research article depth-sensitive raman investigation of

Research ArticleDepth-Sensitive Raman Investigation ofMetal-Oxide-Semiconductor Structures Absorption asa Tool for Variation of Exciting Light Penetration Depth

PaweB Borowicz12

1 Institute of Electron Technology Aleja Lotnikow 3642 02-668 Warsaw Poland2Institute of Physical Chemistry Polish Academy of Sciences Kasprzaka 4452 01-224 Warsaw Poland

Correspondence should be addressed to Paweł Borowicz psborowiczwppl

Received 27 September 2015 Accepted 10 November 2015

Academic Editor Christoph Krafft

Copyright copy 2016 Paweł Borowicz This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Presented work focuses the attention on two regions of MOS structure placed in the vicinity of the semiconductordielectricinterface in particular on part of dielectric layer and thin layer of the substrate In the presented work the application of absorptionas a tool that can vary the absorption depth of excitation light into the semiconductor substrate is discussed The changes of theabsorption depth of visible light allows to obtain Raman signal from places in the substrate placed at different distances from thedielectricsemiconductor interface The series of Raman spectra obtained from visible excitation in the case of varying absorptiondepth allowed to analyze the structure of the substrate as a function of distance from the interface Deep ultraviolet Raman studyregarding part of silicon dioxide layer placed directly at the interface is not discussed so far whichmakes the analysis of the structureof this part of dielectric layer possible Comparison of reported in this work Raman data with structure of siliconsilicon dioxideinterface obtained from other experimental techniques proves the applicability of proposed methodology

1 Introduction

The progress in miniaturization of Metal-oxide-semicon-ductor- (MOS-) type electronic devices results in limitationof active area of semiconductor substrate to the thin layerplaced in the vicinity of interface between semiconductorsubstrate and dielectric layer An example of such device isHigh Electron Mobility Transistors (HEMTs) The thicknessof active area in this device is limited to several dozennanometers [1]

Raman spectroscopy detects small shifts in frequencies ofnormal modes caused by small differences between param-eters of crystal or molecular structure like bond lengths orbond angles This accuracy makes from this experimentaltechnique a very efficient tool for structural study Anexample of this type of application of Raman spectroscopyis delivered by study of changes in semiconductor structurecaused by implantation [2]

Optical microscopy is the experimental technique whichoffers high spatial resolution The transverse resolution is

determined by diffraction limit of microscopic objectiveThediameter of Airy spot can be calculated according to Rayleighor Sparrow criteria [3] In the case of the microscopic lenseswith high numerical aperture (119873

119860)119873119860= 055 the dimension

of Airy spot is placed in the range between 500 nm and700 nm [3] Spatial resolution of Raman microscopy wasapplied in the investigation of spatial distribution of suchparameters likemechanical stress in semiconductor substrate[4 5] or channel temperate in HEMTs [6 7] The thermaleffect observed in HEMTs is caused by self-heating presentin the case of current flow between source and drain of thetransistor

The axial dimension of the focus depends also on 119873119860

The distribution of the intensity across the laser beam canbe described by Gaussian function The axial dimension ofthe laser beam focus in the case of confocal microscopes isnot smaller than 1 120583m [8] The thickness of active area intodayrsquos electronic devices is at the least order of magnitudesmaller than axial dimension of laser beam focus determinedfrom geometrical optics Because of this it is necessary to

Hindawi Publishing CorporationJournal of SpectroscopyVolume 2016 Article ID 1617063 14 pageshttpdxdoiorg10115520161617063

2 Journal of Spectroscopy

introduce the procedure that can avoid the limitation comingfrom geometrical optics

The most important property that can help to over-come the limitation of axial diameter of laser beam focusis absorption Absorption coefficient of each material is afunction of wavelength of incident light It means that onecan change the penetration depth of the light into thematerialby choice of the irradiation wavelength The dependencebetween wavelength and absorption of the material wasapplied for investigation of ohmic contacts with additionalcarbon layer formed at different temperatures [9] Silicidefilm mixed with carbon atoms is transparent for visible lightbecause this visible irradiation of the ohmic contact throughsilicide layer causes the Raman scattering in carbon layerplaced between silicide film and silicon carbide substrateThedeep-ultraviolet excitation applied in the same configurationcannot reach the above-mentioned carbon layer due to strongabsorption of the silicide layer mixed with carbon structuresTherefore Raman scattering excited in deep-ultraviolet spec-tral range delivers information about two types of carbonspecies

(i) carbon layer which is built on the free surface ofsilicides due to carbon atom diffusion

(ii) carbon clusters placed inside of silicide layer [9]

The other problem which was investigated by meansof extraction of signal generated in thin layer from largebackground is related to properties of the interface betweensilicon carbide (SiC) and dielectric layer The Near InterfaceTraps (NITs) in the MOS-type structures can decrease themobility of charge carriers even by two orders of magni-tude Extensive study of the properties of SiCSiO

2interface

showed that carbon plays very important role in formationof the defects that can be candidates for NITs [10ndash13] Themost important Raman bands generated by species built fromcarbon atoms [14] are placed in the same range of Ramanshift as two-phonon spectrum of different polytypes of SiC[15 16] Application of two different excitation wavelengthsin particular visible andultravioletmade the extraction of thescattering coming from the interface from backgroundwhichis formed by two-phonon Raman scattering in SiC substratepossible The extraction was possible due to significantlydifferent penetration depths of exciting radiation from bothused spectral ranges [17]

The other area where the decreasing of two-phononRaman scattering plays a key role is related to Raman studyof properties of dielectric layer The problem was discussedin the literature for the system composed of Si substrateand SiO

2layer Standard configuration of Raman apparatus

includes excitation in visible spectral range In this casesignificant two-phonon signal generated in Si substrate isobserved [18] The intensity of this second-order Ramanscattering is strong enough even tomask the signal form SiO

2

layer [19] Application of deep-ultraviolet excitation makespossible the observation of Raman scattering generated inSiO2layer [20] The increase of Si absorption due to change

of the excitation wavelength from visible spectral range todeep-ultraviolet results in reduction of radiation penetration

depth by about 30 times In turn the intensity of two-phonon Raman scattering coming from Si substrate becomesnegligible and the signal from silicon oxide layer becomesdetectable This was shown for sim50 nm thick SiO

2layer

placed on Si substrate by comparison with bulk materialwhich was commercially available quartz glass Suprasil I[20] The price to pay for this advantage is long irradiationtime The reason for this ldquopricerdquo is small efficiency of Ramaneffect in the case of SiO

2combined with small thickness of

investigated material The typical thickness of SiO2layer of

todayrsquos electronic structures is about two orders ofmagnitudesmaller than the axial dimension of the focus of laserbeam

This work focuses the attention on the properties ofthin layer of semiconductor substrate in the vicinity ofsemiconductordielectric interface The SiSiO

2system is

used as an example The change of the power density ofexciting light on the sample results in change of effectiveabsorption depth Effective absorption depth is the thicknessof the investigated material which is active from the point ofview of measured Raman signal under certain power densitySince the definition of the effective absorption depth is acrucial point in the interpretation of experimental data itwill be discussed in detail in the next chapter Experimentalwhere also themethodology of data analysis is describedThesystematic change of power density makes possible to recordRaman signal from material with different thickness As aresult one can get depth profile of structural properties ofinvestigated material

Another point that will be discussed here is the appear-ance of crystal-like structures of silicon dioxide that shouldbe placed at the SiSiO

2interface [21] As was mentioned

above application of deep-ultraviolet excitation in order toreduce two-phonon signal from Si substrate was discussedfor amorphous part of SiO

2layer [20] However Raman

signal observed for this type of excitation contains alsotraces of narrow lines These traces will be compared herewith Raman spectra reported for crystalline forms of silicondioxide

The paper is organized according to the following outlineSection 2 presents method of sample preparation and theircharacterization Raman apparatus and methodologies ofdata analysis and measurements The special attention waspaid to two aspects

(i) the description of the mathematical model whichlinks the power density of irradiation with thicknessof the layer of material from which the Ramanscattering is recorded

(ii) the discussion of two experimental parameters whichare changed if the power density of exciting lightis varied half-angle of the maximum cone of lightcollected by microscope objective and the dimensionof the laser-beam spot

Section 3 presents the measured data The results of theinvestigation are discussed in Section 4

Journal of Spectroscopy 3

2 Experimental

21 Samples Preparation and Characterization Silicon diox-ide films were manufactured in Division of Silicon Microsys-tem and Nanostructure Technology (Institute of ElectronTechnology Warsaw Poland) Three-inch diameter p-typesilicon wafers were used as substrates Samples were char-acterized by means of spectroscopic ellipsometry transmis-sion electron microscopy and transmissionreflection spec-troscopy Details of sample preparation and characterizationwere already presented in the literature [20]

22 Raman Apparatus Raman spectra were measured withmicro-Raman spectrometer MonoVista 2750i (Spectroscopyamp Imaging GmbH Germany)

Microscopy part of the spectrometer is based on flu-orescence microscope type BX-51 (Olympus Japan) Themicroscope is equipped with four objectives

(i) three of them (magnification 100x 50x and 20x) areworking in visible (VIS) spectral range

(ii) one objective (magnification 40x) is designed fordeep-ultraviolet (deep-UV) spectral range

Images from microscope are recorded with imaging cameraTM 2040 GE (JAI Japan) Motorized stage (Ludl ElectronicUSA) makes the following types of spatially resolved mea-surements possible

(i) line scanning along each coordinate 119909 119910 and 119911(ii) two-dimensional mapping 119909119910 119910119911 and 119909119911(iii) three-dimensional mapping 119909119910119911

Spectroscopy part of the setup is based on imagingspectrograph SpectraPro 2750i equippedwith liquid nitrogencooled spectroscopy CCD camera LN2048 times 512BIUVARSpec-10 System (Princeton Instruments USA) The camerahas maximum efficiency in UV spectral range The spectro-graph has three diffraction gratings

(i) two of them (1800 groovesmm and 2400 groovesmm) are blazed in visible spectral range

(ii) one grating (3600 groovesmm) is blazed in ultravio-let

Large focal length of the spectrograph (750mm) allows highspectral resolution combinedwith single pass of the radiationthrough the spectrograph The spectral resolution of theapparatus is equal to about 01 cmminus1 for VIS spectral rangeand about 1 cmminus1 in deep-UV

In the case of visible excitation the combination ofobjective with magnification equal to 100x and grating with2400 groovesmm was used The combination of deep-UVobjective and grating with 3600 groovesmm was applied torecord the spectra excited in deep-UV

As excitation sources two continuous work (CW) laserswere used Raman scattering inVIS spectral rangewas excitedwith Ar+ laser INNOVA 90C FRED (Coherent Inc USA)In particular the line 488 nm was used Deep-UV excitation

was done by means of semiconductor laser FQCW-266-10(CryLas GmbH Germany) The wavelength of laser line wasequal to 266 nm

