- Email: [email protected]
Characteristics of surface and film morphology in the IBAD deposition process: a Monte Carlo simulation study
Vacuum 70 (2003) 347–352
Characteristics of surface and film morphology in the IBAD deposition process: a Monte Carlo simulation study Waldemar Oleszkiewicza,*, Piotr Romiszowskib a
Faculty of Microsystem Electronics and Photonics, Institute of Microsystem Technology, Wroclaw University of Technology, Z. Janiszewskiego 11/17, Wroclaw 50-372, Poland b Department of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warszaw, Poland
Abstract In this paper, we describe a simulation of film growth process during the deposition with concurrent ion beam bombardment. We examine the process of thin films formation at the atomistic level by means of Monte Carlo (MC) methods. An MC simulation model was used in order to investigate the influence of some deposition process parameters (the angle of the ion beam, temperature of substrates as well as the kinetic energy of particles and the ion-to-atom arrival ratio) on the final morphology and quality of thin films. The mechanism of the physical aspects of film growth, interaction of energetic particles with solid surfaces, internal rearrangements of deposited adatoms were introduced into the model. The simulations were performed on a simple cubic lattice by employing the Metropolis sampling algorithm. The presented model is more complicated than the previously published study. The dislocation pining effect as well the simulated shape of the substrate surface were included into the simulations. Therefore, one can estimate better the role of the process parameters on the internal structure and surface evolution of the deposited films. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Monte Carlo simulation; IBAD; Thin films growth; Morphology
1. Introduction An ion beam assisted deposition (IBAD) is a combination of two distinct physical processes: an ordinary physical vapor deposition (PVD) on a biased or unbiased substrate and simultaneous bombardment of the surface and growing film with a low-energy ion beam. This is a type of ‘‘surface engineering’’ process of substantial technological importance for synthesizing films with superior properties. *Corresponding author. Fax: +48-71-328-3504. E-mail address: [email protected] (W. Oleszkiewicz).
The IBAD method enables one to vary independently the process parameters such as energy of the ion bombardment, the angle of ion beam incidence, density of the ion current, the deposition rate, the pressure of the working gas in the process [1,2]. As a result of these changes of the process parameters, one can obtain the film with expected properties [3–6]. As it is known there is a correlation between the process parameters and the optical quality of the film [7–12]. However, establishing it experimentally is an expensive and time-consuming task. The simulations of the deposition process can be helpful to answer these questions [13–16].
0042-207X/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0042-207X(02)00668-1
W. Oleszkiewicz, P. Romiszowski / Vacuum 70 (2003) 347–352
348
The computer simulation of film growth methods are mostly based on the Molecular Dynamics (deterministic approach) [17–20] and the Monte Carlo (stochastic) method [21–24]. In this paper, we performed a series of simulations of the growth of film deposited in the IBAD process. The presented study, made by means of the Monte Carlo simulation technique, is the continuation of our previous work [25] in which we have investigated the influence of IAR and the angle of ion beam incidence on the optical quality of the layers. In this article, we focused our attention on the influence of the ion beam energy on the final roughness and the morphology of the film.
2. The model The presented simulations are performed with the use of an atomistic model of the growing layer. Fig. 1 shows the scheme of the model. The detailed description of the model was given previously [25], so here we will point out its main assumptions. The simulations were performed for the model which was constructed as follows: the area considered as a substrate was a square consisting
source of atoms source of ions
Px
P
α
Py
SUBSTRATE Fig. 1. Scheme of the model including the pinning effect and the simulated roughness of the substrate.
