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Nuclear Instruments and Methods in Physics Research B 254 (2007) 200-204 www.elsevier.com/locate/nimb

Comparative study of silicon and germanium sputtering by 1-20 keV Ar ions
V.I. Shulga
*
Institute of Nuclear Physics, Moscow State University, 119992 Moscow, Russia Received 16 May 2006; received in revised form 19 September 2006 Available online 2 January 2007

Abstract Sputtering of amorphous Si and Ge targets by 1-20 keV Ar ions has been studied using the binary-collision simulation. Special attention was given to the angular distribution of sputtered atoms; namely, the energy dependence of the exponent n in the function cosnh approximating the angular distribution (h is the polar ejection angle). It has been shown that at all incident energies the value of n for Ge is much higher than that for Si, which is in contrast with analytical predictions. The reasons for this discrepancy are discussed in detail. In addition, the simulated values of the sputtering yield are also considered and compared with the data from the literature. У 2006 Elsevier B.V. All rights reserved.
PACS: 79.20.Аm; 79.20.Ap; 79.20.Rf; 95.75.Pq Keywords: Sputtering; Angular distribution; Sputtering yield; Silicon; Germanium; Computer simulation

1. Introduction Silicon and germanium are of special importance in sputtering investigations. Both materials become amorphous at low ion bombarding fluences, which allows for an accurate comparison between experimental results and theoretical predictions usually made for structureless targets. Noteworthy also is the fact that silicon and germanium (and their composites) are very important materials in micro- and nanoelectronics. Plasma and ion beam technologies, which are extensively used in sputter-deposition systems, are examples of technologies that use these materials. The development of such technologies requires detailed information on all the characteristics of the sputtering process. This paper addresses mainly the angular distributions of sputtered Si and Ge atoms. The interest in this study was motivated by the results of recent experiments [1,2] on

sputtering of Si and Ge targets by 3-10 keV Ar ions at normal incidence. In these experiments, the Rutherford backscattering (RBS) technique was used to analyze the collected material. In both cases (Si, Ge) the target surface was found to be practically flat even at total fluence $1018 ions/cm2 [2]. The angular spectra were approximated by the function cosnh and the best-fit values of n were found. It turned out, that the angular distributions of sputtered atoms are overcosine and that n % 1.3 and 1.7 for Si and Ge, respectively. This is in contrast with a purely cosine (n = 1) angular distribution, which follows from the model of isotropic collision cascades, e.g. [3,4]. Fig. 1 presents all the experimentally reported data of n for Si and Ge targets under Ar ion bombardment [1,2,5-7]. Also shown are the theoretical predictions for keV- [8] and sub-keV ion bombardment [9]. Sigmund [8] took into account a net deflection of ejected atoms to the surface normal in the last (non-compensated) collisions and derived n ? 1 юр8=3ЮNC
3=2 0

;

р 1Ю

*

Tel.: +7 495 939 3562; fax: +7 495 939 0896. E-mail address: shulga@hep.sinp.msu.ru

where N is the target atomic density and C0 is the constant defined in [4]. Stepanova and Dew [9] suggested an

0168-583X/$ - see front matter У 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.11.068


V.I. Shulga / Nucl. Instr. and Meth. in Phys. Res. B 254 (2007) 200-204

201

Ar > Si, Ge, normal incidence
amorphous

2.0

1.5
Si Ge

1.0

Ge
Thompson (1968), Sigmund (1981) Sigmund (1987) Stepanova (2001) Si, Tsuge (1981) Si, Chernysh (2004) Ge, Andersen (1985) Ge, Chini (1996) Ge, Patrakeev (2006)

0.5

Si

0.0

Si and Ge respectively) is taken as the surface binding energy. The target atomic density N is 0.0498 and њ 0.0443 atoms/A3 for Si and Ge respectively. A flat surface at x = 0 is assumed. A typical run consisted of 200,000- 500,000 sputtered atoms. All other parameters were identical with the standard model [14]. The simulated angular distributions of sputtered atoms, Y(h), were fitted by the function cosnh and the corresponding best-fit values of n were found. For better understanding of the difference between the results for Si and Ge targets, some additional simulations of sputtering were carried out for several artificial pseudo-Si targets and for the model, in which the scattering of incident ions in the target was switched off (see subsequently).

n

1

10

Ion energy (keV)
Fig. 1. Survey of predicted (lines) and measured (dots) values of n for amorphous Si and Ge targets sputtered by Ar ions at normal incidence. Lines: predictions made in [3,4,8,9]. Dots: experimental data from [1,2,5-7].

