Growth of giant magnetoresistance multilayers: Effects of processing conditions during radio-frequency diode deposition W. Zou,a) H. N. G. Wadley, and X. W. Zhou Department of Materials Science and Engineering, University of Virginia, Charlottesville, Virginia 22903 S. Ghosal and R. Kosut SC Solutions, Santa Clara, California 95054 D. Brownell Nonvolatile Electronics, Inc., Eden Prairie, Minnesota 55344 共Received 8 February 2001; accepted 29 May 2001兲 The magnetotransport properties of giant magnetoresistance multilayers are significantly effected by the atomic-scale structure of the interfaces between the nonferromagnetic conducting and ferromagnetic 共FM兲 metal layers. The interfacial roughness and the extent of intermixing at these interfaces are both known to be important. A combination of experimental and multiscale modeling studies have been used to investigate control of interface structure during multilayer growth by rf diode deposition and the consequences of such control for magnetotransport. Experiments were conducted to evaluate the dependence of the magnetotransport properties of NiFeCo/CoFe/CuAgAu multilayers upon the growth conditions 共background pressure, input power兲, and to link the roughness of vapor-deposited copper layers to the same process parameters. These experimental studies reveal the existence of intermediate background pressure 共20 mTorr兲 and plasma power 共175 W兲 that resulted in the highest magnetoresistance and a strong sensitivity of copper layer surface roughness to both the power and pressure at which deposition was conducted. By using a combination of modeling technologies, the deposition process conditions have been linked to the atomic fluxes incident upon the sample surface. This was then used to determine the atomic-scale roughness of the film. Energetic metal atoms 共and inert gas ions兲 were found to have very strong effects upon interfacial structure. The models revealed an increase in interfacial roughness when metal 共or inert gas ion兲 translational energy was decreased by either reducing the plasma power and/or increasing the background pressure. Because high-energy metal impacts activated atomic jumping near the impact sites, high plasma power, low background pressure process conditions resulted in the smoothest interface films. However, these conditions were also conducive to more energetic Ar⫹ ion bombardment, which was shown by molecular dynamics modeling to induce mixing of the FM on the copper interface. Intermediate plasma powers/background pressures result in the most perfect interfaces and best magnetotransport. The insights gained by the modeling approach indicate a need to avoid any energetic ion bombardment during the early growth stages of each new layer. This could be accomplished by operating at low power and/or high pressure for the first few monolayers of each layer growth and may provide a growth strategy for further improvement in magnetotransport performance. © 2001 American Vacuum Society. 关DOI: 10.1116/1.1387051兴 I. INTRODUCTION Giant magnetoresistance 共GMR兲 metal multilayers consisting of alternating ferromagnetic and nonferromagnetic layers can exhibit large changes in their electrical resistance when a magnetic field is applied.1–10 Though the phenomenon was only discovered about 12 years ago, it has become the basis for a growing number of important technological applications. For example, multilayers based upon NiFeCo/ CoFe/CuAgAu/CoFe/NiFeCo are used for magnetic-field sensors,4,6 and related devices are being investigated for magnetic random access memories 共MRAM兲.8 GMR-based MRAM has many potentially attractive features, including nonvolatility, low-power consumption, and high access a兲 Electronic mail: [email protected] 2414 J. Vac. Sci. Technol. A 19„5…, SepÕOct 2001 speed. Both classes of applications have motivated interest in the design of economical vapor deposition processes that can produce thermally stable GMR devices with high GMR ratios 共defined as the maximum resistance change divided by the resistance at magnetic saturation兲 and low magnetic saturation fields. The best GMR multilayers appear to require the growth of metal multilayers with well-controlled interfaces.1–3,10–13 