) samples with SiO2 barriers, (b) samples
with Si3N4 barriers.


FIGURE 4.5.14





Vertical current density
measurements on (a) B doped samples, (b) P2O5 doped
samples. Insets show how barrier type and NC dimension influence the vertical
current transport process (showing dominant effect only in each case, not to
scale).


FIGURE 4.5.15


the Si
NC and the matrix dielectrics during the growth of the Si NCs. As a result, Si3N4
is able to constrain
the growth of Si NCs very effectively, within ±1 nm of the intended diameter (i.e. 4 nm, the deposition thickness
of SRO). In contrast, Si NCs with SiO2 barriers are significantly
larger than the
as-deposited thickness of SRO - over 180% larger for undoped and B doped and 375% for P2O5
doped.
Hence, it can be noted that samples with phosphorus (P2O5) dopants
tend to form larger sized Si NCs than undoped samples, while introduction of boron doping tends to
suppress this size increase and slightly reduces NC size. This phenomenon is more pronounced for
samples with SiO2 barriers (Fig. 4.5.14 (a)) than those with Si3N4
barriers (Fig. 4.5.14 (b)).


Si3N4
barriers have lower band gaps (5.3 eV) than SiO2 (9 eV) therefore they should
be more transparent
to charge carrier transport because of the larger tunnelling probability for electrons and holes. To verify this
hypothesis in practice, we compared the current transport of SiO2 barrier
structures with Si3N4 barrier structures via the measurement of
vertical currents under a bias
voltage.


The
current-voltage characteristics of these test structures are shown in
Fig. 4.5.15. It should be noted that these samples are not PV devices. Therefore,
the dark currents measured are primarily affected by the materials’ conductivities and are not related to carrier
recombination. It can be clearly seen from the measurement that for B doped
materials, Si3N4 barriers result in a current enhancement of
approximately an order of magnitude over those with SiO2 barriers (Fig.
4.5.15 (a)).
This can be qualitatively explained by [4.5.19]:





 (4.5.1)


where Te is the tunnelling
probability between quantum dots, d is
the barrier thickness or the separation between dots, m* is the effective mass of electron, ħ is the reduced Plank constant,
Δ E is the energy difference between
the conduction band edge of the barrier material and the conduction band edge of the confined QDs.


Although
the difference in Si NC sizes would play an important role in the
tunnelling event, the variation of Δ E is
still the dominant factor for B doping. On the other hand, for the P2O5
doping, samples with Si3N4 and SiO2 barriers have similar
currents (Fig. 4.5.15 (b)). These apparently contradictory results can be explained by
referring back to the XRD results. The P2O5 doped sample
with SiO2 barriers contains Si NCs with an average size of 15 nm,
this suggests that a single Si NC is physically penetrating three thin layers
on average (inset of Fig. 4.5.15 (b)).


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(a) Raman spectra of SRC
samples after RTA and (b) the same samples with additional furnace annealing.
(Bulk Si wafer peak at 520.5 cm-1 for reference.)


FIGURE 4.5.16


This
greatly reduces the number of barrier layers that the carriers need to tunnel
through. This size effect becomes so significant that it effectively competes with and largely
cancels the increased conductivity due to lower ΔE
for the Si3N4 barrier material.


This
result is very promising for both QD size control and increased vertical currnt
transport in these nitide barrier interlayer Si QD materials.


4.5.2.3.3 Silicon QD nanocrystals embedded in silicon carbide
matrix


Researchers:


Zhenyu
Wan, Shujuan Huang, Gavin Conibeer


Silicon
carbide (SiC) has a lower barrier height than either Si3N4 or SiO2.
Therefore it seems likely that it
should offer a higher tunnelling probability between
QDs and hence a higher conductivity matrix than either. In previous work, we
have demonstrated that both Si and
SiC have been crystallised by high
temperature annealing of a single
thick Si-rich SiC (SRC) layer or of a Si1-xCx/ SiC multilayer structure [4.5.28, 4.5.29]. We believe that the formation of β-SiC
nanocrystals may hinder the formation of Si QDs. Also they may cause current leakage via the SiC grain boundary traps to increase the shunt current in the solar cell. Therefore, the work in 2009
focused on studying the mechanism of
the crystallisation of SiC and
optimising the materials by comparing the
annealing methods of rapid thermal annealing
(RTA) and conventional furnace annealing.
We found that RTA annealed samples revealed
a better degree of crystallisation of Si nanocrystals with a smaller residue of
amorphous Si [4.5.30]. The work in
2010 has been to further improve the
structure by reducing the stress caused
by RTA and by replacing SiC barrier layers with thin silicon nitride layers in order to suppress the growth
of SiC crystals.


 (i) Study of Rta induced stress


Two
different annealing processes have been applied on all SRC amorphous samples: furnace annealing at 1100oC/1hr
and RTA at 1100oC/30 sec. After annealing, Si and SiC nano-crystals were clearly observed in TEM
and XRD. The peak positions of Raman spectra are down-shifted to lower wavenumbers for RTA
samples (Δ=5.4cm-1 from bulk Si) as compared to furnace annealed samples (Δ=2cm-1
from bulk Si), indicating greater tensile stress in the Si nano-crystals, as shown in Fig.
4.5.16 (a).
This is because of a different thermal expansion coefficient for Si and SiC
crystals and the fast temperature ramping rate in RTA. In order to release the stress in RTA samples
an additional annealing process was carried out. Raman analysis indicates that after an additional
furnace anneal at 11000C for 30 min, all samples with different Si concentrations could release most of
their residual stress, as shown in Fig. 4.5.16 (b). However, an additional RTA
could not
release residual stress in low Si concentration samples due to insufficient duration [4.5.31].


 (ii) Si QDs embedded in Sic matrix with Si3N4.
barrier layers


Si3N4
is also considered preferable to SiO2 in term of carrier transport.
It has been proven as a good diffusion barrier to suppress inter-diffusion
between silicon rich layers in multilayer structures during annealing [4.5.27]. In
2010, we have successfully introduced ultra-thin Si3N4
(UT-SiN) barriers (0.2nm-2.0nm) into a Si-NC in SiC matrix structure using sputtering followed by
RTA. Crystallisation of the SiC matrix has been greatly suppressed and a clear layered superlattice
structure can be observed as shown in the TEM of Fig. 4.5.17. The nanocrystal size of all samples was
calculated using XRD peak analysis to quantitatively investigate the optimum
thickness of the Si3N4 barrier layer required to produce confined
crystalline Si-QDs, as shown in Fig. 4.5.18. It is seen that as the Si3N4 barrier layer thickness increases, the
β-SiC peaks decrease, such that β-SiC-NCs almost disappear when the Si3N4 barrier thickness is over
0.8nm.





HRTEM image of annealed 2.0nm
UT-Si3N4 sample. The maintenance of a layered structure
and the presence of Si-QDs can be seen.


FIGURE 4.5.17





XRD analysis and
corresponding grain sizes from the Scherrer formula for all the Si3N4 barrier
thicknesses. Insert: Si (111) and SiC (111) peaks of each sample.


FIGURE 4.5.18


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Absorption edge fitting for
UT-SiN2.0 and UT-SiN0.2 samples respectively, (insert: band gap energy for
different Si3N4 thicknesses).


FIGURE 4.5.19





Temperature-depentent conductitity of different Si2N4 barrier
thickness.


FIGURE 4.5.20


Optical
characterization has been performed to investigate quantum confinement effects for different nanocrystal
sizes. Optical analysis reveals a blue shift in the strong absorption edge, consistent
with quantum confinement effects in small Si NCs matching qualitatively calculated results using effective mass theory
from other groups, as shown in
Fig. 4.5.19.


Temperature
dependent I-V measurements were carried out to investigate the carrier transport mechanism. The
conductivity is best described by the expression, σ = σ0 exp [-(T0/T)1/2]
when the Si3N4 barrier thickness is
greater than 0.5 nm, as illustrated in Fig. 4.5.20. The charge transport mechanism can be
explained well by the percolation-hopping model, similar to the result found in Section
4.5.2.3.1 for Sb doped SiQDs in Si3N4. Finally, we conclude that in future, a 0.5-0.8 nm thick layer of Si3N4
barrier layer would be optimum to achieve both good Si-NC confinement and minimal film
resistivity for a candidate material for photovoltaic applications.


4.5.2.3.4 germanium Nanostructures


Although
the main focus has been on Si nanocrystals during the last decade, other group IV
nanocrystals
have also been studied. Since Ge has smaller electron and hole effective masses and a
larger dielectric constant than Si, the excitonic Bohr radius of bulk Ge is
larger than that of Si. This leads to a more prominent quantum confinement effect in Ge NCs. Furthermore
the lower melting point of Ge at 938.3oC implies that Ge NCs should be able to form at lower
temperatures than Si NCs. This is indeed a significant advantage both for processing compatibility and for
processing costs, although set against this are the greater cost and lower abundance of Ge as compared to Si.


4.5.2.3.4.1 Quantum Dots in Sio2


Researchers:


Santosh Shrestha,
Bo Zhang, Pasquale Aliberti, Gavin Conibeer


 (i) fabrication of germanium quantum dots


The
current work builds on earlier work on Ge nanocrystals carried out in our group
[4.5.32]. The new work uses a different approach to annealing of the samples which gives
a wider range of control of Ge NC formation. Ge NC samples have been fabricated by RF
magnetron sputtering using a combination of a combination target comprising a fused quartz disc and
high purity Ge strips. Sputtering of the Ge-rich oxide (GeRO) layer is achieved by sputtering
with just an Ar background, whereas sputtering of the oxide layers, GeO2/
SiO2, is performed by reactive sputtering with O2. These layers are
alternately deposited to obtain the desired multilayered structure. A thick oxide capping
layer is deposited to prevent oxidation of the GeRO layers during subsequent annealing. Post deposition annealing of
the samples was performed under a low pressure (in-situ in the growth chamber) during which Ge
NCs are formed. Results





Cross-section HRTEM image of
a typical sample containing GeRO layers between GeO2/SiO2
layers following annealing.


FIGURE 4.5.21





(a) Raman spectra and (b) GIXRD image of the as-deposited and annealed
films.


FIGURE 4.5.22


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Raman spectra of the samples annealed for different durations.


FIGURE 4.5.23





Raman spectra of the samples annealed at different temperatures.


FIGURE 4.5.24





Room temperature PL of a multilayer film containing Ge NCs in GeO2/SiO2.


FIGURE 4.5.25





Raman spectra from Ge-NCs in single layer samples grown at different
substrate temperatures.


FIGURE 4.5.26


from
structural characterization using TEM, Raman, XRD and PL have been obtained.


Figure
4.5.21 shows a high resolution TEM image of a section of a typical sample containing
GeRO layers between GeO2/ SiO2. The sample was annealed at 6500C. Ge nanocrystals of about
5nm diameter are
evident. Although there is a slight variation, the NCs appear to be spherical in shape. The clear lattice
fringes observed in the TEM image give direct evidence of the formation of the Ge NCs. It should be noted that the
distance between the lattice fringes is 3.3 A, which is consistent with the lattice spacing
of the {111} planes of the Ge diamond structure.


Fig.
4.5.22 (a) shows Raman spectra of the as-deposited and the annealed samples, including those for bulk Ge as a
reference. For these samples, the sputtering times for each GeRO layer and GeO2/SiO2
layer were 8 minutes and 6 minutes, respectively, and the post deposition annealing was performed
at 6500C for 40 minutes. A broad hump at around 270 cm-1 is observed in the spectra of the as-deposited film which
is attributed to the non-crystalline Ge phase. But in the annealed film, it is replaced
by a sharp peak
at 300.5 cm-1, which is very close to the Ge-Ge optical phonon mode for bulk Ge (300.2 cm-1),
indicating the formation of Ge NCs with good crystallinity. Peak broadening and an
asymmetric shoulder on the lower frequency side can be interpreted by the model
of the optical phonon confinement effect in nanocrystals [4.5.33]. However, it seems that in our Ge system
the high
frequency side of the Raman peak does not show a shift to lower phonon frequencies which is usually the case for NCs.


Figure
4.5.22 (b) shows GIXRD patterns for this sample. In the as-deposited film there are no
obvious peaks but only two broad bands at around 2θ = 260 and 2θ = 490. After annealing,
the sample shows
three sharp peaks at 27.120, 45.130 o and 53.210, corresponding to the groups of planes
{111}, {220} and {311} of crystalline Ge, respectively. This observation confirms good
crystallinity of the Ge phase in the film and agrees well with our Raman results. The average size
of the Ge NCs, calculated from the {111} peak broadening using the Scherer
equation, is about 4.5 nm. This value is slightly smaller than that
estimated from the HRTEM image. The difference in Ge NCs sizes obtained from
these two
methods may possibly be due to spatial non-uniformity of the Ge NCs size; with TEM probing a
much smaller sample region compared to XRD measurement. In addition, the penetration depth of the incident X-rays is
larger than the thickness of our film, thus information obtained from XRD is averaged throughout the whole film.


The
crystallisation of Ge NCs with annealing duration has been investigated with Raman spectroscopy. Fig. 4.5.23
shows Raman spectra for identical multilayer samples with each GeRO and GeO2/SiO2
layer deposited for 6 minutes. The samples were annealed at 6850C for different durations as indicated
in the diagram. The crystallization of Ge is found to take place within the first few minutes of
annealing. However, the noticeable broad hump, which is attributed to small NCs, suggests an early
stage of the crystallization process at this annealing duration. As annealing duration increases,
Raman peaks become sharper and narrower indicating an increase in Ge crystallinity. It is also
observed that the peaks show negligible difference for annealing durations longer than 10 minutes.


The
average size of NCs, as calculated from XRD data, increases with
annealing duration. This is consistent with the Raman results and agrees well with the growth
dynamics by diffusion of neighbouring Ge atoms. Most importantly, the increase in the NCs size
begins to level off after 15 minutes of annealing in this particular case. This
is similar
to the size confinement effect observed for the growth of Si NCs in SiO2 matrix
[4.5.7, 4.5.34]. In our superlattice structure, Ge NCs are confined within the GeRO layers
between GeO2/SiO2 layers,


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A High resolution TEM image of multilayered Ge NCs in SiO2
matrix. 

The sample was grown at 3800C


FIGURE 4.5.27


which
work as barrier layers to the crystal growth. Hence, Ge tends to
precipitate with a diameter approximately equal to the thickness of the GeRO layers.
This control mechanism is more significant for thin layers with thickness of a
few nanometers, within which there is 2D rather than a 3D growth.


Figure
4.5.24 shows the Raman spectra of the samples annealed at different temperatures for 40 minutes, which is enough
to complete the growth process as discussed above. As expected, the small nanocrystalline
asymmetric hump is reduced with the increase in annealing temperature within
the range
of temperatures studied here, just as in the case of annealing durations. The results also
illustrate the formation of Ge NCs in SiO2 matrix at a temperature as low as 620
0C.


A sample
with the identical process sequence as those for structural characterizations was used
for photoluminescence measurements, except that the film was deposited on quartz. Fig. 4.5.25
shows results
of room-temperature PL measurement. The PL spectrum consists of a single broad band
centred at 1.77eV (corresponding to a wavelength of 700 nm) which can be fitted
with three Gaussian distributions.
Measurement on GeO2/SiO2 flm deposited on quartz under similar conditions did not show any observable PL in the range of wavelengths concerned. Thus the PL signal from
the multilayer sample can be
attributed to Ge NCs in the GeRO
layers. Furthermore, a blue shift of PL energy with NCs size has been shown in previous work [4.5.32]. We tentatively consider that this is
due to the band gap increase induced
by the quantum confinement effect in Ge NCs [4.5.35].


 (ii) Low temperature growth of germanium quantum dots


In this section,
a low temperature growth of Ge nanocrystals is discussed. This is advantageous because of the potential
for reduced processing cost and suitability for cheaper substrates such as soda-lime glass.
Samples were grown with RF magnetron sputtering as described earlier, except in this case the
substrate was heated during the film growth and no post annealing process was used [4.5.36].


