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An evaluation of four computer modelling programs for Rutherford backscattering spectrometry analysis of oxidized surfaces
Thin Solid Films, 166 (1988) 201-211
201
AN EVALUATION OF FOUR COMPUTER MODELLING PROGRAMS FOR RUTHERFORD BACKSCATTERING SPECTROMETRY ANALYSIS OF OXIDIZED SURFACES* J. SAULITIS,G. R. JOHNSTONAND J. L. COCKING Materials Research Laboratory, DSTO, Maribyrnong, Victoria 3032 (Australia)
(ReceivedMarch26, 1988)
Rutherford backscattering spectrometry (RBS) is a powerful analytical tool for characterizing the near-surface regions of solid materials. It is one of a number of surface analytical techniques being used to analyse the surface of alloys both before and after oxidation at high temperatures. Four computer programs which have been developed to analyse RBS spectra are described. The different approaches in the design of the programs, which are designated PROFILE, SCATT, RUMP and CALC, are examined. The strengths and weaknesses of each of the programs, including their ease of use in deconvoluting spectra produced from oxidized surfaces, are discussed and contrasted.
1. INTRODUCTION Rutherford backscattering spectrometry (RBS) has evolved to become a powerful analytical tool for characterizing the near-surface regions of solid materials. The advantage of the RBS technique is that this information can be obtained non-destructively. This technique is one of a number of surface analytical techniques used to characterize the surface of alloys which have been oxidized at high temperatures. The complete characterization of the oxide film and its interface with the underlying alloy is of great importance, since the durability of the surface of a metal at high temperature in an oxidizing environment is critically dependent on the adherence and diffusion-inhibiting properties of the oxide scale on its surface. Four different computer programs which have been developed to deconvolute RBS spectra are examined and their relative strengths and weaknesses in their ability to characterize the oxide and its interface with the underlying alloy are discussed in this paper.
* Paper presented at the 15th InternationalConferenceon MetallurgicalCoatings, San Diego, CA, U.S.A.,April 11-15, 1988.
0040-6090/88/$3.50
© ElsevierSequoia/Printedin The Netherlands
202 2.
J. SAULITIS, G. R. JOHNSTON, J. L. COCKING
RUTHERFORD BACKSCATI'ERING SPECTROMETRY
The technique involves the measurement of the energy and number of elastically scattered ions which result from the impact of a beam of monoenergetic megaelectron-volt ions with a solid. The number of elastically scattered ions detected is proportional to the number of atoms present in the volume of material irradiated. The energy loss of an ion in penetrating and backscattering from a solid is related to the mass of the atom which it struck, the angle through which the collision took place and the depth at which the scattering event occurred. Thus backscattered energy spectra contain much useful information concerning the type and concentration of atoms within the first few microns of a surface. The equations used to generat e theoretical Rutherford backscattering spectra have been well documented 1-8 and will not be repeated here. 3.
COMPUTER PROGRAMS
The first computer program, of the four to be discussed, will be designated PROFILE. It was developed in 1974 at BRL by J. E. Youngblood. This program was modified by A. Niiler, R. Birkmire, J. Gerrits and G. H. Swope 7 and was written in FORTRAN 77. It contains 1870 lines of code and has been modified so that it can run on the Materials Research Laboratory VAX-11/780 computer. The second program, designated SCATT, was developed by J. F. Ziegler, R. F. Lever and J. K. Hirvonen at IBM 8. It was originally written in APL, but has been translated into FORTRAN IV. The latter program included improvements, such as the introduction of Coulomb scattering and straggling. The program used contains 1986 lines of code and has been adapted for use on the Materials Research Laboratory VAX- 11/780 computer. The third program, designated RUMP, was developed by L. Doolittle and others in 19859. The version used was designed for the VAX-11/780. A version is also available for use on IBM personal computers. RU MP occupies more memory space than the other three programs. The fourth program, designated CALC, was developed by J. W. Butler4. It was written in BASIC 3.0 with language extensions and designed to run on the series 200 Hewlett-Packard computer. This program contains about 2500 lines of code and it has not been translated for use on the VAX-11 system. Each of the programs differs in its approach. The comparative advantages and disadvantages of each program are discussed with respect to the research program in progress at the Materials Research Laboratory. 4.