Interfacial roughness results in Néel coupling, electron scattering, and weakened antiferromagnetic coupling, which are all deleterious to the GMR properties.2,5 Interfacial 共chemical兲 mixing results in dead 共nonmagnetic兲 layers at the ferromagnetic 共FM兲–nonmagnetic metal spacer layer interfaces, reduced FM layer exchange coupling, and reduced GMR properties.2,5 0734-2101Õ2001Õ19„5…Õ2414Õ11Õ$18.00 ©2001 American Vacuum Society 2414 2415 Zou et al.: Growth of giant magnetoresistance multilayers 2415 FIG. 1. Schematic illustration of rf diode sputter deposition. The target’s plasma sheath potential accelerates positively charged working gas ions towards the target. The resulting energetic ion collisions with the target cause ejection of target atoms. These atoms undergo collisions with working gas atoms and they diffuse to the substrate where they condense. Some positive ions also impact the substrate because of a 共usually small兲 substrate sheath potential. Recent atomistic modeling studies have shown that interfacial structural imperfections are effected by the depositing vapor atom’s incident energy, the deposition rate, and the characteristics of other 共e.g., inert gas ion兲 fluxes incident upon the substrate.9–13 Since these are governed by the deposition process and process conditions, the magnetotransport properties are expected to depend upon the method and conditions used for device growth by vapor deposition.2,14–17 Here, we experimentally investigate the dependence of the magnetotransport properties upon the background pressure and input plasma power during the growth of a GMR sensor multilayer system. A simplified multiscale modeling approach is used to relate these conditions to the atomic fluxes incident upon the growth surface.9–12 Atomistic modeling is then used to investigate the atomic assembly mechanisms during film growth as a function of growth conditions. The dependence of interfacial roughness and mixing upon the growth conditions is identified and compared with ex- FIG. 2. Definitions of sheath and bias voltage in an asymmetric rf diode discharge. JVST A - Vacuum, Surfaces, and Films FIG. 3. GMR multilayer structure studied here. Layer compositions and thickness are shown. Arrows indicate the magnetic alignment of the ferromagnetic alloy layers. FIG. 4. Schematic diagram of the internal layout of the rf diode sputtering deposition chamber used to growth metal multilayers. 2416 Zou et al.: Growth of giant magnetoresistance multilayers 2416 FIG. 5. Dependence of deposition rate for the four targets, 共a兲 shows the effect of the background pressure at a fixed input power 共175 W兲, and 共b兲 shows the effect of the input power at a fixed background pressure. perimentally measured performance of the devices. The study supports the developing view that no existing vapor deposition technology is ideally suited to the growth of GMR multilayers. The modeling aided insights developed here are used to suggest alternative growth strategies for the growth of improved GMR materials. II. EXPERIMENTS The study here focused upon the influence of input plasma power and the background gas pressure on the GMR ratio and the saturation magnetic field of rf diode deposited GMR multilayers. A schematic diagram of a rf diode sputter deposition system with a plane parallel electrode geometry is shown in Fig. 1. An inert gas 共argon兲 plasma is initiated and maintained between the target and the substrate by the rf power source. In the rf discharge, electrons respond more rapidly to the changing electrical field and tend to flow from the plasma to adjacent conducting surfaces at a faster rate than the ions. Plasma potentials are, therefore, developed at both the target and the substrate. The positive working gas FIG. 6. Dependence of magnetotransport properties upon 共a兲 and 共b兲 the background pressure and 共c兲 and 共d兲 the input power for multilayers with a fixed CuAgAu layer thickness of 16 Å. J. Vac. Sci. Technol. A, Vol. 19, No. 5, SepÕOct 2001 2417 Zou et al.: Growth of giant magnetoresistance multilayers 2417 FIG. 7. Simplified flow chart for a multiscale simulation that links the reactor geometry and process conditions to the surface morphology and structure of a