J O U R N A L O F MATERIALS SCIENCE: MATERIALS. IN ELECTRONICS 4(1993) 271--277

Rarnan microprobe: a diagnostic tool for processed silicon. Analysis of microindented silicon

J. J I M E N E Z , E. M A R T I N , A. TORRES, B. M A R T I N , F. RULL, F. S O B R O N * Dto. de Fisica de la Materia Condensada, Cristalografia y Mineralogia, and * Dto de Ingenieria Quimica, Facultad de Ciencias, 47011 Valladolid, Spain

Laser-assisted processesare currently used in silicon technology. The response of the material to the laser beam depends strongly on its own physical properties and on the laser power density. The use of a microRaman system, allows the structural characteristics of the material to be analysed by varying the excitation laser power density on the sample over a large power range with a submicrometre lateral resolution. Results are reported on microindented crystalline silicon, showing that changes in the physical properties of the material, introducing grain boundaries, dislocations and cracking, result in a strong modification of the Raman spectrum. These spectral changes are enhanced for increasing laser power densities. Several mechanisms are pointed out as possible sources of the observed spectral modifications. These results show that Raman microprobe is a very promising technique for the diagnosis of technologically processed semiconductors and devices.

1. I n t r o d u c t i o n Laser-assisted processes are used in VLSI technology. The understanding of the different physical phe- nomena involved in the laser processing and the influ- ence that the properties of the material can have on the temperature rise induced by the laser beam, are of high technological interest. Optical reflectivity [1] and photoacoustic [2] detection were used to study the laser heating in silicon. Raman spectroscopy was shown to be a reliable tool for studying in situ the lattice temperature of silicon under intense laser beams [3], though the temperature data need to be interpreted with care. The use of Raman microprobe is being introduced for the characterization of semiconductors and devices at the micrometre scale [4, 5]. Usually it is used at low enough laser power to avoid local heating, which would result in frequency shift and anharmonic broadening of the Raman peaks obtained; further- more, high laser power density could produce damage in the specimen [6]. Nevertheless, in high melting point semiconductors, such as silicon, the use of high laser power densities reveals interesting properties of the material, as has been previously claimed [7, 8]. Several effects are expected to be induced by such a concentrated laser beam, namely, inhomogeneous temperature distribution [7, 8], stress induced by the temperature gradient [9], electron-phonon coupling [10], and anharmonic decay of phonons [7], all of which are expected to be enhanced by the anomalous temperature reached at the probed volume [3]. The contribution of these effects to the Raman spectrum of silicon has been studied by different authors [7-10], showing the strong influence they have on the dipole-

0957-4522 © 1993 Chapman & Hall

allowed F25 zone-centre phonon; presumably the presence of high concentrations of lattice defects con- tributes to enhance all these effects on the Raman spectrum. It is important to separate, when possible, the contributions from eadh other, in order to elucid- ate the physical causes of the laser beam-induced effects, as well as the capabilities of the Raman micro- probe as a diagnostic tool for processed semiconduc- tors. These effects might not be so well characterized when working under usual Raman excitation condi- tions, owing to the fact that they are all practically unobservable under standard excitation conditions. However, as will be shown below, they are enhanced under intense laser probe beams. Some examples of Raman microprobe measurements are presented that reveal noteworthy differences between the Raman spectra of several silicon specimens depending on the laser power densities used for measurements, and the particular characteristics of the samples. Within this framework, the characteristics of the microRaman measurements, working at high laser power densities in silicon plastically deformed by Vickers indentation are reported.

2. Experimental procedure MicroRaman measurements were performed with a DILOR XY modular Raman spectrometer, working in multichannel detection mode. The microscope was an Olympus BHT. The excitation was made through- out the microscope objective lens in addition to collec- tion of the scattered light, thus working in almost backscattering configuration. The spot gives a gauss-

271

ian distribution of power [11, 12]; the size of the spot in the focal plane is diffraction-limited and depends on the laser wavelength, )~, and the numerical aperture of the objective, NA; the diameter is given by

D = 1.22X/NA (1)

This spot corresponds to nearly 80% of the incident laser power on the sample; the remaining 20% corres- ponds to the higher order harmonics.

