THICKNESS DETERMINATION OF Al FILMS ON Si BY A MONTE CARLO CODE INCLUDING A SECONDARY FLUORESCENCE CORRECTION

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THICKNESS DETERMINATION OF Al FILMS ON Si BY A MONTE CARLO CODE INCLUDING A SECONDARY FLUORESCENCE CORRECTION

A. Armigliato, A. Desalvo, A. Garulli, R. Rosa

To cite this version:

A. Armigliato, A. Desalvo, A. Garulli, R. Rosa. THICKNESS DETERMINATION OF Al FILMS ON Si BY A MONTE CARLO CODE INCLUDING A SECONDARY FLUORESCENCE CORREC- TION. Journal de Physique Colloques, 1984, 45 (C2), pp.C2-29-C2-32. �10.1051/jphyscol:1984207�.

�jpa-00223763�

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J O U R N A L DE P H Y S I Q U E

Colloque C2, supplkment au n02, Tome 45, fbvrier 1984 page C2-29

T H I C K N E S S D E T E R M I N A T I O N OF A 1 F I L M S ON Si BY A MONTE C A R L 0 CODE I N C L U D I N G A SECONDARY FLUORESCENCE CORRECTION

A. ~rmigliato*, A. Desalvoif, A. ~arulli* and R. ~ o s a * :CUR, I s t i t u t o LAMEL, Via Castagnoli, 1, 40126 Bologna, I t a l y

I s t i t u t o Chimico, FacoZtd dfIngegneria, Universitd d i Bologna, I t a l y

Resum6 - On a introduit dans notre programme Monte Carlo une correction pour le rayonnement de fluorescence X di3 aux raies caracteristiques du substrat dans une couche mince. Cette correction a Bt& appliquee avec succss pour Qvaluer avec une meilleure pre'cision 1'Bpaisseur de couches d'Al sur Si.

Abstract - A correction for x-ray characteristic fluorescence in thin films on substrates has been successfully applied to A1 films on Si in order to get a more accurate evaluation of their thicknesses.

INTRODUCTION

Corrections for charateristic fluorescence in electron probe microanalysis are often disregarded by computer programmes dealing with thin unsupported and suppor- ted films. Analytical treatments as applied to unsupported films and fildsubstrate systems were put forward by Nockolds et al. /1/ and Cox et al. /2/ respectively. To account for such an effect we improved our Monte Carlo computer programme (CARLONE) as described elsewhere /3/. In this paper we applied the code to the determination of the mass thickness of Al/Si films. The results were compared with the ones obtained by Rutherford backscattering spectrometry (RBS).

EXPERIMENTAL

By electron beam evapo5ation we prepared a number of A1 films of different thicknesses up to-50 pg/cm , onto Si and boron nitride (BN) substrates. The latter was chosen for RBS measurements, because, as it is known, accurate values of thickness can be obtained by the above technique only if the atomic number of the substrate is lower than that of the film. X-ray microanalysis measurements were performed with two different instruments: i) an ARL-SEMQ fully automated electron microprobe (take-off angle p = 52.5") equipped with WDS spectrometers; ii) a Cambridge Stereo- scan 150 Mark I1 SEM ( p = 30°) equipped with a Tracor-Northern EDS Spectrometer.

The accelerating voltages were 10, 20 and 30 kV in both instruments. The intensity of the AlKa line was measured on both A l / ~ i and A ~ / B N samples, as well as on bulk standards of Al, in order to deduce the corresponding k-ratios. RBS analyses were performed with the 2 MeV Van de Graaff ac elerator of the Laboratori Nazionali di Legnaro. The incident beam was 1.8 MeV

4 H 2

and the backscattered ions were detec- ted at = 150° by a Si surface barrier detector.

MONTE CARLO PROGRAMME

According to /3/ the primary x-ray intensity emitted by the volume element of thickness d(gz) (s stands for "substrafe") around point P is calculated (see Fig. 1).

