PHYSICAL REVIEW B 97, 035303 (2018)
Optical properties of an ensemble of G-centers in silicon
C. Beaufils,
1
W. Redjem,
1
E. Rousseau,
1
V. Jacques,
1
A. Yu. Kuznetsov,
2
C. Raynaud,
3
C. Voisin,
3
A. Benali,
4
T. Herzig,
5
S. Pezzagna,
5
J. Meijer,
5
M. Abbarchi,
4,*
and G. Cassabois
1,†
1
Laboratoire Charles Coulomb (L2C), Université, Montpellier, CNRS, 34095 Montpellier, France
2
Department of Physics, University of Oslo, NO-0316 Oslo, Norway
3
Laboratoire Pierre Aigrain, Ecole Normale Supérieure, Université Paris Diderot, UPMC, CNRS UMR8551, 24 rue Lhomond,
75005 Paris, France
4
CNRS, Aix-Marseille Université, Centrale Marseille, IM2NP, UMR 7334, Campus de St. Jérôme, 13397 Marseille, France
5
Department of Nuclear Solid State Physics, Felix-Bloch Institute for solid-state physics, Universitat Leipzig,
Linnéstraße 5, 04103 Leipzig, Germany
(Received 5 July 2017; published 9 January 2018)
We addressed the carrier dynamics in so-called G-centers in silicon (consisting of substitutional-interstitial
carbon pairs interacting with interstitial silicons) obtained via ion implantation into a silicon-on-insulator wafer.
We performed detailed photoluminescence experiments as a function of excitation energy, incident power,
irradiation fluence, and temperature in order to study the impact of radiative and nonradiative recombination
channels on the spectrum, yield, and lifetime of G-centers. In the framework of the Huang-Rhys theory with
nonperturbative calculations of the acoustic phonon sidebands, we reach an estimation of 1.6 ±0.1
˚
A for the
spatial extension of the electronic wave function in the G-center. The radiative recombination time measured at
low temperature lies in the 6 ns range. The estimation of both radiative and nonradiative recombination rates as
a function of temperature further demonstrates a constant radiative lifetime.
DOI: 10.1103/PhysRevB.97.035303
I. INTRODUCTION
Semiconductor materials are at the heart of the technology
in our knowledge-based society. The most important one is
silicon, which has become a cornerstone in the electronics and
photovoltaics industries. However, the indirect nature of the
band gap in silicon is a severe drawback for optoelectronics
applications. Inspite of the potentials of silicon-based photonic
devices, the fundamental issue of light emission remains a
challenge. For that reason, a number of solutions have been
explored, e.g., alloying silicon and germanium, doping, and
strain engineering [1–9]. For instance, in silicon-germanium
nanostructures, such as quantum wells, nanocrystals, and
nanowires, the quantum confinement of carriers leads to en-
hanced absorption and spatially direct transitions in the visible
and infrared range [10–16].
An alternative viable strategy towards the integration of
optical and electronic devices on the same silicon-based
platform relies on extrinsic impurities embedded in the host
semiconductor matrix. Relaxing the need of a direct band gap,
the presence of extrinsic centers acting as deep levels allows for
optical emission. A plethora of impurities has been intensively
studied in the last 50 years [17–31]. In this framework, par-
ticular attention has been devoted to isovalent carbon-related
defects, so-called G-centers [22,32–52] (sometimes labeled
as A-centers [51,53]) originally highlighted in carbon-rich Si
samples undergoing high-energy irradiation with electrons,
*
marco.abbarchi@im2np.fr
†
guillaume.cassabois@umontpellier.fr
protons, neutrons, and gamma rays, followed by high tem-
perature annealing. Although the intimate composition of this
light emitter has been questioned for a long time [40,54–
57], it is now commonly accepted that it originates from a
substitutional-interstitial carbon pair (C
S
-C
I
) interacting with
an interstitial silicon (Si
I
)[58–63]. The bistability between
the so-called A- and B-forms of G-centers was studied in
detail by combining different experimental techniques, leading
to the full configurational-coordinate energy surfaces of the
three charge states [56]. Moreover, Song et al. showed that the
metastable A-form converts to the B-one under photoinjection,
and that the luminescence of G-centers comes only from
the neutral B-form [56]. More recently, ab initio calculations
predicted the existence of twoother configurations: the C-form,
lying at lower energy, where the carbon pair occupies a regular
silicon site, with possible spin polarization properties [61],
and the D-form, which is a torsion of the C-one along the
carbon-carbon bond [63].
