Contribution of backscattered electrons to the total electron yield produced in collisions of 8 28 kev electrons with tungsten

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1 PRAMANA c Indian Academy of Sciences Vol. 68, No. 3 journal of March 2007 physics pp Contribution of backscattered electrons to the total electron yield produced in collisions of 8 28 kev electrons with tungsten R K YADAV and R SHANKER Atomic Physics Laboratory, Department of Physics, Banaras Hindu University, Varanasi , India Corresponding author. rshanker@bhu.ac.in MS received 2 November 2005; revised 22 September 2006; accepted 4 December 2006 Abstract. It is shown experimentally that under energetic electron bombardment the backscattered electrons from solid targets contribute significantly ( 80%) to the observed total electron yield, even for targets of high backscattering coefficients. It is further found that for tungsten (Z = 74) with a backscattering coefficient of about 0.50, about 20% of the total electron yield is contributed by the total secondary electrons for impact energies in the range of 8 28 kev. The yield of true backscattered electrons at normal incidence (η 0 ), total secondary electrons (δ) and the total electron yield (δ tot ) produced in collisions of 8 28 kev electrons with W have been measured and compared with predictions of available theories. The present results indicate that the constant-loss of primary electrons in the target plays a significant role in producing the secondary electrons and that it yields a better fit to the experiment compared to the power-law. Keywords. Backscattering yields; secondary electron yield; stopping power. PACS Nos b; Hx; i 1. Introduction When energetic electrons collide with a solid metallic target, they lose their energy by a variety of mechanisms: secondary electrons (SE) are emitted as a result of energy transfer process occurring between the incident electrons and the electrons in the solid. Secondary electrons are generated within their escape depth in the range of Å for metals [1]. These electrons may find their way to the surface and escape from it. Primary electrons which have penetrated deeper into the target and got subsequently backscattered towards the surface may also generate secondary electrons within the secondary electron escape depth, which contribute to the total yield of secondary electrons [2,3]. Considerable interest has arisen in the use of secondary electrons resulting from bombardment of a solid target with a focused and highly accelerated beam of electrons in scanning electron microscopy 507

2 R K Yadav and R Shanker (SEM). The quantitative analysis of secondary electrons in studies of microscope images requires a knowledge of the escape depth of secondary electrons inside the target, and also the contribution of backscattered electrons for generating the secondary electrons. Relevance of the secondary electrons in determining the atomic structure of a given target has been considered by several workers (see [4 6]). The emission of secondary electrons is quantified in terms of SE yield from a solid, which is defined as the number of the secondary electrons emitted per incident charged particle. In general, the SE emission from metals takes place due to collisions of both primary and backscattered electrons with the target. This emission strongly depends on the scattering process of the primary electrons for which no detailed theory is available as yet. Theoretical treatment of secondary electron emission is based on many different mechanisms, for example, ion-induced secondary electron emission for incident energy of kev (Parilis and Kishinevskii [7] based on Auger recombination mechanism, Ghosh and Khare [8] based on the relation of the SE yields to the ionization cross-sections at high energy electron impact). Electron-induced secondary electron emission has been described by the elementary theories by Salow [4], Baroody [5] and Bruining [6]. Kanaya and Kawakatsu [1] have modified these theories using a Lindhard power potential formalism to describe SE emission from metals due to both primary and backscattered electrons. In electron-induced SE emission, some of the incident electrons are backscattered from the solid [9 13]. In this process, secondary electrons may be produced by incident as well as backscattered electrons and thus, the total secondary electron yield produced from the target is given by δ = δ i s + δ b s, (1) where δs i is the secondary electron yield from the solid due to the incident electrons passing through the surface and δs b is the secondary electron yield due to the backscattered electrons. Also, the total electron yield from the target is given by [14] δ tot = δ + η α, (2) where η α is the backscattering coefficient which is the number of backscattered electrons per incident electrons at the incidence angle α. In the present work, we report on the measured ratio of backscattering coefficients (η α /η 0 ) for a thick tungsten target as a function of the angle of incidence for electrons having impact energy 10 kev. In addition, results on the secondary electron and total electron yields due to backscattered and primary electrons from tungsten for collisions of electrons with impact energies in the range of 8 28 kev are presented and discussed. Wherever possible, results of the present work have been compared with other published data and with the predictions of the available theoretical models. 2. Experimental Measurements were carried out on a recently developed experimental set-up, the details of which are given and discussed elsewhere [15]. Briefly, a mono-energetic 508 Pramana J. Phys., Vol. 68, No. 3, March 2007

