Monte Carlo model for the deposition of electronic energy in solid argon thin films by kev electrons

Transcription

1 Monte Carlo model for the deposition of electronic energy in solid argon thin films by kev electrons R. Vidal a),b) and R. A. Baragiola University of Virginia, Engineering Physics, Thornton Hall, Charlottesville, Virginia J. Ferrón INTEC, Universidad Nacional del Litoral and Consejo Nacional de Investigaciones Científicas y Técnicas, Güemes 3450, CC 91, 3000 Santa Fe, Argentina Received 21 June 1996; accepted for publication 7 August 1996 The motion of kev electrons in a film of solid argon and the depth distribution of ionizations and excitations are studied using a Monte Carlo simulation. This method does not only allow for accurate inclusion of individual cross sections but also for easy inclusion of finite size effects. We have analyzed the effect of the substrate on electron trajectories and found an important enhancement of the number of electron hole pairs and excitons produced near the interface by electrons reflected from heavy substrates American Institute of Physics. S I. INTRODUCTION The spatial distribution of ionizations, excitations, and the energy deposited in a material by kev electrons play an important role in many fields, such as atmospheric, 1 solid-state, 2 12 and plasma physics. 13 The knowledge of these distributions is an important step in the understanding of many physical phenomena, such as secondary electron emission, 6,7 cathodoluminescence, 8 electron hole-pair generation in semiconductors, 2 low-voltage electron-beam lithography, 9,10 sputtering of frozen gases, 11,12 and charging of insulators. 3 5 The experimental measurement of these spatial distributions cannot be undertaken easily, and in only a few cases are experimental data available. Everhart and Hoff 2 obtained the distribution of deposited electronic energy by measuring the electron hole-pair generation in a metal oxide semiconductor MOS device aluminum silicon dioxide silicon irradiated with electrons in the 5 25 kev energy range. From these measurements they derived an analytical distribution function which they propose should be valid for targets of atomic number 10 Z 15. The spatial distribution of the energy deposition has been derived in some cases in the gas phase 14,15 from the distribution of characteristic luminescence, assuming that the luminescence should be proportional to the deposited energy. From the theoretical point of view several approaches exist to evaluate these spatial distributions. The first is the analytic transport theory which has been used extensively in the field of radiation physics see Ref. 16 and references therein, since Spencer 17 presented a method of solving the transport equation, which converts it into a linked system of differential equations for the spatial moments of the distribution. In transport theory it is usual to work in the energy space, and evaluate what is called the electron degradation spectrum. Once this spectrum is known, quantities of practical interest, such as ionization and excitation yields, can be calculated. A a Permanent address: INTEC, Universidad Nacional del Litoral and CONICET, 3000 Santa Fe, Argentina. b Electronic mail: rav4n@virginia.edu second approach has been presented recently by Dapor 18 that uses the so-called multiple reflection method, and it has been applied to evaluate transmitted and backscattered fractions of electrons, and energy deposited by kev electrons incident on thin films. Finally, there is the Monte Carlo MC method, in which histories of individual collisions are simulated for many particles in a computer, and conclusions are drawn from the statistics of those histories. The advantage of this approach is the relative simplicity of the algorithms, its accuracy, and its great usefulness when one wants to study targets with complicated geometry. The Monte Carlo method has been applied for a long time to study the electron interaction with matter; 19 in a recent example Valkealahti, Schou, and Nieminen 20 used it to calculate the energy deposition of kev electrons in light elements. In the present work we use the MC method to calculate the energy deposition of kev electrons incident on solid Ar films. We calculate depth distributions of deposited energy, ionizations, and excitations to discrete states, and also the mean energy spent per ionization, the so-called W value. A feature of our work is the incorporation of finite size effects to take into account electrons reflected from the substrate backing the Ar films. This situation, not considered in the work by Valkealahti and co-workers, 20 is the usual one in experiments where the films are grown by vapor deposition onto cooled substrates. The organization of the article is the following. In Sec. II we describe our MC code. In Sec. III A we compare some of its outputs to available experimental results on different targets and we present depth distributions of ionizations and excitations, and also W values. In Sec. III B we discuss the effect of the substrate and the angle of incidence of the primary electrons. II. THE MONTE CARLO SIMULATION METHOD The general characteristics of our MC code have been already reported. 