Optical properties of silicon nanocrystals in silica: Results from spectralfiltering effect, m-line technique, and x-ray photoelectron spectroscopyLeonid Khriachtchev, Timur Nikitin, Claudio J. Oton, Rama Velagapudi, Jani Sainio et al. Citation: J. Appl. Phys. 104, 104316 (2008); doi: 10.1063/1.3010304 View online: http://dx.doi.org/10.1063/1.3010304 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v104/i10 Published by the American Institute of Physics. Related ArticlesSpectral patterns underlying polarization-enhanced diffractive interference are distinguishable by complextrigonometry Appl. Phys. Lett. 101, 183104 (2012) Near-infrared enhanced carbon nanodots by thermally assisted growth Appl. Phys. Lett. 101, 163107 (2012) Nanocluster Si sensitized Er luminescence: Excitation mechanisms and critical factors for population inversion Appl. Phys. Lett. 101, 141907 (2012) Silicon nanoparticle-ZnS nanophosphors for ultraviolet-based white light emitting diode J. Appl. Phys. 112, 074313 (2012) High energy-resolution electron energy-loss spectroscopy study on the near-infrared scattering mechanism ofCs0.33WO3 crystals and nanoparticles J. Appl. Phys. 112, 074308 (2012) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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Optical properties of silicon nanocrystals in silica: Results from spectralfiltering effect, m-line technique, and x-ray photoelectron spectroscopy

Leonid Khriachtchev,1,a� Timur Nikitin,1 Claudio J. Oton,2 Rama Velagapudi,3 Jani Sainio,3

Jouko Lahtinen,3 and Sergei Novikov4

1Laboratory of Physical Chemistry, P.O. Box 55, FIN-00014 University of Helsinki, Finland2Optoelectronics Research Centre, University of Southampton, Southampton, SO17 1BJ United Kingdom3Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Finland4Electron Physics Laboratory, Helsinki University of Technology, P. O. Box 3000, FIN-02015 HUT, Finland

�Received 12 August 2008; accepted 17 September 2008; published online 21 November 2008�

The optical properties of silica layers containing silicon nanocrystals are analyzed in terms ofspectral filtering in absorbing planar waveguides �cutoff spectra�, m-line measurements, and x-rayphotoelectron spectroscopy �XPS�. The effects of optical dispersion, approximation of weakguiding, and depth dependence of refractive index in a planar waveguide are studied. We comparethe measured optical properties of silicon-rich silicon oxide samples with the values estimated bythe Bruggeman theory using the XPS structural components. A good agreement between themeasured and calculated refractive indices is found. The results for absorption suggest hightransparency of the nanoscale-suboxide component in contrast to the corresponding bulk material.The Raman intensity of silicon nanocrystals is proportional to the XPS amount of bulk silicon. Theextinction coefficient extracted for the Si component is between the values for crystalline andamorphous silicon. Annealing at higher temperatures decreases the Si component extinctioncoefficient, which is interpreted as a decrease in the amorphous Si fraction. The XPS methodsurprisingly suggests a large proportion of silicon suboxide even after annealing at 1200 °C.© 2008 American Institute of Physics. �DOI: 10.1063/1.3010304�

I. INTRODUCTION

Silicon nanostructures have been extensively studied dueto their peculiar optical and light-emitting properties thatcould be used in photonic devices.1 A popular model for thebroad photoluminescence �PL� around 1.6 eV ��800 nm� isbased on localized-state recombination involving Si=O co-valent bonds.2–4 The oxygen-related light-emitting centerscan be at the interface area between silicon nanocrystals �Si-nc� and the host oxide. This model finds support in the syn-chronous appearance of Si-nc and enhancement of the red PLupon thermal annealing above 1000 °C, which is often ob-served experimentally. On the other hand, some experimentsshow that the red PL can be intense in materials withoutobvious presence of Si-nc embedded in the oxide matrix.5–7

Thus, the light emitting centers can be accommodated in aless ordered structure, which is invisible by Ramanspectroscopy.8–10

As another optoelectronic application, Si-nc in siliconoxide matrix can be used to change the refractive index. Asilicon oxide layer containing Si-nc on top of another silicalayer forms a planar waveguide. Spectral filtering of PL bysuch waveguides was noticed.11 This effect has been laterstudied in Si-nc /SiO2 layers, prepared with variousmethods.9,12–19 In fact, narrow and polarized spectral peaksare filtered from the broadband and unpolarized PL, whenthe spectrum is measured from the waveguide edge along thewaveguide. Two models have been suggested to interpret thisphenomenon. Khriachtchev et al.12–14 utilized the mode lo-

calization as a function of the waveguide generalized fre-quency. Pelant et al.18 suggested the presence of quasiguidedmodes escaping the core layer. These two interpretations areclose to each other and based on the fact that the substrate ismore transparent than the waveguide. An unusual case of thespectral filtering effect by silica layers containing Si-nc wasreported in Ref. 19 when the spectral positions of the TE andTM peaks did not follow the classical waveguide theory foran isotropic planar waveguide. This abnormal behavior wasexplained by optical birefringence of the core material.

