Energy distributions of 7.3 keV electrons passing through iron films for depth-selective Mössbauer spectroscopy

Nuclear Instruments and Methods 205 (1983) 279-286 North-Holland Publishing Company

279

ENERGY DISTRIBUTIONS O F 7.3 k e V E L E C T R O N S PASSING FOR DEPTH-SELECTIVE MOSSBAUER SPECTROSCOPY

THROUGH

IRON

FILMS

J. ITOH, T. T O R I Y A M A , K. S A N E Y O S H I * and K. H I S A T A K E Department of Applied Physics, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo, Japan Received 17 March 1982 and in revised form 11 June 1982

The energy spectra of 7.3 keV electrons passing through iron films were measured with a high resolution electron spectrometer by use of a thin 57Co source. The energy resolution of the spectrometer was set for 1.3% at 7.3 keV. The thicknesses of iron films for electron scatterers were 63, 121, 175, 279 and 385 A. From the measured energy spectra we deduced the energy distributions for a monolayer source. The method of analysis is described in detail. The present energy distributions are in fair agreement with those of the Monte Carlo calculation of Liljequist et al. The weight coefficients for the depth-selective conversion electron MOssbauer spectroscopy are presented for energy resolutions of 1, 2 and 3%.

1. Introduction There has been a n increasing interest in conversion electron MOssbauer spectroscopy (CEMS) as a means of surface studies. If one analyzes the energy of conversion electrons emitted from absorber materials after the recoilless resonance absorption, one can deduce the MOssb a u e r spectrum as a function of d e p t h from the surface. This m e t h o d is the so-called depth-selective CEMS, which was first d e m o n s t r a t e d by Bonchev et al. in 1969 [1]. In order to use depth-selective CEMS, it is necessary to determine the energy distribution as a function of the d e p t h in absorbers accurately. Energy distributions for b e a m electrons of 2 . 5 - 3 0 keV normally incident on foils have been investigated by several authors [2-4]. However, it is difficult to apply these energy distributions for the present purpose because the angular distribution of conversion electrons is considered to be isotropic. Energy distributions of 7.3 keV conversion electrons emerging from absorbers have been measured by Baverstam et al. [5,6] by use of a 57Co source. The energy distributions of 20 keV electrons have been measured by Bonchev et al. [7] for conversion electrons emitted from 119SNO2 after MOssbauer absorption. The energy resolutions of electron spectrometers used in these experiments, however, were too low (larger than 4%) to perform a detailed depth-selective analysis. M o n t e Carlo calculations of energy distributions for C E M S have been performed by Liljequist et al. [8] and

* Present address: Department of Energy Sciences, Tokyo Institute of Technology, Nagatsuta-cho, Midori-ku, Yokohama, Japan. 0 1 6 7 - 5 0 8 7 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 © 1983 N o r t h - H o l l a n d

Proykova [9]. The comparison with experiments has not yet been m a d e extensively, particularly for thin absorbers, although partial comparison was recently made for a 250 A a - F e film [10,11]. In this study, we have measured the energy distributions of 7.3 keV electrons emitted from a thin ~7Co source covered with iron films of various thicknesses with a high resolution electron spectrometer. F r o m the energy distributions, we have derived accurate weight coefficients for the depth-selective CEMS. The results are c o m p a r e d with the calculation of Liljequist et al. [8].

2. Experimental 2.1. Preparation of 5ZCo electron source The thin 57Co source used in this experiment was electro-deposited in a 0.05 mol a m m o n i u m luctate on a N i foil of 5 ~ m thickness. Before electrodeposition we have purified the original SVCo chloric acid solution purchased from N E N by an anion exchange m e t h o d [12 ]. The activity of the source was a b o u t 30 ~Ci a n d the area was 3 m m in diameter.

