Dependence on the incident angle of the electronic energy loss of planarly channeled fast ions

Transcription

1 Nuclear Instruments and Methods in Physics Research B 149 (1999) 45±43 Dependence on the incident angle of the electronic energy loss of planarly channeled fast ions M. Barbatti a, *, N.V. de Castro Faria a, J.C. Acquadro b, R. Donangelo a a Instituto de Fõsica, Universidade Federal do Rio de Janeiro, C.P. 6858, Rio de Janeiro, Brazil b Instituto de Fõsica, Universidade de S~ao Paulo, C.P , S~ao Paulo, Brazil Received 18 May 1998; received in revised form October 1998 Abstract The angular dependence of the electronic energy loss of fast ions was calculated. Models for the transitions from axial to planar channeling and from planar channeling to a random direction are discussed in terms of a simple generalization of the Lindhard±Jin±Gibson Model for the axial±random transition. In order to compare these models with experimental data, the energy loss of.0 MeV He ions channeled through a thin silicon crystal into directions that scan the {001} plane from the [110] axis to the [100] axis was measured. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: p; Bw 1. Introduction When a beam of charged particles traverses a crystal, its interactions inside the material can depend strongly on the target orientation. In particular, when the incident direction is parallel to some of the crystal planes and axes, the incident particles are guided by the repulsive potentials associated to these structures, reducing the number of frontal collisions with the atoms of the crystal. This constitutes the well-known phenomenon of planar and axial channeling. * Corresponding author. Tel.: ; fax: ; barbatti@if.ufrj.br In spite of the fact that the channeling theory is well established [1,], some aspects as the study of the energy loss dependence on the incident angle has received little attention. Jin and Gibson [3] developed a semi-classical model to show the general behavior of the angular pro le, which is in good agreement with MeV He -Si experimental data. The model is based on Lindhard's theory [1] and takes into account angular scannings between axially channeled directions and random directions. In what follows we call it the axial±random Lindhard±Jin±Gibson model (a±r LJG). Dos Santos et al. [4] have used the non-perturbative coupled channels method to study this dependence in channeling of 850 kev He through Si, and, as we shall see, their results are consistent with the a±r X/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S X ( 9 8 )

2 46 M. Barbatti et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 45±43 LJG model. Dygo et al. [5] present, together with an experimental study, a theoretical perturbative treatment of dependence on the incident angle of the energy loss to 65 kev protons through Si. The ab initio approach ± more than the semiclassical one ± provides more exact resuts as well as information on the basic energy loss processes through the computation of the ionization and excitation cross sections. However, the semi-classical models, as the a±r LJG and those that will be developed in this work, have the advantage of showing directly the system dependence on its main parameters, besides being easily adapted to furnish a rst approximation to new experimental arrangements, computational modelings, and general applications of the ion stopping power in the channeling regime. In this work, we have generalized the a±r LJG model to include scannings between planar channels and random directions (p±r LJG model), and between axial and planar channels (a±p LJG model). These three models are compared with our experimental data that we have obtained from.0 MeV He channeled into {001} plane of Si. The experimental set up is discussed in Section. Afterwards, we develop the a±r, a±p and p±r models. Results are shown and discussed in Section 5. The pressure in the scattering chamber was of the order of 10 6 Torr. The ions scattered through 170 were detected and energy analyzed with a surface barrier detector. The total resolution of the detection system for the region of interest was always better than 10 kev. Two typical spectra, one corresponding to an incidence in the [110] axes and the other, to a random direction near this axes, are shown in Fig. 1. In the spectrum of channeled particles we can measure the energy loss in the channeled plus randomic direction. The random spectrum indicates the energy-loss summed for two near random directions. The energy calibration was done with standard elements deposited on thin lms or the surface peak, shown in the gure. The measurement of energy loss in channeling conditions at MeV energy region with hydrogen or helium as projectiles are usually done by transmission in thin self-supporting lms [7]. The transmitted particles are analysed by electrostatic or magnetic analysers, and for higher energies, by surface barrier detectors. The energy loss is then directly extracted from the di erence between the particle energy with and without the lm. It is a large problem obtaining extremely thin self-supporting single crystals for these measurements. In fact, that is an important limitation for low energy measurements with the method of transmission.. Measurements The experiment was performed in the scattering chamber for channeling measurements available at the 5SDH tandem accelerator LAMFI Laboratory of the Instituto de Fõsica of the Universidade de S~ao Paulo. The incident beam of He, with.0 MeV, was collimated to an area of 0:8 0:8 mm that corresponds to an angular divergence of A commercial (VG) -rotation-axis and 3-translation-axis goniometric assembly was used to perform the alignment of the sample and has an angular precision better than two tenth of a milliradian. The two rotations and two of the three translations are computer controlled by a standard code. The sample, furnished by Spire Corporation, was made by epitaxial [100] grown chemical vapour deposition, technique described by Grant et al. [6]. It has a thickness of A. Fig. 1. Channeled and random RBS spectra to.0 MeV He in Si.

