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Considerations on the determining factors of the angular distribution of emitted particles in laser ablation
Applied Surface Science 256 (2010) 4959–4965
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Considerations on the determining factors of the angular distribution of emitted particles in laser ablation I. Konomi a,b,∗ , T. Motohiro a,b , T. Kobayashi b , T. Asaoka b a b
Toyota Technological Institute, 2-12-1 Hisakata, Tempaku-ku, Nagoya 468-8511, Japan Toyota Central Research and Development Laboratories, Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan
a r t i c l e
i n f o
Article history: Received 15 January 2010 Accepted 3 March 2010 Available online 9 March 2010 Keywords: Angular distribution Pulsed laser deposition Direct Simulation Monte Carlo Sublimation energy
a b s t r a c t Simulations of particles which are emitted in laser ablation have been performed by the method of Direct Simulation Monte Carlo to investigate the deposition profiles of the emitted particles. The influences of the temperature, pressure and stream velocity of the initial evaporated layer formed during laser ablation process on the profile of the deposited film have been examined. It is found that the temperature gives a minor influence on the deposition profile, whereas the stream velocity and the pressure of the initial evaporated layer have a greater impact on the deposition profile. The energy in the direction of surface normal (E⊥ ) and that in the parallel direction of the surface (E|| ) are shown to increase and decrease, respectively after the laser irradiation due to collisions between the emitted particles, and this trend is magnified as the pressure increases. As a consequence, the stream velocity in the direction of surface normal increases with the increase in the pressure. A mechanism of the phenomenon that a metal with a lower sublimation energy shows a broader angular distribution of emitted particles is presented. It is suggested that low density of evaporated layer of a metal with a low sublimation energy at its melting point decreases the number of collisions in the layer, leading to the low stream velocity in the direction of surface normal, which results in the broader deposition profile of the emitted particles. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Pulsed laser deposition (PLD) has been in widespread use for the research and development of thin films in search for novel materials [1,2]. This technique has several superior features as follows: (1) stoichiometric metallic alloy or oxide films can be obtained with relative ease, (2) film thickness can be controlled by the number of laser shots, (3) it is possible to obtain metastable materials that cannot be synthesized in bulk. Utilizing above advantages, it has been extensively applied for the formation of multicomponent magnetic films [3], metallic multilayers for X-ray mirrors [4] and metastable metallic alloys [5]. Recently, the application of the technique has extended into the field of electrochemical devices such as secondary batteries especially all-solid-state lithium-ion batteries [6]. An all-solid-battery consists of two electrodes (a cathode and an anode) separated by a solid electrolyte. Various metals or alloys for superior anode materials are under investigation in terms of the low redox potential and high capacity.
∗ Corresponding author at: Battery & Cells Div., Toyota Central Research and Development Laboratories, Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan. Tel.: +81 561 71 7875; fax: +81 561 63 4103. E-mail address: [email protected] (I. Konomi). 0169-4332/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2010.03.009
In order to obtain metallic or alloy films in the aforementioned areas, it is important to know the angular distribution of laserablated particles because possible different angular distributions of different kinds of metals may deteriorate the compositional uniformity of the film. In our previous work, we have presented a systematic study on the angular distribution of different kinds of metals [7] employing an ultraviolet laser (wavelength = 266 nm) and near-threshold laser fluence (2.3 J/cm2 ) which is often used in the deposition of cathodes and solid electrolytes in electrochemical applications like lithiumion batteries. It was found that the exponent n which characterized the angular distribution by a cosn function showed very broad range of values between 3 and 24 depending on the kind of metals. And it was also demonstrated that a simple relation that the exponent n is proportional to the square root of particle atomic weight as reported previously by other study [8] has not been observed. Instead, as Fig. 1 shows [7], a general trend has been found that the metals with higher sublimation energy show larger exponent n values (narrower angular distributions) than those with lower sublimation energy. It is of great interest from both scientific and practical viewpoint of PLD to understand what determines the angular distribution of emitted atoms because it differs considerably depending on the sublimation energy of metals as mentioned above.
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Fig. 1. Relation between the fitted exponent n and sublimation energy of target metals [7]. Fig. 2. Schematic diagram of the coordinate system and simplified cell partition for DSMC simulation.
So far, in order to understand the laser ablation phenomenon, an adiabatic expansion model by Anisimov et al. [9] and Singh and Narayan [10], which applied gas dynamics to laser ablation, has been presented. The model indicated that the angular distribution of ablated particles depends on the lateral dimension and the temperature of an initial evaporated layer and the atomic weight of particles ejected. However, it cannot explain the dependence of the angular distribution on the sublimation energy of the target substance described above because the model does not contain the physical properties of the target material. In general, in laser ablation, laser energy is absorbed in the near-surface region of a target and it is promptly converted to lattice vibration, resulting in a high-temperature surface layer. The heated and melted surface produces a thin evaporated layer immediately above the surface. The initial evaporated layer is expected to expand in which particles make a number of collisions and scatterings with each other [11]. So far, based on the mechanism stated above, desorption of molecules by laser irradiation was analyzed by the method of Direct Simulation Monte Carlo (DSMC) [12]. NoorBatcha et al. [13] and Sibold and Urbassek [14,15] applied this approach to laser desorption of molecular atoms adsorbed on a solid surface. In their simulations, the angular distribution of desorbed atoms becomes narrow as a result of collisions of atoms during the evaporation. However, the influence of the properties of initial evaporated layer such as temperature and pressure on the angular distribution of the emitted particles has not been clarified. Furthermore, although they assumed the molecules to be desorbed with the Maxwell–Boltzmann velocity distribution the initial evaporated layer is expected to have a velocity perpendicular to the surface (stream velocity) in laser ablation [11]. In this work, the DSMC mentioned above has been applied to observe time evolution of the position and motion of particles in the initial evaporated layer. Our aim is to understand what determines the width of angular distribution of emitted particles by investigating the influence of the temperature, the stream velocity and the pressure of the initial evaporated layer on the profiles of deposited films. Finally, considerations are presented which can describe the dependence of angular distribution of emitted particles on sublimation energy of target materials.
