Nonlinear optical properties of
Phosphorous-doped Si nanocrystals
embedded in phosphosilicate glass thinfilms
Kenji Imakita, Masahiko Ito, Minoru Fujii, and Shinji Hayashi
Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe
University, Rokkodai, Nada, Kobe 657-8501, Japanfujii@eedept.kobe-u.ac.jp

Abstract: Nonlinear optical properties of phosphorus (P) -doped silicon(Si) nanocrystals are studied by z-scan technique in femtosecond regime ataround 1.6 eV. The nonlinear refractive index (n2 ) and nonlinear absorption
coefficient (β ) of Si-ncs are significantly enhanced by P-doping. The
enhancement of n2 is accompanied by the increase of the linear absorption in the same energy region, suggesting that impurity-related energy
states are responsible for the enhancement of the nonlinear optical response.
© 2009 Optical Society of America
OCIS codes: (190.4720) Optical nonlinearities of condensed matter; (190.0190) Nonlinear
opticsReferences and links
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1.

Introduction

Silicon nanocrystal (Si-nc) is a topic of great interests in the field of optelectronics becauseof its high quantum efficiency of photoluminescence (PL) and relatively large nonlinear optical responses[1, 2, 3, 4, 5, 6]. The large nonlinear optical response has been reported invarious forms of Si-ncs such as porous Si prepared by electrochemical etching[7, 8], Si-ncs#108533 - $15.00 USD(C) 2009 OSA

Received 9 Mar 2009; revised 10 Apr 2009; accepted 13 Apr 2009; published 20 Apr 200927 April 2009 / Vol. 17, No. 9 / OPTICS EXPRESS 7369

doped SiOx Ny deposited by plasma enhanced chemical vapor deposition (PECVD)[10, 9],Si-ncs doped SiO2 prepared by cosputtering[11], laser ablated Si-ncs deposited on quartz
substrate[12, 13], and so on. In these literatures, dependence of the nonlinear optical responseon the size and volume fraction of Si-ncs has been studied in detail. Although the origin of thelarge nonlinear optical response is still not fully clarified, the quantum confinement effects areoften believed to be responsible[9, 11].
It has been demonstrated experimentally[15, 16, 17, 18, 19] and theoretically [20, 21, 22]that the electronic band structure, and the resultant optical and electrical transport properties of
Si-ncs are significantly modified by impurity doping. Experimentally, PL properties of Si-ncs
were found to be very sensitive to the impurity doping[15, 16, 17]. The doping of either nor p-type impurities results in strong quenching of the PL, due to efficient Auger process between photo-excited electron-hole pairs and impurity-supplied carriers[17]. The quenching canbe suppressed by doping n- and p-type impurities simultaneously because of the compensationof carriers within Si-ncs. The PL of the codoped and compensated Si-ncs appears at very low
energy; the PL peak reaches 0.9 eV in heavily-doped an compensated Si-ncs [15, 16]. Theseobserved phenomena are successfully reproduced, at least qualitatively, by first principles calculations [20, 23].
In this paper, we study the effect of impurity doping on the nonlinear optical properties of
Si-ncs by using the samples of phosphorus(P)-doped Si-ncs embedded in phosphosilicate glass(PSG) thin films. We show that P-doping further enhances the large nonlinear optical responsesof Si-ncs and is thus an effective way to control the nonlinear optical properties of Si-ncs.
2.