After that 'the programme computes the x-ray intensity absorbed by the annular volume element of thickness d(@z) (f stands for "film") centered on point Q (see also / 4 / ) . The x-ray fluorescence intensity at this point is obtained from the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984207

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C2-30 JOURNAL DE PHYSIQUE

absorbed one by the usual procedure, taking into account the jump ratio and the fluorescent yield. The x-ray characteristic fluorescence intensity dIF to be added to the primary radiation dI as generated in the layer d( ~ z ) ~ , is obtained by performing the integrationP'over the angle y from 0 to n/2 and over the layer

~(Qz), from infinity to 0 . The result is given by the formula:

where r. is the jump ratio for the particul\r x-ray, w. is the fluorescent yield, pi is thk relative intens-

Electron ity of the analyzed x-ray in the

beam series and El(x) the exponential integral. The function @ ( @ z)s is obtained by the Monte Carlo simulation and the integration is performed numerically. The resulting total intensity dItot= dIpfdIF, as emitted from the film layer d( @ z ) f, can be handled by CARLONE for any value of film thickness, thus removing the limitation to a thin layer inherent in the analytical approach by Cox et al.

/ 2 / . Notice that in evaluating the

k-ratio, some constants in the fluorescence term do not cancel out, giving however a factor very close to unity. For sake of completness we took into account also the fluorescence due to the radiation, which turns out to be very small (some percent of that due to SiKa ) .

Fig. 1 - Computational scheme of x-ray fluorescence emission for the case of a film over a substrate.

RESULTS AND DISCUSSION

By Monte Carlo simulation we have constructed calibration curves of k Al VS. et for the Al/Si case, both neglecting and taking into account the fluorescence effect.

The results, for the case of the ARL microprobe ( p = 52.5O) at the three operating energies, are displayed in Fig. 2. It is worthwhile to notice that the simulations at a given energy were undertaken using the correlated sampling, i.e. with the same random numbers sequence, both with and without fluorescence. Thus the statistical uncertainty due to the random draws does not overshadow the effect of the fluorescence itself. From Fig. 2 it appears that, while at 10 keV the fluorescence effect is negligible (the curves are practically superimposed) at 20 and 30 keV it is of increasing significance. The experimental k-ratios of four A1 films of increasing thickness are reported in Tab. 1 for both electron microprobe and SEM/EDS. It is important to remind that, due to the inherent lower energy resolu- tion of this latter technique, the net peak intensities of the AlKa peaks are obtained by a multiple least square fitting procedure applied to the overlapped A1-Si peaks /5/. Instead, in the case of microprobe, the AlKa and 'SiKa peaks are very well separated and hence it is only necessary to subtract the background under the peak, as obtained by a linear interpolation. Therefore, particularly at higher accelerating voltages, when the x-ray intensity generated in the film is lower, a

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better accuracy in the determination of k-ratios is expected in case of the microprobe. From the k-ratios reported in Tab. 1 it is possible to deduce the film thickness by comparison with the calibration curves reported in Fig. 2.

Fig. 2 - k-ratio for the AlKa line vs. film thickness for 10(a) , ²⁰(b) and 30 keV (c) incident electrons ( p= ^52.5O). Full curve, with fluorescence; broken curve, without fluorescence.

The results are shown in Tab. 2, together with the corresponding values obtained by RBS analysis; the method employed to determine the film thickness from a RBS spectrum is reported elsewhere /6/. An inspection of Tab. 2 allows one to draw the following conclusions: i) the thickness data obtained with the microprobe are generally in good agreement with those obtained by RBS technique, whereas the SEM/EDS results are less accurate, as previously discussed. ii) the difference between the curves reported in Fig. 2 corresponds to a 10% variation in the k-ratios with and without secondary fluorescence. Neglecting the fluorescence correction results in a worsening of the overall agreement with the nuclear backscattering data.

In conclusion, this work demonstrates that in the Al/Si case, which is of interest in silicon technology, to obtain an accurate evaluation of the film thickness, it is necessary to have available a thickness dependent fluorescence correction. If this correction is inserted into a Monte Carlo code, it is also possible to predict for what thicknesses and accelerating voltages such a correction is significant.