of 100 100 lattice units. The substrate surface was simulated at random in order to obtain initial roughness (in contrast to the previous paper [25] in which we assumed the substrate surface as a flat area). Here, we use a simple cubic lattice with its axes parallel to the axes of the coordinate system, it means that we simulate the (0 0 1) surface growth. At the very beginning of the simulation there were no adatoms deposited on the substrate surface. Then one site of the lattice was picked up at random—this was the location of the first deposited material (adatom or an ion). One can note that the position of the picked site at which the deposited material arrives determines the trajectory of the arriving ion. In our simulations, we assumed that all trajectories are linear. As a result of this assumption, one must realize that as the process of the deposition goes on the trajectories of the ions could cross the already deposited material, therefore we introduced the ‘‘shading’’ algorithm which works as follows: if the arriving ion meets the already deposited adatom then it ends its way to the substrate at this point and is deposited on the surface. In order to mimic the proper interactions between the particles represented in the model, we have assumed kinetic energies of the particles as well as the interactions between them. The temperature of the substrate was set to T: All these parameters are in arbitrary units. The kinetic energy was associated with both the atoms and the ions. The values of the kinetic energy has been set arbitrarily, however, the energy of the ions was much larger than that of atoms. For sake of simplicity, we have also assumed that the masses of both the atoms and ions are equal. All the values of energy in the model had a Gaussian distribution (the values given in the simulation data were the averages). In the presented model, the arriving particles interacted with the already deposited material according to the following scheme:
1. The arriving adatom (or an ion) can transfer its kinetic momentum (namely, its component parallel to the surface) to the particle neighboring its final location on the surface in the process of the elastic collision.
W. Oleszkiewicz, P. Romiszowski / Vacuum 70 (2003) 347–352
3. Results and discussion The results of the simulations are presented in two kinds of graphs: cross sections of the layer show the morphology of the sample film—the cross sections are perpendicular to the substrate surface; the plots present the functional dependencies between some process parameters and the mean final results obtained from the simulations. Profiles presented in Figs. 2a and b show that the morphology of the film depends strongly on the energy of the ion beam. First, one can see that the number of ions incorporated in the growing film decreases as the energy of ions increases. Higher energies cause that the layer becomes more dense, without large vacancies. This is the effect of direct and indirect ion sputtering by the highenergy ions and accompanying internal redistribution of the deposited material in film, which leads to smoother surfaces. This can be seen on a plot of the roughness parameter Ra (in number of monolayers) as a function of ion energy Ei (Fig. 3). The influence of IAR on the morphology of the surface can be seen in Figs. 4a and b. The high density ion beam bombardment (at all other process parameters constant) leads to more loose structure of the film with visible dendritic grains
with open boundaries. Also one can see that for higher values of IAR the thickness of the film increases. In order to explain the influence of IAR on the final structure of the film one should realize that it is the result of the following processes: the surface sputtering of the material and the rearrangement of the growing film. On the other hand, the ions transfer their kinetic energies to the already deposited material, enabling more efficient rearrangement processes, like pinning effect, hopping into the vacancies, etc. The proportions between the elementary processes are responsible for the final morphology of the growing film. As the IAR decreases, the structure of the film becomes more packed and the resulting surface is smoother than that for large values of IAR. This effect can be observed in Fig. 5 where the
5
4
Ra
2. The arriving particle can transfer its kinetic momentum (namely, its component perpendicular to the surface) to the particles located on the surface point. The result of such energy transfer is the possibility of moving some surface particles down into the layer—this is called a pinning effect.
3
2 10
30
40
60
50
70
80
90
100
Fig. 3. Dependence of the roughness Ra (number of monolayers) of the simulated deposited films on the ion beam energy Ei for T=4; a=601; IAR=3.0.
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40
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20
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50
(a)
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60
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90 100
(b)
0
10
20
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50
60
70
80
90 100
Fig. 2. Cross section profiles of the simulated deposited films at various ion beam energy Ei : (a) Ei =10; and (b) Ei =50. For all figures T=4; a=451; IAR=3.0. Black circles represent ions and open circles represent adatoms. The profile of the substrate was simulated.
