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Backscattering of 8–28 keV electrons from a thick Al, Ti, Ag and Pt targets
Journal of Electron Spectroscopy and Related Phenomena 151 (2006) 71–77
Backscattering of 8–28 keV electrons from a thick Al, Ti, Ag and Pt targets R.K. Yadav, R. Shanker ∗ Atomic Physics Laboratory, Department of Physics, Banaras Hindu University, Varanasi 221005, India Received 2 October 2005; received in revised form 1 November 2005; accepted 2 November 2005 Available online 6 December 2005
Abstract Measurements of electron backscattering coefficient η for thick Al, Ti, Ag and Pt targets have been made for incident electrons with energy 8–28 keV. The variations of η with angle of incidence α, impact energy E0 and with target atomic number Z have been studied. The data are compared with available theories. The mean fractional energy absorbed in the backscattering process has been determined and compared with an analytical expression and with Monte-Carlo simulations based on the Kanaya and Okayama electron–electron and electron–nucleus interactions and on the Quinn electron–plasma interactions. The comparison between our experimental data and the model calculations using Monte-Carlo simulations and analytical expression shows a reasonably good agreement among themselves within experimental errors of measurements. © 2005 Elsevier B.V. All rights reserved. PACS: 79.90.+b; 79.20.Hx Keywords: Backscattering coefficient; Mean fractional energy absorbed; Diffusion range; Penetration depth
1. Introduction The technique of surface analysis has become extremely important in modern technology [1,3]. The interaction of electron beam with a solid target has been studied since long [4–9]. Excellent reviews about this subject are given by Bothe [10], Birkhoff [11] and more recently by Neidrig [12], Goldstein et al. [13], Newbury et al. [14] and Feldman and Mayer [15]. When a mono-energetic electron beam impinges on a solid target, some electrons are backscattered without any energy loss. This elastic electron backscattering process plays an important role in many experimental techniques, like, low energy electron diffraction (LEED), scanning electron microscopy (SEM), electron probe microanalysis (EPM), Auger electron spectroscopy (AES), electron lithography physics, radiation damage and elastic peak technique. These techniques have been used for the experimental determination of the inelastic mean free paths (IMFPs) of electrons in the solid. It has become essential to have a precise knowledge of the surface structure and the surface chemical
∗
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composition as well as to understand the surface properties of a solid material. Indeed, any interaction between a solid and the “outside world” takes place through the topmost atoms of the surface of the material. It has then become extremely common to treat, coat, etc., the surface of the material to modify the way in which it interacts with the environment (passivation of the surface against corrosion, coating of glasses to avoid unwanted reflection, etc.). It is then extremely important to control at a microscopic level the way in which the surface treatments affect the interactions of the solid with the “outside worlds” to understand the chemical reactions at the surface of a material, to understand how the electronic surface properties (which differ from those of bulk) affect the behavior of an electronic device, etc. It is well known that when an electron beam impinges on the solid targets, a fraction of the beam is absorbed, another fraction is backscattered, and remaining one is transmitted. The sum of these fractions is equal to 1. Their values depend on the nature of a target bombarded and its thickness. If the target thickness is greater than the maximum penetration range R, then no electrons are transmitted through the specimen, the incident electrons can be only absorbed or backscattered and the fraction of backscattered electrons assumes its maximum value generally indicated as backscattering coefficient η. For understanding the surface
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properties of solids, a number of investigators have proposed their theories. For example, Everhart [16], Archard [17], Body [18], Tomlin [19] and Dashen [20] made calculations about the backscattering coefficient η as a function of the atomic number Z in reasonable agreement with the available experiments. Subsequently, Arnal et al. [21] gave a simple expression for η as a function of tilt angle and atomic number. In addition, it may be noted that there exist experimental works in literature concerning the backscattering coefficient as a function of the angle of incidence by Darlington and Cosslett [22] and Staub [23]. The primary energy and atomic number dependences of the backscattering coefficient were given by Jacob [24], Hunger and Kuchler [25], Williamson et al. [26] and Dapor [27]. The works of Kanaya and Okayama [28], Lantto [29,30], Liljequist [31], Iafrate et al. [32], Niedrig [12], Rogaschewski [33] and Dapor [34,35] were concerned with the more general theoretical problems of calculating transmission, backscattering and absorption of electrons impinging on supported and unsupported thin films. Electron-beam solid–target interaction has also been investigated by using the so-called Monte-Carlo method, a numerical procedure involving random numbers that is able to solve mathematical problems [36]. This method is convenient for the study of electron penetration in matter, since the probabilistic laws of interaction of an individual electron with the atoms constituting the target are known. Consequently, it is possible to compute the macroscopic characteristics of the interaction process by simulating a great number of real trajectories and then averaging them [37]. The backscattering coefficient strongly depends on the target atomic number Z [16,17,24] and also slightly on the primary energy E0 [38–42,27] and on the incidence angle α. It is not realistic to consider the backscattered electrons as perfectly reflected from the surface without dissipation of energy. It is more reasonable to think that they have penetrated a little bit below the surface and have lost a small fraction of their energy. As a consequence, the mean energy of the backscattered electrons EB will be in general a large fraction of the primary energy E0 whose value will depend on the mean path traveled in the solid before emerging from the surface. Once the backscattering coefficient η and the mean energy EB of the backscattered electrons are known, the energy absorbed by the solid target due to electron irradiation can be calculated by considering the energy conservation law. In this paper, we present new experimental data on the backscattering of electrons incident normally and obliquely on different metallic targets, for example, Al (Z = 13), Ti (Z = 22), Ag (Z = 47) and Pt (Z = 78) in the impact energy range 8–28 keV. The dependence of the electron backscattering coefficient on both the incidence angle α and the target atomic number Z has been studied. Further, we have examined our data for the variation of η0 at normal incidence as a function of impact energy E0 . In addition, we have also determined the variation of fractional energy absorbed in the backscattering process with the atomic number Z. Wherever possible, results of the present work have been compared with the other published data and with the predictions of available theoretical models.