In the present work, we develop the analysis of opticalproperties of annealed silicon-rich silicon oxide layers ob-tained with the spectral filtering effect, m-line technique, andx-ray photoelectron spectroscopy �XPS�. We study variousapproximations used previously to extract optical propertiesof planar waveguides, and this analysis fully supports theprevious results. The XPS method provides further insightinto the material structural composition, enabling us to esti-mate the optical properties of the nanoscale material compo-nents using the known Bruggeman theory.

II. EXPERIMENTAL DETAILS

The silicon rich silicon oxide �SiOx ,x�2� films weredeposited by a reactive Si deposition method on silicasubstrates.7,8,13 For two samples �samples A and B�, the SiOx

layer has a Si concentration and thickness gradient along thesample surface, and the name of optical wedge for thesesamples has been used. Slices ��7 cm long� were cut alongthe gradient. We use the displacement D measured from theslice side with the highest silicon concentration. Using thea�Electronic mail: leonid.khriachtchev@helsinki.fi.

JOURNAL OF APPLIED PHYSICS 104, 104316 �2008�

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deposition conditions, the change in the x parameter wasestimated to be �8% with respect to the central values��1.65 and 1.70�.13 These two samples were annealed at1100 °C in nitrogen atmosphere for 1 h. The estimates de-rived from the deposition conditions were confirmed by op-tical and XPS measurements. The third SiOx sample �sampleC� has homogeneous composition and thickness. This samplewas cut into three pieces and annealed at 1100, 1150, and1200 °C in nitrogen atmosphere for 1 h.

The PL and Raman spectra were measured at room tem-perature with an Ar+ laser �488 nm, Omnichrome 543-AP�and a spectrometer �Acton SpectraPro 500I� equipped with acharge-coupled device camera �Andor InstaSpec IV�. The PLlight exiting the waveguide sample in the direction nearlyparallel to the waveguide surface was detected. For the opti-cal wedges �samples A and B�, the emission was detectedperpendicularly to the Si concentration gradient. The trans-mission spectra were recorded with a fiber-optics spectrom-eter �SD2000, Ocean Optics� and a broadband light source�DH-2000, Top Sensor Systems�. The absorption coefficientwas obtained from transmission and reflection measure-ments.20

These samples were also studied with the m-line prismcoupling technique using a 633 nm He–Ne laser and agadolinium–gallium garnet prism.21 The angular dependenceof the reflectance is measured by a Si photodiode, and theguided modes are observed as a decrease in reflectance dueto waveguide absorption. The effective index of each guidedmode is obtained from the incident angle and the refractiveindex of the prism

neff = np sin �0, �1�

where np is the refractive index of the prism �np=1.9648�and �0 is the incidence angle. The mode positions depend onthe refractive index of the waveguide and its thickness. Thecalculated reflection curve can be fitted to the measuredcurve, and thus the layer parameters can be extracted.22

The XPS measurements were carried out with an SSX-100 instrument using monochromated Al K� radiation. Thesample surface was sputtered with Ar+ ions �4 keV� in orderto obtain the composition as a function of depth. The sput-tering was done in the 2 mm area, and the probing spot was0.3 mm in diameter. The sputtering rate was calibrated usinga reference sample with a 280 nm thick SiO2 layer on acrystalline silicon wafer. Before measurements, the samplesurface was presputtered for several seconds in order to re-move surface contaminations.

The SiO2 sample was also used to test the possible effectof preferential sputtering. It was observed that the measuredO/Si ratio from the peak areas was slightly less that 2.0, andthis can be explained by a higher sputtering yield of oxygencompared to Si. The O/Si ratios given below, however, havebeen corrected to feature the value 2.0 in SiO2. We argue thatthis correction is justified because �i� the O/Si peak area ratiodoes not depend on the sputtering time nor on the sputteringenergy, indicating that the sputtering effects only the compo-sition of the outermost layer and �ii� the sputtering does notchange the chemical state of silicon since only the Si 2p peakof SiO2 is seen in the reference sample. As we see no reduc-

tion in the oxidation state of Si, we may argue that thechemical states observed during depth profiling reflect thechemical states of silicon inside the film.

