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Internal stress control of boron thin film
Fusion Engineering and Design 39 – 40 (1998) 493 – 497
Internal stress control of boron thin film N. Satomi *, M. Kitamura, T. Sasaki, M. Nishikawa Electromagnetic Energy Engineering Course, Graduate School of Engineering, Osaka Uni6ersity, 2 -1 Yamadaoka, Suita, Osaka 565, Japan
Abstract The occurrence of stress in thin films has led to serious stability problems in practical use. We have investigated the stress in the boron films to find the deposition condition of the boron films with less stress. It was found that the stress in the boron film varies sufficiently from compressive to tensile stress, that is from − 1.0 to 1.4 GPa, depending on the evaporation conditions, such as deposition rate and the substrate temperature. Hydrogen ion bombardment resulted in the enhancement of the compressive stress, possibly due to ion peening effect, while under helium ion bombardment, stress relief was observed. The boron film with nearly zero stress was obtained by the evaporation at a deposition rate of 0.5 nm s − 1 and substrate temperature of 300°C. © 1998 Published by Elsevier Science S.A. All rights reserved.
1. Introduction The investigation of the internal stress in a thin film is important because of the reliability problems in practical use, as large stress will cause mechanical failure of films, such as adhesion failure and peeling. Boronizations in tokamak experiments have been successfully applied without a peeling problem, probably because of the thin coating: less than 0.2 mm [1 – 5]. However, if thick coatings, of more than several mm, are used in order to obtain a long-lived coating effect, the occurrence of stress in a coating will lead to serious problems. We have investigated the internal stress in the boron films prepared by ion plating [6]. In previous experiments, all films were prepared at a substrate temperature of 300°C and deposition rate of 0.1 * Corresponding author.
nm s − 1. Boron thin films produced by the vacuum evaporation exhibited fairly large compressive stress of −0.5 GPa. For ion plating with d.c. glow Ar plasma, increase in compressive film stress was generally found with increasing negative bias of the substrate in the range from − 100 to −400 V and films with the compressive stress of − 0.8 to −1.5 GPa were obtained. These results were consistent with our observations that the peeling phenomena often occurred in boron films prepared by ion plating, even with a small thickness, around 1 mm, and rarely occurred in boron films prepared by vacuum evaporation with a thickness of over 2 mm. The purpose of this study was to find the optimum preparation condition for boron films in order to minimize internal stress. The measurements of the stress for various deposition conditions are presented, and the optimum preparation conditions and the mechanism of stress are discussed.
0920-3796/98/$19.00 © 1998 Published by Elsevier Science S.A. All rights reserved. PII S0920-3796(98)00251-8
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N. Satomi et al. / Fusion Engineering and Design 39–40 (1998) 493–497
2. Experimental procedure Stress measurements were carried out on boron films deposited by vacuum deposition and ion plating. Fig. 1 shows a schematic diagram of the ion-plating apparatus and the internal stress measurement system. The boron source materials were evaporated by a conventional 270° deflection type EB (4 kV, 500 mA) gun. The substrates used were molybdenum plates (t =0.2 mm, w = 10 mm, l=40 mm). Their temperatures were maintained at 300–900°C by a tungsten heater. The stainless steel vessel was pumped down to less than 1.0 × 10 − 6 Torr using a turbo molecular pump. Film thickness was measured by a quartz-crystal oscillator thickness monitor. For ion plating, glow discharge with a hot filament cathode was used to initiate plasmas, even at low gas pressure. A gas pressure of 1 mTorr and a discharge current of 800 mA were used for our typical experimental conditions. Typical plasma parameters were an electron temperature of 3 eV and an electron density of 6.0× 1015 m − 3. For ion plating deposition, a negative bias in the range of −100 to −400 V was applied to the substrate by an external d.c. power supply. The stress from the change in curvature induced in the substrate was measured using an optically
levered laser method [7]. The light source was a He–Ne laser (P= 0.5 mW, u= 1.3 mrad). The laser beam was focused on the detector by a cylindrical lens with 1000 mm focus length. The resulting translation of the reflected beam was measured by a position-sensitive detector PSD (Hamamatsu S3931). This has a sensitive area of 1× 6 mm and a position resolution of 30 mm.
