of Saloman et al.15 and the shell partial photoelectron cross-sections from Scofield's data16 . The angular ..... Depth. [nmJ. Figure 9. Same as Figure 8 for T\CI.
SECONDARY ELECTRON EMISSION FROM ALKALI HALIDES INDUCED BY X-RAYS AND ELECTRONS
A. Akkerman*, A. Breskin, R. Chechik** and A. Gibrekhterman Department of Physics Weizmann Institute of Science Rehovot, 76100 Israel
INTRODUCTION Secondary electron emission (SEE) from solids, induced by X-rays and charged particles (electrons, ions), is a rather complex process. In a simplified description it can be divided into three independent stages: 1) production of secondary electrons by the primary radiation; 2) transport of secondary electrons in the solid towards the exit surface; 3) escape through the surface. All three stages involve processes which occur inside the solid and thus require, for their exact mathematical representation, the solution of a many-body quantum mechanical problem. Consequently semi-empirical theories and models were developed, which in general explain the majn features of the SEE. During the last few years several reviews of SEE have been published 1 ,2,3. It was shown that simple models 1 may be used to reproduce the secondary electron yields and other integral characteristics of the process, for nearlyfree-electron metals. For noble and transition metals, semiconductors and insulators the simple semi-empirical models are not as successful. It was also shown 2 ,3 that by using microscopic approaches for the basic interaction processes in the models of SEE they can be improved and may be used to calculate, for example, the energy spectra of the secondary electrons. It is known from experiments that several semiconductors and dielectrics, and in particular alkali halides, have a very high secondary electron yield (SEY) which is by an order of magnitude larger than the SEY from metals. The experimentally derived dependence of the maximal SEY versus the optimal energy (to produce the maximal SEY) for these two groups of materials, were presented by Schwarz4 (see fig. 5 in his article). The high SEY from alkali halides is mainly due to their low work function, which is of the order of a few tenth's of an eV. Another important reason for their
*
Also Soreq Nuclear Center, Yavne, Israel
** The Hettie H. Heineman Research Fellow Ionization of Solids by Heavy Particles, Edited by R.A. Baragiola. Plenum Press, New York, 1993
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effective electron emission is the exceptionally low probability for energy losses, by inelastic collisions, of thp secondary electrons in the low energy range (Ee ::; Ec; Ec is the gap energy). The most important process at these low energies is the electron-phonon interaction, with an average energy loss or gain per collision of ",0.01 eV. Consequently the spectrum of secondary electrons is rather narrow, compared to similar spectra from metals. One should note that according to a somewhat arbitrary definition, "true" secondaries are considered as those with energies inferior to 50 e V, and "primaries" (that is, secondaries or slowed down initial electrons) are those having energies superior to 50 eV. The general features of secondary emission from alkali halide layers, irradiated by soft X-rays and electrons, have been known for a long time (see for example ref. 5 and other references therin). Henke et a1. 6 developed a model of SEE which includes a postulated treatment of secondary electron excitation function without details of the mechanisms of interaction. It uses Kane's one-dimensional random walk model 7 for electron transport, with a few fitting parameters. Secondary emission spectra predicted by this model agree satisfactorily with the experimental data, except for a region which is supposed, by the authors of ref. 6, to be responsible for plasmon decay. Some questions concerning the emission of primary electrons, like for example their absolute yield, are not solved by this model. A simpler and more straightforward, semi-analytical, model for SEE was proposed by Fraser8. He uses three parameters: the escape probability P(O) of secondary electrons, created at a distance x from the emitting surface, when x -+ 0; the mean energy for secondary electron generation "I; and the escape length Ls. These parameters cannot be predicted by the model, and are usually extracted from a fit to experimental data. Both models considered above are not based on "first principle" approach. In order to have a coherent picture of the SEE from alkali halides it is necessary to understand the whole process of slowing down of primary and secondary electrons, generated by energetic electrons and X-rays. For that purpose it is desirable to include all the known processes of electron interaction in a single theoretical model. A step in this direction was made by McDonald et a1. 9 , using Monte Carlo simulations of the generation and the transport of secondary electrons. Llacer and Garwin 10 used the same method for low energy electron transport calculations, influenced only by electron-phonon interactions. But the over simplification of the interaction process, used in these models, does not help to elucidate the whole mechanism of creation, multiplication, slowing down and emission of secondary electrons in alkali halides. The effectiveness of the I'vIonte Carlo method for SEE simulations was widely demonstrated in ref. 2. In the present article we report on the development of a new physical model using recent, reliable, theoretical microscopic cross-sections for electron interactions in alkali halides 11 . I\lonte Carlo calculations based on this model were performed. We have chosen CsI and KCl as representatives to verify the model, and calculated the most important integral characteristics of SEE induced by X-rays and electrons over an energy range of 1-30 keY. The aim of this work is to improve the understanding of the SEE process and to present new data, which can be employed in the development of new radiation detection systems based on alkali halide convertors 12 ,13.