The relevance of the G-center for optoelectronics has been
highlighted in many works and it relies on some strategic
aspects of its optoelectronicproperties: (i)emission at 969 meV
(∼1280 nm) with a limited broadening of few meV, matching
the important optical telecommunications wavelength O-band
spreading between 1260–1360 nm; (ii) electrical injection of
carriers, allowing for electroluminescent devices [64–67]; (iii)
stimulated emission [51,53]; (iv) high temperature emission
(above liquid nitrogen) and eventually at room temperature
[68]; and (v) ease of fabrication of high densities of G-centers
via implantation of carbon ions, annealing and irradiation
[66,69–71]. It is worth stressing that differently from conven-
tional III-V homoepitaxial substrates, available only in small
2469-9950/2018/97(3)/035303(12) 035303-1 ©2018 American Physical Society
C. BEAUFILS et al. PHYSICAL REVIEW B 97, 035303 (2018)
sizes (a few inches at most), or diamond substrates (a few
millimeters), silicon wafers can be as large as 12 in. and by
far less expensive. Moreover, for silicon-based optical and
electronic devices implementation, 12 in. silicon-on-insulator
substrates are also available in a wide range of specifications
of thickness and doping.
In spite of the relevance of this topic, there are still many
points to be clarified concerning the carrier dynamics in
G-centers. For instance, the basic question of the lifetime
remains unanswered, albeit of crucial importance for the
brightness of single photon sources based on G-centers. For
that purpose, we performed detailed photoluminescence (PL)
experiments as a function of excitation energy, incident power,
irradiation fluence, andtemperature in order to studythe impact
of radiative and nonradiative recombination channels on the
spectrum, yield, and lifetime of the G-center.
The paper is organized as follows: in Sec. II we describe the
sample fabrication (Sec. II A) and the experimental setups used
for optical spectroscopy (Sec. IIB). Section III isdevoted to our
results and their interpretation: we present the characterization
of the G-centers sample (Sec. IIIA), PL measurements as
a function of incident power revealing the saturation of the
G-centers emission (Sec. III B), time-resolved PL experiments
unraveling the 6 ns lifetime at low temperature (Sec. III C),
the analysis of the phonon sideband leading to an estimation
of 1.6 ± 0.1
˚
A for the spatial extension of the electronic wave
function in a G-center (Sec. III D), and finally a temperature-
dependent study for extracting the radiative lifetime as a
function of temperature (Sec. IIIE). Section IV is the general
conclusion.
II. SAMPLE DESCRIPTION AND
EXPERIMENTAL SETUP
A. Sample fabrication
Following a well-established procedure [69], we implanted
a 220-nm-thick silicon-on-insulatorwafer witha fluence of 2 ×
10
14
cm
−2
carbon ions (the beam energy was 36 keV, resulting
in a 100 nm of the projected carbon range). The sample was
annealed in N
2
atmosphere for 20 s at 1000
◦
C for removing
the radiation damage.
Five different areas of 25 × 25 μm
2
size were then
implanted with protons, using fluences of 0.1, 0.3, 1, 3,
and 9 × 10
14
cm
−2
. The implantation energy was set to
2.25 MeV.
B. Optical spectroscopy
In our experimental setup, the sample was held on the cold
finger of a closed-cycle cryostat for temperature-dependent
measurements from 10 K to room temperature. The optical
illumination was provided either by a cw HeNe laser at 632 nm
(1.96 eV), by a cw laser diode at 532 nm (2.33 eV), or by a
pulsed laser diode emitting at 532 nm with a repetition rate of
20 MHz. The excitation laser was focused onto the sample
with a microscope objective (NA = 0.75), after reflection
on a steering mirror for operating our scanning confocal
microscope. The PL response was collected by the same
objective.
For cw detection, the PL signal was dispersed in a f =
300 mm Czerny-Turner monochromator, equipped with a 600
grooves/mm grating blazed at 1600 nm, and recorded with an
InGaAs array, with a quantum efficiency of 80% at 1300 nm,
over integration times of 60 s.
