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IMPACT OF INTERFACE ON EFFECTIVE BAND GAP OF Si QUANTUM DOTS

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Abstract

We investigated the ground state of approximants consisting of 165 Si atoms (d QD 18.5 Å) with full termination of the Si interface with F-, OH-, NH 2-, CH 3-and H-groups simulating Si QDs embedded in a Fluoride, SiO 2 , Si 3 N 4 , SiC matrix and vacuum, respectively, with ab-initio methods. As the polarity of the Si/matrix interface increases the optical bandgap becomes increasingly dominated by charge transfer at the interface rather than by quantum confinement. For Si QDs with d QD = 7.3 to 37 Å, the interface determines the electronic structure in competition with quantum confinement for strong polar interfaces (NH 2 , OH) and for Hand CH 3-terminations as a secondary effect. We present an estimate of band gaps of different QD materials with the same interface and interprete the ab-initio results in conventional quantum mechanics.
IMPACT OF INTERFACE ON EFFECTIVE BAND GAP OF Si QUANTUM DOTS
Dirk König, James Rudd, Martin A. Green, Gavin Conibeer,
ARC Photovoltaics Centre of Excellence, The University of New South Wales,
Sydney, NSW 2052, Australia
ABSTRACT
We investigated the ground state of approximants
consisting of d 165 Si atoms (dQD d 18.5 Å) with full
termination of the Si interface with F-, OH-, NH2-, CH3-
and H-groups simulating Si QDs embedded in a
Fluoride, SiO2, Si3N4, SiC matrix and vacuum,
respectively, with ab-initio methods. As the polarity of
the Si/matrix interface increases the optical bandgap
becomes increasingly dominated by charge transfer at
the interface rather than by quantum confinement. For
Si QDs with dQD = 7.3 to 37 Å, the interface determines
the electronic structure in competition with quantum
confinement for strong polar interfaces (NH2, OH) and
for H- and CH3-terminations as a secondary effect. We
present an estimate of band gaps of different QD
materials with the same interface and interprete the ab-
initio results in conventional quantum mechanics.
1. COMPUTATIONAL DETAILS, STRUCTURE
OF APPROXIMANTS
We describe the ground state (GS) electronic struc-
ture of Si QDs surrounded by a dielectric as in an
annealed Si rich SiO2 (SRO) layer [1]. We perform a
systematic analysis of Si core approximants by non-
periodic spatial space Density-Functional -- Hartree-
Fock (DF-HF) computations of Si approximants
comprising 1 to 165 Si atoms corresponding to a
spherical QD diameter of dQD = 3.4 to 18.5 Å. All
surface bonds of these Si cores were terminated by the
anions of the dielectric which were saturated with H as
required, resulting in approximants of the type SixXy, X
= F, OH, NH2, CH3 and H. After structural optimization
with a HF/3-21G* functional/MO basis set the
electronic structure was computed by the Becke Lee-
Young-Parr functional B3LYP/6-31G(d) [2] using the
Gaussian03 software package [3].
Parameters of the five largest approximants are
listed in Tab. 1. Fig. 1 shows some approximants of Tab.
1 after optimization with one type of interface bond
termination per Si core pecimen. The highest occupied
molecular orbital (HOMO) lowest unoccupied
molecular orbital (LUMO) gap (Egap) of H-terminated Si
approximants were found to be in very good agreement
with literature data (not shown here).
Fig. 1 The five largest approximants of this work after
structural optimization. Each Si core has a different surface
termination. Top: Si26H32, Si35(NH2)36, Si53(OH)48. Bottom:
Si83(CH3)64, Si165F100. Further data listed in Tab. I.
Table I. Sum formulae, diameter of Si cores (QDs) and
realized surface terminations of approximants. Highly
symmetric approximants are printed in bold, cf. Fig. 1.
Approximant dQD [Å] (Si core) Surface termination
SiX4 3.4 F, OH, NH2, CH3, H
Si5X12 5.8 F, OH, NH2, CH3, H
Si10X16 7.3 F, OH, NH2, CH3, H
Si14X20 8.1 F, OH, NH2, CH3, H
Si18X24 8.8 F, OH, NH2, CH3, H
Si26X32 10.0 F, OH, NH2, CH3, H
Si35X36 11.0 F, OH, NH2, CH3, H
Si53X48 12.7 F, OH, NH2, CH3, H
Si84X64 14.8 F, OH, NH2, CH3, H
Si165X100 18.5 F, H
2. RESULTS
Computed values of Egap are shown in Fig. 2. With
increasing ionicity bond (IOB) interface anions and
adjacent Si atoms, Quantum confinement (QC) becomes
300
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less significant, while the bonds to the interface anions
increasingly determine Egap.
