JOURNAL OF APPLIED PHYSICSVOLUME 88, NUMBER 10

15 NOVEMBER 2000

Breakdown of the k-conservation rule in Si1À x Gex alloy nanocrystals:
Resonant photoluminescence study
Minoru Fujiia)
Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University,
Rokkodai, Nada, Kobe 657-8501, Japan

Dmitri Kovalev, Joachim Diener, and Frederick Koch
Technische Universität München, Physik-Department E16, D85747 Garching, Germany

Shinji Takeoka and Shinji Hayashi
Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University,
Rokkodai, Nada, Kobe 657-8501, Japan

共Received 9 March 2000; accepted for publication 30 August 2000兲
Resonant photoluminescence from Si1⫺x Gex alloy nanocrystals as small as 4 nm in diameter
embedded in SiO2 thin film matrices was studied. In pure Si nanocrystals, phonon structures wereclearly observed, indicating that optical transitions are assisted by momentum-conserving phonons.
These structures are quenched by adding a small amount of Ge atoms in Si nanocrystals, i.e., due
to the formation of Si1⫺x Gex alloy. Furthermore, the lifetime of the radiative recombination becamemuch faster in doped nanocrystals. These results suggest that Si1⫺x Gex alloy formation leads to adisorder in the translation invariance of the crystalline lattice, thus resulting in the breakdown of thek-conservation rule. © 2000 American Institute of Physics. 关S0021-8979共00兲04223-7兴

I. INTRODUCTION

similar manner, the increase of the optical transition oscillator strength due to disorder-induced breakdown of thek-conservation rule has been predicted in Ref. 8 for Si1⫺x Gex
alloy nanocrystals (nc-Si1⫺x Gex ). The PL lifetime ofporous-Si1⫺x Gex is reported to be faster than that of porous
Si.9,10 Therefore, Si1⫺x Gex alloy formation is one of thepromising methods for further improvement of the emission
properties of nc-Si.
The PL properties of nc-Si1⫺x Gex are expected to be
dependent on both the size and the Ge concentration. In theprevious studies of porous Si1⫺x Gex , the size of particles
has not been evaluated.9,10 Therefore, the band structure andthe carrier recombination dynamics of nc-Si1⫺x Gex are still
not fully understood. In Refs. 11 and 12, the possibility of
preparing nc-Si1⫺x Gex by a cosputtering method has beenshown. The size of particles has been measured by highresolution transmission electron microscopy. With increasing
Ge concentration a shift of the PL peak energy from thewidened band gap of nc-Si to that of nc-Ge has been observed. This shift is accompanied by shortening of the PL
lifetime. PL spectra under nonresonant excitation are verybroad and featureless. This inhomogeneous broadening of
the PL band is mainly caused by the nanocrystal size andshape variation. In this work, in order to lift the inhomogeneous broadening, PL spectra are measured under resonant
excitation conditions: only the particles having excitationthreshold at the near-infrared laser energy are selectively excited. In pure nc-Si, resonant PL spectroscopy is widely used
to study the nearly homogeneous spectral shape and to determine the ratio of the NP to phonon-assisted transition as afunction of confinement energy.3 In this work the enhancement of the NP optical transition rate due to alloying is discussed. The conclusions are based on the results of resonant

Different systems containing nanometer-size Si crystals(nc-Si兲 have been intensively studied because they are believed to be promising materials for novel optical devices
and offer a good model system to study zero-dimensional
quantum size effects in indirect-gap semiconductors. A continuous shift of the photoluminescence 共PL兲 peak from theband gap of bulk Si to the visible range has been observedwith a decrease of the nc-Si size.1 By applying a variety of
optical methods such as resonant PL,2,3 resonant two-photon
excited PL,4 PL hole burning5 and magneto-optical
spectroscopy,6 the mechanism of the PL and the symmetry ofabsorbing 共emitting兲 states have been studied in detail. Thesestudies strongly suggest that the PL is due to recombinationof excitons confined in zero-dimensional Si quantum dots.
The PL lifetime becomes shorter with an increase of thedetection energy or decrease of the nc-Si size. This is causedby spatial confinement of an electron and a hole in a small
volume. This confinement increases the uncertainty of their
quasimomenta, thus allowing nonphonon 共NP兲 optical transitions. The increase of the NP transition rate relative to thephonon-assisted one results in shortening of the lifetime.
However, at room temperature, even for particles as small asa few nanometers in diameter, the PL lifetime is still in therange of tens of ␮s. This relatively long lifetime is a major
disadvantage for optoelectronic applications of nc-Si. Therefore a new approach to shorten the radiative exciton lifetime
further is highly desired.
Enhancement of the NP transition rate is observed for
Si1⫺x Gex alloy crystals and quantum wells due to perturbations of the crystal periodicity from alloy fluctuations.7 In aa兲Electronic mail: fujii@eedept.kobe-u.ac.jp

0021-8979/2000/88(10)/5772/5/$17.00

5772© 2000 American Institute of Physics

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J. Appl. Phys., Vol. 88, No. 10, 15 November 2000

FIG. 1. Typical TEM image of nc-Si0.73Ge0.27 .