Figure
4.5.26 shows Raman spectra for a single layer GeRO film deposited at
different temperatures as indicated in the diagram. For clarity, the graph has been divided into three
different regimes. In regime I, the samples grown below 3500C are shown. In this
case, the spectra show no Raman peaks related to nanocrystalline Ge, instead broad bands
centred
around 280 cm1 are observed. The bands are shifted toward higher frequency by about 10 cm1 compared with that
of amorphous Ge (α-Ge) located at around 270 cm 1. This indicates that α-Ge
coexists
with very small particles (12 nm) [4.5.37].


For the
sample grown at Tg = 3200C, the observation of a hump at 280 cm 1
as well as a shoulder at 298 cm-1 implies an increase in the
number and size of small particles. The rapid growth of Ge NCs is found to occur in
Regime II, in which samples grown at temperatures between 3500C and 4000C are shown.
The Raman peak corresponding to the TO phonon mode of the crystalline Ge (c-Ge), near 300.4 cm-1, appears
at Tg = 3500C and becomes sharper with increase in the growth temperature. This range of temperature
is very close to the onset temperature for Ge crystallisation reported in [4.5.38]. However, when
the growth temperature Tg reaches 4200C (Regime III), a drastic degradation
of Ge-Ge peak intensity and shape is observed. These phenomena indicate the
absence of Ge crystallinity in
this temperature range.


Based
on the Raman results discussed above, it is expected that the growth
temperature window is between 350oC and 420oC, in which Ge atoms or clusters can accumulate
and eventually grow into highly crystallised nanocrystals. These temperatures are much lower than the
usual post-deposition annealing temperatures used for Ge NCs fabrication.


A HRTEM
image of a multilayered sample consisting of alternate layers of GeRO and GeO2/SiO2
films is shown in Fig. 4.5.27. In this case the sample was grown at Tg =
380oC without further post-deposition thermal treatment. The TEM image shows close to
spherical Ge NCs with fairly uniform size, separated


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Schematic diagram of a Ge-NC/n:c-Si HJ diode.


FIGURE 4.5.28





(a) The semi-logarithmic plot
of dark I-V curves of a typical i:Ge-NC/ n:c-Si HJ device in both polarities at
room temperature. (b) The measured suns-Voc characteristics of the
HJ device. The red solid circle indicates the 1-sun point.


FIGURE 4.5.29


by the
barrier layers. The Ge NC sizes are in the range of 4.8 - 5.8 nm which is consistent with
the average size ( 4.8 nm) determined from XRD. The image in the inset shows clear lattice fringes
inside one of the Ge-NCs (indicated by the arrow). The fringes are consistent with {111}
planes of the Ge diamond
structure.


 (iii) Electrical properties of ge-Nc thin films


Ge-NC
thin films about 250 nm 300 nm were deposited. The coverage of Ge was 20% of the area of the
composite target. XPS has shown that this resulted in a Ge atomic concentration of 35% in the films. Undoped, Ga-doped and
Sb-doped Ge targets
were used. During the sputtering process the substrates were intentionally heated up to 380 oC for
in-situ growth of Ge-NCs. Finally, RTA treatments at different temperatures, including
650oC, 700oC, 750oC, 800oC were carried out in nitrogen [4.5.39].


The
current conduction characteristics of i:Ge-NC thin films were measured
using HP4140B pA Meter/ DC voltage source with tri-axial wires to eliminate
noise. The relatively high conductivity and carrier concentration in the
i:Ge-NC thin films is quite surprising, taking into consideration that they
were not intentionally doped. Temperature dependent measurement revealed a lnσ OC T-1relationship, suggesting
a thermally activated nearest hopping conduction
mechanism in these films. The carrier transport was considered to occur at the
surface state energy level and a theoretical calculation predicts that the
density of surface states of Ge can provide sufficient free holes to explain
the observed conductivity. RTA treatments further increase the flm conductivity without changing much the structural properties of nanocrystals. This improvement
was tentatively attributed to the modification
of surface structure of NCs and reduction
of oxygen-deficiency-related defects in the SiO2 matrix. The effect of incorporating moderate amounts of Ga and Sb dopants was also investigated. The doped films exhibit similar conduction properties to the intrinsic films,
which means the films were still
dominated by surface state induced hole conduction and that the dopants were
not effectively activated. This is not surprising if one realizes the screening
of shallow dopants in NCs due to the
increase of binding energy and ionization
energy. This effect together with the inherent hole generation effect can make
it very challenging to produce n-type Ge-NC thin films.


 (iv) Ge-nc/c-Si Heterojunction Devices


Heterojunction
(HJ) devices employing Ge-NC thin flms on lightly doped n-type crystalline silicon substrates with impurity concentration of 1 x 1015 cm3 (n:c-Si) were fabricated to evaluate the compatibility
of the nanostructured thin film and investigate
the design parameters required for its application
in photovoltaic devices. The schematic diagram
of the HJ device is illustrated in Fig. 4.5.28. The total area of the device is 1 cm2. The thickness of the Ge-NC layer is about 250 nm. The Ge-NC thin films were post-annealed by RTA at 800oC in order to achieve lower film resistivity and higher
carrier concentration. The Al front
fingers and rear contact were deposited by thermal evaporation. No passivation
or sintering process was performed on the devices.


Figure
4.5.29 shows the dark I-V curves and suns VOC of a typical i:Ge-NC/n:c-Si HJ device at room temperature. The device
shows good current rectification of three orders of magnitude at ± 1.5 V. Since both front and
rear electrodes were ohmic contacts, the rectification effect can be attributed to
the junction. The apparent photovoltage was detected from the illuminated device and the 1-sun
VOCwas found to be 314
mV. The best fitting to the experimental data using a two diode model predicts an effective ideality
factor of 1.01 throughout the entire injection range, which is indicative of a dominating bulk and
surface recombination in the heterojunction device. Whilst this HJ device does not demonstrate
photovoltaic behaviour of the Ge NC material it does show good rectification and is


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XRD spectra of Ge QDs of
various Ge content in Ge-rich nitride layer with a fixed substrate temperature
of 600 0C (left) and TEM image of 40 vol% Ge self-assembled at 600 0C (right).


FIGURE 4.5.30


encouraging
as a starting point for using Ge-NC in true photovoltaic applications.


4.5.2.3.4.2 germanium QW and QD nanostructures embedded in
silicon nitride matrix


Researchers:


Sammy
Lee, Jian Chen, Shujuan Huang, Martin Green


As
discussed above in section 4.5.2.3.1, a silicon nitride matrix (Si3N4)
should increase tunneling probability and hence increase conductivity of Ge
nanostructure materials. In addition a nitride will strongly suppress the
possibility of oxidation of Ge. Ge QDs and QWs were fabricated by co-sputtering followed by
post-annealing and self-organisation by substrate heating.


 (i) ge QDs embedded in silicon nitride matrix


Using a
very similar approach to our previous work on Ge QDs in oxide and Sn
QDs in nitride matrices, alternating layers of germanium-rich nitride (GRN) layers
and Si3N4 layer were alternately co-sputtered on a heated substrate of
either a silicon wafer or quartz slide. The Ge QDs crystallise due to minimisation of surface
energy and the Si3N4 layer deposited on top of the GRN layer truncates
crystal growth.
The temperature of the substrate and the Ge content in GRN layers were the dominant factors
in
controlling the size of the NCs. The structure of the NCs was studied by
GIXRD, Raman spectroscopy and TEM, and the optical properties were studied with transmittance and
reflectance measurements analysed
using a Tauc-plot.


Figure 4.5.30 shows the XRD spectra of
samples of various Ge content in GRN. The Bragg
peaks of
{111}, {220}
and {311} planes sharpen with increasing Ge content, indicating the increase of the nanocrystal
sizes. Using
the Scherrer equation the size of the nanocrystals was estimated as shown in Table 1,
with sizes in agreement with the NC size observed in TEM images.


Figure 4.5.31 summarises the band gap
engineering trend with the size of Ge QDs. The
absorption edge shows a tendency to shift to high photon energy when Ge
nanocrystal size decreases. The absorption coefficient
was calculated by a simplified equation;





where T and R
are the transmission and reflection and d is the thickness
of the film. With decrease in Ge content in the GRN layer, and hence in the diameter of the QDs, the
absorption edge appears to increase by up to 1.0 eV, as estimated with the Tauc-plot method.
However, these data should be considered as indicative of the trend only as there is error in
quantitative values for the shift
in absorption edge due to uncertainty in
extrapolating back to the energy axis.


 (ii) ge QWs with silicon nitride barriers


With a
similar approach to the Ge QD fabrication, Ge QWs were fabricated
by co-sputtering of alternating GRN and Si3N4 layers and followed by furnace annealing or RTA.
The Ge content in GRN was higher in this case in order to give continuous layers. It was varied
between 60vol% to 100vol% and the annealing temperature in N2 was also
varied from
6000C to 9000C for 1 hour. The structural and optical properties were studied
by GIXRD, Raman spectroscopy, TEM and transmission and reflectance measurements.


Fig.
4.5.32 shows the continuous Ge layer with its QW-like-structure between
amorphous Si3N4 barriers. Highly ordered lattice planes can
clearly be
seen in these Ge QW, indicating formation of large single crystal type
structures. Based on Raman and XRD characterisation, the crystallisation temperature shows a
significant dependence on the thickness of either Ge QW or Si3N4 barrier


	
  

 	
  

 	
  

 
	
 Ge vol%

 	
 ∆(2q) of (111)

 	
 NC Size (nm)

 
	 

 	 

 	 

 
	
 30

 	
 5.62

 	
 NA

 
	
 40

 	
 3.85

 	
 2.22

 
	
 50

 	
 2.41

 	
 3.54

 
	
 60

 	
 2.38

 	
 3.59

 
	
 70

 	
 1.92

 	
 4.45

 


Ge NC size estimation from XRD.


TABLE 4.5.1





Absorption edge observed from transmission and reflectance measurements.


FIGURE 4.5.31.





TEM image of the sample containing 60 vol% Ge and furnace annealed at
9000C


FIGURE 4.5.32


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Schematic diagram of the of
the fabricated inter-digitated Si QD in SiO2 devices, with B and P
doping to create the p-n junctions and illustrating the effect of current
crowding due to high lateral resitnce to the back contact.


FIGURE 4.5.33


layers,
varying from 7000C to 9000C. The absorption coefficient estimated
from the transmittance and reflectance measurements also shows an apparent increase in band gap by
up to 1.1eV when the thickness of
the Ge QWs is 1.5nm.


Both Ge
QDs and QWs nanostructures in Si3N4 show evidence of band gap
enhancement. Further work will investigate electrical properties and the possibility of device fabrication.


4.5.2.4 Silicon nanocrystal devices on quartz substrates


Researchers:


Ivan
Perez-Wurfl, Xiaojing Hao, Dawei Dai, Adrian Shi


As
previously reported in the 2008 and 2009 annual reports devices have been
fabricated using the SiQD in SiO2 materials, with p-n junction formation using B or P
of multilayers, respectively [4.5.9, 4.5.10, 4.5.40]. The fabricated p-n diodes consisted of sputtered
alternating layers of SiO2 and SRO onto quartz substrates with in-situ boron
and phosphorus doping. The top B doped bi-layers were selectively etched to
create isolated p-type mesas and to access the buried P doped bi-layers. Aluminium
contacts were deposited by evaporation, patterned and sintered to create ohmic contacts on both p and
n-type layers. The fabricated interdigitated solar cells have an effective area of up to 0.12cm2.
The devices exhibit rectification and a photovoltaic response with Voc up to
493 mV, but with
as yet very small currents and bad fill factors. These are partly due to the very high resistance of the material and in
particular to the relatively long lateral paths to contacts at the back contact, necessitated by groth on
an insulating quartz substrate. The device structure with appropriate contacting is shown
schematically in Fig. 4.5.33. This also shows the current crowding effect which
results
from the high lateral resistance.


4.5.2.4.1 Equivalent circuit model of nanocrystal devices on
quartz substrates


In
order to better understand the limitation imposed by the device on the solar cell
performance, it is necessary to find a good equivalent circuit model specific to our devices. The high resistivity of
the base layer makes it imperative to consider the two dimensional effects of current flow
[4.5.41]. In order to analyse the I-V characteristics
of these diodes we first generalised the model to include any number of diodes in series. The series
connection of diodes is used to explain the ideality factors higher than two normally observed in our
structures. We believe this is a reasonable model as the ideality factor
observed is
almost independent of the diode current. This type of behaviour has also been
observed in multi quantum well laser diodes [4.5.42], where it has been proven
to arise from an unintended series combination of diodes. Based on this series combination of diodes, it
is possible to obtain an expression relating temperature dependent I-V measurements to the band gap [4.5.9]. It is
further possible to linearise the expression around an average measuring
temperature, Tavg, as follows:





 (4.5.2)


where k is Boltzmann’s constant, q is the electron charge, Tnom is the temperature at
which the saturation
current, /o/, is defined, ni is the diode ideality factor, and αiis the saturation current
temperature
exponent. Notice that this equation shows that the I-V
characteristics are related to a sum of band gaps.


As the
current flows from the base contact to the emitter, a linear voltage drop along
the base and under the diode isolation mesa causes an exponential change in
the diode current. This crowding of the current at the edge of the diode


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mesa,
depicted in Fig. 4.5.33, can be modelled adding a current dependence on the series resistance. This series
resistance, Rs, can be
expressed
as the sum of a current independent, Rext
and a current dependent series resistance Rint arising from current crowding:





 (4.5.3)


The value
of this resistance can be found by numerically solving the following transcendental equation:





 (4.5.4)


Within
this mathematical framework it is then possible to extract the value of the series resistance, remove its
effect from the measured /-V characteristics
to extract the actual ideality of the diode current. We normally observe an ideality factor of 3. Based on the
proposed model of at least two diodes in series, without any assumptions, it is only
possible to establish that the value of the band gap extracted from temperature
dependent l-V measurements corresponds to a sum of the band gaps (or activation
energies) of these diodes.


An
interesting behaviour observed in these devices was the apparent lack of correspondence
between the dark and light /-V characteristics.
The series resistance extracted from the diode dark l-V characteristic is too small to explain the limited short circuit current
as well as the low fill factor measured under a simulated 1-sun condition. A more complete circuit
model is necessary to explain this discrepancy. We have proposed a model where the observed behaviour
is due to two distinct areas in the fabricated devices. The photocurrent is produced only in a small
area of the device, this area being proportional to a fraction of the normalized diode area. In a Spice
circuit model this area is given a value smaller than 1, that we denote as
fraction. This
will be a fitting parameter to reproduce the measured dark and illuminated /-V characteristics. Figure 4.5.34 shows the
circuit proposed.


A
relatively large percentage of the device area is responsible for the
measured characteristics in the dark. The current in this area is caused by the
diffusion
of minority carriers caused by the applied voltage (V1 in Fig. 4.5.34) from the p or n side to
the
opposite region. This current is expected to be large due to the low lifetime of the minority carriers (mostly
recombination current in the depletion region). The observed series resistance will be proportional to
the total series resistance, Rtot, and inversely proportional to the area,
R2=Rtot/ (1-fraction), where the
diffusion current occurs. The dark l-V behaviour
is modelled by the top branch of the circuit depicted in Fig. 4.5.34. D_QD1 and D_Sch represent the series
connection of diodes whose band gaps are extracted using Eq. (4.5.2). The series resistance, R2, has the
temperature and current dependence detailed in Eqs. (4.5.3) and (4.5.4).


Only a
small part of the diode area may have a large enough lifetime to
produce a photocurrent. As this photocurrent flows only through this fractional area, the series
resistance is inversely proportional to this fraction: R1=Rtot/fraction.
Since the photocurrent, Iph, flows through R1, the illuminated /-V characteristics are limited by a larger
resistance than
that observed in the dark condition, as long as the fraction of the diode area is smaller than one half. The simulations
depicted in Fig. 4.5.35 show the reduction of lSC as the fraction, f, is varied from 99% to 1% of the total
diode area.