vapor deposited film. ions are accelerated across these sheath potentials to strike both the target and the substrate. The magnitude of the sheath potentials differs in an asymmetric discharge. The voltage drops across the sheaths are inversely related to the sheath capacitances, and thus the substrate and target areas. A bias voltage, therefore, exists, as shown in Fig. 2. As a consequence, one observes that the bombarding ion energy at the typically larger area substrate electrode is less than that at a smaller target electrode. The Ar⫹ ions accelerated across the target sheath bombard the target surface and result in sputtering of metal atoms from the target. These sputtered atoms are then transported to the substrate and deposited. The system geometry, the rf power applied to the plasma, and background pressure determine the energies and fluxes of the ions incident upon the target. These, together with the properties of the target, determine the energy, angular distribution, and flux of the atoms emitted from the target. Scattering of the sputtered metal atoms by working gas atoms during diffusional transport to the substrate modifies these quantities. The final energy and angular distributions of the metal atoms incident upon the substrate, therefore, depend on the target-tosubstrate distance, the working gas type, rf power, and background pressure. Working gas ions are also accelerated JVST A - Vacuum, Surfaces, and Films FIG. 8. Comparison of the plasma model predicted and the measured bias voltage as a function of 共a兲 the background pressure, and 共b兲 the input power. across the substrate sheath and strike the substrate with the energies in the 40–140 eV range.11,12 The energy and flux of both the metal and argon ions as they strike the substrate can have potentially important effects upon the resulting GMR properties.1–13 To evaluate the significance of these effects, GMR multilayers were grown at Nonvolatile Electronics, Inc., 共NVE兲 共Eden Prairie, MN兲. The architecture and composition of the antiferromagnetic coupled multilayers are shown in Fig. 3. A Randex model 2400-6J rf diode system was used to deposit the metal films. Figure 4 shows the internal layout of the rf diode sputtering deposition chamber. The diameter of the targets was 20.32 cm, and the distance between substrate and target was 3.81 cm. Four different composition targets were installed in the chamber. 4-in.-diam silicon wafers were used for the substrates. An amorphous 2000 Å Si3N4 film was grown on top of each wafer using a chemical-vapor- 2418 Zou et al.: Growth of giant magnetoresistance multilayers 2418 FIG. 9. Plasma model results. Effect of pressure upon 共a兲 the argon ion current density, and 共b兲 the ion energy. Effect of power upon 共c兲 the argon ion current density, and 共d兲 the ion energy. Results are shown for just above both the sputtering target and the substrate surface. deposition method. The Si3N4 film acted as an electrically insulating and diffusion inhibiting layer between the silicon wafer and the subsequently deposited metal film. The rms roughness of the Si3N4 film was 1.5 Å. The deposition rate and composition for each target under the different deposition conditions had been measured previously and are shown in Fig. 5. A 40 Å Ta seed layer was deposited at 20 mTorr and 175 W on the substrate prior to the start of multilayer growth 共deposition rate was 104.5 Å/min兲. Over most of the pressure range studied, the deposition rate decreased slightly with background pressure, Fig. 5共a兲. The deposition rate increased with input power. Figure 5共b兲 shows that the variation was almost linear. The layer thicknesses were, therefore, controlled by timing the deposition. The substrate was then moved under each target to deposit a multilayer structure. Figure 6 shows the dependence of the measured GMR ratio and saturation magnetic field (H 90) upon the background pressure and input power. The maximum GMR ratio was achieved at an intermediate background pressure 共20 mTorr兲 and input power 共175 W兲. The saturation magnetic field (H 90) of this condition 共20 mTorr and 175 W兲 was also moderate and reasonably well suited for magnetic sensing applications. been used to explore the