21,22 We consider only two types of interactions between electrons and target atoms: elastic scattering J. Appl. Phys. 80 (10), 15 November /96/80(10)/5653/6/$ American Institute of Physics 5653

2 TABLE I. Binding energies for the contributing shells of the different targets in ev. E exc is the lowest excitation energy in Ar, E val is the effective binding energy of the valence shell for metals. Ar M-shell binding energies and E exc are from Ref. 27. The other binding energies are from Ref. 28. Levels Ar N 2 Al Ag Au 1 L K K M 1,2, M 4, L 2, b 2s 37.0 L M 4, N M s *, b 2p 18.0 L 2, N N 6,7 O M 2, b 2p 15.5 E val 6.8 N 2, O 2, E exc 12.0 E val 15.5 E val 16.0 and inelastic scattering with core and valence electrons. We used the partial wave expansion method to calculate the differential and total elastic scattering cross sections 23 and calculate the phase shifts by solving numerically the radial Schrödinger equation for an atomic potential of the Thomas Fermi Dirac type. 24 Ionizations of core and valence electrons are calculated separately for each atomic level using the Gryzinski excitation function. 25 We used up to five levels to describe the electronic structure of the target atoms. To take into account the valence electrons in different metallic substrates, we used an effective binding energy for the valence level that fits the total inelastic cross sections evaluated semiempirically by Tanuma, Powell, and Penn. 26 For Ar we have used the M-shell binding energies appropriate to the solid state. 27 In Table I we present a summary of the different binding energies used. For Ar we have also included the possibility of excitation processes bound bound transitions as an alternative inelastic interaction. For the sake of simplicity in the MC calculation we considered only the lowest excited states. These arise when an M-shell electron is excited to a unique upper-bound level. Excitations from deeper levels are much smaller than for the M level 29 and were thus neglected. For the calculations, we used the total excitation cross sections presented by Eggarter. 30 The electrons are assumed to follow linear trajectories between two interactions. If we suppose that the distance traveled x between two collisions follows a Poisson distribution then the step length can be calculated using the relation x x i x x i j / i. 2 The first term on the right-hand side is the distance traveled in medium i, and the second term represents the distance traveled in medium j. After an elastic interaction the electron only changes its direction of motion without changing its kinetic energy. The scattering angle is calculated using the elastic scattering differential cross sections and assuming an isotropic distribution for the azimuthal angle. If the electron impact produces an excitation or ionization, the energy loss E is evaluated using the Gryzinski excitation function. If E is greater than the binding energy E b of the shell involved, it ionizes the atom. The outgoing secondary electron has kinetic energy E E b and is assumed to be generated isotropically. We also consider that after an Ar L-shell ionization the atom decays by emitting, isotropically, an Auger electron of 206 ev average energy. 31 The double ionized ion left behind is counted as two ionizations since it is expected to decay rapidly by charge transfer by the process Ar 2 Ar Ar Ar kinetic energy. The trajectory and collision history of each primary electron and all secondary electrons are traced until they leave the solid or their kinetic energy goes below a cutoff energy 14 ev close to the band gap. In each simulation more than incident electrons are traced. After each simulation we obtained the depth distribution of ionizations for each shell, the distribution of ex- x i ln R, 1 where i is the electron mean free path in medium i and R is a uniform random number between 0 and 1. If the electron crosses the interface from medium i to medium j, the change in mean free path between different materials must be taken into account. A way to do this was presented in Ref. 21 where the total traveled distance is corrected as follows: FIG. 1. Normalized energy deposition profiles for 1, 2, and 3 kev electrons incident on nitrogen. The depth is given in units of electron range Ref. 15. Continuous lines are from MC calculations on solid N 2. Simbols are experimental results from Barrett and Hays Ref. 15 for gaseous N J. Appl. Phys., Vol. 80, No. 10, 15 November 1996 Vidal, Baragiola, and Ferrón