With
the circuit model described, it will be possible to extract complementary
information from dark and
illuminated l-V measurements.


In view
of these simulations, it is clear that the electrical characterisation of our
devices needs to take into consideration previously overlooked limitations. For
example, great care should be taken when interpreting the Quantum Efficiency extracted from a spectral
response measurement as the assumed condition of short circuit current may be incorrect even
if the device is externally short circuited (internally, the diode may be forward biased). Moreover, as the current is proportional to the photon flux,
and the flux is generally different at each wavelength tested, the internal bias of the device can be different at each point of the spectrum investigated.


4.5.2.4.2 Demonstrator program for Si nanostructure devices


Using
the approach described in Section 4.5.2.4.1, a device simulator has been developed
in an MS Excel spreadsheet. The Demonstrator is a 2D simulator of the diodes fabricated from Si QD
nanostructures. It is based on a simple diode model with a few fitting parameters and
uses the method in section 0 and in [4.5.9].


	
  

 	
  

 
	
 There
 are three areas which the user can modify:

 
	
  

 
	
 1.

 	
 Measured
 parameters: these come from measured properties of the fabricated diodes. The base resistivity
 and its temperature dependence
 are measured. The device geometry is known. The default values are
 representative ones for the devices.

 
	
  

 	
  

 
	
 2.

 	
 Jo,
 ideality factor, band gap and XTO can be varied to give flexibility in ftting to a specific
 diode properties.

 
	
  

 	
  

 
	
 3.

 	
 The
 variation parameters are Current and Temperature.

 
	
  

 	
  

 
	
 The
 outputs are:

 
	
  

 
	
 1.

 	
 The/-V curves for the range of temperatures
 chosen, in both log-lin and
 lin-lin output.

 
	
  

 	
  

 
	
 2.

 	
 The variation
 of the ideality factor with current for various temperatures.

 
	
  

 	
  

 
	
 3.

 	
 The
 series resistance with temperature.

 
	
  

 	
  

 
	
 4.

 	
 The
 extracted band gap, using either a calculation incorporating a series
 resistance correction or with both a series resistance and a current modification term.

 





Equivalent Spice circuit representation of the fabricated devices.


FIGURE 4.5.34





Spice simulations of 1-sun
I-V characteristics based on the circuit depicted in Fig. 4.5.34. The fraction,
f, represents the normalized area of the diode where the photocurrent is
produced.


FIGURE 4.5.35


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Dark I-V curves.


FIGURE 4.5.36





Local ideality factor.


FIGURE 4.5.37


Some
example outputs, using the default parameter settings, follow:


Figure
4.5.36 shows that a reasonable diode characteristic is shown, with good turn-on and rectification.


Figure
4.5.37 shows the increase in the ideality factor with current is as expected with a diode transiting from
domination by radiative recombination (n=1) to being dominated by Shockley Read Hall
recombination (n=2). But the large regime in which n=3 and then region where it goes to much higher
values, are indicative of a non-physical aspect to the model. The most likely explanation is
that rather than two diodes in series there are actually several, probably a variable number in
different parts of the device, the combination of which lead to a composite ideality factor.


The
demonstrator is useful as an iterative tool used to simulate the real
measured data from a device. The parameters used for such a fit then define the
values of the circuit elements in the EC model. Attachment of physical meaning
to these elements will then require further development and interface with the EMA/quantum
mechanical model.


4.5.2.5 Doping in Si QD nanostructures


Fabrication
of a PV device from the Si QD materials requires a control of work function such as to
allow separation
of photogenerated electron-hole pairs. Methods by which this can be achieved include fabrication of a grown or diffused p-n
junction or p-i-n junction with the Si QD
multilayers as the i-region. These
require careful control of the work functions of the p and n-regions. P-n
junction devices have been fabricated and doping demonstrated. Progress on the
theory explaining these doping
effects using conventional dopants and the possibility of other
modulation doping approaches has been made.


As
discussed in Section 4.5.2.4, rectifying p-n and p-i-n structures can be
fabricated with ‘conventional’ doping by incorporation of B and P during sputtering growth [4.5.9,
4.5.10]. Also, formation of p- and n-type materials is clearly demonstrated in the
Si QD nanostructure materials with Si nitride interlayers doped with either P
or B discussed in Section 4.5.2.3.2; in the Sb doped n-type Si QDs in Si3N4
in Section 4.5.2.3.1; in the p-type GeQD in SiO2 material in section 4.5.2.3.4; and
in MOS type devices doped with either P or B by a diffusion anneal discussed in [4.5.43].


However,
the doping mechanisms taking place in these structures are not well understood.
Theoretical
work has shown that direct doping of the QDs is prevented by segregation of
impurity atoms
from the perfectly crystalline QDs [4.5.44, 4.5.23]. Experimentally this is
supported by data on the free electron density in Si nanocrystals using Electron
Paramagnetic Resonance (EPR), which show that 95% of P atoms are segregated to the surface of the
nanocrystals and that their contribution to doping is at least an order of magnitude
lower than the atomic concentration [4.5.45]. Further evidence that doping causes electronic changes comes
from the quenching of luminescence on the incorporation of P (or Au) in Si nanostructures
[4.5.46] and also from a small enhancement of luminescence observed at low P doping levels followed
by quenching at higher levels [4.5.47]. This latter being explained by the passivation of QD surface
states by low levels of P increasing luminescence and then the saturation of this mechanism by excess
P. This also explains the non-monotonic behaviour of activation energy seen in P doped nanostructures [4.5.10].


If
direct doping of the QDs is not occurring, then another possibility is
modulation doping of the matrix SiO2, as is commonly used in
III-V nanostructures;
but this is ruled out because of the very high ionisation energies of about 5eV that would be required for the
resultant deep defects in a dielectric matrix [4.5.48]. These clearly will not occur at room
temperature, or even at higher temperatures.


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Two models for doping of Si
QD nanostructures. (a) An extended sub-oxide region surrounding the Si QDs
allows doping by P or B at relatively shallow levels. These then can provide
carriers to be captured by the QDs through a modulation doping mechanism. (b)
QD size enhancement (suppression) by P (B) doping results in a type I
heterojunction between P and B doped material. This facilitates carrier
separation due to the much greater mobility of electrons - the Dember effect
[4.5.49].


FIGURE 4.5.40


4.5.2.5.1 Doping mechanisms in Si QD nanostructures


Researchers:


Dawei
Di, Xiaoming Hao, Ivan Perez-Wurfl, Gavin Conibeer


As there
is clear evidence for doping by P and B, a third possibility is that it is the sub-oxide QD/
matrix interface region, with its shallower doping defect levels, that is
doped by the P or B atoms, thus providing free carriers to be captured by the QDs [4.5.49]. As shown in
Fig. 4.5.38, ab-initio calculation of the levels associated with B atoms associated directly with the
interface region on the surface of a Si QD indicate that there are no shallow or deep levels introduced by the
B within the effective band gap (HOMO-LUMO gap). The reason is that the strong affinity of B for
O results in very strong B-O bonds, effectively splitting any available OMOs
and UMOs a
long way apart and well inside the already existing density of states.


However,
this approach considers the interface between Si QD and SiO2 matrix to be very
abrupt. In
fact there is highly likely to be an extended transition region of a sub-oxide
around the QD. If this region is a sufficiently extended silicon sub-oxide (SiOX)
it could provide flat Bloch bands able to be doped in a pseudo bulk-like regime. In order that B and P doping
levels are shallow enough to be ionised in such a region, x would need to be less than
about 0.5. Such a region would be amorphous and hence not able to be modelled with ab-initio methods. But the presence
of such regions can be determined from absorption measurements.


There is
some support for this theory in the absorption data for Si QDs in SiO2
[4.5.5] shown in Fig. 4.5.39. This shows a region of strong absorption with an absorption edge
which blue shifts as the O to Si ratio increases, which translates to an increase in QD size. But
there is also an additional weakly absorbing tail which extends well into the effective band gap
region. This tail is likely to be due to an amorphous region around the Si QDs. An explanation for the band
gap of this being larger than bulk Si is if this region consists of sub-oxide
material. If this region were doped with B or P, it could provide free
carriers to be captured by the QDs in a modulation doping mechanism, thus giving rise
to the p- or n-type behaviour observed. (This is illustrated schematically in Fig. 4.5.40
(a).)


An
alternative explanation for the rectifying character of the junctions obtained
can be
based on the modification to the Si QD crystalisation discussed in Section 4.5.2.3.2, for
P and B doping of Si QDs in oxide with nitride interlayers [4.5.49]. The fact that P (B) doped material produces
larger (smaller) QDs means that its confined energy levels and hence effective band gap
will be smaller (larger) than undoped material under otherwise similar conditions. Thus a junction between a P and a B doped
region will actually
be a type-I heterojunction between small and large band gap materials, respectively, as
illustrated in Fig. 4.5.40 (b).


It is
also very likely that the mobility of electrons in these materials, whilst not
big, will still be much greater than that of holes. Hence photogenerated electrons near the
junction would experience a drift field sweeping them into the P doped material
with its lower conduction band edge, whilst holes with their very limited
mobility would be immobile. This would result in electrons accumulating in the P





Ab-initio calculation using
GAUSSIAN: (a) the density of states for a Si83/84OH62
oxide terminated QD with and without a B atom at the interface; (b) the optimised
Si QD, consisting of Si83B-OH62, with the B atom at top
centre (in pink).


FIGURE 4.5.38





Room temperature absorption
co-efficient of annealed SiOx/ SiO2 multilayer films with
various x (1100oC, 1hour). The inset is an estimate of the approximate optical
band gap (filled squares: strong absorption; empty circles: absorption tail)
[4.5.5].


FIGURE 4.5.39


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Spatial distribution of 4s
and 3d electronic states of Sc (upper) and energetic arrangement of 4s and 3d
states (lower).


FIGURE 4.5.41





Electronic density of states
(DOS) of Si10 QD in 2 ML SiO2 (dotted black), fully
oxidised nanocrystal (grey) and Si10 QD in 2 ML SiO2 with
Sc replacing Si atom in the SiO2 shell at the outermost position
(top). DOS of Sc-doped approximants split into a (spin up, red) and b (spin
down, blue) DOS because of non-even number of electrons within the approximant
due to acceptor state of Sc. The b-highest occupied molecular orbital (HOMO)
1193 indicated in magenta can take up 0.07 electrons from the Si10
QD over two 2 ML (6 A) of perfect SiO2.
The p-lowest unoccupied MO (LUMO) 1194 shown in green can take up a
much bigger proportion of an electron if the Si QD is slightly bigger (e.g. Si35,
dQD = 11A). The Sc-doped nanocrystals are shown with the
iso-density plots of 1.35X10-3 e/A3 for p-HOMO 1193
(lower left) and p-LUMO 1194 (lower right). The atoms of the Si10 QD
and the Sc atom are highlighted in cyan. Si atoms in SiO2 are grey,
O atoms are red, H-atoms terminating the outermost O-bonds are white. All DFT
computations carried out with a Hartree-Fock 3-21G(d) optimisation and
B3LYP/6-31G(d) electronic structure calculation [4.5.23].


FIGURE 4.5.42


material
and being collected in the external circuit as if from an n-type
material, with electrons injected back into the device through the B doped material where they would
recombine with the immobile holes, thus making the B material appear p-type. This qualitatively
mirrors the behaviour observed, but will require corroboration. As it relies on
the difference in electron and hole mobilities, it is essentially the same as
the Dember effect, which is known to produce a photovoltaic effect through carrier separation,
albeit not very efficiently.


It is
also possible that both the sub-oxide doping effect and the mismatched
QD size effects operate in the device. The fact that both mechanisms act in the same direction is
fortuitous as both could therefore contribute to the observed rectifying
photovoltaic behaviour. Differentiation between these or a determination of the relative strengths
will require further study on the effects of doping, interlayers and band
alignments. These will also further optimisation of the devices and lead to better photovoltaic
performance from these Si QD nanostructure
devices.


4.5.2.5.2 ab-initio modelling of modulation doping
possibilities in Si QDs nanostructures


Researchers:


Dirk
KÖnig, James Rudd, Daniel Hiller (IMTEK, University of Freiburg, Germany)


As
discussed in Section 4.5.2.5, direct doping of QDs by dopants is
thermodynamically very unlikely. The alternative of modulation doping of the SiO2
matrix is also not feasible due to the strong anionic nature of O leading to
very deep ionisation energies [4.5.48]. We have concentrated recently on possible candidates for more
efficienct acceptor doping of Si QDs. Modulation acceptors must have an energetic position below
the confined hole level, they must not introduce defect levels in the QD band gap if located at
the interface as an active dopant and as a completely saturated foreign atom,
and they must have one single oxidation number. The transition metal scandium
(Sc) fulfils the
last two requirements. It also has a very suitable valence state
configuration which consists of a full (doubly occupied) 4s shell and one
electron in
the 3d1 state located within the
4s shell. On the energy scale, the 4s electrons have a higher binding energy as compared to the
3d1 and 3d2 states. This provides the 3d1 and 3d2
states with an electrostatic screening which results in a higher binding energy of these states. Thereby
an unoccupied 3d2 state exists at a high binding energy which is able to take up an electron from a
nearby source such as a Si QD, see
Fig. 4.5.41.


Ab-initio
Density Functional Theory calculations on a Si10 QD in 2 mono layers (MLs) of
SiO2 have been carried out, with a Si atom at the outermost position with full O
termination replaced by a Sc atom. The Si10 atom cluster is the smallest
size which still
behaves as a Si QD [4.5.23]. Such a nanoparticle allows us to directly observe the electronic
structure of Sc as a modulation acceptor in SiO2 in the proximity of a Si QD, see
Fig. 4.5.42.


Figure
4.5.42 shows that 0.07 electrons stemming from the Si10 QD (dQD = 7.3A) are localized at the Sc atom over
two 2 ML (6 A) of perfect SiO2. Technological relevant QD sizes start at dQD
≈ 20A, with
a much lesser degree of quantum confinement as compared to a 7.3A QD. It is thus reasonable to
assume that
a Si QD with dQD ≥ 20A will be
positively ionized
to a much greater extent, ensuring that holes are majority carriers in a Si QD super lattice
(SL)
embedded in SiO2. Experimental
verification of this doping mechanism is being carried out. The difference to
conventional acceptor modulation doping as used in III-V electronic devices is the way the Si or Ge QDs are
ionised by Sc in SiO2. As ‘Sc induces a deep acceptor level in SiO2 it cannot be thermally ionized from the SiO2 valence band. Instead, the Sc acceptor state takes up the
electron directly
from the initially occupied state at a lower binding energy presented by a nearby QD, see Fig. 4.5.43. This requires the
Sc acceptor to be within 50A of the Si QD in order to exploit field emission


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Acceptor modulation doping:
Conventional example with GaS QD in AlAs matrix and electron thermally emitted
into acceptor (Mg), such that holes are captured by the QD (left). In SiO2,
charge transfer occurs directly as the Sc state is too deep within the band gap
to be thermally ionized. Instead, the acceptor state is ionised directly from
the QD by feld emission of an electron into the Sc acceptor state.


FIGURE 4.5.43


which
is a consequence of the energy difference between the QD HOMO and the Sc acceptor state.


Acceptor
modulation doping of SiO2 can be accomplished by
incorporation of a small amount of Sc, say one monolayer of Sc, into the SiO2
barriers between
the SRO QD array layers. During the segregation anneal, Sc is incorporated into the SiO2 matrix
and thereby activated as an acceptor. Ab-initio calculation indicates that Sc attached to the Si QD does not
create any levels within the HOMO-LUMO gap of a Si84(OH)64
QD. We can therefore
assume that a Sc atoms bonded onto a Si QD does not result in a detrimental change in its electronic structure.
This concept is now being investigated
experimentally.