III. MAIN EXPERIMENTAL OBSERVATIONS

A. Cutoff spectra

Figure 1�a� shows PL spectra detected from the wave-guide edge along the sample surface �sample C annealed at1100 and 1200 °C�. The two pairs of polarized peaks arefiltered from the broad PL spectrum. This effect has beenexplained by delocalization of guided modes near the modecutoff frequencies in an absorbing planar waveguide.12–14 Ifthe waveguide layer is absorbing and the substrate is moretransparent, then the delocalized modes suffer minimal lossesand the confined modes are efficiently absorbed. The modelocalization is a function of the generalized frequency param-

FIG. 1. �a� Cutoff spectra of sample C annealed at 1100 and 1200 °C. ThePL intensity strongly decreases after annealing at 1200 °C �note the multi-plication factor�. The cutoff spectra are measured from the sample edgealong the waveguide surface, the excitation spot being at a distance of sev-eral millimeters from the sample edge. The positions of the TE peaks aremarked and the other bands have the TM polarization. �b� Transmissionspectrum of sample C annealed at 1100 °C.

104316-2 Khriachtchev et al. J. Appl. Phys. 104, 104316 �2008�

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eter written for an asymmetrical planar waveguide in theform

V = 2��n12 − n2

2�1/2d/� , �2�

where n1 and n2 are the refractive indices of the layer andsubstrate, respectively, d is the waveguide thickness, and � isthe wavelength.23 The modes become delocalized near thecutoff conditions when V= �2m+1�� /2 and Eq. �2� yieldsthe cutoff frequencies. The cutoff frequencies correspond tothe detected narrow peaks �see Fig. 1�. We call a PL spec-trum measured from the waveguide edge along the wave-guide surface a cutoff spectrum because the narrow peaksdisplay the cutoff frequencies.

The classical theory of an isotropic asymmetrical planarwaveguide predicts that the cutoff positions for the TEmodes �with polarization parallel to the sample surface� areat longer wavelengths �lower frequencies� than the TM cut-off positions �with polarization perpendicular to thewaveguide�.23,24 However, the opposite spectral order be-tween the TE and TM peaks was found for some samples asdemonstrated by the upper spectrum in Fig. 1�a�. The re-versed order of the TE and TM peaks was explained byassuming optical birefringence.19 The larger frequency inter-vals between the cutoff peaks were found for the TE polar-ization than for the TM polarization. It follows that the TEpeaks can appear at shorter wavelengths �higher frequencies�than the TM peaks for high mode orders. In this situation, therefractive index is smaller for the TE light than it is for theTM light �nTE�nTM�. The birefringence was found in SiOx

samples with high Si concentrations and annealed at rela-tively low temperatures, and these results were confirmed bym-line measurements.19 The birefringence was tentativelyexplained by nonspherical silicon nanocrystals. Annealing at1200 °C leads to the “classical” order of the polarized peaks�see Fig. 1�a�, lower spectrum�, which indicates a decrease inthe material birefringence.

Figure 1�b� shows a typical transmission spectrum of anannealed silicon-rich silicon oxide layer on a silica substrate.The spacing of the interference patterns is written as

�� = 1/2n1d . �3�

It was suggested to use two Eqs. �2� and �3� to extract twoparameters that are the refractive index and layer thickness.12

This procedure uses the spacing between the TE cutoff fre-quencies � and between the patterns of the transmissionspectra ��. The � /�� spacing ratio is a function of the layerrefractive index as easily calculated from Eqs. �2� and �3� forcutoff conditions and given substrate material �see Fig. 2�.Thus, the measured � /�� spacing ratio yields the layer re-fractive index. The refractive index obtained in this way cor-responds to the TE polarization, and it is averaged over theused spectral interval. Next, the layer thickness is found us-ing the obtained TE refractive index and the optical thicknessgiven by the transmission spectrum. Finally, the TM refrac-tive index is found from the layer thickness and spacingbetween the TM peaks. This approach suggested in Ref. 12 iscalled below a simple model.

The described simple model uses at least four simplifi-cations: �i� Eq. �2� was derived using weak-guiding approxi-

mation �n1−n2�1,23 which is not obvious in practicalcases, �ii� the procedure uses only the spacing between cutoffpeaks disregarding their actual positions, �iii� the materialdispersion was neglected, and �iv� a step-index profile wasassumed whereas the practical refractive index profiles areprobably smooth. These simplifications will be examined be-low. Despite these obvious limitations, the simple modelyielded reasonable results. For example, for sample A, wepreviously extracted n1=1.91 and 1.75, d=2.02 and1.63 �m for position on the sample D=0.5 and 4.5 cm,respectively.13 The birefringence n /n in these points was4.6 and 3.0% �nTM�nTE�, and the nTM values applied to thecritical angle in the layer.19 The trend obtained for n and dagrees with the expectations from the deposition conditions.