3. Results The results of the total stress (the integral of stress over the thickness of the film) are plotted against thickness for vacuum evaporation and ion plating with H in Fig. 2. These data were obtained at typical deposition conditions of substrate temperature of 300°C and deposition rate of 0.1 nm s − 1. As expected from the straight line, the compressive stresses are uniformly generated. An increase in intrinsic compressive film stress is clearly found with increasing negative bias in the range from − 100 to − 400 V, and resulting stresses are higher than those of vacuum evaporation. For He ion plating at 300°C and 0.1 nm s − 1 in Fig. 3, the plots are also almost linear, except for the early phase of deposition. The dependence of
Fig. 1. Schematic of the ion-plating apparatus and the stress-measurement system.
N. Satomi et al. / Fusion Engineering and Design 39–40 (1998) 493–497
Fig. 2. Total stress vs. film thickness for boron films deposited by vacuum evaporation and ion plating with H plasma. All films were deposited at a substrate temperature of 300°C and deposition rate of 0.1 nm s − 1.
the total stress on the bombardment energy of the He ion is not so evident. However, it is important that all compressive stresses attained are lower than those in vacuum-evaporated films. These results are consistent with the data from previous experiments, in which no peeling was found in the films prepared by He ion plating even, with ion bombardment energy up to −400 eV. The dependence of stress in the vacuum-evaporated films on the deposition rate is shown in Fig. 4. At 300°C substrate temperature, a compressive stress was observed over a wide range of deposition rates. The compressive stress decreases towards zero with increasing deposition rate, and the stress changes from compressive to tensile at higher deposition rates. A boron thin film with
Fig. 3. Total stress vs. film thickness for boron films deposited by vacuum evaporation and ion plating with He plasma. All films were deposited at a substrate temperature of 300°C and deposition rate of 0.1 nm s − 1.
495
Fig. 4. Total stress in the boron films prepared by vacuum evaporation as a function of the deposition rate at substrate temperatures of 300 and 150°C.
zero stress was obtained at 0.5 nm s − 1. At a low substrate temperature of 150°C, all stresses were shifted towards tensile, except at very low deposition rates. The maximum compressive stress is −1.0 GPa at 300°C, and the maximum tensile stress is 1.4 GPa at 150°C. The substrate temperature effect on stress at a deposition rate of 0.1 nm s − 1 is shown in Fig. 5. The higher substrate temperature resulted in higher compressive stress. These data may indicate that the compressive stress is caused by enhanced adatom mobility, which is due to increased substrate temperature. The dependence of the density of the boron thin film on the deposition rate is shown in Fig. 6. The deposited mass on the substrate was mea-
Fig. 5. Total stress vs. film thickness for boron films deposited by vacuum evaporation for substrate temperatures of 150, 300 and 500°C. The deposition rate is 0.1 nm s − 1.
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N. Satomi et al. / Fusion Engineering and Design 39–40 (1998) 493–497
Fig. 6. The densities of the boron films as a function of the deposition rate. The substrate temperature is 150°C.
sured by the oscillating quartz resonator placed near the substrate. The volume of the thin film was estimated from the film thickness measured by the surface profile meter (Veeco Dektak [3]). The trend of the change of densities in the film is not clear due to large error, even over the wide range of deposition rates, where the stresses also change significantly. The large error bars are due to the error of the thickness measurements. An average density is about 2.0 g cm − 3, which is considerably less than the 2.35 g cm − 3 of the bulk boron.