4.5.2.6 Summary of group iv nanostructures for tandem cell
elements


In 2010,
significant progress has been made on understanding the transfer of growth parameters of Si QDs to other
matrices. The use of anisotropic structures both to provide diffusion barriers to excessive QD growth
and to provide higher conductivity paths in the transport direction, has shown the validity of
these approaches both for Si3N4 and for SiC matrices.
Knowledge of Ge QD nanostructures has improved significantly with clear p-type behaviour of
Ge QD s in SiO2 and very successful growth of Ge QWs in Si3N4
matrix. The increase
in sophistication of modelling of confined energy in these structures now matches reasonably well with experimental data.


Improved
modelling of confined levels in irregular shaped particles also matches well with experimental data of
other groups. Higher level device modelling is now able to describe the anomalous effects
due to high lateral series resistance in devices and consequent current crowding. This is now
being used to optimise nanostructure growth and device design, so as to push beyond the current
open circuit voltages of 490mV. Part of this is an understanding of doping. This
has progressed with greater knowledge and control over the effects on QSD size of
introduction of
P and B dopants, and modelling of possible doping mechanisms based on modified
modulation doping and these size effects. Alternative modulation dopants are
being modelled with scandium as an acceptor looking like a strong candidate. Further work
will build on this increased understanding of anisoptropic structures, growth
of different
materials and understanding of doping to improve materials and devices further.


4.5.3 hot carrier cells


Researchers:


Shujuan
Huang, Santosh Shreshtha, Dirk KÖnig, Robert Patterson, Pasquale Aliberti, Binesh Puthen Veettil,
Lara Treiber, Ivan Perez-Wurfl, Andy Hsieh, Yu Feng, James Rudd, Stephan Michard, Martin Green, Gavin Conibeer


Hot
carrier solar cells offer the possibility of very high efficiencies
(limiting efficiency above 65% for unconcentrated illumination) but with a structure that
could be conceptually simple compared to other very high efficiency PV devices - such as multi-junction
monolithic tandem cells. For this reason, the approach lends itself to ‘thin film’ deposition techniques,
with their attendant low costs in materials and energy usage and facility to use abundant, non-toxic elements.


An ideal
Hot Carrier cell would absorb a wide range of photon energies and
extract a large fraction of the energy to give very high efficiencies by
extracting ‘hot’ carriers before they thermalise to the band edges. Hence an
important property of a hot carrier cell is to slow the rate of carrier cooling
to allow hot carriers to be collected whilst they are still at elevated
energies (“hot”), and thus allowing higher voltages to be achieved from the cell and hence higher efficiency.
A Hot Carrier cell must also only allow extraction of carriers from the device through
contacts which accept only a very narrow range of energies (energy selective contacts or


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Band diagram of the Hot Carrier cell. The device has four stringent
requirements:


FIGURE 4.5.44





(a) Schematic representation of energy and
particle fluxes interactions used in the model (Particle fluxes - full line
arrow, energy fluxes- dotted line arrow). (b)
HCSC efficiency as a function of carrier extraction energy level.
Parameters used are: thermalisation time = 100 ps, concentration = 1000,
lattice temperature = 300K and absorber layer thickness = 50 nm. [J, F and
E are current density and
particle and energy fluxes as denoted by subscripts for A absorption, E emission and IA Auger
processes.]


FIGURE 4.5.45





Carriers transmission probability versus energy for (a) ideal ESC, (b)
non-ideal ESC.


FIGURE 4.5.46


ESCs).
This is necessary in order to prevent cold carriers in the contact
from cooling the hot carriers, i.e. the increase in entropy on carrier
extraction is minimized
[4.5.50]. The limiting efficiency for the hot carrier cell is over 65% at 1 sun and 85% at maximum concentration -
very close to the limits for an infinite number of energy levels [4.5.1, 4.5.51, 4.5.52]. Fig. 4.5.44 is a
schematic band diagram of a Hot Carrier cell illustrating these two requirements.


	
  

 	
  

 
	
 a)

 	
 To
 absorb a wide range of photon energies;

 
	
  

 	
  

 
	
 b)

 	
 To
 slow the rate of photogenerated carrier cooling in the absorber;

 
	
  

 	
  

 
	
 c)

 	
 To
 extract these ‘hot carriers’ over a narrow range of energies, such that excess
 carrier energy is not lost
 to the cold contacts;

 
	
  

 	
  

 
	
 d)

 	
 To
 allow efficient renormalisation of carrier energy via carrier-carrier
 scattering.

 



In 2010
modelling of Hot Carrier efficiencies has progressed with implementation of real material
properties to give more realistic efficiencies for InN which include Auger processes and more
realistic contact structures. Significant progress has been made on demonstrating
resonance in double barrier selective energy structures. Further work on triple
barrier double Si QW structures has been carried out for rectifying ESCs. This is complemented by improvements in 2/3D
modelling of transport in these ESC structures. For absorbers, modelling of
nanocrystals superlattice arrays has bee applied to real material systems. The growth of such
systems in both III-V QD superlattices with collaborators and with colloidal
Langmuir-Blodgett dispersion of Si nanocrsystals has produced structures which are now being characterised
for their modulation
of phononic properties. Also meausurement of carrier cooling rates has been
extended to other large phononic gap bulk materials including InN, demonstrating the
importance of material
quality. Design of structures for hot carrier cells which should be practical and realisable
has developed, with the device properties more carefully specified and plans for fabricating such
structures in real devices.


4.5.3.1 modelling of hot carrier Solar cell Efficiency


Researchers:


Pasquale Aliberti, Yu Feng,
Santosh Shrestha, Gavin Conibeer, Martin Green


Collaboration with:


Yasuhiko Takeda (Toyota
Central Research Laboratories, Nagoya)


Previous
work was focused on developing a new model to calculate limiting efficiency of
a real HCSC based on an Indium Nitride (InN) absorber layer. InN has been chosen as a
potential material because of its narrow electronic band gap for absorption of a wide range of photon
energies, whilst also having a wide phonon band gap. This is good for
suppression of
phonon decay, and hence for slowing carrier cooling [4.5.53, 4.5.54].


Calculation
of limiting efficiency was performed taking into account real optical and electronic properties of InN,
removing most of the ideality assumptions used in other models [4.5.51, 4.5.52, 4.5.55, 4.5.56]. The
detailed band structure


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(a) HCSC efficiency as a
function of extraction width of ESCs for different extraction energies ΔE.
(b) HCSC efficiency as a function of extraction energy ΔE for different
ESCs energy width. Thermalisation time is 100 ps, lattice temperature is 300 K.
Absorber layer thickness is 50 nm.


FIGURE 4.5.47


of
wurtzite bulk InN has been considered in performing computation of carrier densities, pseudo-Fermi potentials
and II-AR time constants [4.5.57]. Results have been calculated considering ideal energy selective
contacts for the HCSC, which means that contacts have a very high conductivity and a discrete energy
transmission level.


Recently
the limiting efficiency for the hot carrier InN solar cell has been
calculated considering non-ideal ESCs. In this case the carriers are not extracted on a single
energy level, but in a finite energy window. Calculations have been performed taking into account
contact resistance and entropy generation
effects.


The
flux of current travelling through the ESCs towards the cold metal
electrodes can be described using
the following relation.





 (4.5.5)


The
current density in this case is proportional to the occupation
probability at the two sides of the ESC. Equation (4.5.5) has been derived assuming no
correlation
of energy of electrons in three different directions as shown in (4.5.6). This assumption is
acceptable if there is a parabolic dispersion relation at minimum energy point
along the three different directions.





 (4.5.6)


Based
on the energy and carrier conservation, Δμ and TC at steady state are
calculated.





 (4.5.7)


[quantities
as defined in Fig. 4.5.45 (a).]


The
maximum efficiency has been found for a ΔE between 1.15 eV and 1.2
eV with a transmission energy window δE of 0.02 eV. The value of limiting efficiency is
39.6% compared to 43.6% calculated in the previous section using ideal ESCs. The drop in efficiency is mostly
due to the decrease of open circuit voltage related to the decreased extraction level, equation (4.5.7).
This is partially compensated by an increase in extracted current due to increased II rate.


Figure
4.5.47 (a) shows calculated efficiency as a function of for several
values of extraction energy. In all the curves two different trends can be identified. If the value of δE
is too close to zero, the efficiency is very low due to low carrier extraction,
thus a very small value of short circuit current. The conductivity of the contact in this
case is indefinitely large. Enlarging δE, the number of carriers available for extraction increases,
improving JSC, and so the maximum efficiency. In general the efficiency peak
has been
found for values of δE from 0.02 eV to 0.1 eV depending on the extraction energy ΔE. For
the configurations which show higher efficiencies, ΔE < 1.35 eV, the optimum
value of δE goes from 0.02 eV to 0.05 eV. This optimum value for δE of between
is very
close to kTRT. This represents the
variation in energy in the contacts such that approximately the kTRT. will inevitably be lost anyway by carriers
thermalising within the contacts. Thus it sets a lower limit on a reasonable δE. Therefore this result indicates that the transmission energy range has
to be very small and confirms once again the high selectivity requirements of ESCs for HCSC [4.5.58].


In Fig.
4.5.47 (b) the value of maximum efficiency as a function of ΔE is
reported for different values of δE. It can be observed that for small transmission energy window the
extraction energy which allows maximum efficiency is lower compared to the one calculated using ideal
ESCs. This effect is related to the higher occupancy at lower energies, which increases the value of JSCfor contacts with a small transmission window.


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Peak at 1.205eV of the
conductance vs. energy plot for different values of σ for configurational
disorder (left). Conductance vs. energy plot with peak at 1.573 eV for
different values of σ for morphological disorder (right). Conductance
given in units of 2e2/h.


FIGURE 4.5.48





Planar view of the double
barrier structure formed by Si QDs in SiO2 matrix, with SiC barriers
of 2nm width (left). Mean diameter of QDs is 1.8nm. I-V characteristics for the
double barrier structure with SiO2 and SiC barriers at temperature
10K and 300K (right).


FIGURE 4.5.49


4.5.3.2 Energy Selective contacts


The
requirement for a narrow range of contact energies can be met by an energy selective contact
(ESC) based on double barrier resonant tunnelling. Tunnelling to the confined energy levels
in a quantum
dot layer embedded between two dielectric barrier layers, can give a conductance
sharply peaked at the line up of the Fermi level on the ‘hot’ absorber side
of the contact with the QD confined energy level. Conductance both below this energy and above it
should be very significantly lower. This is the basis of the current work on double
barrier resonant tunnelling ESCs.


4.5.3.2.1 modelling of QD structures


Researchers


Binesh
Puthen-Veettil, Dirk KÖnig, Gavin
Conibeer


We
developed a robust 2 dimensional model for describing the transport properties through quantum dot structures
and have used this model to understand the filtering characteristics of Energy Selective Contacts
(ESCs). In this way we are able to compute the effective filtering in 2 dimensions by running numerical
simulations. The model is developed from a discretized SchrÖdinger equation by
considering the sample volume as a collection of discrete points and using an
effective mass approximation method over the entire volume.


During
fabrication of the quantum dots in a dielectric matrix for selective energy contacts,
different kinds of irregularities can be present in the structure, the major
disorders being configurational (disorders in the position of the dots) and morphological
(disorders in the size of the dots). The extent to which configurational and
morphological disorders determine the electrical properties of the overall
structure is investigated using simulation runs of the model. The disorders are assumed to follow a normal
distribution from the mean position and size. The results show the outcome of an average
of 1000 simulation runs with different standard deviation (σ) values.


Figure
4.5.48 shows the simulation results for resonance in 2.6nm Si dot in SiO2 matrix under different orders of
configurational disorders. As the disorders increases from σ =0 to σ =1 the
conductance decreases by 53%, but the resonant energy remains the same at 1.205eV. This shows the confined energy in
the QDs does not change as their size is fixed but the effective filtering reduces dramatically.
Figure 4.5.49 shows the simulation results for a 2.2 nm Si dot in a SiO2 matrix under different
orders of morphological disorders. As the disorder increases from σ =0 to
σ = 1, the conductance decreases by 60% and the resonant peak remains
the same at 1.573eV. But the morphological disorders cause major impact compared to
configurational disorders because of the widening of the energy selection
window. This is due to the distribution in size of the QDs, since QDs with
different sizes have different resonant energies which are slightly different
from the mean resonant
energy, the average of them all increase the spread of the resonant peak thus reducing the
efficiency of the double barrier structure as energy selective contacts.


A planar
representation of the double barrier structure is shown as in Fig. 4.5.49 (left). The
barriers are
usually high band gap dielectric materials like SiO2, Si3N4
or SiC. SiC barriers have advantages over SiO2 barriers that SiC
barriers in double barrier structure makes a very good diffusion barrier for
silicon during processing, which can yield a


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Principle of oa-IV, shown for
electron injection into the sample (left). If free carriers obtain additional
energy by a massive photon flux significantly above the band gap, a smaller
bias field is required to reach a resonant condition. Sample stage of oa-IV
(right); wavelength range indicated. Every 50 nm spectral range has a photon
flux of approximately 50 Suns.


FIGURE 4.5.50


structure
with uniform QD size in the transport direction thus ensuring sharp resonances at the
resonant energies of the structure. Since the conductance of the structure is more in the case of
SiC
barriers because of the lower barrier height of SiC, thicker barriers can be used to give the same conductance as SiO2,
for which the very thin barriers are difficult to fabricate.


Figure
4.5.49 (right) shows the I-V characteristics for the double barrier QD
structure with SiO2 dielectric and SiC barriers at temperature 10K and 300K. As can be seen, the
structures with SiC potential barriers have higher current density at both low
temperature and at room temperature. As the temperature increases, the current density as well
as the
width of the resonant peak increases. Also, the negative differential
resistances appear at slightly lower voltage in structures with SiC barrier
than that in structures with SiO2 barrier. This is due to the increased leakage and
thus the lower confinement energy
for the SiC.


4.5.3.2.2 characterization of Energy Selective contacts using
‘optically assisted I-v’


Researchers:


Dirk
KÖnig, Stephan Michard (RWTH Aachen, Germany), Binesh Puthen-Veettil


Collaboration with:


Daniel
Hiller (IMTEK, University of Freiburg, Germany)


Optically
assisted IV (oa-IV) is a new characterisation method which
investigates an energy selective contact (ESC) fabricated on a Hot Carrier Absorber material with optical
excitations in a pre-defined wave length range. If a very large optical generation rate Gopt
exists adjacent to the ESC, it can probe this HC population immediately next to the contact.
Alternatively, if the HC population within the absorber is known, the ESC can be tested for its
energy selectivity. The basic principle is to provide free carriers with
additional energy by optical means, see Fig. 4.5.50. The resonant level of the ESC can then be reached by carriers at
a lower bias feld,
shifting the tunnelling resonance of the ESC - here a QD array - to lower bias voltages Vblas.


Samples
based on Si were provided by the University of Freiburg, see Fig. 4.5.51. Si is very
far from being an ideal Hot Carrier Absorber due to the complete lack of a gap between optical and acoustic
phonon modes and
hence no propensity to slow carrier cooling. Furthermore, Si has an indirect band gap
in the spectral
range of optical excitation which renders the interpretation of measured data rather
complex due to the absorption coefficient asi changing over two orders
of magnitude. However, for initial proof of concept it is adequate providing the excitation of hot
electron-hole pairs in the material is sufficiently large and collection can be made from very close to the ESC.


A Xenon
(Xe) arc lamp is a continuous light source with one of the most
constant photon fluxes Fhn in the spectral range 1000 to 500 nm. Nevertheless, there are significant
deviations in particular in the long wavelength region (> 800 nm). We therefore
compare oa-IV curves which have the same Vbias for the current
transition from forward to reverse direction, Vbias (j ® 0), indicating a
constant carrier product (constant quasi-Fermi level positions) at the ESC. Under these
conditions, the current density as a function of quasi-Fermi level position can be
assumed to be identical for these curves and this current density can be
treated as a constant offset for
each Vbias value.


