Generation and applications of compressive stress induced by low energy ion beam bombardment D. R. McKenzie Department of Applied Physics, School of Physics, University of Sydney, New South Wales 2006, Australia (Received 30 September 1992; accepted 1 March 1993) Compressive stress is a widespread phenomenon in films subjected to ion beam bombardment. A thermodynamic treatment of materials under a general stress is used to show that preferred orientation will occur as a result of free energy minimization in a biaxial stress field. The equilibrium between structural phases of materials is also affected by stress. Thermodynamics is used to calculate the equilibrium between graphite and diamond under biaxial stress. Recent molecular dynamics studies of the mechanism of compressive stress generation are reviewed in which the phenomena of focused collision sequences and thermal spikes are studied. Experimental work shows compressive stress is linked to preferred orientation in hexagonal boron nitride films and to stabilization of high pressure phases such as cubic BN and tetrahedral amorphous carbon films, in agreement with the thermodynamic analysis. I. INTRODUCTION Compressive stress has been observed in a wide variety of thin film materials, including both metals and dielec-trics. There is general agreement that intrinsic compressive stress, that is stress not caused by differential thermal ex-pansion between substrate and film, is caused by energetic bombardment during the growth of films.I-3 Excessive compressive stress often leads to adhesion failure and therefore is often considered an undesirable property of a thin film. Many applications demand good adhesion, espe-cially those for wear resistant and protective coatings. In spite of this, mild compressive stress has desirable features relating to densification and the technique of ion assisted deposition (lAD) has been developed to exploit some of these. In this article some of the less well-known useful aspects of high compressive stress will be explored including the application to the production of high pressure phases of materials, and of preferred orientation in films. Recent work on the understanding of mechanisms for compressive stress production by ion impacts will also be described. Theories of the microscopic origin of compressive stress began with the idea of \"atomic peening,,4,5 in which atoms are incorporated with a higher density than would other-wise be the case by the impact of energetic species driving them into the film interior. Experimental work6,7 has shown that for energies less than I keY, the compressive stress depends on the rate of momentum transfer to the growing surface, other parameters being constant. Theo-retical treatments8 using the linear cascade theory of for-ward sputtering of Sigmund9 have been able to reproduce this result. More recently, it has become clear that there are limits to the level of compressive stress achievable in a given thin film material. A number of experimental observations has been made which show that as the energy of bombardment increases. the compressive stress initially increases, passes through a maximum and then shows a steady decrease. 10...12 This effect has been ascribed to the relieving of stress by 1928 J. Vac. Sci. Technol. B 11(5), Sep/Oct 1993 very energetic impacts which overcomes the stress genera-tion effect.1I Recently, stress annealing has been incorpo-rated into a simple theoretical modell3 which provides a reasonable fit to experimental data of stress as a function of energy and shows the development of a maximum in com-pressive stress. The presence of compressive stress in a growing film results in the condensation of vapor into a solid under conditions which may be far removed from ambient pres-sure and temperature. The compressive stress in a thin film is actually a biaxial stress field, or approximately so, devel-oped by the forces applied by the substrate onto the film at its edges. There is no force on the film in the direction normal to the substrate. Even though the energetic pro-cesses of impact themselves are essentially nonequilibrium processes, the impact energy spreads through the film and for all but the atoms directly involved in a collision pro-cess, an approximate state of equilibrium under a biaxial stress tensor ail and temperature T exists. A growth zone of a film can be defined as the layer which interacts with incoming species or the energy that accompanies them suf-ficiently so that atomic reorganization can occur. The structure developed therefore should reflect the stress and temperature state in the growth zone. This discussion of compressive stress will commence with a thermodynamic analysis for nonhydrostatic