3. Results and discussion Fig. 2 compares the measured values of n with the results of computer simulations performed using different interatomic potentials. It is seen that for Ge the simulated values of n are quite sensitive to the variation of the potential. The ZBL potential provides the highest values of n while the WHB and LJ potentials lead to much lower values of n. The latter can be explained by a weakness of the WHB and LJ potentials for Ge at large distances which determine the scattering of particles during their ejection from the surface (see Fig. 6 from [15]). It is also seen from Fig. 2 that nWHB > nZBL for Si but nWHB < nZBL for Ge. Again, such a reverse of the WHB and ZBL data correlates well with the behavior of the relevant potentials [15]. The decrease of n at low ion energies (Fig. 2) can be explained by a high contribution of the primary knock-on atoms

approximate semi-empirical description for the angular spectrum of sputtered atoms which takes into account not only the surface scattering (focusing) effect but also the anisotropy of collision cascades in terms of the theory by Roosendaal and Sanders [10]. From Fig. 1, it is obvious that Eq. (1) cannot explain the high experimental values of n for Ge in the energy range E J 5 keV where the estimate [8] should work well. An attempt to understand this contradiction by the use of computer simulation technique is the aim of the present work. In addition, the simulated values of the sputtering yield will be also considered and compared with the data from literature.

2. Simulation The simulations were performed using the computer code OKSANA [11]. The code is based on the binary collision approximation and takes into account weak simultaneous collisions at large distances. An amorphous target is simulated by rotation of a crystalline atomic block, the procedure of rotation being repeated from collision to collision. The atomic block is chosen in the form of a tetrahedron, which is the typical structure for crystalline Si and Ge. The model used was carefully tested in [12] by comparison of the simulated depth profiles of sputtered atoms with the results of the Monte Carlo program TRIM.SP, which assumes a random target. The standard WHB (KrC), ZBL and LJ potentials are applied as the interaction potential V(R) for colliding particles, e.g. [13]. The inelastic energy losses were calculated by the Firsov formula. Allowance was made for the uncorrelated thermal vibration in terms of the Debye model (T = 300 K). The surface barrier is planar and the heat of sublimation (4.70 and 3.88 eV for

Ar > Si, Ge, normal incidence
amorphous

Ge

1.5
Si

n

1.0

WHB ZBL LJ Si, Tsuge (1981) Si, Chernysh (2004) Ge, Andersen (1985) Ge, Chini (1996) Ge, Patrakeev (2006)

0.5

1

10

Ion energy (keV)
Fig. 2. The energy dependences of the exponent n for amorphous Si and Ge targets sputtered by Ar ions at normal incidence. Solid lines are the results of computer simulations performed using different (WHB, ZBL, LJ) interatomic potentials; dots are the experimental data [1,2,5-7].


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V.I. Shulga / Nucl. Instr. and Meth. in Phys. Res. B 254 (2007) 200-204

characterized by a much wider angular distribution for both Si and Ge (near-surface ejection). Eq. (1) yields n = 1.32 and 1.29 for Si and Ge targets, respectively. As it follows from Fig. 1, this equation agrees well with the experimental results for Si but underestimates the values of n for Ge. The question arises: what is the reason (or reasons) for this discrepancy? To answer this question, a series of auxiliary simulations was carried out using the ZBL potential as an example. In one series of simulations we applied the model in which scattering of projectiles on target atoms was ignored (a straight line approximation for ion trajectories), but the generation of recoiling atoms was considered in the usual manner (model 2 in [16]). The results obtained are shown in Fig. 3(a). It is seen that switching off ion scattering decreases the difference between Si- and Ge-values of n but does not eliminate this difference

Ar > Si, Ge, normal incidence

a
1.6

amorphous, ZBL

Ge
1.4

1.2

Si

Si, no ion scattering Ge, no ion scattering

completely. This means that some other factors should be considered to explain the high values of n for Ge. Another series of simulations was performed for the socalled pseudo-Si. By pseudo-Si is meant a usual (normal) amorphous Si target for which one of the characteristics - atomic density N, surface binding energy U, target atomic mass M2 or target atomic charge Z2 - is taken as that for Ge. For example, the change of Z2 from 14 (Si) to 32 (Ge) leads to the variation of two interatomic potentials (for ion-atom and atom-atom interactions) and may show us the effect of the potentials on the values of n. Similarly, the variation of M2 may show us the mass effect in itself, and so on. The simulation results for pseudo-Si targets and usual Si and Ge targets are shown in Fig. 3(b). It is seen that the N and U effects are relatively weak and practically compensate each other, while the Z2 and M2 effects are more important and, taken together, can explain the high values of n for Ge. The point is that atom-atom scattering is much more pronounced for Ge than for Si (Z2 effect), which amplifies the role of surface non-compensated scattering. In addition, Ar ions can be scattered back to the surface in a single collision from Ge atoms but not from Si atoms. Moving towards the surface such backscattered ions may create recoils oriented near the surface normal giving rise to the increase of n (M2 effect); the latter effect is illustrated also by Fig. 3(a). It should be noted that the decrease of the surface binding energy U when going from Si to Ge works in the same direction: the lowering of U leads to higher contribution of low energy atoms for which surface scattering is more pronounced. And conversely, the decrease of N when going from Si to Ge leads to the decrease of n