Thepower of the excitation light was not larger than 1mWon the sample for each excitation wavelengthThe position ofone-phonon Si line depends on the temperature in particularit is shifted by about 2 cmminus1 towards smaller values of Ramanshift if the temperature increases from room temperature to100∘C [22] The power of exciting light should be set withinthe range which makes it possible to avoid local heating ofthe sample caused by absorption of the exciting light Appliedin this work power of exciting light is adjusted within therange used for investigation of the stress in semiconductorsFor example the power of the exciting light on the sampleused for stress mapping in porous Si microcapsules was equalto 1mW [23] The power of laser line on the sample usedin investigation of self-heating effect in electronic devices isequal even to 5mW [7 24 25]

23 Model As was mentioned in Introduction variation ofthe power density results in changes of thickness of thematerial from which the scattering is collected The type ofmeasurement called line scan z allows to record the seriesof Raman spectra for different power density of irradiationlight on SiSiO

2interfaceThis set of different values of power

density is reflected in variation of thickness of material fromwhich Raman signal is collectedThis thickness will be calledeffective absorption depth 120575eff

The concept of tuning of the thickness of material fromwhich Raman signal is collected is based on the fluores-cence measurement in reflection This concept was appliedin Multifunctional Spectrofluorimetric System designed byJasny (ldquofocusing and collimating system type Ardquo) [26] Inthis configuration angle between optical axes of exciting andanalyzing setup was equal to 30∘ It means that the lumines-cence was measured in the configuration similar to the backscattering Measurements were performed in solutions Thethickness of the layer where the excitation light was effectivelyabsorbed was determined by concentration of absorbingagent because the intensity of exciting light was constantIn the case of high concentration of absorbing species thethickness absorbing layer was tended tomonomolecular film

In the case of Raman scattering in solid material (ieSi) excited with laser line the absorption is determined bythe wavelength of exciting light and it is constant for eachwavelength In order to tune the effective absorption depththe power density of the irradiation light must be variedTuning of the power density of exciting light in the caseof constant absorption results in the same effect as tuningof the absorption for constant power density In particularthe thickness of the material where the incoming light iseffectively absorbed is changed Important is the questionabout the lower limit of the thickness of the film where allphotons from incoming light should be absorbed This layershould have the same properties as wholematerial In the caseof crystalline media the smallest part of material which hasthe same properties as large crystals is defined by unit cellIt means that in the case of small density of irradiation light


the thickness of absorbing layer should be compared withdimension of unit cell of the investigatedmaterial In the caseof crystalline silicon this dimension is equal to about 05 nm

The crucial problem in quantitative data analysis is thedevelopment of the model which allows to calculate valuesof effective absorption depth resulting from changes of powerdensity of irradiation light on the sample The absorptionof exciting and scattered light must be taken into accountThe model which links the variation of power density ofirradiation light with effective absorption depth is presentedbelow

Let us start with short overview of basic knowledgenecessary for the development of the announced abovemathematical model The absorption of material is describedby Lambert law [27]

119868 (119897) = 1198680119890minus120572119897 (1)

where 1198680denotes the intensity of incident light 119897 is the optical

pathway through the material 119868(119897) is the intensity of the lightafter the pathway equal to 119897 and120572 is the absorption coefficientof the material In many applications the base equal to 10is used instead of exponential function In such a case theLambert law has the form

119868 (119897) = 119868010minus119861= 119868010minus120573119897 (2)

where quantity 119861 is called absorbance and 120573 denotes anextinction coefficient Lambert law can be expressed in termsof imaginary part of complex refractive index The complexindex of refraction 119899

119888has the form

119899119888= 119899 minus 119894119896 (3)

where 119899 and 119896 denote real and imaginary parts of complexrefractive index respectively Both 119899 and 119896 are functions ofwavelength The sign ldquominusrdquo in (3) results in positive value ofdamping coefficient of electric field 119896 for materials which donot amplify the light Since the intensity is proportional tothe square of electric field amplitude absorption coefficient 120572can be expressed as a function of damping coefficient 119896 by thefollowing equation

120572 =2120596119896

119888 (4)

where 120596 denotes the circular frequency and 119888 is the velocityof light Taking into account dependencies between circularfrequency 120596 frequency ] and wavelength 120582 one can present(4) in the following form

120572 =2 (2120587]) 119896

119888=4120587119888119896

120582119888=4120587119896

120582 (5)

Penetration depth is defined as thickness of absorbingmaterial which corresponds to the decrease of the quantitydescribing electromagnetic wave by 119890 times [28] Sinceintensity is important for further analysis the attentionwill befocused on parameters related to intensity of the light In sucha case the penetration depth 120575 is given by following equation

120575 =120582

4120587119896 (120582)= 120572minus1 (6)

The imaginary part of refractive index used in (6) has theform 119896(120582) in order to emphasize the fact that the dampingcoefficient is a function of wavelength Taking into accountvalues of Si damping coefficient for green lines of Ar+ laser(wavelengths of laser lines usually used in Raman exper-iments 488 nm and 514 nm) [29] one obtains penetrationdepth equal to about 07120583m The application of deep-UVexcitation (typical wavelengths of laser lines 244 nm or266 nm) reduces the value of 120575 to several dozen nanometers[29]

Now we can move to the definition of effective absorptiondepth This quantity is important in the case of micro-Ramanstudy of semiconductor substrates because it determinesthe thickness of material which is investigated Effectiveabsorption depth can be calculated fromproperties of spectralCCD camera used to record the Raman signal and thedamping coefficient 119896 The following approximation will beused in calculation of effective absorption depth due to smalldifference between wavelengths of exciting and scatteredlight the value of damping coefficient 119896 will be taken equallyfor excitation and scattering

Now we focus the attention on crystalline silicon as anexample of absorbing material The first step to determinethe effective absorption depth is to show that the thickness ofSi from which the Raman scattering is collected depends onthe number of incident photons One can express the numberof photons reaching the depth equal to 119911 by the followingequation

119899 (119911) = 1198990119890minus120572119911 (7)

where 1198990is the number of incident photons for unit area

Value 119911 = 0 corresponds to the interface between siliconsubstrate and silicon dioxide layer The maximal depthcorresponds to the thickness of material which is passed onlyby one photon 119911 = 119911max rarr 119899(119911) = 1 It means that one canchange 119911max by varying the number of incident photons 119899

0

Equation (7) can be rewritten as a condition for 119911max

119911max =ln (1198990)

120572 (7

1015840)

The condition specified by (71015840) shows that one can changethe thickness of the material which gives the contribution toRaman scattering by varying the number of incident photonsper unit area 119899

0

Let us move now to the calculation of effective absorptiondepth in the case of Raman scattering CCD cameras usedin spectroscopic measurements have 16-bit analog-digitalconversion It means the maximum intensity of the Ramanline that can be accumulated is equal to 216 = 65536 countsFurther extension of accumulation time results in saturationof line intensity It means that the maximum cannot beobtained because the upper part of the line (over 65536counts) is cutoff The intensity of scattered light 119868(119897) as afunction of thickness of material 119897 is given by followingequation

119868 (119897) = 11986801205930 int

119897

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572119897

2120572 (8)


In (8) 1198680denotes the intensity of excitation and 120593

0describes

the efficiency of the observed Raman effect Integration from0 to 119897 gives the intensity of Raman scattering measuredfrom the layer whose thickness is equal to 119897 The expressionexp(minus2120572119911) under the integral described the statistical weightof the contribution of the scattering coming from thematerialplaced at the depth equal to 119911 Factor 2 in the argument ofexponential function in (8) was introduced because scatteredlight is absorbed in the same manner as exciting light At thispoint the approximation concerning the equality of dampingcoefficient for exciting and scattered light is introduced to themodelThe intensity reaches its maximal value equal to 65536when the thickness is equal to 120575max

eff Equation (8) takes in thiscase the following form

119868 (120575maxeff ) = 11986801205930 int

120575maxeff

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572120575

maxeff

2120572

= 65536

(81015840)

In practice it is convenient to explain 120575maxeff by multiple

of value of penetration depth 120575 defined by (6) The valueof 119868(119899120575) efficiently tends to maximal value of intensity withincrease of 119899 In particular the values of 119868(119899120575)119868(120575max

eff ) ratioare equal 0865 for 119899 = 1 0982 for 119899 = 2 and 0998 forn = 3 The standard deviation of the intensity of Raman linecan be calculated from Poisson distribution because photonstatistics is based on this distributionThe standard deviationis equal to the square root of the intensity understood asa number of counts obtained for Raman shift equal tomaximum position of the line In the case of maximal valueof intensity measurable by 16-bit CCD camera the standarddeviation is equal to Δ(119868(120575max

eff )) = 256 = (65536)12 This

standard deviation is equal to about 04 of the maximummeasurable intensityThe ratio (119868(120575max

eff )minusΔ(119868(120575maxeff )))119868(120575

maxeff )

is equal to 0996 It means that 119868(119899120575) for 119899 = 3 is placedwithinthe range 119868(120575max

eff ) plusmn Δ(119868(120575maxeff ))

To sum up assuming 120575maxeff = 3120575 one obtained the

intensity of Raman scattering which differs from 119868(120575maxeff ) =

65536 by value smaller than standard deviation Δ(119868(120575maxeff ))

In the case of crystalline Si for excitationwavelength equalto 488 nm the maximum of effective absorption depth is equalto 22 120583m The change to deep-UV excitation (wavelength244 nm or 266 nm) reduces 120575max

eff for crystalline Si to the valuefrom the range between 100 nm and 200 nm

The next problem is how to link the effective absorptiondepth 120575eff with intensity of Raman line if the intensity doesnot reach value 119868(120575max

eff ) = 65536 Replacing 119897 by 120575eff in (8)one obtains the following expression

119868 (119897) = 11986801205930 int

120575eff

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572120575eff

2120572 (8

10158401015840)

Dividing (810158401015840) by (8

1015840) one obtains the intensity ratio

119868(120575eff )119868(120575maxeff )

119868 (120575eff)

119868 (120575maxeff )

=1 minus 119890minus2120572120575eff

1 minus 119890minus2120572120575

maxeff (9)

Expanding exp(minus2120572119911) in power series for 119911 = 120575eff and 119911 =120575maxeff one obtains approximate expression for intensity ratio119868(120575eff )119868(120575

maxeff )

119868 (120575eff)

119868 (120575maxeff )

=120575eff120575maxeff (9

1015840)

From (91015840) one can obtain the following expression for 120575eff

120575eff =119868 (120575eff)

119868 (120575maxeff )

120575maxeff = 3

119868 (120575eff)

119868 (120575maxeff )

120575 (10)

In (10) the obtained earlier approximation for maximum ofeffective absorption depth 120575max

eff = 3120575 was introduced

24 Measurement Methodology Two types of measurementswere performed In the case of deep-UV excitation the laserbeam was focused on the SiSiO

2interface Due to small

intensity of the signal long time of irradiation was appliedThe exposition time of single spectrum accumulation wasequal to 1 hour

The second type of measurement is called line scan zThistype of measurement was performed for VIS excitation (120582 =488 nm) The direction perpendicular to the surface of inter-face is marked with 119911 coordinate The following sequence ofsteps was necessary to perform line scan along 119911 coordinateFirst the laser beam was focused on the SiSiO