Fig. 2 Egap as function of dQD for Si QDs with different
interface terminations. The graph is split into two sub-graphs
with different energy scale (atomic limit [left], beyond [right]).
Points of Si10X16 approximants (dQD = 7.3 Å) shown in both
graphs. Arrows indicate high symmetry approximants.
The charge transfer to the QD interface is a function
of IOB and of the ratio of interface anions to Si core
atoms Nx/NSi, cf. Fig. 3 and Eq. (1). In the atomic limit
occuring for Si cores of less than 10 atoms (dQD < 7 Å),
Egap is controlled by the interface anions.
Fig. 3 QSi as function of dQD for Si QDs with different
interface terminations. A hyperbolic dependence can be seen.
For Nx/NSi, an empirical fit was found to be
[Nx/NSi]fit = 1.866 u (6/dSi [Å]) (1)
[Nx/NSi]fit decreases slowly with increasing Si core
size. We assume that for [Nx/NSi]fit t 0.3, or dQD d 37 Å,
the interface termination has a major influence on the
electronic structure of Si cores for strong polar bonds (X
= F, OH, NH2). For weak polar and covalent interface
bonds (CH3, H) QC governs the electronic structure.
From quantum chemical parameters we derive an
estimate (electron transfer parameter: ETP) for Egap
depending on the interface termination:
ETP(Si,X) = IOB(Si–X) u [Eion(Si) + X(Anion)] (2)
X is electron affinity, Eion is ionization energy; for
results, cf. Fig. 4.
Fig. 4 Egap of SixXy approximants arranged after
increasing ionicity (right to left) of the functional group,
compared to the electron transfer parameter ETP. Atomic limit
approximants deviate from the ETP.
The ETP can be used to estimate Egap for Ge and
cubic Sn QDs with the same interface terminations
(dielectric matrix), requiring only the computation of
one approximant per QD size for energetic calibration.
Fig. 5 shows the interpretation of the DF-HF results
in conventional quantum mechanics. With dQD
decreasing, the volume of the interface region Vif
surpasses the QD volume VQD and can decrease the
impact of QC depending on interface energetics.
Fig. 5 Spatial interface impact on the Si QD as a function
of QD size. QDs shown in black have a size of dQD = 30, 12
and 6 Å (right to left). Interface transition region shown in
bright orange (grey) is kept at constant thickness of dif = 3 Å.
With dif = 3 Å, VQD and Vif are equal for dQD = 23.1 Å.
In conclusion, QC competes increasingly with the
nature of the QD interface if the interface bonds are
more polar what can be seen in absolute values of Egap
and ist dependence on dQD. As a result, the absorption
gap of Si (Ge, Sn) QDs is rather constant over a small
range of dQD and also has a much lower limit as
predicted by tight-binding or effective mass
approximation algorithms.
REFERENCES
[1] M. Zacharias, J. Heitmann, R. Scholz, U. Kahler,
M. Schmidt, J. Bläsing, Appl. Phys. Lett. 80, 661
(2002)
[2] D. Becke, Phys. Rev. A 38, 3098 (1988); C. Lee,
W. Yang, R.G. Parr, Phys. Rev. B 37, 785 (1988)
[3] http://www.gaussian.com/citation_g03.htm
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Int'l PVSEC-17
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Chapter
Introduction: Reasons for Application to Solar CellsProperties of Si Nanocrystals Relevant to Solar CellsThe “All-Si” Tandem Cell: Si Nanostructure Tandem CellsIntermediate Level Cells: Intermediate Band and Impurity Photovoltaic cellMultiple Carrier Excitation Using Si QDsHot Carrier CellsConclusions References
  • M Zacharias
  • J Heitmann
  • R Scholz
  • U Kahler
  • M Schmidt
  • J Bläsing
M. Zacharias, J. Heitmann, R. Scholz, U. Kahler, M. Schmidt, J. Bläsing, Appl. Phys. Lett. 80, 661 (2002)
  • D Becke
D. Becke, Phys. Rev. A 38, 3098 (1988);
  • C Lee
  • W Yang
  • R G Parr
C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37, 785 (1988)