Experimental determination of the inelastic mean free path (IMFP) of electrons in Cr, Mo, Ge and Si based on the elastic peak intensity ratio with a Ni reference sample

surface s c i e n c e ELSEVIER

Surface Science 331-333 (1995) 1203-1207

Experimental determination of the inelastic mean free path (IMFP) of electrons in Cr, Mo, Ge and Si based on the elastic peak intensity ratio with a Ni reference sample G. Gergely a,*, M. Menyhfird a, K. P6ntek a, A. Sulyok a, A. Jablonski b, B. Lesiak b, Cs. Dar6czi c a Research Institute for Technical Physics of the Hungarian Academy of Sciences, P.O. Box 76, H-1325 Budapest, Hungary b Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44 / 52, 01-224 Warszawa, Poland c Research Institute for Material Science of the Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary

Received 29 July 1994; accepted for publication 2 December 1994

Abstract The inelastic mean free path (IMFP) of electrons has been determined for selected elemental solids using elastic peak electron spectroscopy (EPES) and a Ni standard. The IMFP was evaluated for the range of 500-3000 eV on Cr, Mo, Ge and Si materials. The Ni standard surface has been prepared by electrolysis and HV vapour deposition. Its quality was verified by AES and STM. The theoretical model relating the elastic peak intensity to the value of the IMFP was based on relativistic scattering cross sections and the multiple elastic scattering events were simulated by a Monte Carlo procedure. Reasonable agreement of the obtained IMFP values and their dependence on the energy with the data by Tanuma et al. and by .Ashley et al. was found. Keywords: Auger electron spectroscopy; Chromium; Electron-solid interactions; Germanium; Metallic films; Molybdenum; Nickel;

Semiconducting surfaces; Silicon; X-ray photoelectron spectroscopy

1. I n t r o d u c t i o n The inelastic mean free path A (IMFP) of electrons is an important material parameter in quantitative surface analysis b y A E S or XPS [1] determining the sampling depth. Knowledge of A is also important for non-destructive depth profiling by elastic peak electron spectroscopy (EPES) [2] and scanning electron microscopy using the elastic peak [3], with

* Corresponding author. E-mail: [email protected]; Fax: + 36 1 1698037.

variation of the primary energy Ep, as well as for high energy XAES, requiring knowledge of A above 2 keV. Tanuma and Powell [4] calculated A for 26 elements and 17 compounds, improving their calculations published in a number o f previous papers. For E = 5 0 - 2 0 0 0 eV their results are now considered as the most up to date data. In another previous work, A s h l e y ' s calculated A data [5] are quite close to those in Ref. [4] and they cover the 0 . 4 - 1 0 keV energy range. The experimental determination of the I M F P is a more difficult task. The classical overlayer method,

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G. Gergely et al. / Surface Science 331-333 (1995) 1203-1207

requiring a perfect thin film bearing the properties of a bulk solid, is rather problematic and confined to certain material systems and it supplies only the escape depth, not A. EPES proved to be an efficient tool for experimental determination of A [6]. It can be applied to any clean and smooth solid surface. A Monte Carlo analysis of multiple elastic scattering was performed and A was determined by comparing the elastic peak intensity I x of a sample with that of an A1 reference standard [7]. Reasonable agreement was found with theoretical data, but systematic lower values were obtained for high atomic number elements (W, Au). Another application of EPES was developed by Dolinski et al. [8] using a retarding field analyzer (RFA). They determined the elastic reflection coefficient re(E) [3] and evaluated their experiments by a Monte Carlo analysis. They found good agreement with Tanuma on Ag and Au. Recently Beilschmidt et al. used Ni as a reference standard and obtained good agreement with Tanuma for certain elements [9]. In the present work Ni was used as a reference sample for Si, Ge, Cr and Mo. Special attention was paid to the surface quality of the samples.