Excitation was performed with the 514.5 nm line of an Ar + laser. The microscope objective in our meas- urements was a x 100 with 0.95 numerical aperture, which results in a 0.9 gm laser spot diameter in the focal plane. This allows work under a high laser power density together with a very good spatial resolution, which is an interesting aspect in relation to the micro- metre-size scale characterization of microelectronic devices. It was also verified that the entire scattered spot entered through the slit, so the Raman spectrum obtained corresponds to the full excited area. Laser focusing was checked at the entrance slit of the spectrometer. Different laser powers were used, providing density powers ranging from 0.1-1 M W c m -2, which ensure non-perturbed meas- urements at the lowest power density and strong perturbation at the highest one.

Intrinsic (1 00) bulk silicon was used for measure- ments. Vickers indentations at room temperature pro- duced strong plastic deformation in localized areas, resulting in microscopic dislocation loops and frac- tures. The Vickers indentations are produced by a diamond pyramid (square base) at room temperature. The loads used were in the range from 0.1-0.5 N producing indentations with a base diagonal ranging from 4.5-10mm. Fig. 1 shows a Nomarski micro- graph of two typical indentations, with their associ- ated cracking pattern.

3. Results and discussion The strong plastic deformation produced by the in- dentation results in grain boundaries and crystallites of different sizes, which then results in a symmetry breakdown. It is expected that the Raman scattering selection rules would be brokendown in the indented volume thus allowing the observation of initially for- bidden modes. The presence of these inhomogeneities is expected to produce discontinuities in the thermal expansion as well as in the thermal conductivity of silicon. These changes will influence the thermoelastic response and the temperature reached by the probed volume. Therefore, the study of these heavily deform- ed areas with the Raman microprobe can help in understanding how the laser heating influences the

................................................................................................................................. lineshape and frequency of the first-order Raman line I! in processed silicon. ii~i The characteristic Raman spectra obtained depend

on different factors, namely the load used for indenta- tion and the position inside the indented area; usually changes in the Raman spectrum are observed at the centre of the indentation, where the plastic deforma- tion is more important. It was claimed that under specific indentation conditions, it is possible to amorphize crystalline silicon [13]; nevertheless, none of the Raman spectra we obtained inside the indenta- tions showed characteristic amorphous-like Raman bands (480 and 180 cm-1), therefore we ruled out the possibility of an amorphous contribution to our ex- perimental results.

Small crystallite size is revealed by the presence of a shoulder in the low-frequency side of the zone-centre

~ ~:~:~ :: 520520 cm-1 b a n d C m - 1 Ramanitselfband.couldThebe observatiOndue to either°flargethe

crystallite size, that does not produce q-relaxation, or

....... ̀.~.~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~::~::~i~i~i~i~i~i~i~i~i~i~i~i~i~!~i.:~.~....~ fact that these bands are slightly larger than those ~ ~ , ~ , , ' . ~ i ~ i ~ i ~ : : ~ i ~ i ~ i ~ i ~ ~ observed in the undeformed silicon accounts for the

presence of residual strain, probably due to the grain boundaries and dislocations introduced by the in- dentation.

