HAL Id: jpa-00205718
https://hal.archives-ouvertes.fr/jpa-00205718
Submitted on 1 Jan 1964
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Optical constants of thin films from the characteristic electron energy losses
R.E. Lavilla, H. Mendlowitz
To cite this version:
R.E. Lavilla, H. Mendlowitz. Optical constants of thin films from the characteristic electron energy losses. Journal de Physique, 1964, 25 (1-2), pp.114-118. �10.1051/jphys:01964002501-2011400�. �jpa- 00205718�
OPTICAL CONSTANTS OF THIN FILMS
FROM THE CHARACTERISTIC ELECTRON ENERGY LOSSES
By R. E. LAVILLA and H. MENDLOWITZ,
National Bureau of Standards, Washington, D. C.
Résumé. 2014 On décrit une méthode-permettant d’obtenir les constantes optiques à l’aide de la corrélation entre le spectre caractéristique d’absorption de l’énergie électronique d’une substance et ses propriétés optiques. Cette méthode est appliquée à une étude des propriétés optiques, dans
l’ultraviolet lointain, d’un métal, l’aluminium, et d’un composé organique, le polystyrène. L’infor-
mation que l’on déduit de cette méthode se prête à une étude de l’oscillateur optique.
Abstract. 2014 A method for obtaining the optical constants by employing the correlation between the characteristic electron energy absorption spectrum of a substance with its optical properties
is described. This method is applied to a study of the optical properties in the far ultraviolet of
aluminum, a metal, and of polystyrene, an organic compound. The information that is derived
by this method lends itself to a study of the optical oscillator strengths.
LE JOURNAL DE PHYSIQUE TOME 25, JANVIER-FÉVRIER 1964,
We present here a procedure for determining the optical properties of materials in the far ultraviolet
by use of data obtained from the energy absorption spectrum of electrons scattered from these mate- rials. We discuss the optical properties, in terms
of the frequency dependent complex dielectric constant, of aluminum in the photon energy range of 12 to 17 eV and of polystyrene in the photon
energy range from 5 to 30 eV.
The optical constants of aluminum from 2 500 A to 6 500 A have been published by Haas and Waylonis [1]. These data were analyzed in terms
of the Drude free electron gas model [2] where the parameters N, the density of free electrons and r, the relaxation time were determined to be 2.4 electrons per atom and 1.2 X 10-15 sec, respecti- vely. These parameters were shown to describe
the optical properties of aluminium for the range 2 500 to 5 u. We now also find that the same two-.
parameter model gives a fairly adequate descrip-
tion of the optical properties in the far ultraviolet.
In electron energy absorption experiments, a
beam of electrons with a well defined energy is incident upon a thin film specimen of the material
to be studied. The energies of the transmitted electrons are determined, and it is found that the energy loss spectrum is a characteristic of the material being investigated [3]. In many cases, it is found that in the characteristic electron energy absorption experiments, where the electrons
have lost energies from 0 to 50 eV, the spectrum
consists of a major absorption line or band and
one or more subsidiary absorption maxima.
Let P(E) be the probability that an incident elec- tron will lose an amount of energy between E and E + dE in interacting with the thin film specimen.
Then the intensity of the natural absorption line Inat(E) is ’
where 8(E) is the Dirac 8-function, and A8(E) being the intensity of the incident beam. P(E)
and Inat(E) are identical in form. However, the
measured absorption Iloss(E) consists of the natural
absorption line folded with the spectrum of the
incident electron beam IO(E) (the smearing arising
from the detection system is taken as negligible in comparison to the incident beam energy distri-
bution). Thus
The type of integral equation displayed in eq. (2)
has wide application in spectroscopical investi- gations and has been studied for quite some time
now [4]. We determine P(E) by taking the
Fourier transfrom of eq. (2) and by the use of the folding theorem. Electronic computers were used
to carry out the calculations. The numerical pro- cedures that we have followed are those described
by Burger and Van Cittert [4]. We employed an
iterative procedure where the zeroth approximation
to P(E) is the measured loss curve. The iteration series was terminated when it was thought that higher order terms would not give any signifi- cantly better results or might even start to diverge.