3 FIG. 3. Backscattering coefficients as a function of energy for electrons normally incident on gold, argon, and nitrogen. All electrons emitted from the sample with energies greater than 50 ev are counted. Open squares are our MC results, and the dashed lines are drawn just to guide the eye. Solid circles and solid squares are experimental data for gold Ref. 32 and for nitrogen Ref. 33, respectively. Open triangles are MC results from Ref. 20. FIG. 2. Energy deposition profiles for 1 and 3 kev electrons incident on a thick solid argon film. Simbols are MC from this work and the broken lines are MC results from Valkealahti and co-workers Ref. 20. differences seen at 3 kev, in the tail of the energy deposition profile, are probably due to the fact that the Valkealahti and co-workers curve shown in Fig. 2 is not their true MC profile, but their Gaussian fit to it. Figure 3 shows backscattering coefficients for normally incident electrons. This coefficient is defined in the usual way, as the number of electrons with kinetic energy greater citations, and the distribution of electronically deposited energy. Unless noted the results presented below are for normal incidence. III. RESULTS AND DISCUSSION A. Depth distributions and W values We compare some outputs from our MC simulations to available experimental results as well as to other MC simulations results for thick films. Figure 1 shows our energy deposition profiles for normally incident electrons on solid nitrogen and experimental profiles obtained for gaseous molecular nitrogen. 15 To make the comparison independent of sample density and primary electron energy we normalize our results for the energy deposition as follows: z R/E d D x, 3 where (z) is a dimensionless distribution, z x/r, D(x) is the MC energy deposition profile, R is the mean electron range we used the values proposed in Ref. 15, and E d is the total deposited energy. As we can see in the figure the agreement is quite satisfactory. In Fig. 2 we compare our energy deposition profiles for normally incident electrons on solid Ar with MC results from Valkealahti and co-workers. 20 The agreement between both MC simulations is quite good at 1 kev incident energy. The FIG. 4. Depth distributions of ionizations plus excitations to discrete states, and deposited energy for 0.3 and 3 kev electrons incident onto a thick solid argon film. J. Appl. Phys., Vol. 80, No. 10, 15 November 1996 Vidal, Baragiola, and Ferrón 5655

4 FIG. 5. The depth distribution of 3p ionizations and excitations for 0.3 and 3 kev electrons normally incident on a thick solid Ar film. Also shown are 3p ionizations and excitations produced by secondary electrons. than 50 ev emitted from the target per incident electron. For nitrogen and gold, the MC results are compared to experimental backscattering coefficients. 32,33 The results for argon are compared to other MC simulations. 20 There is good general agreement in both cases. Figure 4 depicts the depth distribution of ionizations plus excitations, as well as the distribution of deposited energy for 0.3 and 3 kev electrons normally incident on a thick solid Ar film. It can be seen that the two distributions have almost the same shape. For that reason it is possible to transform one into another by using a mean energy for the creation of either an electron hole pair or a direct excitation. This mean energy is 19.7 ev for 3 kev, and the ratio between both distributions is almost constant with depth. Also the mean energy only decreases slightly as the primary energy decreases, from 19.8 ev for 5 kev to 19.5 ev for 0.3 kev electrons. The W value is nearly independent of projectile energy in the calculated range: 26.2 ev for 0.3 kev to 26.3 ev for 5 kev electrons. This value is close to the experimental values of W ev for 3 5 kev electrons on gaseous Ar, 34 and W 27 1 ev for 30 kev electrons on solid Ar. 35 The depth distribution of ionizations and excitations produced by 0.3 and 3 kev electrons incident on a thick solid Ar film are plotted in Fig. 5. One can see the strong contribution of secondary electrons to the creation of electron hole pairs. The amount of 3p ionizations produced by secondary electrons increases with