n

1.0

1

10

Ion energy (keV) Ar > Si, Ge, normal incidence Ar > Si, normal incidence
amorphous, ZBL

b
1.6

amorphous, ZBL

100

Sigmund (1987)

Ge
10

1.2

Si

Si, Si, Si, Si,

Z=Z(Ge) M=M(Ge) U=U(Ge) N=N(Ge)

p, A

n

1.4

A

1

p

1.0

1

10

1

10

Ion energy (keV)
Fig. 3. The simulated values of n for amorphous Si and Ge targets sputtered by Ar ions at normal incidence (the ZBL potential). Solid lines: the standard model; dashed lines: some auxiliary models. (a) Simulations for Si and Ge targets with and without ion scattering and (b) simulations for Si, Ge and pseudo-Si targets (see the text).

Ion energy (keV)
Fig. 4. Comparison of the predicted (dashed lines) and calculated (dots) values of the parameters A and p in the equation n =1+ ANp. Dots approximate the results of computer simulations for an amorphous Si target sputtered by Ar ions at normal incidence (the ZBL potential). Dashed lines correspond to Sigmund's values of A and p, see Eq. (1).


V.I. Shulga / Nucl. Instr. and Meth. in Phys. Res. B 254 (2007) 200-204

203

(Fig. 3(b)), which is in good agreement with the prediction of Eq. (1). The values of n calculated for Si and for a pseudo-Si target using the Ge-value of the atomic density N (Fig. 3(b)) were fitted by the function n =1+ ANp, which generalizes Eq. (1). The values of the fitting parameters A and p found are shown in Fig. 4 together with Sigmund's values of 3=2 њ A = (8/3) C 0 ? 6.483 A3 and p = 1, see Eq. (1). It can be concluded from the figure that Eq. (1) gives quite an accurate account of the density effect at ion energies E J 5 keV. When calculating the angular distribution of sputtered atoms, it is important to control the sputtering yield Y, which is the main characteristic of sputtering. Fig. 5 compares the simulated and experimental yields for amorphous Si and Ge targets bombarded with Ar ions. As above, the

Ar > Si, normal incidence
amorphous

2.5

2.0

WHB/MR

Y (atoms/ion)

1.5

WHB MR

1.0
Laegreid (1961) Southern (1963) Sommerfeldt (1972) Blank (1979) Zalm (1983)

0.5

MR/WHB

0.0

1

10

Ion energy (keV)
Fig. 6. Same as Fig. 5(a) for the WHB and MR potentials. Also shown are the results of simulations for the combined (ion-atom/atom-atom) potentials.

Ar > Si, normal incidence

a
2.0

amorphous

Y (atoms/ion)

1.5

1.0

0.5

WHB ZBL LJ Laegreid (1961) Southern (1963) Sommerfeldt (1972) Blank (1979) Zalm (1983)

simulated data refer to three potentials: WHB, ZBL and LJ. The experimental data were taken from [17-22]. Fig. 5 demonstrates a reasonable agreement between experiments and simulations. From Fig. 5 it is seen that the results of simulations for different potentials are quite close to each other, especially for Si (Fig. 5(a)). This is not because the relevant potentials are almost identical, which is not true. As discussed in [23], the sputtering yield Y can be roughly expressed as the ratio between the stopping power for bombarding ions and that for recoiling atoms: Y / рdE=dxЮion =рdE=dxЮatom : р 2Ю

0.0

1

10

Ion energy (keV) Ar > Ge, normal incidence
amorphous

b
4

Y (atoms/ion)

3

2

1

WHB ZBL LJ Laegreid (1961) Southern (1963) Sommerfeldt (1972) Krebs (1977)

0

1

10

Ion energy (keV)
Fig. 5. Comparison of the simulated (lines) and experimental (dots) values of the sputtering yield for amorphous Si (a) and Ge (b) targets bombarded with Ar ions. Simulations were performed using different potentials: WHB (circles), ZBL (squares) and LJ (diamonds). The experimental data were taken from [17-22].