For
liquid nitrogen (LN2, T = 77 K) measurements, resonant tunnelling
behaviour (negative differential resistance - NDR) was detected for all spectral ranges. With the method
mentioned above, only the oa-IV curves from 800 - 750 nm and 650 -





Sample structure for oa-IV
(upper). Contact area on QD array is 1 mm2, with ≈ 1010
QDs. Optical generation rate Gopt within ballistic transport range to the ESC and its
relative change
for photon wave length intervals used in oa-IV (middle). For these, the absorption coefficient of
c-Si aSi and the
photon flux of the Xe arc lamp Fhn
were used (lower). Full green rectangles show range of measurements which can
be compared. Dashed green rectangles
show measurements which cannot be
compared, but approach the high
optical injection limit. Please note
breaks on left ordinate in both
graphs.


FIGURE 4.5.51


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Schematic representation of time resolved photoluminescence arrangement.


FIGURE 4.5.53





oa-IV results of a typical
sample with optimum barrier thicknesses and QD size at LN2
temperature (upper) and at room temperature (lower). Curves in the wave length
intervals from 800 to 600 nm can be compared due to their identical offset of Vbias
to absolute zero Vbias., showing the free carrier product to be
constant. Curves for 550 - 250 nm and 1000 to 500 nm show maximum optical
injection limit. Both curve groups printed in bold.


FIGURE 4.5.52


600 nm
with Fhn ≈ 50 Suns for each interval could be
directly compared
to each other. In addition, we evaluated the curves with optical excitations in the range of 1000 - 500 nm (Fhn. ≈ 600 Suns) and 550 - 250 nm (Fhn ≈ 140 Suns). The former is near the practical high
concentration limit for solar cells of 1000 Suns.


As shown
in Fig. 4.5.52, for the curves in the 800 to 600 nm region at LN2
temperature, the potential difference between Vbias,. (j ®0) and the average voltage of the resonance (VRes,avg
) shows a decrease
of 48 mV with increasing photon energy (decreasing λ range). As carrier densities (quasi-Fermi
level positions) are identical for these curves, this potential drop corresponds to an increase in free hole
energy of 48
meV. As this energy difference is equal to the effective kT, it can be interpreted as an increase in carrier temperature
of DT = 560 K when going from 800 - 750 nm (1.55 -
1.65 eV) to 650 - 600 nm (1.91 - 2.06 eV). Even at Fhn. ≈ 50 Suns, this
effect is
small. This is due to Si being a very unsuitable absorber material, further corroborated by the
ratio of peak to valley current densities (quality factor of NDR - QFNDR)
dropping from 2.2 to 1.5. Si does not have a phononic band gap so that optical phonons undergo a rapid decay
which tremendously accelerates
carrier cooling.


For the
1000 - 500 nm and 550 - 250 nm ranges, the QFNDR increases significantly to
4.1 and 3.2, respectively.
The potential difference Vbias (j ® 0) -VRes.avg is
shifted by 365 and 200 mV, respectively; a quantitative comparison of both curves to each
other or to the curves in the spectral range from 800 - 600 nm is thus not
feasible. However, it shows that the energy selectivity may increase under high concentration Fhn.


For all
oa-IV curves, a tunnelling feature for electron extraction can be seen at 760
mV forward bias. However, the background current density is much higher than the tunnelling portion of the
current density in this forward bias range,
so no NDR can be seen.


At room
temperature (T = 300 K), NDR was detected only for λ ranges ≤ 600 nm, while the
impact of resonant electron injection is still visible for curves in the 800 - 600 nm
range. The background current density in the bias range around the tunnelling event increases by about
an order of magnitude when going from LN2 to room temperature. This
is due to thermal activation of trap states and increased thermal scattering during carrier transport through the QD
array. It has the same effect on NDR suppression as explained above for electron injection under
forward bias.


The QD
arrays were processed by segregation anneals, comprising some 1010 QDs as
ESCs under
the contact pad. It is very encouraging to see resonant tunnelling transport
even at room temperature
in a material system which was not grown epitaxially. At LN2 temperature (77 K),
an increase in carrier temperature of DT = 560 K was detected when increasing
the photon energy from 1.6 ± 0.05 eV to 1.985 ± 0.075 eV under a constant photon flux of Fhn ≈ 50 Suns. More suitable Hot Carrier
Absorber materials will be investigated.


4.5.3.3 hot carrier absorbers: slowing of carrier cooling


Researchers:


Robert
Patterson, Gavin Conibeer, Santosh Shreshtha, Dirk KÖnig, Pasquale Aliberti, Shujuan Huang, Yukio
Kamikawa, Lara Treiber, Martin
Green 


Carrier
cooling in a semiconductor proceeds predominantly by carriers scattering their energy
with optical phonons. This builds up a non-equilibrium ‘hot’ population of optical phonons which, if it remains hot, will drive a reverse reaction


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to
re-heat the carrier population, thus slowing further carrier cooling. Therefore
the critical factor is the mechanism by which these optical phonons decay into
acoustic phonons, or heat in the lattice. The principal mechanism by which this
can occur
is the Klemens mechanism, in which the optical phonon decays into two acoustic phonons of half its energy and of
equal and opposite momenta
[4.5.59].


The
build up of emitted optical phonons is strongly peaked at zone centre both for compound semiconductor due to the
FrÖlich interaction and for elemental semiconducotrs due to the deformation potential
interaction. The strong coupling of the FrÖlich interaction also means that high energy optical
phonons are also constrained to near zone centre even if parabolicty of the
bands is no
longer valid [4.5.60]. This zone centre optical phonon population determines that the dominant optical phonon decay mechanism is this pure Klemens decay.


4.5.3.3.1 Suppression of phonon decay
in bulk materials


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, possibly large enough to block operation of this Klemens
mechanism, which can be termed a ‘phononic band gap’. Work previously presented [4.5.61] using a simple
1D force constant model and complemented by high accuracy DFT computation [4.5.62]
indicated that GaN, InN and InP all have large phononic band gaps, which are
close to those found experimentally [4.5.63]. We are using time resolved
photoluminescence (tr-PL) to investigate the carrier cooling rates in these
materials.


4.5.3.3.2 time
resolved photoluminescence measurements of bulk phononic band gap materials


Researchers


Pasquale
Aliberti, Dirk KÖnig, Santosh Shrestha, Gavin Conibeer, Martin Green


Collaboration with:


Raphael
Clady, Murad Tayebjee, Tim Schmidt (University of Sydney), Nicholas Ekins-Daukes (Imperial College)


The
potential efficiency boost, which can be achieved by Hot Carrier solar cells, is directly related to the
possibility of extracting high energy carriers from the absorber layer before thermalisation, increasing
the voltage and hence the conversion efficiency. The poor conversion efficiency of photons
with energies above the band gap of the absorber is the main loss mechanism in conventional single
junction solar cells. The investigation of thermalisation time constants of hot carriers is a crucial
step towards the engineering of Hot Carrier cells. The efficiency of an InN
based hot carrier solar cell has been calculated using a complex theoretical
model, see Section 4.5.3.1. I was found that the limiting efficiency is strongly
related to hot carriers relaxation velocity in the absorber [4.5.57].


A
comparison of femtosecond time resolved photoluminescence (tr-PL) spectroscopy
between InP and GaAs was reported in last year’s annual report and is also now
published [4.5.64]. This showed a distinctly longer carrier cooling time constant for the wide
phononic gap InP as compared to almost zero phononic gap of GaAs. It also showed further
evidence for excitation into higher side valleys for both GaAs and InP for appropriate excitation
wavelengths. In 2010 the hot carrier cooling in InN has been investigated using
tr-PL. The wide gap between optical and acoustic branches in the InN phononic
dispersion relation
(wider than that for InP) prevents the Klemens decay of optical phonon into acoustic phonons. This can lead to
slower carrier cooling due to “Hot Phonon Effect” [4.5.65]. The decay of hot
carriers for different excitation wavelengths InN has been investigated.


Tr-PL
experiments have been performed on InN samples using the measurement configuration shown in
Fig. 4.5.53. In this technique a laser pulse acts as a switching gate relating the
photoluminescence signal to the time domain. The PL signal is collected from the sample, after a femtosecond
laser excitation, and focused in a non linear crystal. The gate signal is generated
from the same laser and is focused on the same crystal after passing through an optical delay
stage. The signal is detected using a monochromator and a PMT Our system
configuration provides 150 fs pulses with tunable wavelength over a range of 256 nm
(4.84 eV) to 2.6 μm (0.48 eV).


Figure
4.5.54 is a three dimensional representation of PL as a function of
time for all the probed wavelengths. It can be observed that the PL sharply rises when the carriers
are photo-excited by the laser pulse. The fast decay of the PL shows the thermalisation of
carriers towards respective band edges. The decay is faster for highly energetic carriers
compared to carriers closer to the bandgap. Thus the carrier population quickly degenerates
towards the band edges during the thermalisation process. In InN the thermalisation is most probably
due to
interaction of highly energetic electrons and holes with LO phonons [4.5.66].


To
investigate the rate of the carrier cooling process, the effective temperature
of the carrier population has been calculated fitting the high energy tail of the PL
spectrum for every single time during the cooling transient. The PL has been ftted assuming that
carriers form a Boltzmann-like distribution in a femtosecond time scale using the following equation.





L(ε) represents
the measured PL intensity at energy ε, α(ε) is the measured sample
absorption coefficient,
EGis the InN energy
gap, 0.7 eV in this





3D representation of InN time resolved PL data.


FIGURE 4.5.54


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Some images of the structure
as grown and modelled. (Left) the near-perfect stacking of the structure is
shown. (Centre) in-plane InAs QD arrangement. (Right) simple hexagonal
superlattice structure showing stacking. The QDs are similar to flattened disks
with in plane dimensions of 4050 nm and heights of 7 nm.


FIGURE 4.5.57





Carrier relaxation curves for
InN. The photoexcited carrier density is
1.5 x 1019 cm3. The blue dashed curve is a single
exponential fit.


FIGURE 4.5.55





Schematic of the simple
hexagonal superlattice of InAs QD disks, showing their relative dimensions. The
red square indicates orthorhombic repeat unit for the simple hexagonal system.


FIGURE 4.5.56


case,
and kB is the Boltzmann constant. TC is the
fitted parameter and represents the hot carrier temperature. Figure 4.5.55 shows the carrier
temperature transient, which seems to follow an exponential behaviour quite well (blue line - ft).


The
fitting of the calculated temperature data has been performed using a single exponential.





Here
τTH represents the carriers thermalisation time constant,
whereas C and K are two constant parameters. The fitted value for τTH
is 7 ps. This long
cooling constant can be attributed to the hot phonon effect due to the long lifetime of the
A1(LO) phonon
[4.5.64,4.5.66]. This hot carrier relaxation velocity is still too high to achieve a
considerable efficiency
gain in an InN hot carrier solar cell. However, it has been demonstrated that,
for InN, the
carrier cooling velocity is strictly related to the quality of the material
and slower carrier cooling constants compared to the ones calculated in this
chapter have been reported in the literature [4.5.67].


4.5.3.3.3 Nanostructures for absorbers


Nanostructures
offer the possibility of modification of the phonon dispersion of a composite
material. III-V compounds or indeed most of the cubic and hexagonal compounds can
be considered as very fne nanostructures consisting of ‘quantum dots’ of only one atom (say I
n) in a matrix (say N) with only one atom separating each ‘QD’ and arranged in two interpenetrating
fcc lattices. Modelling of the 1D phonon dispersion in this way gives a close agreement with the phonon
dispersion for zinc-blende InN extracted from real measured data for wurtzite material.


Similar
‘phonon band gaps’ should appear in good quality nanostructure superlattices, through coherent Bragg reflection
of modes such that gaps in the superlattice dispersion open up [4.5.61]. There is a close analogy with photonic structures in which modulation of
the refractive index in a
periodic system
opens up gaps of disallowed photon energies. Here
modulation of the ease with which phonons are transmitted (the acoustic impedance) opens up gaps of disallowed phonon energies.


4.5.3.3.3.1 force constant modelling of iii-v QD materials by
Sk growth


Researchers:


R.
Patterson, Y. Kamikawa, G. Conibeer


Collaboration with:


Yoshitaka
Okada - University of Tokyo


3D
force constant modelling, using the reasonable assumption of simple
harmonic motion of atoms in a matrix around their rest or lowest energy position, reveals such
phononic gaps [4.5.68]. The model calculates longitudinal and transverse modes and can be used to
calculate dispersions in a variety of symmetry directions and for different combinations of QD
sub-lattice structure and super-lattice
structure.


III-V
Stranski-Krastinov grown QD arrays of InAs in InGaAs and InGaAlAs
matrices are fabricated at the University of Tokyo using MBE. We are
investigating these
for evidence of phonon dispersion modulation and potential slowed carrier cooling. In order to understand
the expected phonon dispersions these are being modeeled using the 3D force constant technique.


Lattice
matched and strain compensated material pairs that may produce large phonon bandgaps are of
interest. Previous iterations in the design of these structures indicated the
importance of separating “light” and “heavy” atoms to different parts of the nanostructure. Initially,
the lightest atom in the system, As, was present in both the QD and the matrix. This meant that
the reduced mass of both regions (proportional to the sum of the inverses


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Dispersion curves for InAs
QDs in a simple hexagonal SL. The matrix is
In0.5Ga0.5xAlxAs with (x = 0.4). There
is a large phonon bandgap present in the system due to the presence of Al. The
gap seems very tolerant to Al location. (Far left): <100>, (Centre):
<110>, (Left): <111> directions.


FIGURE 4.5.58





Densities of states (DOS) for
the dispersion curve immediately to the left. Note small changes in the DOS
could be due to pseudo-random locations of the Ga and Al particles or to
differences in crystalline direction. (Far left): <100>, (Centre):
<110>, (Left): <111> directions respectively.


FIGURE 4.5.59


of each
atomic mass) was very similar as the light element dominates in this case.


On this
iteration structures with an In0.5 Ga0.5-x Alx As matrix (with x=0.4) and InAs QDs were grown. Significant Al content
was introduced into these structures with the expectation that this light element, segregated to
the matrix material, might produce appreciable phonon bandgaps. A schematic of the
structure is shown in Fig. 4.5.56. Some images derived from characterisation of the structure are
presented in Fig. 4.5.57. The superlattice of QDs has a simple hexagonal structure. Extraordinary
periodic out-of-plane stacking is achievable and largely defect free structures can be grown
on the order of microns.


Force
constant modelling of this structure predicts an appreciable phonon
bandgap, as shown in Fig. 4.5.58 and Fig. 4.5.59. This bandgap is due almost entirely to the
presence of the Al in the system. A small bandgap is present due to the mass
difference between In, Ga and As, but it is less than a quarter of the size
shown in Fig. 4.5.58 and Fig. 4.5.59. Due to computational constraints the size of the QDs is
quite small, only about a nanometre in diameter. While actual sizes for these structures are too
computationally intensive to model without extreme effort, recent modelling with gradually
increasing size suggests that the dispersion relations scale linearly with
size. That is,
once the discrete distances (bond lengths) are small relative to the superlattice unit cell
dimension, the dispersion should look exactly the same when scaled such that
the relative dimensions are preserved. This will be investigated in greater
detail in further work.


4.5.3.3.3.2 fabrication and characterisation of highly
ordered nanoparticle arrays for hot carrier absorber


Researchers:


Lara
Treiber, Shujuan Huang, Gavin
Conibeer


As
demonstrated by the work on modelling
phonon modulation, periodic core-shell QD
arrays offer a way to significantly
change the phonon modulation in a
superlattice because the core and
shell can be of materials of very
different force constant, directly leading to a strong phonon confinement. Deposition methods are being investigated to fabricate such highly ordered QD arrays.