Experimental procedure

P-doped Si-ncs embedded in PSG thin films were prepared by a cosputtering method. Si, SiO2
and PSG were simultaneously sputter-deposited in Ar gas on a quartz substrate. Then the deposited films were annealed in a N2 gas (99.999 % ) atmosphere for 30 min at 1150 ◦ C to grownanocrystals in the films. The size of Si-ncs was estimated by cross-sectional transmission electron microscopy (TEM) observations[24]. The average diameter (D) was about 4.0 nm, and thestandard deviation was about 1.0 nm. The concentration of excess Si (CexSi ) and P2 O5 (CP ) wereobtained by electron probe micro analysis (EPMA). CexSi was about 6.7 vol% and P2 O5 waschanged from 0 to 1.2 mol% . The linear refractive indices were estimated from the volume
ratio of Si and SiO2 with the application of the Bruggeman effective medium theory [25] andwas about 1.54 at 800 nm.
The thickness of the samples was estimated by physical-contact-type surface roughness
measurement and was about 12μ m. The evidence that P atoms are doped in substitutional sitesof Si-ncs and are electrically active was shown in our previous work by infrared absorption andelectron spin resonance (ESR) spectroscopy [19]. The nucleation of phosphorous particles canbe ruled out because they are thermodynamically unstable in SiO2 matrix.
PL spectra were measured by using a single grating monochromator and an InGaAs nearInfrared diode array. The spectral response of the detection system was calibrated with the aidof a reference spectrum of a standard tungsten lamp. For the measurement of the nonlinear optical properties, a z-scan method was used. Details of the z-scan method is found elsewhere[14].
Briefly, in the z-scan method, the tight focusing gaussian beam is vertically irradiated onto asample and the sample is moved along the direction of the beam propagation (z axis). The transmitted light intensity is recorded as a function of the distance from the focal point (z). When allof the transmitted light is detected (open aperture), the transmittance (Top (z)) is determined by
the nonlinear absorption coefficient (β ), and its dependence on z is
Top (z) = 1 +#108533 - $15.00 USD(C) 2009 OSA

β I0 L,
1 + (z/z0 )2(1)

Received 9 Mar 2009; revised 10 Apr 2009; accepted 13 Apr 2009; published 20 Apr 200927 April 2009 / Vol. 17, No. 9 / OPTICS EXPRESS 7370

where I0 , L, and z0 are the peak intensity of the beam, sample thickness and the diffraction
length of the beam, respectively. Note that Top doesn’t depend on the nonlinear refractive index(n2 ) but only on β , thus open aperture measurement provides the information on β .
When a small aperture is placed in front of the detector to cut peripheral regions of thetransmitted light (closed aperture), the transmittance (Tcl ) depends both on n2 and β . The
information on n2 is extracted by the division of Tcl by Top ,Tcl /Top (z) = 1 +4Δφ,((z/z0 )2 + 9)((z/z0 )2 + 1)

(2)

where Δφ is the nonlinear phase change. n2 is obtained from Δφ as,n2 =λ α Δφ,2π I0 (1 − e−α L )(3)where α and λ are the linear absorption coefficient and the wavelength of the beam, respectively.
For the gaussian beam, we used the mode-locked Ti:shaphire femtosecond laser with thepulse width of 70 fsec and the repetition frequency of 82 MHz. The photon energy was changed
from 1.48 to 1.65 eV. The incident beam was focused on a sample by a lens with the focus lengthof 100 mm. The beam waist and diffraction length determined by a knife edge method were18 μ m and 1.1 mm, respectively. The peak intensity of the beam was typically 10 GW/cm2 .
No notable change of nonlinear optical properties was observed in the intensity range of 0.5-20
GW/cm2 , suggesting that thermal effect was negligible in this measurement condition[10, 9].
The validity of the obtained data was checked by measuring a fused quartz plate as a reference.
3.

Results and discussion

Figure 1 summarizes the PL and absorption properties of P-doped Si-ncs. Details of these properties are found in the literatures[17, 19]. In Figure 1(a), the absorption spectra of P-doped(CP =0.8mol% ) and pure Si-ncs are shown. In pure Si-ncs, absorption due to the valenceto-conduction-band transition starts at around 1.5 eV. In P-doped Si-ncs, in addition to theinterband transition, intra-valence-band transitions appear below 1.3 eV. The observation of
the intraband transitions evidences the doping of electrically active shallow impurities in Sincs[17, 19]. In Fig. 1(a), we also notice that interband transition of P-doped Si-ncs near theband edge is larger than that of pure Si-ncs. This absorption enhancement is very similar tothat observed in P-doped bulk Si[29, 30], and is probably due to the impurity-related states predicted by some theoretical calculations[31]; P-doping causes the formation of the energy state
just below the conduction band of Si-ncs, and enhances the absorption near the band edge. It
should be noted here that each Si-nc should have discrete impurity-related states, because thenumber of impurity atoms in Si-ncs is very small and hence the formation of an impurity bandis not expected. Apparently, this seems to contradict with the observed very broad enhancement
near the band edge. The broadness can be attributed to the inhomogeneities of the number- andposition-distributions of P atoms within a Si-nc and the size- and shape-distributions of Sincs. It should be stressed here that the size of pure and P-doped Si-ncs is similar and thus thedifference of the spectral shape cannot be attributed to the size difference.
The inset of Fig. 1(a) shows the PL spectra of pure and P-doped Si-ncs. Both samples exhibita broad PL band at around 1.3 eV. The PL is assigned to the recombination of electron-hole pairs
within Si-ncs. This is evidenced by the temperature and the photon-energy dependence of the
PL-lifetime[2], and also by the resonantly excited PL spectra[27]. In Figure 1(b), PL intensity
at 1.3 eV and absorbance at 0.5 eV are plotted as a function of CP . In the lower CP region#108533 - $15.00 USD(C) 2009 OSA