PL studies of pure nc-Si and nc-Si1⫺x Gex combined withthe dependence of the PL lifetime on the Ge concentration.
II. EXPERIMENT

Si1⫺x Gex nanocrystals were prepared by a cosputtering
method. Details of the preparation procedure can be foundelsewhere.11,12 Si, Ge, and SiO2 sputtering targets were simultaneously sputtered in Ar gas at 0.3 Pa using a multitarget sputtering apparatus. After deposition, the films were annealed in N2 gas ambient at 1100 °C to grow nc-Si1⫺x Gex in
SiO2 matrices. To determine the size and the shape of particles, a cross-sectional image of samples was monitoredwith a transmission electron microscope 共TEM兲. The
samples for TEM observations were prepared by a standard
procedure including mechanical and Ar ion thinning techniques. The TEM observations were made using a JEM2010共JEOL兲 electron microscope operated at 200 kV.
Nonresonant PL was excited by the 488 nm line of an Ar
ion laser and detected with a single monochromatorequipped with a Ge pin diode. For resonant PL measurements, a Ti:sapphire laser was used for excitation. The spectral shape of the PL was detected using a monochromator
combined with a Si charge coupled device 共CCD兲 array. To
suppress stray laser light, the asynchronous mechanicalchopping technique was applied.3 The resonant PL measurements were done at 4.2 K. All spectra were corrected to thesensitivity of the detection system. Time resolved PL measurements were performed with a fast 共4 ns rise–fall time兲
photomultiplier and a digital oscilloscope. The samples were
mounted in a cryostat operated in the temperature range from
1.5 to 300 K and the PL was excited by the 488 nm line of an
Ar ion laser.
III. RESULTS

Figure 1 shows a typical cross-sectional transmission
electron micrograph of a particle 共about 3 nm in diameter兲embedded in amorphous SiO2 matrix. The spacing of thelattice fringes is 0.321 nm, which is between those of the
兵111其 planes of Si 共0.314 nm兲 and Ge 共0.327 nm兲 bulk crystals. This is evidence that nc-Si1⫺x Gex is formed.

Fujii et al.

5773

FIG. 2. PL spectra of nc-Si1⫺x Gex at room temperature.

The nonresonant PL spectra of nc-Si1⫺x Gex with various Ge contents are shown in Fig. 2. Pure nc-Si 共3.8 nm indiameter兲 has a PL peak at 1.45 eV. As the Ge content increases, the PL peak shifts to lower energies and reaches
1.24 eV for the sample with x⫽0.27. Although the size ofnc-Si1⫺x Gex slightly increases with the Ge content 共from 3.8
to 4.6 nm兲, the observed shift seems to be governed by
Si1⫺x Gex alloy formation. For pure nc-Si a size variationfrom 3.8 to 4.6 nm results in the shift of the PL peak on theorder of 50 meV.13,14 This value is much smaller than theexperimentally observed one (⬃200 meV兲. The spectral
shape is almost identical for all samples, although the PL
bandwidth increases for those having larger values of x.
Under nonresonant excitation no distinct PL features areobserved and the full width at half maximum 共FWHM兲 ofthe PL bands is about 250 meV 共see Fig. 2兲. The large
FWHM is due to inhomogeneous broadening. The standard
method to lift this broadening is the resonant excitation mentioned before. Figure 3共a兲 shows the normalized resonant PL
spectra of pure nc-Si at different excitation energies. Theenergy positions of the exciting light are shown by arrows.
When the excitation is moved into the nonresonant PL band,
distinct features appear in the spectra. This PL structure becomes more pronounced when the excitation energy is at thelow-energy tail of the nonresonant PL band. For clarity the
first derivative of the spectrum excited at 1.46 eV is shownin Fig. 3共b兲. From the energy separation of these PL features
they can be assigned to optical transitions involving 1TA,
1TO, TO⫹TA and 2TO momentum-conserving phonons inabsorption/emission cycle.
Figure 4 shows the resonant PL spectra ofnc-Si0.89Ge0.11 . As the excitation energy moves into thenonresonant PL band and approaches its maximum an illdefined structure is observed. Even in the first derivative of
the PL spectrum excited at 1.4 eV 关Fig. 4共b兲兴 only one peakis clearly distinguishable. This peak corresponds to the energy of the transverse optical 共TO兲 momentum-conserving
phonon of Si. In pure nc-Si, the phonon structure becomes
more pronounced if the excitation energy is below the maximum of the nonresonant PL. On the contrary, fornc-Si1⫺x Gex , the phonon structure is completely smeared