4. Discussion The stresses observed in the metallic films by vacuum evaporation are almost always tensile [8]. Thus, the boron is an exceptional material which can be deposited under compression by vacuum evaporation. As shown in Fig. 2, the stresses measured are uniformly generated in the films. This suggests that the interfacial effects, such as lattice misfits and dislocations between the film and the substrate, scarcely contribute to the stress, and the measured data do not depend on the substrate material. From our experimental results, we conclude that in our boron films both mechanisms of tensile and compressive stress may operate simultaneously during deposition. As shown in Fig. 6, amorphous films usually show a density less than the bulk density, since their structures are rich in defects, such as large micropores, open voids, etc. Tensile stress in the amorphous films is due partly to attractive interatomic forces in these
defects. Mu¨ller has recently used molecular dynamic computer simulations to explain the internal stress as being related to the film structure [9]. He showed that increasing the substrate temperature and decreasing the deposition rate resulted in the transition from a porous film to a densely packed film with less microvoids. He also showed that under ion bombardments the tensile stress decreased due to disappearance of defects as a function of ion bombardment energy [10]. Our results shown in Figs. 2, 4 and 5 are consistent with his simulation results and are explained by the change in the tensile stress, if the stresses measured in our boron films are the sum of tensile and compressive stresses. At present we have no model for the compressive stress in the evaporated boron film. The compressive stress is also caused by the bombardment of the film surface by energetic ions. This bombardment effect is called atom or ion peening. A detailed analysis of the ion-peening effect has been provided by Windischmann [11]. In this model, the compressive stress induced is proportional to the product of the sputtering yield and the ion-to-atom flux ratio. In Fig. 7, the compressive stress induced by ion bombardment, Ds, which is obtained by subtracting its values for vacuum evaporation films and by normalizing it with the ion-to-atom flux ratio, is plotted against the H ion bombarding energy. The solid line in Fig. 7 is the best-fitting sputtering yield curve given by the empirical formula [12]. The energy
Fig. 7. Incremental compressive stress, Ds, which is obtained by subtracting the value of the vacuum-evaporated boron film, as a function of the energy of H ion bombardment. The solid line is the best fitting curve of the sputtering yield calculated from the empirical formula.
N. Satomi et al. / Fusion Engineering and Design 39–40 (1998) 493–497
dependence of the data is in good agreement with that of sputtering yield. The effect of H ion bombardment on the compressive stress can thus be explained by the ion-peening model. However, we cannot apply this peening model for results of He bombardments, since stress relief rather than stress enhancement was observed. Although we have no clear explanation for this, the possible counter effect is the formation of growing film surface with defects and open voids due to large sputtering by He ions.
5. Conclusions We found that boron films show significantly large compressive or tensile stress, depending on the deposition conditions. In the CVD boronization used in the tokamak experiments, boron films are deposited under ion bombardment, accelerated in the cathode sheath to energies approaching the discharge voltage of 300 – 500 V. From the viewpoint of hydrogen recycling, this boronization should be carried out at a wall temperature of above 300°C to minimize the hydrogen contents in the film. In order to obtain a boron film with almost zero stress, the desirable deposition rate is about 0.5 nm s − 1 for He plasma, and is considerably higher than this value for H plasma, if a wall temperature of 300°C is used.
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497
References [1] J. Winter, H.G. Esser, L. Ko¨nen, et al., Boronization in TEXTOR, J. Nucl. Mater 162 – 164 (1989) 713. [2] U. Schneider, W. Poschenrieder, M. Bessenredt-Weberpals, et al., Boronization of ASDEX, J. Nucl. Mater. 176/177 (1990) 350. [3] H.F. Dylla, M.G. Bell, R.J. Hawryluk, et al., Effects of boronization of the first wall in TFTR, J. Nucl. Mater. 176/177 (1990) 337. [4] G.L. Jackson, J. Winter, K.H. Burrell, et al., Boronization in DIII-D, J. Nucl. Mater. 196 – 198 (1992) 236. [5] M. Saidoh, N. Ogiwara, M. Shimada, et al., Initial boronization of JT-60U tokamak using decaborane, Jpn. J. Appl. Phys. 32 (1993) 3276. [6] N. Satomi, S. Sato, K. Tanaka, M. Saidoh, M. Nishikawa, Mechanical properties of boron coatings, J. Nucl. Mater. 220 – 222 (1995) 752. [7] H.C. Liu, S.P. Murarka, Elastic and viscoelastic analysis of stress in thin films, J. Appl. Phys. 72 (1992) 3458. [8] F.M. D’Heurle, J.M.E. Harper, Note on the origin of intrinsic stress in films deposited via evaporation and sputtering, Thin Solid Films 171 (1989) 81. [9] K.H. Mu¨ller, Dependence of thin-film microstructure on deposition rate by means of a computer simulation, J. Appl. Phys. 58 (1985) 2573. [10] K.H. Mu¨ller, Stress and microstructure of sputter-deposited thin films: molecular dynamics investigations, J. Appl. Phys. 62 (1987) 1796. [11] H. Windischmann, An intrinsic stress scaling law for polycrystalline thin films prepared by ion beam sputtering, J. Appl. Phys. 62 (1987) 1800. [12] N. Matsunami, Y. Yamamura, Y. Itikawa et al., Energy dependence of the yields of ion-induced sputtering of monatomic solids, IPPJ-AM-32, 1983.