3 M. Barbatti et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 45±43 47 The technique used in our work is based on the ideas explained by dos Santos et al. [4,8]. It is essentially a Rutherford backscattering technique, in which the particle traverses the silicon channel, it is backscattered by some amorphous lm at the rear surface of the target, and again traverses the silicon in a not aligned direction. The measured energy loss is the sum of the channeled and the ``random'' losses, the latter being known or could be easily measured. The advantage of this method is that it does not need extremely thin self supporting lms. In fact, in reference dos Santos et al. was employed a SIMOX sample, consisting of a very thin Si [1 0 0] crystal on top of a (5000 A) buried layer of SiO build in a [100] Si wafer. On the other hand, it is necessary to note that the low energy tail of RBS spectrum includes not only backscattered ions at the back surface of target but also those ions dechanneled and backscattered at several other crystal layers. In this case, data analysis demands knowledge of the fraction of dechanneled backscattered ions at the depth x, v x and this is an additional factor that makes it di cult to accomplish. Instead, to simplify data analysis, we have evaporated a thin Au lm ( 800 A) on the front face of the target holder (Fig. ). The He backscattered ions from the Au lm form a clear peak in the RBS spectrum, allowing us to read the detected energy of the backscattered particles on the Si±Au interface. This information is the basis for energy loss calculations (Fig. 1). As the Au peak is completely separated from the Si signal, it does not contain any contribution due to dechanneled and Fig.. Schematic drawing of the Si crystal mounted on the sample holder with a thin gold layer in between (not on scale) backscattered ions at the Si target, and it is not necessary to know the dechanneling fraction v x. Note that the Au peak position contains ± besides the channeled energy loss information, and the random energy loss after backscattering ± contributions due to elastic collisions in the Au lm. We assume that a channeled ion experiences an average energy loss h de=dr ch i, until it is scattered by a collision with a Au target atom. If the target thickness is L, the beam energy E 0, the energy of the ion immediately before it is scattered E 1, and h is the incident angle measure from the normal of the surface, then de dr ch ˆ E0 E 1 L= cos h : 1 The energy immediately after backscattering is given by E ˆ ke 1, where the kinematic factor k depends on the masses of the ion and of the target atom, and on the backscattering angle [9], h. After they are scattered the ions are no longer channeled, and their energy loss rate de=dr r, is well known [10]. We have obtained a good adjustment for these values between zero and 4.0 MeV by the parametric form: de dr r ˆ a 0 a 1 exp b 3 E a exp b 0 b 1 E b E ; where the coe cients a i ; i ˆ 0; 1; take the values 10.69, 43.1, 10.33, respectively, and b i ; i ˆ 0; 1; ; 3 the values 1.67, 0.578, , 5.741, respectively. The nal energy of the ions is thus given by E f ˆ E Z Lf 0 de dr dr; r 3 where L f ˆ L cos h 10 ). In this way, from the measured value of the energy E f and Eq. () we determine E, which in turn determines E 1. Thus, we are able to calculate the average energy loss for the channeled ions, de=dr ch, by substitution into Eq. (1). The results of our data analysis are presented in Figs. 3±5. We note that, as expected, the energy loss shows a reduction for incidence close to the channel direction, similar to backscattering scannings.