equation by Nanbu [16]. In this study, we have modified the simulation code developed by Nanbu [16–18] to be applicable to laser ablation phenomena. The simulation procedure is outlined briefly as follows. First, a group of particles (which corresponds with “initial evaporated layer” afterward), which is emitted by laser irradiation from an area of a target, is assumed to be formed directly on the target. The particles make collisions in the evaporated layer and move away from the surface of the target and finally are supposed to deposit at a position where a substrate is placed: the collision process and motions of particles are calculated at every time interval. Fig. 2 shows the schematic diagram of the coordinate system and simplified cell partition used in the DSMC procedure and Fig. 3 shows the schematic flow chart of the DSMC. As shown in Fig. 2, the space in which the particles travel and make collisions ranges between x = 0 and x = a (a = 15.04) in the x-axis and between y = −b
2. Simulation procedure The simulations have been performed according to the procedure of DSMC developed by Bird [12]. This method has been developed originally to solve the motion of rarefied gas numerically and has been proved to be a numerical analysis of the Boltzmann
Fig. 3. Schematic flow chart of the Direct Simulation Monte Carlo method.
I. Konomi et al. / Applied Surface Science 256 (2010) 4959–4965
and y = b (b = 15) in the y-axis and it is divided by the coordinate xi = i(i + 41)/6800, yi = 0.1i. The area is composed of 90,000 cells as shown schematically in Fig. 2. The size of each cell is determined from xi = (i + 20)/3400 and yi = 0.1 (i = 1–300). The diameter of the initial evaporated layer was assumed to be 2 mm. Firstly, the particles which are supposed to evaporate from a laser-irradiated area are placed in the first cell (x1 , y150 ) and (x1 , y151 ) which is shown in the shaded area in Fig. 2. The initial position and velocity of each particle are determined by random numbers. The velocity of each particle is supposed to have the Maxwell–Boltzmann distribution which has a stream velocity us toward the target surface normal direction. The velocity distribution function is shown below: f (vx , vy , vz ) =
1 (2RT0 )3/2
exp
−
(vx − us )2 + v2y + v2z
2RT0
where R = k/m, k is the Boltzmann constant, m is the particle mass, T0 is the temperature, vx , vy , and vz are the velocities in the directions of x, y and z, respectively. The reason why us is introduced is that there is a possibility that particles are emitted to the direction of surface normal like an explosion when sub-surface temperature is very high [19–21] or adiabatic expansion in the first dense evaporated layer may occur mainly to the direction of surface normal [11].
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The number of particles flowing in the area is calculated as follows:
Fin = 2hn ∗
RT K(u∗)t 2
where 2h is the length in the y-direction of the first cell, n* is the √ number density of particles, K(u*) = exp(−u*2) + u*(1 + erf(u*)), u* is the stream velocity relative to the velocity of sound [17,18]. Next, each particle is moved according to its velocity during the time interval (t) which is considerably lower than the mean free time: time in which a particle travels a mean free path. A fraction of particles are scattered with other particles; average number of collisions which take place in a cell in t is calculated by the maximum collision method described in detail in Refs. [17,18]. The particles were assumed to make a hard-sphere collision. The velocity of each particle after a collision is calculated based on the law of momentum conservation [22]. The time interval t of the calculation was set to be 20% of the mean free time. When the particle reaches the position of x = a, the particle is supposed to deposit there. The simulation is continued to the time when all the particles leave the simulated space or deposit on the deposition place, and finally the profile of deposited particles is obtained.
Fig. 4. Contour plot of time evolution of the density of an evaporated layer: t = (a) ; (b) 2; (c) 8; (d) 16.