THE MODELLING PROCESS
The programs are used to deconvolute the RBS spectra by a process of successive simulations. The user must arrive at an inspired first estimate of the structure of the surface of the samples as a function of depth. Some prior knowledge of this structure, from some other form of surface analysis technique, is often useful if specific experience with the behaviour of the sample is lacking. In general,
COMPUTER MODELLING PROGRAMS FOR RBS ANALYSIS OF OXIDIZED SURFACES
203
characterization of the sample is made by dividing the sample into a composition matrix. The matrix is made up of layers, in which each layer is assigned a composition. In each of the four programs the assumption is made that the composition within each layer is uniform. The individual layers may be varied in thickness in order to reflect the variation in composition with depth. When the model of the sample is formulated, units for depth and concentration must be assigned. In RBS analysis the apparent thickness used is the areal density and not the more commonly understood dimension of length. Since, to a first approximation, the sizes of the atoms of all elements are the same, a monolayer of atoms contains about 1015 atoms cm-2. This is often taken to be the natural unit to be used in RBS analysis. In order to convert from the dimensions of atoms per area to a length unit, such as hngstr6ms, the density of the material in the region of interest must be known. The use of ~mgstr6ms as a descriptive unit is attractive since it gives an easily visualized model for the characterization of the material. Unfortunately, it carries with it the corollary that the appropriate relative density must be known. Differences between estimated and actual densities will lead to errors when the theoretical spectra are generated by the computer. The four programs use different units for describing depth in the simulation model. CALC, SCATT and R U M P can use areal density, with units of atoms per square centimetre. SCATT and R U M P can also formulate the depth in hngstr6ms. P R O F I L E originally used micrograms per square centimetre, but a conversion routine was added so that units of hngstr6ms or atoms per square centimetre could be incorporated. Concentrations are usually expressed in atomic or weight per cent. SCATT, CALC and R U M P can also use the ratio of relative concentrations of atoms within a designated layer. CALC is usually run with normalized atom fractions, but also accepts normalized weight per cent. The maximum dimensions of the composition matrix differ for each program. The composition matrix for SCATT is 5 elements in 55 layers. Thus SCATT can simultaneously model up to five elements in forming a spectrum. CALC can offer a matrix of 8 elements and 55 layers. P R O F I L E offers a matrix of 10 elements and 100 layers, while R U M P uses a maximum of 20 elements and 20 layers. All but SCATT can further divide the layers into sublayers. Once the model of the sample has been assigned, the program calculates a spectrum. This calculated spectrum is compared with the experimental spectrum and the model is modified until, after a series of iterations, the model matches the experimental spectrum. 5. STRENGTHS AND WEAKNESSES OF THE PROGRAMS
5.1. Thickness limits
While none of the programs places a limit on the thickness of the sample that can be analysed, in practice two of the programs have difficulty with thick samples. At thicknesses of around 7000 ~ SCATT fails under certain configurations, such as when many elements are being modelled. Prior to failure the run times increase from the normal condition of about 16-20 s central processing unit time to 30min and more. P R O F I L E begins to malfunction at thicknesses around 700 lag c m - 2, which is
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J. SAULITIS, G. R. JOHNSTON, J. L. COCKING
equivalent to around 5500 A for a sample whose composition is Co-28wt.%Cr7wt.~Al. At these thicknesses the run times are of the order of 20-30 min. CALC and R U M P do not experience difficulty with thick samples. For example, with CALC the run time is only about 1 min for a 2 ~tm thick sample which has been divided into 50 layers. In each program the dimension of a layer determines the integration step size for the calculation. If the energy spread corresponding to each layer is much greater than the detector resolution, the spectrum generated will assume a stepped appearance. SCATT overcomes this problem by having the operator input the appropriate integrating depth step in hngstr6ms. CALC and P R O F I L E solve this problem by subdividing the layers into sublayers, the number of which is left to the discretion of the operator. 5.2. Ease o f use