2.2. Electron scatterers As scatterers for electrons, iron films have been deposited successively on the 57Co source by vacuum evaporation. The thicknesses of deposited films were d e t e r m i n e d with an in-situ quartz crystal oscillator, which had been calibrated by an X-ray fluorescence m e t h o d by use of a 71Ge source [13]. The thicknesses of the scatterers are shown in table 1.

J. Itoh et al. / Energy distributions

280 Table 1 Thickness of electron scatterers. a

b

c

Thickness of deposited iron film (A)

0

63.2 _+3.5

Integrated thickness (~,)

0

63.2 + 3.5

d

57.6 _+3.5

53.8 + 3.5

121 _+5

2.3. Electron spectrometer

e

175 _+6

f

104_+ 3.8

105 ± 3.8

279_+ 7

385 _+8

al. [6]. It should be noted that there appears no L-Auger peak in the spectrum even with the 63 A scatterer. This fact indicates that the scatterer almost covered the source surface, although the deposition of such a thin film might have a chance to make an island structure.

The electron spectrometer used in the present experiment was of a retarding-field type, which was described in refs. 14 and 15. The acceptance angle for the electrons emerging from the surface was taken from 30 ° to 60 ° to the surface normal. The energy resolution was set for 1.3% at 7.3 keV. The transmission for this setting was 2.4% of 4~r.

3. Analysis

3.1. General 2.4. Results Let us consider a monolayer source which emits electrons with a monoenergy E 0 isotropically. The source is assumed to be e m b e d d e d at the depth x in a material. The energy distribution of those electrons which pass through the material and emerge from the surface with an energy E and an angle 0, is described as T(x, O, E), where 0 is the angle relative to the surface normal. If the monolayer source is on the surface of the material, the energy distribution can be expressed by To(0, E); the

The energy spectra of electrons emitted from the 57Co source with scatterers of various thicknesses are shown in fig. 1. In the figure it can be seen that, as the thickness of the scatterer increases, the heights of the K-conversion and K-Auger electron peaks become smaller and the energies of the peaks become lower. The rates of changes in both peak heights and energies are considerably larger than those reported by Baverstam et

8x10 ~

i

i

K-Conversion 7.3keV) a no deposition b 63 ~,

KLL-Auger (5.6keV) ,---Q

C 121

d 17s LXY-Auger (-600ev)

~

Q P4

e-

~t

• 279 f 385

1t / 1

ib

a

KLM-Auger

/c

10

~..-f 0

1,o

I

3,0

I

I

5,o

61o

8.0

Energy (keV) Fig. 1. Energy spectra of electrons emitted from a thin 57Co source covered with iron films of various thickness. The energy resolution of the electron spectrometer used for the present measurement was 1.3% at 7.3 keV. The acceptance angle of the spectrometer was set from 30 ° to 60 ° relative to the surface normal.

J. Itoh et al. / Energr'distributions function T~(0, E ) is almost isotropic but not m o n o e n ergetic due to the c o n t r i b u t i o n of backscattered electrons. T(x, O, E) can be expressed as follows:

T(x, O, E)

= r E 0 T~(0,

E')L(x, O, E - E')dE'

rain

~- To(O, E) • L ( x , O, E), (1) where L(x, O, E - E') is the energy " l o s s " distribution for those electrons which are emitted isotropically in the forward direction with an energy E ' , pass through a layer of thickness x and emerge with an angle 0 and an energy E; the energy E - E ' is the energy loss. The symbol * indicates a convolution with respect to energy. Hereafter we choose Emi n SO that the m a x i m u m energy loss E 0 - Emi n is small enough c o m p a r e d to the initial energy Eo. If electron sources are uniformly distributed from x to x + s, as was p r o b a b l y the case in the present experiment, the energy distribution of those electrons emerging from the surface, Ts(x, O, E), is given by T~(x, 0, E ) = f(" + ~ T ( x ' , 0,

E)dx',

(2)

where we assume the source material is the same as the scatterer with respect to energy loss. Let us consider the case that the energy spectrum for this source is measured with a n electron spectrometer which has an acceptance angle between 01 a n d 0 z a n d the spectrometer profile R(E). The measured energy spectrum F(x, E) will be

or

= if012[

0, E)dx'] d0] • R(E)

(3)

F o r simplicity if we write the integration of T(x, O, E) from 01 to 02 as T(x, E), then F(x, E) can be written as

F(x,e)=

[/;+ r(x',E)dx ] *R(E).