W. Oleszkiewicz, P. Romiszowski / Vacuum 70 (2003) 347–352
350 50
50
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(b)
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Fig. 4. Cross section profiles of the simulated deposited films at various ion-to-atom arrival ratio (IAR): (a) IAR=0.1; and (b) IAR=5.0. For all figures T=6; a=451; Ei =20. Black circles represent ions and open circles represent adatoms. The profile of the substrate was simulated.
6
6
IAR
T 2 4 6
T= 6
20
30
5
Ra
Ra
5
α=45 [deg]
0.5 1.0 5.0
4
4
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1
2
IAR
3
4
5
2 10
40
α [deg]
50
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Fig. 5. Dependence of the roughness Ra (number of monolayers) of the simulated deposited films on the ion-to-atom arrival ratio (IAR) for different substrate temperature values T (see legend) for a=451, Ei =20. Temperature T is given in arbitrary units.
Fig. 6. Roughness Ra (number of monolayers) of the simulated deposited films as a function of the angle of the ion beam incidence a for the IAR (see legend) for substrate temperature T=6. Temperature T is given in arbitrary units.
roughness of the simulated surface is plotted against the values of IAR for given T and a: One can observe also that Ra depends strongly on the temperature T of the substrate. The dependence of Ra on the angle of incidence a is given in Fig. 6. The curves which are calculated for T ¼ 6 are almost flat, which means that under these conditions the roughness depends on a insignificantly. In order to describe the characteristics of the surface we plotted the curves showing the distribution of the local thickness of the film vs. the number of monolayers N (here we mean thickness as the distance from the substrate surface to the surface of the layer counted perpendicularly to the surface). The plots in Figs. 7a and b show the Gaussian-type distribution with the position of the
maximum depending on both the IAR and T: One can observe that for low values of IAR the curves are narrow, which means that the surface is smoother than that for high IAR values. Comparison of the results for T ¼ 2 (Fig. 7a) and T ¼ 6 (Fig. 7b) shows that the influence of the IAR on the quality of the simulated surface is more pronounced for high temperature.
4. Conclusions The presented model is based on simple assumptions and we realize that it does not reflect the real process of the IBAD process, but, despite its simplicity, it seems to work properly describing
W. Oleszkiewicz, P. Romiszowski / Vacuum 70 (2003) 347–352
351
IAR 0.1 0.5 1.0 3.0 5.0
0.18 0.16 0.14
frequency
0.12 0.10 0.08 0.06 0.04 0.02 0.00
0
(a)
10
20
30
40
N 0.20 0.18
IAR 0.1 0.5 1.0 3.0 5.0
0.16 0.14
frequency
0.12 0.10 0.08 0.06 0.04 0.02 0.00
(b)
0
10
20
30
40
50
N
Fig. 7. Plot of the profile simulated surface height distribution for different IAR parameter values (see legend) for: a=451, Ei =20; T ¼ 2 (a) and 6 (b).
the course and final results of the deposition process. Our results show the significance of some parameters, namely IAR, energy of the ion beam and temperature on the properties of films, mainly the morphology of the layer. We found that the high-energy ion beam creates more dense and smoother film. The increase of the substrate temperature T stimulates the columnar growth of the deposited film. The high IAR values cause that the structure of the film is porous and contains more vacancies. Such morphological effects can be observed in the films deposited by means of PVD process enhanced by an ion beam. Concluding, we found that the presented model
can be useful in projecting the deposition experiments and in prediction of some final properties of the films.
References [1] Alberts L, Leutenecker R, Wolf GK. Surf Coat Technol 1996;84:443–7. [2] Ensinger W. Nucl. Instrum Meth Phys Res B 1997;127/ 128:796–809. [3] Mudholkar MS, Thompson L. J Appl Phys 1995;77(10):5138–43. [4] Kohzaki M, Matsumuro A, Hayashi T, Muramatsu M, Yamaguchi K. Thin Solid Films 1997;308-309:239–44.