2interface

This position was assumed as 119911 = 0 Then the measurementsof Raman spectra were performed for different values of119911 coordinate The range of coordinate which was scannedspread from minus20120583m to 20120583m The difference between twosubsequent 119911 positions in other words the step of the scanwas equal to 1 120583m The exposition time for single spectrumwas equal to 1 minute

There are two important parameters of the setup whichchange when the sample is moved along optical axis fromthe position corresponding to focal spot These parametersare half-angle of the maximum cone of light collected bymicroscope objective and the power density of the laser lightexciting Raman scattering Let us now discuss how theseparameters change if the sample ismoved from focus positionby 119911 = 20 120583m

Figure 1 presents the beam path between microscopeobjective and the sample The cone of the light that canbe collected by objective is described by hyperboloid Theasymptote of the hyperboloid is defined by numerical aper-ture of the objective The numerical aperture 119873

119860is the

function of half-angle Θ of the maximum cone of light thatcan enter the microscope objective The other importantparameters of the objective are as follows

(i) 119891 focal length

(ii) 119908 working distance

(iii) Φ diameter of the entrance pupil

(iv) 21199030 diameter of the focal spot


f

w

Microscope objective

Focal plane

Shape offocused

laser beam

x

zΘ

2r0

Φ

Figure 1 Schematic presentation of laser beam focused by micro-scope objective 119891 focal length 119908 working distance 2119903

0 diameter

of the focal spot Θ half-angle of maximum cone of light collectedby microscope objectiveΦ entrance diameter of the objective and119909 119911 coordinates

Numerical aperture half-angle focal length and diameter ofentrance pupil fulfill the following equation

119873119860= sin (Θ) = sin(arctan( Φ

2119891)) (11)

Thediameter of the focal spot can be calculated fromRayleighor Sparrow [3] criterion for diffraction limit of Airy spot

21199030= 119862

120582

2119873119860

(12)

where 119862 = 1 in the case of Sparrow criterion or 119862 = 122 forRayleigh criterion

Let us start the discussion of experiment methodologyfrom half-angle Θ In the case of Olympus objective M PlanSemi-ApochromatMPLFLN 100x used in experiment param-eters 119908 and 119891 are equal to 10mm and 18mm respectivelyNumerical aperture of this objective is equal to 09 The half-angle Θ and entrance pupil diameter Φ are equal to

Θ = arcsin (119873119860) = 6416

∘

Φ = 2119891 tan (Θ) = 2119891 tan (arcsin (119873119860)) = 74mm(13)

Shift of the sample from position of focal spot towardsmicroscope objective by distance 119911 results in change of half-angle of maximum cone of the light collected by objectiveThe value of half-angle Θ1015840 for shifted sample is equal to

Θ1015840= arctan( Φ

2 (119891 minus 119911)) (14)

In the case of used objective and shift equal to 119911 = 20 120583m theangle Θ1015840 is equal to 6431∘ It means that half-angle changes

by 015∘ The value of ldquonumerical aperturerdquo1198731015840119860in the case of

being defocused by 20 120583m position of the sample is equal to

1198731015840

119860= sin (Θ1015840) = 090114 (15)

The relative change of numerical aperture caused by defocus-ing by 20120583m is equal to

120590 =

100381610038161003816100381610038161198731015840

119860minus 119873119860

10038161003816100381610038161003816

119873119860

= 00013 (16)

The relative change of numerical aperture 120590 = 013 issmaller than the standard deviation-to-signal ratio in the caseof maximum signal that can be measured with CCD camera(04)

Let us now focus the attention on the changes of spotdimension caused by defocusing The diameter of focal spot21199030calculated from Rayleigh criterion for the MPLFLN 100x

objective and laser line 488 nm is equal to 0331120583m Asreported in the literature values of focal spot should notexceed 07 120583m [3] As was mentioned above the shape oflongitudinal section of focused laser beam is described byhyperbola

1199092

1198862minus1199112

1198872= 1 (17)

Let us take into account the most unfavorable option itmeans 119886 = 119903

0asymp 035 120583m Parameter 119887 can be calculated

from the slope of the hyperbola asymptote This slope isdefined by half-angle of maximum cone of the light detectedby objective in other words by numerical aperture 119873

119860 In

the case of assumed diameter of focal spot the value of 119887parameter is equal to

119887 = 1199030tan (90∘ minus Θ) asymp 0169 120583m (18)

Since power density changes in the same way as the area ofthe spot the ratio 11990921199032

0determines changes of power density

as a function of shift from position of focal spot 119911 (for focalspot 119911 = 0)

1199092

1199032

0

= 1 +1199112

1198872 (19)

In the case of defocusing by 119911 = 20 120583m the power density ofexciting light decreases (11990921199032

0) = 14005 times which means

by five orders of magnitudeTo sum up the shift of the sample along the optical axis

of microscope objective from focal plane by 20 120583m results in

(i) negligible change of half-angle of maximum cone ofthe light collected by objective

(ii) decrease of the power density of exciting light by fiveorders of magnitude

It should be also emphasized that assumption (in the calcula-tion of power density diameter of focal spot) introduces thecondition which is significantly unfavorable in comparisonwith Rayleigh of Sparrow criteria


It should be also mentioned that standard technique usedto decrease the intensity of cw laser light does not offer thisrange of intensity tuning as defocusing Standard methodused to decrease cw laser line intensity is based on highpolarization degree of this light Introducing linear polarizerinto the laser beam makes it possible to vary the intensity viachanging the angle 120595 between direction of polarizer axis andthe direction of the laser beam polarization The changes ofintensity are in this case described by cos2(120595) (Malusrsquo law)The change of angle 120595 between 0∘ and 89∘ corresponds to thedecrease of the light intensity by 3283 times by three ordersof magnitude This value is significantly smaller than thedecrease obtained from defocusing of laser beam Moreoverin the case of polarizer application some values of 120575eff placednear the interface are not available for experimental studyThese values of 120575eff are extremely interesting from the pointof view of manufacturing technology of todayrsquos electronicdevices

25 Data Analysis Data obtained from excitation in differentspectral ranges were focused on different type of informationThe spectra recorded for visible excitation were focused onone-phonon Si line In the case of deep-UV excitation theattention was focused on Raman scattering generated in SiO

2

layer Because of this different procedures were applied toanalyze the data recorded for excitation in different spectralranges

In order to obtain the parameters like maximum positionand FWHM of one-phonon Si line the following mathemat-ical procedure was applied In the first step of the procedureall signals except silicon line were treated as backgroundThis backgroundwas removedwith spline polynomials Afterbackground removal Lorentzian profile was fitted to theone-phonon Si line Maximum position FWHM and theintensity of one-phonon Si line were taken as equal to thefollowing parameters of fitted Lorentzian function center ofthe profile its FWHM and the height

In the case of ultraviolet Raman spectrum the attentionwas focused on the scattering generated in silicon dioxidelayer In such a case one-phonon Si line disturbs the signalcoming from SiO

2 This line was reconstructed with fitting

Lorentzian profile Fitted function was subtracted from themeasured deep-UV Raman spectra in order to remove one-phonon Si line This procedure of removal of one-phononSi line was already discussed in the literature [20] Obtainedfrom subtraction spectrum was assigned to scattering fromsilicon dioxide layer Broad bands are generated in the part ofthe layer which has an amorphous structureThis assignmentwas discussed in detail previously [20] In this work narrowlines which appear on the background generated in amor-phous form of SiO

2were compared with data reported for

different crystalline forms of silicon dioxide

3 Results

Figure 2 presents the analysis of one-phonon Si line obtainedfrom line scan z Maximum position of the line is presented

Stre

ss (G

Pa)

0010 0100 10000001Effective absorption depth 120575eff (120583m)

5205052055520605206552070520755208052085

Ram

an sh

ift(c

mminus

1 )


minus04

minus02

0

02

Maximum position of one-phonon silicon line as a function of effective absorption depth

(a)

Inte

nsity

(au

)


286

288

290

292

294

Ram

an sh

ift(c

mminus

1 )

001 01 10001

Effective absorption depth 120575eff (120583m)

0105

2 times 1053 times 105

of effective absorption depthFWHM of one-phonon silicon line as a function

(b)

Figure 2 Raman data obtained with excitation in visible spectralrange (a) position of maximum of one-phonon Si line as a functionof effective absorption depth and (b) FWHM of one-phonon Si lineas a function of effective absorption depth Insets present followingfunctions of effective absorption depth panel (a) mechanical stressin silicon calculated from position of one-phonon Si line and panel(b) intensity of the one-phonon Si line

in part (a) and the analysis of FWHM of the line is shown inpart (b) of the figure

The main plot in panel (a) shows the maximum positionof one-phonon Si line as a function of effective absorptiondepth The position of the maximum changes with 120575eff in thefollowing way

(i) for values of 120575eff below 4 nm the linear decreaseof maximum position with the increase of 120575eff isobserved the range of Raman shift where the maxi-mumposition is changed spreads from 52083 cmminus1 to52057 cmminus1 and the exception is the first point whichdoes not fit to the behavior presented by other points

(ii) for 120575eff from the range between 4 nm and 90 nm themaximumposition reaches the plateau and the valuesof the parameter are placed between 52055 cmminus1 and52058 cmminus1

(iii) for 120575eff larger than 90 nm maximum positionincreases asymptotically to the limit equal to52065 cmminus1

The inset in panel (a) shows the stress calculated from thesimple model for uniaxial stress [4 30]

The main panel in part (b) of Figure 2 shows FWHMas a function of effective absorption depth This dependencemay be treated as constant in the whole range of 120575eff Thevalues of FWHM are placed within the range (289 plusmn 002)


454

393

3543

3532

1

Si5197

cmminus1

Raman scattering from SiSiO2 120582exc = 266nm

Inte

nsity

(au

)

000204060810

400 600 800 1000 1200200Raman shift (cmminus1)

Inte

nsity

(au

)

0005

0109

1


Measured spectrumFitted Lorentzian profile

Figure 3 Raman spectrum of silicon dioxide layer placed on siliconsubstrate after removal of one-phonon Si line Maxima of narrowlines assigned to crystalline forms of silicon dioxide are given inthe main plot (blue numbers) The maximum of one-phonon Siline is also given in main plot (black number) The inset presetsthe spectrum before removal of one-phonon Si line (black) andLorentzian function used for reconstruction of silicon line (red)

cmminus1 The inset in Figure 2(b) presents the intensity as afunction of effective absorption depth For 120575eff smaller than100 nm intensity increases with the value of 120575eff For largerpenetration depths than 100 nm stabilization of the intensityis observed

The deep-UV Raman spectrum of SiO2layer is presented

in Figure 3 In themain plot one-phonon Si linewas removedFitted to one-phonon Si line Lorentzian profile was sub-tracted from the spectrum (as described in previous chapter)The maxima of narrow lines which are compared with datareported for crystalline forms of silicon dioxide are given inthe figure The inset in Figure 3 shows the spectrum beforethe removal of Si one-phonon line together with Lorentzianfunction used for reconstruction of one-phonon Si line Inorder to present the spectrum coming from SiO