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3. Results and discussion 3.1. Time evolution of the density of emitted particles Fig. 4(a)–(d) shows contour plots that illustrate time evolutions of the particle density of an initial evaporated layer. The particles are introduced from x = 0 during time corresponding to laser irradiation time. Fig. 4(a) corresponds with the density of the evaporated layer just after the laser irradiation. In each contour plot in Fig. 4, the density is depicted in different gray scales. Note that the value of maximum density (the central part) decreases rapidly with increasing time: the maximum density at t = is between 0.34 and 0.4, while the one at t = 16 is much lower between 0.0086 and 0.01. It can be seen that the particles proceed almost only in the direction of the x-axis after time 2, but, as time advances the particles expand not only in the direction of the x-axis but also in the yaxis. The particle density becomes elliptic after 16 passes. When particles arrives at the plane of x = a, it is supposed to deposit on the site with the probability of unity. If simulations are performed for a sufficient number of particles statistically, a profile of the deposited particle can be obtained. The profile of deposited particles is supposed to vary depending on the initial conditions of the initial evaporated layer. The dependences of the profiles on some of the initial conditions in the evaporated layer are calculated and are shown in the following sections. 3.2. Dependence of the deposition profile on properties of initial evaporated layer 3.2.1. Dependence on the temperature Fig. 5(a)–(c) shows the profiles of deposited particles on the plane of x = a. In Fig. 5(a)–(c), the initial temperatures were assumed to be 2000, 6000 and 12,000 K, respectively. The pressure and the stream velocity of the evaporated layer were assumed to be 10,000 Pa and 0, respectively in all cases. Diamonds and solid line designate a simulated profile and a curve obtained by fitting the simulated data with a cosn function, respectively. The n in the figure indicates the exponent n of a cosn function. It can be seen that the exponent n decreases slightly from 4 to 3.4 when the temperature increases from 2000 to 6000 K. However, the n remains the same value when increasing temperature even more to 12,000 K. 3.2.2. Dependence on the pressure Fig. 6(a)–(c) shows the deposition density profiles of emitted particles on the plane of x = a. In Fig. 6(a)–(c), the initial pressures were assumed to be 10,000, 30,000 and 60,000 Pa, respectively. The temperature and the stream velocity of the layer were assumed to be 2000 K and 0, respectively in all cases. As shown in Fig. 6, as the pressure in the layer increases from 10,000 to 60,000 Pa, the exponent n increases from 4 to 6.4. It is found that the pressure in the initial evaporated layer gives a significant influence on the deposition profile of the emitted particles. 3.2.3. Dependence on the stream velocity to the direction of surface normal direction Fig. 7(a)–(c) shows the deposition density profiles of emitted particles on the plane of x = a. In Fig. 7(a)–(c), the initial stream velocities us were assumed to be 0, 1 and 2 (the velocity is the relative value to the velocity of sound), respectively. The temperature and the pressure of the initial evaporated layer were assumed to 2000 K and 10,000 Pa, respectively in all cases. From the value of n = 4 at us = 0, the exponent n increases with the increase in us , reaching much higher value of 13 when us becomes 2. It demon-
Fig. 5. Deposition density profiles of emitted particles at the position of x = a: (a) 2000 K; (b) 6000 K; (c) 12,000 K (pressure = 10,000 Pa, us = 0).
strates clearly that the increase in the stream velocity us causes n to increase drastically. From these results described above, it is considered that the deposition density profile is not greatly affected by the temperature in the initial evaporated layer even though the temperature is assumed to increase to the value of 12,000 K which seems high enough in comparison with the melting points of any metals. The reason for this is speculated that even though the temperature increases, it only causes the velocity of particles to increase isotropically, which lead to a minor influence on the deposition density profile. On the other hand, as Fig. 7 shows, the stream velocity of
I. Konomi et al. / Applied Surface Science 256 (2010) 4959–4965
Fig. 6. Deposition density profiles of emitted particles at the position of x = a: (a) 10,000 Pa; (b) 30,000 Pa; (c) 60,000 Pa (temperature = 2000 K, us = 0).
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Fig. 7. Deposition density profiles of emitted particles at the position of x = a: (a) us = 1; (b) us = 2; (c) us = 3 (temperature = 2000 K, pressure = 10,000 Pa).
3.3. Energy (velocity) change as a function of pressure of initial evaporated layer the initial evaporated layer to the x-axis has a great impact on the width of deposition density profile. It means that a kind of unidirectional velocity to the direction of surface normal is required for the density profile to become narrow. Regarding the influence of the pressure in the initial evaporated layer, discussion will be made in the next section.
In order to understand why the increase in the pressure of the initial evaporated layer causes the exponent n to increase, we have calculated the total kinetic energy (Etotal ), the kinetic energy in the direction of x-axis (E⊥ ) and the kinetic energy in the direction of y-axis (E|| ) of all emitted particles as a function of time. Fig. 8(a)–(c)
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in the number of collisions in the evaporated layer. These results indicate that as the number of collisions increases, the E⊥ increases and E|| decreases more rapidly and focusing of the energy flow to the direction of surface normal occurs. Consequently, the velocity in the direction of surface normal (v⊥ ) increases and the velocity in the parallel direction of the surface (v|| ) decreases as the pressure increases. In other words, the stream velocity toward the x-axis increases with the increase in the pressure of the evaporated layer. The kinetic reason for this behavior is described in Refs. [13–15,23]: after a collision, the direction of the faster particle will be closer to that of the center of mass of the group of the particles, which is on the average the surface normal direction. The increase in the stream velocity leads to the narrower deposition density profile as shown in Fig. 7. This explains why the deposition density profile becomes narrower at higher pressure of the initial evaporated layer as shown in Fig. 6. 3.4. Considerations on the relation of sublimation energy and exponent n in the angular distribution of emitted particles
Fig. 8. Dependence of the total energy (Etotal ), the energy in the direction of surface normal (E⊥ ) and the energy in the parallel direction of the surface (E|| ) of all particles as a function of time: pressure is assumed to be (a) 1000 Pa, (b) 10,000 Pa and (c) 60,000 Pa, respectively.