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5774

J. Appl. Phys., Vol. 88, No. 10, 15 November 2000

FIG. 3. 共a兲 Normalized resonant PL spectra of pure nc-Si. Excitation energies are indicated by arrows. T⫽4.2 K. 共b兲 The first derivative of the spectrum excited at 1.46 eV. Phonon related structures are clearly seen.

out when the excitation energy is at the low-energy tail of thenonresonant PL. Very similar excitation energy dependence
was observed for all samples with different Ge concentrations (0.09⭐x⭐0.27).
Figure 5 shows the PL decay time at various detectionenergies for pure nc-Si and nc-Si1⫺x Gex . In bulk crystals,
the measured PL decay time ( ␶ meas) is defined by the relative
strength of radiative ( ␶ r ) and nonradiative ( ␶ nr ) transitions:⫺1⫺1
␶ meas⫽ ␶ r⫺1 ⫹ ␶ nr
, where both times can be affected by thetemperature. The quantum yield ( ␩ ) is defined as ␩
⫽ ␶ nr /( ␶ r ⫹ ␶ nr ). Under the assumption that the contributionof the nonradiative transition is negligible at low temperatures, the temperature dependences of ␶ r and ␶ nr are extracted from ␶ meas(T) and ␩ (T). 15 From the observed temperature dependences of the PL lifetime and the intensity, it
was found that, at temperatures below 150 K, ␶ meas⬇ ␶ r , andabove 150 K, the contribution of the nonradiative recombination is non-negligible. Therefore only lifetime values measured below 150 K have been taken into account since in thisrange the lifetime can be regarded as a radiative one.
The radiative lifetime becomes shorter as the Ge concentration increases 共Fig. 5兲. As was mentioned before, the sizeof the particles increases slightly as the Ge concentration
increases. This should lead to opposite lifetime behavior.

Fujii et al.

FIG. 4. 共a兲 Normalized resonant PL spectra of nc-Si0.89Ge0.11 . Excitationenergies are indicated by arrows. T⫽4.2 K. 共b兲 The first derivative of thespectrum excited at 1.40 eV.

FIG. 5. Temperature dependence of the PL decay time detected at various
energies for nc-Si, nc-Si0.89Ge0.11 and nc-Si0.73Ge0.27 .

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Fujii et al.

J. Appl. Phys., Vol. 88, No. 10, 15 November 2000

Therefore, the observed shortening of the lifetime is not asize effect but a result of Ge doping. The radiative lifetime ofnc-Si0.73Ge0.27 is about five times shorter than that of purenc-Si. Delerue et al.8 calculated the band gap energy andrecombination rate of a hydrogen-passivated Si0.8Ge0.2 particle. They demonstrated that the radiative efficiency ofnc-Si0.8Ge0.2 increases by a factor of 5 compared to that ofpure nc-Si. This value is in agreement with that observed inthis work.
IV. DISCUSSION