stress. This is followed by a summary of molecular dynamics sim-ulations of ion impact phenomena. Finally, a case study of compressive stress in boron nitride is presented. A. Thermodynamics of non hydrostatic stresses in solids Some thermodynamic considerations relating to the growth of films under biaxial compressive stress are dis-cussed in this section. The Gibbs free energy function G is the quantity which determines the relative stability of var-ious phases of a material. The phase with the lowest value of G at a given (uij,T) is the stable phase under those conditions. The phase boundary line between two phases is ©1993 American Vacuum SOCiety 1928 0734-211X/93/11(5)/1928/8/S1.00 1930 D. R. McKenzie: Generation and applications of compressive stress 1930 ite sample with c in the stress plane relative to the shape of the sample at zero stress and temperature To. The strain at zero stress points at other temperatures is obtained using thermal expansion data for graphite. The strain at finite stress is obtained using the compliances of graphite Sjjkl and their temperature and stress dependences. The strain of the diamond phase must be obtained relative to the standard graphite sample at To by assuming a particular route for the transformation at To. The result obtained for the strain will be dependent on this assumed route. We will assume a route in which graphite transforms to the rhom-bohedral form without change of shape by translation of every third layer of graphite by a small amount. The rhom-bohedral form of graphite then transforms to diamond sim-ply by forcing the layers together so that graphite layers are rumpled into sl bonded sheets covalently bonded.19 The c axis of graphite then becomes the (111) direction of diamond. The strain occurring in rhombohedral graphite upon transformation to diamond is of the form (9) The volume strain is -(28+y). Here we will restrict the analysis to a comparison of the biaxial and hydrostatic stress levels at the equilibrium line at one temperature, To. For a hydrostatic stress field, the Gibbs function for graphite is Gg( To,a,,) =Gg( Tom -~ (2Sa) +sW)ai, (10) where the compliances S~p are those of graphite. In this simplified analysis, we will assume the compliances are constant. This is a good approximation for diamond, and for graphite, it does not introduce gross errors. The Gibbs function for diamond is Gd( To,a,,) =Gd( To,O) -(28+y)a,,-i si1)~· (11) The difference between the Gibbs functions of Eqs. (10) and (11) is 6.G( To,a,,) =6.G( Tom + (28+y)ah -~ (-3s\\1) +2S\\f)+SW)ai· (12) For a biaxial stress field, the corresponding result is 6.G( To ,ab) = 6.G( Tom + (28+y)ab -i (-2s11)+s\\r+sw)ai· (13) Using the quantities given in Table I, the stresses to achieve a zero result in Eqs. (12) and (13) may be evaluated. These are the stresses ah and ab required to achieve equi-librium between graphite and diamond. The results, also given in Table I, show that the value for ah is close to the value of 1.6 GPa obtained by Berman and Simon. 17 For the biaxial stress case, the larger value of 1.7 GPa is required. This value, although larger, is not as large as the 2.4 GPa given by the neglect of the shear stress component of the biaxial stress. J. Yac. Sci. Techno!. B, Yol. 11, No.5, Sep/Oct 1993 II. MOLECULAR DYNAMICS STUDIES OF COMPRESSIVE STRESS GENERATION Thermodynamics can tell us nothing about the mecha-nisms leading to compressive stress, merely the response of materials to a stress imposed on them. To shed light on the role of energetic bombardments in creating compressive stress, it is necessary to examine the processes with ex-tremely fine resolution in time and space. Direct experi-mental investigations with simultaneously a time resolu-tion of better than a picosecond and a spatial resolution at the atomic level are beyond reach at present. If the inter-actions can be modeled in a computer with sufficient accu-racy, however, molecular dynamics approaches are capable of yielding a wealth of new insights. Here I will review some recent work on both two-and three-dimensional (20 and 3D, respectively) model systems using molecular dy-namics. A. 20 studies of a metal One of the principal motivations for the study of Marks and co-workers2o was the desire to know more about so-called thermal \"spikes.