RESTITUTION OF SURFACE PROFILES FROM MICRODENSITOMETER ANALYSIS OF ELECTRON MICROGRAPHS OF SURFACE REPLICAS

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RESTITUTION OF SURFACE PROFILES FROM MICRODENSITOMETER ANALYSIS OF ELECTRON

MICROGRAPHS OF SURFACE REPLICAS

G. Rasigni, M. Rasigni, F. Varnier, J. Palmari, A. Llebaria

To cite this version:

G. Rasigni, M. Rasigni, F. Varnier, J. Palmari, A. Llebaria. RESTITUTION OF SURFACE PROFILES FROM MICRODENSITOMETER ANALYSIS OF ELECTRON MICROGRAPHS OF SURFACE REPLICAS. Journal de Physique Colloques, 1983, 44 (C10), pp.C10-367-C10-370.

�10.1051/jphyscol:19831074�. �jpa-00223532�

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JOURNAL DE PHYSIQUE

Colloque C10, suppl6ment au n012, Tome 44, d k e m b r e 1983 page C10-367

R E S T I T U T I O N OF SURFACE P R O F I L E S FROM MICRODENSITOMETER A N A L Y S I S OF ELECTRON MICROGRAPHS OF SURFACE R E P L I C A S

G. Rasigni, M. Rasigni, F. Varnier, J . P . Palmari and A . ~ l e b a r i a *

Centre d'~tudes des Couches Minces, Universite' Aix-Marseille 111, rue Henri Poincare', 13397 MarseiZZe Cedex 13, France

r~aboratoire dtAstronomie Spatiale, 13012 Marseille, France

R6sum6

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On pr6sente une nouvelle mgthode d'stude des surfaces rugueuses s'appuyant sur une analyse microdensitom6trique de microqraphies obtenues par la technique des r6pliques.On en d6- duit les fonctions d'autocovariance et les spectres de rugosite de diffgrentes surfaces rugueuses. Les rgsultats sont com~args avec ceux fournis par d'autres m6thodes.

Abstract

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A new method for studying surface roughness is pre- sented that uses a microdensitometer to analyse electron micrographs of shadowed surface replicas. Autocovariance functions and roughness spectrums are deduced for various rough surfaces.

Results are compared with those provided by other techniques.

The structure of a rough surface is characterized by its profile S(x,y).

From this profile it is possible to determine the autocovariance function G(x,y) that summarizes statistical information or the various chqracteristic lengths describing the surface. The Fourier transform g(k) of G(x,y) is the roughness spectrum (or spectral density function) that plays an important part in scattering and polaritonsl problems.

This paper is devoted to a new method for determining surface profile and statistical parameters of various rough surfaces.

I

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EXPERIMENTAL PROCEDURES.

A thin layer of carbon is evaporated on the deposit whose structure is to be determined (replication technique2). We obtain a replica that is shadowed with a P-Pt to show some contrast in an electron microscope. An image is obtained on an electron-micrograph plate by transmission electron microscopy. The electron-micrograph image is then digitized with a PDS 1010 A microdensitometer which measures the microqraph density d at regular interval in both the x (shadow direc- tion) and the y directions. The analysis is made line by line. Thus one obtains a grid of n scanning lines with m points by line. In a previous paper2 we have shown that the-slopes of the surface elements are proportional to the micrograph density d. It ensues that the surface profile S ( x ) for a line may be obtained for any x by integrating density data.

Actually, as previously discussed2, we have to eliminate random noise prior to calculations. Different filtering alsorithms have the- refore been used. Figure 1 shows the different steps leading to the determination of the surface profile. Figure 2 shows for surfaces of Mg and CaF2 deposits together the photomicrograph and the perspective view of the surface obtained by means of a computer plotting program.

A good approach of the real profile is obtained. We have checked out the validity of this procedure by reconstructing the microqraphs images from surface profiles obtained by microdensitometer analysis (quan- tization and rescaling processes3). These micrographs images compare

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19831074

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ClO-368 JOURNAL DE PHYSIQUE

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ELECTRON MICROGRAPH OF SURFACE REPLICA Microdensitometer analysis

measurements (line by line)

+

^d^(x)(PROPORTIONAL TO -S ' (x))

P

(x)

value <p(x) >

~(x)=a>(x)-<a,(xt)>

A(x)-B(x)=C(x) (proportional to S(x))

u*

Calibration

+

^s(x) (SURFACE PROFILE FOR A LINE)

GI-

Computer plotting program RECONSTRUCTION OF SURFACE PROFILE

Fig.1. Different steps of calculations leading to the determination of the surface profile.

Fig.2. Electron photomicrographs of the shadowed surface carbon replica for magnesium and CaF2 deposits

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Perspectives views of the surfaces obtained by microdensitometer analysis, using compu- ter plotting program. (Perspective angle 18').

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favorably with the original imaqes.

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AUTOCOVARIANCE FUNCTIONS.