2. Experimental The measurements were carried out on the same experimental set up which has been developed in our laboratory for studies of electron–atom/molecule collision processes except some minor modifications. Details of the modified experimental set up are given and discussed in our previous paper [43]. Briefly, a mono-energetic beam of electrons was derived from a custom built electron gun (M/S P. Staib GmbH, Germany), which provided a focused beam of about 3 mm spot size at the target (20 mm × 14 mm) situated at about 500 mm away from the gun. The accuracy of positioning the beam spot on the target was estimated to be about ±1 mm. During measurements, the current of incident beam was kept at about 10 nA. The base pressure of the scattering chamber was maintained at better than 2 × 10−6 Torr. The chamber is equipped with a movable target holder in the vertical plane at its center, which facilitates positioning the target in front of the beam. High purity thick Al (0.5 mm, 99.9995%), Ti (0.1 mm, 99.99%), Ag (0.1 mm, 99.998%) and Pt (0.1 mm, 99.99%) targets were mounted on the target holder. For plate current ip , a semispherical aluminum collector plate (0.5 mm thick) placed behind the grid was used to monitor the current produced by the scattered electrons from the target. In this configuration, the high-energy backscattered electrons could reach the collector plate kept at Earth potential through a high precision resistance of 33 M. A dual switch was used to measure the plate current ip and the target current it one after the other with the help of a digital voltmeter (DVM) connected across the precision resistor. Relative calibration of the two measuring devices was insured before recording the actual corresponding currents. It may be pointed out here that three successive measurements of η were made in our experiments for each incidence angle and for each impact energy. The average of these measurements was taken to finally calculate η. The statistical uncertainty of measurements for η was about 2.4%. Finally, the backscattering coefficient η defined as the ratio ip /(ip + it ) was calculated from values of two measured currents. Uncertainty of measurements originates from two sources, namely fluctuations of the beam energy and of the beam current. Here, the uncertainties in the beam energy and in the beam current are determined to be about ±1 and ±5%, respectively. Hence, the total uncertainty including the statistical error of measurements for η is around 5.5%. 3. Results and discussion The measured values of η as a function of angle of incidence α, (0◦ ≤ α ≤ 60◦ ) relative to the surface normal of a thick, polished and chemically pure target, for example, Al, Ti, Ag and Pt for different impact energies E0 (E0 = 8–28 keV) are summarized and presented in Table 1. At angles of incidence higher than 60◦ , the measurements for η become less reliable. This is because at these angles, the electron beam does not fall fully on to the target surface: rather a large fraction of it passes by the target at a grazing angle. The backscattering coefficient is generally found to increase smoothly with α (see our data and
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Table 1 Measured values of electron backscattering coefficient η as a function of the angle of incidence α for Al (Z = 13), Ti (Z = 22), Ag (Z = 47) and Pt (Z = 78) targets at different impact energy E0 Z
Ep (keV)
α (◦ ) 0◦
10◦
20◦
30◦
40◦
50◦
60◦
Al (Z = 13)
8 12 16 20 24 28
0.172 0.161 0.152 0.148 0.141 0.135
0.175 0.165 0.155 0.151 0.144 0.138
0.187 0.174 0.164 0.159 0.151 0.146
0.213 0.197 0.184 0.178 0.168 0.161
0.252 0.233 0.217 0.210 0.198 0.188
0.308 0.286 0.267 0.259 0.245 0.232
0.378 0.353 0.331 0.321 0.305 0.290
Ti (Z = 22)
8 12 16 20 24 28
0.246 0.241 0.235 0.229 0.221 0.218
0.257 0.251 0.243 0.236 0.227 0.223
0.278 0.271 0.261 0.253 0.242 0.237
0.313 0.305 0.293 0.284 0.271 0.265
0.361 0.352 0.338 0.328 0.313 0.306
0.425 0.415 0.399 0.388 0.371 0.364
0.504 0.492 0.477 0.463 0.444 0.436
Ag (Z = 47)
8 12 16 20 24 28
0.390 0.388 0.392 0.394 0.390 0.392
0.397 0.395 0.400 0.402 0.397 0.400
0.414 0.412 0.417 0.420 0.414 0.417
0.445 0.443 0.448 0.451 0.445 0.448
0.489 0.487 0.492 0.495 0.489 0.492
0.549 0.546 0.552 0.555 0.549 0.552
0.624 0.621 0.627 0.630 0.624 0.627
Pt (Z = 78)
8 12 16 20 24 28
0.438 0.451 0.469 0.473 0.479 0.483
0.446 0.460 0.478 0.481 0.487 0.491
0.464 0.479 0.497 0.500 0.506 0.510
0.496 0.512 0.530 0.533 0.539 0.543
0.541 0.557 0.576 0.579 0.584 0.588
0.602 0.618 0.638 0.641 0.645 0.649
0.679 0.695 0.716 0.719 0.722 0.725
The total uncertainty of measurements in η(α) is about 5.5%.
