METHOD AND SIMULATOR FOR SIMULATING THE DEVELOPMENT OF RESIDUAL STRESS IN IAPVD FILMS

Abstract: A method running on a computer for simulating the development of residual stress in the growth of IAPVD films using finite element analysis, comprising the stages of simulating the development of strain associated with the condensation of an nth layer of the film, simulating the development of strain associated with the ion bombardment of the set of layers of the film from the nth to the (n-x)th layer, and alternating the above two steps for n=x to n=N, where N is the number of layers in the film and x<<N. The residual stress is calculated based on the levels of strain generated in the above process steps.

Description: METHOD AND SIMULATOR FOR SIMULATING THE DEVELOPMENT OF RESIDUAL STRESS IN IAPVD FILMS The present invention relates to the simulation of the development of residual stress in Ion Assisted Physical Vapour Deposited (IAPVD) films, in order to facilitate the design of new IAPDV films with a low or a desired predetermined residual stress field. IAPVD films belong to the family of films deposited by condensation. Purely condensed films tend to be highly porous and the adhesion of such films to the substrate on which they are grown tends to be poor. In the growth of an IAPVD film, as the film is grown by a process of condensation, the growing film is simultaneously bombarded with ions of inert gas, for example Argon at energies of around 20eV to 1keV. The films produced by IAPVD are close to fully dense and adhere more strongly to the substrate on which they are grown. Also, by using IAPVD, to a certain extent the structure of the resulting film can be controlled. Because of their high density and good adhesion, IAPVD films have a wide range of applications including use as wear protection and anti- corrosion layers and in electronic semiconductors. IAPVD films typically have a high level of residual stress. This residual stress comprises two components, thermal stress which forms as the IAPVD layer cools to room temperature after the deposition process is completed, and an intrinsic stress which is caused by the process of deposition. Previous experimental work has shown that the residual stress in an IAPVD film is related to parameters of the deposition process, such as incident ion and atom fluxes and energies. The recognised source of residual stress is that it arises from defects created in the coating during condensation and ion bombardment. These defects cause local lattice distortion which results in macroscopic strain in the coating. Purely condensed coatings tend to have a tensile strain roughly equal to tensile yield for that material arising from the attraction of neighbouring atoms over vacancy defects. IAPVD coatings can have a compressive residual stress caused by the inclusion of interstitial defects of either inert gas or knock-on implanted coating atoms. These interstitials again individually cause local lattice distortion and result in macroscopic strain in the coating. Thus, IAPVD films, unless annealed, have an inherent high level of residual stress which can lead to poor adhesion to the substrate and to failure of the coating during its lifetime. In particular, the residual stress in IAPVD films tends to cause the film to curl away from the substrate on which it is grown. Therefore, it is desirable to understand the nature of this residual stress and its relationship with the deposition parameters used in the growth of an IAPVD film to facilitate the design of growth processes to generate IAPVD films with acceptably low residual stress fields and/or desired predetermined residual stress fields. Recent studies into the molecular dynamics of IAPVD films indicate that trapped inert gas species, used in the ion bombardment play a major role in the mechanism for the creation of intrinsic stress in an IAPVD film. However, molecular dynamics analyses the growth of an IAPVD layer on a molecular level, is computationally expensive and cannot easily be extrapolated to analyse the macro-molecular levels of residual stress in an IAPVD film which cause the problems referred to above. Therefore, when a new IAPVD film is to be designed for a particular application and from particular materials, it is necessary to experiment with IAPVD growth process parameters in order to produced the new IAPVD film with an acceptably low residual stress. This experimental process can be time consuming as many IAPVD films have to grown and tested in order to establish the required process parameters. An attempt has been made to model the compressive components of residual stress in an IAPVD coating. In his book "Thin Solid Films" at page 226, CA. Davis presents an analytical model which assumes that compressive stress is caused by knock-on implantation of coating atoms. This process can be described by linear cascade theory. However, the Davis model relies on interstitial coating atoms causing the compressive stress in IAPVD coatings, which would mean that deposited coatings should be over dense, which has not been observed experimentally. Recent molecular dynamics work has indicated that the compressive stress is related to the inclusion of interstitial bombarding gas atoms in the structure and indicates the importance of the role of vacancies in the lattice. Accordingly, the present invention aims to provide a method and a simulator for calculating the development of stress in IAPVD coatings which can be used for predicting growth process parameters which will result in the growth of coatings with a low or a predetermined desired level of residual stress. According to the present invention