F(O,E)=

T(x',E)dx' *R(E).

(5)

Now we try to obtain the relation between F(0, E ) a n d F(x, E). If we integrate b o t h sides of eq. (1) from 01 to 0 2, eq. (1) becomes

T(x, E) = T~(O,E)* L(x, E),

can approximately be written as

T(y + x, E) = T(y, E)* L(x, E).

(6)

where we denote the integration of L(x, O, E) from 0~ to 0 2 by L(x, E). Supposing that electrons have passed through a very thin layer of thickness y before arriving at the scatterer of thickness x, the energy distribution of the electrons emerging from the scatterer, T(y + x, E),

(7)

This equation is valid if the thickness of y is so small that the energy distribution of the electrons emerging from the d e p t h y is the same for all forward directions [16]. F r o m eqs. (4) a n d (7), F(x, E) can be rewritten as follows:

F ( x , E ) = [ foST(y+ x,E)dy] * R(E) =[foST(y,E)*L(x,E)dy]*R(E). Exchanging the order of the convolution of L(x, relation:

(8)

E)

and

R(E), we can o b t a i n the following F(x, E) = F(O, E)* L(x, E).

(9)

It should be noted that the convolution is only m a d e in the energy interval Emi n _< E < E 0. F r o m eq. (9), we can o b t a i n the energy loss distributions.

3.2. Estimation of source thickness from transmission We must know if the present source is thin enough to satisfy eq. (7). We can estimate the source thickness by using either transmission or energy distribution of electrons. The transmission data obtained from M o n t e Carlo calculations agree with those of previous experiments, although the energy distributions do not [17-19]. Therefore we first estimate the thickness of the source from the comparison of the transmission obtained from the present experiment with calculation. To do this, we first obtain the relation between transmission and the area of the energy spectrum F(x, E). If the energy resolution of an electron spectrometer is good enough, as was the case in the present experiment, the ratio of area of F(x, E) to that of F(0, E ) in the proper energy interval can be expressed in terms of T(x) from eqs. (4) and (5) as follows:

(4)

It is noted that the energy spectrum of the source with no scatterer can be written as

281

fE o

L'm,,F(x' E)dE

ex + s

j,

T(x')dx'

l(x)

(10) rE,, F(0,

E)dE

Jof T(x')dx'

Emin

Here T(x) is the energy- a n d angle-restricted transmission [8] and is written as T(x) =/

leo

T(x,E)dE.

(11)

*' Em~n

T h e quantity s is the thickness of the source to be obtained. For the transmission T(x) in eq. (10), we use that of M o n t e Carlo calculation of Liljequist et al. [8], whose energy and angle intervals are 6.3 to 7.3 keV and 37 ° to 53 °, respectively. This angle interval is almost the same as that of the present experiment (30 ° to 60°). For the

282

J. ltoh et al. / Energy distributions

crepancy between experimental l ( x ) values and those from the calculation larger than 250 ~, suggests that the calculated transmission is larger than the experimental one in this region. This will be discussed in sect. 4.

s=80~ 1.0(

04

3.3. Energy distribution of K-conversion electrons 3.3.1. Energy loss distribution

',+o

20'0

Depth x (J,]

3d0

The energy loss distribution of K-conversion electrons L(x, E) is obtained from eq. (9). For this purpose, we tentatively made a deconvolution of F(x, E) with F(0, E). In the deconvolution, the discrete fast Fourier transform [20] was used to save calculation time. In order to estimate the error caused by the limitation of the energy range in the deconvolution, F(0, E ) was convoluted again with L(x, E). It was found that the results reproduced the original energy spectrum within an error of 6%.

