Photoelectron determination of mean free paths of 50–1500 eV electrons in the alkali halides

Thin Solid Films, 36 (1976) 231-234 © Elsevier Sequoia S.A., Lausanne-Printed in Switzerland

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PHOTOELECTRON DETERMINATION OF MEAN FREE PATHS OF 50-1500 eV ELECTRONS IN THE ALKALI HALIDES*

F. L. BATTYE, R. C. G. LECKEY, J. LIESEGANG AND J. G. JENKIN Physics Department, La Trobe University, Bundoora, Victoria 3083 (Australia) (Received August 25, 1975)

1. INTRODUCTION

Various kinds of electron spectrometry are now widely used for pure, applied and industrial research problems. The investigation of surfaces and thin Films on surfaces is one such area. Before such techniques can become truly quantitative, however, an accurate knowledge of the mean free path of electrons in solids is necessary. Recent studies have shown that the energy dependence of the total inelastic scattering cross section for electrons is similar in a number of metals and their oxides 1. Only in a few cases, however, have consistent sets of values been obtained by a particular technique over a range of electron energies. The energy region 50-1500 eV, where the values of the mean free path are the smallest, is particularly lacking in reliable values. In conjunction with a photoelectron investigation of the band structure of the alkali halides 2'3 we measured the variation of the electron mean free path in NaC1 and NaF in this energy range. A photoelectron overlayer technique was used, in which the attenuation of electrons originating in a substrate and passing through a dissimilar overlayer is measured 4-6. The method is of interest in the present context because it involves the production and measurement of thin overlayer films. The effects of island formation were investigated, and a model is presented which describes the effects of such nucleation on the experimental data. A theoretical interpretation, based on a tight-binding model, was developed. It is shown to give good agreement with the experimental results for NaC1 and NaF. It is also used to predict the likely variation of the mean free path with energy for other alkali halides. 2. EXPERIMENTAL Details of the X-ray photoelectron spectrometer system used have been given previously 6'7 . The intensity of each substrate photoelectron line is a simple function of the overlayer thickness t as follows: I(t)substrate = I(O)e-t/x where k(E) is the electron mean free path. The geometry of our spectrometer, and to a minor extent the asymmetry of photoemission from states of other than s symmetry, * Paper presented at the Third International Conference on Thin Films, "Basic Problems, Applications and Trends", Budapest, Hungary, August 25-29, 1975; Paper 10-02.

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require that this equation be modified. Such equations have been given in detail previously 6 (see Fig. l(a)). Because of the strength of certain photoelectron lines in NaC1 and NaF, it was also possible to measure the increase in intensity o f overlayer photoelectrons as a function of film thickness. Then I(t)overlayer ~ / ( 0 ) ( 1

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In conjunction with measurements of the attenuation of photoelectrons originating in Cu or Au substrates, and with the use of both A1 Ke and C Ke radiation, it proved possible to determine the electron mean free path at nine energies between 70 and 1400 eV. Substrate and overlayers were prepared in situ by vacuum evaporation o f high purity materials. Film thickness and deposition rate were automatically regulated by a quartz crystal control system, which had been previously calibrated using a multiple beam interferometer. Deviations of experimental results from the quasi-exponential decay referred to above are a sensitive test o f film uniformity. Evidence of some degree o f nucleation in thin layers of both NaC1 and NaF was found. Provided a freshly evaporated substrate was used, however, it was established that NaC1 films of thickness greater than 30 A ( > 17 )~ in NaF) gave consistent results. The mean free paths reported here were obtained from films of thickness greater than these critical values. In addition, a discussion of island formation was developed which adequately explains the deviations observed for the thinnest films used. The values o f the mean free path extracted from such data are consistent with those obtained by the use of thicker films.