4 48 M. Barbatti et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 45±43 3. The A±R LJG model Fig. 3. Angular dependence of energy loss from {001} planar to [100] axial channeling. For all energy loss measured the error bars are Fig. 4. Angular dependence of energy loss from random direction to [110] axial channeling. Lindhard, in his seminal work on the theory of channeling [1], derives a relation between the electronic energy loss and the transverse energy, which we brie y review here. He assumes that, in the case of a channeled projectile, the energy loss depends on both the global and local electronic densities, de dr ch ˆ S e 1 a a NZ a a.š; 4 where S e is the electronic stopping cross section, N the mean target density (atoms/volume), Z the target atomic number (hence, NZ is the target global electronic density),. is the local electronic density at position R, and a a is a constant taking values between 0 (when only the global density is considered) and 1 (only the local term contributes). From Poisson's equation in cylindrical coordinates, and assuming that the potentials of two adjacent rows do not overlap, we can show that the mean local density felt by a projectile with transverse energy E? is given by. a E? ˆ Nd Z 1 e r d min dr U r min ; 5 where Z 1 is the projectile atomic number, d is the distance between atoms in the rows that de ne the channel, and the minimum distance between the projectile and the atomic rows, r min has an implicit dependence with the transverse energy E? given by U r min ˆ E? : Since Lindhard's potential for a row of atoms is, in the continuum approximation, given by " # U r ˆ Z1Z e ln ac 1 ; 6 d r we immediately obtain "!# E?. a E? ˆ NZ 1 exp ; 7 Ew 1 Fig. 5. Comparison between the dependence on incident angle of the energy loss and of the backscattering number. where we have used w 1 ˆ Z 1Z e = Ed, in which E is the incident energy of the projectile. Substituting the above equation into Eq. (4), we obtain

5 M. Barbatti et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 45±43 49 the channeled electronic stopping cross section S e E? ˆ 1 NZ de=dr ch, S e E? E? ˆ 1 a a exp S e! : 8 Ew 1 Jin and Gibson [3] have written the energy loss as a function of the incident angle of the projectile on target. They have noticed that, since E? ˆ Eh before the ion penetrates the target, an increase in the incident angle h (de ned by the beam line and the channel axis) should cause an increase in the transverse energy E?. Then, the relative stopping is given by S e h=w 1 S e ˆ 1 a a exp! h : 9 According to Eq. (9) the angular half width at half maximum is given by r h 1= ln ˆ 0:59: 10 w 1 In terms of the backscattering half width at half maximum of the channel, using w 1= ˆ a r w 1, one has h 1= w 1= ˆ 0:59 a r ; 11 where a r takes into account thermal e ects in the lattice. For He incident on Si at room temperature [], a r ˆ 0:84. Hence, the ratio between the channel half width get from energy loss and the one get from backscattering results is, according to the a±r LJG model, 0:70, whatever the channel or the ion incident energy considered. This model agrees well with the axial±random scanning experimental data, but should be modi ed in order to be compared with data of axial±planar (a±p) and planar±random (p±r) scannings. This is done in the following section. w 1 4. The modi ed LJG models 4.1. The a±p LJG model ions go through three di erent regimes: (i) pure axial channeling (h w 1 ), (ii) mixed axial and planar channeling (h w 1 ), and (iii) pure planar channeling (h w 1 ). The fraction of axially channeled ions decreases gradually with incident angle. We assume that this behavior may be described through an exponential dependence exp be?, where b is a constant. Since the transition between the two regimes takes place over an energy interval of the order of Ew 1, we choose b ˆ 1=Ew 1. We assume, as in the a±r LJG model, that the stopping power can be divided into global and local density contributions. From the considerations above, we split the local contribution in Eq. (4) into axial and planar density terms. This leads to the equivalent of Eq. (8), S e E? ˆ 1 a a a a exp be?. a E? S e NZ 1 exp be?. p NZ ; 1 where, as Lindhard [1], we have supposed that the two contributions to the channeling stopping cross section are proportional to the random stopping cross section. In the above equation, the local density. a E? is the same as in Eq. (7), and. p the density of electrons involved in planar channeling. The relative energy loss as a function of the incident angle is obtained as before, S e h=w 1 ˆ 1 a a 1. p S e NZ a a 1.! p exp h NZ w 1! a a exp 3 h : 13 w 1 The angular width is then obtained from the equation above, and takes the values: 1 0 0Š h 1= ˆ 0:365; w 1 14 As the incident angle scans the transition from axial to planar channeling, we suppose that the 1 1 0Š h 1= ˆ 0:383; w 1 15