~o

Fig. 2. The function l(x), defined in eq. (10) in the text, as a function of depth x. Closed circles are the experimental values. Solid curves are the calculated ones obtained from ref. 8 with the parameter of source thickness s.

energy interval we also adopted 6.3 to 7.3 keV with Liljequist et al. Between 6.3 and 6.4 keV, however, the K L M - A u g e r electron peak superimposes the tail of the K-conversion peak. In this region, we obtained F(x, E) by extrapolating the tail of the K-conversion peak exponentially. The comparison between the left h a n d side of eq. (10) obtained from the experimental energy spectra and the right h a n d side from the calculated transmission with s = 80, 100, 200 and 260 ~, is shown in fig. 2. F r o m the figure, the source used in the present experiment is tentatively estimated to have a thickness between 100 a n d 200 A. A more sensitive estimation will be made from the energy distribution in sect. 3.4. The d i s -

5

i

I

i

i

._~

i

•

c

•

-

-

*

i

i

3.3.2. Energy distribution We can obtain the energy distribution of the K-conversion electrons T(x, E) from the energy loss distribution L(x, E) [see eq. (6)]. To do this, it is necessary to estimate the profile of T~(0, E). Since T,.(0, E ) is the energy distribution of a monolayer source, as is mentioned in sect. 3.1, it consists of the monoenergetic peak of the K-conversion electrons and the spectrum of the backscattered electrons mixed with the K M X - A u g e r electrons; the energy and intensity of the K M X - A u g e r electrons was measured to be 7.0 keV and 1.5% of the K-conversion electrons with a high resolution iron-free

i

i

i

i

Present analysis Monte C a r l o

0

N 2

"...

3B

°°o,~11 ..@..;+';:'" I

I~ II

i

0

........

[ .......

" 7

.........

,

,

,

,

6.5

,

,

,

7.0 Energy

E (keV) +

Fig. 3. Energy distributions T(x, E) of 7.3 keV electrons from a monolayer electron source embedded at depth .~. in metallic iron. Dots are those obtained from the present analysis and solid curves are those from the Monte Carlo calculation [8.23].

J. ltoh et al. / Energy distributions

.c

4

=I0~

s=110~

c5 la_

2

s

]

s~-90~,

0

615

I

7.0

Energy E (keY)

I

7.5

Fig. 4. Comparison between experimental energy spectrum with no scatterer and those obtained from the present analysis for different values of source thickness s.

spectrometer [21]. The energy spectrum of the backscattered electrons was estimated from the experimental result of K a n t e r [22] taking the backscattering coefficient as 0.2. Fig. 3 shows the energy distributions T(x, E) thus o b t a i n e d together with those of the M o n t e Carlo calculation of Liljequist et al. [8,23] for comparison, whose angle interval is from 37 ° to 53 ° , as m e n t i o n e d in sect. 3.2. It is noted that the area of T(x, E) in the energy interval from 6.3 to 7.3 keV is normalized to the restricted transmission of Liljequist et al. [8], because it is

283

difficult to o b t a i n the absolute transmission T(x) for a thin scatterer from the present experiment; it is very difficult to prepare either a m o n o l a y e r source or a very thin scatterer• As seen in the figure, the present energy distribution T(x, E) is smaller t h a n those of the M o n t e Carlo calculation in the highest energy region. The cause of the discrepancy m a y come from the deconvolution procedure by use of the approximate relation of eq. (7). If the present deconvolution procedure does not m a k e a large error, the experimental energy loss is larger t h a n that of the calculation in this region. This is consistent with the decrease of the experimental transmission c o m p a r e d with the calculated one [8], as was already shown in fig. 2. In other words, as the scatterers b e c o m e thicker, the experimental intensity of the electrons with a n energy higher than 6.3 keV decreases.