B. M-line measurements

M-line prism coupling measurements show a number ofdark reflection bands corresponding to the waveguide modes.Figure 3 presents the result of fitting performed for sample A�D=4.5 cm� assuming a step-index profile. The fitting pro-cedure yielded for this sample d=1.51 �m, n1=1.735, andn /n=2% �nTM�nTE�. The nTM value corresponds hereto the light propagation along the waveguide and it isdescribed as the extraordinary refractive index. Forsample A �D=0.5 cm�, we previously obtained d=2.0 �m,n1=1.835, and n /n=7%.19 These data agree with the val-ues obtained from the cutoff spectra �see the previous sec-tion� and show the same trends of all parameters. In particu-lar, they confirm the Si concentration and thickness gradientalong the sample surface and the material birefringence.

C. XPS measurements

The energy windows corresponding to the O 1s and Si2p peaks were measured. We fitted the Si 2p spectrum bythree peaks corresponding to the silicon binding energy inbulk silicon �Si, sometimes called metallic silicon�, siliconsuboxide �SiO�, and silicon dioxide �SiO2� �see Fig. 4�. Inthe fit 80%-Gaussian 20%-Lorentzian peaks were used afterShirley background subtraction.25 The energy calibration wasperformed using the O 1s line at 532.7 eV. The energies ofSiO2 and Si were fixed at 103.3 and 99.7 eV,26 respectively,

FIG. 2. Ratio of the cutoff spacing � to the spacing in the transmissionspectra �� as a function of layer refractive index obtained from Eqs. �2� and�3�. The curve was calculated with the substrate refractive index of 1.456.

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and the energy of SiO was kept free but it remained at101.9�0.2 eV in all the fits. The best fits were obtainedwith full width at half maximum values of �1.9 eV, and thisvalue is close to the widths obtained for “pure” Si and SiO2

states. It should be pointed out that the silicon suboxide com-ponent described here as SiO is not well defined but corre-sponds to a superposition of various suboxide states.

The Si oxidation states were measured at differentdepths after sputtering and then averaged over the depth to

yield the average O/Si concentration and structural compo-nents. The material composition varies with depth �see Fig.5�. The SiO2 component is stronger and the Si component isweaker near the surface. A similar variation was found forsimilar samples also previously.7 The estimated thicknessvaries from 1.8 to 2.2 �m for sample A and from 1.5 to1.8 �m for sample B, which is in reasonable agreement withthe cutoff and m-line measurements. However, the layerthickness obtained from XPS measurements has relativelylarge uncertainty due to the calibration method. According toour measurements, the averaged O/Si ratio changes for dif-ferent positions on the optical wedges, in agreement withexpectations from the deposition conditions.

The relative amounts of the composition components asa function of the O/Si ratio are shown in Fig. 6. When theO/Si ratio increases, the SiO2 amount increases and the Siamount decreases. The SiO component is relatively stable forthe O/Si ratio in the 1.35 to 1.7 range.

IV. ANALYSIS AND DISCUSSIONS

A. Dispersion within the simple model

Figure 7 presents the data obtained for various positionson sample A �optical wedge�. The values shown by solid

0 0.5 1 1.5 2 2.51.4

1.6

1.8

2

Depth (µm)

n

1.4 1.5 1.6 1.7 1.80.7

0.8

0.9

1

1.1

TE

1.4 1.5 1.6 1.7 1.80.7

0.8

0.9

1

1.1

TM

nef f

OrdExt

CalcExp

CalcExp

FIG. 3. M-line measurements of sample A �D=4.5 cm�. The calculated andmeasured curves are shown. The first calculated peak with the smallestintensity and the largest neff is not experimentally detected. The upper panelpresents the refractive index profile obtained in the fitting procedure. Theordinary refractive index corresponds to the TE polarization.

FIG. 4. Si, SiO, and SiO2 components in the XPS spectrum of sample A�D=0.5 cm�.

FIG. 5. XPS depth profiles for sample A �D=0.5 cm�. One sputtering cyclecorresponds to �100 nm.

FIG. 6. Composition components of SiO2, SiO, and Si as a function of theO/Si ratio obtained by the XPS method. The relative amounts of Si atomswith corresponding bonding are shown. The data points correspond to dif-ferent positions on samples A and B. The lines guide the eyes.