primary energy from 34% for 0.3 ev electrons to 61% for 5 kev electrons. Similarly the number of excitations produced by secondary electrons increased from 46% to 70% as the electron energy goes from 0.3 to 5 kev. Due to the energy dependence of the ionization and excitation cross sections, 3p ionizations and excitations to bound states are clearly favored over processes in other shells, in the case of secondary electron excitations. We also calculated G values, the number of a particular species produced for each 100 ev of electron energy absorbed, a magnitude of common use in radiation research. They are presented in Table II for the different primary species ions and excitons, as well as for subexcitation electrons i.e., electrons that have kinetic energies lower than the first electronic-excitation threshold, and are therefore incapable of producing excitons or electron hole pairs. The excitons are the products of initial excitations and do not include those formed at a later stage from electron hole recombination. Table II includes the deposited energy, which differs from the incident energy due to the energy carried away by the secondary and backscattered electrons. We have also included in Table II some results of previous MC simulations for Ar gas. 31 TABLE II. Number of initial species produced per 100 ev deposited energy G values for electrons incident on solid Ar. The values in parentheses are from Ref. 30 for Ar gas. Electron incident energy ev s ionizations p ionizations s ionizations p ionizations Excitations Subexcitations Deposited energy ev W ev J. Appl. Phys., Vol. 80, No. 10, 15 November 1996 Vidal, Baragiola, and Ferrón

5 FIG. 8. Increase in the total number of ionizations plus excitations over the number expected for an Ar-like substrate, for a 400 Å solid Ar film supported on Au, as a function of the incidence angle. The symbols are our MC results, and the solid line is drawn just to guide the eye. FIG. 6. Depth distribution of excitations plus ionizations for 1 and 3 kev electrons normally incident on solid Ar films, supported on a gold substrate, and for different film thicknesses. Also shown are 3p ionizations plus excitations produced by secondary electrons lower curves. B. Substrate effects for thin solid Ar films FIG. 7. Depth distribution of ionizations plus excitations for 3 kev electrons incident on a 400 Å solid Ar film supported on Au for different incidence angles. Results for a thick 3000 Å solid Ar film have also been included for comparison. So far we have discussed depth distributions for ionizations and excitations for electrons incident on thick solid Ar films, where all the energy of the projectile is either dissipated in the film or is carried away by escaping secondary and backscattered electrons. One of the key advantage of our MC code is that we can also study thin films supported on different substrates. In Fig. 6 we show depth distributions of ionizations plus excitations for 1 and 3 kev electrons normally incident on Ar films of different thicknesses deposited on a gold substrate. One can see the strong influence of the substrate on the generation of electron hole pairs and excitons near the interface. This is very remarkable when the film and substrate have very different atomic numbers this implies large differences in elastic cross sections for the two materials. The enhancement in the number of ionizations and excitations for heavy substrates is due to electrons reflected from the substrate. The effect tends to decrease when the thickness of the film approaches the primary electron penetration depth about 340 Å for 1 kev electrons and 1600 Å for 3 kev electrons. Electron hole pairs and excitons generated by secondary electrons show a similar dependence with depth. For light substrates the contribution of backscattered electrons becomes smaller, and when the substrate is lighter than Ar e.g., Al the number of ionizations and excitations at the interface is smaller than for a thick argon film at the same depth from the surface. We have also studied the change in the depth distributions of ionizations plus excitations with primary electron incidence angle. That it is shown in Fig. 7 for 3 kev electrons incident on a 400 Å solid Ar film deposited on a gold substrate. The depth distributions change noticeably with electron impinging angle. While near the surface the number of ionizations plus excitations increases monotonously with incidence angle, the inverse dependence is observed at the Ar/Au interface. The increase in the energy deposition at the surface is simply due to the increase of the electron path length. This increase is nearly proportional to the inverse of the cosine, and is independent of the film thickness. On the other hand, the decrease of the number of ionizations plus J. Appl. Phys., Vol. 80, No. 10, 15 November 1996 Vidal, Baragiola, and Ferrón 5657