3.4. Estimation of source thickness from energy distribution The source thickness can also be estimated from the m e a s u r e d energy spectrum F(0, E ) by use of eq. (5). In the integration of the right h a n d side of the equation, we obtain T(x, E) for various thicknesses in Ax = 10 ,~ steps by " c o n v o l u t i o n interpolation" [5] of the experim e n t a l energy distributions already shown in fig. 3 and then sum them up to a certain thickness s. In the interpolation we use the restricted transmission of Liljequist et al. [8]. For R ( E ) , we use the spectrometer profile taken from refs. 14 a n d 15. Fig. 4 shows the comparison between the experimental energy spectrum F(0, E ) having no scatterer and those o b t a i n e d from the right h a n d side of eq. (5) with

81 6 [t

------7.25keY j 7 . 3 (xt/2o)

%

j7.2

x

7.1

X

7.0 2

63

200

6.6

,oo

xc oo

800

,ooo

Fig. 5. Weight function T(x, E,) of 7.3 keV electrons with the parameter of electron energy E~ having 8 eV width.

J. ltoh et aL / Energy distributions

284 5

b c d e

._~

x=63 ]k x=121 x=175 x=279

,

.E

~ b

-,~

~×- 2 ~

c

" "

¢ •

i

O

(

i

6.5

7.0

7.5

Energy E(keV)

Fig. 6. Comparison of experimental energy spectra with various scatterers with those obtained from the present analysis assuming source thickness s = 100~,.

s = 90, 100 and 110 ,h,. It was found from a chi-square test that the spectrum of s = 100 A agreed best with the experimental one. Thus the thickness of the source s is determined to be 100 + 5 A. This value is consistent with the estimation from the transmission described in sect. 3.2.

3.5. Weight function The energy distribution T(x, E) can be regarded as a function of x rather than of E. In this respect, the function T(x, E) is considered to be the probability that the electrons emitted at a depth x can emerge from the surface with an energy E. This function is called the weight function [8], which is useful for the depth-selective CEMS. Fig. 5 shows the weight function, which was obtained from the experimental energy distributions T(x, E) by the convolution interpolation and extrapolation. In this calculation, we used the calculated transmission after making reduction of its value larger than 150 A so that the l ( x ) curve of s = 100 A, agrees with the experimental data shown in fig. 2.

4. Discussion

4.1. On the energy distribution The reliability of the energy distributions obtained from the present analysis mainly depends on whether

eq. (7) is still valid f o r y = 100 A, which is the estimated thickness of the source used for the present experiment. It is very difficult to verify the validity of the approximation, but we can check the consistency of the present analysis with the experimental results. For this purpose, we compared the experimental spectra with those obtained from the right hand side of eq. (4) with s = 100 ~,, as is shown in fig. 6. As seen in the figure, the agreement is satisfactory. Therefore it can be said, at least, that we have been able to obtain energy distributions T(x, E) which can reproduce the experimental spectra. It is noted that, according to Liljequist [16], even if y is not very thin and the energy distribution varies slightly, eq. (7) may still be correct in the case that the energy distribution integrated from 0~ to 02 is approximately equal to an average over the energy distributions for all forward directions. Since the present electron spectrometer accepted electrons from 30 ° to 60 ° , the measured energy distributions can be considered to be approximately an average over the energy distributions from 0 ° to 90 °. Therefore we can conclude that eq. (7) is approximately valid for the present case. By making use of the electrons emitted after the recoilless resonance absorption, one can also obtain the energy distributions [7]. In the procedure of this method it is necessary to prepare thin absorbers which have a constant recoilless fraction up to the top of the surface. However, it is a very difficult task. Furhtermore, the S / N ratio is much worse than in the case of the source experiment. Consequently an accurate energy distribution cannot be obtained by this method. The restricted transmission of the Monte Carlo calculation agrees with the experimental one for thicknesses less than 150 A. In the thicker region, however, the calculated transmission becomes larger than the experimental one. This discrepancy seems to suggest that the cross section of the inelastic process is assumed to be small in the calculation. This fact has also been suggested by the comparison of the energy distributions, as is described in sect. 3.2. If the effects of plasmon excitation and inner shell electrons are taken into account in the calculation, the agreement with the experiment might become better.