Internal stress control of boron thin film N. Satomi *, M. Kitamura, T. Sasaki, M. Nishikawa Electromagnetic Energy Engineering Course, Graduate School of Engineering, Osaka Uni6ersity, 2 -1 Yamadaoka, Suita, Osaka 565, Japan
Abstract The occurrence of stress in thin films has led to serious stability problems in practical use. We have investigated the stress in the boron films to find the deposition condition of the boron films with less stress. It was found that the stress in the boron film varies sufficiently from compressive to tensile stress, that is from − 1.0 to 1.4 GPa, depending on the evaporation conditions, such as deposition rate and the substrate temperature. Hydrogen ion bombardment resulted in the enhancement of the compressive stress, possibly due to ion peening effect, while under helium ion bombardment, stress relief was observed. The boron film with nearly zero stress was obtained by the evaporation at a deposition rate of 0.5 nm s − 1 and substrate temperature of 300°C. © 1998 Published by Elsevier Science S.A. All rights reserved.
1. Introduction The investigation of the internal stress in a thin film is important because of the reliability problems in practical use, as large stress will cause mechanical failure of films, such as adhesion failure and peeling. Boronizations in tokamak experiments have been successfully applied without a peeling problem, probably because of the thin coating: less than 0.2 mm [1 – 5]. However, if thick coatings, of more than several mm, are used in order to obtain a long-lived coating effect, the occurrence of stress in a coating will lead to serious problems. We have investigated the internal stress in the boron films prepared by ion plating [6]. In previous experiments, all films were prepared at a substrate temperature of 300°C and deposition rate of 0.1 * Corresponding author.
nm s − 1. Boron thin films produced by the vacuum evaporation exhibited fairly large compressive stress of −0.5 GPa. For ion plating with d.c. glow Ar plasma, increase in compressive film stress was generally found with increasing negative bias of the substrate in the range from − 100 to −400 V and films with the compressive stress of − 0.8 to −1.5 GPa were obtained. These results were consistent with our observations that the peeling phenomena often occurred in boron films prepared by ion plating, even with a small thickness, around 1 mm, and rarely occurred in boron films prepared by vacuum evaporation with a thickness of over 2 mm. The purpose of this study was to find the optimum preparation condition for boron films in order to minimize internal stress. The measurements of the stress for various deposition conditions are presented, and the optimum preparation conditions and the mechanism of stress are discussed.
0920-3796/98/$19.00 © 1998 Published by Elsevier Science S.A. All rights reserved. PII S0920-3796(98)00251-8
494
N. Satomi et al. / Fusion Engineering and Design 39–40 (1998) 493–497
2. Experimental procedure Stress measurements were carried out on boron films deposited by vacuum deposition and ion plating. Fig. 1 shows a schematic diagram of the ion-plating apparatus and the internal stress measurement system. The boron source materials were evaporated by a conventional 270° deflection type EB (4 kV, 500 mA) gun. The substrates used were molybdenum plates (t =0.2 mm, w = 10 mm, l=40 mm). Their temperatures were maintained at 300–900°C by a tungsten heater. The stainless steel vessel was pumped down to less than 1.0 × 10 − 6 Torr using a turbo molecular pump. Film thickness was measured by a quartz-crystal oscillator thickness monitor. For ion plating, glow discharge with a hot filament cathode was used to initiate plasmas, even at low gas pressure. A gas pressure of 1 mTorr and a discharge current of 800 mA were used for our typical experimental conditions. Typical plasma parameters were an electron temperature of 3 eV and an electron density of 6.0× 1015 m − 3. For ion plating deposition, a negative bias in the range of −100 to −400 V was applied to the substrate by an external d.c. power supply. The stress from the change in curvature induced in the substrate was measured using an optically
levered laser method [7]. The light source was a He–Ne laser (P= 0.5 mW, u= 1.3 mrad). The laser beam was focused on the detector by a cylindrical lens with 1000 mm focus length. The resulting translation of the reflected beam was measured by a position-sensitive detector PSD (Hamamatsu S3931). This has a sensitive area of 1× 6 mm and a position resolution of 30 mm.