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PHOTOELECTRON DETERMINATION IN ALKALI HALIDES

233

To derive expressions for the attenuation of substrate photoelectrons from nonuniform thin films of alkali halides we were guided by the experimental findings of Schultz 8. Clusters of adatoms were assumed to be of truncated spherical shape with contact angle 0 and separated by a constant inter-island distance D. Photoelectron emission was then analysed under these new sample conditions. The form of the attenuation curve as a function of average f'dm thickness was determined experimentally at a particular electron energy. The result was then fitted by use of the parameters D and 0; thus we obtained a value for ~(E). The applicabili# of the above treatment of nucleation has been verified for NaC1 and NaF. As may be seen from Fig. l(b), the growth in intensity of C1- LMM Auger electrons from NaC1 overlayers of thickness less than approximately 25 A is poorly represented by assuming uniform films, but it is well described by taking D = 100 A and 0 = 90 ° (broken curve). The mean free path of 19 A thus obtained on the basis of films with island formation is in agreement with the value of(19 + 2) A obtained from a 30 A film. Full details will be published later. 3. RESULTS AND DISCUSSION Experimentally determined values of X(E) in NaC1 and NaF are shown in Fig. 2. In order to elucidate the predominant scattering mechanisms in these materials, we recorded the energy loss spectrum in the neighbourhood of the Na ls photoline, and we compared it with optical data and with previously reported characteristic energy loss spectra. It is concluded that collective processes do not play a dominant role in electron scattering in NaC1 or NaF. Because of this result, and the fact that the outermost valence bands C1- 3p and F - 2p are relatively tightly bound 9 , we calculated the inelastic scattering cross section on the basis of the tight-binding approximation, using the theoretical formalism of Lotz l°.

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ELECTRON KINETIC ENERGY (eV) Fig. 3. The predicted energy dependence of the electron attenuation length in the halides of Li (curve 1), Na (curve 2), K (curve 3), Rb (curve 4) and Cs (curve 5), calculated on the basis of the tight-binding model.

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The success of this approach may be judged from Fig. 2, where the predictions for NaC1 and NaF are compared with the experimental data. The agreement in the case o f NaF is particularly encouraging, and it is perhaps significant that more difficulty was experienced in preparing uniform films of NaC1 than of NaF. An alternative approach to the problem o f calculating mean free paths has recently been presented by Powel111 . It makes use o f the relationship between the differential scattering cross section and the complex dielectric function, and it leads to the broken curve in Fig. 2. Following the success of the tight-binding approach in the above materials we have extended our calculations to most of the remaining alkali halides. The predicted variation of the mean free path with energy for these materials is presented in Fig. 3. Despite the wide variations in a variety o f atomic properties, the )~(E) curves in Fig. 3 are remarkably similar, giving some credence to the notion of a universal curve. The variations that do exist can be correlated with the variations in binding energies 9 of the outermost valence (halide) levels in these salts. ACKNOWLEDGMENTS We gratefully acknowledge continuing support from Professor D. Elwyn Davies, Messrs. C. S. Ducza, K. B. A. Flisikowski and G. J. Newton, and financial assistance from the Australian Research Grants Committee. REFERENCES 1 I. Lindau and W. E. Spicer, J. Electron Spectrosc., 3 (1974) 409. 2 R. T. Poole, J. G. Jenkin, J. Liesegang and R. C. G. Leckey, Phys. Rev., Sect. B, 11 (1975) 5179. 3 R. T. Poole, J. Liesegang, R. C. G. Leckey and J. G. Jenkin, Phys. Rev., Sect. B, 11 (1975) 5190. 4 M. Klasson, J. Hedman, A. Berndtsson, R. Nilsson, C. Nordling and B. Melnik, Phys. Scr., 5 (1972) 93. 5 R.G. Steinhardt, J. Hudis and M. L. Perlman, Phys. Rev., Sect. B, 5 (1972) 1016. 6 F. L. Battye, J. G. Jenkin, J. Liesegang and R. C. G. Leckey,Phys. Rev., Sect. B, 9 (1974) 2887. 7 P.C. Kemeny, A. D. McLachlan, F. L. Battye, R. T. Poole, R. C. G. Leckey, J. Liesegang and J. G. Jenkin, Rev. Sci. lnstrum., 44 (1973) 1197. 8 L.G. Schultz, J. Chem. Phys., 1 7 (1949) l153;Acta Crystallogr., 5 (1952) 130. 9 R. T. Poole, J. G. Jenkin, R. C. G. Leckey and J. Liesegang, Jpn. J. Appl. Phys., SuppL 2, Part 2 (1974) 771. 10 W. Lotz, Z. Phys., 206 (1967) 205. 11 C. J. Powell, Surf. Sci., 44 (1974) 29.