THE SIMULATION MODEL
The first stage in the simulation of the SEE induced by X-ray absorption, is the
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calculation of the spatial distribution of the primary photoelectrons in the solid. For high energy X-rays, also Compton electrons should be considered. For thin layers the simulation of the spatial distribution of photoelectrons is done using the forced Monte Carlo scheme 14 . The total X-ray attenuation coefficients are taken from the tables of Saloman et al. 15 and the shell partial photoelectron cross-sections from Scofield's data 16 . The angular distribution of the ejected photoelectrons is used in Fisher's form 17. Auger electrons following the photo- and electron ionization processes are also taken into account as primaries. The problem is thus reduced to secondary emission following primary electron transport in the layer. Many of the previous simulation works of SEE from metals, induced by electrons (see for example ref. 2,18), were performed using the direct Monte Carlo scheme (for details see 19,20). The basic assumptions used in this scheme are: 1) the electrons interact at random point.s in the bulk of the t.arget; 2) the type of interaction (e.g. elastic or inelastic) is selected randomly, according to the relative cross-sections of the processes; 3) the inelastic scattering includes several mechanisms of interaction: ionization,' excitation, collective interaction, etc; the particular mechanism is selected according to its relative cross-section; 4) the energy and the angle of deflection of each scatt.ered primary electron (i.e. the most energetic electron) and of the ejected secondary electron (low energy electron) are sampled from the cumulative probability distributions, obtained by integration of the double differential cross-section of the corresponding interaction. Hence, the results of the simulation calculations depend 'on the adequacy of the cross-sections used to describe the interaction process. As already pointed out we cannot use the exact theoretical cross-sections, because this implies solving the many-body interaction problem in the solid. On the other hand, systematic experimental data for electron interaction cross-sections in solids is rat.her scarce. Only a few indirect dat.a is available and can be used: t.he stopping power for electrons transmitted through a layer, the mean free path for inelastic scattering extracted from the optical properties, and electron energy loss spectra in thin films. The last type of data show the existence of a collective excitation process, namely plaslnon creation, as well as exciton creation and ionization of the inner atomic shells. It seems, therefore, reasonable to use in the simulation model two types of interactions: individual interaction with electrons in the unperturbed inner shells of free atoms and excitation of electrons from the outer shells, which contribute to the solid effects (valence band), in a collective manner. These include plasmon and electron-hole excitations, and interactions of slow electrons with the lattice vibrations. As was mentioned above, models based on these approaches for metals show results which are in satisfactory agreement with experimental data. Another model, which treat.s the valence electrons as tightly-bound, was proposed by Szajman et al. 21 In this model there are no collective excitations and the only inelastic process is the ionizations of bound shells of free atoms. The agreement of the Inelastic Mean Free Paths (IMFP) calculated in the framework of this model with experimental measurements is good but it does not necessarily mean that this model will correctly predict the SEE characteristics. Calculations based on Szajman's et a1. 21 model are presently in progress and will be compared with the calculations based on our model. The most crucial and important characteristic for verification of the model is the energy spectrum of secondary electrons. A summary of the main processes of electron interactions included in our model and affecting the SEE :Ire presented in table 1. The table also lists the main theoretical approaches and approximat.ions used to describe these processes.
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Table 1. Summary of all the processes included in our simulations, the methods of cross-section calculation and the relevant references. Inelastic Interactions
Elastic Scattering-
Partial wave expansion 22
Ionization
Plasmon excitation
Electron-hole excitation
Electron- phonon interaction
Binary encounter approx. 23
Quinn's th eory 24
Dielectric function th eory 25,26
Time-dependent perturbation theorylO
Elastic Scattering Elastic scattering plays an important role in the transport of electrons in the solid, in particular for low energy electrons. This was pointed out in ref. 2, is evident from our calculations and was recently convincingly argued by Sigmund27 . We do not use elastic scattering cross-sections which are affected by the solid, like those obtained2 using the '"muffin-tin" potential in AI, mainly due to the lack of such potentials for the relevant atoms. Rather, we followed the standard way22 , calculating the differential and total cross-sections by the "partial wave expansion" method. Solving the Dirac equation we used the screened potential proposed by Green et a1. 28 , without inclusion of polarization and exchange effects. The calculations were done for Ar and Xe atoms, since their atomic numbers, Z=18 and 54, correspond exactly to the mean values of that of KCI and Csl. We gradually reduced the potential to 0 at a distance ro, which is equal to half the interatomic separation in CsI and KCI, thus including in a very approximate way the solid structure. The results of our calculations of the differential cross-sections for CsI, compared to Fink's et al 29 , are shown in fig. 1. The total macroscopic elastic cross-section, or the IMFP, were calculated using Ar and Xe atoms with the bulk density of KCI (p=1.984 g/cm3 ) and of CsI (p=4.51 g/cm3) respectively. Figs. 2 and 3 compare the calculated cross-sections with the experimental 3o data . For AI' our results agree quite well with the experimental ones, with maximal deviation of about 30%. For Xe the agreement of the calculated IMFP with the experimental data is poorer, with deviations of up to 100% for electron energies Ee < 100 eV. A somewhat better agreement is obtained with calculations which included polarization and exchange effects, but a marked difference still remains. For energies lower than 20 e V there exist no experimental data of the IMFP, and therefore we assume that they are constant and equal to the value at 20 eV. The most relevant data in this range exist for solid Xe, where it was shown experimentally31 that the cross-section decreases drastically for energies below 2 eV. If this is also true for more complicated systems, such as alkali halides, it may explain the high transparency of the material to low energy electrons, as reflected in the secondary emission electron spectra. But as also follows from ref. 31 there is a large discrepancy between the various experimental data sets, which is a result of trapping of low energy electrons by impurities and othe~' defects in the solid. Since a real layer of alkali halide is certain to contain many impurities and lattice defects, the material transparency at the 362
very low energy range may not be very large. Our calculations in fact do show great sensitivity of the results to the elastic cross-section at the very low energy range. In the absence of good relevant experimental data we have to use our estimated values of the cross section. Inelastic Scattering Valence band excitations. In our calculations we assumed that the eight outer electrons in KCI and in CsI are the valence electrons. This follows from the estimated6 plasmon energies Epe of these alkali halides. We assume the following
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