2layer the

break in ordinate axis was introduced in the inset

4 Discussion

Before discussion of the spectroscopic data obtained in thiswork we will sum up the information about SiSiO

2interface

and its close vicinity The data from the literature describedhere will be used to analyze the results of Raman studyreported in this work

The transition area between crystalline Si (c-Si) andamorphous SiO

2(a-SiO

2) was the subject of interest already

in the seventies of last century [31] The most simple modelof the interface assumed step-like transition between c-Siand a-SiO

2 Properties of this type of interface were the

subject of ab initio theoretical study [32] The structure of a-SiO2was simulated by means of 120573-cristobalite structure [32]

120573-Cristobalite is one of the crystalline forms of SiO2 The

results obtained from photoemission spectroscopy suggestedgradual type of transition between a-SiO

2and c-Si [31] The

transition nonstoichiometric layer was marked as SiO119909 The

thickness of this layer was estimated as equal to 4 AProposed types of SiSiO

2interfaces were divided into

three categories due to the intermediate structure between a-SiO2and c-Si [33]

(i) step-like interface means no intermediate layerbetween a-SiO

2and c-Si

(ii) with intermediate SiO2layer the intermediate layer

is an ordered structure in which crystallographicparameters can match the parameters of c-Si

(iii) with intermediate SiO119909layer in this case the interme-

diate layer is a mixture of silicon and silicon dioxide

Authors of [33] analyzed following issues related to structureof transition area between c-Si and a-SiO

2

(i) the data obtainedwithHigh-ResolutionTransmissionElectron Microscopy (HRTEM)

(ii) the results of theoretical calculations(iii) compliance of crystalline structure of different forms

of silicon dioxide and c-Si

They came to following conclusions

(i) the transition between a-SiO2and c-Si should have

the gradual character(ii) the thickness of the transition layer should be equal to

5 A and its structure should be similar to tridymite(iii) cristobalite as structure of transition layer should

be excluded due to large mismatch of crystallinestructure parameters of cristobalite and c-Si thedifferences reach even 40 of parameter values

The structure of the transition area between a-SiO2and

c-Si was also investigated by means of spectroscopic ellip-sometry [34] Authors of [34] compared experimental datacovering VIS and UV spectral range with different models ofthe system a-SiO

2interfacec-Si They came to the following

conclusion the interface should have gradual character andits thickness should be equal to 7 A The model assumingstep-like transition between a-SiO

2and c-Si is a good starting

point for investigation of interface structure [35] Howeverthe statistics coming out from experimental data point togradual type of interface It means that intermediate layershould have finite and nonzero thickness [35] In other wordsexperimental data suggest gradual character of the transitionbetween a-SiO

2and c-Si

Application of Core-Level Photoemission Spectroscopy(CLPS) confirmed the presence of Si atoms in intermediate-oxidation state in the vicinity of interface [36] The presenceof atoms corresponding to following oxidation states Si1+Si2+ and Si3+ points to gradual character of the interfaceIn particular atoms Si3+ should not be observed in the caseof step-like transition between a-SiO

2and c-Si [36] Authors

of [36] proposed that transition area (interface) is composedof two sublayers One sublayer should be placed in siliconsubstrate In this part Si atoms in intermediate-oxidation stateshould be present The other component of interface shouldextend up to 30 A into the silicon dioxide layer This area ofSiO2should contain the material which has higher density

than the a-SiO2 Also the energy factor related to the stress

appearing due to interaction between a-SiO2layer and c-Si

substrate suggests gradual type of interface [36] Step-liketransition should create larger stress than the transition areahaving finite and nonzero thickness The interface modelwhich includes Si atoms in intermediate-oxidation state is


more favorable than step-like transition due to energeticconditions on interface [37] Energy related to mismatchof crystalline structures of a-SiO

2and c-Si is significantly

smaller in the case of models assuming gradual transitionbetween crystalline semiconductor substrate and amorphousdielectric layer [37]

Simulation of the images obtained from HRTEM givesresults consistent with experimental data if the gradual typea-SiO

2c-Si interface is assumed [38] The surface of ⟨100⟩

oriented c-Si is not smooth if the interface has finite andnonzero thickness [37 38] If smooth c-Si surface is assumedthe simulated interface becomes step-like The attempt tosimulate more simple interface which takes into accountthe data obtained from deep electron shells results in thestructure called sawhorse [39] Sawhorse consists of two Siand six O atoms SindashSi bond is placed parallel to the interfaceplane Each Si atom is bonded to threeO atomsThe sawhorseis bounded to c-Si and a-SiO

2via O atoms To sum up

the attempt to simplify the interface leads to at least onelayer of sawhorses However according to discussion in [39]it proposed that model does not take into account defectsIntroducing the defects into the model will complicate it andshould increase the thickness of the intermediate layer

Investigation of morphology of c-Si ⟨100⟩a-SiO2inter-

face by means of Scanning Tunneling Microscopy (STM)showed strong disorder in Si structure in the vicinity ofinterfaceThis disordered Si built the layer which is parallel tothe interfaceThe thickness of this layer is of the order of 100 A[40] Ion bombardment was used to disclose the interfaceThe disclosed surface of c-Si is not smoothThe hillocks werefound on disclosed silicon surface Horizontal dimension ofobserved hillocks is equal to about 50 AThe typical height ofhillocks is equal to about 10 A [40]

Ellipsometry investigation of ⟨100⟩ oriented Si wafersafter oxidation at different condition showed that the thick-ness of transition area between silicon substrate and oxidelayer depends on the condition of oxidation process [41] Asa model of the transition layer the mixture of amorphoussilicon (a-Si) with SiO

2was assumed The thickness of this

interface was of the order of 1 nm The other result reportedin [41] is related to contribution of the signal coming frominterface to the whole ellipsometry signal This contributiondecreases with the increase of the thickness of SiO

2layerThis

observation led authors of [41] to the conclusion that SiO2

layer can be treated as structure composed of two sublayersOne sublayer with high refractive index is placed in thevicinity of the substrate This sublayer can be treated as thispart of interface (transition area) which is extended into SiO

2

layer [36] The second sublayer is composed of a-SiO2and

can be treated as quasibulk material Authors of reference[41] came to the conclusion that the interface has certainroughness This roughness does not depend on the type ofc-Si surface which is oxidized

Results obtained by means of Deep Level Transient Spec-troscopy (DTLS) suggest the similarity between a-SiO

2c-Si

interface and amorphous silicon doped with hydrogen (a-SiH) [42]

To sum up transition area between crystalline siliconsubstrate and amorphous silicon dioxide layer has gradual

character This layer in the literature marked with SiO119909

can be treated as a mixture of amorphous or polycrystallinesilicon with silicon dioxide This transition layer can bedivided into two sublayersThe sublayer placed in the vicinityof c-Si wafer is characterized by the dominance of siliconstructuresThe other sublayer is composed of silicon dioxidehowever the density of the dioxide in this sublayer shouldbe larger in comparison with a-SiO

2 The optimization of

the energy in transition region between c-Si and a-SiO2is

the reason for the presence of SiO119909layer and its segregation

into two sublayers one with predominance of silicon and theother with oxide structures Similar segregation of SiO

119909layer

into two sublayers is also observed for homogeneous SiO119909

layer after Rapid Thermal Annealing [43] One sublayer isdominated by higher concentration of Si structures in theother sublayer the main component is SiO

2

To discuss obtained data in this work in terms of interface(transition area) that consists of two sublayers analysis twotypes of Raman signal must be taken into account The firstproblem to be discussed is the dependence between shift ofone-phonon Si line position and structural changes of thesubstrate The other problem to analyze is the presence ofthe trace of crystalline SiO

2in Raman scattering generated

in dioxide layer Before coming to the obtained results inthis work let us first sum up the literature data necessary toassign measured Raman spectra to different form of siliconand silicon dioxide The changes of the Si and SiO

2related

to different values of absorption depth will be correlated withthe literature data concerning transition between c-Si and a-SiO2reported above

At first the dependence between one-phonon line andsilicon structure will be reported

Transition from monocrystalline Si to polycrystallinesilicon is observed in Raman spectrum as a shift of one-phonon line towards smaller values of Raman shift [44]The shape of the line becomes asymmetric [44] The limitof these structural changes is defined by a-Si In the case ofa-Si the maximum position of one-phonon line is equal toabout 480 cmminus1 FWHMof this line is many times larger thanthe FWHM of c-Si [45] Detailed study of the dependencebetween the type of silicon (crystalline polycrystalline oramorphous) and position of one-phonon line was done for Silayer deposited on different substrates Presence of all typesof material in particular c-Si polycrystalline Si and a-Siresults in complicated shape of Raman line because the line iscomposed of three components crystalline polycrystallineand amorphous [46] The position of crystalline componentcan also change in the range of about 2 cmminus1 For exampleas reported in [46] maximum of Raman line observed for c-Si changes from 52091 cmminus1 to 51917 cmminus1 if concentrationof defects in crystalline structure increases Authors of [46]determined the position of one-phonon Raman line for poly-crystalline Si as equal to about 510 cmminus1 and as mentionedabove for a-Si as equal to about 480 cmminus1

The other factor that influences the position of maximumof one-phonon line is the admixture gas [46] Generallyamorphous components are shifted towards smaller values ofRaman shift crystalline to larger An important parameter


related to presence of doping gas is its concentration Smallvalues of hydrogen concentration improve the quality of crys-talline structure Large concentration produces an oppositeeffect Authors of [46] also calculated the stress inducedby doping agent They used the formula developed for a-Si by Anastassakis Similar results were obtained for siliconmicrocapsules containing porous silicon [23] Authors of[23] assumed that one-phonon Si line is a mixture of twocomponents

(i) polycrystalline which has the maximum of one-phonon line placed between 515 cmminus1 and 520 cmminus1

(ii) amorphous which has the maximum of one-phononline placed between 495 cmminus1 and 510 cmminus1

The stress inmicrocapsules was calculated within the approx-imation of uniaxial stress As a reference it means statewithout stress the maximum position for monocrystalline Siwas assumed in particular 5203 cmminus1

Properties of polycrystalline Si layer depend on its thick-ness and the deposition temperature In the case of poly-crystalline Si film deposited on monocrystalline Si substratethe structure of the layer depends on the distance from thesubstrate [47] If the deposition temperature is equal to 620∘Cmaximum position changes gradually with the distancefrom the substrate or thickness of the layer In particularmaximum position of one-phonon Si line moves towardssmaller values of Raman shift if the thickness of the layer orthe distance frommonocrystalline Si substrate increasesThedependence of maximum position upon the distance fromthe monocrystalline substrate is attributed to the changes ofcrystal dimension This type of behavior is called phononconfinement effect and can be described as a result oflimitation of phonon propagation area caused by small sizeof crystals [48] In particular if average dimension of the Sicrystal decreases from49 nm to 22 nm themaximumof one-phonon line shifts from 5197 cmminus1 to 5177 cmminus1 Describedabove behavior is not observed if the deposition temperatureis from the range between 570∘C and 590∘C It suggeststhat gradual change of crystal dimension with the distancefrommonocrystalline substrate is caused by temperatureThethreshold temperature which activates the process is equal toabout 600∘C