3 Collisions of 8 28 kev electrons with tungsten beam of electrons was generated from a custom-built electron gun (M/s P.Staib GmbH, Germany) and was focused onto a 3 mm spot size on the target (20 mm 14 mm 0.5 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 the measurements, the incident beam current was kept at about 10 na. The base pressure of the scattering chamber was maintained at Torr. The chamber is equipped with a movable target holder in the vertical plane at its center to position the target in front of the beam. A high purity (99.90%) tungsten target with 0.5 mm thickness was mounted on the target holder. In order to measure the secondary electrons, we have used a suppressor grid biased at 50 V with respect to the target. A semi-spherical 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. Both the suppressor grid and the collector plate were fixed in front of the target. The integrated assembly of the target holder and the target could be moved up or down or rotated with respect to the direction of the beam. The angular positioning of the target with respect to the direction of the incident beam was made between α = 0 and 60 with an accuracy of ±1. All measurements were carried out under a high vacuum (< Torr) condition. For conditioning the specimen, one of its faces was mechanically polished until it reflected light specularly. This face was made to interact with the beam. It was cleaned with acetone repeatedly and degreased in the alcohol vapor bath before being transferred to the scattering chamber. The backscattered electrons reach the collector plate kept at earth potential through a high precision resistance of 33 MΩ. The plate and the target current were measured through a dual switch with the help of a digital voltmeter (DVM) connected across a precision resistance. 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 0 and δ tot were made in our experiments for each impact energy E. The average of these measurements finally was taken. The statistical uncertainty of measurements was found to be about 5%. The electron energy of impact E was varied from 8 to 28 kev. At an angle of incidence higher than 60, the accuracy of measurements for η α becomes less reliable as at these angles the electron beam does not necessarily fall fully onto the surface of the target, rather a large fraction of it scatters at a grazing angle. 3. Results and discussion The variation of ratio (η α /η 0 ) as a function of angle of incidence α for impact energy E = 10 kev for W and Au targets has been studied and shown in figure 1. The ratio is seen to increase smoothly with α. The nature of angular variation of the data from our results for W is found to be similar to that for Au from other workers (Fitting et al [16] and Staub [17]). From this comparison, it is noted that our data for W are in satisfactory agreement with those of Staub for Au [17] but the data for Au from Fitting et al [16] are seen to lie slightly lower than ours. However, on comparing the above data for W and Au, it is concluded that three sets of data for not too different Z-elements are in a good agreement with each other within the Pramana J. Phys., Vol. 68, No. 3, March

4 R K Yadav and R Shanker Figure 1. Variation of the ratio (η α/η 0) as a function of incidence angle α for W and Au at E = 10 kev. experimental uncertainties. The angular dependence of the backscattered electrons for W at 8 kev electron impact has been measured recently in our laboratory and the results are reported (see, ref. [15]). In order to predict the variation of η with α, two simple theories of backscattering are available: one due to Everhart [18] and other due to Archard [19]. Bruining [6] derived a relation for emission of secondary electrons according to which the expression for angle-dependent backscattering coefficient η α is given as η α = η 0 exp[γx d (1 cos α)], (3) where η α and η 0 are the backscattering coefficients for angle of incidence α and for α = 0 respectively, γ is the absorption coefficient and x d is the diffusion range. The constant γx d in eq. (3) is then found to be a simple function of η 0 for all elements and for all impact energies [20], γx d = ln η (4) Combining the above relation with Bruining s expression (see, eq. (3)), one obtains 510 Pramana J. Phys., Vol. 68, No. 3, March 2007

