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APPLIED PHYSICS LETTERS
VOLUME 84, NUMBER 20
17 MAY 2004
Strong quantum-confinement effects in the conduction band
of germanium nanocrystals
C. Bostedta)
Lawrence Livermore National Laboratory, 7000 East Ave, Livermore, California 94550
and Institut für Experimentalphysik, Universität Hamburg, Germany
T. van Buuren, T. M. Willey, N. Franco, and L. J. Terminello
Lawrence Livermore National Laboratory, 7000 East Ave, Livermore, California 94550
C. Heske
Department of Chemistry, University of Nevada, Las Vegas, Nevada 89154
T. Möller
Hamburger Synchrotronstrahlungslabor Hasylab at DESY, Hamburg, Germany
共Received 26 January 2004; accepted 24 March 2004; published online 5 May 2004兲
Quantum-confinement effects in the conduction band of deposited germanium nanocrystals are
measured to be greater than in similar-sized silicon nanocrystals. The germanium particles are
condensed out of the gas phase and their electronic properties are determined with x-ray absorption
spectroscopy. The conduction band edge shifts range from 0.2 eV for 2.7 nm particles up to 1.1 eV
for 1.2 nm particles. © 2004 American Institute of Physics. 关DOI: 10.1063/1.1751616兴
Over the last decade nanometer-sized structures have attracted tremendous interest due to their size-dependent
properties.1 Germanium nanocrystals embedded in SiO2 matrixes have drawn significant attention since their blue luminescence was first reported.2 However, the source of the luminescence is not fully understood and it has been attributed
to surface species3 as well as quantum confinement effects.4
Little is known about the electronic structure of germanium
nanocrystals upon size reduction. Various calculations suggest strong confinement in Ge and thus a critical particle
size, below which the band gap of germanium becomes
larger than that of silicon.5–7 These predictions have been
questioned in recent calculations, which suggest that germanium and silicon nanoparticles should exhibit a similar band
gap due to structural changes in the Ge conduction band.8
To date, no experimental investigations exist which can
unambiguously identify quantum-size effects at the conduction band edge of germanium nanocrystals. Moreover, the
theoretical approaches to this matter are contradictory. The
present experiments focus on probing the size-dependent
electronic structure of germanium nanocrystals with synchrotron radiation based x-ray absorption 共XAS兲. This technique has been previously shown to be very powerful to
study the conduction band of reduced-dimensional structures.9 It allows the independent investigation of the conduction band edges, not possible with optical spectroscopy techniques. Consequently it is possible to unambiguously identify the origin of changes in the electronic structure, and to
answer the questions concerning the extent of quantum confinement in germanium nanocrystals and its comparison to
silicon.
The germanium nanoparticles are condensed out of the
gas-phase and subsequently deposited in situ at the synchrotron facility.10 Their average size can be tuned from 1 to 5
a兲
Electronic mail: [email protected]
nm and they exhibit a narrow size-distribution of 20% full
width at half maximum 共FWHM兲 as determined by atomic
force microscopy.10 As substrates, HF-etch cleaned silicon
wafers are used for the XAS measurements. The produced
films consist of randomly scattered, individual, and nontouching particles. Structural analysis of nanoparticles reveals the bulk-like cubic 共diamond兲 crystal structure.10
The electronic structure of the deposited nanocrystals is
probed with XAS at the high resolution and high flux undulator beamline 8.0 of the Advanced Light Source at the
Lawrence Berkeley National Laboratory.11 In XAS a Ge 2p
core electron is excited into the empty states of the conduction band. The conduction band minimum has both, s- and
p-like contributions12 and hence the excitation of a p electron into the bottom of the conduction band 共CB兲 is dipole
allowed. If the conduction band minimum of the clusters
shifts to higher energies by ⌬E CB due to confinement effects
in the nanoclusters, the absorption threshold will also shift
by ⌬E CB to higher energies. The experimental resolution of
the absorption measurements at the Ge L edge 共around 1219
eV兲 is approximately 0.3 eV,11 small enough to permit observation of small CB shifts in our clusters. It should be noted
that this resolution describes the experimental, i.e., gaussian
broadening of the spectra. Peak positions can be fit and compared with higher accuracy. In Fig. 1 the XAS data of a Ge
bulk crystal reference and three nanocrystal samples with
decreasing average sizes are shown. The absorption edge is
blueshifted with decreasing particle size, consistent with the
predictions of the quantum-confinement model. The nanocrystal edges are slightly broadened with respect to the bulk
and their density-of-states features are washed out. This effect was observed in earlier experiments on Si nanocrystals,
where it had been attributed to the particle size distribution.9
Each individual cluster size contributes with its distinct
quantum shift to the overall absorption edge, resulting in an
edge broadening. None of the reported fingerprints for oxide
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© 2004 American Institute of Physics
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Appl. Phys. Lett., Vol. 84, No. 20, 17 May 2004
Bostedt et al.
