Numerical simulation of the discharge in d.c. magnetron sputtering

Thin Solid Films 351 (1999) 37±41

Numerical simulation of the discharge in d.c. magnetron sputtering Eiji Shidoji a,*, Nobuhiko Nakano b, Toshiaki Makabe b a

Research Center, Asahi Glass Co., Ltd., 1150 Hazawa-cho, Kanagawa-ku, Yokohama 221-8755, Japan b Department of Electrical Engineering, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan

Abstract Numerical simulation of d.c. magnetron discharge for sputtering in Ar is performed using a hybrid model consisting of a particle model and a ¯uid model. The various discharges with different anode's size are simulated to investigate the effect of ®lm conductivity on the anode and the substrate. In the case of a large area anode formed by the deposition of conductive material, the plasma potential becomes higher, suppressing the excess electron ¯ux to the large anode. In the case of a small anode formed by an non-conductive ®lm deposition, the plasma potential becomes lower, dragging a large number of electrons into the small anode. The low plasma potential lowers the potential difference between the cathode and plasma, and the production rate of an electron-ion pair decreases in the cathode sheath region under a constantly applied voltage mode, therefore decreasing the plasma density. It is shown that the plasma potential and the density changes with ®lm conductivity or anode size under a constantly applied voltage. High energy ion injection to the central part of the glass substrate is estimated at the beginning of the ®lm deposition. This implies that the ®lm property at the central part of the non-conductive substrate will differ from the one at the other position due to the difference of the ion impact to the substrate. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Ion bombardment; Conductivity; Simulation; Magnetron

1. Introduction Direct-current (d.c.) magnetron sputtering system has been widely used for many years to deposit ®lms on glass and other materials. Magnetron sputtering system has been used for coating large area substrate because coated ®lms present a good uniformity. The d.c. magnetron discharge system can deposit a non-conductive ®lm as well as a conductive ®lm by using reactive sputtering. A number of measurements [1±5] and simulations [6±10] of the magnetron discharge has been reported during this past decade. A self-consistent model of the magnetron discharge in Ar using Monte Carlo particle simulation has been discussed [10]. In fact, although the magnetron discharge under , mTorr pressure condition can be calculated using the particle model, lengthy and costly computation time is necessary to obtain a steady state pro®le. We have developed a hybrid model consisting of a particle and a ¯uid model in order to simulate low pressure discharges for plasma processing within a reasonable computational time [11]. In this paper, we study the in¯uence of the sputtered ®lm's conductivity on the magnetron discharge system. * Corresponding author. Present address: Research Center, Asahi Glass Co., Ltd., 1150 Hazawa-cho, Kanagawa-ku, Yokohama 221-8755, Japan. Fax: 1 81-45-374-8893. E-mail address: [email protected] (E. Shidoji)

In the case of the deposition of a conductive ®lm, the electrical property of the boundary close to the discharge changes gradually during the deposition because the conductive ®lm covers the glass substrate and the effective area of the anode expands. In the case of the deposition of a non-conductive ®lm, the metal anode gradually diminishes in size. According to the change of the effective size of the anode, the property of the discharge is changed in both the conductive ®lm deposition and in the non-conductive ®lm deposition. The size and potential effects of the anode in the magnetron discharge have been investigated [12±14]. The anode effects reported in Ref. [14] concern the lot type anode located beside the cathode. No investigation of a large size change of the anode due to ®lm deposition has been reported. In this paper, we numerically investigate the effect of the metal anode size in d.c. magnetron discharge for sputtering, a matter of practical importance in conductive or non-conductive ®lm deposition.

2. Simulation model The detailed procedure for creating a simulation model is described in Ref. [11] and is brie¯y described as follows. Fast electrons are treated by the particle model in order to express the individual movement of highly non-equilibrium

0040-6090/99/$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0040-609 0(99)00151-0

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E. Shidoji et al. / Thin Solid Films 351 (1999) 37±41

The net ionization rate, Si(x,z;t), is also calculated from the number of ionizations. Both rates are the source terms in the ¯uid equation. Ions and bulk electrons other than the fast electrons described above are treated by the ¯uid model. The conservation equation of the number density of bulk electrons and ions is, respectively,

2nbe … x; z; t† 1 7´fnbe … x; z; t†vbe 2 De 7nbe … x; z; t†g 2t ˆ Sbe … x; z; t†

…2†

and

2ni … x; z; t† 1 7´fni … x; z; t†vdi 2 Di 7ni … x; z; t†g ˆ Si … x; z; t† 2t …3†

Fig. 1. Schematic diagram of the d.c. magnetron sputtering system considered in this study.