R U M P , with its interactive program package, is the most versatile program. It offers the useful feature of being able to exit from R U M P to use the features of the VAX and then to return to continue the analysis without loss of previous work. R U M P commands can be gathered together in a MACRO file which can speed up an operation which has a long set of fixed instructions. CALC is the easiest program to use. CALC and R U M P are the only programs which incorporate some degree of error recovery in the event of having input incorrect parameters. Both have optionally preset default conditions. CALC make much use of the programmable key features of the Hewlett-Packard series 200 (HP9836A) computer to speed up and simplify its use. It uses on-screen editing graphics, in colour, and provides a convenient on-screen overlay plot of the concentration vs. depth profile for the elements used. SCATT and P R O F I L E were oriented for use in mainframe computers and have a more rigid structure, which requires a preformed ASCII file containing all the data for the simulation. These programs were modified at the Materials Research Laboratory to interact with control programs to form control files and to perform the calculations. The data-forming modifications include interacting prompts for the input parameters. The drawback of this arrangement is that the programs are specifically VAX oriented and take up more memory. In addition, this arrangement does not provide a fully rounded software package which R U M P , in contrast, does. SCATT is very sensitive to the size and configuration of its run parameters. Run-time errors occur under some combinations of parameters, even though the individual parameters have not exceeded their operating ranges. The result is that the program can easily generate a state where access violations can occur because the bounds of the arrays are exceeded. This is a fundamental fault in the program. This fault can cause failure of the program from things as diverse as the size of the channel width or the interpolation of the step size. For example, SCATT will run successfully for four elements with a channel width of 3.9 keV for the multichannel analyser. If an extra element is introduced the program will 0nly run if the channel width is increased to 5.0 keV or more. Another example shows that even apparently unrelated descriptors can interact to cause program failure. SCATT is nominally capable of using 55 layers. The program will run successfully if a combination of 20 layers at a detector collection angle of 150° is used. However, if the collection angle is
COMPUTER MODELLING PROGRAMS FOR RBS ANALYSIS OF OXIDIZED SURFACES
205
reduced to 120° the program will only run successfully if the number of layers is reduced to 13, while at the same time ensuring that the total thickness of the model is within 7000/~. 5.3. Presentation of data With the exception of RUMP, the level of sophistication of the output depends on the peripherals of the computer system used. PROFILE and SCATT rely for their graphics on the VDU and the digital plotters as driven by the Materials Research Laboratory graphics package 1°. CALC and RUMP have the visual display integrated with the program. All programs can give their yield output in counts, but RUMP and PROFILE can also use normalized yields which is more convenient in analysis. The original SCATT output was in the form of a line printer histogram. This was modified to also give visual graphics. All programs give hard copy spectral outputs of yield vs. channel, but PROFILE and RUMP can also give various additional outputs. PROFILE as originally received included a comprehensive graphics capability. Since the graphics software was not supported by the Materials Research Laboratory VAX-11 system, PROFILE was modified to use the Materials Research Laboratory graphics package. 5.4. Energy straggling The phenomenon of energy straggling places a finite limit on the precision to which the energy losses, and hence depths, can be resolved. Straggling is an energydependent process Lll'1z that requires a considerable amount of computation to predict its effect. All four programs incorporate energy straggling, based on the Bohr model, as an option. In addition PROFILE and SCATT give the option of using further refinements to improve the effectiveness of the energy loss calculations. Straggling is only a second-order effect and its omission is not vital to the general analysis. Its implementation, however, may more than double the computation time. 5.5. Hardware effects Analysis by RBS does not require standards to be quantitative. The application of experimental conditions enables the resolution of the system to be determined. Quantitative analyses can be obtained directly from the experimental results. The parameters for evaluating the energy resolution of the system differ for each program; PROFILE is the most comprehensive while SCATT has the least sophistication. The uncertainty in the experimental beam energy can lead to ambiguities of several hundred ~mgstrrms in the generated depth profile which cannot be compensated for by the programs. 5.6. General There are many difficulties in constructing a model which is representative of a sample. Several of these have been mentioned above. In addition to those none of the programs makes provision to account for voids, gas bubbles, small precipitates, uneven spalling of the oxide or uneven growth of oxide, e.g. down grain boundaries or over different phases within an alloy. Of the four programs only RUMP
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J. SAULITI$, G. R. JOHNSTON, J. L. COCKING