origin of the relationships between the experimental observations and growth conditions. The details of the approach are described in Refs. 11, 12, and 13. A CFD analysis of the reactor yielded the velocity and pressure distribution of the argon working gas flow in the sputtering chamber and, in particular, between the target and the substrate. A one-dimensional plasma model was used to deduce the bias voltage, the argon ion energy, and flux incident upon both the target and the substrate.11,12,16 Results of a three-dimensional 共3D兲 MD analysis of sputtering18–21 were used to quantify the yield, the energy, and the angular distributions of the copper atoms sputtered from the target by argon ion impact. A DSMC atom transport model was then used to track 共by analyzing binary collisions between the metal and the background gas atoms兲 the propagation of metal atoms from the target to the substrate. This enabled calculation of their incident energy and angle as a function of working gas pressure, spacing, temperature, and the plasma power.15,17 The outputs of these transport calculations were finally used as inputs in a two-dimensional 共2D兲 KMC model recently developed to simulate the atomic assembly 共and thus structure兲 of a film as a function of the process conditions.22–26 III. MULTISCALE MODELING IV. SIMULATION RESULTS A multiscale modeling approach, Fig. 7, has been used to investigate the origin of the GMR dependence upon process conditions and to investigate deposition strategies for interface morphology control.11–13 A combination of computational fluid dynamics 共CFD兲, plasma dynamics, molecular dynamics 共MD兲, direct simulation Monte Carlo 共DSMC兲 vapor transport, and kinetic Monte Carlo 共KMC兲 models has Figure 8 shows a comparison between the measured and plasma model simulated bias voltage 共i.e., the magnitude of the difference between the two sheath voltages兲, as a function of the background pressure and input power during deposition of copper film. Good agreement between the simulations and the experimental measurements performed with the NVE rf diode sputtering chamber was obtained. J. Vac. Sci. Technol. A, Vol. 19, No. 5, SepÕOct 2001 2419 Zou et al.: Growth of giant magnetoresistance multilayers FIG. 10. Model predicted average energy of copper atoms and argon ions incident upon the substrate. 共a兲 shows the effect of background pressure at a fixed input power 共175 W兲, and 共b兲 shows the effect of input power at a fixed background pressure of 20 mTorr. Figures 9共a兲 and 9共b兲 show the pressure dependence of the Ar⫹ ion current densities 共or ion flux兲 and the ion energy at both electrodes computed using the plasma model. The energy and ion flux at the target are seen to be about a factor of 10 higher than those at the substrate. Even so, significant ion fluxes with energies in the 50–100 eV range impact the substrate under the conditions used to grow the GMR films. The energy of the ions at both electrodes decreased sharply with pressure. However, the Ar⫹ ions fluxes at both electrodes are seen to rise slightly as the pressure increased from 10 to 50 mTorr. The reason for the decrease in ion energy with pressure resulted from more collisions between ions and working gas across the target sheath. The collision frequency also increased with the pressure, and therefore, the probability of argon gas ionization ratio also increased. Figures 9共c兲 and 9共d兲 show that increasing the input power also significantly increases the Ar⫹ ion current density 共flux兲 and energy. The energy of the Ar⫹ ion was governed by the voltage at the sheath, which is proportional to the input power. The results also show that the energy of the Ar⫹ ions at the substrate was JVST A - Vacuum, Surfaces, and Films 2419 much smaller than the Ar⫹ ion energy at the target. The ion flux increased 2.5 times as the power was increased from 50 to 350 W. Typically, the ion flux impacting the substrate was about a tenth of that impacting the target. A DSMC transport model was used to track the paths of representative sputtered atoms of specified energy and emission direction as they propagated through the background gas. This enabled the likehood that an atom reached the substrate to be determined