Received 9 Mar 2009; revised 10 Apr 2009; accepted 13 Apr 2009; published 20 Apr 200927 April 2009 / Vol. 17, No. 9 / OPTICS EXPRESS 7371

) 1 (a)
m
μ
21
(/
ec
na 0.1
br
os
bA
0.01

y16
it
pure
P-doped
s12
n
Si-nc
Si-nc
e 8
t
n
I 4
x10
L
P0
1.0 1.2 1.4 1.6 1.8
Photon Energy (eV)P dopedpure Si-nc

Si-nc

0.5

1.0

1.5

2.0

2.5

Photon Energy (eV)

)
s
it
n
u
.
b
r
a
(
y
t
i
s
n
e
t
n
I
L
P

20 (b)
A
0.2 bsor15ba
at 0.5 eV
at 1.3 eVn10
0.1 ce
/1
5
2μ
m
0
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2
P2O5 concentration (mol%)Fig. 1. (a)Absorption spectra of pure and P-doped Si-ncs (CP =0.8mol% ). The inset shows
the PL spectra of the same samples. (b)P2 O5 concentration (CP ) dependence of PL intensity
at 1.3 eV (Left axis) and absorbance at 0.5 eV (Right axis).

(below 0.4mol% ), no notable infrared absorption is observed, and PL intensity increases withincreasing CP . Carriers are thus not supplied within Si-ncs. The increase of the PL intensity
in the CP region is, as discussed in reference[28], considered to be due to the termination of
dangling bond defects at the surface of Si-ncs by electrons supplied by doping. In the higher
CP region (above 0.6mol% ), the infrared absorption increases and PL intensity decreases withincreasing CP . The PL quenching is accompanied by the shortening of the PL lifetime, and isconsidered to be nonradiative Auger recombination of photo-excited electron-hole pairs with
the interaction with supplied carriers. It should be noted here that re-absorption by nearby
clusters cannot explain the strong quenching because the samples are almost transparent in theenergy range (optical transmittance > 80% ).
Figure 2 shows the results of z-scan measurements for (a) a closed aperture (Tcl ), (b) an open
aperture (Top ), and (c) the ratio (Tcl /Top ). Open squares and solid curves represent experimental
data and fitted results, respectively. In Figs. 2(b) and 2(c), Eqs. (1) and (2), respectively, are used
for the fittings. The solid curve in Fig. 2(a) is generated by using the parameters obtained by
the fittings of Figs. 2(b) and 2(c). The agreement between the experimental data and the fitted
curves is very good and the diffraction length estimated from the fitting coincides well with thatmeasured by a knife edge method. In Fig. 2(c), all the z-scan spectra show valley to peak traces.
This indicates that the sign of n2 is positive for all the samples. We can see that the magnitudeof the transmittance change depends on CP . It increases with increasing CP , suggesting that n2
increases with increasing CP .
Figure 3 shows the results of the analysis of the z-scan spectra. For the pure Si-ncs sample,
i.e. CP =0, the n2 and β are ∼ 1.7 × 10−13 cm2 /W and ∼ 1.0 cm/GW respectively. The observed
n2 is three orders of magnitudes larger than that of SiO2 , and one order of magnitude than thatof bulk-Si.