This was found to be at the first or second approxi-
mation. We have attempted a few different
approximation methods for aluminum and have
finally decided on the Burger and van Cittert
method since seemed to give the most consistent
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01964002501-2011400
115
results. Our earlier reported results [5] were
obtained by following the procedure of Stokes [4],
which gave results that differ somewhat from those
reported here. The BvC method is probably most
suited for the case of aluminum because the widths of the Io(E) function and hoss(E) are both quite
narrow and of comparable magnitude. In other
cases it is quite reasonable to expect that other approximation methods would be more advan-
tageous. One must recognize that the various
numerical methods employed to solve the type of
integral equation shown in eq. (2) present inherent difficulties [6] and one cannot often determine the
rate of convergence of the approximation method,
if at all.
After obtaining P(E), one can correlate this
function with the optical properties. Those cha-
racteristic electron energy absorption line (bands)
which arise from the longitudinal components of
the electromagnetic field interacting with the
matter in bulk (no surface effects) can be described
by [2, 3, 7].
where e*(E) is the complex conjugate of the energy
(frequency) dependent complex dielectric constant.
We obtain from the experimental data by using
eq. (3) the imaginary part of the reciprocal of e*(E),
and the real part of the reciprocal of e*(E) is
obtained by employing the Kronig-Kramers dis- persion relations [8]. This procedure may be
utilized provided that the functional behavior of
Im(l/e*) is not too pathological, an assumption
which we can reasonably make because of causa-
lity requirements [9].
FIG. 1. - Characteristic electron energy loss spectra of
aluminum.
In figure 1 we display the characteristic electron energy absorption spectrum of aluminum in the
forward direction [10] which was taken on a film
of about 800 A thickness by an improved version
of the electron spectrometer described by Marton
and Simpson [11]. Note that the profile of the major absorption peak at 14.75 eV is almost
symmetrical on a relatively flat continuum and the
low-lying peak is barely detectable.
FIG. 2. - Experimentally observed profile of major loss
of aluminum , the convolution of the
experimental Io(E) distribution with the first BvC appro-
ximation to the natural line shape -
and the convolution of the experimental Io(E) with the
second approximation - - -
-.
In figure 2 we show an expanded version to the major absorption peak. In order to check consis-
tency, we folded the derived P(E) with experimen- tally determined energy distribution of the inci- dent beam. The convolutions of the first and second approximations to P(E) with lo(E), and
the experimentally obtained loss curve is also shown in figure 2 for comparison. We retained both
approximations to the unfolding of P(E) because,
as we mentioned earlier, we cannot readily deter-
mine if the higher approximations will give results
better than the first. We see that they both
follow the original experimental curve reasonably
well. The differences of the derived data curves
from the original data give us an estimate of the
uncertainties in the final results. In fact, because io(E) is so narrow, we can obtain significantly
informative results from the zeroth order approxi-
mation. Some of the difficulties are not entirely
due to the numerical procedures but arise from our
inability to read the experimental values in the
wings to an accuracy better than 10 % and in
some cases in the region where the curves are very
close to the background even 20 % might be an optimistic estimate.
The optical constants are displayed in figure 3.
The values have, been obtained by invoking the
sum rule to normalize the intensity of the absorp-
tion curve [12], that is
A being Planck’s constant divided by 21t and co2=:z 47rNe-/m*, cop is the free electron plasma
frequency and was approximated by taking it equal to the frequency of the major electron energy
absorption peak [13]. For N we obtain 2.6 elec-
trons per atom when the effective mass of the
electron, m* is taken equal to the mass of the
free electron.