there is provided a method running on a computer for simulating the development of residual stress in the growth of IAPVD films using finite element analysis, comprising the steps of: simulating the development of strain associated with the condensation of an nth layer of the film, simulating the development of strain associated with the ion bombardment of a first set of layers of the film from the nth to the (n-x)th layer, and alternating the above two steps for n=x to n=N, where N is the number of layers making up the film and x<N. According to the method the simultaneous process of condensation and ion bombardment in IAPVD growth is divided into two separate alternating process stages. The first is the process stage of condensation and the second is the process stage of ion bombardment. Both these process stages are in themselves relatively simple to model separately using a finite element analysis approach to generate macroscopic strain level predictions. In the method, growth of the coating is split into the sequential growth of a series of N layers. For a layer n, for n going from x to N, the development of strain in that layer is calculated due to the process of condensation using finite element analysis. Then the development of strain due to ion bombardment is calculated for that same layer n and the several layers lying below it in the coating (the set of layers from the nth layer to the (n-x)th layer) again using finite element analysis. This is because as a coating is grown the effects of ion bombardment at any one time will only extend into these top few layers of the coating. Then the process goes on the simulate strain due to condensation of the n+1th layer followed by ion bombardment of the set of layers from n-x+1 to n+1. In this way, the simulation of the strain due to condensation and strain due to ion bombardment is alternated for n=x to n=N. For the first few layers of the coating for which n≤x, the effects of the ion bombardment process will extend below the bottom coating layer of the coating. In this case the ion bombardment step can be simulated for all the coating layers below the layer n, ignoring the effects of ion bombardment on the substrate layer on which the coating is grown. Alternatively, an appropriate depth of the substrate on which the coating is grown can be included in the ion bombardment simulation in addition to all the coating layers below the layer n, until n>x. In the simplest version of the method according to the present invention, the development of strain in the first few layers of the coating for which n≤x due to ion bombardment can be ignored altogether. Preferably, the method comprises the stages of: simulating the development of strain associated with the condensation of an nth layer of the film, simulating the development of strain associated with the ion bombardment of a first set of layers of the film from the nth to the (n-x)th layer, alternating the above stages for n=x to n=N, where N is the number of layers making up the film and x<N, and calculating the stress associated with the strains simulated in the above process stages. The stage of simulating the strain associated with the condensation of an nth layer of the film may comprises the stage of calculating the strain associated with vacancies in the lattice structure of said layer. A condensed coating is generally very porous, with many vacancies in the lattice structure, which vacancies result in strain in the coating. This is the major source of strain from the process of condensation. Preferably, the process of condensation of an nth layer of the coating is simulated as a substantially instantaneous process and so the effects of relaxation of strain due to thermal diffusion can be ignored in this part of the simulation. The strain associated with the condensation of an nth layer of the film can be assumed to be equal the yield strength of the coating material. The stage of simulating the development of strain associated with the ion bombardment of the first set of layers of the film, may comprise the stage of: simulating the development of strain due to the implantation of atoms in the set of layers according to the following equation: dεinst = - kij I (equation 1) dt where dεjnst = the rate of change of strain due to implantation, dt ki = a constant dependant on the coating material, j = bombarding ion flux, and I = bombarding ion energy. It should be noted that the implanted atoms can be atoms of the ion bombardment material or atoms of the coating layer. The stage of simulating the development of strain associated with the ion bombardment of the first set of layers of the film, may also comprise the stage of: simulating the relaxation of strain due to thermal spike migration of interstitial atoms in the set of layers according to the following equation: dsinst.reia = - k 2 ε in stj f !