shows the Etotal , E⊥ and E|| at the initial pressure of (a) 1000 Pa, (b) 10,000 Pa and (c) 60,000 Pa, respectively. Naturally, all the energies increase until the end of the inflow of the particles during laser irradiation time (t = 20 ns). As can be seen from Fig. 8(a), E⊥ and E|| do not show any changes after the laser irradiation at the pressure of 1000 Pa. On the other hand, when the pressure increases to 10,000 Pa as shown in Fig. 8(b), E⊥ increases and E|| decreases after the laser irradiation; Etotal decreases slightly shortly after the laser irradiation time because some of the particles which are backscattered and reach the target as a result of collisions were eliminated in the simulation afterwards. The degrees of the increase in E⊥ and decrease in E|| are magnified with the increase in the pressure to 60,000 Pa as shown in Fig. 8(c). This effect is caused by the increase
In this section, based on the results of the simulation described above, we consider the reason for the experimental finding that the metals with higher sublimation energy show narrower angular distributions than those with lower sublimation energy as shown in Fig. 1 in the laser ablation. When laser beam is irradiated onto a target surface, laser energy is promptly converted to lattice vibration, resulting in a hightemperature surface in the near-surface region to the melting point [19,20]. Atoms in the near-surface region evaporate rapidly as temperature increases. In equilibrium state, the equilibrium vapor pressure of a metal with a lower sublimation energy shows a higher vapor pressure at the same temperature. As described in Section 3.2.2, when the vapor pressure increases, the stream velocity increases due to collisions in the layer. This indicates that a metal with a lower sublimation energy exhibits the narrower deposition profile and larger n value. However, it is contrary to the experimental results as shown in Fig. 1 [7]. In fact, the temperature should remain the melting point for some time during laser irradiation [20]. In general, a metal which has a low sublimation energy has a low melting point and tends to show very low vapor pressure at its melting point: for example, the vapor pressures of In and Sn are <10−10 Pa [24]. On the other hand, the metals with a higher sublimation energy have a large vapor pressure at its melting point: for example, the vapor pressures of Ta and Ti at their melting point are 0.78 and 0.49 Pa, respectively. Therefore, when metals which have a low sublimation energy are laser-ablated, the vapor pressure is expected to be low, thus, the number of collisions which take place should be small. As a consequence, the focusing effect of the velocity of the particles to the surface normal shown in Fig. 8 is small compared to the case in which metals with a higher sublimation energy is ablated and the number of collisions is larger. It is considered that this is the reason why the metals which have lower sublimation energy tend to show wider angular distribution, in other words, lower exponent n. 4. Conclusion We have performed the simulation of particles which are evaporated by laser irradiation by the method of DSMC. The temperature of initial evaporated layer shows a minor effect on the deposition profile of emitted particles, whereas the stream velocity which is strongly related to the pressure of initial evaporated layer has a significant influence on the deposition profile. The stream velocity increases as the increase in the pressure due to the collisions which the particles experience in the evaporated layer.
I. Konomi et al. / Applied Surface Science 256 (2010) 4959–4965
The reason for the previous experimental finding that a metal with a low sublimation energy shows a broader angular distribution can be considered as follows: low density of evaporated layer of the metal with a low sublimation energy at its melting point decreases the number of collisions in the initial evaporated layer, leading to the low stream velocity in the direction of surface normal, which finally makes the angular distribution of emitted particles broader. Acknowledgements The authors are grateful to H. Azuma, Y. Ukyo and K. Kawahara for their helpful discussion and encouragement. References [1] D.B. Chrisey, G.K. Hubler, Pulsed Laser Deposition of Thin Films, John Wiley & Sons, Inc., New York, 1994. [2] R. Eason, Pulsed Laser Deposition of Thin Films, John Wiley & Sons, Inc., New York, 2006. [3] C.J. Yang, A.W. Kim, J.S. Kang, J. Appl. Phys. 83 (1998) 6620. [4] H. Mai, W. Pompe, Appl. Surf. Sci. 54 (1992) 215. [5] H.U. Krebs, Int. J. Non-equilib. Process 10 (1997) 3.