5 Collisions of 8 28 kev electrons with tungsten Figure 2. Plot of δ, η 0 and δ tot as a function of impact energy E (8 28 kev). (,, ): present experiment; : Al [24]. Theory: solid curves (δ: [14], η 0 : [21], δ tot: [14,21]). η α = B(η 0 /B) cos α, (5) which yields the value of B (a constant) to be The least squares fit to our experimental data and those of Staub with eq. (5) is made and shown in figure 1. The comparison between theory and experiment shows a good agreement among themselves within the experimental errors. Further, a plot of our measured values of η 0 as a function of E is shown in figure 2, which exhibits a linear dependence. Hunger and Kuchler [21] have also made a theoretical study of this variation in the range of 4 40 kev. The curve shown in the figure is the prediction of their theoretical calculations which is found to be in a good agreement with our experimental data. For studying the behavior of electrons penetrating a solid target, there are two theories available: (i) diffusion and (ii) large-angle elastic scattering. Two sources of energy loss, one due to nuclear and other due to electronic stopping, affect the electron beam. The corresponding momentum transfers are small because electrons are light particles, but the relative energy loss is very large. Thus, the range of Pramana J. Phys., Vol. 68, No. 3, March

6 R K Yadav and R Shanker penetrating electrons is given by the electronic stopping power wherein the incident electron excites or ejects the atomic electrons with an energy-loss defined as [22], [ de Z = ρ dx AE ln E ] kev/cm, (6) I where E is the impact energy; I = ( Z 1.19 )Z ev [23] is the mean excitation potential of the target material and electron energy range x = E 0 /(de/dx) and ρ is the density of the target material. The yield of secondary electrons produced by the incident electrons of energy E from W can be calculated [14] as δs i = [ln(5.69)e ] (7) E and the yield of secondary electrons produced by the backscattered electrons is obtained as [14], ( ) δs b η = E E max [ ln 103 E ln EE max E max I ln E ] 10 3, (8) E max where E max = 800 ev (for Z = 79), is the energy at which the maximum of de/dx curves occurs. The measured yield of true backscattered electrons (η 0 ), total secondary electrons (δ) and the total electron yield (δ tot ) produced by the collisions of 8 28 kev electrons with W are shown in figure 2. The theoretical curve for secondary electrons produced by primary plus backscattered electrons is obtained using eqs (7) and (8). From the figure, it is seen that the backscattered electrons contribute significantly to the observed total secondary electrons (δ). For targets of high Z such as tungsten, the backscattering coefficients are found to be about 50% and the contribution of total secondary electrons to the total electron yield is seen to range from 29 to 10% for impact energies ranging from 8 to 28 kev, that is, on an average about 20% of the total electron yield is contributed by the total secondary electrons. This finding agrees approximately with what one would expect from the smaller rate of energy loss and from the smaller path lengths traveled by the backscattered electrons in the secondary electrons escape region compared to that by the incoming primaries. In figure 2, the open circles represent the total secondary electron yield for Al (Z = 13) [24] wherein the data are normalized at E = 20 kev. It is also noted that the total secondary yield increases as E decreases; this happens because increasing amount of energy is dissipated by the primary electrons in the region close enough to the surface for a large fraction of the excited internal secondary electrons to escape. For a sufficiently high impact energy, the penetration depth of the primary beam becomes large compared to the escape depth of secondary electrons, and since the number of secondary electrons created per unit path length is a decreasing function of energy, the number of internal secondary electrons created within the escape depth of the surface decreases with increasing primary energy. 512 Pramana J. Phys., Vol. 68, No. 3, March 2007