The
Langmuir-Blodgett (LB) technique fabricates thin films from
colloidal dispersions of quantum dots (QDs). The LB technique allows for controllable, uniform film formation
and subsequent transfer onto a solid substrate, such as quartz [4.5.69]. Through
surface passivation of the QDs, interparticle spacing can also be controlled. Figure 4.5.60 illustrates the
set-up of the LB apparatus and the
functionalized QDs.


In 2010
work has focused on fabrication of periodic thin films of Si
nanoparticles (NPs) provided by the University of Minnesota. The Si NPs under
investigation are surface passivated with dodecane (C12H26),
a long chain hydrocarbon rendering the surface hydrophobic. The particles were dispersed
in chloroform and investigated using TEM, UV-vis spectroscopy and
photoluminescence (PL). Using TEM imaging the average diameter was found to be
3.0 ±0.5 nm. Fig. 4.5.61 shows a droplet of solution (dispersed in chloroform)
and the inset highlights the lattice fringes confirming the presence of silicon
- a 3.14 A
lattice spacing corresponding to the {111} planes.





Langmuir-Blodgett set-up for flm fabrication with surface functionalized
Si NPs.


FIGURE 4.5.60





(Upper) TEM images of Si NPs
dried on a grid. (Lower) TEM image of Si NP monolayer deposited at 50 mN/m of SP


FIGURE 4.5.61


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(Left) Optical absorption of
Si monolayers deposited at various surface pressures (SP). (Right) PL of Si NP
films at varying SP, as compared to the Si NP solution.


FIGURE 4.5.62





Conceptual Integrated Device


FIGURE 4.5.63


Monolayer
structures of Si NPs have been successfully deposited using the LB method and characterisation has been
on-going using TEM, UV-vis, PL and Raman spectroscopy. Figure 4.5.61 (right) illustrates TEM image of
the Si films fabricated at 50 mN/m surface pressures (SP) of the water trough. As noted, high contrast
is difficult to achieve due to the small density difference of Si and the
carbon-passivating chain. As a result, to further quantify the coverage and
regularity, computer recognition software is required; on which work is on-going. It is
difficult to see for this reason, but Fig. 4.5.61 (right) appears to show a dense
packing of Si NPs.


UV-Vis
spectroscopy was used to study the optical absorption of the films.
As illustrated in Fig. 4.5.62 (left) for single layers of Si NPs at varying compression surface
pressures (SP), the absorption clearly increases when SP increases,
corresponding to higher packing densities of Si NPs. The PL spectra of the above films show
narrow and symmetric peaks at 1.6 1.7 eV, as shown in Fig. 4.5.62 (right), which are in good
agreement with the estimated bandgap using the ‘effective mass approximation’. The red shift in emission
energy from Si NP films as compared to the solution corresponds to the electronic
energy transfer from small particles to larger ones when they are closely packed [4.5.70].


Investigation
of the electronic and phononic properties of the monolayer and multilayer structures are on-going
using low-wavenumber Raman and time resolve PL spectroscopy.


4.5.3.3.3.3 implementation of nanostructures for hot carrier
cells


In order
to use a nanoparticle array as a Hot Carrier absorber, and hence
utilise slowed carrier cooling due to modified phonon dispersion, then a way to fabricate a complete
structure with ESCs must be established. A structure in which nanoparticles are
arranged in a uniform 3D array should give the required phononic band gap. The
degree to which this needs to be ordered is still under investigation. Certainly a large
difference between masses is beneficial between the nanoparticles and the matrix and this can be
best achieved in an array of ‘core shell QDs’ in which the core and shell have very different acoustic
impedance in order to promote coherent reflection and hence confinement of phonons [4.5.61]. The
matrix in which such an array is embedded needs to allow transport of carriers to
contacts and also electron-electron and preferably hole-hole scattering to
renormalise carrier energies. Such a structure should also have a narrow electronic band gap so
as to absorb a wide range of photon energies. This combination of properties is challenging but not
mutually exclusive because phononic properties are largely independent of electronic properties.
Energy selective contacts are also required for such a structure. These would most likely be arranged
at the top and bottom of the absorber. (A hole contact might not need to be selective because the
hole population only contains a small fraction of the hot carrier energy and
hence thermalisation of holes is less important.) These ESCs would be QD or QW
double barrier structures. (Addition of an extra layer to give double QD/QW triple
barrier structures should also give rectification at the contact.) Such a
QD array / double barrier QD ESC structure is shown schematically in Fig.
4.5.63.


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Physical picture of the ND HC
Solar Cell (upper) with a carrier diffusion feld (core/shell thickness ratio
not to scale), embedded into a wide band gap solar cell [4.5.71]. Iso-valent
impurities provide an energy selective level for electrons. Band diagram of the
ND HC Solar Cell matched to the physical structure (lower). Direct generation
of hot exciton (1), energy selective extraction of hot electron from Hot
Carrier absorber (2), thermionic emission/diffusion of holes over the barrier
(3), electron-electron-scattering with renormalization of carrier energies and
possible energy loss by phonon emission (4), free carrier re-absorption (5),
impact ionization (6) and carrier generation in the wide band gap matrix (7).


FIGURE 4.5.64


Nanoparticle cell design incorporating EScs and absorber


Researcher:


Dirk
KÖnig


A full
Hot Carrier cell requires control of optical, electronic and phononic
properties in the same structure. One possible approach is the ‘nano-dot (ND)
Hot Carrier cell’ embedded into the i-region of a wide band gap solar cell as shown in Fig.
4.5.64.


Hot
Carrier solar cells must have a continuous electronic density of states (DOS)
to maximise maximum photon absorption and elastic electron-electron scattering. The
latter refills the depleted electronic energy levels from which electrons are
extracted through the ESC. On the other hand, if they do not have a phononic
band gap themselves the NDs must not be much bigger than the ballistic mean free path in
order to prevent inelastic scattering by which carriers cool down rapidly. However, optical phonons
can be confined in the nanocrystals as mentioned in Section 4.5.3.3.3 by arranging for a
mismatch between optical phonon energies in the two materials. Core shell nanocrystals can be used
to realise this [4.5.61, 4.5.62]. In addition the shell can be doped with iso-valent impurities
which form split-off subbands within the electronic band gap of the material, such as boron replacing
gallium in gallium nitride (GaN) [4.5.71]. Such an ESC would only work for one carrier type as
co-doping of a thin nano-shell appears not to be technologically feasible. For some III-V compounds with a
very high effective mass ratio between holes and electrons such that most of the excess energy during
optical generation is taken up by the electron, thermalisation of holes does not represent a large loss in
energy. Hence thermionic emission of holes over a low barrier can be used to transport holes into
the bulk of the device to be collected by the junction with little loss in efficiency.


4.5.3.3.4 hot carrier absorber: choice of materials


Researchers:


G.
Conibeer, R. Patterson, P. Aliberti, S. Huang, Y. Kamikawa, D. KÖnig,
Binesh Puthen-Veettil, S.Shrestha,
M.A. Green


The
properties required for a good hot carrier absorber material are
listed below in order of
priority.


	
  

 	
  

 
	
 1.

 	
 Large
 phononic band gap (EO(min) - ELA) - in order to suppress
 Klemens decay of optical phonons this must be at least as large as the maximum acoustic phonon
 energy. Hence a large mass difference (or large force constant difference) between
 constituent elements is required
 [4.5.61].

 
	
  

 	
  

 
	
 2.

 	
 Narrow
 optical phonon energy dispersion (ELO -EO(min)) -
 in order to minimise the loss of energy to TO phonons by Ridley decay. This requires a high symmetry atomic
 or nano-structure, preferably cubic with degenerate optical phonon energies at zone
 centre.

 
	
  

 	
  

 
	
 3.

 	
 Small
 electronic band gap - to allow a wide range of photon absorption. This should be less
 than 1eV. For 1 sun concentration the optimum is 0.7eV - as a band gap below this energy gives no advantage in
 the balance between absorption and emission. As the concentration ratio increases this
 optimum band gap decreases to zero at maximum concentration [4.5.1].

 
	
  

 	
  

 
	
 4.

 	
 A
 small LO optical phonon energy (ELO). This reduces the amount of
 energy lost per LO phonon emission, requiring a greater number to be emitted for a given
 energy loss [4.5.62]. However, it is difficult to have both a small ELO and the large phononic
 gap required in 1. This condition requires further investigation, but does still argue for a small ELO.

 
	
  

 	
  

 
	
 5.

 	
 An
 absolute small maximum acoustic phonon energy (ELA). This maximises the
 phononic gap if ELO is also small. A small ELA requires a large
 mass for
 the heavy atom and/or small force constant for its bonds.

 
	
  

 	
  

 
	
 6.

 	
 Good
 renormalisation rates in the material, i.e. good e-e and h-h scattering (e=electron,

 


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Use of the periodic table to
analyse possible analogue compounds of InN based on atomic mass combination and
electro-negativity.


FIGURE 4.5.65


	
  

 	
  

 
	
  

 	
 h=hole).
 This requires a reasonable DOS at all energies above E , or at least only very
 narrow gaps between energy levels, ≤ kT300K. This in turn requires a good
 overlap of
 wavefunction for carriers through the material, i.e. poor electronic confinement or a reasonable
 conductor. This condition is met in all inorganic semiconducotrs quite easily, with e-e
 scattering rates of less than 100fs for reasonable carrier concentrations. It may not be met in organic semiconductors or in nanostructures with large
 barrier heights.

 
	
  

 	
  

 
	
 7.

 	
 Good
 carrier transport in order to allow transport of hot carriers to the
 contacts. This is similar to 6, except that it only need be in the
 direction of the contacts, probably the z growth direction. A reasonably low
 resistance is probably good.

 
	
  

 	
  

 
	
 8.

 	
 It
 should be possible to make good quality, highly ordered, low
 defect material. Preferably it should be easy and cheap to do this.

 
	
  

 	
  

 
	
 9.

 	
 Earth
 abundant and readily available and processable constituent elements and processes.

 
	
  

 	
  

 
	
 10.

 	
 No or
 low toxicity of elements, compounds and processes.

 
	
  

 	
  

 
	
  

 	
 [(ELO
 , EO(min) & ELA are the maximum optical, minimum optical and
 maximum acoustic phonon energies respectively.]

 



InN has
most of these properties, except 4, 8 & 9, and is therefore a
good model material for a hot
carrier cell absorber.


Analogues of InN


As InN
is a model material, but has the problems of abundance and bad material quality,
another approach is to use analogues of InN to attempt to emulate its near ideal properties. These
analogues can be II-IV-nitride compounds, large mass anion III-Vs, group IV compounds/alloys or
nanostructures.


II-IV-Vs: ZnSnN; ZnPbN; HgSnN; HgPbN


With
reference to Fig 4.5.65, it can be seen that replacement of In on the
III sub-lattice with II-IV compounds is analogous and is now quite widely being investigated
in the Cu2ZnSnS4 analogue to CuInS2 [4.5.72].


ZnGeN
can be fabricated [4.5.73] and is most directly analogous with Si and GaAs. However, its band gap is large at
1.9eV. It also has a small calculated phononic band gap [4.5.74]. ZnSnN has a smaller electronic
gap (1 eV) and larger calculated phononic gap [4.5.74]. It is however difficult to fabricate,
and also its phononic gap is not as large as the acoustic phonon energy making it difficult to
block Klemens decay completely. HgSnN or HgPbN should both have smaller Eg and larger phononic
gaps. These
materials have not yet been fabricated [4.5.75].


Large mass cation:


The Bi
and Sb compounds have large predicted phononic gaps and Bi is a relatively abundant material, with
only low toxicity [4.5.75]. BiB has the largest phononic gap but AlBi, Bi2S5, Bi2O3
(bismuthine) are also attractive. Similarly
SbB has a large predicted phononic
gap. That for AlSb is the same size as
the acoustic phonon energy and its band gap is 1.5eV, making it marginal as an absorber material and
similar to InP.


Group IIIA III-Vs


LaN and
YN both have large phononic gaps whilst that for ScN is too small.


The
Lanthanides can also form III-Vs. ErN and other RE nitrides can be grown by MBE. The phononic band gaps of the
Er compounds are predicted to be large, because of the heavy Er cation, but its
discrete energy levels make it not useful as an absorber, although the combination of properties
in a nanostructure could be
advantageous.


Group IV
alloy/compounds:


All of
the combinations Si/Sn, Ge/C or Sn/C look attractive with large gaps predicted in 1D models. However being
all group IVs they only form weak compounds. Unfortunately SiC, whether 3C, 4H or 6H, has too narrow a
phononic gap. Nonetheless GeC does form a compound and is of significant interest [4.5.76].


There
are also several other inherent advantages of group IV compounds/alloys all of
which are associated with the four valence electrons of the group
IVs which result in predominantly covalent bonding:


	
  

 	
  

 
	
 a)

 	
 The
 elements form completely covalently bonded crystals primarily in a diamond structure (tetragonal
 is also possible as in βSn). However for group IV compounds the decreasing
 electronegativity down the group results in partially ionic bonding. This is not strong in
 SiC and whilst it tends to give co-ordination numbers of 4, can nonetheless result in several
 allotropes of decreasing symmetry: 4c, 4h, 6h. However, as the difference in
 period increases for the as yet theoretical group IV compounds, so too does the difference
 in electronegativity and hence also the bond ionicity and the degree of order. For a
 hot carrier absorber this is ideal because it is just such a large difference in the
 period which is needed to give the large mass difference and hence large phononic
 gaps. All of GeC, SnSi, SnC (and the Pb compounds) have computed phononic gaps large enough to block Klemens
 decay, and should also tend to form ordered diamond structure compounds.

 
	
  

 	
  

 
	
 b)

 	
 Because
 of their covalent bonding, the group IV elements have relatively small
 electronic band gaps as compared to their more ionic III-V and much more
 ionic II-VI analogues
 in the same period: e.g. Sn 0.15eV, InSb 0.4eV, CdTe 1.5eV. In fact to achieve approximately
 the same electronic band gap one must go down one period from group IV to III-V and down another period from III-V to
 II-VI: e.g. Si 1.1eV, GaAs 1.45eV, CdTe 1.5eV. This means that for group IV compounds
 there is greater scope for large mass difference compounds

 



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Cross-sectional electron micrograph of a 30-bilayer porous silicon
distributed Bragg reflector.


FIGURE 4.5.66


	
  

 	
  

 
	
  

 	
 whilst
 still maintaining small electronic band gaps. A small band gap of course being important for
 broadband absorption in an absorber - property 3 in the desirable properties for hot
 carrier absorbers listed above.

 
	
  

 	
  

 
	
 c)

 	
 The
 smaller Eg would tend to be for the larger mass compounds
 of Pb or Sn. Which, to give large mass difference, would be compounded with Si or
 Ge. This trend towards the lower periods of group IV also means that the maximum
 optical phonon and maximum acoustic phonon energies will be smaller for a given mass
 ratio - the desirable
 properties 4 and 5.

 
	
  

 	
  

 
	
 d)

 	
 Furthermore,
 unlike most groups, the group IV elements remain abundant for the higher mass
 number elements - desirable property 9. Property 10 is also satisfied because the
 group IVs have low toxicity.

 



Nanostructures:


As
discussed in section 4.5.3.3.3 QD nanostructures can be viewed in the same way as compounds. Their
phononic properties can be estimated from consideration of their combination force
constants. Hence it is possible to ‘engineer’ phononic properties in a wider range of
nanostructure combinations. Of the materials discussed above the Group IVs lend themselves most
readily to formation of nanostructures instead of compounds due to their predominantly
covalent bonding, which allows variation in the coordination number. Therefore the
nanostructure approaches of section 4.5.3.3.3 are consistent with a similar description as analogues
of InN, whether it be III-V QDs, colloidally dispersed QDs or for core shell QDs.