The Raman spectra obtained in intrinsic silicon and inside the indentation area for two different laser power densities are shown in Fig. 2. These spectra illustrate the different behaviours studied. The shape of the spectra depends on the laser power density. For

i iiiiiiiiiiiiiii!iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii bulk silicon there are no significant changes, while notable differences are observed inside the deformed

Figure 1 (a,b) Nomarski micrographs of Vickers microindenta- a rea . Obviously these differences are the consequence tions, showing the cracking pattern, of the response of the deformed material to the high

272

e -

i -

e..

e -

E ee"

! ! 500 520

W a v e n u m b e r (cm -1)

S /

(b) i ~ I

500 520 W a v e n u m b e r (cm -1)

Figure 2 (a) Raman spectra in bulk silicon, (b) indented silicon. Laser power density: ( ) 0.2 M W c m - 2 (___) 0.6 M W cm-2.

laser power exposure. The existence of extended de- fects, such as grain boundaries and dislocations, with the corresponding residual stresses, must change the thermal conductivity and the thermal expansion coef- ficients, with the subsequent changes induced in both the temperature reached by the laser probed volume and the thermoelastic properties of the material [14, 15]. Therefore, the modifications observed in the Raman spectra might be produced by different factors, governed by the thermal conductivity, thermal ex- pansion and optical absorption changes due to the damage produced by the indentation; these changes should result in increased heating, in-homogeneous temperature distribution, and stresses produced by strong temperature gradients generated by the focused laser beam.

The series of Raman spectra obtained at low laser power density for different points of indented areas

shown in Fig. 3a reveals that when working under such conditions only small differences between them can be observed; namely, a slightly deformed zone- centre phonon allowed Raman bands and shifts in the peak frequency, revealing the existence of residual

t , _

E rr" J

-11' i %~ t

(a)

500 520 Wave number (cm -1)

e'-

=d <_

t -

n- -

Z s • J %%.

o

(b) I I

500 520 Wave number (cm -1)

Figure 3 Raman spectra obtained at different points of an indenta- tion. (a) 0.2 M W c m -2, (b) 0.8 M W c m -z. ( - - ) Reference bulk silicon.

273

stresses. As long as the excitation laser power is increased, strong band deformation and frequency shifts are observed, Fig. 3b. The origin of these defor- mations must be analysed and will constitute a char- acteristic of the material. In other words, the high power laser beam enhances the interaction between the sample defects and the probe beam, resulting in the observation of the above-mentioned effects.

The temperature effects are clearly seen in the spec- tra of Fig. 3, which are compared to the undeformed bulk silicon spectra obtained under the same laser probing conditions. The spectra of crystalline silicon exhibit, for the range of laser power densities used, a well-defined Lorentzian lineshape, from which the mean lifetime of phonons is determined. This lifetime is calculated from the slope of log [c(t)], where c(t) is the vibrational correlation function, which is obtained from the Fourier transform of the spectrum (c(t)) oc FT[I (w)] (see Appendix). This calculation can take into account the contribution of the function appar- atus, crystallite size and residual stresses. The function apparatus was considered for convenience in order to avoid its influence in our experiments which were carried out with a spectral slit resolution below the limit discussed in the Appendix. The crystallite size was not taken into account, because the Raman spec- tra obtained at low laser power revealed that the contribution of small crystallites is negligible; indeed at low laser power, the spectra obtained in the in- dented areas fit the undeformed silicon spectrum ob- tained under similar conditions; thus the crystallite size was, in general, not small enough to produce significant Raman shift and broadening. Furthermore the phonon lifetime calculation was performed on the linear part of the correlation function, c(t). In cases where a shoulder appeared on the low-frequency side due to small crystallites, its contribution was neglected after deconvolution. Finally, the residual stresses must exist due to the presence of cracks [16], it is quite difficult to assess the distribution of stresses in these areas owing to the loss of symmetry produced by the indentation, as well as the absence of information about the geometry of the stresses; therefore, it was neglected in our phonon lifetime estimations. In fact, the contribution of the stresses to the frequency shift can hardly account for the spectral broadening meas- ured under high laser power density. Nevertheless, a detailed inspection of the spectrum reveals a tail in the high-frequency wing of the Raman band that could arise from the presence of compressive stresses, in fact, such a tail cannot be accounted for by a temperature increase. Analysis of this tail is out of the scope of this paper, but will be considered in a forthcoming study.