_ 1 5/3 (equation 2) dgi nst.re i ax = the relaxation in strain due to thermal spike migration, dt k 2 = a constant dependant on the coating material, εinst = the strain due to implantation after ion bombardment has occurred, j = bombarding ion flux, I = bombarding ion energy, and IO(INT) = the effective excitation energy of an interstitial atom. The stage of simulating the development of strain associated with the ion bombardment of the first set of layers of the film, may also comprise the stage of: simulating the relaxation of strain due to thermal spike migration of lattice vacancies in the set of layers according to the following equation: dginstreiax = - k 2 Sj ns tj f I l 5 3 (equation 3) dgjn st reiax = the relaxation in strain due to thermal spike migration, dt k 2 = a constant dependant on the coating material, εi nst = the strain due to implantation after ion bombardment has occurred, j = bombarding ion flux, I = bombarding ion energy, and IO ( VA C) = the effective excitation energy of a lattice vacancy. Preferably, the stage of simulating the development of strain associated with the ion bombardment of the first set of layers of the film additionally comprises the stage of simulating the development of strain associated with thermal diffusion of a second set of layers in the film from the 1st layer (ie. the layer adjacent to the substrate) to the nth layer, in order that strain relaxation due to thermal diffusion can be included in the simulation. According to a second aspect of the present invention there is provided a computer program product comprising a computer readable medium having thereon computer program code means such that when the product is loaded onto a computer the computer executes the method described above. The computer readable medium might, for example, comprise a computer disc or a CDROM. According to a third aspect of the present invention there is provided a computer program element comprising computer program code means for making a computer execute the method described above. According to a forth aspect of the present invention there is provided a computer program element for making a computer execute the method described above. According to a fifth aspect of the present invention there is provided a residual stress development simulator for simulating the development of residual stress in the growth of IAPVD films, comprising: first finite element analysis means for simulating the development of strain associated with the condensation of an nth layer of the film, second finite element analysis means for simulating the development of strain associated with the ion bombardment of a first set of layers of the film from the nth to the (n-x)th layer, means for alternating the use of the first and second finite element analysis means for n=x to n=N, where N is the number of layers in the film and x<N. Preferably, the simulator comprises: first finite element analysis means for simulating the development of strain associated with the condensation of an nth layer of the film, second finite element analysis means for simulating the development of strain associated with the ion bombardment of a first set of layers of the film from the nth to the (n-x)th layer, means for alternating the use of the first and second finite element analysis means for n=x to n=N, where N is the number of layers in the film and x<N, and finite element analysis means for calculating the stress associated with the strains simulated by the first and second finite element analysis means. The first means for simulating the strain associated with the condensation of an nth layer of the film may comprise means for calculating the strain associated with vacancies in the lattice structure of said layer and the stress associated with the condensation of an nth layer of the film may be assumed to equal the yield strength of the coating material. The second means for simulating the development of strain associated with the ion bombardment of the first set of layers of the film, may comprise: means for simulating the development of strain due to the implantation of atoms in the first set of layers according to the following equation: d jnst = - kij I dt where dεj nst = the rate of change of strain due to implantation, dt ki = a constant dependant on the coating material, j = bombarding ion flux, and I = bombarding ion energy. The second means for simulating the development of strain associated with the ion bombardment of the first set of layers of the film, may also comprise: means for simulating the relaxation of strain due to thermal spike migration of interstitial atoms in the first set of layers according to the following equation: dgmst relax = " k 2 ει ns tj I I I dg mst r e l ax = the relaxation in strain due to thermal spike migration, dt k 2 = a constant dependant on the coating material, ε ιnst = the strain due to implantation after ion bombardment has occurred, j = bombarding ion flux, I = bombarding ion energy, and I O( I N T ) = the effective excitation energy of an interstitial atom. The second means for simulating the development of strain associated with the ion bombardment of the first set of layers of the film, may also comprise: means for simulating the relaxation of strain due to thermal spike migration of lattice vacancies in the first set of layers according to the following equation: dgmst relax = " k 2 ει ns tj I _-_!__ I dt I lθ(VAC) J dgmst re l ax = the relaxation in strain due to thermal spike migration, dt k 2 = a constant dependant on the coating material, εinst = the strain due to implantation after ion bombardment has occurred, j = bombarding ion flux, I = bombarding ion energy, and I O(V AC ) = the effective excitation energy of a lattice vacancy. Preferably, the second means for simulating the development of strain associated with the ion bombardment of the first set of layers of the film additionally comprises means for simulating the development of strain associated with thermal diffusion in a second set of layers in the film from the 1 st layer to the nth layer. In order that the present invention is more fully understood and to show how the same may be carried into effect, reference shall now be made, by way of example only, to the Figures as shown in the accompanying drawing sheets, wherein: Figure 1 shows the parts of the coating which are analysed for three consecutive process steps of the process according to the present invention. Figure 