For time-resolved measurements, the PL signal was de-
tected by an InGaAs photodiode with a cut-off detection at
1700 nm, after spectral selection with a long-pass filter at
1250 nm. The additional use of 20-nm-bandpass filters allowed
us to spectrally address different parts of the emission spectrum
of G-centers. The temporal decay was recorded by means of
time-correlated single-photon counting measurements with an
overall temporal resolution of 400 ps.
For photoluminescence excitation (PLE) measurements, we
used a cw-TiSa oscillator and a pseudo-cw source (supercon-
tinuum Fianium SC400-4) filtered by a holographic tunable
bandpass filter (Photon, etc.) with a bandwidth of 2 nm.
The average power density was monitored when tuning the
excitation energy but remained on the order of 4–10 kW cm
−2
all throughout the excitation window. The data are normalized
to a constant power density of 10 kW cm
−2
.
We finally give some general information about the emis-
sion of G-centers in our sample, with respect to the in-
depth characterization presented in Ref. [56]. In our optical
measurements, there was no transientrise of the PLsignal when
illuminating the sample (within the temporal window given by
our detector integration time, down to 100 ms), showing (i)
that the steady state of the neutral B-form was immediately
reached in our case, and (ii) that we were far from the high
n-type doping regime studied by Song et al. [56] where the
transient switch between the two metastable A- and B-forms
was observed on a 1 min scale.
III. RESULTS
In this section we present our results that elucidate some
of the fundamental optoelectronic properties which were not
addressed by means of the experimental facilities available at
early stages of the G-center investigations. We first describe
the characterization of the G-centers sample (Sec. IIIA), then
power-dependent PL measurements showing the saturation of
the G-centers emission (Sec. III B), followed by the first time-
resolved PL measurements unraveling the decay dynamics
on a 6-ns time scale at low temperature (Sec. III C), and
demonstrating in the temporal domain the existence of phonon
sidebands which are discussed in detail in Sec. III D, and
eventually the temperature-dependent experiments (Sec. III E)
focusing on the emission energy, zero-phonon line (ZPL)
width, PL signal intensity, and recombination decay time.
A. Characterization of the G-centers sample
As described in the literature, the best procedure for the
generation of a high density of G-centers in silicon requires
a two-step procedure: (i) introduction of carbon atoms in the
silicon matrix, and (ii) irradiation in order to kick a carbonatom
into an interstitial site, next to a substitutional carbon [69–71].
As a matter of fact, starting from a given carbon concentration
in a silicon sample, one expects the concentration of G-centers
to increase with the irradiation fluence.
035303-2
OPTICAL PROPERTIES OF AN ENSEMBLE OF G- … PHYSICAL REVIEW B 97, 035303 (2018)
FIG. 1. (a) Photoluminescence (PL) raster scan of the pad irradiated with a proton fluence of 9 × 10
14
cm
−2
, for a cw-excitation energy of
2.33 eV, at 10 K. (b) PL signal intensity versus proton fluence. (c) PL signal intensity vs detection energy, on a semi-log scale, for a cw-excitation
energy of 2.33 eV in the center of the pad seen in (a). (d) PL signal intensity (red symbols) vs excitation energy, for a central detection energy
of 969 meV (black dashed arrow on the PL spectrum recalled in solid blue line) in the same ensemble of G-centers in silicon at 10 K, for a
constant incident power of 10 kW cm
−2
.
We first characterized the impact of the proton implantation
by mapping the PL signal intensity in five areas implanted with
different proton fluences. Figure 1(a) displays the PL raster
scan performed on the pad irradiated with a proton fluence of
9 × 10
14
cm
−2
(part of the next pad being observable on the
right side). The strong increase of the PL signal intensity in
the implanted region demonstrates a dramatic influence of the
irradiation.
We further analyzed the PL signal intensity as a function
of the proton fluence. The results are plotted in Fig. 1(b) on
a log-log scale. The increase of the G-centers emission with
the proton fluence appears slightly superlinear, with a power
law of exponent 1.25 ± 0.05. The G-centers concentration
increases indeed with the proton fluence, with a nonlinear
behavior possibly stemming from the complex nature of the
defect involving two carbon atoms, which was also reported in
the literature in the regime of the low implanted densities [69].