electrons in the sheath region. On the other hand, the ions and the bulk electrons are treated with the ¯uid model in order to calculate the spatial distribution of charged particles within a reasonable computational time. Initially, a secondary electron is ejected from the cathode surface by ion impact. The initial velocity of the secondary electron is taken to be zero. The fast electron originated from the cathode is traced by using the equation of motion dv… x; z; t† q ˆ fE… x; z; t† 1 v… x; z; t† £ B… x; z†g dt m

…1†

as well as by the investigation of the collision event with neutral Ar under the condition of magnetic and electric ®elds, B(x,z) and E(x,z;t). Here, v(x,z;t) is the velocity of the fast electron as a function of positions x, z, and time t (see Fig. 1), while m and q are the mass and the charge of the electron. Ionization, excitation, and elastic momentum transfer collision between the electron and Ar are considered. The energy of the electron is decreased by each collision. When the total energy of an electron is less than 8 eV, it is treated as the bulk electron. The net generation rate of the bulk electron, Sbe(x,z;t), is estimated by the number of electrons whose energy drops to 8 eV in each time interval. Table 1 The anode and substrate conditions and total current of each case. The total current is estimated at the value pre 1 cm in the y direction

Case (A) Case (B) Case (C)

Film

Anode

Current (mA/cm)

None Conductive Non-conductive

± Large Small

2.8 2.9 1.0

where nbe(x,z;t) and ni(x,z;t) are, respectively, the number density of bulk electrons and ions as a function of positions x, z, and time t, vde and vdi the drift velocity, and De and Di the diffusion coef®cient of the electron and the ion. While the electron swarm parameter in Eq. (2) is a function of electric and magnetic ®elds, that of ions in Eq. (3) are suf®ciently considered as the only function of the electric ®eld under the present magnitude of the magnetic ®eld. 2D space potential V(x,z;t) and electric ®eld E…x; z; t†2 7 V are given by Poisson's equation, q 7´7V … x; z; t† ˆ 2 fni … x; z; t† 2 nbe … x; z; t† 2 nfe … x; z; t†g 10 …4† where nfe is the number density of fast electrons, and 1 0 is the permittivity. The numerical procedure is as follows: First, we calculate the electric ®eld by solving Eq. (4). Second, we use Eq. (1) to trace the trajectory of fast electrons ejected from the cathode or generated by the ionization, and investigate by the Monte Carlo method the net rates of the ionization Si, and generation of the bulk electrons with 1 . 8 eV, Sbe. Third, we calculate the number density of the bulk electrons and the ions by Eqs. (2) and (3). Finally, we calculate the ion ¯ux to the cathode surface, and use that calculation to estimate the number density of secondary electrons emitted from the cathode. The time evolution of the discharge is iterated until the 2D spatial distribution of charged particles becomes a steady state. 3. Results and discussion Fig. 1 shows the schematic diagram of the cross section of the rectangular magnetron sputtering system considered in the present study. The size of the discharge region is 10 £ 5 cm. The magnetic ®eld, con®ning electrons ef®ciently in the region close to the cathode (target), is generated by the permanent magnet unit behind the cathode. The anode surrounds the discharge region, leaving the cathode sepa-

E. Shidoji et al. / Thin Solid Films 351 (1999) 37±41

Fig. 2. Comparison of the two-dimensional distributions of the potential. (A),(B),and (C) are the results under the condition of A, B, and C, respectively. External conditions are 5 mTorr, 2330 V, and g ˆ 0:1 under the magnetic ®led, 100 G on the target surface at X ˆ 3:0 cm in Ar.

rated from the anode by the insulator with a speci®c permittivity of 5.0 and thickness of 0.5 cm. The glass substrate, with a speci®c permittivity of 2.25 and thickness of 0.07 cm, is arranged close to the anode, and faces the cathode. The width of the glass substrate, 7.5 cm, is equal to the width of the cathode. The calculations are performed for three different-sized anodes (Table 1). Case A is the condition prior to the deposition on the substrate. Case B is the condition after the deposition of the conductive ®lm on the substrate. The