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Received 9 Mar 2009; revised 10 Apr 2009; accepted 13 Apr 2009; published 20 Apr 200927 April 2009 / Vol. 17, No. 9 / OPTICS EXPRESS 7372

1.2(a) Closed
1.1
CP (mol%)0
LC 1.0
T
0.9
0.8
1.2
0.8
1.05 (b) Open C (mol%)
P
0
1.00
P
0.8
O0.95
T
1.2
0.90
1.2 (c) Ratio
CP (mol%)
P 1.1
O
0
T
/
LC 1.0
T
0.8
0.9
1.2
at 1.54 eV
0.8
-4
0
4
Z (mm)
Fig. 2. z-scan measurements for (a) a closed aperture (Tcl ), (b) an open aperture (Top ) and(c) the ratio of the two results (Tcl /Top ). The squares are experimental results and the solid
curves are results of fittings. P2 O5 concentration (CP ) is changed from 0 to 1.2mol% .

2

3
1
-

8
7
)6
W
/5
m
c4
01 3
(
n2
1
0
2

0.0 0.2 0.4 0.6 0.8 1.0 1.2
P2O5 concentration (mol%)

11
10
9
8 β
7 (cm
6 /
5 G
W
4 )
3
2
1
0

Fig. 3. P2 O5 concentration dependence of n2 (left axis) and β (right axis).

#108533 - $15.00 USD(C) 2009 OSA

Received 9 Mar 2009; revised 10 Apr 2009; accepted 13 Apr 2009; published 20 Apr 200927 April 2009 / Vol. 17, No. 9 / OPTICS EXPRESS 7373

2

3
-1

22
20
18
16
)
W
/ 14
m
c 12
01 10
( 8
n
6
4
2
0
2

ec CP(mol%)na0.1 1.2
br
0.8
os
bA
0 - 0.6
0.0
1.5 1.6 1.7
Photon Energy (eV)CP(mol%)1.2
0.8
0 - 0.6
1.50
1.55
1.60
Photon Energy (eV)Fig. 4. n2 spectra of samples with different P2 O5 concentration (CP ). The inset shows theabsorption spectra of the same samples.

Two different models have been proposed as the origin of the large n2 . The first one is a quantum confinement effect. This model has been proved by size-dependent n2 enhancement[9]. The
other one is that the surface state of Si-ncs is responsible for the large n2 . Klimov et al studied
the transient absorption spectra of Si-ncs prepared by ion-implantation, and found a Si/SiO2
interface state at around 1.6 eV, in addition to the size-dependent quantized states[32]. Vijayalakshumi et al showed that the surface state was responsible for the n2 enhancement at around
1.6 eV in these samples[33, 34]. At present, no definite conclusion is obtained on the origin of
the large n2 and further intensive research is required to clarify the origin. However, since theinvestigation of pure Si-ncs is out of the scope of this work, we are going to focus on the effectof P-doping.
By P doping, n2 increases from 1.7 to 7.0 ×10−13 cm2 /W, and β increases from 1.0 to 7.0
cm/GW. It is interesting to note that in the low CP region, both n2 and β are independent of
CP and are similar values to those of the pure Si-ncs sample. As shown in Figure 1, in the
low CP region, carriers are not generated within Si-ncs; supplied electrons are considered tobe consumed for the termination of the dangling-bond-defects on the surface of Si-ncs. On theother hand, in the high CP region, both n2 and β increases with increasing CP . One possible
origin of this enhancement is the impurity-related state formed just below the conduction bandof Si-ncs[31]. In the high CP region, the states enhance optical absorption near the band edgeof the Si-ncs. The enhanced absorption results in the enhancement of n2 .
In order to validate this possibility, we investigated the relation between n2 and absorption.
Figure 4 shows the photon-energy dependence of n2 . The error bars represents the fluctuation of
average laser power and beam waist and also the estimation arising from the fitting procedure.
For all the samples, n2 increases with increasing the photon energy. The inset of Figure 4
shows the absorption spectra of the same samples. We can see clear similarity between them.
This suggests that the impurity-related state is responsible for the observed enhancement of thenonlinear optical response by P doping.