Figure 1(c) displays the normalized PL signal intensity as
a function of detection energy, for a cw-excitation energy of
2.33 eV in the center of the pad [Fig. 1(a)]. The sharp and most
intense emission line centered at 969 meV stems from the ZPL
of the G-center, i.e., the direct radiative recombination without
phonon emission. At lower energy, we observe an additional
component related to phonon-assisted recombination, as later
discussed in Secs. III C and IIID.
Although some absorption measurements around the ZPL
energy were reported in the literature [20], there is to the
best of our knowledge no PLE spectroscopy of the G-centers.
PLE provides a combined information on the two processes
of absorption and carrier relaxation, and its knowledge is
important for characterizing the spectral dependence of the
effective pumping efficiency for a given incident power. Under
excitation above the band gap, one expects the PLE spectrum
to largely reflect the silicon absorption.
Red symbols in Fig. 1(d) label the PLE spectrum in an
ensemble of G-centers in silicon at 10 K. It was recorded
by monitoring the emission intensity around the ZPL [black
dashed arrow in Fig. 1(d)], as a functionof the excitation energy
for a constant incident power of 10 kW cm
−2
(i.e., in the linear
regime, as detailed in Sec. IIIB).
In the semi-log plot of the PLE spectrum in Fig. 1(d),we
first observe that the PL signal increases by two orders of
magnitude when tuning the excitation energy from 1.2 to 3
eV. The fundamental band gap of silicon is indirect, and at low
temperature, it lies at an energy of about 1.16 eV. Consequently,
our investigated range corresponds to a nonresonant, above
band gap excitation. In this case, the relaxationof the photogen-
erated carriers first consists of a nonradiative relaxation down
to the extrema of the conduction and valence bands, followed
by the capture in the G-centers. The excitation energy being
always larger than the silicon band gap in Fig. 1(d), the PLE
spectrum essentially reproduces the absorption of silicon thin
films [72].
B. Saturation
In this section we study the existence of saturation
effects in the emission of G-centers. We demonstrate a
035303-3
C. BEAUFILS et al. PHYSICAL REVIEW B 97, 035303 (2018)
FIG. 2. Photoluminescence (PL) signal intensity of an ensemble
of G-centers versus incident power, at 10 K. Experimental data (red
circles) and fit (blue line) according to Eq. (2), modeling the saturation
of identical two-level systems excited by a Gaussian excitation spot,
and assuming a saturation power P
sat
= 35 kW cm
−2
. The green
dashed line shows a linear dependance as a function of incident power.
sublinear increase of the emission as a function of exci-
tation power, and we estimate the saturation power from
the quantitative interpretation of our data in an ensemble of
G-centers.
1. Sublinear power dependence
We measured the dependence of the PL signal intensity
of an ensemble of G-centers, as a function of the incident
power P , at 10 K, for a cw-excitation energy of 1.96 eV.
The experimental data are plotted as red circles in Fig. 2.
At low incident power (P<20 kW cm
−2
), the emission
intensity increases quasilinearly with P . In contrast, for P
20 kW cm
−2
, a sublinearity of the PL signal intensity is clearly
resolved.
We checked that there was no thermal effect biasing our
power-dependent experiments under strong excitation, since a
temperature rise induces a decrease of the PL signal intensity
together with a thermal shift and broadening, as will be dis-
cussed later in Sec. III E. Thermal shift and broadening being
absent in our power-dependent experiments, we conclude that
the sublinearity of the emission intensity in Fig. 2 is the
signature for saturation effects in G-centers that we analyze
quantitatively below.
2. Saturation of an ensemble of two-level systems
In the following we assume that, in our experiments, an
ensemble of G-centers is excited by a laser spot with a Gaussian
profile, that all G-centers are identical, and that their emission
intensity follows a standard saturation curve with a saturation
power density P
sat
. Such a framework only provides a first
approximation for the interpretation of our measurements,
since it does not take into account, for instance, the different
defect orientations in the sample, however it allows us to reach
a first order estimate of P
sat
.