4.2. Application to the depth-selective conversion electron MOssbauer spectroscopy Since M r s s b a u e r absorbers are considered to be composed of monolayer sources which emit conversion electrons, we can apply the energy distributions T(x, E) derived in the present analysis to the depth-selective

Fig. 7. Weight coefficient W(E,, xj) of 7.3 keV electrons emitted from each sublayer. The depth x I and the half-thickness A of each sublayer is A: xZ = 25 ~,, A = 25 A, B: xj = 75 ,~, A = 25 A, C: x i = 150 A, A = 50 ,~, D: xj = 250 A, A = 50 A, E: x / = 350 A, A = 50 ,~, F: xj = 500 A, A = 100 A, and G: xj = 800 A, A = 200 ,~. The dotted curve is the summation of these seven curves. (a) is for l% energy resolution, (b) for 2% and (c) for 3% at 7.3 keV.

6

,

(a) 5

,

Subl ayers o- 5o~

A

B

'~

/t

I/

5 o - Ioo

C 100-200 D 200-300 E 300 - 400 F 400- 600 G 600-1000

4

285

1%

.'I '/ I IA . r .I ..'

.......

,/

~Ii1('x'Ii55)" ..................... B

t_)

0

6.5

4I

,

J(b)

,

,

,

,

,

~ 3 I" / /

. " .

C 100-200

."

I

D 2 0 0 - 3OO E 3 o o - 4oo F 4 o 0 - 600

/

G 6oo -lOOO

'

'

i

i

.....

......... ................ /,,~ .......................

615 i

' i

'

Energy i

'

Ei {keV} I

'

~0

i

i

i

d

I

2

:

8.5

i

I

."

/

c

I

................

.............. / ........... /

/

Energy

Ei(keV)

7.0

f'Lx

/

.......~

,2,1

0

"\

, ".

50-100

D 200- 300 E 300- 400 F 400-600 G 600-1000

.\

I \ / \ L-.B \

_\

.

c lOO-2OO

~(-

/.~

/

'

(C) 3 % Subl ayers A 0- 50/~ B

,

.~

A O-50A B 5o-100

I~ 2

-

, ...

Sublayers

I /

3

,

2%

I

0-

7.0

Energy Ei (keY)

-~A

\\

.\

/It~. - \ I/

\~

. \

//\\.\

J. ltoh et al. / Ener~, distributions

286

CEMS. The M6ssbauer spectrum taken as a function of electron energy E,, M ( E i, v), is expressed by n

M(E,,v)=

c o m m u n i c a t i o n s concerning the analysis of the present experimental results.

_ _

Y'~ W ( E , , x y ) . D ( x : , v ) ,

(12)

]-- l

References

where W(E,, xj) is the weight coefficient of the j t h sublayer, v is the Doppler velocity, n is the n u m b e r of sublayers and D(x/, v) is the MOssbauer spectrum at a d e p t h of x:. The weight coefficient for homogeneous absorbers is obtained from the energy distributions T(x, E) as follows: : ~ , +~[r(x,e).R( a w(E,,x:) = :fJ~.