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symbols were obtained previously by using the simple modelillustrated in Fig. 2.13 The optical thickness needed for theextraction procedure was previously averaged over the mea-sured spectral region �500 to 1000 nm�, which is clearly anapproximation. Indeed, the material presumably has differentrefractive indexes and hence different optical thicknesses atdifferent cutoff frequencies. To take this effect into consid-eration, the transmission curves were fitted by the function

y = P1 + P2�1 − exp�− P3�� − P4���

�1 + P7 sin�2�/��P5�1 + P8�1 − �/1070�3�� + P6�� ,

�4�

where Pi are the fitting parameters. This function was con-structed to fit typical transmission spectra. The term�1+ P8�1−� /1070�3� describes the wavelength dependenceof the spacing��, and it can fit the dispersion curve of siliconinclusions in silica described by the Bruggeman theory. Theadditional analysis shows that the obtained results are notvery sensitive to the shape of this dispersion function.

The fit of the experimental transmission spectra with Eq.�4� revealed an expected increase in optical thickness towardshorter wavelengths, with the parameter P8 of about −0.2.Furthermore, the optical thicknesses extracted by Eq. �4� are

smaller by �3% than the values previously obtained assum-ing zero dispersion.13 The thickness and refractive index canbe extracted from the simple model with taking into accountdispersion. In this generalized procedure, the refractive indexin Eq. �2� is corrected by the dispersion at actual cutoff fre-quencies. This makes the extraction procedure a little morecomplicated than previously. The results are presented byopen circles in Figs. 7�b� and 7�c�. The agreement with thevalues obtained with the averaged refractive index is evi-dently good, and the differences are within experimental er-ror. Furthermore, taking into account the dispersion does notchange much the data on optical birefringence �see Fig. 8�. Itcan be concluded that the weak material dispersion is notcrucial while extracting the refractive index from waveguidecutoff spectra.

B. Results of exact equations

The consideration of this section is based on a model ofreflection from a multilayer system.22 This approach has twoimprovements with respect to the simple model describedabove. First, the equations used here do not limit refractiveindexes of the optical system, and we call these equationsexact equations. Second, this analysis calculates both spac-ing and position of cutoff peaks. Similarly to the previoussection, we take into account the material dispersion derivedfrom the transmission spectra �parameter P8 in Eq. �4��.

In this procedure, a multilayer system is considered. Theincidence medium is the prism �index 1.9648�, followed by athin air gap �50–100 nm� that provides evanescent couplingto the waveguide layer. The rest of the optical system con-sists of the guiding layer and silica substrate. Mode couplingis observed as a decrease in reflectance when varying theincident angle. The calculation was done with a standardtransfer-matrix approach. Birefringence leads to a depen-dence of the TM-wave index on the incident angle that wastaken into account. Varying the incidence angle leads to avariation in the effective index, and by varying the wave-length one can obtain how the peak positions change with

FIG. 7. Optical parameters of sample A obtained with different models. Thedata shown by solid circles �no dispersion, see Fig. 2� are from Ref. 13. Thedata shown with open circles are the present data obtained by Eqs. �2� and�3� taking into account dispersion �see Eq. �4��. The optical thickness in plot�a� is given for 600 nm. The data shown with stars are the result from theexact equations �Ref. 22�.

FIG. 8. Birefringence of sample A obtained with different models �nTM

�nTE�. The data shown by solid circles �no dispersion, see Fig. 2� are fromRef. 13. The data shown with open circles are the present data obtained byEqs. �2� and �3� taking into account dispersion �see Eq. �4��. The data shownwith stars are the result from the exact equations �Ref. 22�. The nTM indexcorresponds to the critical angle.

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wavelength. The wavelength, at which the effective index ofeach peak becomes the cladding index, is the cutoff wave-length of the mode. This approach provides all the cutoffmodes. Another advantage is that smooth index profiles canbe simulated since a smooth profile can be approximated asmany thin layers with varying index of refraction �see later�.

The optical parameters obtained with this procedure arepresented in Figs. 7 and 8 with stars where a single wave-guide layer with a fixed refractive index was considered. Theobtained results do not differ much from the results obtainedwith the simple model of Ref. 12 �see Fig. 2�. Systematicallylarger birefringence can only be noticed as a clear differencewhereas other differences are within experimental error. Atthe first glance, it is somewhat surprising that the simplemodel presented in Fig. 2 produces such adequate resultsdespite the practical layers are not weakly guiding. However,the theory of planar waveguides shows that the increase inthe �n1−n2� difference influences mainly the cutoff positionsbut not the interval between these positions.23 The presentexperimental results support this theoretical conclusion.

C. Sample composition and optical properties

Now, we use the sample composition obtained from theXPS measurements to describe optical parameters using theBruggeman theory.27–29 The equation for a three-componentmixture, which is considered here, is given by

a� �a − �m

�a + 2�m + b� �b − �m

�b + 2�m + c� �c − �m

�c + 2�m = 0, �5�

where a, b, and c are the volumetric fractions of each com-ponent, �a,b,c are the respective dielectric constants, and �m isthe effective dielectric constant. This formula allows to findthe effective optical parameters �refractive index and extinc-tion coefficient� if the material structural composition isknown. The XPS measurements provide three compositioncomponents where Si atoms are bonded as in bulk Si, SiO,and SiO2 materials. The XPS method gives the relativeamounts of Si atoms in these components that are recalcu-lated using the material densities to the volumetric fractionsused in the Bruggeman theory.