2 shows a flow chart of the process steps according to the present invention. Figure 3 shows a graph of mean residual in-plane stress with respect to ion energy generated from data from a simulation according to the present invention. Figure 4 shows a graph of the variation of stress through a coating thickness with respect to ion energy generated from data from a simulation according to the present invention. Figure 5 shows a graph of in-plane shear stress through the coating thickness with respect to ion energy generated from data from a simulation according to the present invention. Figure 6 shows a graph similar to that in Figure 3 but generated from experimental data. One affect which results from ion bombardment in the growth of an IAPVD coating and which generates a compressive strain in the coating is the implantation of atoms of the coating material and of bombarding ions in the lattice structure of the coating. This can be modelled using linear cascade theory and results in equation 1 set out above. The implantation of atoms into a growing coating will occur at a significant rate only in a bombardment zone of the coating which is close to the surface of the coating. Therefore, this effect need only be modelled at any stage in the growth process for those layers of coating close to the surface of the coating. Thermal spike migration is another effect which alters the strain in a coating. In the spike migration process a local temperature increase at a location in the crystal lattice of the coating caused by an impact from an incident atom or ion during the bombardment process can, if sufficient energy is deposited by the impact, result in the migration of an interstitial atom or a lattice vacancy and accordingly lead to a reduction in residual strain. The relaxation due to thermal spike migration can be calculated in accordance with equation 2 above for the migration of interstitial atoms and by equation 3 above for vacancies. Again, this effect only occurs for those layers of the coating close to the surface of the coating. While the distribution of ion impacts during the bombardment process below the coating surface in a direction perpendicular to the surface of the coating is Gaussian, in the simulation described below is it assumed to be linear and uniformly distributed across the bombardment zone. The development of stress during the growth of an IAPVD coating is modelled in a finite element simulation of IAPVD coating growth using a Fortran sub-routine which is described below and is appended to the commercially available Abaqus 5.7 software run on a Silicon Graphics Indigo computer. It should be noted that material dependant values, ki to k 5 used in the simulation described below can be determined for different materials experimentally. The numerical simulation treats the IAPVD coating process as series of alternating condensation and ion bombardment stages. In the condensation stage a fine layer of coating material is added and in the bombardment stage the top layers of the coating are subjected to the effects of ion bombardment. This is shown in Figure 1. In the stage of the simulation shown in the top drawing in Figure 1 , a new layer of coating (2) is added to the previously grown layers of the coating (4) which have been grown on a substrate (6) during previous stages of the simulation. The growth of a layer (2) by condensation is simulated in this stage and the strain in the layer (2) associated with vacancies in the layer is calculated by assuming that it is equal to the yield strength of the coating material. In the next stage of the simulation, shown in the central drawing in Figure 1 , the top three layers (8) of the coating are subjected to ion bombardment and the strains associated with implantation (using equation (1)) and thermal spike migration (using equations (2 and 3)) are calculated. In the next stage of the simulation shown in the bottom drawing of Figure 1 , a new layer of coating (10) is added to the previously grown layers of the coating (4) which have been grown on a substrate (6) during previous stages of the simulation, including the stages shown in the top drawing of Figure 1. In this way the simulated stages of layer growth and ion bombardment are alternated. The alternating stages are repeated many times until the full thickness of the coating is deposited. It will be appreciated that as the depth (D) of each added layer (eg. 2,10 in Figure 1) is set to a smaller value in the simulation, the simulation approaches more closely the simulation of the simultaneous condensation and ion bombardment which occurs in the growth of an IAPVD coating. However, if the depth (D) of each added layer is set to a smaller value the computation power required carry out the simulation increases. Figure 2 shows a flow diagram of the process stages of the simulation. The steps in the simulation are numbered k = 1 to K and K ≡ 3N where N is the number of layers in the coating. In stage (12) the Abaqus 5.7 software meshes the simulation as is well known in finite element analysis, based on data input into the software relating to the geometry of the finite element structure, the nature of the simulation, and the material properties of the materials involved in the simulation. Once stage (12) is completed the Abaqus software proceeds to stage (14) in which all of the elements created during the meshing stage (12) and which represent the coating layer are deactivated. The element de- activation process is internal to the Abaqus software and as such is standard in the art and so is not further described here. With stage (14) complete the Abaqus software proceeds