Log c(t) versus t plots for undeformed crystalline silicon at different laser power densities are shown in Fig 4; the experimental lifetime so deduced decreases as the laser power density increases as expected; it should be noted that over the full laser power density range used the log c(t) is a straight line. This behaviour is different for the indented silicon, where the log c(t) function deviates from a straight line, especially for the high laser power densities (Fig. 5), accounting for very short relaxation times. On the other hand, the devi-

274

5

._J

~m ~

0

g

"o g

IIx

' h

0 i 1

0 5 10 Time (ps)

Figure 4 Ln c(t) versus t for bulk silicon at different laser power densities. Calculated phonon lifetimes: (A) 2.16 ps, 0.1 MWcm-2; ( I ) 2.15 ps, 0.2 MWcm-2; (A) 2.03 ps, 0.4 MWcm-2; (D) 1.90 ps, 0.8 MWcm -2.

lOi k

A

v

S

_9

~SAk

• A •

A •

• • •| mm

• A • •

m ~' m • • • & •

A

t,

0 I m

0 5 10 Time (ps)

Figure 5 Ln c(t) versus t for indented silicon showing the deviation from the Lorentzian shape beyond 3 ps. Phonon relaxation times: (A) 1.55 ps, 0.2 MWcm-2; (zS) 0.82 ps, 0.5 MWcm-2; (m) 0,66 ps, 0.8 MWcm -2.

ation from a straight line confirms the presence of different contributions to the phonon relaxation. Usu- ally the presence of defects produces a relaxation of the momentum conservation rule, resulting in a Raman peak broader than the ideal one. The sensitiv- ity of the Raman effect to the inhomogeneous broadening is not always easily measured, because it requires a sufficiently high defect concentration to be observed. This is the reason why at low laser power density this inhomogeneous contribution can be hard- ly observed in many cases. However, we show that

even for the cases where this inhomogeneous contri- bution is not easily detected, the high power density, which in undamaged crystals affects only the homo- geneous contribution to the lifetime, can also reveal the inhomogeneous contribution through thermally induced effects, that are strongly dependent on the defect distribution. In fact, the phonon lifetime is limited by the presence of defects; thus, when these defects are not present in concentrations high enough to be observed under standard conditions, the limita- tion they provide to the phonon lifetime is enough to be easily observed under high laser power density, through the heating induced in the sample.

In the indented areas the evolution of the Raman spectra with increasing laser power density reveals the presence of the different contributions above men- tioned. There are clear temperature enhancements, which are confirmed by the Stokes to antiStokes intensity ratio [3], Fig. 6. Because of the inhomogen- eous heating, the estimated temperature is a low limit. It should be noted that for increasing laser power densities, the estimated temperature is significantly increased in the indented area, which does not occur in any large amount for bulk silicon. This high temper- ature is produced by the low thermal conductivity of the indented silicon. In other words, in such a case,the Raman spectrum modifications are produced by an- omalous temperature enhancements, compared to the bulk silicon, for which the Stokes to antiStokes intens- ity ratio for the same laser power density excitation conditions, does not reveal such a temperature in- crease. This is consistent with the estimated phonon lifetime for both undeformed and indented silicon, which account for the poor thermal conductivity in the indented silicon. It should be noted that the phonon lifetime in the linear part of log I c(t)], the phonon lifetime calculated was significantly shorter than that calculated for crystalline silicon, which sup- ports the poor thermal conductivity in deformed sili- con. This temperature enhancement could also be favoured by a higher optical absorption due to the damage in the indented material, compared to the undeformed matrix. The local heating produces phonon shift and broadening; it should be pointed out

4o l o

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, . , , I: 0 - ' - Z'-_ . . . . / 1 I V . , ,

600 500 400 //-4019 -500 -600 0 Raman shift (cm -1)

F i g u r e 6 Stokes and antiStokes Raman spectra for indented silicon: (a) ( ) 0.2MWcm -2, 310K; (b) (---) 0.4MWcm -2, 376K; (c) ( .--)0.8 MW cm -z, 560 K.

that in addition to the temperature enhancement, the fact that the temperature estimated from the linewidth differs from that estimated from the peak frequency can be understood in terms of either an inhomogen- eous heating or the existence of residual stresses.