3. Results The results of the total stress (the integral of stress over the thickness of the film) are plotted against thickness for vacuum evaporation and ion plating with H in Fig. 2. These data were obtained at typical deposition conditions of substrate temperature of 300°C and deposition rate of 0.1 nm s − 1. As expected from the straight line, the compressive stresses are uniformly generated. An increase in intrinsic compressive film stress is clearly found with increasing negative bias in the range from − 100 to − 400 V, and resulting stresses are higher than those of vacuum evaporation. For He ion plating at 300°C and 0.1 nm s − 1 in Fig. 3, the plots are also almost linear, except for the early phase of deposition. The dependence of
Fig. 1. Schematic of the ion-plating apparatus and the stress-measurement system.
N. Satomi et al. / Fusion Engineering and Design 39–40 (1998) 493–497
Fig. 2. Total stress vs. film thickness for boron films deposited by vacuum evaporation and ion plating with H plasma. All films were deposited at a substrate temperature of 300°C and deposition rate of 0.1 nm s − 1.
the total stress on the bombardment energy of the He ion is not so evident. However, it is important that all compressive stresses attained are lower than those in vacuum-evaporated films. These results are consistent with the data from previous experiments, in which no peeling was found in the films prepared by He ion plating even, with ion bombardment energy up to −400 eV. The dependence of stress in the vacuum-evaporated films on the deposition rate is shown in Fig. 4. At 300°C substrate temperature, a compressive stress was observed over a wide range of deposition rates. The compressive stress decreases towards zero with increasing deposition rate, and the stress changes from compressive to tensile at higher deposition rates. A boron thin film with
Fig. 3. Total stress vs. film thickness for boron films deposited by vacuum evaporation and ion plating with He plasma. All films were deposited at a substrate temperature of 300°C and deposition rate of 0.1 nm s − 1.
495
Fig. 4. Total stress in the boron films prepared by vacuum evaporation as a function of the deposition rate at substrate temperatures of 300 and 150°C.
zero stress was obtained at 0.5 nm s − 1. At a low substrate temperature of 150°C, all stresses were shifted towards tensile, except at very low deposition rates. The maximum compressive stress is −1.0 GPa at 300°C, and the maximum tensile stress is 1.4 GPa at 150°C. The substrate temperature effect on stress at a deposition rate of 0.1 nm s − 1 is shown in Fig. 5. The higher substrate temperature resulted in higher compressive stress. These data may indicate that the compressive stress is caused by enhanced adatom mobility, which is due to increased substrate temperature. The dependence of the density of the boron thin film on the deposition rate is shown in Fig. 6. The deposited mass on the substrate was mea-
Fig. 5. Total stress vs. film thickness for boron films deposited by vacuum evaporation for substrate temperatures of 150, 300 and 500°C. The deposition rate is 0.1 nm s − 1.
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Fig. 6. The densities of the boron films as a function of the deposition rate. The substrate temperature is 150°C.
sured by the oscillating quartz resonator placed near the substrate. The volume of the thin film was estimated from the film thickness measured by the surface profile meter (Veeco Dektak [3]). The trend of the change of densities in the film is not clear due to large error, even over the wide range of deposition rates, where the stresses also change significantly. The large error bars are due to the error of the thickness measurements. An average density is about 2.0 g cm − 3, which is considerably less than the 2.35 g cm − 3 of the bulk boron.