FIG. 3. - The optical properties of aluminum derived from the first BvC approximation A, the second BvC
approximation x, and compared with the Drude free electron gas model with parameters r = 0 . 7 X 10-15 s, ,r = 1.5 x 10-lb s, and N = 2.6 electrons per atom, and optical measurements.
The optical constants which are obtained are compared with those given by the Drude model [2]
where the real and imaginary parts are given in
terms of the frequency w (liú.) = Eloss) by
For the Drude mode], we have takeii the para- meters, N the density of free electrons to be 2.6 per atom and the relaxation time to be in the range from 0.7 to 1.5 X 10-15 sec, respectively.
We chose the same value of N for this model as was taken for the sum rule in eq. (4). The values
of T were obtained by calculating the integrated
half-width of the unfolded major absorption peak
and also by taking the ratio of
The first method gave 0:75 X 10-15 s and the second method gave most of the values in the range mentioned above. Actually, since alumi-
num is not really a free electron gas one cannot
expect that the Drude model will completely des-
cribe the material. The deviations of the imagi-
nary part of e(W) from the curves obtained from
this model probably arise from an optical transition
or onset of photo electron emission. The results obtained by direct optical methods by Madden [14]
and also Hunter [15] are also included for compa-
rison in figure 3.
In some cases, the total oscillator strength expressed by the sum rule (eq. (4)), is of interest in itself as in the case of polystyrene. In the case
of aluminum, a metal, the electron energy absorp-
tion spectrum is satisfactorily understood in terms of collective effects that occur when the absolute
magnitude of the dielectric constant deviates from
unity. Note that the major electron energy
absorption peak occurs where both the real and .
the imaginary part of E( 6)) are small. However,
in an organic polymer compound like polystyrene
one might expect that in the ultraviolet region photon energies up to about 7 eV, the absolute
magnitude of the dielectric constant should differ little from unity. Thus the imaginary part of c(E)
which determines the optical absorption should
not differ significantly from imaginary part of the reciprocal of E*( 6)) which determines the electron energy absorption. In order to test this assump-
tion, it is necessary to know the number of elec- trons participating in the interaction over the entire energy range in order to normalize the inte-
gral in eq. (4).
FIG. 4. - Characteristic electron energy loss spectra of atactic polystyrene, the dashed curve indicates the pro- file of the major absorption that was assumed.
117
The electron energy absorption spectrum in
atactic polystyrene [16] is displayed in figure 4.
Note the broad band at about 21 eV with a very a
large half-width of the order of 10 to 15 eV which is characteristic of the carbon compounds. The
dashed curve indicated the high energy profile of
the major absorption. Further, notice that there is a subsidiary absorption peak at about 7 eV which might possibly be correlated with the known
optical absorption in molecular benzene and its derivatives. If the magnitude of e(E) is unity in
this region or close to unity then the electron absorption would be of a local nature and arise
from the excitation of the 7t electrons in the ben-
zene rings. However, if the magnitude of e(E)
differs from unity, then we can expect that the
effect is collective in nature and the imaginary part
of s(E) differs from the imaginary part of the reciprocal of E(w).
In the case of polystyrene, we did not unfold the
natural loss distribution from the raw data because
we felt that for our present purposes it is not
necessary). to obtain any additional refinement
beyond the zeroth approximation. The energy dependent dielectric constants that we have deter- mined are shown in figure 5. These were directly
FIG.
5. - The opticalproperties of
polystyrene derivedfrom electron energy absorption data.