When raising the incident power P , the G-centers at the
spot center are the first to saturate. Nonetheless, the region
comprising saturated G-centers becomes progressively larger
when increasing P . However, at the spot periphery, there
are always nonsaturated G-centers. As a consequence, power-
dependent measurements in an ensemble of G-centers cannot
display the standard saturation curve expected for a single
two-level system.
In order to be more quantitative, we calculated the emis-
sion intensity assuming a two-dimensional distribution of
G-centers, which is a reasonable assumption given the 220 nm
thickness of our silicon-on-insulator sample. The recorded PL
signal intensity thus reads
I
PL
∝
∞
0
2πrdr
P
0
e
−r
2
/w
2
1
1 +
P
0
e
−r
2
/w
2
P
sat
, (1)
where P
0
is the power density at the center of our Gaussian
laser spot of waist w, and the right term of the integrand is the
saturation function of a two-level system. P being the average
incident power over the laser spot area, one finds P = P
0
/ln2.
A straightforward integration results in
I
PL
= I
0
ln
1 +
P
(P
sat
/ln2)
, (2)
with I
0
the emission intensity for an incident power of P
sat
(e −
1)/ln2.
In Fig. 2 a fit according to Eq. (2) provides an excellent
agreement with our experimental data, by taking for our fitting
parameter P
sat
a value of 35 ± 7kWcm
−2
.
The quantitative interpretation of our power-dependent
experiments shows that the saturation of the emission can
be resolved by ensemble measurements in G-centers, thus
leading to an estimation of the saturation power. Such a
strategy is specific to point defects where the assumption of
an identical saturation power P
sat
for all emitters is crucial.
This hypothesis is not met in other nanostructures, such
as epitaxial quantum dots or nanocrystals. In these latter
cases, where inhomogeneous line broadening arising from
size dispersion dominates, the fluctuations of the fundamental
properties (lifetime, dephasing time) are important enough
to prevent the observation of saturation effects by ensemble
measurements.
The 35 ± 7kWcm
−2
value of P
sat
can be used to roughly
estimate the order of magnitude of the carrier capture volume
in G-centers. Assuming a simple Poissonian model for the level
occupation probability [73,74], the average number of excitons
within a G-center is one at saturation. Provided a lifetime
of ∼6 ns as obtained by time-resolved experiments (see the
following section) and an absorption length of ∼5 × 10
−4
cm
for a laser excitation at 1.96 eV, the steady-state carrier density
results in ∼2 × 10
17
cm
−3
. Assuming a spherical geometry of
the extrinsic center, the capture volume is represented by the
inverse of this carrier density, and it leads to a capture radius
of 20 ± 2nm.
This value is quite similar to the one found in extrinsic
centers in III-V alloys [75]. While point defects represent
a modification of the crystal lattice at the atomic scale, the
capture volume is strikingly much wider than the defect
size, approximately two orders of magnitude larger than the
extension of the electronic wave function within the G-center
(see Sec. III D). The capture radius further gives an interesting
estimate of t he effective volume where the captured charge car-
riers may influence the optical response via spectral diffusion
035303-4
OPTICAL PROPERTIES OF AN ENSEMBLE OF G- … PHYSICAL REVIEW B 97, 035303 (2018)
FIG. 3. (a) PL spectrum of G-centers in silicon at 10 K. The blue
and red shaded areas indicate the spectral width of the two bandpass
filters used for spectrally selective time-resolved measurements of the
ZPL and phonon sideband, respectively. (b) Time-resolved PL signal
intensity for the whole spectrum (black line), the ZPL only (blue line),
and the phonon sideband only (red line). The average incident power
is 1 kW cm
−2
. The green line indicates an exponential decay with a
time constant of 5.9 ns.
[74,76], this phenomenon providing an important contribution
to the ZPL broadening, as later discussed in Sec. III E 3.
C. Recombination dynamics
As a marker of the residual carbon concentration in silicon,
G-centers were extensively studied decadesago, in the prospect
of growing bulk silicon crystals as pure as possible [20].
Surprisingly, the prominent question of the lifetime value
remains unanswered, primarily because of the limited temporal
resolution of the earlier experiments, so that only the upper
bound of 4 μs is mentioned in the review of Davies [20]
(Thonke et al. having nevertheless inferred to the upper
bound of 10 ns in Ref. [54]). In the following, we unravel
the recombination dynamics by means of time-resolved PL
measurements with a temporal resolution of 400 ps.