Thepresence of compressive stress in polycrystalline formis caused by partial oxidation of polycrystalline Si layer [49]Detailed investigation of partial oxidation of polycrystallineSi layer showed the correlation between the stress and thecrystal dimensionThe effect is important in the case of smallgrains [50] Author of [50] showed the shift of one-phonon Siline corresponding to compressive stress in the case of grainswhose diameter is equal to 50 A If the size of crystallinegrains increases to 300 A the shift of maximum position ofone-phonon Si line is not observed It means that increaseof grain dimension over certain limit removes compressivestress caused by local oxidation [50]

Authors of [49] divided silicon into three categoriesdue to maximum position of one-phonon line crystallinepolycrystalline and amorphous Polycrystalline Si layers arecharacterized by the presence of the stress which cannot be

removed even by means of thermal annealing The valueof this nonremovable stress does not exceed 200MPa [51]The shift of maximum position of one-phonon silicon linetowards smaller values of Raman shift observed for polycrys-talline Si is treated as a trace of tensile stress [52 53] Positionof the maximum recorded for c-Si was used as a referenceThe type of stress in polycrystalline Si layer depends also onthe substrate [54] If glass plate is used as a substrate thermaleffects related to cooling of the sample lead to tensile stress[54] Application of sapphire as a substrate changes the typeof stress to compressive [54]

The other point to be discussed is related to the spec-trum presented in Figure 3 in particular to the origin ofnarrow lines placed on the background composed of Ramanscattering assigned to vibrations in a-SiO

2layer [20] Since

these lines are narrow they should be compared with Ramanspectra reported for crystalline forms of silicon dioxide Theoxide sublayer of the interface between amorphous silicondioxide and crystalline silicon [36] should be composed ofSiO2which has the structure similar to crystalline silicon

dioxide [21] Since the crystal-like sublayer is thin observednarrow lines should be compared with strong lines of crys-talline forms of SiO

2 Let us now complete the information

necessary for discussion of the results obtained in this workThe following strong lines of crystalline forms of silicon

dioxide are placed in the same range of Raman shift as themain band of a-SiO

2

(i) tridymite 355 cmminus1 403 cmminus1 422 cmminus1 449 cmminus1and 457 cmminus1 [55]

(ii) cristobalite 380 cmminus1 426 cmminus1 [56] 421 cmminus1 [55]and 420 cmminus1 [57]

(iii) 120572-quartz 465 cmminus1 [55](iv) coesite 522 cmminus1 [55] and 521 cmminus1 [58](v) moganite 449 cmminus1 463 cmminus1 and 501 cmminus1 [55]

Due to strong coincidence between one-phonon line gener-ated in c-Si and line reported for coesite this crystalline formof SiO

2must be excluded from the discussion of deep-UV

Raman scatteringLet us start the discussion of Raman data obtained in this

work fromVIS spectral rangeThe crucial point is the relationbetween position of one-phonon Si line and the structure ofsilicon

Changes of maximum position of one-phonon Si linewith the effective absorption depth reflect changes of siliconstructure and influence of oxygen which can penetrate into Sisubstrate In the range of effective absorption depth up to 6 nmpolycrystalline or crystalline formwith large concentration ofdefects is expected

Linear decrease of the maximum position from5208 cmminus1 to 52055 cmminus1 observed for 120575eff below 2 nmshould be caused by partial oxidation of Si substrate in thisrange of effective absorption depth Oxygen diffused intothe Si substrate due to polycrystalline structure or largeconcentration of defects This oxygen caused local oxidationof silicon The increase of molar volume between SiO

2and

Si results in local stress which has compressive character


The amount of oxygen that can penetrate into the substratedecreases with the distance from the interface This effectis reflected in Raman spectrum as a decrease of maximumposition of one-phonon Si line (see Figure 2(a)) The effectobserved in this work is similar to local oxidation ofpolycrystalline silicon reported in [50]

For 120575eff from the range between 2 nmand 6 nmmaximumposition of one-phonon Si line is stabilized The value ofthis plateau is equal to 52055 cmminus1 This position of Si linesuggests that the structure should have crystalline characterwith significant concentration of defects [49] Polycrystallineform should be excluded because in such a case the position ofone-phonon Si line should be shifted by several cmminus1 towardssmaller values of Raman shift In the case of polycrystallineform of silicon the precise position of maximum of one-phonon line is a function of grain dimension [46 48]

For 120575eff larger than 6 nm the asymptotic increase of max-imum position from 52055 cmminus1 to 52665 cmminus1 is observedThis behavior can be interpreted as gradual reduction of ten-sile stress caused in crystalline form of silicon by interactionwith dioxide layer The asymptotic position 52065 cmminus1 isequal to themean value ofmaximumposition of one-phononSi line calculated from data reported in the literature [4 4550 59 60] As reported in the literature values of maximumposition of one-phonon line observed for crystalline siliconare placed in the range between 5203 cmminus1 and 521 cmminus1

FWHM observed for different values of 120575eff is placed inthe range between 287 cmminus1 and 291 cmminus1 No unequivocaltendency in the dependence between FWHM and 120575eff can beobserved Because of this FWHM can be treated as constantand equal to (289 plusmn 002) cmminus1 Maximum deviation frommean value equal to 002 cmminus1 is significantly smaller thanspectral resolution of the apparatus which is equal to about01 cmminus1 The mean value of FWHM equal to 289 cmminus1 is inagreement with typical values reported for crystalline form ofSi [50 59]

To sum up changes of one-phonon Si line in the vicinityof the border between a-SiO

2and c-Si are influenced by three

factors

(i) stress generated due to differences in molar volumebetween silicon and dioxide arising due to siliconoxidation

(ii) structure of Si wafer in the vicinity of the borderbetween substrate and oxide layer

(iii) effects caused by oxygen diffusion into the thin siliconlayer placed in the vicinity of the border betweensilicon dioxide layer and silicon wafer

Let us move now to the discussion of the results obtainedfrom deep-UV excitation As was mentioned before narrowlines placed on the background composed of bands assignedto a-SiO

2should be compared with data reported for crys-

talline forms of silicon dioxide Lines 321 cmminus1 and 335 cmminus1have no equivalents among strong lines reported for differentcrystalline forms of SiO

2These lines (321 cmminus1 and 335 cmminus1)

have the best correlationwith followingweaker lines reportedfor different crystalline forms of SiO

2 330 cmminus1 reported for

tridymite [55] 328 cmminus1 observed for coesite [58] and with317 cmminus1 present in spectra recorded formoganite [55] Otherlines presented in Figure 3 have following correlation withstrong lines reported in the literature for different crystallineforms of silicon dioxide

(i) line with maximum at 354 cmminus1 has the best correla-tion with line centered around 355 cmminus1 reported fortridymite

(ii) line with maximum at 393 cmminus1 is placed betweenlines 380 cmminus1 and 403 cmminus1 reported for cristobaliteand tridymite respectively

(iii) line with maximum at 454 cmminus1 has best correlationwith

(a) lines 449 cmminus1 and 457 cmminus1 reported fortridymite

(b) line 449 cmminus1 recognized in moganite Ramanspectra

It should be emphasized that the discussed above lines354 cmminus1 393 cmminus1 and 454 cmminus1 can be correlated withstrong lines reported for tridymite Tridymite and crystallinesilicon show the smallest mismatch between crystallineparameters [33] This results in favorable energy conditionsin the transition area between a-SiO

2and c-Si

Line 454 cmminus1 is placed in the same range of Raman shiftas bands observed for Si nanocrystals [61] The conditions ofsample preparation in [61] were conductive for creation ofnanocrystalline Si grains In particular thermal annealing ofthe sampleswas performed at 1200∘CThe time of this anneal-ing was equal to 2 hoursThe surface oxidation of Si substrateis rapid process The time necessary for manufacturing isbelow 1minute Itmakes the condition for diffusion of Si atominto SiO

2layer unfavorable so the line withmaximumplaced

at 454 cmminus1 should be assigned rather to SiO2crystalline form

compared to Si nanocrystals

5 Summary

The behavior of Raman spectra shows complex structuralchanges in the transition area between amorphous silicondioxide and crystalline silicon This interface (transitionarea) has gradual character as was suggested on the basisof experimental techniques like HRTEM ellipsometry andCLPS as well as on the basis of theoretical calculations [33ndash36]

The other important conclusion coming from analysisis the segregation of the interface into two sublayers Thesublayers can be called oxide sublayer and silicon sublayerRaman spectra registered for visible excitation point to crys-talline silicon with large concentration of structural defectsor polycrystalline form of silicon as a main component ofsilicon sublayer of interface Oxygen diffusion into siliconsublayer is observed as gradual change of one-phonon linemaximum position with change of effective absorption depthExcited in ultraviolet spectral range Raman scattering sug-gests the presence of oxide sublayer in the area of interface


The structure of silicon dioxide placed within this sublayershould be similar to tridymite This is in agreement with theanalysis of the mismatch between the crystalline structure ofsilicon and different forms of crystalline silicon dioxide [33]

This work presents also the methodology of the investi-gation that makes possible the extraction of the informationfrom thin layer near the border between silicon dioxide andsilicon The key property that makes this extraction possibleis the absorption of the exciting radiation by material understudy By variation of power density of the exciting lightthe effective absorption depth may be changed In this waythe signal from different parts of the studied sample canbe recorded An important point of the investigation is thedevelopment of the model that makes link measured Ramanscattering possible with the effective absorption depth As aresult the analysis of material properties as a function ofabsorption depth is possible

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R Lai X B Mei W R Deal et al ldquoSub 50 nm InP HEMTdevice with Fmax greater than 1 THzrdquo in Proceedings of the IEEEInternational Electron Devices Meeting (IEDM rsquo07) pp 609ndash611IEEE Washington DC USA December 2007

[2] K Krol M Sochacki M Turek et al ldquoInfluence of nitrogenimplantation on electrical properties of AlSiO

24H-SiC MOS

structurerdquo Materials Science Forum vol 740ndash742 pp 733ndash7362013

[3] A Sarua J Hangfeng M Kuball et al ldquoIntegrated micro-Ramaninfrared thermography probe for monitoring of self-heating in AlGaNGaN transistor structuresrdquo IEEE Transac-tions on Electron Devices vol 53 no 10 pp 2438ndash2447 2006

[4] I de Wolf ldquoMicro-Raman spectroscopy to study local mechan-ical stress in silicon integrated circuitsrdquo Semiconductor Scienceand Technology vol 11 no 2 pp 139ndash154 1996

[5] S J Harris A E OrsquoNeill W Yang et al ldquoMeasurement ofthe state of stress in silicon with micro-Raman spectroscopyrdquoJournal of Applied Physics vol 96 no 12 pp 7195ndash7201 2004