In areas that do not exhibit temperature-induced Raman shift and broadening, another effect is ob- served, and this is the existence of stress induced by the inhomogeneous heating produced by the laser beam. The consequence of this is a splitting of the zone- centre phonon of c-Si [17]. It should be remembered that the Raman selection rules are not conserved in the indented volume, in which considerable misori- entation and twinning must exist due to the strong deformation produced by the indentation; therefore, the observation in these areas of a priori forbidden TO modes is not a surprising result. This is shown in Fig. 7. The amount of splitting agrees with that ob- served by other authors in measurements carried out with different stress experimental configurations [18]. In our case it seems probable that we are dealing with shear stresses [16] at grain boundaries, where an enhanced absorption, together with poor thermal con- ductivity, produces inhomogeneous heating with the corresponding temperature gradients that give rise to thermoelastic effects. The fact that the frequency shift is observed toward the high-frequency side, compared with the undeformed matrix, implies that the observed stress is mainly compressive. It should be noted that the small crystallite size volume, revealed by the low- frequency shoulder in the Raman spectrum is simul- taneously heated, as observed from the frequency shift produced by the increasing laser power (Fig. 7), reach- ing the values expected for high local temperature; showing that the temperature reached by the probed volume under high laser power density increases with the amount of damage.

Another important point of interest to consider is the influence that the carrier generation by the cw laser excitation could have on the Raman spectra. It is well known that high carrier concentrations produce a softening of the Raman zone-centre phonon of silicon [19]. The problem of the free carrier-phonon coupling has been extensively studied in heavily doped silicon. Strong broadening and frequency shift have been reported mainly for free carrier densities lying around 102°-1021 cm -3 [10, 19, 20]. It is not easy to establish a correlation between our observations and a photo- generated carrier-phonon coupling mechanism, be- cause we do not know the carrier concentration at the indented areas. Nevertheless, the indentation pro- duces grain boundaries and dislocations, which are known to introduce traps and recombination centres, which result in a lowering of the carrier lifetime, with the corresponding carrier depletion in the neigh- bouring region [21]. Because of this, it is rather improbable that the free carrier contribution is a dominant mechanism to the zone-centre phonon broadening and frequency shift reported here. In addi- tion to this, the temperature enhancement seems evid- ent in the spectra series of Fig. 7, where the shift of the low-frequency shoulder can hardly be accounted for by a Fano-like mechanism [10, 22]. It should be noted

275

1.0 ¢-

< > .

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E ¢-

E a:: (a)

500 520 W a v e n u m b e r ( cm -1)

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#

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E r~

(b) d , •

2~ & l x LX [

500 520 Wave number (cm -1)

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i

500 520 Wave number (cm 1)

Figure 7 Raman spectra in indented silicon, showing phonon split- ting at high laser power density. The, low-frequency shoulder corres- ponds to small crystallite size. ( ) Experimental spectra. The symbols are the deconvoluted spectra. (a) 0.2 M W cm- 2, (b) 0.4 M W c m -z, (c) 0.8 M W c m -2.

that the Stokes to antiStokes integrated intensity ratio also accounts for temperature-related effects. Further- more, the second-order modes (300 cm- 1) (not shown here) are significantly enhanced [23, 24] at high laser density power, which again supports the role played by the induced temperature enhancement of the probed volume in the Raman spectra [25]. This temperature increase is an indirect assessment of the lowering of the thermal conductivity due to the pre- sence of crystalline material.