together with atoms incident energy and the incident angle. More than 10 000 atoms were analyzed to obtain statistical representations of these data. The sputtered atom average energy was then deduced at a fixed distance 共3.81 cm兲 from the target for different chamber pressures and input powers. The energy of sputtered copper atoms after propagating from the target to substrate are shown in Fig. 10, together with that for the Ar⫹ ion. The gas pressure controlled the frequency of argon atom collisions with sputtered atoms as they traveled from the target to the substrate. The number of collisions was proportional to the pressure, since these collisions transfer energy from hot copper atoms to the thermalized argon gas. This leads to a reduction in both copper atom kinetic energy and deposition efficiency as the gas pressure increases, Fig. 10共a兲. It is also noted that the Ar ion flux incident upon the substrate also has an incident energy that drops sharply with background pressure. The power dependence of the copper atom and Ar⫹ ion energies are shown in Fig. 10共b兲. The copper atoms’ energy rose weakly with power because of the rise of the emitted atom energy with power was overcome by energy transfer to the working gas during transport to the substrate. The metal flux, its energy, and incident angle distributions were used as inputs in a 2D KMC model to predict surface morphology of copper film, see Figs. 11 and 12.22–25 The KMC model implements hot atom effects 共reflection, resputtering, bias, and athermal diffusion兲 deduced from MD calculations and is described in Ref. 22–25. The KMC analysis reveals that the roughness of copper films increased as the plasma power was decreased and/or the background pressure was increased and was corroborated by atomic-force microscopy images of copper films. To compare trends, we normalized the experimental and simulated data by dividing by the first data point of each data set. Figure 13 shows that the normalized roughness deduced from experiments and by simulation had a similar dependence upon the power and pressure used during deposition. The modeling of copper deposition indicates that under the conditions that led to a maximum GMR ratio 共20 mTorr/ 175 W兲, the copper atoms were effectively thermalized. Thermally activated atom hopping was the principle mechanism of film growth when the power was low and/or the pressure was high. The initial rise in the GMR ratio with power is in part a result of the surface smoothing associated with more energetic metal atom impacts. The drop in GMR as the pressure is increased beyond 20 mTorr also is linked to a reduction in surface mobility as metal atom energy decreases. However, the occurrence of a peak followed by a reduction in the GMR ratio by further increasing the plasma 2420 Zou et al.: Growth of giant magnetoresistance multilayers 2420 FIG. 11. Comparison of simulated and atomic-force microscopy results for copper surface roughness for different input power values at a fixed background pressure of 20 mTorr. Also shown are the deposition rate, average copper atom energy, and substrate temperature. These values were used in the KMC simulation shown on the left. power cannot be explained by a metal impact energy mechanism. The most likely cause for the reduction in the GMR ratio appears to be related to changes in the Ar⫹ ion flux and impact energy at the substrate. A 3D MD model was used to explore the effect of Ar⫹ ion impacts with a model interface as a function of the ion J. Vac. Sci. Technol. A, Vol. 19, No. 5, SepÕOct 2001 energy 共and, therefore, process conditions兲. Details of the method can be found in Refs. 18–21. The model geometry is shown in part 共a兲 of Fig. 14. The light and dark balls in the Fig. 14 represent copper and cobalt atoms, respectively. The substrate is copper, which contains 120 共224兲 planes in the y direction, 12 共111兲 planes in the z direction, and 52 共220兲 2421 Zou et al.: Growth of giant magnetoresistance multilayers 2421 FIG. 12. Comparison of simulated and atomic-force microscopy results for copper surface roughness for different background pressure values at a fixed input power of 175 W. Also shown are the deposition rate, average copper atom energy, and substrate temperature. These values were used in the KMC simulation shown on the left. planes in the x direction. An array of cobalt pyramids was constructed on the copper surface to simulate cobalt island nucleation. To minimize the effects of the small crystal size, periodic boundary conditions were used. A fixed boundary condition was applied to the lowest monolayer of atoms to avoid translation. The temperature of the three layers above JVST A - Vacuum, Surfaces, and Films this fixed layer was kept at a fixed substrate temperature of 300 K using a thermostat algorithm. 