6 430 M. Barbatti et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 45± Š where we have used the values. p =NZ ˆ 0: Š and. p =NZ ˆ 0:61 obtained in Section 5, 1 0 0Š 1 1 0Š Eq. (), which arises from a a ˆ 0:33, a a ˆ 0:38, and a p ˆ 0: The p±r LJG model Although, to the best of our knowledge, there are no data available on the planar channeling± unchanneled transition, we found appropriate to extend the LJG model to particular case where we take a scanning normal to the plane. The p±r LJG model can be derived analogously as the a±r LJG case, seen in the previous section. We have used the planar Lindhard potential q U p z ˆ Ew a z=a c z=a ; 16 where w a ˆ pnz 1 Z e a=e 1= is the characteristic angle for planar channeling p analogous to w 1 in axial channeling, c ˆ 3 and n is the planar atomic density (atoms/area). By using Poisson's equation and taking the average over the transversal coordinate z, the average electronic density is 3. z min ˆ NZ 6 z min =a 7 4 q 15: 17 z min =a c Since U p z min ˆ E?, z min =a ˆ c?? ; 18 where? ˆ E? = Ew a. The normalized electron density is then given by 3.? =NZ ˆ z min =a 7 4 q 5: 19 z min =a c The relative energy loss is 3 S e E? ˆ 1 a p 6 z min =a 1 q 7 4 5; 0 S e z min =a c where a p is a constant analagous to a a, and can assume values between 0 and 1. In terms of the incident angle, 3 S e h=w a S e ˆ 1 a p c h=wa 6 41 h=w a r 7 5 : c c h=w a 4 h=w a 4 1 p From Eq. (1) the half width is h 1= =w a ˆ c 1:3, or in p terms of backscattering half width, h 1= =w 1= ˆ c =ar ˆ 1:73, where we have used [] a r ˆ 0: Results and discussion Eqs. (9), (13) and (1) are the theoretical predictions for the energy loss angular pro le in the cases of axial±random, axial±planar, and planar± random scannings, respectively. The parameter a a in Eqs. (9) and (13) and the parameter a p in Eq. (1) should be determined independently, either by simulation [11±13], or by direct measurements [8,7]. These parameters determine the minimum energy loss, i.e., the energy loss when the beam is perfectly aligned with the channel. In the a±p model, since we scan two channeled levels, besides a a we have to obtain the parameter. p =NZ, which determines the minimum of planar level in Eq. (13). Note that. p =NZ plays the same role as the a p. This gives us a relation between these parameters 1 a p ˆ 1 a a 1. p NZ : The normalized energy loss angular width, h 1= =w 1= is independent of a a and a p in both the a±r and the p±r models. Note, however, that in the a±p case the angular width depends on. p =NZ. Hence, while the angular widths predicted by the a±r and p±r models do not depend on the details of the system considered, the angular a±p width should be determined in each case. Table 1 compares our predictions for the angular widths with experimental data obtained by us and by other recent works [3,4]. The backscat-