\" A working definition of a thermal spike is a region around the impact site which has more or less random thermal motion greatly above the equilibrium lattice value, but localized in space and time. The advan-tage of 20 studies is that for a manageable number of atoms, the system boundaries can be made sufficiently re-mote that phenomena occurring under the impact site can be followed for usefully long distances and for usefully long times after the event. A simulation of nickel containing 5000 atoms in a \"two-dimensional\" array has revealed some surprising new information. Figure I shows the de-velopment of the subsurface phenomena. There are four principal ways in which the primary energy is dissipated after impact. These are discussed in turn. B. Focused collision sequences The idea of a focused collision sequence has quite a long history, beginning with the proposal of Silsbee21 that en-ergy can be directed along close packed directions by self-focusing of momentum. The process was originally pro-posed to explain the spot patterns produced when single crystals are sputtered. Figure I shows that energy is indeed propagated along the close packed directions underneath the impact site. The energy packet, termed a \"focuson,\" is concentrated at the front of the collision sequence and travels at supersonic velocities. The very high velocity re-sults from the fact that the amplitude of displacement is large, so that the repulsive cores of the atomic potentials are brought into contact. C. Sound generation by focused COllision sequences As for other supersonic projectiles, the focuson gener-ates a cone of normal sound. This cone acts as the principal energy loss mechanism for the focuson. Another important loss mechanism is the retaining of energy by all atoms taking part in the collision sequence. The focuson is even-tually dissipated as a normal sound wave once its velocity becomes comparable with the sound velocity. 1933 D. R. McKenzie: Generation and applications of compressive stress 1933 FIG. 5. An electron micrograph of a hexagonal BN film under an average compressive stress of 4 GPa on a silicon substrate. viewed in cross section. The inset shows the diffraction pattern from the film. showing preferred orientation with the (0001) spots parallel to the substrate. mal to the substrate surface. This orientation is consistent with the thermodynamic analysis which requires the most compressible direction to lie in the stress plane. When viewed from the direction normal to the sub-strate, the preferred orientation is seen in electron micro-scope images A as a strong fringe pattern with the character-istic 3.3 spacing of the layers. The directions of the sheets show no preferred orientation in this projection. This again is consistent with the thermodynamic analysis. J. Vac. Sci. Technol. B, Vol. 11, No.5, Sep/Oct 1993 D. Formation of high pressure phases The effectiveness of biaxial stress in stabilizing high pressure phases is well illustrated by the carbon and boron nitride systems. 1. Carbon films Pure carbon films may be deposited using energetic dep-osition. Techniques such as vacuum arc deposition 16 and laser ablation27 produce high fluxes of highly ionized plas-mas. Sputtering also produces some energetic neutrals which produce effects in the coating.28 The vacuum arc technique will be discussed here as an example. In the case of a carbon vacuum arc, the natural beam energy has a value of 22 eV.29 In order to remove macro-scopic graphite from the cathodic arc source operating in vacuum, a curved magnetic solenoid is often used.3O The filtered beam is essentially all energetic ions and electrons and its energy of impact may be modified by the use of substrate bias. The use of electron energy loss and diffrac-tion techniques has shown that amorphous films with a high degree of tetrahedral bonding (approaching 90% in ideal conditions) are produced when the ion energy lies in the range 20-200 eV.ll This energy range corresponds to the development of high compressive stress. For all films deposited under a variety of substrate temperatures and biases, a high degree oftetrahedral bonding is found when-ever the stress exceeds a well defined value. This value agrees reasonably well with the stress found for the equi-librium phase boundary between graphite and diamond in Sec. II. Because of the nonuniformity of stress with distance from the substrate, a film with an average value of stress equal to a threshold value may in fact have a large fraction of its thickness below the threshold. It will therefore be necessary for average stress to exceed the threshold by a significant amount in order to ensure that a large fraction of the film volume has a stress greater than the threshold. An important parameter, the temperature of the growth zone, is not easy to determine experimentally. The thermo-dynamic theory predicts a rise with temperature in the level of stress necessary to achieve tetrahedral bonding since the diamond/graphite equilibrium line bas a positive slope in the stress-temperature plane (see Fig. 6). The most important parameters affecting the growth zone tem-perature