#108533 - $15.00 USD(C) 2009 OSA

Received 9 Mar 2009; revised 10 Apr 2009; accepted 13 Apr 2009; published 20 Apr 200927 April 2009 / Vol. 17, No. 9 / OPTICS EXPRESS 7374

1x10

)
W
/
2
m
c(
n2

1x10

1x10

1x10

1x10

1x10

-11

-12

P-doped
Si-nc:PSG
Si-nc:SiO2

CP

-13

-14

-15

-16

CexSi

GeSe3

TeO2

Fused SF-59
SilicaBK-7
1.5

GallateAs2S3Miller's rule
2.0

2.5

Refractive Index

Fig. 5. n2 is plotted as a function of linear refractive index. The dashed line is the predictionof the Miller’s rule. Circles, squares and triangles are the results of several kinds of typicalglasses, P-doped Si-ncs embedded in PSG (P-doped Si-nc:PSG) and pure Si-ncs embeddedin SiO2 (Si-nc:SiO2 ), respectively.

In Figure 5, n2 is plotted as a function of a linear refractive index (n0 ). The dashed line is theprediction of the Miller’s rule[35, 36]. The circles, squares and triangles are the data of several
kinds of glasses[37, 38, 40, 39], P-doped Si-ncs embedded in PSG (P-doped Si-nc:PSG), andpure Si-ncs embedded in SiO2 (Si-nc:SiO2 ), respectively. CexSi is changed from 3.3 to 10.5 vol%for Si-nc:SiO2 and CP is changed from 0 to 1.2mol% for P-doped Si-nc:PSG. The results of
Si-nc:SiO2 are quoted in our previous reports[11], where n2 are obtained by the z-scan methodwith the same conditions as those of the present study. We can see that Si-nc:SiO2 has relatively
large n2 and small n0 compared to other typical glasses. For example, n2 of Si-nc:SiO2 is about
three orders of magnitudes larger than that of a silica glass, while n0 (=1.54) is similar to thatof a silica glass. These properties are very suitable for the optical switching systems because
smaller n0 minimizes the optical coupling loss with the conventional SiO2 fiber. As can be seenin Fig. 5, P-doping further enhances n2 (at maximum 5 times) with no significant change ofn0 . In this point, P-doped Si-ncs have great potential toward the realization of Si-based opticalswitching systems. It is definitely worth studying the n2 of P-doped Si-ncs in other wavelength
region, especially at around 1.5μ m used in optical telecommunication industry.
4.

Conclusion

Nonlinear optical properties of P-doped Si-ncs are studied by z-scan technique in femtosecond
regime at around 1.6 eV. n2 of Si-ncs is enhanced as much as 5 times by P-doping with nosignificant changes of n0 . This is a great improvement because generally the enhancement of
n2 is accompanied by the enhancement of n0 , which leads to the increase of the optical coupling loss with a conventional SiO2 fiber. P-doped Si-nc is thus considered to be a promising
candidate material for the realization of Si-based optical switching devices. We also showedthat in the energy region of the n2 enhancement, optical absorption is enhanced. This suggeststhat impurity-related energy states are responsible for the observed enhancement of the nonlinear optical response. The present results indicate that, in addition to the size and volume
fraction of Si-ncs, impurity control is a parameter to control nonlinear optical responses of Sincs. Also, since this is, to our knowledge, the first report on the nonlinear optical propertiesof impurity-doped semiconductor nanocrystals, our study of P-doped Si-ncs will lead us to thebetter understanding of nonlinear optical properties of this kind of materials.
#108533 - $15.00 USD(C) 2009 OSA

Received 9 Mar 2009; revised 10 Apr 2009; accepted 13 Apr 2009; published 20 Apr 200927 April 2009 / Vol. 17, No. 9 / OPTICS EXPRESS 7375

Acknowledgments
This work is supported by Asahi Glass Co. Ltd. and a Grant-in-Aid for Scientific Researchfrom the Ministry of Education, Culture, Sports, Science and Technology, Japan. We would
like to thank Dr. Tomoharu Hasegawa and Dr. Madoka Ono for their experimental supports andexcellent discussions for this work.

#108533 - $15.00 USD(C) 2009 OSA

Received 9 Mar 2009; revised 10 Apr 2009; accepted 13 Apr 2009; published 20 Apr 200927 April 2009 / Vol. 17, No. 9 / OPTICS EXPRESS 7376