E)ldx}

~-E,' (13)

where Zi is the half-thickness of the sublayer. Using the above equation, we obtained the weight coefficients for energy resolutions of 1, 2 and 3% at 7.3 keV, as shown in fig. 7. The spectrometer profile R ( E ) for each energy resolution was taken from refs. 14 and 15. Some of curves shown in fig. 7b can be compared with fig. 2 in ref. 10. These data are lower than the present ones especially in the lower energy region p r o b a b l y due to a different acceptance angle. It should be noted that the weight coefficients shown in fig. 7 can be used for other materials than metallic iron after making a correction of d e p t h [8]; x ( F e ) s h o u l d be c h a n g e d to x ' = x(Fe)p(Fe)/p', where p(Fe) and p' are the density of metallic iron and the other material to be studied, respectively.

5. Conclusion Using a thin 57Co source, we have obtained accurate energy distributions of 7.3 keV electrons passing through iron films with a high resolution electron spectrometer and have c o m p a r e d them with the M o n t e Carlo calculation [8]. The agreement between the experiment and the calculation is fairly good. F r o m the obtained energy distributions we have derived the weight coefficients for the depth-selective MOssbauer spectroscopy. For the determinations of more accurate energy distributions, a thinner electron source is necessary. The authors wish to t h a n k Dr. D. Liljequist for his illuminating discussions a n d giving us helpful private

[1] Zw. Bonchev, A. Jordanov and A. Minkova, Nucl. Instr. and Meth., 70 (1969) 36. [2] J.R. Young, J. Appl. Phys. 28 (1957) 524. [3] V.E. Cosslett and R.N. Thomas, Brit. J. Appl. Phys. 15 (1964) 1283. [4] R. Shimizu, Y. Kataoka, T. Matsukawa, T. Ikuta, K. Murata and H. Hashimoto, J. Phys. D: Appl. Phys. 8 (1975) 820. [5] U. B~iverstam, T. Ekdahl, CH. Bohm, B. RingstrtSm, V. Stefansson and D. Liljequist, Nucl. Instr. and Meth. 115 (1974) 373. [6] U. B~iverstam, C. Bohm, T. Ekdahl, D. Liljequist and B. RingstfiSm, M6ssbauer effect methodology, vol. 9, eds., I.J. Gruverman, C.W. Seidel and D.K. Dieterly (Plenum, New York, 1974) p. 259. [7] TSV. Bonchev, A. Minkova, G. Kushev and M. Grozdanov, Nucl. Instr. and Meth. 147 (1977) 481. [8] D. Liljequist, T. Ekdahl and U. B~iverstam, Nucl. Instr. and Meth. 155 (1978) 529. [9] A. Proykova, J. Phys. D: Appl. Phys. 13 (1980) 291. [10] T. Shigematsu, H-D. Pfannes and W. Keune, Phys. Rev. Lett. 45 (1980) 1206. [11] D. Liljequist, Nucl. Instr. and Meth. 185 (1981) 599. [12] K.A. Kraus and G.E. Moore, J. Am. Chem. Soc. 75 (1953) 1460. [13] K. Saneyoshi, J. ltoh, T. Toriyama and K. Hisatake, Nucl. Instr. and Meth. 188 (1981) 253. [14] T. Toriyama, K. Saneyoshi and K. Hisatake, J. Physique 40 (1979) Coll. C2-14. [15] T. Toriyama et al., to be submitted to Nucl. Instr. and Meth. [16] D. Liljequist, private communication (May, 1982). [17] R. Shimizu, Y. Kataoka, T. ikuta, T. Koshikawa and H. Hashimoto, J. Phys. D: Appl. Phys. 9 (1976) 101. [18] A.J. Green and R.C.G. Leckey, J. Phys. D: Appl. Phys. 9 (1976) 2123. [19] D. Liljequist, J. Phys. D: Appl. Phys. 11 (1978)839. [20] B. Gold and C.M. Rader, Digital processing of signals (McGrow-Hilk New York, 1969). [21] K. Hisatake, Genshikaku Kenkyu 13 (1968) 13. [22] H. Kanter, Ann. Physik 20 (1957) 144. [23] D. Liljequist, private communication (May, 1980).