150 Ar⫹ ions then bombarded the surface at a normal incident angle. Figure 14 shows that this resulted in significant smoothing and intermixing of the copper and cobalt by an exchange mechanism analogous to that described in Ref. 20. The modeled depen- 2422 Zou et al.: Growth of giant magnetoresistance multilayers 2422 FIG. 14. Simulated surface morphology following 150 argon ion impacts. The initial configuration 共a兲 consisted of cobalt atom clusters on a perfect 关111兴 copper crystal. Ion impacts results in smoothing of the clusters and alloying 共intermixing兲 by an exchange mechanism. The extent of both the smoothing and intermixing depends upon the energy of the argon ions, which is governed by process conditions. The energy values were deduced from the plasma model. FIG. 13. Normalized roughness as a function of 共a兲 background pressure, and 共b兲 input power. dence of intermixing upon the input power and the background pressure is shown in Fig. 15. The results indicate that significant intermixing 共alloying兲 of cobalt atoms in the copper occurs, and that it increased with increasing ion impact energy, which in turn depended upon the process power/ pressure. As a consequence, the intermixing fraction decreased with increasing background pressure and/or decreasing input power. Intermixing results in a dead magnetic layer at the nonmagnetic and ferromagnetic interface, which can contribute to a reduction in GMR properties.2 By combining the simulations of roughening and intermixing, Fig. 16, it can be seen that the existence of a GMR ratio maximum 共at 175 W/20 mTorr兲 results from the competing effects of increased adatom surface mobility induced flatting and ion impact induced intermixing as either the power increase or pressure decrease. The latter dominates at high power/low pressure and results in a loss in GMR ratio. Likewise, the former is promoted by high power and low pressure. The highest GMR ratio was obtained under conditions when some energetic adatom 共and ion兲 smoothing occurred with minimal intermixing. Simulations of metal deposition 共with no Ar⫹ ion bombardment兲 have suggested processes that reduce both the inJ. Vac. Sci. Technol. A, Vol. 19, No. 5, SepÕOct 2001 terfacial roughness and the chemical intermixing, which has led to a proposed energy modulated deposition technology.18,19,20 During an energy modulated method, low incident metal atom energies are used to deposit the first few monolayers of each new metal layer and higher energies are used for the reminder of the layer. This strategy was found to result in an optimal combination of interfacial roughness and interfacial mixing. In rf diode sputtering, a modulated Ar⫹ ion energy deposition could be implemented by using low power and/or high pressure 共low Ar⫹ ion energy兲 growth for several angstroms of each metal layer 共with reduced intermixing兲 and using high power and/or lower pressure 共high Ar⫹ ion energy兲 for growth of the remaining layer 共with smooth interface兲. Such a modulated plasma power and/or pressure strategy may significantly improve the performance of giant magnetoresistive multilayers grown by rf diode sputter deposition. V. SUMMARY Multilayers grown by rf diode deposition are found to exhibit a maximum GMR ratio when grown at intermediate pressure and plasma power 共175 W/20 mTorr兲. This is thought to be linked to the interface structure of the CoFe on CuAgAu interface. A combination of surface characterization and modeling methods has been used to analyze the rf 2423 Zou et al.: Growth of giant magnetoresistance multilayers FIG. 15. Simulation predicted intermixing as a function of 共a兲 the background pressure, and 共b兲 the input power. 