Figure 9�a� presents the Raman band intensity at�515 cm−1 specific for Si-nc as a function of the full Sivolume. The Si volume is proportional to the volumetric sili-con fraction multiplied by the layer thickness. A linear de-pendence crossing the origin is observed, i.e., the Ramanintensity presumably measures the same Si component asXPS. The Raman and XPS data show that not all siliconexcess in silicon rich silicon oxide is in the Si componentthat is measured by XPS and Raman spectroscopy. In otherwords, the silicon in suboxides evidenced by XPS does notcontribute to the Raman band of Si-nc.

Figures 9�b� and 9�c� show the absorption coefficientand refractive index versus the silicon volumetric fractionprovided by XPS. The experimental absorption coefficient�triangles� is a nearly linear function of the silicon volumet-ric fraction passing the origin. Clearly, the correlation be-tween Raman intensity and absorption coefficient takes placeas discussed elsewhere.8 First, we consider a model with

transparent SiO2 �n=1.456�, absorbing SiO �complexrefractive index n�=2.05+0.055i�, and absorbing silicon�n�=4.37+0.079i� �see circles in Fig. 9�. These values cor-respond to bulk SiO2, SiO, and Si materials.30 While therefractive index is described reasonably well by this model,the description of absorption clearly fails: it is too high forlow Si amounts. It follows that the nanoscale suboxide ismuch more transparent than bulk SiO. This result agrees withthe model of Si /SiO2 superlattices with transparent suboxideinterfaces.31,32 The high transparency of suboxide might beconnected with its nanoscale structure.

The model with transparent SiO �n=2.05� and thesilicon component representing crystalline silicon�n�=4.37+0.079i� lead to too small absorption �diamonds inFig. 9�. On the other hand, if the parameters of amorphoussilicon are used �n�=4.45+1.25i�, the absorption becomestoo high �squares in Fig. 8�. It is plausible to suggest that thesilicon component is partially amorphous and partially crys-tallized after annealing at 1100 °C, which has been repeat-edly discussed in literature.9,10,33,34 A good agreement withexperiment is obtained by assuming that about a half of the

FIG. 9. �a� Raman intensity as a function of the full volume of silicon and��b� and �c�� optical parameters as a function of volumetric silicon fraction.Solid symbols present the experimental results of samples A and B. Opensymbols are calculated by the Bruggeman theory with the followingcomplex refractive indexes for SiO and Si components: 2.05+0.055i and4.37+0.079i �circles�, 2.05 and 4.37+0.079i �diamonds�, and 2.05 and4.45+1.25i �squares�. The Raman data are from Ref. 13. The refractiveindex of silica is 1.456. The compositions of samples A and B �variouspositions� were measured by the XPS method.

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Si component is amorphous. However, one should not forgetthat the material components are nanostructured and mighthave optical parameters different from the correspondingbulk materials. We used the Bruggeman theory to extract theextinction coefficients of the Si component and obtained avalue of 0.55�0.10. The extinction coefficient shows nosystematic dependence on the Si concentration.

D. Effect of refractive index profile

The step-index profile is an approximation used in allprevious discussion. It is the last of four simplifications usedin the simple model developed in Ref. 12. The XPS measure-ments evidence a smooth depth profile of the composition,which means in turn a smooth profile of refractive index. Weperformed this analysis on sample C annealed at 1100 °C.According to the XPS measurements, sample C has the mostpronounced change in refractive index as a function of depthcompared to the other samples. As a consequence of thesmooth index profile, we failed to obtain a satisfactory fit ofthe experimental m-line curve with a step-index profile. Onthe other hand, using the profile provided by the XPS mea-surements and Bruggeman theory, a good fit of experimentaldata was found for a thickness of 1.9 �m �see Fig. 10�. The2.4% birefringence �nTM�nTE� was required to fit the TMlines.

By using equations obtained in Ref. 22, we calculatedthe cutoff spectra corresponding to the parameters obtainedfrom the m-line measurements. For each index, a whole dis-

persion curve was generated using the dispersion functionassumed in Eq. �4� with P8=−0.2. As a result, we obtainedan excellent agreement with the experimental cutoff posi-tions marked with black horizontal bars �see Fig. 11�. Itshould be emphasized that this excellent agreement wasachieved without changing any parameter of the m-line fit.

