Effects of strong magnetic field on plasma immersion ion implantation of dielectric substrates

Vacuum 83 (2009) 1427–1430

Contents lists available at ScienceDirect

Vacuum journal homepage: www.elsevier.com/locate/vacuum

Effects of strong magnetic field on plasma immersion ion implantation of dielectric substrates Hamid Ghomi*, Mohammadreza Ghasemkhani Laser and Plasma Research Institute, Shahid Beheshti University, Evin 1983963113, Tehran, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 September 2008 Received in revised form 23 April 2009 Accepted 26 April 2009

In this paper the effects of a strong magnetic field on plasma immersion ion implantation (PHI) of dielectric substrates were investigated. A plasma fluid model and finite difference schemes were used to simulate a one-dimensional system of plasma immersion ion implantation. The effect of secondary electron emission from the electrode on PHI was also taken into consideration. It was found that the magnitude and direction of the magnetic field have slight effects on sheath thickness but have considerable effects on current densities in the y and z directions which are perpendicular to the direction of the electric field (the x direction). The simulations showed that the current densities in the y and z directions increased significantly with increasing magnitude of the magnetic field at a given fixed angle, the reason being attributed to the rotational force exerted on the ions by the magnetic field. With a fixed magnetic field, increasing the angle of the magnetic field, q, with respect to the electric field produced a continuous increase in current density in the y direction from zero to its maximum at q ¼ 90 but the current density in the z direction could be described as saddle-shaped being zero at both ends. Crown Copyright Ó 2009 Published by Elsevier Ltd. All rights reserved.

Keywords: Plasma immersion ion implantation Plasma fluid model Sheath Current density Ion dose

1. Introduction Plasma immersion ion implantation (PIII) is an established and cost-effective method that has been found to have important effects on the surface-related properties of materials [1–3]. These effects have made possible several areas of applications to both researchers and industry such as in microelectronics and semiconductor industry, metallurgical processes and recently surface treatment of insulating materials [4–7]. PHI creates a thin surface layer of modified material, resulting in increased hardness, fatigue life, and corrosion resistance; reduced wear and sliding friction and modified electrical and optical properties [2,4]. In PHI the target is immersed in weakly ionized plasma and biased repetitively to a negative high voltage. When the voltage pulse is applied, almost instantaneously (on a time scale of upe) electrons are repelled to uncover a region of uniform ion density called the ‘‘matrix sheath’’, while ions respond much slower (on a time scale of upi) [3]. When a high voltage pulse is applied to the electrode a strong electric field directs ions onto the target surface with enough energy to penetrate the atomic structure of the target and come to rest many atomic layers below the surface. In order to maintain the ion flux, the sheath edge propagates into plasma at about ion acoustic speed to uncover more ions until the end of the voltage pulse [1,8]. Since * Corresponding author. Tel.: þ98 21 2243 1776; fax: þ98 21 2243 1775. E-mail address: [email protected] (H. Ghomi).

the main ion acceleration is concentrated in plasma sheath, understanding the sheath structure can help to better understanding of ion properties in sheath reign and thereby to better understanding of PIII operation itself. Currently a good understanding of the basic PIII mechanism exists both experimentally and theoretically and many aspects of it have been investigated [2]. Plasma fluid model and particle-in-cell (PIC) simulations usually are used to numerically evaluate various features of PIII [8–12]. Introducing a magnetic field in a PIII system affects charged particles motion and will make PHI operation more complex. Until recently little research has been reported concerning the influence of an external magnetic field on PIII dynamics. Keidar and coworkers [13] performed an experiment to investigate how the sheath thickness in PIII alters in the presence of a transverse magnetic field. They found that the steady-state sheath thickness increases with increasing the magnetic field strength. Secondary electron emission (SEE) has always been a matter of issue in the PIII process and its effect should be included in calculations when the SEE coefficient is large [13–15]. Tan and coworkers [16,17] have exploited a transverse magnetic field to suppress secondary electrons and the associated generation of X-rays. Although strong magnetic fields are rarely feasible in laboratory experiments, their approximate effect on PHI can easily be estimated by numerical computations. Davoudabadi and Mashayek [18] have investigated the effect of strong magnetic field on the sheath and found that the presence of magnetic field induces fluctuations in ion density.