The band gap energy of bulk Si1⫺x Gex alloys changes
from that of Si to Ge depending on x. Si has conduction band
minima in the vicinity of the X points of the Brillouin zone(⌬ minima兲, while Ge has minima at the L points. The dependences of the band gap energy at ⌬ minima and at the L
point on the Ge concentration are quite different. Thus, theband structure strongly depends on the Ge content. The band
structure of Si1⫺x Gex is known to be Si like up to a Ge
concentration of about 85%. The ⌬ minima have the lowest
energy for bulk Si1⫺x Gex with low Ge concentration, and thecrossover between ⌬ and L minima occurs at the aforementioned Ge concentration. In bulk Si1⫺x Gex alloy crystals andquantum wells with small x, PL peaks corresponding to themomentum-conserving TO phonons of Ge–Ge, Si–Ge and
Si–Si vibrations at ⌬ minima were observed.7,16 Similarly,
since the highest Ge concentration in the samples used isabout 0.3, the band structure is expected to be Si like. Thus
phonons corresponding to Ge–Ge, Si–Ge and Si–Si vibrations at ⌬ minima are expected to be involved in the opticaltransitions.
However, as shown in Fig. 4, only an ill-defined structure is present under excitation near to the maximum of thenonresonant PL band. This structure can be assigned to TO
phonons of Si. Furthermore, with a further decrease of theexcitation energy, the structure is smeared out. No phonon
structures corresponding to a Si1⫺x Gex alloy have been observed.
The smearing of the phonon structures which is possibly
due to the breakdown of the k-conservation rule 共caused by
Ge doping兲 is also consistent with shortening of the radiative
lifetime 共Fig. 5兲. In Ref. 3 the ratio of NP to phonon-assistedtransitions for porous-Si and oxidized nc-Si has been estimated. It was found that NP transitions become dominant as
the nc-Si size decreases. Furthermore, for the same confinement energy, NP transitions are about three times stronger in
nc-Si with a SiO2 shell. In the samples studied, Ge doping is
considered to further break the momentum-conservation ruledue to perturbation in the lattice periodicity by Ge atoms.
The enhancement of NP processes leads to smearing of thephonon-related features and shortening of the lifetime. By
applying the method used in Ref. 3, the ratio of the NP tophonon-assisted transitions can be estimated from the resonant PL spectra if the phonon structures are clearly observed.
However, the phonon structure observed for nc-Si1⫺x Gex isill defined, and quantitative discussion of the ratio is notpossible.
Another possible mechanism which can make the observation of the phonon structure difficult is the distribution of5775

the Ge concentration. Besides the size and the shape distribution of nc-Si, particles are expected to have a varying Ge
content as well. Therefore, at a certain excitation energy,
particles with smaller size and higher Ge concentration are
simultaneously excited with those having larger size andlower Ge concentration. Since the relative strength of Ge–
Ge, Si–Ge and Si–Si vibrations as well as the vibration energies depend on the Ge concentration, its distribution resultsin smearing of the phonon structures.
The presence of the Si TO-phonon replicas under excitation at relatively high energy 关1.4 eV, Fig. 4共b兲兴 supports
the existence of a Ge concentration distribution. Particles
with low Ge concentration 共or pure nc-Si兲 are expected tohave, on average, larger band gaps and can be excited resonantly at a certain excitation energy. Since the number ofsuch particles is small, as confirmed by Raman spectroscopy
and electron diffraction studies,12 the PL structure is ill defined.
The Ge concentration distribution also affects the temperature dependence of the PL lifetime 共Fig. 5兲. In purenc-Si, the temperature dependence of the PL lifetime can be
fitted well within the framework of the model proposed by
Calcott et al.2 This model considers the ground exciton stateas the spin singlet and the spin triplet states with the triplet
one being the amount of ⌬ lower in energy.2 At low temperatures, the PL originates from the triplet exciton, while athigh temperatures the PL is dominated by recombination of
the thermally occupied singlet exciton state. From the fitting
procedure, the lifetimes of the triplet ( ␶ T ) and the singlet( ␶ S ) states and ⌬ are estimated to be 4.7 ms, 71 ␮s and 5.8
meV, respectively, at the detection energy of 1.46 eV. The
value of ⌬ obtained is slightly larger than that measured forporous Si at the same detection energy. The difference between these two systems of Si nanoparticles in surface termination may result in a small difference in the value of ⌬. 3
In pure nc-Si, the transition from slow to fast lifetime
takes place at 10–20 K and is abrupt. On the contrary, in
nc-Si1⫺x Gex , the transition starts at lower temperatures andis gradual. In general, this would indicate a smaller value of⌬. However, no combination of all three parameters can reproduce the observed temperature dependence as well as for
nc-Si. The gradual transition thus does not imply a smaller
value of ⌬. To our mind the gradual transition may be explained by a Ge concentration distribution. Due to the distribution, particles with different sizes can contribute to the PL
at the same detection energy. The size distribution is accompanied by the distribution of ⌬, thus making the slow-to-fast
lifetime transition gradual.

V. CONCLUSION

Addition of a small amount of Ge to Si nanocrystals isfound to smear the phonon structures in their resonant PL
spectra. This result and shortening of the radiative lifetime of
the PL suggest that the lattice periodicity of nc-Si is lifteddue to alloying. This results in the breakdown of thek-conservation rule and enhancement of the optical transition
oscillator strength.

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5776

ACKNOWLEDGMENTS

The authors are grateful to Kimiaki Toshikiyo for his
valuable assistance in sample preparation. This work was
supported by a Grant-in-Aid for Scientific Research from the
Ministry of Education, Science, Sports and Culture, Japan,
and a Grant for Research for the Future Program 共Grant Nos.
JSPS-RFTF 96P-00305 and JSPS-RFTF-98P-01203兲 fromthe Japan Society for the Promotion of Science.
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