It is an interesting question whether it is possible to con-struct a step-index profile giving the experimental cutoff andtransmission spectra. We performed calculations for a step-index profile with the same thickness �1.90 �m� and aver-age refractive index of 1.81 for the TE polarization. Thishomogeneous layer has the same optical thickness as thelayer with varying index �Fig. 10�. For this homogeneouslayer, the calculated cutoff positions deviate from the experi-mental values by 10–30 nm. The obtained shift in the peakpositions could not be compensated by changing dispersion;however, the agreement could be improved by slightlyvarying the waveguide thickness. An excellent agreementwith experiment was obtained for refractive index of1.8097, thickness of 1.85 �m, and birefringence of 3.0%

0 0.5 1 1.5 2 2.5 31.4

1.6

1.8

2

Depth (µm)

n

1.4 1.5 1.6 1.7 1.8

0.6

0.8

1

TE

1.4 1.5 1.6 1.7 1.80.6

0.8

1

TM

neff

OrdExt

CalcExp

CalcExp

FIG. 10. M-line measurements using a smooth refractive index profile pro-vided by the XPS measurements and Bruggeman theory �sample C annealedat 1100 °C�. The ordinary refractive index corresponds to the TE polariza-tion and the extraordinary index corresponds to the TM polarization.

FIG. 11. �Color online� Modal spectrum for �a� TE and �b� TM polarizationconsidering the index profile shown in Fig. 10. The dotted line marks thesubstrate refractive index; therefore the cutoff modes are the ones that crossthis line. The horizontal black bars show the positions of the experimentallyobserved cutoff modes.

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�nTM�nTE�. However, it should be reminded that the fit ofthe m-line curves using these parameters is not satisfactory,and the smooth profile is required in this case.

It was expected that the smooth index profile is not cru-cial to obtain good description of the delocalized cutoffmodes. In the cutoff calculations with varying index, themain changes in the mode positions are seen for the mostconfined modes. The cutoff mode is the least confined so thatit does not change much when the refractive index has agradient. In order to support this intuitive image, we com-pared two 2-�m-thick layers with a constant index of 1.8 andwith a refractive index linearly increasing from 1.7 to 1.9. Itis found that the cutoff positions for these two modelwaveguides are practically the same. The mode positions at900 nm are at effective indexes of 1.7887, 1.7544, 1.6963,1.6131, and 1.5049 without gradient whereas the values of1.8228, 1.754, 1.6904, 1.6085, and 1.5008 are obtained withthe varying index. Indeed, only the most confined modechanges substantially. In contrast, the refractive index profileis more critical for the m-line curve treating all modes sincethe confined modes are most affected by the refractive indexprofile.

The obtained results on sample C �annealed at 1100 °C�are interesting to compare with the results of the simplemodel with zero dispersion �see Fig. 2�. From the cutoff andtransmission spectra, we obtained the TE refractive index of1.82, thickness of 1.91 �m, and birefringence of 3.6%, i.e.,the agreement between the least and the most accurate ap-proaches is quite satisfactory.

E. Effect of annealing temperature

Sample C was annealed at three temperatures �1100,1150, and 1200 °C�, and this changed the optical parameters.As estimated with the simple model with zero dispersion�Fig. 2�, the effective refractive index slightly decreases withthe increasing annealing temperature �see Table I�. The ef-fective sample thickness obtained from optical measure-ments also changes; however, this might be, to some extent,because different parts of the sample were measured. Theprofilometric measurements give a layer thickness of�2.0�0.1� �m, i.e., in agreement with the optical estimates.The measured refractive index was compared with the indexestimated from the Bruggeman theory using the XPS resultsand the refractive indices of 1.456, 2.05, and 4.37 for SiO2,SiO, and Si components, respectively. Table I shows a verygood agreement between experiment and theory.

The material birefringence decreases for higher anneal-ing temperatures. The cutoff spectrum of sample C annealedat 1200 °C exhibits the classical order of polarized

peaks.23,24 It was suggested in Ref. 19 that the birefringence�nTM�nTE� originates from nonspherical shapes of Si-ncwith smaller dimensions along the waveguide layer. This im-age was confirmed by transmission electron microscopymeasurements. Nonspherical Si-nc were also observed byYurtsever et al.35 in a similar material. The birefringence inporous silicon was explained by the form of Si structures.36

The decrease in birefringence at higher temperatures sug-gests spherical reshaping of Si-nc or/and randomization oftheir orientations.

The XPS data on these three samples should be com-mented �see Table I�. It seems that the silicon amount de-creases with the increasing annealing temperature, whichcannot be the case for annealing in nitrogen atmosphere. Thechanges in relative amounts of different chemical states of Sican be rather explained by thermal reorganization of the SiOx

network. Annealing at higher temperatures can reorganizemetastable double bonds to single bonds and decreases thenumber of dangling bonds. In this situation, the increasingproportion of silicon dioxide accompanied with a decrease insilicon suboxides is reasonable.