4057
ment effects in Ge are increasingly stronger than in Si. The
difference between the Ge and Si conduction band edge
shifts grows from 0.1 eV for 2.7 nm particles up to 0.7 eV
for 1.2 nm particles.
In a previous optical study on chemically prepared germanium and silicon nanocrystals, stronger quantum confinement for specific optical transitions from the upper split-off
conduction band to the valence band at ⌫ in germanium with
respect to silicon nanocrystals were observed.4 However, no
conclusions could be drawn about the extent of quantum
confinement at the band edges. In other studies about the
optical properties of germanium nanocrystals embedded in a
SiO2 matrix ambiguous results were obtained.3,14 It was later
concluded that the optical properties of these systems were
dominated by interface and defect states.7 In the present
FIG. 1. X-ray absorption spectra of a Ge bulk crystal and three nanocrystal
samples. The XAS edges of the nanoparticles are blueshifted with respect to
study, relying on synchrotron radiation based spectroscopy
the bulk edge. The arrows indicate the inflection point of each absorption
techniques, the conduction band edges are investigated indeedge.
pendently and the whole particle electronic structure is
probed. Thus, we were able to conclusively show that gercontamination or Ge–Si alloying, appearing as distinct feamanium exhibits stronger quantum confinement at the contures between 3 and 6 eV above the absorption threshold,13
duction band edge than silicon.
are evident in the data. Therefore, it can be concluded that
From a theoretical point of view there is an ongoing and
the nanocrystals neither exhibit significant particle—
vibrant discussion about quantum confinement in germanium
substrate interactions nor do they display oxide contaminananocrystals.5– 8 Two independent empirical tight binding
tions.
calculations,6,7 which have been able to describe silicon sysIn Fig. 2 the data points from the XAS experiments for
tems well, are in good agreement with the obtained experithe Ge conduction band shifts are summarized. For comparimental results on germanium. They both predict stronger
son previously published silicon data points9 are added to the
quantum confinement effects in Ge compared to Si. Howgraph. In case of Ge the conduction band shifts range from
ever, these calculations are tailored to describe the optical
0.2⫾0.1 eV for 2.7⫾0.3 nm particles up to 1.1⫾0.2 eV for
properties of nanocrystals involving valence excitons. There1.2⫾0.4 nm particles. The error bars in x indicate the
fore, they are not able to predict the behavior of the conducFWHM of the particle size distributions. The larger error
tion band edge for decreasing particle sizes. In contrast to
bars for the 1.2, 1.6, and 1.8 nm XAS data are due to a wider
these tight binding calculations, another theoretical approach
FWHM of the size distribution for these samples which were
utilizing the empirical pseudopotential method predicts that
condensed in an Ar buffer.10 The error bars in y indicate the
the band gap of germanium and silicon should be similar
uncertainty in determining the edge shift. The Si conduction
upon size reduction.8 The predicted similarities in the elecband shifts range from 0.1⫾0.1 eV for 2.8⫾0.3 nm particles
tronic structure of Si and Ge are explained with sizeup to 0.4⫾0.1 eV for 1.1⫾0.2 nm particles. The observed
dependent structural changes in the conduction band of gershift of the Ge conduction band edge is larger than the shift
manium: the conduction band minimum is found to move
of the Si conduction band edge over the complete range of
from the L point to the X point for reduced particle sizes and
investigated particle sizes. Additionally the quantum confinethus the germanium conduction band minimum becomes
silicon-like for small sizes.8 In our experiments we always
find stronger quantum confinement effects for germanium
compared to silicon upon size reduction 共Fig. 2兲 what is in
contrast to these EPM calculations. The conduction band
minimum of germanium shifts from 0.2 eV for 2.7 nm particles up to 1.1 eV for 1.2 nm particles 共Fig. 2兲, compared to
0.1 up to 0.4 eV for similar particle sizes in the case of
silicon.9 However, the experimental data allows only statements about the absolute conduction band shift and none
about the possible existence of the L-to-X crossover in Ge.