0042-207X/$ – see front matter Crown Copyright Ó 2009 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2009.04.073

1428

H. Ghomi, M. Ghasemkhani / Vacuum 83 (2009) 1427–1430

In the present work, using plasma fluid equations in one dimension and finite difference methods, we focus simultaneously on effects of secondary electron emission of a dielectric layer on the cathode and a strong uniform DC magnetic field on PIII parameters. The calculations have shown that sheath thickness slightly decreases with increasing magnetic field while current densities in the y and z directions can increase considerably. 2. Model description We assume a low-pressure collisionless plasma with density n0 in which an oblique uniform magnetic field is placed in the x–z plane and makes an angle 6 with the negative x direction. The metal electrode is covered by a dielectric layer and connected to a pulsed high voltage system Fig. 1. The magnetic force exerted on charged particles in the systems considered here is considerably weaker than the electric force since in PHI the strength of electric field is very intense and even a relatively large magnetic field cannot distort the distribution of electrons very much. So, we suppose that the fast motion of electrons in the fluid regime can be averaged to lead to the Boltzman distribution. Also, on account of the relative magnitude of the negative high voltage we can neglect the thermal motion of ions. Thus, the one-dimensional plasma fluid equations with convenient normalization of parameters are:

v2 4 ¼ ðni  ne Þ ðPoisson0 s equationÞ vx2

(1)

ne ¼ expð4Þ ðBoltzman equationÞ

(2)

vux vux þ ux ¼ vt vx

 

 v4 þ uy a sin q vx

(3)

 ðequation of motion of ions in x directionÞ   vuy vux þ ux ¼  ux a sin q þ uy a sin q vt vx  ðequation of motion of ions in y directionÞ

Fig. 1. Configuration of magnetic field in a PIII system.

ð4Þ

vuz vuz þ ux ¼ uy a cos q vt vx  ðequation of motion of ions in z directionÞ

(5)

vni vðni ui Þ ¼ 0 ðequation of continuity for ionsÞ þ vx vt

(6)

where ux, uy, uz are the ion drift velocities in thepx,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y, z directions kTe =mi Þ, x is the respectively normalized to Bohm velocity ðuB ¼ distance frompffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the dielectric surface normalized to Debye ffi length ðlD ¼ 30 kTe =e2 n0 Þ, ni(x, t) and ne(x, t) are the ion and electron densities normalized to uniform density n0, t is time , and upe are the ion and electron plasma normalized to u1 pi , u ppiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi frequencies ðupi ¼ e2 n0 =30 mi Þ; 4ðx; tÞ is thepelectric ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi potential inside the sheath normalized to ðkTe =eÞ; a ¼ B0 30 =mi n0 ; mi is the ion mass and 30 is the permittivity of free space. Finite difference schemes were used in order to solve equations (1)–(6). We used Taylor’s expansion in order to linearize the Poisson’s equation [9,19].

e4 ¼ ej eð4jÞ yej ð1 þ 4  jÞ:

(7)

Substituting this transform into Eq. (1) we have

  v2 4  ej 4 ¼  ni  ej þ jej ; 2 vx

(8)

where j is the potential of the preceding time and 4 is the potential of present time. Given an initial value of j, we obtain the new value 4 from the solution of two-point boundary value problem of Eq. (8). Then taking 4 as a new initial value for the next step, we solve Poisson’s equation again. This process is iterated until it converges. In order to solve equations above they should be subjected to appropriate initial and boundary conditions. Before the inception of the voltage pulse we suppose that we have uniform quasi-neutral plasma with motionless ions. We also assume that in the plasmasheath boundary we have quasi-neutrality condition i.e. the potential drops down to zero and ions enter into the plasma with the Bohm velocity. During the voltage on time, because of implanted positive ions, the dielectric surface charges up and its potential varies in time. Furthermore, dielectric substrate itself will cause a reduction in the applied voltage on the dielectric surface. Thus, for boundary conditions we can write ð4ðxjsh ; tÞ ¼ 0; ux ðxjsh ; tÞ ¼ 4ð0; tÞ ¼ 4s ðtÞÞ. Where, 4s(t) is the instantaneous surface potential and should somehow be determined. Using Gauss’ law, Emmert derived a relation for the voltage at the dielectric–plasma interface in terms of instantaneous sheath

Fig. 2. Sheath variation versus time in different magnetic fields at q ¼ 30 .