the theoretical curves shown in Fig. 1 for impact energies E0 = 8 and 28 keV). It is seen from Table 1 that the values of η for Al, Ti, Ag and Pt at angles of incidence between 0◦ and 60◦ in step of 10◦ are found to lie in the range 0.172–0.378, 0.246–0.504, 0.390–0.624 and 0.438–0.679 for impact energy of 8 keV and 0.135–0.290, 0.218–0.436, 0.392–0.627 and 0.483–0.725 for 28 keV, respectively (see also Fig. 1). The nature of angular variation is found to be similar for all targets except the difference in their magnitudes. In general, the experimental data for the angular variation of η for elements of high and low atomic numbers are not extensively available in the literature. Nevertheless, the values of η for Mg (Z = 12), Ti, Ag and Pt targets at normal angle of incidence have been reported earlier by Hunger and Kuchler [25] to be 0.156, 0.257, 0.395 and 0.467 at 7.5 keV and 0.135, 0.246, 0.396 and 0.492 at 31.0 keV, respectively. In comparison to these values, our values of η are found for Al, Ti, Ag and Pt to be 0.172, 0.246, 0.390 and 0.438 at 8 keV and 0.135, 0.218, 0.392 and 0.483 at 28 keV, respectively. This comparison shows a small a discrepancy of about 5% between our values and those of Hunger and Kuchler at the considered angles of incidence. This discrepancy may arise due to the following reasons: firstly, the greater instability of the primary beam current at the considered low energies could influence the measured η value if the two electron currents, i.e., ip and it , used for determining η are not measured simultaneously. Secondly, the surface contamination may also influence the results of backscattering.
There is no method by which the perfect cleaning of the specimen surface is possible. In order to minimize the effect of the residual gases on the backscattering process, it is necessary to have the target either in an ultra high vacuum or in an environment with a known residual gas content [22,44]. In view of the above requirement, a cylindrical stainless steel (SS.304 L) chamber was employed in the present work, which minimizes the absorption of contaminated gases more effectively than would a chamber made out of any other material. The pressure obtained in the scattering chamber was always better than 2 × 10−6 Torr, so that the contamination was minimized to a satisfactory level. Concerning the theoretical predictions for the variation of η with α, two theories of backscattering of electrons are available: one of Archard [17] and other of Everhart [16]. The Everhart theory assumes the production of backscattered electrons (BE) to be described simply in terms of single large angle elastic scattering within the material along with an energy-loss related to the depth to which the electrons penetrate before scattering. Archard assumed that the electrons travel in the target in a straight-line path for a certain distance, which remains constant for a given element and a given beam energy, after which they diffuse evenly in all directions. It should be mentioned here that neither of these theories separately represent the property of backscattering for all elements. The Archard theory predicts the variation of η with α, because altering the angle of incidence will alter the depth at
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Fig. 1. Backscattering coefficient for various elements: (a) 8 keV and (b) 28 keV electron impact as a function of the angle of incidence α—() Pt; (䊉) Ag; () Ti; () Al; (—) theory [45,46].
which diffusion starts and hence η. If for normal incidence, the penetration depth is Xd , the diffusion which starts at the end point of Xd will be only at a distance Xd cos α from the surface, and thus the electron has a less chance of being absorbed. Bruining [45] derived a relation for the emission of secondary electrons, which is also applicable to the backscattering process and it is given by, ηα = η0 exp[γXd (1 − cos α)]
(1)
where ηα and η0 are the backscattering coefficients at angle of incidence α and at α = 0◦ , respectively, γ is the absorption coefficient and Xd is the diffusion range (the penetration depth). The constant (γXd ) in Eq. (1) is then found to be a simple function of η0 for all the elements and all energies. Darlington [46] proposed a relation, γXd = − ln η0 − 0.119
(2)
Combining this with Bruining’s expression [see Eq. (1)], one obtains the relation, η cos α 0 ηα = B (3) B
Fig. 2. Backscattering coefficient η0 at normal incidence for impact energy: (a) 8 keV and (b) 28 keV as a function of the atomic number Z—() present data for 8 and 28 keV; () present experiment at 12 keV; (䊉) Monte-Carlo [28]; () Monte-Carlo [28,48]; () Monte-Carlo [49]; () and () Monte-Carlo [50]; (—) theory [27].
where B is an arbitrary constant. A best least squares fit to our experimental data yields a value of B as 0.891. The plots of theoretical and experimental values of ηα with α for impact energies of 8 and 28 keV on Pt target have been shown in Fig. 1(a and b) wherein the theory is normalized at α = 40◦ . The comparison of our data with results obtained from Darlington expression in these figures shows a good agreement among themselves. A similar agreement is also found for data of all other impact energies considered here within the experimental errors of measurement (curves are not shown). Fig. 2 represents the variation of η0 with Z. The backscattering coefficient has been measured for a large number of elements and also for a large range of primary energy. The theoretical treatments for the energy dependence of η0 and for the variation of η0 with Z are given by Dapor [27], √ 1 + 3ε Z − 1 η0 = 1 − √ 3 (1 + ε Z − 1)
(4)
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75
where ε = 0.0811 + 0.0037E0 , for 0 ≤ E0 ≤ 6.7 keV ε = 0.1051 + 1.078 × 10
−4
and
E0 , for 6.7 ≤ E0 45 keV
(5)
In Fig. 2, the experimental values of backscattering coefficient have been compared with the calculations using Eqs. (4) and (5) for Al, Ti, Ag and Pt targets at impact energies 8, 12 and 28 keV. The general form of the η0 –Z curve can be understood by separating the electron–specimen interaction into an elastic component, which represents scattering through a significant angle without energy-loss and an inelastic component, which does not give the angular deflection, but it reduces the electron impact energy. The elastic scattering through a large angle increases as Z2 (Rutherford [47]), while the energy-loss has only a slight Z dependence (Bethe [9]); thus, η0 is expected to be larger for heavier elements than for lighter ones. Our experimental results at 8 keV are found to be in a good agreement with Dapor’s calculations using his analytical expression as well as with his Monte-Carlo calculations at 5 keV [28,48], 10 keV [49] and 5 and 10 keV [50] (see Fig. 2(a)). Further, the present data at 12 and 28 keV are also found to be in a good agreement with his Monte-Carlo calculations at 10 keV [28] and 30 keV [49] (see Fig. 2(b)). The variation of mean fractional energy absorbed (EA /E0 ) as a function of Z has been examined and results are displayed in Fig. 3. The mean fractional energy of backscattered electrons (EB /E0 ) has been calculated using the Monte-Carlo simulations and it has been measured by Bishop [42]. Here, EA and EB are the absorbed energies and the energy of backscattered electrons. The mean path of the backscattered electrons before emerging from the surface is supposed to be equal to the elastic mean free path corresponding to EB [51] 3/5 EB g = (6) E0 g+1 where g=
3 kn 2/3 Z 5 ke
(7)
Fig. 3. Fractional energy absorbed (EA /E0 ) from a thick target for: (a) 8 keV and (b) 28 keV electron impact at normal incidence as a function of Z—() present data for 28 keV; () present data 12 keV; (䊉) Monte-Carlo [28]; () Monte-Carlo [28,48]; () Monte-Carlo [49]; () and () Monte-Carlo [50]; (—) theory [51].