7 Collisions of 8 28 kev electrons with tungsten Figure 2 also shows the increasing trend of η 0 with impact energy E. The reason why η 0 increases with E for high Z targets such as W and Au can be understood by noting the fact that for these elements, the elastic and nuclear scattering of incident electrons become more dominant with increasing impact energies. From the yield curves of elements W, Ti and Pt, a universal yield curve can be obtained by plotting values of δ/δ max vs. E/E max (see figure 3) following the procedure of Baroody [5], where δ max is the maximum secondary emission coefficient. However, the prediction of Baroody s theoretical universal yield curve has assumed the Whiddington s law. This curve is found to deviate considerably from the experimental data for various materials. A better fit to the experimental data but still using simple secondary electron emission theory, has been obtained by Lye and Dekker [25], assuming the range energy relationship of electrons given by Young [26]. From the transmission experiments of Young, it is found that the practical range R of electrons follows the relationship R = CE n+1, where C is a constant and n = It may be pointed out here that the Whiddington s law assumes n = 1 in the power-law theory. However, a better agreement of the experimental data for W from our experiment and the data from Baroody s paper for Ti and Pt metals is obtained if n = 0.15 is used in the expression given by Lye and Dekker [25]. The universal yield curve of Lye and Dekker is written as follows: δ 1 = δ max g n (Z m ) g n ( Zm E E max ), (9) g n (Z) = 1 exp( Zn+1 ) Z n, (10) where Z n+1 = γr, Z m represents the value of Z when g n (Z) becomes maximum. A curve is plotted between δ/δ max and E/E max using eq. (9) for the value of n = The resulting curve is shown by a solid line in figure 3. In this context, it may be mentioned here that the range energy results are described quite accurately by Young using the relation R = E 1.35 for aluminum oxide for which the value of n = 0.35, where R is expressed in mg/cm 2 and E in kev. Lye and Dekker [25] compared their experimental results by taking n = 0.35 in theory and found a satisfactory agreement with the experiment. It may be pointed out here that the value used by Young for n = 0.35 was for aluminum oxide and not for a metal. It is interesting to note that the value of n = 0.15 is found to yield a good agreement with ours as well as with Baroody s experimental data for metallic elements. At still higher energies, where data for metals are not readily available, we have found that the yields for W, Pt and Ti vary as E 0.15 which fit the experimental data reasonably well. The smaller value of n (n = 0.15) compared to n = 0.35 [25] is indicative of the fact that the yields of secondary electrons in metals vary more slowly with E compared to that in metal oxides. This may be because of the fact that the stopping powers of electrons in metals [27] and metal oxides [25] vary differently. In figure 3, the experimental data are seen to follow the constant-loss principle and not the power law. In contrast, the constant-loss indicates the importance of straggling of the primaries in the target, which is usually neglected in the power-law theory [25]. As a consequence of this, the effective energy loss per Pramana J. Phys., Vol. 68, No. 3, March

8 R K Yadav and R Shanker Figure 3. Variation of the reduced secondary electron yields (δ/δ max) with the reduced primary energy (E/E max ), where δ max and E max are defined in the text. Different symbols show the experimental data points for various elements; : W, : Pt, : Ti. The solid curve represents the prediction from Lye and Dekker [25] for a case of constant-loss while the dotted line curve represents the prediction for power-law. unit depth per incident electron will also be different from the calculated values on the basis of a single range for all primaries. In fact, if all primaries are assumed to have the same range, most of the energy losses will occur near the end of the range and thus the production of secondary electrons will be a function of depth as indicated by power-law. In straggling, the act of equalizing the energy losses leads to essentially a constant value over the entire range. 4. Conclusions The present work deals with the contribution of backscattered electrons to the secondary electron yields by the collisions of 8 28 kev electrons with tungsten. It is shown that the backscattered electrons contribute significantly to the observed total electron yield δ tot. For targets of high Z, the contribution of total secondary electrons to the total electron yield is seen to range from 29 to 10% for the impact energies from 8 kev to 28 kev, i.e. on average, about 20% of the total electron yield forms the total secondary electrons. The total secondary electron yield increases as the impact energy E decreases; this is because increasing amount of energy is dissipated by the primary electrons in the region close enough to the surface for a large fraction of the excited internal secondary electron to escape. The plotted curve (solid line in figure 3) for δ/δ max vs. E/E max for n = 0.15 gives a better fit to the experimental data for W from our experiment and to the data from Baroody s 514 Pramana J. Phys., Vol. 68, No. 3, March 2007