6 excitations at the interface is produced by roughly the same effect, i.e., the increase of the path length of the electrons near the surface reduces the penetration depth, thus the backscattering enhancement due to the substrate turns to be less important. To quantify the angular dependence of the substrate effect, we need to normalize the total ionization plus excitation yield with respect to the thick Ar film case, i.e., overlayer and substrate are made of Ar. These results are shown in Fig. 8. There we can see that the substrate effect diminishes with impinging angle. This diminution is related to the decrease of the electron penetration depth with angle. IV. CONCLUSIONS We have performed MC simulations to evaluate the distributions of ionizations and excitations produced by kev electron bombardment of argon films supported on different substrates. The simulations predicts an important contribution of secondary electrons to the production of ionizations and excitations. They also show that the depth distributions of ionizations and excitations can be converted to a deposited energy distribution by using a mean energy, which depends only slightly on incident electron energy in the working range. In addition, the contribution of electrons backscattered from the substrate to the number of ionizations and excitations produced near the interface is important for heavy substrates. An observable consequence of this would be a noticeable increase in the number of particles emitted after the decay of electron hole pairs or excitons e.g., electronic sputtering yields, luminescence, or in the secondary electron emission coefficient for thin films on heavy substrates. ACKNOWLEDGMENTS The authors thank A. Gras-Martí, M. Inokuti, and J. Schou for valuable discussions. R.V. would like to acknowledge the support of the CONICET Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina and the Fundación Antorchas A-13019/1. This work was supported by NSF DMR , CONICET PID 3748/92, and Fundación Antorchas A M. J. Berger, S. M. Seltzer, and K. Maeda, J. Atmos. Terr. Phys. 32, T. E. Everhart and P. H. Hoff, J. Appl. Phys. 42, S. Jurac, R. A. Baragiola, R. E. Johnson, and E. C. Sittler, Jr., J. Geophys. Res. 100, J. Cazaux and P. Lehuede, J. Electron Spectrosc. Relat. Phenom. 59, J. Cazaux and C. Le Gressus, Scanning Microsc. 5, H. J. Fitting and D. Hecht, Phys. Status Solidi A 108, J. Schou, Phys. Rev. B 22, B. G. Yacobi and D. B. Holt, Cathodoluminiscence Microscopy of Inorganic Solids Plenum, New York, 1990, p P. A. Peterson, Z. J. Radzimski, S. A. Schwalm, and P. E. Russell, J. Vac. Sci. Technol. B 10, Y.-H. Lee, R. Browning, N. Maluf, G. Owen, and R. F. W. Pease, J. Vac. Sci. Technol. B 10, R. E. Johnson and J. Schou, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 43, O. Ellegaard, R. Pedrys, J. Schou, H. Sørensen, and P. Børgesen, Appl. Phys. A 46, R. E. Johnson, Energetic Charged-Particle Interactions with Atmospheres and Surfaces Springer, Berlin, 1990, p A. Cohn and G. Caledonia, J. Appl. Phys. 41, J. L. Barrett and P. B. Hays, J. Chem. Phys. 64, D. Srdoc, M. Inokuti, and I. Krajcar-Bronic, in Atomic and Molecular Data for Radiotherapy and Radiation Research, IAEA-TECDOC-799 IAEA, Vienna, 1995, pp L. V. Spencer, Phys. Rev. 98, M. Dapor, Phys. Rev. 43, ; M. Dapor, Surf. Sci. 269/270, R. Shimizu and Z.-J. Ding, Rep. Prog. Phys. 55, S. Valkealahti, J. Schou, and R. M. Nieminen, J. Appl. Phys. 65, R. Vidal, J. Ferrón, and R. H. Buitrago, Appl. Surf. Sci. 20, J. Ferrón, E. C. Goldberg, L. S. De Bernardez, and R. H. Buitrago, Surf. Sci. 123, N. F. Mott and H. S. W. Massey, Theory of Atomic Collisions, 3rd ed. Oxford University, Oxford, 1965, p R. A. Bonham and T. G. Strand, J. Chem. Phys. 39, M. Gryzinski, Phys. Rev. A 138, A S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Interface Anal. 17, D. Menzel, Appl. Phys. A 51, J. A. Bearden and A. F. Burr, Rev. Mod. Phys. 39, L. R. Peterson and J. E. Allen, Jr., J. Chem. Phys. 56, E. Eggarter, J. Chem. Phys. 62, K. Unnikrishnan and M. A. Prasad, Radiat. Res. 80, H. Sørensen and J. Schou, J. Appl. Phys. 49, J. Schou and H. Sørensen, J. Appl. Phys. 49, R. L. Platzman, Int. J. Appl. Radiat. Isot. 10, W. E. Spear and P. G. Le Comber, in Rare Gas Solids, edited by M. L. Klein and J. A. Venables Academic, London, 1977, Vol. II, p J. Appl. Phys., Vol. 80, No. 10, 15 November 1996 Vidal, Baragiola, and Ferrón