The variation of η0 at normal incidence with impact energy E0 (8–28 keV) has also been studied in this paper. A plot of η0 as a function of E0 exhibits a linear dependence as shown in Fig. 4. Hunger and Kuchler [25] have studied this variation and have
Here, kn = 1.12 × 10−14 eV5/3 cm2 and −14 eV5/3 cm2 . ke = 3.60 × 10 The mean fractional energy absorbed EEA0 can be obtained by energy conservation as, EA EB = 1 − η0 E0 E0
(8)
In Fig. 3(a), the experimental data for 8 keV are found to be in a good agreement with the theoretical predictions of Dapor [51] as well as with his Monte-Carlo calculations at 5 keV [28,48], 10 keV [49] and 5, 10 keV [50]. Monte-Carlo calculations and the analytical treatment are particularly good for low energy (5 keV) electron irradiating the solid targets having mean atomic number (Z < 20). The data at 28 and 12 keV are also seen in good agreement with analytical expression [51] as well as with the Monte-Carlo calculations at 10 keV [28] and 30 keV [49] (see Fig. 3(b)).
Fig. 4. Plot of η0 as a function of E0 (E0 = 8–28 keV): () Pt; (䊉) Ag; () Ti; () Al; (—) theory [25].
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suggested an analytical expression for this case. This expression shows a linear dependence of η0 with E0 . The variations of 0 as a function of Z and the impact energy E0 (keV) are given by these authors [25] as, ln η0 (Z, E0 ) = m(Z) ln E0 + c(Z) m(Z)
η(Z, E0 ) = E0
exp c(Z)
or
Acknowledgments Authors acknowledge the financial support from Department of Science and Technology (DST), New Delhi, for conducting this work under a research project: SP/S2/L-08/2001. The help received from S. Mondal is very much appreciated.
(9)
where m(Z) = 0.1382 − 0.921 Z−0.5 and exp c(Z) = 0.1904 − 0.2236 ln Z + 0.1292[ln Z]2 − 0.01491[ln Z]3 . In their paper, Hunger and Kuchler have concluded that for elements of low atomic numbers, the value of η0 decreases with E0 , whereas for materials with high atomic numbers, η0 shows a contrary behavior with E0 . The variation of η0 with E0 for Al, Ti, Ag and Pt is shown in Fig. 4 for our experimental data and it is compared with the theory of Hunger and Kuchler (see. Eqs. (3) and (9)). It is seen from this figure that the theoretical results for elements, for example, Pt and Al, are in a good agreement with our data within the experimental uncertainty of measurements and similar agreement is also obtained for Ag and Ti targets (curves are not shown). It is noted that η0 increases with E0 for high Z, which can be understood by noting the fact that for elements with high Z, the elastic- and the nuclear-scattering of incident electrons become dominant with increasing impact energy, so that most of the incident electrons get backscattered when they impinge on such targets. 4. Conclusions The present work deals with the measurements of the backscattering of 8–28 keV electrons from a thick Al, Ti, Ag and Pt targets. The dependence of the electron backscattering coefficient on both the incidence angle α and the target atomic number Z has been studied and discussed. The comparison of η values for present targets (Al, Ti, Ag and Pt) with those of Hunger and Kuchler for their targets (Mg, Ti, Ag and Pt) shows a small discrepancy of about 5% at the considered angle of incidence. In Fig. 2, the experimental values of backscattering coefficient have been compared with the calculations using Eqs. (4) and (5) for Al, Ti, Ag and Pt targets for impact energies of 8, 12 and 28 keV. The present results for 8 keV are found to be in good agreement with Dapor’s theory in comparison with those of Monte-Carlo calculations for 5 keV [28,48]. Similar agreement is obtained for results of 12 and 28 keV. In addition, we have examined our data for variation of η0 at normal incidence as a function of impact energy E0 . It is noted that η0 increases with E0 for high Z, which could be understood by noting the fact that for elements with high Z, the elastic and the nuclear scattering of incidence electrons become dominant with increasing impact energy. Furthermore, we have also determined the mean fractional energy absorbed (EA /E0 ) with atomic number Z. For this, the experimental data are found to be in a better agreement with the theoretical prediction of Dapor [51] than that with the calculations of Monte-Carlo simulations at 5 keV [28] and 10 keV [28].
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R.K. Yadav, R. Shanker / Journal of Electron Spectroscopy and Related Phenomena 151 (2006) 71–77 [46] E. H. Darlington, Ph.D. Thesis, University of Muenster, Germany, unpublished, 1937. [47] E. Rutherford, Philos. Mag. 21 (1911) 669. [48] M. Dapor, Phys. Lett. A 143 (1990) 160. [49] M. Dapor, Phys. Rev. B 46 (1992) 618. [50] M. Dapor, Eur. Phys. J. Appl. Phys. 18 (2002) 155.