352
W. Oleszkiewicz, P. Romiszowski / Vacuum 70 (2003) 347–352
[5] Jin N, Yusun L, Houming Z, Yudong F, Yi W. Surf Coat Technol 2001;145:71–4. [6] Malkow Th, Bull SJ. Surf Coat Technol 2001;137:197–204. [7] Cevro M, Carter G. Opt Eng 1995;34:596–606. ’ [8] Oleszkiewicz W, Oleszkiewicz E, Zukowska K. OptoElectron Rev 1997;5:133–6. [9] Wang X, Kolitsch A, Prokert F, Moeller W. Surf Coat Technol 1998;103-104:334–9. [10] Pulker HK. Surf Coat Technol 1999;112:250–6. ’ [11] Oleszkiewicz W, Oleszkiewicz E, Zukowska K. SPIE Proc 1999;3820:423–8. [12] Shimizu I, Setsuhara Y, Miyake S, Kumagai M, Ogata K, Kohata M, Yamaguchi K. Surf Coat Technol 2000;131:187–91. [13] Mueller KH. Phys Rev B 1987;35:7906–13. [14] Brett MJ. J Vac Sci Technol A 1988;6:1749–51. [15] Srolovitz DJ, Mazor A, Bukiet BG. J Vac Sci Technol A 1988;6:2371–80.
[16] Ektessabi AM, Sato S, Kitamura H, Masaki Y. Vacuum 1993;44:213–7. [17] Richards PM. Mater Res Soc Symp Proc 1991;202: 353–8. [18] Gilmer GH, Roland C. Radiat Effects Defects Solids 1994;130–131:321–43. [19] Smith RW, Srolovitz DJ. J Appl Phys 1996;79:1448–57. [20] Lugscheider E, Hayn G. Surf Coat Technol 1999; 116–119:568–72. [21] Ozawa S, Sasajima Y, Heermann DW. Thin Solid Films 1996;272:172–83. [22] Chason E, Kellerman BK. Nucl Instrum Methods Phys Res B 1997;127/128:225–9. [23] Gilmer GH, Huaang H, Diaz de la Rubia T, Torre JD, Baumann F. Thin Solid Films 2000;365:189–200. [24] Adams JB, Wang Z, Li Y. Thin Solid Films 2000;365: 201–10. [25] Oleszkiewicz W, Romiszowski P. Vacuum 2001;63:613–7.
Characteristics of surface and film morphology in the IBAD deposition process: a Monte Carlo simulation study Waldemar Oleszkiewicza,*, Piotr Romiszowskib a
Faculty of Microsystem Electronics and Photonics, Institute of Microsystem Technology, Wroclaw University of Technology, Z. Janiszewskiego 11/17, Wroclaw 50-372, Poland b Department of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warszaw, Poland
Abstract In this paper, we describe a simulation of film growth process during the deposition with concurrent ion beam bombardment. We examine the process of thin films formation at the atomistic level by means of Monte Carlo (MC) methods. An MC simulation model was used in order to investigate the influence of some deposition process parameters (the angle of the ion beam, temperature of substrates as well as the kinetic energy of particles and the ion-to-atom arrival ratio) on the final morphology and quality of thin films. The mechanism of the physical aspects of film growth, interaction of energetic particles with solid surfaces, internal rearrangements of deposited adatoms were introduced into the model. The simulations were performed on a simple cubic lattice by employing the Metropolis sampling algorithm. The presented model is more complicated than the previously published study. The dislocation pining effect as well the simulated shape of the substrate surface were included into the simulations. Therefore, one can estimate better the role of the process parameters on the internal structure and surface evolution of the deposited films. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Monte Carlo simulation; IBAD; Thin films growth; Morphology
1. Introduction An ion beam assisted deposition (IBAD) is a combination of two distinct physical processes: an ordinary physical vapor deposition (PVD) on a biased or unbiased substrate and simultaneous bombardment of the surface and growing film with a low-energy ion beam. This is a type of ‘‘surface engineering’’ process of substantial technological importance for synthesizing films with superior properties. *Corresponding author. Fax: +48-71-328-3504. E-mail address: [email protected] (W. Oleszkiewicz).