H. Ghomi, M. Ghasemkhani / Vacuum 83 (2009) 1427–1430

thickness and applied voltage 40 [20]. Thomas Oates and coworkers modified this equation and embedded the secondary electron emission coefficient in Emmert’s equation [21]. According to them, the surface potential at the dielectric–plasma interface can be obtained through the equation below [21]

4s ðtÞ ¼

40  ½ð1 þ gÞqdn0 ðsðtÞ  s0 Þ=30 k ; 1 þ ½4d=3sðtÞk

(9)

1429

where q is the elementary charge, n0 is the ion density in the plasma ahead of the sheath, d is the dielectric thickness, k is the ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 230 40 =en0 is the ion matrix sheath dielectric constant, s0 ¼ thickness [3], s(t) is the instantaneous sheath thickness at time t and g is the secondary electron emission coefficient. However, g is not a constant and depends on the surface potential. In general, the variation of g with ion energy for various materials can be expressed approximately by [22]

g ¼ g0

sffiffiffiffiffiffiffiffiffiffiffi 4s ðtÞ

40

(10)

where g0 is the SEE coefficient at the target bias 40. Thus, Eqs. (l)–(6) in company with Eq. (9) provide a set of self-consistent equations that predicts the behavior of plasma sheath and other PHI parameters in the presence of a magnetic field. Equation (9) can be solved to get the boundary condition on the dielectric surface. Applying this boundary condition to Eqs. (l)–(6) we can develop other parameters in space and time using finite difference schemes. For simplicity, the target bias was switched to 40 ¼ 30 KV with zero rise and fall time. We applied a normalized grid spacing of Dx ¼ 2, and a normalized time step of Dt ¼ 0.004 to solve the equations. The simulation was run to a final normalized time of t ¼ 78 (s ¼ 10 ms) which is a usual time in PIII processing. Nitrogen is widely used in microelectronics industry, so it was chosen as a working gas (most of ions are N2). Other parameters are kTe ¼ 1 eV, ion density n0 ¼ 109 cm3, emission coefficient of secondary electron (40 ¼ 30 kV) g0 ¼ 18.5 and relative permittivity of dielectric k ¼ 8.8. 3. Numerical results and discussion The effects of the magnitude and direction of a uniform DC magnetic field on PIII operation were studied. In all of the calculations the dielectric thickness was taken as d ¼ l mm and to highlight the effect of secondary electrons, simulations were run considering SEE. Fig. 2 shows effect of the strength of the magnetic field on sheath thickness. It shows that even at high magnetic fields, the sheath thickness decreases by less than 5% as would be expected from the dominant effect of the electric field. Fig. 3 depicts normalized current densities ðJ ¼ j=ðen0 u0 Þ; pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi where u0 ¼ 2e40 =M Þ is the characteristic ion velocity [8] versus normalized time (t ¼ t/u1 pi ) in x, y and z directions. Fig. 3 shows for q ¼ 30 that the current density in the x direction nearly remains unchanged with variation of the magnetic field, but current

Fig. 3. Effects of the magnitude of the magnetic field on current densities at q ¼ 30 . (a) x direction (current density in this direction only changes slightly by changing the magnitude of the magnetic field and thus one representative curve has been drawn for this), (b) y direction, (c) z direction.

Fig. 4. Magnetic field effects on implanted dose in the x direction at q ¼ 30 .

1430

H. Ghomi, M. Ghasemkhani / Vacuum 83 (2009) 1427–1430

This could be attributed to a reduction of ion current component in the x direction by the deflation caused by the applied magnetic field. Fig. 5 shows the variation of normalized current densities versus normalized time at constant magnetic field B ¼ 0.5 T for varying angle of incidence, 0. In the y direction (Fig. 5a), three values of angle q ¼ 10 , 45 and 90 are shown but the simulation showed that the current density continuously increases from zero at q ¼ 0 to its maximum value at q ¼ 90 . In the z direction (Fig. 5b) the current density plots have a saddle shape that is zero at both ends. At the commencement of the voltage pulse, J(z) has a maximum at q ¼ 45 , the peak shifting towards larger angles with increasing time and reaching about q ¼ 55 at the end of pulse. The behavior of the current density J(z) with time may be sharply contrasted with that of J(y) which decreases to small values after having reached a maximum value quite early on during the pulse. 4. Conclusion

Fig. 5. Effects of the incident angle on current densities at B ¼ 0.5 T: (a) y direction (b) z direction.