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Further reading [2] D.P. Woodruff, T.A. Delchar, Modern Techniques of Surface Science, Cambridge University Press, Cambridge, 1994.
Backscattering of 8–28 keV electrons from a thick Al, Ti, Ag and Pt targets R.K. Yadav, R. Shanker ∗ Atomic Physics Laboratory, Department of Physics, Banaras Hindu University, Varanasi 221005, India Received 2 October 2005; received in revised form 1 November 2005; accepted 2 November 2005 Available online 6 December 2005
Abstract Measurements of electron backscattering coefficient η for thick Al, Ti, Ag and Pt targets have been made for incident electrons with energy 8–28 keV. The variations of η with angle of incidence α, impact energy E0 and with target atomic number Z have been studied. The data are compared with available theories. The mean fractional energy absorbed in the backscattering process has been determined and compared with an analytical expression and with Monte-Carlo simulations based on the Kanaya and Okayama electron–electron and electron–nucleus interactions and on the Quinn electron–plasma interactions. The comparison between our experimental data and the model calculations using Monte-Carlo simulations and analytical expression shows a reasonably good agreement among themselves within experimental errors of measurements. © 2005 Elsevier B.V. All rights reserved. PACS: 79.90.+b; 79.20.Hx Keywords: Backscattering coefficient; Mean fractional energy absorbed; Diffusion range; Penetration depth
1. Introduction The technique of surface analysis has become extremely important in modern technology [1,3]. The interaction of electron beam with a solid target has been studied since long [4–9]. Excellent reviews about this subject are given by Bothe [10], Birkhoff [11] and more recently by Neidrig [12], Goldstein et al. [13], Newbury et al. [14] and Feldman and Mayer [15]. When a mono-energetic electron beam impinges on a solid target, some electrons are backscattered without any energy loss. This elastic electron backscattering process plays an important role in many experimental techniques, like, low energy electron diffraction (LEED), scanning electron microscopy (SEM), electron probe microanalysis (EPM), Auger electron spectroscopy (AES), electron lithography physics, radiation damage and elastic peak technique. These techniques have been used for the experimental determination of the inelastic mean free paths (IMFPs) of electrons in the solid. It has become essential to have a precise knowledge of the surface structure and the surface chemical
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composition as well as to understand the surface properties of a solid material. Indeed, any interaction between a solid and the “outside world” takes place through the topmost atoms of the surface of the material. It has then become extremely common to treat, coat, etc., the surface of the material to modify the way in which it interacts with the environment (passivation of the surface against corrosion, coating of glasses to avoid unwanted reflection, etc.). It is then extremely important to control at a microscopic level the way in which the surface treatments affect the interactions of the solid with the “outside worlds” to understand the chemical reactions at the surface of a material, to understand how the electronic surface properties (which differ from those of bulk) affect the behavior of an electronic device, etc. It is well known that when an electron beam impinges on the solid targets, a fraction of the beam is absorbed, another fraction is backscattered, and remaining one is transmitted. The sum of these fractions is equal to 1. Their values depend on the nature of a target bombarded and its thickness. If the target thickness is greater than the maximum penetration range R, then no electrons are transmitted through the specimen, the incident electrons can be only absorbed or backscattered and the fraction of backscattered electrons assumes its maximum value generally indicated as backscattering coefficient η. For understanding the surface
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properties of solids, a number of investigators have proposed their theories. For example, Everhart [16], Archard [17], Body [18], Tomlin [19] and Dashen [20] made calculations about the backscattering coefficient η as a function of the atomic number Z in reasonable agreement with the available experiments. Subsequently, Arnal et al. [21] gave a simple expression for η as a function of tilt angle and atomic number. In addition, it may be noted that there exist experimental works in literature concerning the backscattering coefficient as a function of the angle of incidence by Darlington and Cosslett [22] and Staub [23]. The primary energy and atomic number dependences of the backscattering coefficient were given by Jacob [24], Hunger and Kuchler [25], Williamson et al. [26] and Dapor [27]. The works of Kanaya and Okayama [28], Lantto [29,30], Liljequist [31], Iafrate et al. [32], Niedrig [12], Rogaschewski [33] and Dapor [34,35] were concerned with the more general theoretical problems of calculating transmission, backscattering and absorption of electrons impinging on supported and unsupported thin films. Electron-beam solid–target interaction has also been investigated by using the so-called Monte-Carlo method, a numerical procedure involving random numbers that is able to solve mathematical problems [36]. This method is convenient for the study of electron penetration in matter, since the probabilistic laws of interaction of an individual electron with the atoms constituting the target are known. Consequently, it is possible to compute the macroscopic characteristics of the interaction process by simulating a great number of real trajectories and then averaging them [37]. The backscattering coefficient strongly depends on the target atomic number Z [16,17,24] and also slightly on the primary energy E0 [38–42,27] and on the incidence angle α. It is not realistic to consider the backscattered electrons as perfectly reflected from the surface without dissipation of energy. It is more reasonable to think that they have penetrated a little bit below the surface and have lost a small fraction of their energy. As a consequence, the mean energy of the backscattered electrons EB will be in general a large fraction of the primary energy E0 whose value will depend on the mean path traveled in the solid before emerging from the surface. Once the backscattering coefficient η and the mean energy EB of the backscattered electrons are known, the energy absorbed by the solid target due to electron irradiation can be calculated by considering the energy conservation law. In this paper, we present new experimental data on the backscattering of electrons incident normally and obliquely on different metallic targets, for example, Al (Z = 13), Ti (Z = 22), Ag (Z = 47) and Pt (Z = 78) in the impact energy range 8–28 keV. The dependence of the electron backscattering coefficient on both the incidence angle α and the target atomic number Z has been studied. Further, we have examined our data for the variation of η0 at normal incidence as a function of impact energy E0 . In addition, we have also determined the variation of fractional energy absorbed in the backscattering process with the atomic number Z. Wherever possible, results of the present work have been compared with the other published data and with the predictions of available theoretical models.