[6] L-Y Yang X-Y Xue K Zhang X-F Zheng X-H Ma andY Hao ldquoChannel temperature determination of a multifingerAlGaNGaN high electron mobility transistor using a micro-Raman techniquerdquo Chinese Physics B vol 21 no 7 Article ID077304 2012

[7] G Zhang S Feng J Li Y Zhao and C Guo ldquoDetermination ofchannel temperature for AlGaNGaN HEMTs by high spectralresolution micro-Raman spectroscopyrdquo Journal of Semiconduc-tors vol 33 no 4 Article ID 044003 2012

[8] C J de Grauw N M Sijtsema C Otto and J Greve ldquoAxialresolution of confocal raman microscopes gaussian beamtheory and practicerdquo Journal of Microscopy vol 188 no 3 pp273ndash279 1997

[9] P Borowicz A Kuchuk Z Adamus et al ldquoVisible and deep-ultraviolet Raman spectroscopy as a tool for investigation ofstructural changes and redistribution of carbon in ni-based

ohmic contacts on silicon carbiderdquo ISRN Nanomaterials vol2012 Article ID 852405 11 pages 2012

[10] K C Chang N T Nuhfer L M Porter and Q WahabldquoHigh-carbon concentrations at the silicon dioxide-silicon car-bide interface identified by electron energy loss spectroscopyrdquoApplied Physics Letters vol 77 no 14 pp 2186ndash2188 2000

[11] W Lu L C Feldman Y Song et al ldquoGraphitic features on SiCsurface following oxidation and etching using surface enhancedRaman spectroscopyrdquoApplied Physics Letters vol 85 no 16 pp3495ndash3497 2004

[12] Y Sasaki Y Nishina M Sato and K Okamura ldquoRaman studyof SiC fibres made from polycarbosilanerdquo Journal of MaterialsScience vol 22 no 2 pp 443ndash448 1987

[13] A Gavrikov A Knizhnik A Safonov et al ldquoFirst-principles-based investigation of kinetic mechanism of SiC(0001) dryoxidation including defect generation and passivationrdquo Journalof Applied Physics vol 104 no 9 Article ID 093508 2008

[14] A C Ferrari and J Robertson ldquoInterpretation of Raman spectraof disordered and amorphous carbonrdquo Physical Review BmdashCondensed Matter and Materials Physics vol 61 no 20 ArticleID 14095 2000

[15] J C Burton L Sun F H Long Z C Feng and I TFerguson ldquoFirst- and second-order Raman scattering fromsemi-insulating 4H-SiCrdquo Physical Review B vol 59 no 11 pp7282ndash7284 1999

[16] W Windl K Karch P Pavone et al ldquoSecond-order Ramanspectra of SiC experimental and theoretical results from abinitio phonon calculationsrdquo Physical Review B vol 49 no 13pp 8764ndash8767 1994

[17] P Borowicz T Gutt T Małachowski and M Latek ldquoCarbonicinclusions on SiCSiO

2interface investigated with Raman

Scatteringrdquo Diamond amp Related Materials vol 20 no 5-6 pp665ndash674 2011

[18] P A Temple and C E Hathaway ldquoMultiphonon Ramanspectrum of siliconrdquo Physical Review B vol 7 no 8 pp 3685ndash3697 1973

[19] A Chabli ldquoOptical characterization of layers for silicon micro-electronicsrdquo Microelectronic Engineering vol 40 no 3-4 pp263ndash274 1998

[20] P Borowicz M Latek W Rzodkiewicz A Łaszcz A Czer-winski and J Ratajczak ldquoDeep-ultraviolet Raman investigationof silicon oxide thin film on silicon substrate versus bulkmaterialrdquo Advances in Natural Sciences Nanoscience amp Nan-otechnology vol 3 no 4 Article ID 045003 2012

[21] A G Revesz and H L Hughes ldquoThe structural aspects ofnon-crystalline SiO

2films on silicon a reviewrdquo Journal of Non-

Crystalline Solids vol 328 no 1ndash3 pp 48ndash63 2003[22] V A Volodin and V A Sachkov ldquoImproved model of optical

phonon confinement in silicon nanocrystalsrdquo Journal of Exper-imental and Theoretical Physics vol 116 no 1 pp 87ndash94 2013

[23] D Naumenko V Snitka M Duch N Torras and J EsteveldquoStress mapping on the porous silicon microcapsules by Ramanmicroscopyrdquo Microelectronic Engineering vol 98 pp 488ndash4912012

[24] Y Ohno M Akita S Kishimoto K Maezawa and T MizutanildquoTemperature distributions in AlGaNGaN HEMTs measuredby micro-Raman scattering spectroscopyrdquo Physica Status Solidi(C) no 1 pp 57ndash60 2002

[25] S Rajasingam J W Pomeroy M Kuball et al ldquoMicro-Ramantemperature measurements for electric field assessment inactive AlGaN-GaN HFETsrdquo IEEE Electron Device Letters vol25 no 7 pp 456ndash458 2004


[26] J Jasny ldquoMultifunctional spectrofluorimetric systemrdquo Journal ofLuminescence vol 17 no 2 pp 149ndash173 1978

[27] N V Tkachenko ldquoIntroductionrdquo inOptical Spectroscopy Meth-ods and Instrumentation chapter 1 pp 2ndash5 Elsevier 2006

[28] M Born and E Wolf ldquoOptics of metalsrdquo in Principles ofOptics Electromagnetic Theory of Propagation Interference andDiffraction of Light chapter 13 p 614 Pergamon Press 1970

[29] M N Polyanskiy ldquoRefractive index databaserdquo 2015 httprefractiveindexinfo

[30] B Dietrich V Bukalo A Fischer et al ldquoRaman-spectroscopicdetermination of inhomogeneous stress in submicron silicondevicesrdquo Applied Physics Letters vol 82 no 8 pp 1176ndash11782003

[31] THDiStefano ldquoField dependent internal photoemission probeof the electronic structure of the Si-SiO

2interfacerdquo Journal of

Vacuum Science amp Technology vol 13 no 4 pp 856ndash859 1976[32] F Herman and R V Kasowski ldquoElectronic structure of defects

at SiSiO2interfacesrdquo Journal of Vacuum Science amp Technology

vol 19 no 3 pp 395ndash401 1981[33] A Ourmazd D W Taylor J A Rentschler and J Bevk ldquoSi rarr

SiO2transformation interfacial structure and mechanismrdquo

Physical Review Letters vol 59 no 2 pp 213ndash216 1987[34] D E Aspnes and J B Theeten ldquoOptical properties of the

interface between Si and its thermally grown oxiderdquo PhysicalReview Letters vol 43 no 14 pp 1046ndash1050 1979

[35] C R Helms ldquoMorphology and electronic structure of SindashSiO2interfaces and Si surfacesrdquo Journal of Vacuum Science amp

Technology vol 16 no 2 pp 608ndash614 1979[36] F J Himpsel F R McFeely A Taleb-Ibrahimi J A Yarmoff

and G Hollinger ldquoMicroscopic structure of the SiO2Si inter-

facerdquo Physical Review B vol 38 no 9 pp 6084ndash6096 1988[37] I Ohdomari H Akatsu Y Yamakoshi and K Kishimoto

ldquoStudy of the interfacial structure between Si (100) and ther-mally grown SiO

2using a ball-and-spoke modelrdquo Journal of

Applied Physics vol 62 no 9 pp 3751ndash3754 1987[38] I Ohdomari T Mihara and K Kai ldquoComputer simulation

of high-resolution transmission electron microscope imagesbased on ball-and-spoke models of (100) SiSiO

2interfacerdquo

Journal of Applied Physics vol 60 no 11 pp 3900ndash3904 1986[39] M M Banaszak Holl S Lee and F R McFeely ldquoCore level

photoemission and the structure of the SiSiO2interface a

reappraisalrdquoApplied Physics Letters vol 65 no 9 pp 1097ndash10991994

[40] R M Feenstra and G S Oehrlein ldquoSurface morphologyof oxidized and ion-etched silicon by scanning tunnelingmicroscopyrdquo Applied Physics Letters vol 47 no 2 pp 97ndash991985

[41] C Zhao P R Lefebvre and E A Irene ldquoA spectroscopicimmersion ellipsometry study of SiO

2-Si interface roughness

for electron cyclotron resonance plasma and thermally oxidizedSi surfacesrdquoThin Solid Films vol 313-314 pp 286ndash291 1998

[42] N M Johnson D K Biegelsen M D Moyer S T Chang E HPoindexter and P J Caplan ldquoCharacteristic electronic defectsat the SiminusSiO

2interfacerdquo Applied Physics Letters vol 43 no 6

pp 563ndash565 1983[43] B J Hinds F Wang D M Wolfe C L Hinkle and G

Lucovsky ldquoInvestigation of postoxidation thermal treatments ofSiSiO

2interface in relationship to the kinetics of amorphous

Si suboxide decompositionrdquo Journal of Vacuum Science andTechnology B vol 16 no 4 pp 2171ndash2176 1998

[44] M D Efremov V V Bolotov V A Volodin and S AKochubei ldquoRaman scattering anisotropy in a system of (1 1 0)-oriented silicon nanocrystals formed in a-Si filmrdquo Solid StateCommunications vol 108 no 9 pp 645ndash648 1998

[45] I de Wolf C Jian and W M van Spengen ldquoThe investigationof microsystems using Raman spectroscopyrdquo Optics and Lasersin Engineering vol 36 no 2 pp 213ndash223 2001

[46] Z P Ling J Ge R Stangl A G Aberle and T MuellerldquoDetailed micro raman spectroscopy analysis of doped siliconthin film layers and its feasibility for heterojunction siliconwafer solar cellsrdquo Journal of Materials Science and ChemicalEngineering vol 1 no 5 Article ID 38124 pp 1ndash14 2013

[47] A A Parr C Bodart D Demonchy and D J Gardiner ldquoDepthprofiling variously deposited LPCVD polysilicon films usingRamanmicroscopyrdquo Semiconductor Science andTechnology vol16 no 7 pp 608ndash613 2001

[48] KWAduQ XiongH RGutierrez G Chen andP C EklundldquoRaman scattering as a probe of phonon confinement andsurface optical modes in semiconducting nanowiresrdquo AppliedPhysics A vol 85 no 3 pp 287ndash297 2006

[49] A A Parr D J Gardiner R T Carline D O King and GM Williams ldquoStructural variations in polysilicon associatedwith deposition temperature and degree of annealrdquo Journal ofMaterials Science vol 36 no 1 pp 207ndash212 2001

[50] M Kawata S Nadahara J Shiozawa M Watanabe and TKatoda ldquoCharacterization of stress in doped and undopedpolycrystalline silicon before and after annealing or oxidationwith laser raman spectroscopyrdquo Journal of Electronic Materialsvol 19 no 5 pp 407ndash411 1990

[51] R C Teixeira I Doi M B P Zakia J A Diniz and J WSwart ldquoMicro-raman stress characterization of polycrystallinesilicon films grown at high temperaturerdquoMaterials Science andEngineering B vol 112 no 2-3 pp 160ndash164 2004