4. Conclusion The use of a Raman microprobe allows the properties of processed silicon to be analysed with a submicro-

276

metre lateral resolution. By using high laser power density, it is possible to detect deformations in the Raman spectra, which are related to the properties of the material. It is difficult to separate the value of the different contributions to the phonon shift and broadening of the Raman spectra, owing to the fact that they are related to each other. Nevertheless, the most important contribution seems to be provided by the strong heating caused by the defect-induced de- crease of the thermal conductivity, which is in agree- ment with the phonon lifetime shortening. In fact, a modelling for the estimation of the thermal conductiv- ity is now in progress. The Raman microprobe pro- vides information on the response of processed silicon to a laser beam, which will be valuable for improving the laser-assisted processes in microelectronics tech- nology. It constitutes a promising tool for the dia- gnosis of processed silicon. Recently, we have ob- served similar effects in SOI-SIMOX structures [26-28], which have been analysed in terms of the anomalous heating produced by the laser probe beam.

Acknowledgements The authors thank J. A. de Saja for valuable discus- sions. This work was financially supported by CICYT (project PB88-0573) and Junta de Castilla y Le6n.

Appendix: Phonon relaxation time The phonon relaxation time is obtained from either the full width at medium height (FWMH) of the Raman bands, T, or the integral breadth 13 = A/I(wm,x), where A is the integrated Raman intens-

ity and I(Wmax) is the intensity at the maximum wave number. The F W M H is accurately calculated from the slope of log I c(t)[ versus t, where c(t) is the vibrational correlation function

I(w) ~ ~c(t) e-lWtdt (A1)

(w = 2nv is the angular frequency). The influence of the apparatus function slit, finite

crystallite size or other factors contributing to the band width, can be measured through a form factor, F/13, which ranges from 0.6366 for a Lorentzian line- shape, to 0.9395 for a Gaussian lineshape.

When the line profile I(w) is asymmetrical, log [ c(t) [ versus t deviates from the linearity expected for a pure Lorentzian behaviour. This can be observed by com- paring Figs. 4 and 5.

If the Raman band exhibits a shoulder, the analysis is achieved by a self deconvolution procedure

Iexp (V) = ~9 (V) h (v - v') dv' (A2)

where g(v) is the ideal spectrum and h(v - v') is the perturbation function.

The Fourier Transform of Equation A2 gives

FT[Iexp(v)] = I ( t ) = g ( t )h ( t ) (A3)

9(t) is the deconvoluted function, and from the reverse Fourier Transform

F T - x t ( t ) -- g(v) (A4) h(t)

> >

v v v

- - a - - b - - c

(a) t (ps) (b) t (ps) (c) t (ps)

Figure AI Plots of the Raman intensity and the corresponding correlation function (a). The deconvoluted plots, the perturbation function, h, and the ideal spectrum, #, with their corresponding correlation functions are shown in (b) and (c), respectively. (c) Linear In Ic(t) l once the perturbation function, in this case the apparatus function, has been eliminated.

the spectrum is obtained. By a least square fitting method we can obtain deconvoluted spectra and the band parameters without any previous assumptions (Fig. 7).

The apparatus function (slit function) is corrected in order to obtain accurate values of the correlation function slope. Using the described deconvolution procedure, the perturbation function, h(v - v'), can be assimilated to the apparatus function, so the decon- volution allows its influence to be eliminated and thereby the ideal spectrum, g(v) to be obtained. The spectral slit width was changed from 1 cm -1 to 3 cm-1 in order to determine its influence on the spectrum. For 1 c m - 1 spectral slit width, there was no noticeable apparatus function influence; the bulk sili- con spectra were highly Lorentzian; therefore, this was the spectral slit width used in our experiments. For increasing slit width, the spectrum is deformed. Fig. A1 shows the plots of le~ p (v) versus, v, the slit function, h (v) versus v and the corrected spectrum, g(v) versus v, as well as their corresponding correla- tion functions, c(t), for a spectral slit width of 3 c m - 1, showing how the slit function perturbs the experi- mental spectrum.

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Received and accepted 18 May 1993

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