The IBAD method enables one to vary independently the process parameters such as energy of the ion bombardment, the angle of ion beam incidence, density of the ion current, the deposition rate, the pressure of the working gas in the process [1,2]. As a result of these changes of the process parameters, one can obtain the film with expected properties [3–6]. As it is known there is a correlation between the process parameters and the optical quality of the film [7–12]. However, establishing it experimentally is an expensive and time-consuming task. The simulations of the deposition process can be helpful to answer these questions [13–16].
0042-207X/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0042-207X(02)00668-1
W. Oleszkiewicz, P. Romiszowski / Vacuum 70 (2003) 347–352
348
The computer simulation of film growth methods are mostly based on the Molecular Dynamics (deterministic approach) [17–20] and the Monte Carlo (stochastic) method [21–24]. In this paper, we performed a series of simulations of the growth of film deposited in the IBAD process. The presented study, made by means of the Monte Carlo simulation technique, is the continuation of our previous work [25] in which we have investigated the influence of IAR and the angle of ion beam incidence on the optical quality of the layers. In this article, we focused our attention on the influence of the ion beam energy on the final roughness and the morphology of the film.
2. The model The presented simulations are performed with the use of an atomistic model of the growing layer. Fig. 1 shows the scheme of the model. The detailed description of the model was given previously [25], so here we will point out its main assumptions. The simulations were performed for the model which was constructed as follows: the area considered as a substrate was a square consisting
source of atoms source of ions
Px
P
α
Py
SUBSTRATE Fig. 1. Scheme of the model including the pinning effect and the simulated roughness of the substrate.
of 100 100 lattice units. The substrate surface was simulated at random in order to obtain initial roughness (in contrast to the previous paper [25] in which we assumed the substrate surface as a flat area). Here, we use a simple cubic lattice with its axes parallel to the axes of the coordinate system, it means that we simulate the (0 0 1) surface growth. At the very beginning of the simulation there were no adatoms deposited on the substrate surface. Then one site of the lattice was picked up at random—this was the location of the first deposited material (adatom or an ion). One can note that the position of the picked site at which the deposited material arrives determines the trajectory of the arriving ion. In our simulations, we assumed that all trajectories are linear. As a result of this assumption, one must realize that as the process of the deposition goes on the trajectories of the ions could cross the already deposited material, therefore we introduced the ‘‘shading’’ algorithm which works as follows: if the arriving ion meets the already deposited adatom then it ends its way to the substrate at this point and is deposited on the surface. In order to mimic the proper interactions between the particles represented in the model, we have assumed kinetic energies of the particles as well as the interactions between them. The temperature of the substrate was set to T: All these parameters are in arbitrary units. The kinetic energy was associated with both the atoms and the ions. The values of the kinetic energy has been set arbitrarily, however, the energy of the ions was much larger than that of atoms. For sake of simplicity, we have also assumed that the masses of both the atoms and ions are equal. All the values of energy in the model had a Gaussian distribution (the values given in the simulation data were the averages). In the presented model, the arriving particles interacted with the already deposited material according to the following scheme:
1. The arriving adatom (or an ion) can transfer its kinetic momentum (namely, its component parallel to the surface) to the particle neighboring its final location on the surface in the process of the elastic collision.