to stage (15) which sets k to 2. Stages (16) and (17) ensure that for every third step in the process for which mod(k,3)=2, ie. k=2, 5, 8 etc, the next layer of the coating is activated. When the simulation begins, k is set to 2 at stage (15) and so from stage (15) the process passes from stage (16) via the "YES" route to stage (17) and at stage (17) the first layer of the coating (ie. the layer of coating adjacent to the substrate) is activated. Because the elements representing the first layer are the only ones which are activated the subsequent processing steps (18) and (24) in the iterative loop (26) are carried out only in relation to this first layer. At stage (18) the Abaqus software calls the Fortran sub-routine described below, at stage (20) the Abaqus software uses the strain levels passed back to it by the Fortran sub-routine at stage (18) to calculate the associated stress for the current process step (ie. k=2), then k is set to k+1 (ie. k=3) at stage (22) and if the new k is less than K the process now goes back via the iterative loop (26) to stage (16). It can be seen that the iterative loop (26) is completed for three steps (ie. k=2, k=3 and k=4) before the next coating layer is activated at stage (17) (ie. when k=5). Thus, for each third cycle of the iterative loop (26), ie. only when mod(k,3) = 2, a successive layer of the coating is activated, until the coating is complete and the process leaves the iterative loop (26) when k>K and proceeds to stage (28). The Fortran sub-routine does nothing for steps in which mod(k,3) = 2. When mod(k,3) = 0 the Fortran sub-routine simulates strain development due to coating condensation and when mod(k,3) = 1 the Fortran sub-routine simulates strain development due to ion bombardment. It should be noted that for each step k, the Abaqus software calls the sub-routine repeatedly. The Abaqus software calls the sub-routine for each element in the analysis and for each incremental time step making up the current step k. --,_,-,, PCT/GB00/01441 16 At stage (18) for steps in which mod(k,3) = 0, ie. steps 3, 6, 9 etc, the Fortran sub-routine simulates the condensation of the coating layer which was last activated at stage (17) (hereafter referred to the top growth layer) for each element i = 1 to Y, where Y is the number of elements in the analysis and for each incremental time step in the step k. In lines 94 to 104 of the sub-routine of Table 1, which is described below, the strain in the top growth layer which is due to the effects of vacancies in the lattice of the layer created during the process of condensation is calculated. It is assumed that the coating material is deposited with sufficient vacancy defects to cause a stress level which is equal to the yield strength of the coating material. The sub-routine is repeated for each incremental time step to generate a value for the incremental strain for each element in the top growth layer which incremental strain value is passed to the Abaqus software for use in stage (20) described below. The simulation of the condensation process is assumed to be substantially instantaneous and so the effects on strain due to thermal diffusion (discussed below) are assumed to be negligible and so are not included here. In other words the effects on strain due to thermal diffusion need only be simulated in one of the condensation or the ion bombardment stages, because in the real IAPVD process these stages occur simultaneously. The ion bombardment simulation is also carried out at stage (18), but for steps in which mod(k,3) = 1, ie. steps 4, 7, 10 etc, by the Fortran sub- routine. The ion bombardment is simulated for each element i = 1 to Y, in lines 06 to 114 of the sub-routine for each incremental time step in the step k. This calculates the level of incremental strain resulting from ion bombardment of the top growth layer and the two growth layers directly below it and takes into account the effects of implantation, thermal spike migration and thermal diffusion. The values of incremental strain are passed to the Abaqus software for use in stage (20) as described below. At each stage (20) in the process the Abaqus software calculates on a cumulative basis the level of stress for each element in the analysis based on the values of incremental strain passed to it by the Fortran sub-routine in the preceding stage (18). During the deposition and bombardment process the coating heats up, which temperature change is simulated by the Abaqus software in the stages and steps of the simulation. At stage (28) the Abaqus software simulates the cooling of the coating to room temperature and calculates the associated stress generated. As this is an instantaneous process stage, no thermal diffusion effects are included in this stage. From stage (28) the process proceeds to stage (30) and the analysis ends. The Fortran sub-routine which is used to carry out stage (18) of the process shown in Figure 2, is set out in Table 1 , located at the end of this document. Each step k in the process is split into time increments and the sub-routine is repeated at stage (18) for each time increment in the step for each element in the analysis and each time the sub-routine is repeated relevant incremental strain values are passed to the Abaqus software for use in a stress calculation at the next stage (20) in the process. In line 32 of the sub-routine the communication of data between the Abaqus software and the sub-routine of Table 1 is enabled. In line 34 group material properties data are transferred from the Abaqus software to the Fortran sub-routine. At line 36 several variables are transferred from the Abaqus software to the