4.5.3.3.5 Summary of hot carrier solar cell research


2010
has seen significant development in most areas of Hot Carrier solar cell work. The modelling of
efficiencies not only now includes real material parameters for highly promising absorber
materials such as InN, but also is now extended to Energy Selective contacts of finite width.
The transport across such contacts is further modelled for a range of QD matrix
combinations. Work on ESCs has seen further more detailed demonstration of the necessary
resonance in double barrier resonant tunnelling structures, with additional evidence
for hot carrier populations, albeit very small, from illuminated I-V measurements with the ‘optically
assisted I-V technique. Measurement of InN with time-resolved PL has indicated some
evidence for slowed carrier cooling, further corroborating the importance of a large
phonon band gap to block optical phonon decay, but also highlights the
importance of material quality. Modelling of nanostructures for absorber materials has
focussed on real III-V QD structures, showing phonon bandgaps which will soon be measured in phonon dispersion measurements.
Progress on the Langmuir-Blodgett approach to ordered nanoparticle arrays has seen development of ordered single layer
arrays of Si nanoparticles. The potential application of nanostructures to fully integrated
devices has started to be investigated conceptually, with various designs considered.
Similarly the possibility of absorber materials which are analogous to InN is also being
investigated. These many aspects of Hot Carrier cells will see further development and
consolidation in 2011 with recent success in significant additional funding.


4.5.4 up-conversion


Researchers:


Craig
Johnson, Gavin Conibeer


Collaboration with:


Peter
Reece (Physics, UNSW)


Up-conversion in novel silicon-based materials


Up-conversion
(UC) in erbium-doped phosphor compounds (particularly NaYF4:Er) has been shown to be a
promising means of enhancing the sub-band-gap spectral response of conventional Si solar cells without modification of the
electrical properties of the cell [4.5.77]. In this scheme, a layer containing the phosphor is applied
to the rear of a high-efficiency bifacial cell. After absorbing two long-wavelength (1500nm)
photons - which are transmitted by the cell - the excited Er ions can relax by
emitting a photon with an energy greater than the Si band gap, thereby increasing
the current that can be extracted from
the cell.


While
phosphors have demonstrated high-efficiency UC behaviour, their use presents
particular challenges with regard to fabrication and cost. Our work in the last year has focused on the
development of Er-doped porous Si (PSi:Er) as an alternative UC material. PSi is
unique in that its porosity -and hence the material refractive index - can be varied as a function
of depth, allowing for the elaboration of high-quality monolithic Si optical structures such
as distributed Bragg reflectors (DBRs). A cross-sectional electron micrograph of such a structure
is shown in Fig. 4.5.66. Its porous substructure also allows for deep infusion of dopant
atoms via techniques such as
electroplating.


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Simulated reflectivity
spectra of PSi DBRs with varying numbers of bilayers; layer thicknesses were
adjusted to fix the short-wavelength stop band edge at 1550nm (marked with red
dashed vertical line).


FIGURE 4.5.68





Band structure in the
neighborhood of the fundamental band gap of an infinite 1D photonic crystal
(left) and group velocity in the material (right).


FIGURE 4.5.67


We have
previously reported room-temperature UC luminescence from Er-doped nanoporous Si when excited at very high
power densities with a 1550nm laser. In the past year we have focused on increasing the efficiency of this
UC luminescence by modifying the
PSi structure as described above.


The
dependence of the efficiency of the UC process on irradiance is
non-linear in the range of “sun-like” incident power. That is, the concentration
of the
incident radiation into a small Er-doped region results in greater efficiency
than for non-concentrated radiation over a proportionally large-area device. Typically,
concentration is achieved using lenses or non-imaging optics, but we have examined an analogous
electromagnetic field enhancement in the vicinity of optically-active Er ions by the excitation
of slow-light modes in these PSi:Er DBRs.


Field enhancement in 1D PSi:Er photonic crystals


Though
their use preceded the advent of the photonic crystal concept, DBRs can be described as one-dimensional
photonic crystals. The regular variation of the optical thickness of multiple alternating layers
results in wavelength-dependent interference behaviour manifesting as discrete bands of allowed and disallowed
electromagnetic modes, as shown in the left panel of Fig. 4.5.67. The “edge” of a photonic
band is a spectral region in which the effect of coherent scattering processes
changes abruptly between transmission and reflection of incident photons as determined by the superposition of
Bloch waves. Insofar as the group velocity vg
of an incident wave can be said to transition between “positive” and
“negative” values
- implying energy propagation into and out of the structure, respectively, in bands of strong
transmission and strong reflection - there exists an inversion point at which vg is zero, corresponding to a
standing wave established by the superposition of scattered Bloch
components. As can be seen in the right panel of Fig. 4.5.67, group velocity is
drastically suppressed
across a broad region near the zero-point. For steady-state equilibrium conditions,
this slowing of energy propagation requires a proportional increase in energy density, that is, an enhancement of the
electromagnetic field strength within the structure. It can be shown that the efficiency increase
for a two-step UC process is proportional to (c/nvg
- 1)I 0,
where c is the speed of light in vacuum, n is the average refractive index of the multilayer material,
and /0" is the incident field intensity [4.5.78]. In this way the
slow-light mode acts to augment the interaction that converts energy from the
field into atomic potential energy, resulting in a boost in the efficiency of the
process until saturation is
reached.


Simulation of field enhancement in 1D Pc structures


Using a
1D transfer matrix calculation, we simulated the reflectivity
characteristics of a series of PSi DBRs with 10, 20, 30 and 40 high-/low-porosity bilayers.
As shown in
Fig. 4.5.68, the reflectivity characteristic of a DBR contains a wide photonic stop-band. The structural parameters
were tuned slightly in each case as the number of bilayers increased to produce a
short-wavelength band edge minimum at 1550nm, the excitation wavelength of
interest (marked with a dashed
red line).


Maximum
transmission of 1550nm light into the structure is clearly required for efficient
coupling into
the Er ions. From Fig. 4.5.68 it is evident that an increased number of layers “compresses” the reflectivity
characteristic, resulting in a steeper


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Intensity-valued mode profile
in DBRs with varying numbers of high/low-porosity bilayers for a leading band
edge fxed at 1550nm. All intensities are normalized to the incident field
intensity and each plot is independently color-scaled to show maximum detail.
The air and substrate interfaces with the DBR are indicated by the dashed black
(upper) and red (lower) lines, respectively


FIGURE 4.5.69


band
edge and a narrower transmission window between the stop band and the neighboring interference fringe.


Figure
4.5.69 shows the calculated field intensity profile for these DBRs in
the spectral region between 1500 and 1600nm. The results have been normalized to the
incident field intensity and each plot is independently colour-scaled to show maximum detail.
They clearly demonstrate that considerable field enhancement is possible
throughout the depth of such a multilayer structure, with peak relative
intensities of more than 11 for the 30-bilayer structure and more than 18 for
the 40-bilayer
structure. However, it is also clear that the regions of enhancement are increasingly narrowly-concentrated as the
number of bilayers increases. This is due to the additional interference fringes in the
reflectivity characteristic of the DBR that arise with additional layers, as is apparent from
Fig. 4.5.69.
Calculations for more than 40 layers show that enhancements of up to 80 are possible for a large number of bilayers
though the peak narrows to less than 1nm wide for 100 bilayers.


Conclusion


These
simulations show that drastic field intensity enhancement is in
principle achievable in Er-doped PSi DBRs. Our current work is focused on the fabrication of suitable
samples by anodic chemical etching, electroplating, and high-temperature annealing.
Angular-dependent room temperature photoluminescence studies are underway to probe the effect of the
photonic band edge on the efficiency of UC in the optically-active Er ions within
the structures. This Si-based approach to efficient up-conversion is
conceptually promising and by optimising our fabrication techniques to improve the quality of our
optical structures we expect it will prove to be valuable work.


4.5.5 Plasmonics for 3rd generation structures


Researcher:


Supriya
Pillai


Plasmonics
is the study of the interaction of light on a thin metal dielectric interface resulting in the collective
oscillation of the free electrons in the metal. This gives rise to exciting properties that are very different
from the bulk metal. It is an emerging area of technology for photovoltaic applications with potential for light
management at the nanoscale. Ever since our
proof-of concept results were
published in 2007 [4.5.79], there has
been a huge increase in interest in incorporating
nanoparticles on solar cells due to their demonstrated light trapping
properties. The large optical polarisation
associated with the nanoparticles results in a strong enhancement of the electric field around the vicinity of the
particles along with strong
scattering. This optical property is being utilised for improving light
trapping in thin-flm solar cells.


The
scattering or near field enhancement is strongest at the surface plasmon resonance (SPR) frequency and this can be
tuned by changing the size, shape, dielectric medium around the particles. SPR tunability offers
control in manipulating light in the regime where the absorption of the solar cells are weak. Our
recent work (see section 4.4 Thin Film) has shown the benefits of having the particles
on the rear as opposed to previous work with front located particles [4.5.80]. By having
the particles
on the back of the cell any potential loss due to absorption in the metal or losses due to sub-resonance
photocurrent suppression resulting from destructive interference of the scattered and transmitted light into
the semiconductor layer can be avoided [4.5.81]. An additional advantage is that
because the scattering plasmonics layer is electrically decoupled from the cell, the
antireflection layer on the front and the plasmons


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Schematic representation
showing an example of surface plasmon resonance tunability by varying the of
size of the metal nanoparticles for wavelength dependent light trapping in a
tandem solar cell.


FIGURE 4.5.70


can be
optimised independently of each other. Our recent work has also made
use of an additional reflecting layer (paint) along with the nanoparticle layer on the rear side
of the cell to maximise the randomisation of light and to ensure no light is lost [4.5.80].


In this
study we focus our interest on the use of plasmonics for low-dimensional structures like
quantum dot structures for possible applications in tandem solar cells. PL measurements were used
to characterise the samples. The analysis is based on the reciprocity of light that a good
absorber can be a good emitter and the proof-of concept established with EL measurements in an earlier study
[4.5.82]. Hence the PL enhancement would be synonymous to an increase in photocurrent for an optimised QD cell. The tunability of plasmon
resonance allows the possibility of increasing the photocurrent of each cell in
a tandem cell configuration. Optimising the nanoparticle parameters can help achieve wavelength dependent light trapping which will
be an encouraging step towards increasing
the performance of a tandem solar
cell. Figure 4.5.70 shows one way of
achieving the SPR tunability by varying
the size of the nanoparticles in a tandem cell configuration.


The
sample under study is a 4nm single layer silicon QD structure in an oxide
matrix with a 6nm capping oxide layer with an emission wavelength of 930nm (1.3eV). Mass
thicknesses of 10, 14, 18 and 22 nm silver were deposited and the particles annealed at 2000C in nitrogen for
an hour. A 532nm, 10mW Nd:YAG laser was used to illuminate the samples for both the front
(incident on QD layer) and rear side (incident on the quartz slide) locations
of the silver
nanoparticles and the PL plots studied. PL measurements were carried out on
these samples and
the effect of different size particles were investigated both before and after
the deposition of the
nanoparticles.


The
self assembly techniques of nanoparticle fabrication give a varied size and shape
distribution very suitable for a broadband response. This is particularly noted for
particles corresponding to thicker Ag layers as can be seen from the PL plots in
Fig. 4.5.71. The red-shift of the enhancement peaks with larger particles
are also clearly evident. More details of this work has been reported in
[4.5.83].


Rear
located nanoparticles perform better than front located nanoparticles, consistent with the results from thin-film
cells. We believe this is because of the change in scattering cross-section of the nanoparticles due to
the changes in the driving feld and also due to the change in the mode of
excitation (from air for front located nanoparticles and from Si for rear
located nanoparticles) for the two different locations on the samples. More work need to be done to
better understand the mechanism. Further work will also concentrate on using alternate
approaches for tuning the resonance position close to the band-edge (emission wavelength for
PL) to increase the scattering properties and hence absorption in the weakly absorbing range.


4.5.6 concluding remarks for the third generation section


In 2010
work has proceeded significantly in all the areas of Third
Generation research, with improved fabrication and characterisation of materials and complexity of modelling
which together give an overall better understanding and optimisation of devices.


Group IV
based nanostructure materials have seen significant improvement in device design. With interlayers, in both SiNx
and SiC matrices, used to effectively control both the uniformity of size of Si QDs and carrier transport
in the growth direction. Modelling now allows the confined energy levels of complex QD shapes to
be calculated and their overlap to form mini-bands estimated in more detail. At the same
tiome improved characterisation is giving a much clearer idea on the shape and distributions of Si QDs
and is now allowing choice of growth parameters to give uniform size spherical QDs
to be grown. Ge nanostructure materials have seen improved control of p-type conductivity in


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PL plots from a 4nm single
layer QD structure in an oxide matrix with a 6nm capping oxide layer (right
axis) along with the corresponding enhancement plots (left axis) with silver
nanoparticles corresponding to 10, 14, 18 and 22 nm mass thickness of silver
for (a) silver nanoparticles on the front and (b) silver nanoparticles on the
rear.


FIGURE 4.5.71


Ge QDs
and very highly crystalline growth of Ge QWs. Homojunction Si nanostructure devices have demonstrated
improved conduction, there has been continued demonstration of rectifying
properties for heterojunctions with c-Si and heterojunctions between two nanostructured materials are now
starting to exploit the advantages of
both.


Hot
carrier cells have seen further development of efficiency modelling
which now not only includes material parameters such as Auger coefficients for real
promising absorber materials such as InN, but also includes the effects of real
non-ideal energy selective contacts. There has been significant improvement in measurement of negative differential
resistance in Si QD based energy selective contacts is now allowing and this overlaps well with
continuing improvement in modelling the transport through such structures in various matrices.
Carrier cooling measurements on the candidate absorber material InN have shown evidence for phonon
bandgaps building on the slowed carrier cooling seen in InP previously. Modelling of
analogues of these materials in nanostructures now predicts the phonon properties of rea lIII-V QD arrays
grown by collaborators. In addition colloidally dispersed Si nanoparticles have now been fabricated
as coherent single layer nanoparticle arrays and are progressing towards multi-layer structures.
Theoretical work on the potential materials for absorbers with controlled phon dispersion and
hence slowed carrier cooling has progressed on approapratie analogues for InN and devices
involving various nanostructure configurations are being analysed conceptually.


Up-conversion
has seen a further significant development of the use of porous-Si as a host for
Er up converting species. The porosity of porous-Si can be controlled to give
layers of alternating refractive index which can be used as distributed Bragg reflectors to modifiy
the photonic density of states such that there is strong enhancement of photonic modes at the critical Er
absorption at 1500nm. This has been demonstrated and can lead directly to large
increase in the up-conversion efficiency, thus tackling one of the key problems
of rare earth up-conversion
that it is inherently non-linear and dependent on concentration.


Plasmonics,
whic has previously been shown to enhance emission and absorption from both 1st
and 2nd
generation cells, has now been applied to the Si annostructured layers of 3rd
generatrion materials. This has shown significant enhancement in luminescence
demonstrating the strong potential to achieve local concentration with a global 1 sun illumination. This is
particularly useful for several of the non-linear 3rd generation approaches.


The
development of all the 3rd generation projects in 2010 now allows
much greater understanding of the materials and devices. Work in 2011 will see
consolidation of this into improved devices. Several new areas of funding
will contribute to this and also allow development of new project areas.


References:


	
  

 	
  

 
	
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 4.5.11

 	
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 4.5.12

 	
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 4.5.16

 	
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 4.5.20

 	
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 4.5.21

 	
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 to Programming”. 2009: Springer. 406.

 
	
  

 	
  

 
	
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 4.5.24

 	
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 4.5.25

 	
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 4.5.26

 	
 Y-H. So, M.A. Green, G.
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 quantum dots in Si-rich nitride/Si3N4 superlattice synthesized by magnetron
 sputtering”, Applied Physics Letters, accepted Feb 2011.