W. Oleszkiewicz, P. Romiszowski / Vacuum 70 (2003) 347–352
3. Results and discussion The results of the simulations are presented in two kinds of graphs: cross sections of the layer show the morphology of the sample film—the cross sections are perpendicular to the substrate surface; the plots present the functional dependencies between some process parameters and the mean final results obtained from the simulations. Profiles presented in Figs. 2a and b show that the morphology of the film depends strongly on the energy of the ion beam. First, one can see that the number of ions incorporated in the growing film decreases as the energy of ions increases. Higher energies cause that the layer becomes more dense, without large vacancies. This is the effect of direct and indirect ion sputtering by the highenergy ions and accompanying internal redistribution of the deposited material in film, which leads to smoother surfaces. This can be seen on a plot of the roughness parameter Ra (in number of monolayers) as a function of ion energy Ei (Fig. 3). The influence of IAR on the morphology of the surface can be seen in Figs. 4a and b. The high density ion beam bombardment (at all other process parameters constant) leads to more loose structure of the film with visible dendritic grains
with open boundaries. Also one can see that for higher values of IAR the thickness of the film increases. In order to explain the influence of IAR on the final structure of the film one should realize that it is the result of the following processes: the surface sputtering of the material and the rearrangement of the growing film. On the other hand, the ions transfer their kinetic energies to the already deposited material, enabling more efficient rearrangement processes, like pinning effect, hopping into the vacancies, etc. The proportions between the elementary processes are responsible for the final morphology of the growing film. As the IAR decreases, the structure of the film becomes more packed and the resulting surface is smoother than that for large values of IAR. This effect can be observed in Fig. 5 where the
5
4
Ra
2. The arriving particle can transfer its kinetic momentum (namely, its component perpendicular to the surface) to the particles located on the surface point. The result of such energy transfer is the possibility of moving some surface particles down into the layer—this is called a pinning effect.
3
2 10
30
40
60
50
70
80
90
100
Fig. 3. Dependence of the roughness Ra (number of monolayers) of the simulated deposited films on the ion beam energy Ei for T=4; a=601; IAR=3.0.
50
40
40
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90 100
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90 100
Fig. 2. Cross section profiles of the simulated deposited films at various ion beam energy Ei : (a) Ei =10; and (b) Ei =50. For all figures T=4; a=451; IAR=3.0. Black circles represent ions and open circles represent adatoms. The profile of the substrate was simulated.
W. Oleszkiewicz, P. Romiszowski / Vacuum 70 (2003) 347–352
350 50
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Fig. 4. Cross section profiles of the simulated deposited films at various ion-to-atom arrival ratio (IAR): (a) IAR=0.1; and (b) IAR=5.0. For all figures T=6; a=451; Ei =20. Black circles represent ions and open circles represent adatoms. The profile of the substrate was simulated.
6
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T 2 4 6
T= 6
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α=45 [deg]
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Fig. 5. Dependence of the roughness Ra (number of monolayers) of the simulated deposited films on the ion-to-atom arrival ratio (IAR) for different substrate temperature values T (see legend) for a=451, Ei =20. Temperature T is given in arbitrary units.
Fig. 6. Roughness Ra (number of monolayers) of the simulated deposited films as a function of the angle of the ion beam incidence a for the IAR (see legend) for substrate temperature T=6. Temperature T is given in arbitrary units.
roughness of the simulated surface is plotted against the values of IAR for given T and a: One can observe also that Ra depends strongly on the temperature T of the substrate. The dependence of Ra on the angle of incidence a is given in Fig. 6. The curves which are calculated for T ¼ 6 are almost flat, which means that under these conditions the roughness depends on a insignificantly. In order to describe the characteristics of the surface we plotted the curves showing the distribution of the local thickness of the film vs. the number of monolayers N (here we mean thickness as the distance from the substrate surface to the surface of the layer counted perpendicularly to the surface). The plots in Figs. 7a and b show the Gaussian-type distribution with the position of the
maximum depending on both the IAR and T: One can observe that for low values of IAR the curves are narrow, which means that the surface is smoother than that for high IAR values. Comparison of the results for T ¼ 2 (Fig. 7a) and T ¼ 6 (Fig. 7b) shows that the influence of the IAR on the quality of the simulated surface is more pronounced for high temperature.