Fortran sub-routine. At line 38 the Fortran sub-routine sets up some of its own variables. At lines 44 to 80 data is entered into the sub-routine. Line 44 enters the number of layers (NLYS) in the coating, which in the sub-routine in Table 1 is set to 50. Line 46 enters the thickness of the coating (CTX) which is 0.5 x 10 3 nm. Line 48 enters the thickness of the substrate (STX) which is 0.1 x 10 6 nm. Line 50 enters the net bombarding flux of incident ions (J) which is 3.9363958ions/nm 2 /s (j in equations 1 to 3 above). Line 52 enters the bombarding ion energy (I) which is 200eV (cf. I in equations 1 to 3 above). Line 54 enters the effective excitation energy (IZ) for thermal spike relaxation which is 10eV (I O ØNT ) and I O ΓV A C ) in equations 2 and 3 above). Line 56 enters the coefficient of incorporated gas atoms (KONE) which is 0.45 x 10 ~6 (ki in equation 1 above). Line 58 enters the coefficient of spike relaxation for incorporated gas atoms (KTWO) which is (1.0 x 10^/4 (k 2 in equation 2 above). Line 60 enters the coefficient bulk thermal diffusion for incorporated atoms (KTHREE) which is 1. Line 62 enters the coefficient of bulk thermal diffusion for vacancies (KFOUR) which is 1. Line 64 enters the coefficient of spike relaxation for vacancies (KFIVE) which is (2.0 x lO "4 )/^ (k 3 in equation 3 above). Line 66 enters the depth of the implantation or bombardment zone (D) which is 30nm. Line 70 enters the elastic modulus of the coating (E) which is 0.11 x 10 3 . Line 72 enters the elastic yield of the coating (UTS) which is 0.5. Line 74 enters the Boltzmann constant (R). Line 76 enters the activation energy for thermal diffusion into a vacancy (UV) which is 0.25. Line 78 enters the activation energy for thermal diffusion of an interstitial atom (Ul) which is 0.35. Line 80 calculates the mean temperature of the coating where TEMP represents the temperature at the end of the current step k and DTEMP is the change in temperature over the current step k. Lines 82 to 90 set values for incremental strain relaxed by thermal diffusion of interstitial atoms, incremental strain relaxed by thermal diffusion of vacancies, incremental strain due to implantation of atoms, incremental strain relaxed by thermal spike migration of interstitial atoms and incremental strain relaxed by thermal spike migration of vacancies respectively to zero at the beginning of the sub-routine, each time it is run through. Line 92 identifies those elements which are in the coating layer, ie. those coating layer elements which have been activated in a preceding stage (17) of a preceding step in the process. For elements which are in the coating layer lines 94 to 104 are applied. At line 94 the subroutine identifies those steps in the process for which mod(k,3) = 0, ie. it identifies those process steps for which k = 3, 6, 9, etc and for these steps k, lines 96 to 104 are applied. Lines 96 to 100 identify those elements in the top coating layer and for these elements line 101 calculates the incremental strain (INC1V) for the relevant time increment for the relevant element in the top layer of the coating due to the condensation of the top layer of the coating. At line 102 the rate of change of incremental strain with respect to the rate of change of strain is set to zero. Lines 106 to 115 simulate the ion bombardment and calculate for each element in the relevant coating layers the incremental strain due to the bombardment process. At line 106 the sub-routine tests whether the current step in the analysis is one that requires the simulation of ion bombardment, ie. whether mod(k,3) = 1. If it is then the upper and lower boundaries of the bombardment region (UB and LB) are set at lines 107 and 108 respectively. At lines 109 and 110 the incremental strain for elements in all the previously grown layers due to relaxation by thermal diffusion is calculated, in accordance with Fick's law according to the following equations: TERMA = -DTIME.KTHREE.(2.7182818285) ( - UI/(R MTEMP)) for thermal diffusion of atoms, and TERMB = -DTIME.KFOUR.(2.718281 8 285) ("UV/(R MTEMP)) for thermal diffusion of vacancies, where TERMA = Incremental strain due to thermal diffusion of interstitial atoms, TERMB = Incremental strain due to thermal diffusion of vacancies, DTIME = incremental time step, KTHREE and KFOUR are material dependant constants, Ul = activation energy for release of interstitial atom, UV = activation energy for release of vacancy, R = Boltzmann Constant, and MTEMP = mean temperature of coating over time step. At line 111 the sub-routine selects those elements which lie in the bombardment zone and these elements are subjected to lines 112 to 114. At line 112 the incremental strain (TERMC) due to the effects of implantation in the bombardment layer (dεjnst in equation 1) is calculated in accordance with equation 1 above. At lines 113 and 114 incremental strains (TERMD and TERMSE) due to relaxation by thermal spike migration of implanted atoms (dεinst.reiax in equation 2) and vacancies (dεin st. r e i a x in equation 3) are calculated respectively in accordance with equations 2 and 3 above. The sub-routine is repeated so that it calculates the incremental strains associated with coating condensation if the step is one in which mod(k,3) = 0 or the incremental strains associated with ion bombardment if the step is one in which mod(k,3) =1 for each time increment in the step k and for each element in the analysis and each time the sub-routine is repeated the relevant incremental stain value is passed back to the Abaqus software, for use in subsequent stress calculations at stage (20). At lines 116 to 119 the sub-routine makes