2423 FIG. 16. Best compromise that results in least surface roughness, and interface mixing corresponds to the pressure and power conditions that result in the highest GMR ratio 关see Figs. 6共a兲 and 6共c兲兴. ACKNOWLEDGMENTS diode deposition of metal multilayers. As the pressure is decreased or the power increases from the optimum 共20 mTorr/ 175 W兲, measurements of the copper layer deposition and calculations indicate a rise in the copper atom’s impact energy, which induces significant copper surface flattening. This is also accompanied by a sharp rise in the impact energy of Ar⫹ ions, which also contribute to smoothing. MD calculations show that their impact also causes alloying of the cobalt on the copper interface 共by an impact exchange process兲. This mixing becomes more severe as the impact energy increases. An optimal combination of smoothing and mixing is achieved at intermediate background pressure and plasma power. Since mixing is more difficult after several monolayers of CoFe have been deposited, the use of low power to deposit the 50% of the CoFe on Cu layer followed by higher power for its completion may result in improved GMR devices. JVST A - Vacuum, Surfaces, and Films The authors are grateful to the Defense Advanced Research Projects Agency 共A. Tsao and S. Wolf, Program Managers兲 and the National Aeronautics and Space Administration for support of this work through NASA Grants Nos. NAGW1692 and NAG-1-1964. We greatly appreciated help form J. F. Groves and Y. G. Yang of the University of Virginia and S. Subhas and Jon Ebert of SC Solutions 共Santa Clare, CA兲, and D. Wang of Nonvolatile Electronics, Inc. 共Eden Prairie, MN兲. P. M. Levy, J. Magn. Magn. Mater. 140-144, 485 共1995兲. J. C. S. Kools, J. Appl. Phys. 77, 2993 共1995兲. 3 W. H. Butler, X. G. Zhang, D. M. C. Nicholson, and J. M. MacLaren, Phys. Rev. B 52, 13399 共1995兲. 4 J. Daughton, J. Brown, E. Chen, R. Beech, A. Pohm, and W. Kude, IEEE Trans. Magn. 30, 4608 共1994兲. 5 U. Hartmann, Magnetic Multilayers and Giant Magnetoresistance 共Springer, New York, 1999兲. 1 2 2424 Zou et al.: Growth of giant magnetoresistance multilayers 6 J. Daughton and J. Brown, in Conference Information: Proceedings Sensors Expo Boston, Boston, MA 共Helmers Publishing, 1995, Peterborough, NH, 1995兲, Vol. 16-18, pp. 97–105. 7 G. Binasch, P. Grunberg, F. Saurenbach, and W. Zinn, Phys. Rev. B 39, 4828 共1989兲. 8 G. A. Prinz, Science 282, 1660 共1998兲. 9 E. E. Fullerton et al., Phys. Rev. Lett. 68, 859 共1992兲. 10 S. Honda et al., J. Magn. Magn. Mater. 126, 419 共1993兲. 11 S. Desa, S. Ghosal, R. L. Kosut, J. L. Ebert, T. E. Abrahamson, A. Kozak, W. Zou, X. W. Zhou, J. F. Groves, and H. N. G. Wadley, J. Vac. Sci. Technol. A 17, 1926 共1999兲. 12 S. Deas, S. Ghosal, R. L. Kosut, J. L. Ebert, A. Kozak, T. E. Abrahamson, W. Zou, X. W. Zhou, J. F. Grovers, Y. G. Yang, and H. N. G. Wadley. Thin Solid Films 共submitted兲. 13 W. Zou, Master Thesis, University of Virginia 共1999兲. 14 H. Schlichting, Boundary-Layer Theory, 7th ed. 共McGraw-Hill, New York, 1979兲. 15 J. F. Groves, Ph.D. dissertation, University of Virginia 共1998兲. J. Vac. Sci. Technol. A, Vol. 19, No. 5, SepÕOct 2001 2424 16 M. A. Lieberman and A. L. Lichtenberg, Principles of Plasma Discharges and Materials Processing 共Wiley, New York, 1994兲. 17 G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows 共Clarendon, New York, 1994兲. 18 X. W. Zhou, S. Subha, and H. N. G. Wadley 共unpublished兲. 19 X. W. Zhou and H. N. G. Wadley, J. Appl. Phys. 84, 2301 共1998兲. 20 X. W. Zhou and H. N. G. Wadley, J. Appl. Phys. 87, 553 共2000兲. 21 R. E. Johnson, in Energetic Charged-Particle Interactions with Atmospheres and Surfaces, Physics and Chemistry in Space Planetology, edited by L. J. Lanzerotti, M. Hill, and D. Stoffler 共Springer, Berlin, 1990兲, Vol. 19, p. 68. 22 Y. G. Yang, R. A. Johnson, and H. N. G. Wadley, Acta Mater. 45, 1455 共1997兲. 23 Y. G. Yang and H. N. G. Wadley, Acta Mater. 共submitted兲. 24 X. W. Zhou and H. N. G. Wadley, Surf. Sci. 431, 42 共1999兲. 25 X. W. Zhou and H. N. G. Wadley, Surf. Sci. 431, 58 共1999兲. 26 X. W. Zhou, R. A. Johnson, and H. N. G. Wadley, Acta Mater. 45, 1513 共1997兲.
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