[52] X-Z Bo N Yao S R Shieh T S Duffy and J C Sturm ldquoLarge-grain polycrystalline silicon films with low intragranular defectdensity by low-temperature solid-phase crystallization withoutunderlying oxiderdquo Journal of Applied Physics vol 91 no 5 pp2910ndash2915 2002

[53] A Ogura K Egami andM Kimura ldquoMinimization of residualstress in SOI films by using AlN interlaid insulatorrdquo JapaneseJournal of Applied Physics vol 24 no 8 pp L669ndashL671 1985

[54] K Kitahara T Ishii J Suzuki T Bessyo and N WatanabeldquoCharacterization of defects and stress in polycrystalline siliconthin films on glass substrates by raman microscopyrdquo Interna-tional Journal of Spectroscopy vol 2011 Article ID 632139 14pages 2011

[55] K J Kingma and R J Hemley ldquoRaman spectroscopic study ofmicrocrystalline silicardquo American Mineralogist vol 79 no 3-4pp 269ndash273 1994

[56] M Zhang and J F Scott ldquoRaman studies of oxide mineralsa retrospective on cristobalite phasesrdquo Journal of Physics Con-densed Matter Condensed Matter vol 19 no 27 Article ID275201 2007

[57] D C Palmer R J Hemley and C T Prewitt ldquoRaman spectro-scopic study of high-pressure phase transitions in cristobaliterdquoPhysics ampChemistry ofMinerals vol 21 no 8 pp 481ndash488 1994

[58] P Mohanty V Ortalan N D Browning I Arslan Y Fei andK Landskron ldquoDirect formation of mesoporous coesite singlecrystals from periodic mesoporous silica at extreme pressurerdquoAngewandte Chemie vol 49 no 25 pp 4301ndash4305 2010


[59] N Nakano L Marville and R Reif ldquoRaman scattering inpolycrystalline silicon doped with boronrdquo Journal of AppliedPhysics vol 72 no 8 pp 3641ndash3647 1992

[60] P Zorabedian and F Adar ldquoMeasurement of local stress inlaserrecrystallized lateral epitaxial silicon films over silicondioxide using Raman scatteringrdquoApplied Physics Letters vol 43no 2 pp 177ndash179 1983

[61] V A Volodin M D Efremov V A Gritsenko and S AKochubei ldquoRaman study of silicon nanocrystals formed in SiNxfilms by excimer laser or thermal annealingrdquo Applied PhysicsLetters vol 73 no 9 pp 1212ndash1214 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


introduce the procedure that can avoid the limitation comingfrom geometrical optics

The most important property that can help to over-come the limitation of axial diameter of laser beam focusis absorption Absorption coefficient of each material is afunction of wavelength of incident light It means that onecan change the penetration depth of the light into thematerialby choice of the irradiation wavelength The dependencebetween wavelength and absorption of the material wasapplied for investigation of ohmic contacts with additionalcarbon layer formed at different temperatures [9] Silicidefilm mixed with carbon atoms is transparent for visible lightbecause this visible irradiation of the ohmic contact throughsilicide layer causes the Raman scattering in carbon layerplaced between silicide film and silicon carbide substrateThedeep-ultraviolet excitation applied in the same configurationcannot reach the above-mentioned carbon layer due to strongabsorption of the silicide layer mixed with carbon structuresTherefore Raman scattering excited in deep-ultraviolet spec-tral range delivers information about two types of carbonspecies

(i) carbon layer which is built on the free surface ofsilicides due to carbon atom diffusion

(ii) carbon clusters placed inside of silicide layer [9]

The other problem which was investigated by meansof extraction of signal generated in thin layer from largebackground is related to properties of the interface betweensilicon carbide (SiC) and dielectric layer The Near InterfaceTraps (NITs) in the MOS-type structures can decrease themobility of charge carriers even by two orders of magni-tude Extensive study of the properties of SiCSiO

2interface

showed that carbon plays very important role in formationof the defects that can be candidates for NITs [10ndash13] Themost important Raman bands generated by species built fromcarbon atoms [14] are placed in the same range of Ramanshift as two-phonon spectrum of different polytypes of SiC[15 16] Application of two different excitation wavelengthsin particular visible andultravioletmade the extraction of thescattering coming from the interface from backgroundwhichis formed by two-phonon Raman scattering in SiC substratepossible The extraction was possible due to significantlydifferent penetration depths of exciting radiation from bothused spectral ranges [17]

The other area where the decreasing of two-phononRaman scattering plays a key role is related to Raman studyof properties of dielectric layer The problem was discussedin the literature for the system composed of Si substrateand SiO

2layer Standard configuration of Raman apparatus

includes excitation in visible spectral range In this casesignificant two-phonon signal generated in Si substrate isobserved [18] The intensity of this second-order Ramanscattering is strong enough even tomask the signal form SiO

2

layer [19] Application of deep-ultraviolet excitation makespossible the observation of Raman scattering generated inSiO2layer [20] The increase of Si absorption due to change

of the excitation wavelength from visible spectral range todeep-ultraviolet results in reduction of radiation penetration

depth by about 30 times In turn the intensity of two-phonon Raman scattering coming from Si substrate becomesnegligible and the signal from silicon oxide layer becomesdetectable This was shown for sim50 nm thick SiO

2layer

placed on Si substrate by comparison with bulk materialwhich was commercially available quartz glass Suprasil I[20] The price to pay for this advantage is long irradiationtime The reason for this ldquopricerdquo is small efficiency of Ramaneffect in the case of SiO

2combined with small thickness of

investigated material The typical thickness of SiO2layer of

todayrsquos electronic structures is about two orders ofmagnitudesmaller than the axial dimension of the focus of laserbeam

This work focuses the attention on the properties ofthin layer of semiconductor substrate in the vicinity ofsemiconductordielectric interface The SiSiO

2system is

used as an example The change of the power density ofexciting light on the sample results in change of effectiveabsorption depth Effective absorption depth is the thicknessof the investigated material which is active from the point ofview of measured Raman signal under certain power densitySince the definition of the effective absorption depth is acrucial point in the interpretation of experimental data itwill be discussed in detail in the next chapter Experimentalwhere also themethodology of data analysis is describedThesystematic change of power density makes possible to recordRaman signal from material with different thickness As aresult one can get depth profile of structural properties ofinvestigated material

Another point that will be discussed here is the appear-ance of crystal-like structures of silicon dioxide that shouldbe placed at the SiSiO

2interface [21] As was mentioned

above application of deep-ultraviolet excitation in order toreduce two-phonon signal from Si substrate was discussedfor amorphous part of SiO

2layer [20] However Raman

signal observed for this type of excitation contains alsotraces of narrow lines These traces will be compared herewith Raman spectra reported for crystalline forms of silicondioxide

The paper is organized according to the following outlineSection 2 presents method of sample preparation and theircharacterization Raman apparatus and methodologies ofdata analysis and measurements The special attention waspaid to two aspects

(i) the description of the mathematical model whichlinks the power density of irradiation with thicknessof the layer of material from which the Ramanscattering is recorded

(ii) the discussion of two experimental parameters whichare changed if the power density of exciting lightis varied half-angle of the maximum cone of lightcollected by microscope objective and the dimensionof the laser-beam spot

Section 3 presents the measured data The results of theinvestigation are discussed in Section 4


2 Experimental

























119868 (119897) = 1198680119890minus120572119897 (1)



119868 (119897) = 119868010minus119861= 119868010minus120573119897 (2)


119888has the form

119899119888= 119899 minus 119894119896 (3)


120572 =2120596119896

119888 (4)


120572 =2 (2120587]) 119896

119888=4120587119888119896

120582119888=4120587119896

120582 (5)


120575 =120582

4120587119896 (120582)= 120572minus1 (6)




119899 (119911) = 1198990119890minus120572119911 (7)



0


119911max =ln (1198990)

120572 (7

1015840)


0


119868 (119897) = 11986801205930 int

119897

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572119897

2120572 (8)



0describes



119868 (120575maxeff ) = 11986801205930 int

120575maxeff

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572120575

maxeff

2120572

= 65536

(81015840)




eff )) = 256 = (65536)12 This



maxeff )










119868 (119897) = 11986801205930 int

120575eff

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572120575eff

2120572 (8

10158401015840)

Dividing (810158401015840) by (8


119868(120575eff )119868(120575maxeff )

119868 (120575eff)

119868 (120575maxeff )

=1 minus 119890minus2120572120575eff

1 minus 119890minus2120572120575

maxeff (9)


maxeff )

119868 (120575eff)

119868 (120575maxeff )

=120575eff120575maxeff (9

1015840)


120575eff =119868 (120575eff)

119868 (120575maxeff )

120575maxeff = 3

119868 (120575eff)

119868 (120575maxeff )

120575 (10)







2interface




119860is the







f

w


Focal plane

Shape offocused

laser beam

x

zΘ

2r0

Φ


0 diameter



119873119860= sin (Θ) = sin(arctan( Φ

2119891)) (11)


21199030= 119862

120582

2119873119860

(12)



Θ = arcsin (119873119860) = 6416

∘




2 (119891 minus 119911)) (14)




1198731015840

119860= sin (Θ1015840) = 090114 (15)


120590 =

100381610038161003816100381610038161198731015840

119860minus 119873119860

10038161003816100381610038161003816

119873119860

= 00013 (16)




1199092

1198862minus1199112

1198872= 1 (17)




119860 In






1199092

1199032

0

= 1 +1199112

1198872 (19)











2








3 Results


Stre

ss (G

Pa)


5205052055520605206552070520755208052085

Ram

an sh

ift(c

mminus

1 )


minus04

minus02

0

02


(a)

Inte

nsity

(au

)


286

288

290

292

294

Ram

an sh

ift(c

mminus

1 )

001 01 10001


0105



(b)










454

393

3543

3532

1

Si5197

cmminus1


Inte

nsity

(au

)

000204060810


Inte

nsity

(au

)

0005

0109

1







2layer the


4 Discussion


2interface



2(a-SiO







2and c-Si [31] The






2and c-Si






2















2and c-Si





















2layerThis



2




2c-Si









119909layer



2




2related















2layer [20] Since






2










2and









factors

















2and c-Si





5 Summary








References



24H-SiC MOS




















































2interfacerdquo










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


2 Experimental

























119868 (119897) = 1198680119890minus120572119897 (1)



119868 (119897) = 119868010minus119861= 119868010minus120573119897 (2)


119888has the form

119899119888= 119899 minus 119894119896 (3)


120572 =2120596119896

119888 (4)


120572 =2 (2120587]) 119896

119888=4120587119888119896

120582119888=4120587119896

120582 (5)


120575 =120582

4120587119896 (120582)= 120572minus1 (6)




119899 (119911) = 1198990119890minus120572119911 (7)



0


119911max =ln (1198990)

120572 (7

1015840)


0


119868 (119897) = 11986801205930 int

119897

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572119897

2120572 (8)