some preliminary strain calculations and at 120 to 124 the DESWA values which are the incremental strain values are calculated and are passed back to the ABAQUS program by the sub-routine at line 126. The STATEV values are used for debugging purposes only. The process of the growth of an IAPVD film of a typical ceramic material on a metal substrate was simulated using the above process and the results in Figures 3 to 5 were generated. Figure 3 shows the variation of mean compressive stress in the coating with respect to ion energy. The form of the graph in Figure 3 is similar to that derived by experiment in Figure 6. At lower ion energies, stress increases with ion energy as more atoms are implanted in the coating. At higher ion energies as the mobility of the lattice defects in the coating is increased and interstitial atoms and vacancies can migrate as quickly as they are created and stress decreases. Figure 4 shows the variation of in-plane stress through the coating to the substrate surface for different ion energies. The substrate (to the left in Figure 4) is slightly in tension whereas the coating is in compression. The gradient of the curves of the in-plane stress through the coating explains why coatings tend to curl up after de-bonding from the substrate. This is caused by new layers being deposited on the surface and undergoing modification by ion bombardment. The material in the bombardment zone tends to swell as atoms are implanted, which affects the stress in the material throughout the coating, creating the stress distribution. Near the surface the stress tends to zero because the material has not been as fully modified by the impinging ions as elsewhere in the coating. For brittle materials maximum stress is a good indication of the likelihood of failure of the coating. Figure 5 shows a plot of in-plane shear stress through the substrate and coating for different ion energies. The maximum shear calculated is beneath the interface in the substrate. For ductile materials where failure is considered to be when the material has gone plastic, maximum shear stress can be a good indication of the likelihood of failure. From the results obtained in Figures 3 to 5, it is clear that the simulation according to the present invention is a valuable tool in the design of growth processes to generate coatings with low or a desired level of residual stress. For example, for a particular set of materials, the simulation can be used to predict the most appropriate ion energy to generate a low stress coating, thus replacing the current practice of experimental trial and error.

Claims: CLAIMS 1. A method running on a computer for simulating the development of residual stress in the growth of IAPVD films using finite element analysis, comprising the stages of: simulating the development of strain associated with the condensation of an nth layer of the film, simulating the development of strain associated with the ion bombardment of a first set of layers of the film from the nth to the (n-x)th layer, and alternating the above two stages for n=x to n=N, where N is the number of layers making up the film and x<N. 2. A method according to claim 1 comprising the stages of: simulating the development of strain associated with the condensation of an nth layer of the film, simulating the development of strain associated with the ion bombardment of a first set of layers of the film from the nth to the (n-x)th layer, alternating the above stages for n=x to n=N, where N is the number of layers making up the film and x<N, and calculating the stress associated with the strains simulated in the above process stages. 3. A method according to claim 1or claim 2 wherein the stage of simulating the strain associated with the condensation of an nth layer of the film comprises the stage of calculating the strain associated with vacancies in the lattice structure of said layer. 4. A method according to claim 3 wherein the strain associated with the condensation of an nth layer of the film is calculated to equal the yield strength of the coating material. 5. A method according to any one of the preceding claims wherein the stage of simulating the development of strain associated with the ion bombardment of the first set of layers of the film, comprises the stage of: simulating the development of strain due to the implantation of atoms in the set of layers according to the following equation: Sinst' = - kij I , where ε, nst ' = the rate of change of strain due to implantation, ki = a constant dependant on the coating material, j = bombarding ion flux, and I = bombarding ion energy. 6. A method according to any one of the preceding claims wherein the stage of simulating the development of strain associated with the ion bombardment of the first set of layers of the film, comprises the stage of: simulating the relaxation of strain due to thermal spike migration of interstitial atoms in the set of layers according to the following equation: d mst relax = " k 2 ε, n stj I I I dgm st r ela x = the relaxation in strain due to thermal spike migration, dt k 2 = a constant dependant on the coating material, ms t = the strain due to implantation after ion bombardment has occurred. j = bombarding ion flux, I = bombarding ion energy, and IO (IN T ) = the effective excitation energy of an interstitial atom. 7. A method according to any one of the preceding claims wherein the stage of simulating the development of strain associated with the ion bombardment of the first set of layers of the film, comprises the stage of: simulating the relaxation of strain due to thermal spike migration of lattice vacancies in the set of layers according to the following equation: dgmst relax = " k 2 8mstj I 1 I d m st re l ax = the relaxation in strain due to thermal spike migration, dt k 2 = a constant dependant on the coating material, ε,n st = the strain due to implantation after ion bombardment has occurred, j = bombarding ion flux, I = bombarding ion energy, and O ( VA C ) = the effective excitation energy of a lattice vacancy. 