 
	
  

 	
  

 
	
 4.5.27

 	
 D. Di, I. Perez-Wurfl, G.
 Conibeer, M.A. Green, Solar Energy
 Materials & Solar Cells 94 (2010) 2238-2243.

 
	
  

 	
  

 
	
 4.5.28

 	
 G. Conibeer, M.A. Green, D.
 Konig, I. Perez-Wurfl, S. Huang, X. Hao,
 D. Di, L. Shi, S. Shrestha, B. Puthen-Veettil, Y So, B. Zhang and Z.
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 voltage and current transport”, Progress in Photovoltaics: Res. Appl. 18
 (2010) In press, Published online in Wiley Online Library (wileyonlinelibrary.com).
 DOI: 10.1002/pip.1045, accepted Sept 2010

 
	
  

 	
  

 
	
 4.5.28

 	
 D. Song, E. Cho, Y Cho, G.
 Conibeer, Y Huang, S. Huang, MA. Green, “Evolution of Si (and SiC)
 nanocrystal precipitation in SiC matrix”, Thin Solid Films 516 (2008)
 3824-3830, doi:10.1016/j. tsf.2007.06.150

 
	
  

 	
  

 
	
 4.5.29

 	
 D. Song, E-C. Cho, G.
 Conibeer, Y Huang, C. Flynn, MA. Green, “Structural characterization of
 annealed Si1-xCx/SiC multilayers targeting formation of Si nanocrystals in a
 SiC matrix”, Journal of Applied Physics, 103 (2008) 083544.

 
	
  

 	
  

 
	
 4.5.30

 	
 Z. Wan, S. Huang, M.A.
 Green, G. Conibeer, Physica Status Solidi C, “Residual stress study of
 silicon quantum dot in silicon carbide matrix by Raman measurement”, EXCON
 ‘10 Proceedings special issue, accepted September 2010.

 
	
  

 	
  

 
	
 4.5.31

 	
 Zhenyu Wan, Shujuan Huang,
 Martin Green and Gavin Conibeer, Rapid thermal annealing and crystallization
 mechanisms study of silicon nanocrystal in silicon carbide matrix, Nanoscale
 Research Letters, 7541289134788882, accepted January 2011.

 
	
  

 	
  

 
	
 4.5.32

 	
 F. Gao, M.A. Green, G.
 Conibeer, E-C. Cho, Y Huang, I. Perez-Wurfl, C. Flynn, “Fabrication of
 multilayered Ge nanocrystals by magnetron sputtering and annealing”,
 Nanotechnology, 19 (2008) 455611.

 
	
  

 	
  

 
	
 4.5.33

 	
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 4.5.34

 	
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 Puzzer, S. Huang, D. Song, C. Flynn, S. Park,
 X. Hao, D. Mansfield, “Silicon quantum dot nanostructures for tandem
 photovoltaic cells”, Thin Solid Films, 516 (July 2008) 6748.

 
	
  

 	
  

 
	
 4.5.35

 	
 B. Zhang, S.K. Shrestha, P.
 Aliberti, M.A. Green, GJ. Conibeer, Characterisation of size-controlled and
 red luminescent Ge nanocrystals in multilayered superlattice structure, Thin
 Solid Films 518 (2010) 5483-5487.

 
	
  

 	
  

 
	
 4.5.36

 	
 B. Zhang, S.K. Shrestha,
 M.A. Green, GJ. Conibeer, “Size controlled synthesis of Ge nanocrystals in
 SiO2 at temperatures below 400 degree C using magnetron
 sputtering”, Applied Physics Letters, 96, 26901 (2010).

 
	
  

 	
  

 
	
 4.5.37

 	
 Y.Sasaki, C. Horie, Phys.
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 4.5.38

 	
 Karmous et al., Phys. Rev.
 B 73 (2006) 075323.

 
	
  

 	
  

 
	
 4.5.39

 	
 B. Zhang, S. Shrestha ,
 M.A. Green , G. Conibeer, Surface states induced high p-type conductivity in
 nanostructured thin film composed of Ge nanocrystals in SiO2
 matrix, Applied Physics Letters, 97, 132109 (2010).

 
	
  

 	
  

 
	
 4.5.40

 	
 XJ.
 Hao, E-C. Cho, C. Flynn, YS. Shen, S.C. Park, G. Conibeer, M.A. Green, Solar Energy
 Materials & Solar Cells, “Synthesis and characterization of boron-doped
 Si quantum dots for all-Si quantum dot tandem solar cells”, 93 (2009)
 273-279.

 
	
  

 	
  

 
	
 4.5.41

 	
 I. Perez-Wurfl, A. Gentle,
 X. Hao, M.A. Green, G. Conibeer and D-H. Kim, Proceedings of 24th EPVSEC,
 Hamburg, Germany, (2009).

 
	
  

 	
  

 
	
 4.5.42

 	
 J.M.
 Shah, Y-L. Li, Th. Gessmann, E. F. Schubert., Journal of applied physics. 94 (2003) 2627.

 
	
  

 	
  

 
	
 4.5.43

 	
 L. Ma, D. Lin, G. Conibeer,
 I. Perez-Wurfl, “Introducing dopants by diffusion to improve the conductivity
 of silicon quantum dot materials in 3rd generation photovoltaic devices”,
 Physica Status Solidi, accepted Sept10

 
	
  

 	
  

 
	
 4.5.44

 	
 G. Cantele, E. Degoli, E.
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 113303;G.M. Dalpian, J.R. Chelikowsky, “Self-Purification in Semiconductor
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 4.5.45

 	
 A.R. Stegner, R.N. Pereira,
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 in freestanding silicon nanocrystals from the gas phase: Phosphorus
 incorporation and defect-induced compensation”, Physical Review B, 80 (2009)
 165326.

 



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 4.5.46

 	
 A.L. Tchebotareva, MJ.A. de
 Dood, J.S. Biteen, H.A. Atwater, A. Polmana, “Quenching of Si nanocrystal
 photoluminescence by doping with gold or phosphorous”, Journal of
 Luminescence, 114 (2005) 137-144.

 
	
  

 	
  

 
	
 4.5.47

 	
 M. Fujii, A. Mimura, S.
 Hayashi, K. Yamamoto, C Urakawa, H. Ohta, Journal of Appl. Phys., 87 (2000)
 1855-1857.

 
	
  

 	
  

 
	
 4.5.48

 	
 D. KÖnig, S. Shrestha, J.
 Rudd, G. Conibeer, M. A. Green, “Doping of Si-Based Dielectrics for Providing
 Majorities to Si Quantum Dots: Acceptors in SiO2”, Proc. 24th
 European PVSEC, (Hamburg 2009).

 
	
  

 	
  

 
	
 4.5.49

 	
 G. Conibeer, M.A. Green, D.
 Konig, I. Perez-Wurfl, S. Huang, X. Hao,
 D. Di, L. Shi, S. Shrestha, B. Puthen-Veettil, Y. So, B. Zhang and Z.
 Wan, “Silicon quantum dot based solar cells: addressing the issues of doping,
 voltage and current transport”, Progress in Photovoltaics: Res. Appl. 18
 (2010) In press, Published online in Wiley Online Library (wileyonlinelibrary.com).
 DOI: 10.1002/pip.1045, accepted Sept 2010.

 
	
  

 	
  

 
	
 4.5.50

 	
 Santosh K. Shrestha,
 Pasquale Aliberti, Gavin J. Conibeer, Energy selective contacts for hot
 carrier solar cells, Solar Energy Materials and Solar Cells, 94 (Sept 2010)
 1546-1550.

 
	
  

 	
  

 
	
 4.5.51

 	
 P. WÜrfel, Sol. Energy
 Mats. and Sol. Cells. 46 (1997) 43.

 
	
  

 	
  

 
	
 4.5.52

 	
 R. Ross, AJ. Nozik, J. Appl
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 4.5.53

 	
 V.Y. Davydov, et al.,
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 band gap”, Physica Status Solidi (B), 229 (2002) p. r1-r3.

 
	
  

 	
  

 
	
 4.5.54

 	
 D. Fritsch, H. Schmidt, M.
 Grundmann, “Band dispersion relations of zinc-blende and wurtzite InN”,
 Physical Review B, 69 (2004) 165204.

 
	
  

 	
  

 
	
 4.5.55

 	
 YTakeda,T. Ito,T. Motohiro,
 D. KÖnig, S.K. Shrestha, G. Conibeer, “Hot carrier solar cells operating
 under practical conditions”, Journal of Applied Physics, 105 (2009)
 074905-10.

 
	
  

 	
  

 
	
 4.5.56

 	
 Wurfel, P., A.S. Brown,
 T.E. Humphrey, and M.A. Green, Particle conservation in the hot-carrier solar
 cell”, Progress in Photovoltaics, 13 (2005) 277-285.

 
	
  

 	
  

 
	
 4.5.57

 	
 P. Aliberti, Y Feng, Y Takeda,
 S.K. Shrestha, M.A. Green, GJ. Conibeer, “Investigation of theoretical
 efficiency limit of hot carrier solar cells with bulk InN absorber”, Journal
 of Applied Physics, 108 (2010) 094507-10.

 
	
  

 	
  

 
	
 4.5.58

 	
 G.
 Conibeer, C.W.Jiang, D. KÖnig, S.K. Shrestha, T. Walsh, M.A. Green, “Selective energy
 contacts for hot carrier solar cells”, Thin Solid Films, 216 (2008)
 6968-6973.

 
	
  

 	
  

 
	
 4.5.59

 	
 P.G. Klemens, Phys. Rev.
 148 (1966) 845.

 
	
  

 	
  

 
	
 4.5.60

 	
 G. Conibeer, R. Patterson,
 P. Aliberti, L. Huang, J-F Guillemoles, D. KÖnig, S. Shrestha, R. Clady, M.
 Tayebjee, T. Schmidt, M.A. Green “Hot Carrier solar cell Absorbers”, 24th
 European PVSEC, Hamburg (Sept. 2009).

 
	
  

 	
  

 
	
 4.5.61

 	
 G. Conibeer, NJ.
 Ekins-Daukes, J-F. Guillemoles, D. KÖnig, E-C. Cho, C-W. Jiang, S. Shrestha
 and M.A. Green, “Progress on Hot Carrier Cells”, Solar Energy Materials and
 Solar Cells, 2009, 93, 713.

 
	
  

 	
  

 
	
 4.5.62

 	
 D. KÖnig, K.
 Casalenuovo,YTakeda, G. Conibeer, J.F. Guillemoles, R. Patterson, L.M. Huang,
 M.A. Green, “Hot Carrier Solar Cells: Principles, Materials and Design”,
 Physica E, 42 (2010) 2862-2866.

 
	
  

 	
  

 
	
 4.5.63

 	
 H. Bilz, W. Kress, “Phonon
 dispersion relations in Insulators”, Springer-Verlag (1979).

 
	
  

 	
  

 
	
 4.5.64

 	
 R. Clady, MJ.Y Tayebjee, P.
 Aliberti, D. Konig, NJ. Ekins-Daukes, GJ. Conibeer, T.W. Schmidt, M.A. Green,
 “Interplay between Hot phonon effect and Intervalley scattering on the
 cooling rate of hot carriers in GaAs and InP”, Progress in Photovoltaics,
 accepted March 2011.

 
	
  

 	
  

 
	
 4.5.65

 	
 K.T
 Tsen, J.G. Kiang, D.K. Ferry, H. Lu, WJ. Schaff, H.W. Lin, S. Gwo, “Direct measurements of
 the lifetimes of longitudinal optical phonon modes and their dynamics in
 InN”, Applied Physics Letters, 90 (2007) 3.

 
	
  

 	
  

 
	
 4.5.66

 	
 YC.
 Wen, YC, C.Y Chen, C.H. Shen, S. Gwo, C.K. Sun, “Ultrafast carrier thermalization in InN”,
 Applied Physics Letters, 89 (2006) 3; M.D.Yang, et al., “Hot carrier
 photoluminescence in InN epilayers”, Applied Physics A - Materials Science
 & Processing, 90 (2008)
 123-127.

 
	
  

 	
  

 
	
 4.5.67

 	
 F. Chen, A.N. Cartwright,
 H. Lu, WJ. Schaff, “Ultrafast carrier dynamics in InN epilayers”, Journal of
 Crystal Growth, 269 (2004) 10-14.

 
	
  

 	
  

 
	
 4.5.68

 	
 R. Patterson, M. Kirkengen,
 B. Puthen Veettil, D Konig, M.A. Green, G. Conibeer, Sol. Ener. Mats. And
 Sol. Cells, 94 (2010) 1931-1935.

 
	
  

 	
  

 
	
 4.5.69

 	
 S. Huang, K. Minami, H.
 Sakaue, S. Shingubara, T Takahagi, “Effects of the surface pressure on the
 formation of Langmuir-Blodgett monolayer of nanoparticles”, Langmuir, 20
 (2004), 2274.

 
	
  

 	
  

 
	
 4.5.70

 	
 C. R. Kagan, C. B. Murray,
 M. Nirmal, M. G. Bawendi, Phys. Rev. Lett. “Electronic Energy Transfer in
 CdSe Quantum Dot Solids”, 76 (1996) 1517.

 
	
  

 	
  

 
	
 4.5.71

 	
 D. KÖnig, “Photovoltaic
 Device Physics at the Nanoscale”, Chapter 3 (pp. 73 - 146) in L. Tsakalakos
 (Ed.), “Nanotechnology for Photovoltaics”, Taylor & Francis, April 2010;
 ISBN-13:9781420076745

 
	
  

 	
  

 
	
 4.5.72

 	
 TK. Todorov, K.B. Reuter,
 D.B. Mitzi, Advanced Materials, 22 (21010) 1-4.

 
	
  

 	
  

 
	
 4.5.73

 	
 W.R. L. Lambrecht,
 “Structure and phonons of ZnGeN2”,
 Phys. Rev. B 72 (2005) 155202

 
	
  

 	
  

 
	
 4.5.74

 	
 T.R. Paudel, W.R.L.
 Lambrecht, Phys. Rev. B, 79 (2009) 245205.

 
	
  

 	
  

 
	
 4.5.75

 	
 S.C. Erwin, I. Zutic,
 Nature Materials, 3 (2004) 410-414.

 
	
  

 	
  

 
	
 4.5.76

 	
 Z.T
 Liu, J.Z. Zhu, N.K. Xu, X.L. Zheng, Jap. J. Appl. Phys., 36 (1997) 3625.

 
	
  

 	
  

 
	
 4.5.77

 	
 A. Shalav, B.S. Richards,
 M.A. Green, “Luminescent layers for enhanced silicon solar cell performance:
 Up-conversion”, Sol. Energy Mats. and Solar Cells, 91 (2007) 829-842.

 
	
  

 	
  

 
	
 4.5.78

 	
 C.M. Johnson, PJ. Reece,
 GJ. Conibeer, “Up-conversion luminescence enhancement in erbium-doped porous
 silicon photonic crystals for photovoltaics”, Photonics West Conference, San
 Francisco, Jan 2011.

 
	
  

 	
  

 
	
 4.5.79

 	
 S. Pillai, K. R. Catchpole,
 T Trupke, and M. A. Green, J. Appl. Phys., 101 (2007) 093105.

 
	
  

 	
  

 
	
 4.5.80

 	
 Z.
 Ouyang, S. Pillai, F. Beck, O. Kunz, S. Varlamov, K. R. Catchpole, P. Campbell, and M. A. Green,
 App. Phys. Lett, 96 (2010) 261109.

 
	
  

 	
  

 
	
 4.5.81

 	
 S. H. Lim, W. Mar, P.
 Matheu, D. Derkacs, and E. T. Yu, J. Appl. Phys., 101 (2007) 104309.

 
	
  

 	
  

 
	
 4.5.82

 	
 S.
 Pillai, K. R. Catchpole, T Trupke, G. Zhang, J. Zhao, and M. A. Green, Appl. Phys. Lett. 88 (2006)
 161102.

 
	
  

 	
  

 
	
 4.5.83

 	
 S. Pillai, I. Perez-Wurfl,
 G. J. Conibeer, and M. A. Green, physica status solidi (c) 8 (2011) 181.

 


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