2. Experimental The measurements were carried out on the same experimental set up which has been developed in our laboratory for studies of electron–atom/molecule collision processes except some minor modifications. Details of the modified experimental set up are given and discussed in our previous paper [43]. Briefly, a mono-energetic beam of electrons was derived from a custom built electron gun (M/S P. Staib GmbH, Germany), which provided a focused beam of about 3 mm spot size at the target (20 mm × 14 mm) situated at about 500 mm away from the gun. The accuracy of positioning the beam spot on the target was estimated to be about ±1 mm. During measurements, the current of incident beam was kept at about 10 nA. The base pressure of the scattering chamber was maintained at better than 2 × 10−6 Torr. The chamber is equipped with a movable target holder in the vertical plane at its center, which facilitates positioning the target in front of the beam. High purity thick Al (0.5 mm, 99.9995%), Ti (0.1 mm, 99.99%), Ag (0.1 mm, 99.998%) and Pt (0.1 mm, 99.99%) targets were mounted on the target holder. For plate current ip , a semispherical aluminum collector plate (0.5 mm thick) placed behind the grid was used to monitor the current produced by the scattered electrons from the target. In this configuration, the high-energy backscattered electrons could reach the collector plate kept at Earth potential through a high precision resistance of 33 M. A dual switch was used to measure the plate current ip and the target current it one after the other with the help of a digital voltmeter (DVM) connected across the precision resistor. Relative calibration of the two measuring devices was insured before recording the actual corresponding currents. It may be pointed out here that three successive measurements of η were made in our experiments for each incidence angle and for each impact energy. The average of these measurements was taken to finally calculate η. The statistical uncertainty of measurements for η was about 2.4%. Finally, the backscattering coefficient η defined as the ratio ip /(ip + it ) was calculated from values of two measured currents. Uncertainty of measurements originates from two sources, namely fluctuations of the beam energy and of the beam current. Here, the uncertainties in the beam energy and in the beam current are determined to be about ±1 and ±5%, respectively. Hence, the total uncertainty including the statistical error of measurements for η is around 5.5%. 3. Results and discussion The measured values of η as a function of angle of incidence α, (0◦ ≤ α ≤ 60◦ ) relative to the surface normal of a thick, polished and chemically pure target, for example, Al, Ti, Ag and Pt for different impact energies E0 (E0 = 8–28 keV) are summarized and presented in Table 1. At angles of incidence higher than 60◦ , the measurements for η become less reliable. This is because at these angles, the electron beam does not fall fully on to the target surface: rather a large fraction of it passes by the target at a grazing angle. The backscattering coefficient is generally found to increase smoothly with α (see our data and
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Table 1 Measured values of electron backscattering coefficient η as a function of the angle of incidence α for Al (Z = 13), Ti (Z = 22), Ag (Z = 47) and Pt (Z = 78) targets at different impact energy E0 Z
Ep (keV)
α (◦ ) 0◦
10◦
20◦
30◦
40◦
50◦
60◦
Al (Z = 13)
8 12 16 20 24 28
0.172 0.161 0.152 0.148 0.141 0.135
0.175 0.165 0.155 0.151 0.144 0.138
0.187 0.174 0.164 0.159 0.151 0.146
0.213 0.197 0.184 0.178 0.168 0.161
0.252 0.233 0.217 0.210 0.198 0.188
0.308 0.286 0.267 0.259 0.245 0.232
0.378 0.353 0.331 0.321 0.305 0.290
Ti (Z = 22)
8 12 16 20 24 28
0.246 0.241 0.235 0.229 0.221 0.218
0.257 0.251 0.243 0.236 0.227 0.223
0.278 0.271 0.261 0.253 0.242 0.237
0.313 0.305 0.293 0.284 0.271 0.265
0.361 0.352 0.338 0.328 0.313 0.306
0.425 0.415 0.399 0.388 0.371 0.364
0.504 0.492 0.477 0.463 0.444 0.436
Ag (Z = 47)
8 12 16 20 24 28
0.390 0.388 0.392 0.394 0.390 0.392
0.397 0.395 0.400 0.402 0.397 0.400
0.414 0.412 0.417 0.420 0.414 0.417
0.445 0.443 0.448 0.451 0.445 0.448
0.489 0.487 0.492 0.495 0.489 0.492
0.549 0.546 0.552 0.555 0.549 0.552
0.624 0.621 0.627 0.630 0.624 0.627
Pt (Z = 78)
8 12 16 20 24 28
0.438 0.451 0.469 0.473 0.479 0.483
0.446 0.460 0.478 0.481 0.487 0.491
0.464 0.479 0.497 0.500 0.506 0.510
0.496 0.512 0.530 0.533 0.539 0.543
0.541 0.557 0.576 0.579 0.584 0.588
0.602 0.618 0.638 0.641 0.645 0.649
0.679 0.695 0.716 0.719 0.722 0.725
The total uncertainty of measurements in η(α) is about 5.5%.