4. Discussion The stresses observed in the metallic films by vacuum evaporation are almost always tensile [8]. Thus, the boron is an exceptional material which can be deposited under compression by vacuum evaporation. As shown in Fig. 2, the stresses measured are uniformly generated in the films. This suggests that the interfacial effects, such as lattice misfits and dislocations between the film and the substrate, scarcely contribute to the stress, and the measured data do not depend on the substrate material. From our experimental results, we conclude that in our boron films both mechanisms of tensile and compressive stress may operate simultaneously during deposition. As shown in Fig. 6, amorphous films usually show a density less than the bulk density, since their structures are rich in defects, such as large micropores, open voids, etc. Tensile stress in the amorphous films is due partly to attractive interatomic forces in these
defects. Mu¨ller has recently used molecular dynamic computer simulations to explain the internal stress as being related to the film structure [9]. He showed that increasing the substrate temperature and decreasing the deposition rate resulted in the transition from a porous film to a densely packed film with less microvoids. He also showed that under ion bombardments the tensile stress decreased due to disappearance of defects as a function of ion bombardment energy [10]. Our results shown in Figs. 2, 4 and 5 are consistent with his simulation results and are explained by the change in the tensile stress, if the stresses measured in our boron films are the sum of tensile and compressive stresses. At present we have no model for the compressive stress in the evaporated boron film. The compressive stress is also caused by the bombardment of the film surface by energetic ions. This bombardment effect is called atom or ion peening. A detailed analysis of the ion-peening effect has been provided by Windischmann [11]. In this model, the compressive stress induced is proportional to the product of the sputtering yield and the ion-to-atom flux ratio. In Fig. 7, the compressive stress induced by ion bombardment, Ds, which is obtained by subtracting its values for vacuum evaporation films and by normalizing it with the ion-to-atom flux ratio, is plotted against the H ion bombarding energy. The solid line in Fig. 7 is the best-fitting sputtering yield curve given by the empirical formula [12]. The energy
Fig. 7. Incremental compressive stress, Ds, which is obtained by subtracting the value of the vacuum-evaporated boron film, as a function of the energy of H ion bombardment. The solid line is the best fitting curve of the sputtering yield calculated from the empirical formula.
N. Satomi et al. / Fusion Engineering and Design 39–40 (1998) 493–497
dependence of the data is in good agreement with that of sputtering yield. The effect of H ion bombardment on the compressive stress can thus be explained by the ion-peening model. However, we cannot apply this peening model for results of He bombardments, since stress relief rather than stress enhancement was observed. Although we have no clear explanation for this, the possible counter effect is the formation of growing film surface with defects and open voids due to large sputtering by He ions.
5. Conclusions We found that boron films show significantly large compressive or tensile stress, depending on the deposition conditions. In the CVD boronization used in the tokamak experiments, boron films are deposited under ion bombardment, accelerated in the cathode sheath to energies approaching the discharge voltage of 300 – 500 V. From the viewpoint of hydrogen recycling, this boronization should be carried out at a wall temperature of above 300°C to minimize the hydrogen contents in the film. In order to obtain a boron film with almost zero stress, the desirable deposition rate is about 0.5 nm s − 1 for He plasma, and is considerably higher than this value for H plasma, if a wall temperature of 300°C is used.
.
497
References [1] J. Winter, H.G. Esser, L. Ko¨nen, et al., Boronization in TEXTOR, J. Nucl. Mater 162 – 164 (1989) 713. [2] U. Schneider, W. Poschenrieder, M. Bessenredt-Weberpals, et al., Boronization of ASDEX, J. Nucl. Mater. 176/177 (1990) 350. [3] H.F. Dylla, M.G. Bell, R.J. Hawryluk, et al., Effects of boronization of the first wall in TFTR, J. Nucl. Mater. 176/177 (1990) 337. [4] G.L. Jackson, J. Winter, K.H. Burrell, et al., Boronization in DIII-D, J. Nucl. Mater. 196 – 198 (1992) 236. [5] M. Saidoh, N. Ogiwara, M. Shimada, et al., Initial boronization of JT-60U tokamak using decaborane, Jpn. J. Appl. Phys. 32 (1993) 3276. [6] N. Satomi, S. Sato, K. Tanaka, M. Saidoh, M. Nishikawa, Mechanical properties of boron coatings, J. Nucl. Mater. 220 – 222 (1995) 752. [7] H.C. Liu, S.P. Murarka, Elastic and viscoelastic analysis of stress in thin films, J. Appl. Phys. 72 (1992) 3458. [8] F.M. D’Heurle, J.M.E. Harper, Note on the origin of intrinsic stress in films deposited via evaporation and sputtering, Thin Solid Films 171 (1989) 81. [9] K.H. Mu¨ller, Dependence of thin-film microstructure on deposition rate by means of a computer simulation, J. Appl. Phys. 58 (1985) 2573. [10] K.H. Mu¨ller, Stress and microstructure of sputter-deposited thin films: molecular dynamics investigations, J. Appl. Phys. 62 (1987) 1796. [11] H. Windischmann, An intrinsic stress scaling law for polycrystalline thin films prepared by ion beam sputtering, J. Appl. Phys. 62 (1987) 1800. [12] N. Matsunami, Y. Yamamura, Y. Itikawa et al., Energy dependence of the yields of ion-induced sputtering of monatomic solids, IPPJ-AM-32, 1983.