1. Spectrally selective time-resolved PL measurements
The black line in Fig. 3(b) is the time-resolved trace of
the PL s ignal intensity, spectrally integrated over the whole
emission spectrum of G-centers, from 1250 to 1700 nm (see
Sec. II B). On the semi-log scale of Fig. 3(b), we observe that
the decay of the PL signal is purely exponential over the two
measured decades, with a characteristic time constant of 5.9 ns.
This lifetime is slightly longer than the 1.3 ns value in InAs
quantum dots [77,78], but shorter than the 11 ns one in the
prototypical NV center in diamond [79]. The isolation of single
G-centers would thus open the prospect of obtaining bright
single photon emitters in silicon.
An interesting and original insight into the optical response
of G-centers isreached byperforming spectrally selectivetime-
resolved PL experiments. By means of bandpass filters, we
measured the recombination dynamics of the ZPL [blue shaded
area in Fig. 3(a)], and of the low-energy sideband [red shaded
area in Fig. 3(a)]. The corresponding time-resolved traces are
plotted as blue and red lines in Fig. 3(b), respectively. They are
strictly identical with the same time-constant of 5.9 ns found
above. This observation indicates the common nature of these
two recombination channels.
Although the low-energy part of the PL spectrum was early
identified as coming f rom phonon-assisted recombination in
analogy to the general phenomenology in point defects [20],
spectrally selective time-resolved PL measurements provide
here a powerful way for establishing that recombination
processes leading to photons of different energy share the
same microscopic origin. In fact, the recombination dynamics
of an electronic two-level system in a phonon bath occurs
either via direct radiative recombination (corresponding to the
ZPL), or via phonon-assisted recombination (corresponding
to the phonon sidebands). Whatever the number of emitted
or absorbed phonons, all these mechanisms contribute in
parallel to the recombination dynamics of the excited state
of the two-level system. As a matter of fact, the lifetime
depends on the electronic dipole and on the strength of the
electron-phonon interaction. Still, whatever the detuning with
the ZPL, one expects thevery same dynamics when performing
time-resolved PL measurements. In other words, the decay
time of the ZPL and phonon sidebands must be equal. This
general property is surprisingly very poorly documented in the
literature [80,81]. Figure 3 nicely illustrates it in the context of
the optical response of G-centers in silicon.
Before further analyzing the spectrum of the phonon side-
band in G-centers (see Sec. III D), we present below our mea-
surements of the lifetime as a function of the proton fluence.
2. Lifetime versus proton fluence
Although the absolute estimation of the areal density of G-
centers is still currently very difficult, especially in the absence
of single G-centers spectroscopy, we studied the possible
influence of the G-centers concentration on the recombination
lifetime. Our motivation was to examine if the close proximity
of G-centers could induce any nonradiative relaxation channel.
In order to investigate this point, we performed time-
resolved PL experiments on 40–50 different locations for each
of the pads irradiated by a given proton fluence (see Sec. IIA).
Because of the limited incident power of our pulsed laser diode
(average incident power of 1 kW cm
−2
), only the three highest
proton irradiation fluences were accessible. The results are
summarized in Fig. 4, where the inset shows the histogram
of the measured lifetimes for the area implanted with 3 × 10
14
proton cm
−2
. The symbols in Fig. 4 correspond to the mean
value of the recorded statistical distributions, with the error
bars representing the standard deviations. Although the mean
lifetime values decrease from 6.1 to 5.9 ns on raising the proton
dose, the variation is still within the experimental error bar of
±0.2 ns. Consequently, no definite conclusion can be drawn
on a possible influence of the G-centers concentration on their
lifetime, within the 1–9 × 10
14
proton cm
−2
dose range.
D. Phonon-assisted recombination
The spectrally selective time-resolved PL measurements
brought a direct illustration, in the time domain, of the com-
mon microscopic origin of the different recombination paths
highlighted as shaded areas in Fig. 3. Although the low-energy
sideband was interpreted early as arising from phonon-assisted
emission, we revisit below the emission spectrum of G-centers
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