Most of the surfaces we have studied were statistically homoge- neous and isotropic. So we can limit our discussion to one dimension.

Moreover we assume that our data are stationary and ergodic. If we characterize the height of the surface with respect to a plane defined as the average height <S(x)>

,

by writing

we can define the autocovariance function (ACF) as " - S

G(x)=Lim ^a+-- _a

6

H(xl) H (x+x') dx'

,

^{( 2 )}

where a is the distance measured on a straight line alonq the surface.

The ACF may be estimated by using discrete counterparts of Equ.2 (es- timators), or the FFT algorithm5. Figure 3 shows ACF for the surface of a CaF2 thin deposit. The initial portion of G(x) replotted on an expanded scale is fairly close to Gaussian, namely G ( ~ ) = 6 ~ e x p ( - x ~ / o ~ ) where 6 is the rms (root mean square) and a the autocorrelation length Such a study has been carried out for numerous

surface^^-^.

We found in any case that initial portions of.G(x) have a reasonable Gaussian form and that a increases with 6 . These results disagree with conclu- sions obtained by other authors6.

Fig.3. Autocovariance function for the surface of a CaF2 thin deposit (thickness 500

A) .

^The

initial portion of G(x) is reported on an expanded x scale and the dashed curve is the Gaussian function G (x) =6 2exp (-x2/02)

,

with 6=28.5

fi

and a=182

A .

1 2

Lag x (IO'AI

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ROUGHNESS SPECTRUM.

The estimation of the rouqhness spectrum g(k) for the random process H(x) can be done in some ways. The most interesting method is to calculate the ACF by using the FFT algorithm and Fourier transform. The Wiener-Khinchine theorem states that the resulting function is the roughness spectrum. The computation of the ACF as an intermedia- te result allows us the incorporation of a lag window W(x)which corres- ponds to a spectral window w(k) in the spectral domain. It is so possible to perform an arbitrary amount of smoothing in the spectral es- timate. From a practical point of view, we used the process described by Rabiner and

old^

based on covariance computation via the FFT and we have chosen a Bartlett window8.~igure 4 shows g(k) vs k for a surface of an Ag deposit. Attention must be drawn to the fact that g(k)

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JOURNAL DE _PHYSIQUE

is not throughout a Gaussian function and exhibits a peak at low spa- tial frequency. The dependence of 1nlg(k)] vs k 2 represented on Fig.5 shows that the values of ( 6 , ~ ) deduced from the Kretschman procedure9 clearly depend on the k range.

1

^---.-;..\ ^{Ag- 1}

4. R.oughness spectrum g(k) and roughness function In g(k) as a function of k2 for the surface of a sil-

"'7' ^l

ver deposit.

In a general way the values of 6 and a heretofore reported in the literature are smaller and greater respectively than the values of 6 and o we have determined.The reason for these discrepancies lies in the poor lateral resolution of methods such as interferometry,pro- filometry6 or ATR (attenuated total reflexion).These methods probably average over microroughnesses and do not detect them.

IV

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CONCLUSION.

The method we have developed is particularly useful in studying oxidizable surfaces, given that carbon replicas are made in situ.

Moreover it can display wdth good accuracy roughnesses smaller than 50

fi

on the plane and 10 A in the height of the surface respectively.

So this method is very promising and may have many applications espec- cially in optics (scattering) solid state physics (polaritons), bio- logy (reconstruction of membranes surface)and metallurgy.

REFERENCES

1.- "Surface Polaritons, Electromagnetic Waves at Surfaces and Interfa- ces", edited by AGRAMOVITCH V.M. and MILLS D.L. (Xorth-Holland,

-

Amsterdam, 1982).

2.- RASIGNI M, RASIGNI G, PALMARI J.D and LLEBARIA A., J. Opt. Soc.

Am. 71 (1981) 1124.

3.- RASIEI M., VARNIER F., RASIGNI G., PALFIARI J.P. and LLEBARIA A., J. Opt. Soc. Am. 71 (1981) 1549.

4.- RASIGNI M., RASIGE G., PALMARI J.P. and LLEBARIA A., J. 0pt.SOC.

Am 71 (1981) 1230.

5

.-

R A S ~ N I G., VARNIER F., RASIGNI M.

,

PALTIARI J.P. and LLEBARIA A.

J. Opt. Soc. Am. 73 (1983) 222; Phys. Rev. B

g

(1982) 2315.

6.- ELSON J.M. and BENNETT J.M., J. Opt. Soc. Am.

69

(1979) 31.

7.- RABINER L.R. and GOLD B., Theory and Application of Digital Signal Processing (Prentice Hall, Englewood ~ l i f f s, N. J., 1975)

.

8.- RASIGNI G., VARNIER F., RASIGNI M., PALflARI J.P. and LLEBARIA A., Phys. Rev. B 27 (1983) 819.

9.- KRETSCHMANN E, Opt. Comm.

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