semiconductors, STM could not be performed in ambient atmosphere. Electrolytic Ni layers deposited on highly polished brass substrates (LORIX Ltd) exhibited similar surface properties as those of evaporated samples. An amorphous Si layer was prepared by ion implantation. Amorphous Ge was produced by vapour deposition on a Si substrate. The Mo sample was a d = 50 /xm foil (Planseel Reutte) treated by mechanical polishing and lapping before Ar + ion bombardment. Etching by H 2 0 2 w a s attempted but resulted in a surface oxide layer. A roughness value r = 1.5 nm was found before and a value r b = 2 nm after Ar + sputtering. The Cr sample with d = 100 nm was prepared by HV evaporation of Cr on a Si substrate with a deposition rate of 1 nm s -1. The roughness values were r = 0.7 nm before and r b = I nm after Ar + sputtering. The Ni reference samples have been prepared by evaporating Ni in HV at 100°C on a polished Si wafer (with natural SiO 2 surface layer). The deposition rate was 1 nm s -a, d = 100 nm. The roughness values were r = 0.8 nm and r b = 0.8-1.2 nm.

3. Experimental techniques 2. Preparation of the samples

Measurements of the elastic peak height ratio Ix/INi were performed using an on-line computer-

The EPES measurements were carried out on freshly prepared surfaces for energy values in the range E = 0.5-3 keV. Cleaning by Ar + ion bombardment was performed on rotating samples at 4° glancing incidence of the ions, 2 keV, 5 / z A and 300 /zm beam diameter, using the apparatus described in Ref. [10]. By this method a constant depth resolution of 3 nm was achieved, producing a low surface roughness r. The surface roughness was measured with a scanning tunnelling microscope (STM) type RMK at the Institute of Materials Science, Budapest. Commercially available Si and Ge wafers and poly-Si have been used. Using the ion bombardment cleaning procedure, the native oxide layers have been removed and the surface layer was disordered by the sputtering. Considering the 3 nm depth resolution and the escape depth of the electrons, determined by their IMFP, the same EPES results have been obtained on poly- and single crystals of different orientation [2]. Due to fast oxidation of these

operated electron spectrometer and a Riber OPC 103 CMA with integral gun, in the analogue mode [2]. The sample surfaces were monitored by a low magnification (50 × ) secondary emission imaging electron beam 0 = 50 / ~ m , Ip = 1 /zA, for choosing the proper areas and avoiding defects, e.g. scratches. Both the sample and the Ni reference standard were mounted on a rotating sample holder. The elastic peak and the adjacent background with plasmon loss peaks were recorded. The I x and INi intensities were corrected for spectrometer transmission [11] and deconvoluted. As also found by Zommer on Mo, the elastic peak intensity is rather more informative than the peak area [12]. The correction might be nearly 10% for Si, and it is much less for Ni, Cr and Mo due to the plasmon losses. The FWHM of the elastic peak is determined by the Boersch width of the electron gun and the recorded peak is broadened by the spectrometer energy window.

G. Gergely et aL / Surface Science 331-333 (1995) 1203-1207

4. M o n t e

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Carlo analysis

The same procedure was applied as described in Ref. [7]. The theory describing the elastic backscattering probability and the IMFP has been described in detail in earlier publications [%i3]. Below only a brief outline is given. A functional relation exists between the IMFP and the elastic backscattering probability I x, appearing in the elastic peak intensity of the sample: A = I(Ix). It can be transformed to I x = g(A). A similar equation can be written for the standard reference sample: I, = gs(As). Both I x and 1, are affected by the angular distribution and measurement conditions. In our experiments a CMA was used with a normal angle of incidence and a 138 + 3.5 ° angular window of detection. The unknown IMFP can be determined from:

I x / I , = g( A ) / g , ( A s ) ,

(1)

assuming that accurate values of As are known. This is a critical point of the procedure. In our present work the A, values for the Ni reference sample were taken from Tanuma [4] for E = 0.5-2 keV and those from Ashley [5] above 2 keV. Details of the Monte Carlo algorithm are described in Ref. [14]. In the usual simulation scheme, the trajectories are assumed to consist of linear steps between elastic collisions and the electron motion is approximated by a Poisson stochastic process. The elastic scattering events are modelled by the relativistic differential scattering cross-section d o - / d O calculated from the partial wave expansion method applied [14] to the Thomas-Fermi-Dirac potential [15]. The electron history in the solid is pursued until the electron leaves it or until the total trajectory length becomes too long to give a noticeable contribution to the backscattering current. The contribution associated with an electron is given by

AI, = e x p ( - x i / A ) ,

measured data

2.5

-~- 2

i

E

i

i

I

] i

i

1 i §1.