[6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
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M. Inaba, T. Doi, Y. Iriyama, Z. Ogumi, J. Power Sources 81 (1999) 554. I. Konomi, T. Motohiro, T. Asaoka, J. Appl. Phys. 106 (2009) 013107. E. Buttini, A. Thum-Jager, K. Rohr, J. Phys. D 31 (1998) 2165. S.I. Anisimov, D. Bauerle, B.S. Luk’yanchuk, Phys. Rev. B 48 (1993) 12076. R.K. Singh, J. Narayan, Phys. Rev. B 41 (1990) 8843. J.C.S. Kools, T.S. Baller, S.T. De Zwart, J. Dieleman, J. Appl. Phys. 71 (1992) 4547. G.A. Bird, Molecular Gas Dynamics, Claredon, Oxford, 1976. I. NoorBatcha, R.R. Lucchese, Y. Zeiri, Phys. Rev. B 36 (1987) 4978. D. Sibold, H.M. Urbassek, Phys. Rev. A 43 (1991) 6722. D. Sibold, H.M. Urbassek, J. Appl. Phys. 73 (1991) 8544. K. Nanbu, J. Phys. Soc. Jpn. 49 (1980) 2042. The Japan Society of Mechanical Engineers (Ed.), Numerical Simulation Using an Atom/Molecule Model, Corona, Tokyo, 1996. (in Japanese). S. Ohmiya, M. Yasuhara, Numerical Fluid dynamics, University of Tokyo Press, 1992, pp. 287–324 (in Japanese). F.P. Gagliano, U.C. Paek, Appl. Opt. 13 (1974) 274. S. Otsubo, T. Minamikawa, Y. Yonezawa, A. Morimoto, T. Shimizu, Jpn. J. Appl. Phys. 29 (1990) L73. A. Vertes, R.W. Dreyfus, D.E. Platt, IBM J. Res. Dev. 38 (1994) 3. W.G. Vincenti, C.H. Kruger Jr., Introduction to Physical Gas Dynamics, John Wiley & Sons, 1967. J. Cowin, D. Auerbach, C. Becker, Surf. Sci. 78 (1978) 545. A. Koma, K. Yagi, M. Tsukada, M. Aono, Handbook for Engineering of Surface Property (Hyomen Bussei Kougaku Handobukku), Maruzen, Tokyo, 1987 (in Japanese).
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Considerations on the determining factors of the angular distribution of emitted particles in laser ablation I. Konomi a,b,∗ , T. Motohiro a,b , T. Kobayashi b , T. Asaoka b a b
Toyota Technological Institute, 2-12-1 Hisakata, Tempaku-ku, Nagoya 468-8511, Japan Toyota Central Research and Development Laboratories, Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan
a r t i c l e
i n f o
Article history: Received 15 January 2010 Accepted 3 March 2010 Available online 9 March 2010 Keywords: Angular distribution Pulsed laser deposition Direct Simulation Monte Carlo Sublimation energy
a b s t r a c t Simulations of particles which are emitted in laser ablation have been performed by the method of Direct Simulation Monte Carlo to investigate the deposition profiles of the emitted particles. The influences of the temperature, pressure and stream velocity of the initial evaporated layer formed during laser ablation process on the profile of the deposited film have been examined. It is found that the temperature gives a minor influence on the deposition profile, whereas the stream velocity and the pressure of the initial evaporated layer have a greater impact on the deposition profile. The energy in the direction of surface normal (E⊥ ) and that in the parallel direction of the surface (E|| ) are shown to increase and decrease, respectively after the laser irradiation due to collisions between the emitted particles, and this trend is magnified as the pressure increases. As a consequence, the stream velocity in the direction of surface normal increases with the increase in the pressure. A mechanism of the phenomenon that a metal with a lower sublimation energy shows a broader angular distribution of emitted particles is presented. It is suggested that low density of evaporated layer of a metal with a low sublimation energy at its melting point decreases the number of collisions in the layer, leading to the low stream velocity in the direction of surface normal, which results in the broader deposition profile of the emitted particles. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Pulsed laser deposition (PLD) has been in widespread use for the research and development of thin films in search for novel materials [1,2]. This technique has several superior features as follows: (1) stoichiometric metallic alloy or oxide films can be obtained with relative ease, (2) film thickness can be controlled by the number of laser shots, (3) it is possible to obtain metastable materials that cannot be synthesized in bulk. Utilizing above advantages, it has been extensively applied for the formation of multicomponent magnetic films [3], metallic multilayers for X-ray mirrors [4] and metastable metallic alloys [5]. Recently, the application of the technique has extended into the field of electrochemical devices such as secondary batteries especially all-solid-state lithium-ion batteries [6]. An all-solid-battery consists of two electrodes (a cathode and an anode) separated by a solid electrolyte. Various metals or alloys for superior anode materials are under investigation in terms of the low redox potential and high capacity.
∗ Corresponding author at: Battery & Cells Div., Toyota Central Research and Development Laboratories, Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan. Tel.: +81 561 71 7875; fax: +81 561 63 4103. E-mail address: [email protected] (I. Konomi). 0169-4332/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2010.03.009
In order to obtain metallic or alloy films in the aforementioned areas, it is important to know the angular distribution of laserablated particles because possible different angular distributions of different kinds of metals may deteriorate the compositional uniformity of the film. In our previous work, we have presented a systematic study on the angular distribution of different kinds of metals [7] employing an ultraviolet laser (wavelength = 266 nm) and near-threshold laser fluence (2.3 J/cm2 ) which is often used in the deposition of cathodes and solid electrolytes in electrochemical applications like lithiumion batteries. It was found that the exponent n which characterized the angular distribution by a cosn function showed very broad range of values between 3 and 24 depending on the kind of metals. And it was also demonstrated that a simple relation that the exponent n is proportional to the square root of particle atomic weight as reported previously by other study [8] has not been observed. Instead, as Fig. 1 shows [7], a general trend has been found that the metals with higher sublimation energy show larger exponent n values (narrower angular distributions) than those with lower sublimation energy. It is of great interest from both scientific and practical viewpoint of PLD to understand what determines the angular distribution of emitted atoms because it differs considerably depending on the sublimation energy of metals as mentioned above.
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Fig. 1. Relation between the fitted exponent n and sublimation energy of target metals [7]. Fig. 2. Schematic diagram of the coordinate system and simplified cell partition for DSMC simulation.