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®lm is electrically connected to the anode, and the effective anode facing the discharge is large. Case C is the condition after the deposition of the non-conductive ®lm with a speci®c permittivity of 4.84 and thickness of 0.01 cm. The effective conductive anode is then formed only in the d±e region (Fig. 1). Each calculation is performed at 5 mTorr in argon under the conditions of a magnetic ®eld of 100 G on the cathode surface without a normal component and an applied voltage to the cathode of 2330 V. The secondary emission coef®cient of the electron is taken to be 0.1. We assume a uniform ®lm deposition in the a - d region(Fig. 1). As initial conditions, the number of fast electrons are taken to be zero, and the density of bulk electrons and that of ions is assumed to be 1:5 £ 1011 cm 23 at the peak with a distribution proportional to cos2 {…x 2 3†=5†} in the x direction and {1 2 …z 2 10†2 }=36 in the z direction. Fig. 2 compares the two dimensional distribution of the potential. Fig. 2A,B are the results observed for the case A and B, respectively. Fig. 2C shows the result at 100 ms from the initial density condition toward the disappearance of the discharge in case C. In all cases, a sharp potential gradient is formed in front of the cathode. The sheath width becomes narrower in the vicinity of X ˆ 3:0 cm, where the magnetic force line becomes parallel to the cathode surface. The negative potential of the glass substrate in case A is caused by the ambipolar diffusion ¯ow of electrons and ions with different masses. In case B, since the area functioning as the anode is expanded around the discharge region, a large number of electrons are easily absorbed into the expanded anode. The potential difference between the grounded anode and the bulk plasma region is large so as to suppress the excess electron ¯ux to the anode. As a result, the plasma potential of case B is higher than that of case A. In case C, since the non-conductive ®lm is covered around the discharge region, the effective anode is restricted to the d± e region. A strong electric ®eld is formed in front of the small anode in order to drift electrons. The plasma potential (274 V) is much lower than the grounded anode, and the potential difference between the cathode and the bulk plasma region becomes smaller. As a result, the number of ions injected to the cathode and the number of secondary electrons ejected from the cathode become smaller and the discharge gradually disappears. It is necessary to apply a much higher voltage to the cathode in order to sustain the steady discharge in the small anode. When the system is controlled under a constant power, the applied voltage of the cathode becomes higher in case C as compared with that of A and B. Fig. 3A,B show the two-dimensional electron density of cases A and B. The peak position of the electron density in each case is located on the line X ˆ 3:0 cm, where the sheath width is narrow due to the highest rate of electron trapping by the external magnetic ®eld. This means that the most active region with the highest ion ¯ux density to the cathode (target) is formed at X ˆ 3:0 cm, and the maximum erosion is performed by ion sputtering. In case B, the

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E. Shidoji et al. / Thin Solid Films 351 (1999) 37±41

Fig. 5. Electron and ion ¯uxes to the surrounding materials. External conditions are the same as in Fig. 2.

Fig. 3. Comparison of the two-dimensional distributions of the electron density: (A) and (B) are the results under the conditions of A and B. Other external conditions are the same as in Fig. 2.

number of electrons in front of the glass substrate is smaller than that in case A. This is the result of suppression of electrons toward the glass substrate in case B having a wide and strong anode sheath as compared with that in case A. The maximum electron density in case B is larger than that in case A because the potential difference between the bulk plasma and the cathode in case B is larger than that in case A due to the change of the plasma potential. Almost

Fig. 4. Comparison of the potential distributions in front of the substrate: (A) and (B) are results under the conditions of A and B. Other external conditions are the same as in Fig. 2.

all electrons and ions which ¯ow to the surrounding materials contribute to the total current in case B and the total dissipated power is larger than that of A (see Table 1). Fig. 4A,B show the 2D potential in front of the substrate in case of A and B. A strong potential gradient is locally formed in front of the central part of the glass substrate in case A. This shows that a large number of electrons have been absorbed onto the insulating glass substrate until the discharge becomes a steady state. This potential gradient suppresses the absorption of the excess electrons to the substrate. In fact, the electrons migrate toward the glass substrate without spatial trapping by the magnetic ®eld because the magnetic force lines are almost perpendicular to the glass substrate in the vicinity of the central axis. In case B, the strong local potential gradient is not formed in front of the surrounding conductive substrate, whose potential is equal to the anode. A weak and almost uniform ®eld is created close to the substrate. The electron ¯ux to the conductive and non-conductive substrates is shown in Fig. 5. In case A, while the small degree of the electron ¯ux is controlled by the ambipolar diffusion to the insulating substrate, most electrons ¯ows to the anode (b±c region) in order to sustain the discharge. In case B, the electron is absorbed into the large-size anode consisting of the side anode and conductive substrate. The electron current density incident on the side anode, however, is much less that that in case A because the total current is controlled by the size and con®guration of the cathode under the constant applied voltage. At the central part of the conductive substrate, electrons migrate directly along the magnetic ®eld toward the substrate. The other electrons, controlled by the weak magnetic ®eld (,10 G) almost parallel to the substrate, ¯ow weakly to the conductive plane. At the anode (b±c region), a large number of electrons are absorbed because of a very weak magnetic ®eld. The ion ¯ux to the glass substrate is also shown in Fig. 5. In case A, a large number of ions are accelerated by the strong potential gradient in front of the central part of the non-conductive substrate (see Fig. 4A). These ions have a high energy (,100 eV) due to the strong potential gradient.