The absorption coefficient decreases after annealing at1200 °C. The decrease in absorption is larger than the de-crease in the Si component suggested by the XPS method. Asa very probable explanation, the higher annealing tempera-ture decreases the proportion of disordered �amorphous� sili-con. The Raman measurements support this explanation: theRaman bands become narrower after annealing at highertemperatures and the low-frequency Raman intensity below500 cm−1 attributed to disordered silicon decreases. How-ever, a change in optical gap cannot be excluded either,which complicates the quantitative analysis. By using theBruggeman theory, we extracted the extinction coefficient ofthe Si component, and the result is presented in Table I. Theobserved decrease in the extinction coefficient of the Si com-ponent after annealing at 1200 °C can be reasonably con-nected with progressing Si crystallization. It should be no-ticed that the obtained extinction coefficient is four timeshigher than that of crystalline silicon even after annealing at1200 °C. This fact can be connected with remaining struc-tural disorder of small Si-nc in silica.7,37

V. CONCLUDING REMARKS

Optical and structural properties of silicon-rich siliconoxide containing Si-nc have been studied by using PL cutoffspectra, m-line prism coupling technique, and XPS. The re-sults obtained in this work can be divided into two groups.

First, we carefully analyzed limitations of the simplemodel used previously to extract optical properties of silicon

TABLE I. Experimental and estimated parameters of sample C annealed at three different temperatures. Thickness d and refractive index n are from cutoffspectra. Absorption coefficient � is from transmission measurements. The volumetric fractions of SiO2, SiO, and Si provided by XPS are given. nest andkest �Si� are the refractive index of the materials and extinction coefficient of the Si component estimated from the Bruggeman theory, respectively.

Tann �°C� dexp ��m� nexp n /nexp �%� �exp �cm−1� SiO2 �vol %� SiO �vol %� Si �vol %� nest kest �Si�

1100 1.91 1.824 3.6 4450 61.2 28.2 10.6 1.835 0.411150 2.02 1.777 1.9 3594 64.2 26.7 9.1 1.792 0.411200 2.09 1.750 0.0 2291 66.3 25.1 8.6 1.770 0.28

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oxide layers containing Si-nc.12–14,19 The discussed simplifi-cations are �i� the weak-guiding approximation �n1−n2�1,�ii� the use of only the spectral intervals between cutoffpeaks, �iii� the neglected material dispersion and �iv� the as-sumed step-index profile. As a result, we conclude that thesesimplifications are not crucial for extractions of optical pa-rameters in the present case because more accurate ap-proaches lead to very close results. Thus, the simple modelsuggested in Ref. 12 and illustrated in Fig. 2 can be success-fully used to estimate optical parameters from cutoff andtransmission spectra. The generality of this conclusion re-quires further verification. Using the modified model, wefound material dispersion in our samples and confirmed pre-vious results on birefringence of Si-nc in silica.19 The presentresults can be applied to different experimental situationsbecause the spectral narrowing at cutoff wavelengths hasbeen observed for variety of materials.38–42

Second, we have analyzed the measured optical proper-ties and the values estimated by the Bruggeman theory usingthe Si, SiO, and SiO2 structural components provided by theXPS measurements. The refractive index of the nanostruc-tured suboxide agrees with that of the corresponding bulkmaterial. On the other hand, the obtained results suggest hightransparency of the nanostructured suboxide component, incontrast to the SiO bulk material. The Si component pos-sesses extinction coefficient, which is between the values forcrystalline and amorphous silicon. Annealing at higher tem-peratures decreases the Si-nc extinction coefficient, whichcan be interpreted as a decrease in amorphous Si fraction.However, the extinction coefficient of the Si component ismuch higher than the value for crystalline silicon even afterannealing at 1200 °C, which suggests a disorder of Si-ncembedded in silica matrix. Moreover, the XPS spectra evi-dence a large proportion of suboxide phase even after an-nealing at 1200 °C.

The present results suggest preparation of more system-atic research on this subject. In particular, ranges of tempera-ture annealing and O/Si ratios are worth increasing for betterunderstanding of the mechanisms discussed in the presentwork. Analysis of light-emitting properties of these and ad-ditional samples in correlation with the structural and opticalproperties is of clear interest; however, this exceeds thescope of the present work.

ACKNOWLEDGMENTS

The Academy of Finland supported this work, partiallythrough CoE CMS and FinNano Program �OPNA�. C.J.O.acknowledges support from the EU 6th framework programthrough an EIF Marie Curie Fellowship Project No. 41102.

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