8. A method according to any one of the preceding claims wherein the stage of simulating the development of strain associated with the ion bombardment of the first set of layers of the film additionally comprises the stage of simulating the development of strain associated with thermal diffusion in a second set of layers in the film from the 1st layer to the nth layer. 9. A residual stress development simulator for simulating the development of residual stress in the growth of IAPVD films, comprising: first finite element analysis means for simulating the development of strain associated with the condensation of an nth layer of the film, second finite element analysis means for simulating the development of strain associated with the ion bombardment of a first set of layers of the film from the nth to the (n-x)th layer, and means for alternating the use of the first and second finite element analysis means for n=x to n=N, where N is the number of layers in the film and x<N. 10. A simulator according to claim 9 comprising: first finite element analysis means for simulating the development of strain associated with the condensation of an nth layer of the film, second finite element analysis means for simulating the development of strain associated with the ion bombardment of a first set of layers of the film from the nth to the (n-x)th layer, means for alternating the use of the first and second finite element analysis means for n=x to n=N, where N is the number of layers in the film and x<N, and finite element analysis means for calculating the stress associated with the strains simulated by the first and second finite element analysis means. 1. A simulator according to claim 9 or claim 10 wherein the first means for simulating the strain associated with the condensation of an nth layer of the film comprises means for calculating the strain associated with vacancies in the lattice structure of said layer. 12. A simulator according to claim 11 wherein the strain associated with the condensation of an nth layer of the film is calculated to equal the yield strength of the coating material. 13. A simulator according to any one of claims 9 to 12 wherein the second means for simulating the development of strain associated with the ion bombardment of the first set of layers of the film, comprises: means for simulating the development of strain due to the implantation of atoms in the first set of layers according to the following equation: dεmst = - kij I dt where d ms t = the rate of change of strain due to implantation, dt ki = a constant dependant on the coating material, j = bombarding ion flux, and I = bombarding ion energy. 14. A simulator according to any one of claims 9 to 13 wherein the second means for simulating the development of strain associated with the ion bombardment of the first set of layers of the film, comprises: means for simulating the relaxation of strain due to thermal spike migration of interstitial atoms in the first set of layers according to the following equation: dginst. relax = ~ 2 εmstj I I I d in st. r e iax = the relaxation in strain due to thermal spike migration, dt k 2 = a constant dependant on the coating material, εin st = the strain due to implantation after ion bombardment has occurred, j = bombarding ion flux, I = bombarding ion energy, and Irj ( i NT) = the effective excitation energy of an interstitial atom. 15. A simulator according to any one of claims 9 to 14 wherein the second means for simulating the development of strain associated with the ion bombardment of the first set of layers of the film, comprises: means for simulating the relaxation of strain due to thermal spike migration of lattice vacancies in the first set of layers according to the following equation: dgjnst.relax = " k 2 8j ns tj I I I dt I lθ(VAC) J dgjnst.r e la = the relaxation in strain due to thermal spike migration, dt k 2 = a constant dependant on the coating material, εin st = the strain due to implantation after ion bombardment has occurred, j = bombarding ion flux, I = bombarding ion energy, and I O( VAC) = the effective excitation energy of a lattice vacancy. 16. A simulator according to any one of claims 9 to 15 wherein the second means for simulating the development of strain associated with the ion bombardment of the first set of layers of the film additionally comprises means for simulating the development of strain associated with thermal diffusion for a second set of layers in the film from the 1st layer to the nth layer. 17. A computer program product comprising a computer readable medium having thereon computer program code means such that when the product is loaded onto a computer the computer executes the method according to any one of claims 1 to 8. 18. A computer program element comprising computer program code means for making a computer execute the method according to any one of claims 1 to 8. 19. A computer program element for making a computer execute the method according to any one of claims 1 to 8.

Inventors: WARD DAVID J, WILLIAMS ANDREW F, WARD, DAVID, J., WILLIAMS, ANDREW, F.
Applicants: BRITISH NUCLEAR FUELS PLC, WARD DAVID J, WILLIAMS ANDREW F, WARD, DAVID, J., WILLIAMS, ANDREW, F.
Application year: 2000
Main classification: C23C14
IPC codes: C23C14, G05B17