the theoretical curves shown in Fig. 1 for impact energies E0 = 8 and 28 keV). It is seen from Table 1 that the values of η for Al, Ti, Ag and Pt at angles of incidence between 0◦ and 60◦ in step of 10◦ are found to lie in the range 0.172–0.378, 0.246–0.504, 0.390–0.624 and 0.438–0.679 for impact energy of 8 keV and 0.135–0.290, 0.218–0.436, 0.392–0.627 and 0.483–0.725 for 28 keV, respectively (see also Fig. 1). The nature of angular variation is found to be similar for all targets except the difference in their magnitudes. In general, the experimental data for the angular variation of η for elements of high and low atomic numbers are not extensively available in the literature. Nevertheless, the values of η for Mg (Z = 12), Ti, Ag and Pt targets at normal angle of incidence have been reported earlier by Hunger and Kuchler [25] to be 0.156, 0.257, 0.395 and 0.467 at 7.5 keV and 0.135, 0.246, 0.396 and 0.492 at 31.0 keV, respectively. In comparison to these values, our values of η are found for Al, Ti, Ag and Pt to be 0.172, 0.246, 0.390 and 0.438 at 8 keV and 0.135, 0.218, 0.392 and 0.483 at 28 keV, respectively. This comparison shows a small a discrepancy of about 5% between our values and those of Hunger and Kuchler at the considered angles of incidence. This discrepancy may arise due to the following reasons: firstly, the greater instability of the primary beam current at the considered low energies could influence the measured η value if the two electron currents, i.e., ip and it , used for determining η are not measured simultaneously. Secondly, the surface contamination may also influence the results of backscattering.
There is no method by which the perfect cleaning of the specimen surface is possible. In order to minimize the effect of the residual gases on the backscattering process, it is necessary to have the target either in an ultra high vacuum or in an environment with a known residual gas content [22,44]. In view of the above requirement, a cylindrical stainless steel (SS.304 L) chamber was employed in the present work, which minimizes the absorption of contaminated gases more effectively than would a chamber made out of any other material. The pressure obtained in the scattering chamber was always better than 2 × 10−6 Torr, so that the contamination was minimized to a satisfactory level. Concerning the theoretical predictions for the variation of η with α, two theories of backscattering of electrons are available: one of Archard [17] and other of Everhart [16]. The Everhart theory assumes the production of backscattered electrons (BE) to be described simply in terms of single large angle elastic scattering within the material along with an energy-loss related to the depth to which the electrons penetrate before scattering. Archard assumed that the electrons travel in the target in a straight-line path for a certain distance, which remains constant for a given element and a given beam energy, after which they diffuse evenly in all directions. It should be mentioned here that neither of these theories separately represent the property of backscattering for all elements. The Archard theory predicts the variation of η with α, because altering the angle of incidence will alter the depth at
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Fig. 1. Backscattering coefficient for various elements: (a) 8 keV and (b) 28 keV electron impact as a function of the angle of incidence α—() Pt; (䊉) Ag; () Ti; () Al; (—) theory [45,46].
which diffusion starts and hence η. If for normal incidence, the penetration depth is Xd , the diffusion which starts at the end point of Xd will be only at a distance Xd cos α from the surface, and thus the electron has a less chance of being absorbed. Bruining [45] derived a relation for the emission of secondary electrons, which is also applicable to the backscattering process and it is given by, ηα = η0 exp[γXd (1 − cos α)]
(1)
where ηα and η0 are the backscattering coefficients at angle of incidence α and at α = 0◦ , respectively, γ is the absorption coefficient and Xd is the diffusion range (the penetration depth). The constant (γXd ) in Eq. (1) is then found to be a simple function of η0 for all the elements and all energies. Darlington [46] proposed a relation, γXd = − ln η0 − 0.119
(2)
Combining this with Bruining’s expression [see Eq. (1)], one obtains the relation, η cos α 0 ηα = B (3) B
Fig. 2. Backscattering coefficient η0 at normal incidence for impact energy: (a) 8 keV and (b) 28 keV as a function of the atomic number Z—() present data for 8 and 28 keV; () present experiment at 12 keV; (䊉) Monte-Carlo [28]; () Monte-Carlo [28,48]; () Monte-Carlo [49]; () and () Monte-Carlo [50]; (—) theory [27].
where B is an arbitrary constant. A best least squares fit to our experimental data yields a value of B as 0.891. The plots of theoretical and experimental values of ηα with α for impact energies of 8 and 28 keV on Pt target have been shown in Fig. 1(a and b) wherein the theory is normalized at α = 40◦ . The comparison of our data with results obtained from Darlington expression in these figures shows a good agreement among themselves. A similar agreement is also found for data of all other impact energies considered here within the experimental errors of measurement (curves are not shown). Fig. 2 represents the variation of η0 with Z. The backscattering coefficient has been measured for a large number of elements and also for a large range of primary energy. The theoretical treatments for the energy dependence of η0 and for the variation of η0 with Z are given by Dapor [27], √ 1 + 3ε Z − 1 η0 = 1 − √ 3 (1 + ε Z − 1)
(4)
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where ε = 0.0811 + 0.0037E0 , for 0 ≤ E0 ≤ 6.7 keV ε = 0.1051 + 1.078 × 10
−4
and
E0 , for 6.7 ≤ E0 45 keV
(5)
In Fig. 2, the experimental values of backscattering coefficient have been compared with the calculations using Eqs. (4) and (5) for Al, Ti, Ag and Pt targets at impact energies 8, 12 and 28 keV. The general form of the η0 –Z curve can be understood by separating the electron–specimen interaction into an elastic component, which represents scattering through a significant angle without energy-loss and an inelastic component, which does not give the angular deflection, but it reduces the electron impact energy. The elastic scattering through a large angle increases as Z2 (Rutherford [47]), while the energy-loss has only a slight Z dependence (Bethe [9]); thus, η0 is expected to be larger for heavier elements than for lighter ones. Our experimental results at 8 keV are found to be in a good agreement with Dapor’s calculations using his analytical expression as well as with his Monte-Carlo calculations at 5 keV [28,48], 10 keV [49] and 5 and 10 keV [50] (see Fig. 2(a)). Further, the present data at 12 and 28 keV are also found to be in a good agreement with his Monte-Carlo calculations at 10 keV [28] and 30 keV [49] (see Fig. 2(b)). The variation of mean fractional energy absorbed (EA /E0 ) as a function of Z has been examined and results are displayed in Fig. 3. The mean fractional energy of backscattered electrons (EB /E0 ) has been calculated using the Monte-Carlo simulations and it has been measured by Bishop [42]. Here, EA and EB are the absorbed energies and the energy of backscattered electrons. The mean path of the backscattered electrons before emerging from the surface is supposed to be equal to the elastic mean free path corresponding to EB [51] 3/5 EB g = (6) E0 g+1 where g=
3 kn 2/3 Z 5 ke
(7)
Fig. 3. Fractional energy absorbed (EA /E0 ) from a thick target for: (a) 8 keV and (b) 28 keV electron impact at normal incidence as a function of Z—() present data for 28 keV; () present data 12 keV; (䊉) Monte-Carlo [28]; () Monte-Carlo [28,48]; () Monte-Carlo [49]; () and () Monte-Carlo [50]; (—) theory [51].