Tab. 1 - Experimental k-ratios ( ~ 1 0 ~ ~ ) of four A1 films analysed at three accelerating voltages (Eo = 10,20 and 30 kev) by both electron microprobe and SEM/EDS.

SEM/EDS

10 20 3 0

7.39k0.18 2.57+0.11 1.28+0.06 12.80k0.10 3.97k0.05 2.0320.07 18.90k0.10 5.62k0.10 3.07+0.07 25.40k0.10 6.99k0.08 4.15'0.09 MICROPROBE

1

10 20 30

~l/Sil

~ 1 / S i 2 Al/Si3 Al/Si4

6.32k0.06 1.7620.06 1.0320.01 11.08k0.10 2.95'0.12 1.74k0.01 16.63k0.15 4.22'0.20 2.46'0.05 22.54'0.25 5.93'0.12 3.33'0.05

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C2-32 JOURNAL DE PHYSIQUE

Tab. 2 - ^Masst h i c k n e s s ( p g / ~ m L ) o f t h e f i l m s r e p o r t e d i n Tab. 1, a s o b t a i n e d by x-ray m i c r o a n a l y s i s ( e l e c t r o n microprobe and SEM/EDS) t h r o u g h t h e Monte C a r l o c a l i b r a t i o n c u r v e s . The c o r r e s p o n d i n g RBS r e s u l t s a r e a l s o shown f o r comparison.

ACKNOWLEDGEMENTS

The a u t h o r s a r e i n d e b t e d t o S . G u e r r i f o r p r e p a r a t i o n of t h e f i l m s , t o R - R i n a l d i f o r t h e u s e o f e l e c t r o n microprobe f a c i l i t y o f t h e U n i v e r s i t y o f Modena, and t o M.

B e r t i and A.V.Drigo f o r t h e RBS measurements.

RBS

13.720.4 22.620.7 34.021.0 43.021.3

-

REFERENCES

SEM/EDS

10 20 3 0

16.020.4 18.4c0.8 15.2k0.8 25.2k0.6 27.8c0.4 24.2k1.0 35.220.6 38.4k0.6 36.2c0.9 44.8t0.6 47.220.8 48.421.0 MICROPROBE

20 30

/1/ NOCKOLDS C., NASIR M . J . , CLIFF G. and LORIMER G.W., i n " E l e c t r o n Microscopy and A n a l y s i s 1979", I n s t . Phys. Conf. S e r i e s No. 52 (1980) p.417.

/2/ COX M.G.C., LOVE G. and SCOTT V.D., J. Phys D: Appl. Phys. 2 (1979) 1447.

/3/ ARMIGLIATO A., DESALVO A. and ROSA R., J. Phys. D: Appl. Phys. 15 (1982) L121.

/ 4 / MAURICE F., i n "Microanalyse e t Microscopie E l e c t r o n i q u e 2 Balayage" (F.

Maurice, L.Meny a n d R . T i x i e r E d s ) , E d i t i o n s de P h y s i q u e , Orsay (19791, p.206.

/5/ SCHAMBER F.H., WODKE N.F. and Mc CARTHY J. J . , Proc. 8 t h I n t . Conf. o n X-ray O p t i c s and Microan. (D.R. Beaman, R.Ogilvie and D.B. W i t t r y Eds.) P e n d e l l Publ. Co, Midland (1980) p.124.

/6/ CHU W-K, MAYER J . W . a n d NICOLET M-A, " B a c k s c a t t e r i n g S p e c t r o m e t r y " , Academic P r e s s , New York, 1979.

A l / S i l

~ l / s i 2 A l / S i 3 A l / S i 4

13.020.2 14.0f0.6 14.420.2 22.420.2 23.4t0.7 24.8i0.2 31.6k0.4 32.8t1.6 34.420.8 41.020.4 44.8t0.8 45.620.8