incorporates any means of manipulating the input data, such as subtracting the background. In addition, only RUMP has a routine for automatically varying parameters to yield the best fit. PROFILE includes a curve fit by the least-squares method and gives the option, as does RUMP, of using a five-point smoothing routine on the experimental spectrum before manual fit to the calculated spectrum is made. CALC also includes an option in which the experimental spectrum is smoothed. SCATT incorporates a thermal interdiffusion calculation feature, which provide an additional means of investigating the structure of ion-implanted specimens that have undergone high temperature oxidation. SCATT can calculate the thermal interdiffusion of two or more layers of the sample allowing for a simple generation of graded concentrations. RUMP allows a composition gradient to be automatically assigned by selection of any of seven equations from a menu. This option obviates the need for the operator to assign manually small changes in composition to a large number of sublayers to achieve a good fit of a sample which has a regular composition gradient. In order to obtain increased depth resolution, the target can be tilted so that the total path length required to reach a given point below the surface is increased ~a, 14. All four programs have been designed to be capable of calculating spectra for different detection angles. SCATT, however, begins to malfunction at angles less than 135°. 6. EXAMPLES The samples used in these examples are coupons of Co-22wt.%Cr-1 lwt.%A1 which were polished on one side to a 1/4 ~tm diamond paste finish. To allow direct comparisons of the effects of implanted species on oxidation mechanisms, one-half of the polished face on each sample was implanted with hafnium ions. The samples were oxidized at 700°C in air for 1 h. Previous investigations~s showed that the microstructure of the non-implanted Co-Cr-A1 prior to oxidation consisted of a matrix of t-CoAl and irregularly shaped precipitates of an ~-Co solid solution, which were between 5 and 20 pm in diameter. PROFILE, CALC and RUMP produced calculated spectra which were in better agreement with the experimental spectra than SCATT. An example of the spectra obtained from RUMP is presented in Fig. 1. Deconvolution of the experimental spectrum, which was collected on a microprobe with a spatial resolution of around 10 ~n, showed that the oxide that formed on the fl phase had an outer oxide which was a mixture of CoO, Cr203 and A120 a over a layer of AI20 a. The hafnium resides near the outer part of the A1203 layer. Deconvolution of the same spectrum using PROFILE (Fig. 2) using different units for the analysis (micrograms per square centimetre rather than atoms per square centimetre) produced a fit which was not quite as good in the fine details but which produced a composition matrix which was essentially the same. All programs produced spectra which diverged from the experimental spectra at the low energy end. Because SCATT uses only a limited number of layers the calculated spectra were not always as smooth as those produced by the other programs. In addition,
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the samples stretched the operating parameters of the program to their limits. During analysis of oxidized samples, the simultaneous accommodation of the oxygen edge (at the low energy end of the spectrum) and the hafnium edge (at the high energy end)just spanned the normal operating range of the program. ENERGY (MeV] 1,0
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Fig. 1. (a) Experimental Rutherford backscattering spectrum (e) from the J3phase of hafnium-implanted Co-Cr-Al oxidized in air for 1 h at 700 °C, together with the theoretical spectrum ( ). (b) Elemental concentration profiles generated by RUMP: A, cobalt; O, oxygen; "k, hafnium; O, aluminium; ©, chromium.
208
J. S A U L I T I S , G . R. J O H N S T O N , J. L. C O C K I N G
If the oxidized sample was ideal, i.e. the oxide formed in a layer of even thickness over the surface, the models of the spectra calculated by both the backward and glancing collection angles should result in identical composition matrices. The samples in these experiments were composed of two phases which
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COMPUTER MODELLING PROGRAMS FOR RBS ANALYSIS OF OXIDIZED SURFACES
209
oxidized differently. In those experiments in which the spectra were collected from an instrument whose beam diameter was greater than 1 m m it was not possible to generate a single composition matrix for the two collection angles. An example of this is shown in Fig. 3 for spectra generated by CALC. A reasonable fit was generated for the spectrum collected at 150 ° . When the same concentration profile was used to generate a spectrum at 130 ° the fit was poorer.
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(b) Fig. 3. Rutherford backseattering spectra gathered at (a) 150 ° and (b)' 130 ° of oxidized hMniumimplanted C o . r - A 1 , using an instrument with a beam diameter of greater than I ram. Since the precipitate phase in the alloy was 5-20 lain in diameter, and since the oxides which grew on the two phases were of different thicknesses, it was not possible to match the experimental (e) and theoretical ( ) spectra with a unique composition matrix. In this example CALC was used; however, the problem is common to all four programs.