In this context it should also be mentioned that both the
cubic and tetragonal phase have been suggested for Ge
nanoparticles.15 The creation of either phase has been explained with the employed synthesis routes.10 The presently
investigated samples have been shown with electron diffraction to be in the cubic phase for particles above 3 nm and for
smaller sizes no indications for phase transitions, monitored
FIG. 2. Measured conduction band edge shifts for Ge nanocrystals 共solid
by Ge 3d core level photoemission, have been found.
squares兲 and its comparison to similarly sized Si particles 共see Ref. 9兲 共open
circles兲. The data show much stronger quantum effects in Ge compared
On a final note an estimate for the overall band gap
to Si.
behavior
shall be done. It has been reported experimentally9
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4058
Bostedt et al.
Appl. Phys. Lett., Vol. 84, No. 20, 17 May 2004
and theoretically16 that the band gap in semiconductor
nanocrystals opens with a fixed ratio of the valence to the
conduction band edge shift ⌬E VBM :⌬E CBM . This ratio was
determined experimentally for Si nanocrystals to
Si
Si
:⌬E CBM
⬇2 and for Ge theoretically to be
⌬E VBM
Ge
Ge
⬇1. The overall nanocrystal band gap can be
⌬E VBM :⌬E CBM
extrapolated from this ratio and the well-known bulk band
NC
bulk
gap according to E gap
⫽E gap
⫹⌬E CBM⫹R * ⌬E CBM9 with
R⫽2 for Si and R⫽1 for Ge. Using the quantum shift data
from Fig. 2 for 1.2 nm particles a nanoparticle gap of 2.4 eV
results for Si and a gap of 3.0 eV results for Ge. This estimate shows that the band gap of Ge may become larger than
that of Si upon size reduction what is expected to have a
significant impact on the importance of Ge as a material for
reduced-dimensional structures.
In conclusion strong quantum confinement effects in the
conduction band of deposited germanium nanocrystals have
been observed. With respect to the bulk value the conduction
band edge of germanium has been determined to shift from
0.2 eV for 2.7 nm particles up to 1.1 eV for 1.2 nm particles.
In the range of investigated particle sizes the quantum size
effects of Ge nanocrystals are always stronger compared to
Si particles of similar size. These results reveal that germanium nanocrystals exhibit a high tunability of their electronic
properties making them a promising material for potential
optoelectronic applications.
This work was performed under the auspices of the U.S.
Department of Energy by the University of California,
Lawrence Livermore National Laboratory under Contract
No. W-7405-Eng-48. The Advanced Light Source is supported by the U.S. DOE under Contract No. DE-AC0376SF00098, LBNL. C.B. acknowledges partial financial support from the Deutscher Akademischer Austauschdienst
DAAD in the HSP-III program under Contract No. D/97/
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