~,

:

J

t

'

i

!

25

30

0,5" ~ 5

t0

15

20

[MFP(A)

35

40 46

Fig. 1. Comparison of corrected experimental I x / I s results with calculated master curves for Cr.

accuracy of the elastic backscattering probability within a given solid angle falls in the range 1-2%. The necessary number of trajectories varies between 2 × 10 5 and 2 × 10 6.

5. R e s u l t s

The Ix/1 , master curves have been calculated for Si, Ge, Cr and Me in the E = 0.5-3 keV energy range, versus A as the free parameter. They are plotted in Figs. 1 - 4 versus A on the abscissa. For each primary energy value, A was deduced from the intercepts of the experimental (with spectrometer correction) I x / I s data with the master curves. In

(2)

where x i is the total trajectory length. The elastic backscattering probability within the CMA angular conditions is calculated from 1 "

IE=-

E AIi,

(3)

h i =--1

where n is the total number of electron trajectories. The Monte Carlo calculations are performed until the

0

10

20

30

40 IMFP (A)

50

,

60

70

Fig. 2. Comparison of corrected experimental I x / I s results with calculated master curves for Si.

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G. Gergely et aL / Surface Science 331-333 (1995) 1203-1207

2.5

!

i

70-

'

60

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

50 . . . . . . . . . . . . . . . . . . .

~

~'~

40 .

u-

30 .

.

.

.

.

.

.

.

.

Ge

~ ~ A M G e "

AGe

1.5 .

.

.

. -

. , . , , ~

....cS::........... 2 0 ....... 7 . . . . . . . . . .

10 . O. -

i

i i.

o

I

5

O,

,

10

~5

20 2s IMFP (A)

35

a0

! i

4o

45

Fig. 3. Comparisonof corrected experimental I x / I , results with calculated master curves for Me.

2 i

1.6

[

I

1.4

~ 1.2 125~_~' I o

1

I

04

1

ola o~0

: 5

,

i

i

]

i

I

i

! i

~ i

i z/

~

[

i

'

i

i

i

k i

i 15

~

i

i 25

20

i 1 35

30

40

i i 45

.

.

---z

.

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

.

560 1600 1500 2000 2500 3000 3500 E (eV)

Fig. 6. Comparison of experimental IMFP data (full line) with calculated data of Tanuma et al. (dotted line) denoted by T Me and those for Ge, calculated by Ashley et al. [5], denoted by AGe. The calculated IMFP data for Ni are denoted by T Ni.

Figs. 5 and 6 experimental and calculated h values are compared with T a n u m a ' s and P o w e l l ' s data. Electrolytic and vapour deposited Ni layers resulted in similar I S values. In practice, amorphous Ge and Si and polycrystalline Si resulted in similar experimental elastic peak height ratios as those of single crystalline wafers. The surface quality of the M e sample (STM) was less good than that of the other samples. The Cr surface exhibited some oxygen contamination, possibly due to preparation conditions.

I

i 10

.

:..~F:~ ' - : ~ "

- - -

Mo

50

IMFP (A)

Fig. 4. Comparison of corrected experimental I x/18 results with calculated master curves for Ge. 7o A

60

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

40 . . . . . . . . . . . 0-

LL 30

0

.

.

.

....

A

~I~I::::::T-Cr

.7 ......... i"

$i

~ 7 ~ T Si

.

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

. .--.~ T Ni

500 1000 1500 2600 2500 3000 3500 E (eV)

Fig. 5. Comparison of experimental IMFP (full line) data with calculated data (dotted line) of Tanuma [1] denoted by T Si and T Cr, respectively. Above 2 keV the values of Tanuma et a£ have been extrapolated. The calculated IMFP data for Ni are denoted by T Ni.