So far, in order to understand the laser ablation phenomenon, an adiabatic expansion model by Anisimov et al. [9] and Singh and Narayan [10], which applied gas dynamics to laser ablation, has been presented. The model indicated that the angular distribution of ablated particles depends on the lateral dimension and the temperature of an initial evaporated layer and the atomic weight of particles ejected. However, it cannot explain the dependence of the angular distribution on the sublimation energy of the target substance described above because the model does not contain the physical properties of the target material. In general, in laser ablation, laser energy is absorbed in the near-surface region of a target and it is promptly converted to lattice vibration, resulting in a high-temperature surface layer. The heated and melted surface produces a thin evaporated layer immediately above the surface. The initial evaporated layer is expected to expand in which particles make a number of collisions and scatterings with each other [11]. So far, based on the mechanism stated above, desorption of molecules by laser irradiation was analyzed by the method of Direct Simulation Monte Carlo (DSMC) [12]. NoorBatcha et al. [13] and Sibold and Urbassek [14,15] applied this approach to laser desorption of molecular atoms adsorbed on a solid surface. In their simulations, the angular distribution of desorbed atoms becomes narrow as a result of collisions of atoms during the evaporation. However, the influence of the properties of initial evaporated layer such as temperature and pressure on the angular distribution of the emitted particles has not been clarified. Furthermore, although they assumed the molecules to be desorbed with the Maxwell–Boltzmann velocity distribution the initial evaporated layer is expected to have a velocity perpendicular to the surface (stream velocity) in laser ablation [11]. In this work, the DSMC mentioned above has been applied to observe time evolution of the position and motion of particles in the initial evaporated layer. Our aim is to understand what determines the width of angular distribution of emitted particles by investigating the influence of the temperature, the stream velocity and the pressure of the initial evaporated layer on the profiles of deposited films. Finally, considerations are presented which can describe the dependence of angular distribution of emitted particles on sublimation energy of target materials.
equation by Nanbu [16]. In this study, we have modified the simulation code developed by Nanbu [16–18] to be applicable to laser ablation phenomena. The simulation procedure is outlined briefly as follows. First, a group of particles (which corresponds with “initial evaporated layer” afterward), which is emitted by laser irradiation from an area of a target, is assumed to be formed directly on the target. The particles make collisions in the evaporated layer and move away from the surface of the target and finally are supposed to deposit at a position where a substrate is placed: the collision process and motions of particles are calculated at every time interval. Fig. 2 shows the schematic diagram of the coordinate system and simplified cell partition used in the DSMC procedure and Fig. 3 shows the schematic flow chart of the DSMC. As shown in Fig. 2, the space in which the particles travel and make collisions ranges between x = 0 and x = a (a = 15.04) in the x-axis and between y = −b
2. Simulation procedure The simulations have been performed according to the procedure of DSMC developed by Bird [12]. This method has been developed originally to solve the motion of rarefied gas numerically and has been proved to be a numerical analysis of the Boltzmann
Fig. 3. Schematic flow chart of the Direct Simulation Monte Carlo method.
I. Konomi et al. / Applied Surface Science 256 (2010) 4959–4965
and y = b (b = 15) in the y-axis and it is divided by the coordinate xi = i(i + 41)/6800, yi = 0.1i. The area is composed of 90,000 cells as shown schematically in Fig. 2. The size of each cell is determined from xi = (i + 20)/3400 and yi = 0.1 (i = 1–300). The diameter of the initial evaporated layer was assumed to be 2 mm. Firstly, the particles which are supposed to evaporate from a laser-irradiated area are placed in the first cell (x1 , y150 ) and (x1 , y151 ) which is shown in the shaded area in Fig. 2. The initial position and velocity of each particle are determined by random numbers. The velocity of each particle is supposed to have the Maxwell–Boltzmann distribution which has a stream velocity us toward the target surface normal direction. The velocity distribution function is shown below: f (vx , vy , vz ) =
1 (2RT0 )3/2
exp
−
(vx − us )2 + v2y + v2z
2RT0
where R = k/m, k is the Boltzmann constant, m is the particle mass, T0 is the temperature, vx , vy , and vz are the velocities in the directions of x, y and z, respectively. The reason why us is introduced is that there is a possibility that particles are emitted to the direction of surface normal like an explosion when sub-surface temperature is very high [19–21] or adiabatic expansion in the first dense evaporated layer may occur mainly to the direction of surface normal [11].
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The number of particles flowing in the area is calculated as follows:
Fin = 2hn ∗
RT K(u∗)t 2
where 2h is the length in the y-direction of the first cell, n* is the √ number density of particles, K(u*) = exp(−u*2) + u*(1 + erf(u*)), u* is the stream velocity relative to the velocity of sound [17,18]. Next, each particle is moved according to its velocity during the time interval (t) which is considerably lower than the mean free time: time in which a particle travels a mean free path. A fraction of particles are scattered with other particles; average number of collisions which take place in a cell in t is calculated by the maximum collision method described in detail in Refs. [17,18]. The particles were assumed to make a hard-sphere collision. The velocity of each particle after a collision is calculated based on the law of momentum conservation [22]. The time interval t of the calculation was set to be 20% of the mean free time. When the particle reaches the position of x = a, the particle is supposed to deposit there. The simulation is continued to the time when all the particles leave the simulated space or deposit on the deposition place, and finally the profile of deposited particles is obtained.