7 M. Barbatti et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 45± Table 1 Channel angular width measured by stopping power E 0 Type Channels h 1= h 1= =w 1= a±r LJG model a±r 0.70 dos Santos et al., a±r [100] % Jin and Gibson, 86.0 a±r [100] % present work.0 a±r [110] % a±p LJG model.0 a±p [100] {001} a±p LJG model.0 a±p [110] {001} 0.45 present work.0 a±p [100] {001} % present work.0 a±p [110] {001} % p±r LJG model ± p±r {001} 1.73 tering measurement of the channel half width is signi cantly larger than the energy loss width measured in a±r and a±p scannings, as indicated by values of h 1= =w 1= < 1 (see Fig. 5). The discrepancies between the a±r and a±p LJG models and experimental results are smaller than 10%. We predict that the angular width obtained through backscattering measurements in p±r scanning should be smaller than the one obtained from the energy loss. However, as indicated in the previous section, there are no p±r scannings available to compare with our predictions. Although the models presented here seem to be adequate to predict angular widths, they are not able to reproduce some details of the pro les, for example, the compensation region in the perimeter of the channel in which the energy loss is higher than the random one, or occasional microchannels in scanning. In the case of the a±p model (see Fig. 3), the compensation region begins to appear as a consequence of taking into account the ion distribution in two di erent regimes. It predicts the same qualitative behavior, but does not agree in magnitude with the experimental results. As it has been noticed by Jin and Gibson [3], the valence electrons of Si are distributed along the channel in an approximately uniform way. Therefore the increase in the energy loss when the incident angle increases is caused by interactions between He ions and electrons of the L shell of Si, since the K-electron contribution is very small [14]. In the a±p case the phenomenon should be similar for the fraction of ions axially channeled, while the fraction of the ions channeled in the planar mode does not give directional contribution to the energy loss. Hence, as the incident angle increases, the increase in the a±p energy loss is smoother than that of the a±r energy loss (see Fig. 6). This implies an azimuthal dependence of energy loss, which would not be expected if the ions with a determined E? were uniformly distributed in the allowed region of the channel, as in Linhard's equilibrium hypothesis [1]. Although the a±p energy loss increases in a smoother way than the a±r energy loss, one notices that due to the di erence between assymptotical levels in one and another case, the angular width in the a±p case is smaller than the one found in the a±r case (Fig. 6). Fig. 6. Comparison between angular pro les measured from random to axial channel and from plane to same axial channel.

8 43 M. Barbatti et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 45±43 Acknowledgements We would like to thank Dr. F. Namavar, from Spire Corporation, for providing the target, Leonardo P.G. de Assis from the IM-UFRJ, for help with data analysis, and Carla F. Barbatti, from CBPF, for useful discusions. This work was partially supported by CNPq, FINEP and FA- PERJ. References [1] J. Lindhard, Mat. Fys. Medd. Dan. Vid. Selsk. 34 (1965) 14. [] D.S. Gemmell, Rev. Mod. Phys. 46 (1) (1974) 19. [3] H.S. Jin, W.M. Gibson, Nucl. Instr. and Meth. B 13 (1986) 76. [4] J.H. dos Santos, P.L. Grande, M. Behar, H. Budinov, G. Schiwietz, Phys. Rev. B 55 (7) (1997) 433. [5] A. Dygo, M.A. Boshart, L.E. Seiberling, N.M. Kabachnik, Phys. Rev. A 50 (6) (1994) [6] M.W. Grant, P.F. Lyman, J.H. Hoogenraad, B.S. Carlward, D.A. Arms, L.E. Seiberling, F. Namavar, J. Appl. Phys. 73 (1993) 486. [7] F.H. Eisen, G.J. Clark, J. Bottiger, J.M. Poate, Rad. E ects. 13 (197) 93. [8] J.H.R. Dos Santos, P.L. Grande, H. Boudinov, M. Behar, R. Stoll, C. Klatt, S. Kalbitzer, Nucl. Instr. and Meth. B 106 (1995) 51. [9] W.K. Chu, J.W. Mayer, M.A. Nicolet, Backscattering Spectrometry, Academic Press, New York, [10] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon Press, New York, [11] A. Simionescu, G. Hobbler, S. Bogen, L. Frey, H. Ryssel, Nucl. Instr. and Meth. B 106 (1995) 47. [1] S.T. Nakagawa, Nucl. Instr. and Meth. B 80 (1993) 7. [13] R. Agnihotri, A.P. Pathak, Nucl. Instr. and Meth. B 67 (199) 39. [14] B.R. Appleton, C. Erginsoy, W.M. Gibson, Phys. Rev. 161 () (1967) 330.