obtained by employing the Kronig-Krarners dis- persion relations to obtain the real part of the reciprocal of F-*(E), and were normalized so as to agree both qualitatively and with the same order of magnitude as the data on optical absorption of
Buck and Weinreb [17]. Note the behavior of the real part of the dielectric constant in the region
of 5 to 8 eV. Since its magnitude becomes quite
small and changes sign in this region, we might expect that the material will exhibit reflectivity
maxima in this region, This possibility was sug-
gested to Hunter and he found reflection maxima
as predicted [18]. Thus we may feel fairly satis-
fied that the real part of e(E) is significantly
different from unity in this region, and that the electron energy absorption peak is enhanced by
collective effects even in the 7 eV region. After having normalized this data in the manner dis- cussed above, we find that the sum rule for elec- tron energy absorption accounts for about 25 to 30 of the 56 electrons of the monomeric unit of the
molecule, a result which is quite surprising. Also
the optical oscillator strength for the 7 eV optical absorption is equivalent to about one half electron
per " molecule ". This value does not agree very well with the optical oscillator strengths previously
estimated in studies on benzene-like molecules which gave values from about 0.7 to 1 electron per
"
molecule " [19]. However, the electron energy
absorption oscillator strength does not appear to vary significantly when some of the hydrogens in polystyrene are replaced by deuterium or fluo-
rine [17]. Thus one might expect that the 25 to
30 electrons which contribute to the oscillator
strength are primarily from carbon atoms rather
than from the other constituents of the molecule.
We do not yet understand why only carbon atoms
should participate in the interaction. The most
significant aspect of our result is that materials.
which are essentially different from a metal do
exhibit collective type interactions, I E( 6)) differs significantly from unity even in the 7 eV photon
energy region.
We have shown here how one may utilize the characteristic electron energy absorption spectra
to obtain optical constants and also the study of
the oscillator strengths over a fairly large energy
region. There are still a number of shortcomings
in this method, the most important being the nor-
malization problem which we hope will be comple- tely overcome once accurate cross sections are
obtained.
Acknowledgements. - We are indebted to
N. Swanson and H. Fowler for permission to use
their unpublished aluminum data and N. Swanson for the polystyrene data. We also gratefully acknowledge the use of J. R. Nelson’s basic com-
puter program for the K - K dispersion inte- gration, J. J. Spijkerman for writing the computer
program for the BvC unfolding procedure and
R. Deslattes for helpful discussions regarding unfolding. We extend our sincere thanks to A. Weinreb for the unpublished optical data on polystyrene, and W. R. Hunter for use of his opti-
cal data on aluminum and for measuring the reflec-
tivity of polystyrene. We also want to thank
J. Smith for preparing the figures and L. Marton
and J. A. Simpson for various courtesies granted to
us in their laboratory,
BIBLIOGRAPHIE [1] HAAS (G.) and WAYLONIS (J. E.), J. Opt. Soc. Am.,
1961, 51, 719.
[2] MENDLOWITZ (H.), Proc. Phys. Soc., London, 1960, 75, 664.
[3] MARTON (L.), LEDER (L.) and MENDLOWITZ (H.), Adv.
in Electronics and Electron Physics, ed by L. Marton, Academic Press Inc., N. Y., 1955, 7, 183.
[4] BURGER (H. C.) and VAN CITTERT (P. H.), Z. Physik., 1932, 79, 722 ; Z. Physik, 1933, 81, 428. STOKES (A. R.), Proc. Phys. Soc., London, 1948, 61, 382.
PORTEUS (J. O.), J. Appl. Physics, 1962, 33, 700.
FELLGETT (P. B.) and SCHMEIDLER (F. B.), M. N., 1952,112, 445. ROLLETT (J. S.) and HIGGS (L. A.),
Proc. Phys. Soc., London, 1962, 79, 87. This gives
a representative list and each can be consulted for further references.
[5] LAVILLA (R.) and MENDLOWITZ (H.), Phys. Rev. Lett., 1962, 9, 149.
[6] Fox (L.) and GOODWIN (E. T.), Phil. Trans. Roy.
Soc., London, 1953, A 245, 501.
[7] FROHLICH (H.) and PELZER (H.), Proc. Phys. Soc., London, 1955, A 68, 525 ; HUBBARD (J.), Proc.
Phys. Soc., London, 1955, A 68, 441.