6. Conclusion

The IMFP results deduced from a Monte Carlo analysis o f the elastic peak height ratio of the sample and a Ni reference are in reasonable agreement with theoretical data of Tanuma et al. and Ashley. The surface quality of the sample might affect the experimental results, however S T M proved a nearly constant surface roughness (close to 1 nm) after ion bombardment. It is hoped that an improvement can be obtained from further development of Monte Carlo analysis and differential elastic cross section calculations. The discrepancies with M e might be attributed to the small collecting angle of the C M A (0 = 138 _ 3.5 ° ) and the deep minima in the d o - / d O curves, published in the literature. The deep minima have been tabulated by Fink [16], Reimer [17] and Joy [18] as

G. Gergely et al. /Surface Science 331-333 (1995) 1203-1207

well. T h e i r positions, h o w e v e r , are v a r y i n g w i t h e n e r g y E and are not identical. T h e y can strongly affect the m u l t i p l e elastic scattering processes.

Acknowledgements This r e s e a r c h p r o g r a m is part o f O T K A 1224 and T 7 6 9 4 Projects and w a s supported by the N a t i o n a l R e s e a r c h F u n d o f H u n g a r y . E l e c t r o l y t i c N i samples h a v e b e e n prepared by Dr. J. Loranth ( L O R I X Ltd, Hungary). A m o r p h o u s silicon was prepared in the R e s e a r c h Institute o f Materials Science, Budapest. T h e authors express their thanks to Prof. D.C. Joy, M e t a l and C e r a m i c s Division, O a k R i d g e N a t i o n a l Laboratories, T e n n e s s e e , for sending his scattering cross sections results to R e s e a r c h Institute o f T e c h n i cal Physics, Budapest.

References [1] C.J. Powell, A. Jablonski, S. Tanuma and D.R. Penn, J.Electron Spectrosc. Relat. Phenomen. 68 (1994) 605. [2] G. Gergely, Surf. Interface Anal. 3 201 (1981); Scanning 8 (1986) 203.

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[3] R. Schmid, K.H. Gaukler and H. Seiler, Scanning Electron Microscopy I1 (SEM Inc., AMF O'Hare, 1983) p. 501. [4] S. Tanuma, C.J. Powell and D.R. Penn, Surf. Interface Anal. 17 (1991) 911, 926. [5] J.C. Ashley and C.J. Tung, Surf. Interface Anal. 4 (1982) 52. [6] A. Jablonski, P. Mrozek, G. Gergely, M. Menyhard and A. Sulyok, Surf. Interface Anal. 6 (1989) 291. [7] B. Lesiak, A. Jablonski and G. Gergely, Vacuum 40 (1990) 67; Phys. Scr. 39 (1989) 363. [8] W. Dolinski, S. Mroz, J. Palczynski, B. Gruzza, P. Bondot and A. Porte, Acta Phys. Polon. A 8 (1992) 1103. [9] H. Beilschmidt, I.S. Tiliuin and W.S.M. Werner, Surf. Interface Anal. 22 (1994) 120. [10] A. Bama, A. Sulyok and M. Menyhfird, Surf. Interface Anal. 19 (1992) 77. [11] G. Gergely, L. Guczi, A. Jablonski, B. Lesiak, A. Sulyok and Z. Zsoldos, Proc. 12 ICXOM 1989, Cracow, Eds. S. Jasienska and L.J. Maksymowicz (Academy of Mining and Metallurgy, Cracow, 1989) p. 505. [12] L. Zommer, B. Lesiak and A. Jablonski, Phys. Rev. B 47 (1993) 13759. [13] A. Jablonski, Surf. Interface Anal. 14 (1989) 659. [14] A. Jablonski and S. Tougaard, Surf. Interface Anal. 22 (1994) 129. [15] A. Jablonski, Physica A 183 (1992) 361. [16] D. Gregory and M. Fink, At. Data Nucl. Data Tables 74 (1982) 52. [17] L. Reimer and B. L6dding, Scanning 6 (1984) 128. [18] Z. Czyzewski, D. O'Neill, MacCallum, A. Romig and G.C. Joy, J. Appl. Phys. 68 (1990) 3066.