E. Shidoji et al. / Thin Solid Films 351 (1999) 37±41

This suggests that the impact of these high energy ions causes ion bombardment of the ®lm and damage the ®lm's micro structure. As a result, the ®lm's property changes with the ®lm's position. At the anode (b±c region) the ion ¯ux in case A is small as compared with that in case B because of the low potential difference between the bulk plasma region and the anode surface. The ion ¯ux in case B is larger than that in the case A except at the center of the substrate because of higher plasma potential. The ion's energy is low, see Fig. 4B. At the beginning of the ®lm deposition, high energy ions are injected to the central part of the glass substrate as in case A. Although high energy ions are not injected into the ®lm after the formation of conductive ®lm, the total ®lm property will be affected by the high energy ion injection at the beginning of the deposition. This, therefore, implies that the property of the ®lm at the central part of the substrate differs from that at the other position. 4. Conclusions We performed a two-dimensional self-consistent simulation of the d.c. magnetron discharge. The effect of ®lm conductivity to the magnetron discharge was investigated. In the case of conductive ®lm, the plasma potential becomes high so as to suppress the excess electron current to the large-sized anode. On the other hand, in the case of nonconductive ®lm, the plasma potential become low, dragging the electrons to the small-sized anode. The change of the plasma potential causes a change in plasma density and total current under a constantly applied voltage mode due to the change of potential difference between the cathode and the bulk plasma. We con®rm that plasma potential and plasma

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density change in relation to ®lm conductivity or anode size. This suggests that the ®lm property at the central part of the non-conductive substrate will differ from that at the other position due to the high energy ion impact on the surface. Acknowledgements This work is partly supported by a Grant from the Asahi Glass Foundation. References [1] L. Gu, M.A. Lieberman, J. Vac. Sci. Technol. A 6 (1988) 2960. [2] A.E. Wendt, M.A. Lieberman, H. Meuth, J. Vac. Sci. Technol A 6 (1988) 1827. [3] A.E. Wendt, M.A. Lieberman, J. Vac. Sci. Technol A 8 (1990) 902. [4] S. Miyake, N. Shimura, T. Makabe, A. Itoh, J. Vac. Sci. Technol A 10 (1992) 1135. [5] A. Itoh, N. Makabe, S. Shimura, IEEE Trans, Plasma Sci. 24 (1996) 109. [6] T.E. Sheridan, M.J. Goeckner, J. Goree, J. Vac. Sci. Technol. A 8 (1990) 30. [7] M.J. Goeckner, J. Goree, T.E. Sheridan, IEEE Trans, Plasma. Sci. 19 (1991) 301. [8] K. Nanbu, I. Warabioka, Prog.: Astronautics & Aeronautics 160 (1994) 428. [9] E. Shidoji, M. Nemoto, T. Nomura, Y. Yoshikawa, Jpn. J. Appl. Phys. 33 (1994) 4281. [10] K. Nanbu, S. Segawa, S. Kondo, Vacuum 47 (1996) 1013. [11] E. Shidoji, H. Ohtake, N. Nanano, T. Makabe, Jpn. J. Appl. Phys 38 (1999) in press. [12] S. Zheng, G. Sun, P. Wang, X. Liao, Rev. Sci. Inst. 65 (1994) 1331. [13] J.R. Doyle, A. Nuruddin, J.R. Abelson, J. Vac. Sci. Technol. A 12 (1994) 886. [14] A. Belkind, F. Jansen, Surf. Coat. Technol. 99 (1998) 52.