[8] KRONIG (R. de L.), J. Opt. Soc. Am., 1926, 12, 547 ; Ned. Tijdschr. Natnurk, 1942, 9, 402. KRAMERS (H. A.), Estratto dagli Atti del Congresso Inter. di Fisica, Como, 1927, 545.
[9] MACDONALD (J. R.) alld BRACHMAN (M. K.), Rev. Mod.
Physics, 1956, 28, 393.
[10] FOWLER (H.) and SWANSON (N.), Unpublished data.
Similar spectra are given in MARTON (L.) and al., Phys. Rev., 1962, 126, 182.
[11] MARTON (L.) and SIMPSON (J. A.), Rev. Sc. Instr., 1958, 29, 567.
[12] FANO (U.), Phys. Rev., 1956, 103, 1202.
[13] MENDLOWITZ (H.), J. Opt. Soc. Am., 1960, 50, 739.
[14] MADDEN (R. P.), Physics of Thin Films, 1962, 1, 123, Academic Press, N. Y., ed by G. Haas ; MADDEN, CANFIELD and HAAS, J. Opt. Soc. Am., 1963, 53,
620.
[15] HUNTER (W. R.), Unpublished data.
[16] SWANSON (N.) and POWELL (C. J.), J. Chem. Physics, 1963, 39, 430.
[17] BUCK (W. L.) and WEINREB (A.), Unpublished report
ANL 63-26 and private communication from A. Weinreb.
[18] HUNTER (W. R.), Unpublished data.
[19] KLEVENS (H. B.) and PLATT (J. R.), J. Chem. Physics, 1949, 17, 470 ; TURNER (D. W.), in Determination
of Organic Structures by Physical Methods, 2, 339, ed by F. C. Nachod and W. D. Phillips, 1962,
Academic Press, N. Y. These are typical refe-
rences for the oscillator strengths of benzene and benzene derivatives.
DÉTERMINATION ET ÉTUDE DES PROPRIÉTÉS OPTIQUES
DES COUCHES MINCES DE PALLADIUM Par PIERRE LOSTIS,
Institut d’Optique, Paris.
Résumé. 2014 Description succinte de la préparation des couches minces, ainsi que des méthodes de mesure utilisées (spectrophotométrie, déphasages, études aux rayons X
et au
microscope élec- tronique). Constantes optiques du palladium dans la région spectrale comprise entre 2 000 et25 000 Å, et quelques remarques à leur sujet.
Abstract. 2014 A brief description is given of the preparation of thin films, and of the methods used for their measurement (spectrophotometry, phase-changes, X-rays and electron-microscopy).
Optical constants of palladium are given in the spectral region between 2 000 and 25 000 Å
and these are discussed.
LE JOURNAL DE PHYSIQUE TOME 25, JANVIER-FÉVRIER 1964,
Le but de 1’expos6 est de donner les r6sultats que nous avons obtenus sur les couches minces de
palladium. Cependant, avant de donner ces r6sul- tats, il nous parait important de d6crire les modes
op6ratoires de 1’etude ; en effet, il est n6cessaire de connaitre les conditions dans lesquelles les couches ont ete r6alis6es et les diff6rent6s mesures optiques qui ont ete faites, puis de montrer la structure des
couches 6tudi6es.
Rdalisation des couches. - Les couches ont 6t6 r6alis6es sous une pression de l’ordre de 10-6 mm
de Hg, d6pos6es sur un support en silice. Le net- toyage du support et de 1’enceinte a ete soigneu-
sement fait par voie chimique, puis, avant 1’6vapo-
ration du m6tal, le support 6tait degaze a 350 °C ;
le chauffage du support a ete obtenu uniquement a
1’aide du rayonnement d’une plaque de tantale
chauffée. Le chauffage du creuset qui 6tait form6
de tiges de tungst6ne se faisait par effet Joule.
La vitesse d’évaporation 6tait de l’ordre de 100 A/s : il semble que ce param6tre ait une grande importance sur la qualite des couches ;
d’autre part, quand la vitesse d’6vaporation est de