0describes



119868 (120575maxeff ) = 11986801205930 int

120575maxeff

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572120575

maxeff

2120572

= 65536

(81015840)




eff )) = 256 = (65536)12 This



maxeff )










119868 (119897) = 11986801205930 int

120575eff

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572120575eff

2120572 (8

10158401015840)

Dividing (810158401015840) by (8


119868(120575eff )119868(120575maxeff )

119868 (120575eff)

119868 (120575maxeff )

=1 minus 119890minus2120572120575eff

1 minus 119890minus2120572120575

maxeff (9)


maxeff )

119868 (120575eff)

119868 (120575maxeff )

=120575eff120575maxeff (9

1015840)


120575eff =119868 (120575eff)

119868 (120575maxeff )

120575maxeff = 3

119868 (120575eff)

119868 (120575maxeff )

120575 (10)







2interface




119860is the







f

w


Focal plane

Shape offocused

laser beam

x

zΘ

2r0

Φ


0 diameter



119873119860= sin (Θ) = sin(arctan( Φ

2119891)) (11)


21199030= 119862

120582

2119873119860

(12)



Θ = arcsin (119873119860) = 6416

∘




2 (119891 minus 119911)) (14)




1198731015840

119860= sin (Θ1015840) = 090114 (15)


120590 =

100381610038161003816100381610038161198731015840

119860minus 119873119860

10038161003816100381610038161003816

119873119860

= 00013 (16)




1199092

1198862minus1199112

1198872= 1 (17)




119860 In






1199092

1199032

0

= 1 +1199112

1198872 (19)











2








3 Results


Stre

ss (G

Pa)


5205052055520605206552070520755208052085

Ram

an sh

ift(c

mminus

1 )


minus04

minus02

0

02


(a)

Inte

nsity

(au

)


286

288

290

292

294

Ram

an sh

ift(c

mminus

1 )

001 01 10001


0105



(b)










454

393

3543

3532

1

Si5197

cmminus1


Inte

nsity

(au

)

000204060810


Inte

nsity

(au

)

0005

0109

1







2layer the


4 Discussion


2interface



2(a-SiO







2and c-Si [31] The






2and c-Si






2















2and c-Si





















2layerThis



2




2c-Si









119909layer



2




2related















2layer [20] Since






2










2and









factors

















2and c-Si





5 Summary








References



24H-SiC MOS




















































2interfacerdquo










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of





119868 (119897) = 1198680119890minus120572119897 (1)



119868 (119897) = 119868010minus119861= 119868010minus120573119897 (2)


119888has the form

119899119888= 119899 minus 119894119896 (3)


120572 =2120596119896

119888 (4)


120572 =2 (2120587]) 119896

119888=4120587119888119896

120582119888=4120587119896

120582 (5)


120575 =120582

4120587119896 (120582)= 120572minus1 (6)




119899 (119911) = 1198990119890minus120572119911 (7)



0


119911max =ln (1198990)

120572 (7

1015840)


0


119868 (119897) = 11986801205930 int

119897

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572119897

2120572 (8)



0describes



119868 (120575maxeff ) = 11986801205930 int

120575maxeff

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572120575

maxeff

2120572

= 65536

(81015840)




eff )) = 256 = (65536)12 This



maxeff )










119868 (119897) = 11986801205930 int

120575eff

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572120575eff

2120572 (8

10158401015840)

Dividing (810158401015840) by (8


119868(120575eff )119868(120575maxeff )

119868 (120575eff)

119868 (120575maxeff )

=1 minus 119890minus2120572120575eff

1 minus 119890minus2120572120575

maxeff (9)


maxeff )

119868 (120575eff)

119868 (120575maxeff )

=120575eff120575maxeff (9

1015840)


120575eff =119868 (120575eff)

119868 (120575maxeff )

120575maxeff = 3

119868 (120575eff)

119868 (120575maxeff )

120575 (10)







2interface




119860is the







f

w


Focal plane

Shape offocused

laser beam

x

zΘ

2r0

Φ


0 diameter



119873119860= sin (Θ) = sin(arctan( Φ

2119891)) (11)


21199030= 119862

120582

2119873119860

(12)



Θ = arcsin (119873119860) = 6416

∘




2 (119891 minus 119911)) (14)




1198731015840

119860= sin (Θ1015840) = 090114 (15)


120590 =

100381610038161003816100381610038161198731015840

119860minus 119873119860

10038161003816100381610038161003816

119873119860

= 00013 (16)




1199092

1198862minus1199112

1198872= 1 (17)




119860 In






1199092

1199032

0

= 1 +1199112

1198872 (19)











2








3 Results


Stre

ss (G

Pa)


5205052055520605206552070520755208052085

Ram

an sh

ift(c

mminus

1 )


minus04

minus02

0

02


(a)

Inte

nsity

(au

)


286

288

290

292

294

Ram

an sh

ift(c

mminus

1 )

001 01 10001


0105



(b)










454

393

3543

3532

1

Si5197

cmminus1


Inte

nsity

(au

)

000204060810


Inte

nsity

(au

)

0005

0109

1







2layer the


4 Discussion


2interface



2(a-SiO







2and c-Si [31] The






2and c-Si






2















2and c-Si





















2layerThis



2




2c-Si









119909layer



2




2related















2layer [20] Since






2










2and









factors

















2and c-Si





5 Summary








References



24H-SiC MOS




















































2interfacerdquo










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



0describes



119868 (120575maxeff ) = 11986801205930 int

120575maxeff

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572120575

maxeff

2120572

= 65536

(81015840)




eff )) = 256 = (65536)12 This



maxeff )










119868 (119897) = 11986801205930 int

120575eff

0

119890minus2120572119911

119889119911 = 11986801205930

1 minus 119890minus2120572120575eff

2120572 (8

10158401015840)

Dividing (810158401015840) by (8


119868(120575eff )119868(120575maxeff )

119868 (120575eff)

119868 (120575maxeff )

=1 minus 119890minus2120572120575eff

1 minus 119890minus2120572120575

maxeff (9)


maxeff )

119868 (120575eff)

119868 (120575maxeff )

=120575eff120575maxeff (9

1015840)


120575eff =119868 (120575eff)

119868 (120575maxeff )

120575maxeff = 3

119868 (120575eff)

119868 (120575maxeff )

120575 (10)







2interface




119860is the







f

w


Focal plane

Shape offocused

laser beam

x

zΘ

2r0

Φ


0 diameter



119873119860= sin (Θ) = sin(arctan( Φ

2119891)) (11)


21199030= 119862

120582

2119873119860

(12)



Θ = arcsin (119873119860) = 6416

∘




2 (119891 minus 119911)) (14)




1198731015840

119860= sin (Θ1015840) = 090114 (15)


120590 =

100381610038161003816100381610038161198731015840

119860minus 119873119860

10038161003816100381610038161003816

119873119860

= 00013 (16)




1199092

1198862minus1199112

1198872= 1 (17)




119860 In






1199092

1199032

0

= 1 +1199112

1198872 (19)











2








3 Results


Stre

ss (G

Pa)


5205052055520605206552070520755208052085

Ram

an sh

ift(c

mminus

1 )


minus04

minus02

0

02


(a)

Inte

nsity

(au

)


286

288

290

292

294

Ram

an sh

ift(c

mminus

1 )

001 01 10001


0105



(b)










454

393

3543

3532

1

Si5197

cmminus1


Inte

nsity

(au

)

000204060810


Inte

nsity

(au

)

0005

0109

1







2layer the


4 Discussion


2interface



2(a-SiO







2and c-Si [31] The






2and c-Si






2















2and c-Si





















2layerThis



2




2c-Si









119909layer



2




2related















2layer [20] Since






2










2and









factors

















2and c-Si





5 Summary








References



24H-SiC MOS




















































2interfacerdquo










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


f

w


Focal plane

Shape offocused

laser beam

x

zΘ

2r0

Φ


0 diameter



119873119860= sin (Θ) = sin(arctan( Φ

2119891)) (11)


21199030= 119862

120582

2119873119860

(12)



Θ = arcsin (119873119860) = 6416

∘




2 (119891 minus 119911)) (14)




1198731015840

119860= sin (Θ1015840) = 090114 (15)


120590 =

100381610038161003816100381610038161198731015840

119860minus 119873119860

10038161003816100381610038161003816

119873119860

= 00013 (16)




1199092

1198862minus1199112

1198872= 1 (17)




119860 In






1199092

1199032

0

= 1 +1199112

1198872 (19)











2








3 Results


Stre

ss (G

Pa)


5205052055520605206552070520755208052085

Ram

an sh

ift(c

mminus

1 )


minus04

minus02

0

02


(a)

Inte

nsity

(au

)


286

288

290

292

294

Ram

an sh

ift(c

mminus

1 )

001 01 10001


0105



(b)










454

393

3543

3532

1

Si5197

cmminus1


Inte

nsity

(au

)

000204060810


Inte

nsity

(au

)

0005

0109

1







2layer the


4 Discussion


2interface



2(a-SiO







2and c-Si [31] The






2and c-Si






2















2and c-Si





















2layerThis



2




2c-Si









119909layer



2




2related















2layer [20] Since






2










2and









factors

















2and c-Si





5 Summary








References



24H-SiC MOS




















































2interfacerdquo










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




2








3 Results


Stre

ss (G

Pa)


5205052055520605206552070520755208052085

Ram

an sh

ift(c

mminus

1 )


minus04

minus02

0

02


(a)

Inte

nsity

(au

)


286

288

290

292

294

Ram

an sh

ift(c

mminus

1 )

001 01 10001


0105



(b)










454

393

3543

3532

1

Si5197

cmminus1


Inte

nsity

(au

)

000204060810


Inte

nsity

(au

)

0005

0109

1







2layer the


4 Discussion


2interface



2(a-SiO







2and c-Si [31] The






2and c-Si






2















2and c-Si





















2layerThis



2




2c-Si









119909layer



2




2related















2layer [20] Since






2










2and









factors

















2and c-Si





5 Summary








References



24H-SiC MOS




















































2interfacerdquo










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


454

393

3543

3532

1

Si5197

cmminus1


Inte

nsity

(au

)

000204060810


Inte

nsity

(au

)

0005

0109

1







2layer the


4 Discussion


2interface



2(a-SiO







2and c-Si [31] The






2and c-Si






2















2and c-Si





















2layerThis



2




2c-Si









119909layer



2




2related















2layer [20] Since






2










2and









factors

















2and c-Si





5 Summary








References



24H-SiC MOS




















































2interfacerdquo










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of















2layerThis



2




2c-Si









119909layer



2




2related















2layer [20] Since






2










2and









factors

















2and c-Si





5 Summary








References



24H-SiC MOS




















































2interfacerdquo










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of











2layer [20] Since






2










2and









factors

















2and c-Si





5 Summary








References



24H-SiC MOS




















































2interfacerdquo










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of








factors

















2and c-Si





5 Summary








References



24H-SiC MOS




















































2interfacerdquo










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of






References



24H-SiC MOS




















































2interfacerdquo










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of























2interfacerdquo










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of














Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

research article depth-sensitive raman investigation of

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