The variation of η0 at normal incidence with impact energy E0 (8–28 keV) has also been studied in this paper. A plot of η0 as a function of E0 exhibits a linear dependence as shown in Fig. 4. Hunger and Kuchler [25] have studied this variation and have
Here, kn = 1.12 × 10−14 eV5/3 cm2 and −14 eV5/3 cm2 . ke = 3.60 × 10 The mean fractional energy absorbed EEA0 can be obtained by energy conservation as, EA EB = 1 − η0 E0 E0
(8)
In Fig. 3(a), the experimental data for 8 keV are found to be in a good agreement with the theoretical predictions of Dapor [51] as well as with his Monte-Carlo calculations at 5 keV [28,48], 10 keV [49] and 5, 10 keV [50]. Monte-Carlo calculations and the analytical treatment are particularly good for low energy (5 keV) electron irradiating the solid targets having mean atomic number (Z < 20). The data at 28 and 12 keV are also seen in good agreement with analytical expression [51] as well as with the Monte-Carlo calculations at 10 keV [28] and 30 keV [49] (see Fig. 3(b)).
Fig. 4. Plot of η0 as a function of E0 (E0 = 8–28 keV): () Pt; (䊉) Ag; () Ti; () Al; (—) theory [25].
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suggested an analytical expression for this case. This expression shows a linear dependence of η0 with E0 . The variations of 0 as a function of Z and the impact energy E0 (keV) are given by these authors [25] as, ln η0 (Z, E0 ) = m(Z) ln E0 + c(Z) m(Z)
η(Z, E0 ) = E0
exp c(Z)
or
Acknowledgments Authors acknowledge the financial support from Department of Science and Technology (DST), New Delhi, for conducting this work under a research project: SP/S2/L-08/2001. The help received from S. Mondal is very much appreciated.
(9)
where m(Z) = 0.1382 − 0.921 Z−0.5 and exp c(Z) = 0.1904 − 0.2236 ln Z + 0.1292[ln Z]2 − 0.01491[ln Z]3 . In their paper, Hunger and Kuchler have concluded that for elements of low atomic numbers, the value of η0 decreases with E0 , whereas for materials with high atomic numbers, η0 shows a contrary behavior with E0 . The variation of η0 with E0 for Al, Ti, Ag and Pt is shown in Fig. 4 for our experimental data and it is compared with the theory of Hunger and Kuchler (see. Eqs. (3) and (9)). It is seen from this figure that the theoretical results for elements, for example, Pt and Al, are in a good agreement with our data within the experimental uncertainty of measurements and similar agreement is also obtained for Ag and Ti targets (curves are not shown). It is noted that η0 increases with E0 for high Z, which can be understood by noting the fact that for elements with high Z, the elastic- and the nuclear-scattering of incident electrons become dominant with increasing impact energy, so that most of the incident electrons get backscattered when they impinge on such targets. 4. Conclusions The present work deals with the measurements of the backscattering of 8–28 keV electrons from a thick Al, Ti, Ag and Pt targets. The dependence of the electron backscattering coefficient on both the incidence angle α and the target atomic number Z has been studied and discussed. The comparison of η values for present targets (Al, Ti, Ag and Pt) with those of Hunger and Kuchler for their targets (Mg, Ti, Ag and Pt) shows a small discrepancy of about 5% at the considered angle of incidence. In Fig. 2, the experimental values of backscattering coefficient have been compared with the calculations using Eqs. (4) and (5) for Al, Ti, Ag and Pt targets for impact energies of 8, 12 and 28 keV. The present results for 8 keV are found to be in good agreement with Dapor’s theory in comparison with those of Monte-Carlo calculations for 5 keV [28,48]. Similar agreement is obtained for results of 12 and 28 keV. In addition, we have examined our data for variation of η0 at normal incidence as a function of impact energy E0 . It is noted that η0 increases with E0 for high Z, which could be understood by noting the fact that for elements with high Z, the elastic and the nuclear scattering of incidence electrons become dominant with increasing impact energy. Furthermore, we have also determined the mean fractional energy absorbed (EA /E0 ) with atomic number Z. For this, the experimental data are found to be in a better agreement with the theoretical prediction of Dapor [51] than that with the calculations of Monte-Carlo simulations at 5 keV [28] and 10 keV [28].
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Further reading [2] D.P. Woodruff, T.A. Delchar, Modern Techniques of Surface Science, Cambridge University Press, Cambridge, 1994.