Here, (dE/dx)ion correlates with the recoil density near the surface and the ratio 1/(dE/dx)atom correlates with the ejection probability. When varying the ion-atom and atom- atom potentials simultaneously, we decrease (or increase) the stopping powers (dE/dx)ion and (dE/dx)atom but their ratio, i.e. the sputtering yield, remains almost constant (a compensation effect). This effect is more pronounced if the atomic numbers of ions, Z1, and atoms, Z2, are close to each other, just as we have in case of Ar on Si (Fig. 5(a)). It was interesting to compare the results of simulations for essentially different potentials V(R), say, for the WHB and MR potentials, where the abbreviation MR refers to ` the Moliere potential with Robinson's screening length њ as = 0.075 A [24]. For Ar on Si the simulated yields are shown in Fig. 6. Note that at large interatomic distances VMR ( VWHB for both Ar-Si and Si-Si interactions [15]. From Fig. 6, it is seen that even for these (essentially different) potentials the sputtering yields are fairly close to each other. But the situation changes drastically for the combined (WHB/MR and MR/WHB) potentials, in which the ion-atom and atom-atom potentials are not identical: the values of Y calculated using the two combined potentials differ roughly by a factor of 3.


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V.I. Shulga / Nucl. Instr. and Meth. in Phys. Res. B 254 (2007) 200-204 [7] T.K. Chini, M. Tanemura, F. Okuyama, Nucl. Instr. and Meth. B 119 (1996) 387. [8] P. Sigmund, Nucl. Instr. and Meth. B 27 (1987) 1. [9] M. Stepanova, S.K. Dew, J. Vac. Sci. Technol. A 19 (2001) 2805. [10] H.E. Roosendaal, J.B. Sanders, Radiat. Eff. 52 (1980) 137. [11] V.I. Shulga, Radiat. Eff. 82 (1984) 169. [12] V.I. Shulga, W. Eckstein, Nucl. Instr. and Meth. B 145 (1998) 492. [13] W. Eckstein, Computer Simulation of Ion-Solid Interactions, Springer, Berlin, 1991. [14] V.I. Shulga, P. Sigmund, Nucl. Instr. and Meth. B 119 (1996) 359. [15] V.I. Shulga, Nucl. Instr. and Meth. B 164-165 (2000) 733. [16] V.I. Shulga, Nucl. Instr. and Meth. B 152 (1999) 49. [17] N. Laegreid, G.K. Wehner, J. Appl. Phys. 32 (1961) 365. [18] A. Southern, W.R. Willis, M.T. Robinson, J. Appl. Phys. 34 (1963) 153. [19] H. Sommerfeldt, E.S. Mashkova, V.A. Molchanov, Phys. Lett. A 38 (1972) 237. [20] K.H. Krebs, in: Atomic and Molecular Data for Fusion, IAEA, Wien, 1977, p. 185. [21] P. Blank, K. Wittmaack, J. Appl. Phys. 50 (1979) 1519. [22] P.C. Zalm, J. Appl. Phys. 54 (1983) 2660. [23] V.I. Shulga, Nucl. Instr. and Meth. B 174 (2001) 77. [24] M.T. Robinson, in: R. Behrisch (Ed.), Top. Appl. Phys. 47 (1981).

Acknowledgements The author would like to thank Drs. V.S. Chernysh, A.S. Patrakeev and K.M. Abdul-Cader for informative discussions. This work was supported by Grant No. I 0751/ 2140 of the federal program `Integration of Science and Higher Education on 2002-2006 Years'. References
[1] V.S. Chernysh, V.S. Kulikauskas, A.S. Patrakeev, K.M. AbdulCader, V.I. Shulga, Radiat. Eff. Defects Solids 159 (2004) 149. [2] A.S. Patrakeev, V.S. Chernysh, V.I. Shulga, Poverkhnost (3) (2006) 32 (in Russian); V.S. Chernysh, A.S. Patrakeev, V.I. Shulga, Radiat. Eff. Defects Solids 161 (2006) 701. [3] M.W. Thompson, Philos. Mag. 18 (1968) 377. [4] P. Sigmund, in: R. Behrisch (Ed.), Top. Appl. Phys 47 (1981). [5] H. Tsuge, S. Esho, J. Appl. Phys. 52 (1981) 4391. [6] H.H. Andersen, B. Stenum, T. Sorensen, H.J. Whitlow, Nucl. Instr. and Meth. B 6 (1985) 459.