4. Conclusions The presented model is based on simple assumptions and we realize that it does not reflect the real process of the IBAD process, but, despite its simplicity, it seems to work properly describing
W. Oleszkiewicz, P. Romiszowski / Vacuum 70 (2003) 347–352
351
IAR 0.1 0.5 1.0 3.0 5.0
0.18 0.16 0.14
frequency
0.12 0.10 0.08 0.06 0.04 0.02 0.00
0
(a)
10
20
30
40
N 0.20 0.18
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(b)
0
10
20
30
40
50
N
Fig. 7. Plot of the profile simulated surface height distribution for different IAR parameter values (see legend) for: a=451, Ei =20; T ¼ 2 (a) and 6 (b).
the course and final results of the deposition process. Our results show the significance of some parameters, namely IAR, energy of the ion beam and temperature on the properties of films, mainly the morphology of the layer. We found that the high-energy ion beam creates more dense and smoother film. The increase of the substrate temperature T stimulates the columnar growth of the deposited film. The high IAR values cause that the structure of the film is porous and contains more vacancies. Such morphological effects can be observed in the films deposited by means of PVD process enhanced by an ion beam. Concluding, we found that the presented model
can be useful in projecting the deposition experiments and in prediction of some final properties of the films.
References [1] Alberts L, Leutenecker R, Wolf GK. Surf Coat Technol 1996;84:443–7. [2] Ensinger W. Nucl. Instrum Meth Phys Res B 1997;127/ 128:796–809. [3] Mudholkar MS, Thompson L. J Appl Phys 1995;77(10):5138–43. [4] Kohzaki M, Matsumuro A, Hayashi T, Muramatsu M, Yamaguchi K. Thin Solid Films 1997;308-309:239–44.
352
W. Oleszkiewicz, P. Romiszowski / Vacuum 70 (2003) 347–352
[5] Jin N, Yusun L, Houming Z, Yudong F, Yi W. Surf Coat Technol 2001;145:71–4. [6] Malkow Th, Bull SJ. Surf Coat Technol 2001;137:197–204. [7] Cevro M, Carter G. Opt Eng 1995;34:596–606. ’ [8] Oleszkiewicz W, Oleszkiewicz E, Zukowska K. OptoElectron Rev 1997;5:133–6. [9] Wang X, Kolitsch A, Prokert F, Moeller W. Surf Coat Technol 1998;103-104:334–9. [10] Pulker HK. Surf Coat Technol 1999;112:250–6. ’ [11] Oleszkiewicz W, Oleszkiewicz E, Zukowska K. SPIE Proc 1999;3820:423–8. [12] Shimizu I, Setsuhara Y, Miyake S, Kumagai M, Ogata K, Kohata M, Yamaguchi K. Surf Coat Technol 2000;131:187–91. [13] Mueller KH. Phys Rev B 1987;35:7906–13. [14] Brett MJ. J Vac Sci Technol A 1988;6:1749–51. [15] Srolovitz DJ, Mazor A, Bukiet BG. J Vac Sci Technol A 1988;6:2371–80.
[16] Ektessabi AM, Sato S, Kitamura H, Masaki Y. Vacuum 1993;44:213–7. [17] Richards PM. Mater Res Soc Symp Proc 1991;202: 353–8. [18] Gilmer GH, Roland C. Radiat Effects Defects Solids 1994;130–131:321–43. [19] Smith RW, Srolovitz DJ. J Appl Phys 1996;79:1448–57. [20] Lugscheider E, Hayn G. Surf Coat Technol 1999; 116–119:568–72. [21] Ozawa S, Sasajima Y, Heermann DW. Thin Solid Films 1996;272:172–83. [22] Chason E, Kellerman BK. Nucl Instrum Methods Phys Res B 1997;127/128:225–9. [23] Gilmer GH, Huaang H, Diaz de la Rubia T, Torre JD, Baumann F. Thin Solid Films 2000;365:189–200. [24] Adams JB, Wang Z, Li Y. Thin Solid Films 2000;365: 201–10. [25] Oleszkiewicz W, Romiszowski P. Vacuum 2001;63:613–7.