9 Collisions of 8 28 kev electrons with tungsten paper for Ti and Pt materials. The experimental data follow the constant-loss principle. The constant-loss indicates the importance of straggling of the primaries in the target. In straggling, the tendency of equalizing the energy losses brings essentially a constant value over the entire range. Acknowledgements The work presented here has been financially supported by the Department of Science and Technology (DST), New Delhi, under a research project, SP/S2/L- 08/2001. The authors would like to thank Mr S Mondal for his help in the experiment and for fruitful discussions. References [1] K Kanaya and H Kawakatsu, J. Phys. D5, 1727 (1972) [2] K Kanaya, S Ono and F Ishigaki, J.Phys. D11, 2425 (1978) [3] S Thomas and E B Pattinson, J. Phys. D3, 349 (1970) [4] H Salow, Z. Phys. 41, 434 (1940) [5] E M Baroody, Phys. Rev. 78, 780 (1950) [6] H Bruining, in Physics and applications of secondary electron emission (Pergamon, London, 1954) ch. 6 [7] E S Parilis and L M Kishinevskii, Sov. Phys. Solid State 3, 885 (1960) [8] S N Ghosh and S P Khare, Phys. Rev. 125, 1254 (1962) [9] H Kanter, Phys. Rev. 121, 681 (1961) [10] H Niedrig, J. Appl. Phys. 53, R15 (1982) [11] E J Sternglass, Phys. Rev. 95, 345 (1954) [12] L Reimer and C Tolkamp, Scanning 3, 35 (1980) [13] K F J Heinrich, Proc. 4th Conf. on X-ray Optics and Microanalysis edited by R Castaing et al (Hermann, Paris, 1966) 159 [14] D M Suszcynsky and J E Borovsky, Phys. Rev. A45, 6424 (1992) [15] R K Yadav, A Srivastava, S Mondal and R Shanker, J. Phys. D36, 2538 (2003) R K Yadav and R Shanker, Phys. Rev. A70, (2004) [16] H J Fitting, C Hinkforth, H Glaefeke and J C Kuhr, Phys. Status Solidi A126, 85 (1991) [17] P-F Staub, J. Phys. D27, 1533 (1994) [18] T E Everhart, J. Appl. Phys. 31, 1483 (1960) [19] G D Archard, J. Appl. Phys. 32, 1505 (1961) [20] E H Darlington, Ph.D. Thesis (University of Muenster, Germany, 1973) unpublished [21] H J Hunger and L Kuchler, Phys. Status Solidi A56 k, 45 (1979) [22] H Bethe and V Ashkin, Experimental nuclear physics edited by E Serge (Wiley, New York, 1953) vol. 1, p. 166 [23] F Salvat and J Parellada, J. Phys. D17, 185 (1984) [24] K L Hunter, I K Snook, D L Swingler and H K Wagenfeld, J. Phys. D23, 1738 (1990) [25] R G Lye and A J Dekker, Phys. Rev. 107, 977 (1957) [26] J R Young, Phys. Rev. 103, 292 (1956) [27] J Sempau, J M Fernandez-Varea, E Acosta and F Salvat, Nucl. Instrum. Methods B207, 107 (2003) Pramana J. Phys., Vol. 68, No. 3, March