The application of a magnetic field at various (non-zero) angles of incidence to the electric field in a PIII system produces current density components in perpendicular directions to the electric field direction. With increasing strength of the magnetic field, current densities in these directions have been shown to increase but the current density in the direction of the electric field and also the sheath length remain approximately unchanged. Current densities in y and z directions are significantly affected by the direction of the magnetic field. With increasing angle of magnetic field, the current density in the y direction continuously increases but in the z direction it can be described in a three-dimensional plot of current density against time and incidence angle as saddleshaped. References

densities in y and z directions continuously increase with increasing magnetic field. The effects may be attributed to rotational forces acting on the ions under the combined influence of electric and magnetic field components. Results are presented for B ¼ 0.3, 1, 2 T in y and z directions, where as shown in Fig. 1 the main component of the magnetic force coincides with the y direction and for this reason the current density in the y direction is substantially larger than that in the z direction and even with the highest magnetic fields (2 T), its magnitude is comparable with the current density in the x direction. The graphs show that current densities initially have a very sharp slope reaching a maximum value and then decrease comparatively slowly. After a period of time (at about tnormalized ¼ 40) the current densities reach an approximately constant value maintained until the end of the applied pulse. A discontinuity is observed at approximately tnormalized ¼ 5, particularly obvious in the z direction. The implanted dose (Dose ¼ q1c0(40  4s(t)), where q is the elementary charge and c0 ¼ 30 k=d is the capacitance per unit area of the dielectric layer [23]) on the dielectric surface can be one of the important parameters in PIII. Fig. 4 suggests that with increasing the strength of the magnetic field, the implanted dose on the dielectric surface slightly decreases.

[1] Conard JR, Radtke JL, Dodd RA, Worzala FJ, Tran NC. J Appl Phys 1987;62:4591. [2] Andres A. Handbook of plasma immersion ion implantation and deposition. New York: Wiley; 2000. [3] Liberman MA, Lichtenberg AJ. Principles of plasma discharge and materials processing. New York: Wiley; 2005. [4] Kowk DTK. IEEE Trans Plasma Sci 2006;34:1059. [5] Chu PK, Chan C. Surf Coat Technol 2001;136:151. [6] Roth JR. Industrial plasma engineering, vol. 2. Philadelphia: IOP; 1995. [7] Lacoste A, Coeur FL, Arnal Y, Pelletier J, Grattepain C. Surf Coat Technol 2001;135:268. [8] Lieberman MA. J Appl Phys 1989;66:2926. [9] Emmert GA, Henry MA. J Appl Phys 1992;71:113. [10] Hong MP, Emmert GA. J Appl Phys 1995;78:6967. [11] Paulus M, Stals L, Rude U, Rauschenbach B. J Appl Phys 1999;85:761. [12] Briehl B, Urbassek HM. Surf Coat Technol 2002;156:131. [13] Keidar M, Monteiro OR, Anders A, Boyd ID. Appl Phys Lett 2002;81:1183. [14] George MJ, Fetherston RP, Hitchon WN, Horswill NC, Keiter ER, Shamim MM, et al. Phys Rev E 1995;51:3760. [15] Kwok D, Pu S, Fu R, Jin F, Chu PK. Appl Phys Lett 2007;90:131503. [16] Ueda M, Tan IH, Dallaqua RS, Rossi JO. Surf Coat Technol 2007;201:6597. [17] Tan IH, Ueda M, Dallaqua R, Oliveria R, Rossi JO. J Appl Phys 2006;100:033303. [18] Davoudabadi M, Mashayek F. Phys Plamas 2005;12:73505. [19] Gong Y, Wang X, Duan P, Yu J, Wang D. Phys Plasmas 2005;12:43501. [20] Emmert GA. J Vac Sci Technol B 1994;12(2):880. [21] Oates TWH, Pigott J, McKenzie DR, Bilek MMM. IEEE Trans Plasma Sci 2003;31:438. [22] Shamim MM, Scheuer JT, Fetherston RP, Conard RJ. J Appl Phys 1991;70:4756. [23] Li XC, Wang YN. Thin Solid Films 2006;506:307.