Fig. 4. Contour plot of time evolution of the density of an evaporated layer: t = (a) ; (b) 2; (c) 8; (d) 16.
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3. Results and discussion 3.1. Time evolution of the density of emitted particles Fig. 4(a)–(d) shows contour plots that illustrate time evolutions of the particle density of an initial evaporated layer. The particles are introduced from x = 0 during time corresponding to laser irradiation time. Fig. 4(a) corresponds with the density of the evaporated layer just after the laser irradiation. In each contour plot in Fig. 4, the density is depicted in different gray scales. Note that the value of maximum density (the central part) decreases rapidly with increasing time: the maximum density at t = is between 0.34 and 0.4, while the one at t = 16 is much lower between 0.0086 and 0.01. It can be seen that the particles proceed almost only in the direction of the x-axis after time 2, but, as time advances the particles expand not only in the direction of the x-axis but also in the yaxis. The particle density becomes elliptic after 16 passes. When particles arrives at the plane of x = a, it is supposed to deposit on the site with the probability of unity. If simulations are performed for a sufficient number of particles statistically, a profile of the deposited particle can be obtained. The profile of deposited particles is supposed to vary depending on the initial conditions of the initial evaporated layer. The dependences of the profiles on some of the initial conditions in the evaporated layer are calculated and are shown in the following sections. 3.2. Dependence of the deposition profile on properties of initial evaporated layer 3.2.1. Dependence on the temperature Fig. 5(a)–(c) shows the profiles of deposited particles on the plane of x = a. In Fig. 5(a)–(c), the initial temperatures were assumed to be 2000, 6000 and 12,000 K, respectively. The pressure and the stream velocity of the evaporated layer were assumed to be 10,000 Pa and 0, respectively in all cases. Diamonds and solid line designate a simulated profile and a curve obtained by fitting the simulated data with a cosn function, respectively. The n in the figure indicates the exponent n of a cosn function. It can be seen that the exponent n decreases slightly from 4 to 3.4 when the temperature increases from 2000 to 6000 K. However, the n remains the same value when increasing temperature even more to 12,000 K. 3.2.2. Dependence on the pressure Fig. 6(a)–(c) shows the deposition density profiles of emitted particles on the plane of x = a. In Fig. 6(a)–(c), the initial pressures were assumed to be 10,000, 30,000 and 60,000 Pa, respectively. The temperature and the stream velocity of the layer were assumed to be 2000 K and 0, respectively in all cases. As shown in Fig. 6, as the pressure in the layer increases from 10,000 to 60,000 Pa, the exponent n increases from 4 to 6.4. It is found that the pressure in the initial evaporated layer gives a significant influence on the deposition profile of the emitted particles. 3.2.3. Dependence on the stream velocity to the direction of surface normal direction Fig. 7(a)–(c) shows the deposition density profiles of emitted particles on the plane of x = a. In Fig. 7(a)–(c), the initial stream velocities us were assumed to be 0, 1 and 2 (the velocity is the relative value to the velocity of sound), respectively. The temperature and the pressure of the initial evaporated layer were assumed to 2000 K and 10,000 Pa, respectively in all cases. From the value of n = 4 at us = 0, the exponent n increases with the increase in us , reaching much higher value of 13 when us becomes 2. It demon-
Fig. 5. Deposition density profiles of emitted particles at the position of x = a: (a) 2000 K; (b) 6000 K; (c) 12,000 K (pressure = 10,000 Pa, us = 0).
strates clearly that the increase in the stream velocity us causes n to increase drastically. From these results described above, it is considered that the deposition density profile is not greatly affected by the temperature in the initial evaporated layer even though the temperature is assumed to increase to the value of 12,000 K which seems high enough in comparison with the melting points of any metals. The reason for this is speculated that even though the temperature increases, it only causes the velocity of particles to increase isotropically, which lead to a minor influence on the deposition density profile. On the other hand, as Fig. 7 shows, the stream velocity of
I. Konomi et al. / Applied Surface Science 256 (2010) 4959–4965
Fig. 6. Deposition density profiles of emitted particles at the position of x = a: (a) 10,000 Pa; (b) 30,000 Pa; (c) 60,000 Pa (temperature = 2000 K, us = 0).
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Fig. 7. Deposition density profiles of emitted particles at the position of x = a: (a) us = 1; (b) us = 2; (c) us = 3 (temperature = 2000 K, pressure = 10,000 Pa).
3.3. Energy (velocity) change as a function of pressure of initial evaporated layer the initial evaporated layer to the x-axis has a great impact on the width of deposition density profile. It means that a kind of unidirectional velocity to the direction of surface normal is required for the density profile to become narrow. Regarding the influence of the pressure in the initial evaporated layer, discussion will be made in the next section.