are the substrate temperature, the thermal con-ductivity, and the power input from the vapor source. Sub-strate temperature has been shown to have a strong effect, as at high temperatures a glassy carbon film is produced rather than the tetrahedral material 31 at the same stress value.On the other hand, very low substrate tempera-tures enable sputtering to produce tetrahedral material rather than the si bonded amorphous carbon that is pro-duced on room-temperature substrates.28 The thermodynamic treatment is not able to deal with the time dependent effects in film growth. The growth zone is more or less rapidly chilled to the substrate temperature, and this time dependence will be important in determining the degree of order produced in the deposited film. The tetrahedral structure has a relatively small difference in 1934 D. R. McKenzie: Generation and applications of compressive stress 1934 (\"uhit\" Boron ~itridt· • Bt.'rman and I..;imoll r~ll(ulalillli IIc'\\\"goll:1I BortHI 'itride 10011 15110 zooo 15011 I'emllt>fillure (K) FIG. 6. The phase diagram of boron nitride in the pressure-temperature plane. Shown is the region in which cubic BN is formed in the presence of catalysts [from Bundy ;Jnd Wentorf (Ref. 32)J. and the boundary line between graphite and diamond calculated by Berman and Simon (Ref. 17). free energy between its amorphous and crystalline forms, so that the material will be able to produce a low free energy state under high stress conditions by forming a dense tetrahedral structure with disorder. An attempt to incorporate the time scale into the phase diagram has been made31 and is reproduced in Fig. 7 for carbon films grown by vacuum arc. The most important effect is the spreading, at low substrate temperatures, of the phase boundary line into a transition zone with a variable ratio of sl to sl bonding. At high substrate temperatures the growth zone remains sufficiently hot, even after chilling, to enable or-dering to take place and the boundary becomes sharp. 2. Boron nitride films Boron nitride has a graphitelike phase (hexagonal bo-ron nitride, h·BN) and a diamondlike phase (cubic boron nitride, c-BN) which are analogous to the carbon equiva-lents. The analogy with carbon is clearly seen in Fig. 6 showing the graphite/diamond equilibrium line drawn on C,Ia,,:--y Carhon TC'l1ll'CCalurc I K I FIG. 7. A schematic phase diagram for carbon films rapidly cooled to a well-defined temperature (horizontal axis) under a hydrostatic pressure (vertical axis) (from Ref. 31). J. Vac. Sci. Techno!. B, Vol. 11, No.5, Sep/Oct 1993 100 Z • III 80 u I -0) CI> 60 • • • • • • • ~ • CI> c: U ... 40 Q. CI> • 20 • • o 2 4 6 8 10 12 Compressive Stress (GPa) FIG. 8. The percentage of c-BN in films prepared by reactive ion plating as a function of the average compressive stress in the film. There is a rapid increase in the c-BN content at a threshold compressive stress. Repro· duced from Ref. 26. the phase diagram of BN deduced from work on high pres-sure high temperature synthesis.32 In this section, the evi-dence for formation of the cubic form by biaxial compres-sive stress will be reviewed. Ion plating has been successfully used to synthesize c_BN.33 The method is ideal for forming coatings under compressive stress as it allows for variation of the incident ion energy by varying the substrate bias. Boron is evapo-rated from an e-gun into an argon/nitrogen gas mixture with a secondary plasma used to create ionization. The switching over from h-BN to c-BN at a threshold compressive stress is shown in data from Ref. 26 shown in Fig. 8, The percentage of c-BN was determined by the infrared absorption intensity of the characteristic absorp-tion line at 1050 cm -I. The existence of a sharp threshold stress for c-BN formation is a convincing demonstration of the predictive value of the model. The threshold stress oc-curs in both c-BN and tetrahedral amorphous carbon at -3 G Pa. This is rather higher than the predicted 1. 7 G Pa, and probably reflects the need to achieve an average stress significantly over the threshold in order to give a large fraction of the film under sufficient stress to induce the high pressure phase throughout the film. The hardness of the films below and above the threshold was determined by ultralow load indentation testing, the results of which are shown in Fig. 9. There is a large dif-ference in the hardness of a h-BN film prepared under moderate stress and a c-BN film prepared under high stress conditions. IV. CONCLUSIONS The ability of compressive stress to produce preferred orientations and to stabilize high pressure phases of mate-rials gives a valuable tool to the thin film technologist for creating thin films with special properties.