In order to understand why the increase in the pressure of the initial evaporated layer causes the exponent n to increase, we have calculated the total kinetic energy (Etotal ), the kinetic energy in the direction of x-axis (E⊥ ) and the kinetic energy in the direction of y-axis (E|| ) of all emitted particles as a function of time. Fig. 8(a)–(c)
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in the number of collisions in the evaporated layer. These results indicate that as the number of collisions increases, the E⊥ increases and E|| decreases more rapidly and focusing of the energy flow to the direction of surface normal occurs. Consequently, the velocity in the direction of surface normal (v⊥ ) increases and the velocity in the parallel direction of the surface (v|| ) decreases as the pressure increases. In other words, the stream velocity toward the x-axis increases with the increase in the pressure of the evaporated layer. The kinetic reason for this behavior is described in Refs. [13–15,23]: after a collision, the direction of the faster particle will be closer to that of the center of mass of the group of the particles, which is on the average the surface normal direction. The increase in the stream velocity leads to the narrower deposition density profile as shown in Fig. 7. This explains why the deposition density profile becomes narrower at higher pressure of the initial evaporated layer as shown in Fig. 6. 3.4. Considerations on the relation of sublimation energy and exponent n in the angular distribution of emitted particles
Fig. 8. Dependence of the total energy (Etotal ), the energy in the direction of surface normal (E⊥ ) and the energy in the parallel direction of the surface (E|| ) of all particles as a function of time: pressure is assumed to be (a) 1000 Pa, (b) 10,000 Pa and (c) 60,000 Pa, respectively.
shows the Etotal , E⊥ and E|| at the initial pressure of (a) 1000 Pa, (b) 10,000 Pa and (c) 60,000 Pa, respectively. Naturally, all the energies increase until the end of the inflow of the particles during laser irradiation time (t = 20 ns). As can be seen from Fig. 8(a), E⊥ and E|| do not show any changes after the laser irradiation at the pressure of 1000 Pa. On the other hand, when the pressure increases to 10,000 Pa as shown in Fig. 8(b), E⊥ increases and E|| decreases after the laser irradiation; Etotal decreases slightly shortly after the laser irradiation time because some of the particles which are backscattered and reach the target as a result of collisions were eliminated in the simulation afterwards. The degrees of the increase in E⊥ and decrease in E|| are magnified with the increase in the pressure to 60,000 Pa as shown in Fig. 8(c). This effect is caused by the increase
In this section, based on the results of the simulation described above, we consider the reason for the experimental finding that the metals with higher sublimation energy show narrower angular distributions than those with lower sublimation energy as shown in Fig. 1 in the laser ablation. When laser beam is irradiated onto a target surface, laser energy is promptly converted to lattice vibration, resulting in a hightemperature surface in the near-surface region to the melting point [19,20]. Atoms in the near-surface region evaporate rapidly as temperature increases. In equilibrium state, the equilibrium vapor pressure of a metal with a lower sublimation energy shows a higher vapor pressure at the same temperature. As described in Section 3.2.2, when the vapor pressure increases, the stream velocity increases due to collisions in the layer. This indicates that a metal with a lower sublimation energy exhibits the narrower deposition profile and larger n value. However, it is contrary to the experimental results as shown in Fig. 1 [7]. In fact, the temperature should remain the melting point for some time during laser irradiation [20]. In general, a metal which has a low sublimation energy has a low melting point and tends to show very low vapor pressure at its melting point: for example, the vapor pressures of In and Sn are <10−10 Pa [24]. On the other hand, the metals with a higher sublimation energy have a large vapor pressure at its melting point: for example, the vapor pressures of Ta and Ti at their melting point are 0.78 and 0.49 Pa, respectively. Therefore, when metals which have a low sublimation energy are laser-ablated, the vapor pressure is expected to be low, thus, the number of collisions which take place should be small. As a consequence, the focusing effect of the velocity of the particles to the surface normal shown in Fig. 8 is small compared to the case in which metals with a higher sublimation energy is ablated and the number of collisions is larger. It is considered that this is the reason why the metals which have lower sublimation energy tend to show wider angular distribution, in other words, lower exponent n. 4. Conclusion We have performed the simulation of particles which are evaporated by laser irradiation by the method of DSMC. The temperature of initial evaporated layer shows a minor effect on the deposition profile of emitted particles, whereas the stream velocity which is strongly related to the pressure of initial evaporated layer has a significant influence on the deposition profile. The stream velocity increases as the increase in the pressure due to the collisions which the particles experience in the evaporated layer.
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The reason for the previous experimental finding that a metal with a low sublimation energy shows a broader angular distribution can be considered as follows: low density of evaporated layer of the metal with a low sublimation energy at its melting point decreases the number of collisions in the initial evaporated layer, leading to the low stream velocity in the direction of surface normal, which finally makes the angular distribution of emitted particles broader. Acknowledgements The authors are grateful to H. Azuma, Y. Ukyo and K. Kawahara for their helpful discussion and encouragement. References [1] D.B. Chrisey, G.K. Hubler, Pulsed Laser Deposition of Thin Films, John Wiley & Sons, Inc., New York, 1994. [2] R. Eason, Pulsed Laser Deposition of Thin Films, John Wiley & Sons, Inc., New York, 2006. [3] C.J. Yang, A.W. Kim, J.S. Kang, J. Appl. Phys. 83 (1998) 6620. [4] H. Mai, W. Pompe, Appl. Surf. Sci. 54 (1992) 215. [5] H.U. Krebs, Int. J. Non-equilib. Process 10 (1997) 3.
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