210
J. SAULITIS, G. R. JOHNSTON, J. L. COCKING
7. CONCLUSIONS (1) PROFILE, CALC and RUMP gave better agreement with experimental spectra than SCATT. (2) Of the programs examined, only CALC could be used after a brief introduction period by a non-specialist user of a computer. (3) CALC is oriented to Hewlett-Packard BASIC. To translate the program to a more common language that can be used on a system such as the VAX-11 is probably not practical. (4) SCATT and PROFILE in their original forms were slow and difficult to use. Their operation and control parameters assumed a great deal of knowledge that a person who was unfamiliar with computer programming was unlikely to have. The formulation of the control data and their running made them unsuitable for an interactive type of operation. (5) RUMP was comparatively easy to use, but required initial implementation by a computer expert. (6) SCATT and PROFILE could be adapted to run in smaller, dedicated computers. Their versatility could be increased in much the same fashion as was achieved with CALC. Considerable work would be needed to achieve this successfully. RUMP can be and has been implemented on PC systems. (7) SCATT and PROFILE had very long simulation cycle times. They are not practical for analysing large numbers of samples. (8) The oxides which form on alloys which have been oxidized at high temperatures may be too complex to be successfully analysed with the RBS technique alone, especially if the diameter of the incident beam is larger than the individual phases present in the sample. (9) For the samples analysed, mass resolution was not a problem and the use of straggling calculations did not visibly improve the analysis. ACKNOWLEDGMENTS
The authors wish to thank RMIT for RBS with the Tandetron accelerator and the University of Melbourne, Physics Department, for microprobe RBS with the Pelletron accelerator. REFERENCES 1 W.K. Chu, J. W. Mayer and M. A. Nieolet, Backscattering Spectrometry, Academic Press, New York, 1978. 2 W.K. Chu, J. W. Mayer and M. A. Nicolet, Thin Solid Films, 17 (1973) l~tl. 3 J.W. Mayer and E. Rimini (eds.), Ion Beam Book for MaterialAnalysis, Academic Press, New York, 1977. 4 J.W. Butler, M R L Rep. MRL-I040, 1987. 5 D . K . Briee, Thin SolidFilms, 19 (1973) 121-135. 6 M. Braun, Vacuum, 34 (1984) 1045-1052. 7 A. Niiler, R. Birkmire and J. Gerrits, Tech. Rep. A R E R L TR-02233, 1980. 8 J.E. Ziegler, R. F. Lever and J. K. Hirvonen, Ion Beam Surf. Anal., 1 (1976) 163-183. 9 L. Doolittle, Nucl. lnstrum. Methods B, 9 (1985) 344; 15 (1986) 227.
COMPUTER MODELLING PROGRAMS FOR RBS ANALYSIS OF OXIDIZED SURFACES
10 11 12 13 14 15
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S.R. Kennett, M R L Tech. Note 485, 1984. E. Bonderup and P. Hvelplund, Phys. Rev. A, 4 (1971) 562-569. P. Bcscnbaeh, J. U. Andersen and E. Bonderup, Nucl. Instrum. Methods, 168 (1980) 1-15. J.S. Williams, Nucl. In.strum. Methods, 149 (1978) 207-217. J. Schou, S. Steenstrup, A. Johansen and L. T. Chaderton, Ion Beam Surf. Anal., 1 (1976) 255-263. J.A. Sprague, G. R. Johnston, F. S. Smidt, Jr., S. Y. Hwang, G. H. Meier and F. S. Pettit, in S. C. Singhal (ed.), High Temperature Protective Coatings, Metallurgical Society ofAIME, Warrendale, PA, 1982, pp. 93-103.
201
AN EVALUATION OF FOUR COMPUTER MODELLING PROGRAMS FOR RUTHERFORD BACKSCATTERING SPECTROMETRY ANALYSIS OF OXIDIZED SURFACES* J. SAULITIS,G. R. JOHNSTONAND J. L. COCKING Materials Research Laboratory, DSTO, Maribyrnong, Victoria 3032 (Australia)
(ReceivedMarch26, 1988)
Rutherford backscattering spectrometry (RBS) is a powerful analytical tool for characterizing the near-surface regions of solid materials. It is one of a number of surface analytical techniques being used to analyse the surface of alloys both before and after oxidation at high temperatures. Four computer programs which have been developed to analyse RBS spectra are described. The different approaches in the design of the programs, which are designated PROFILE, SCATT, RUMP and CALC, are examined. The strengths and weaknesses of each of the programs, including their ease of use in deconvoluting spectra produced from oxidized surfaces, are discussed and contrasted.
1. INTRODUCTION Rutherford backscattering spectrometry (RBS) has evolved to become a powerful analytical tool for characterizing the near-surface regions of solid materials. The advantage of the RBS technique is that this information can be obtained non-destructively. This technique is one of a number of surface analytical techniques used to characterize the surface of alloys which have been oxidized at high temperatures. The complete characterization of the oxide film and its interface with the underlying alloy is of great importance, since the durability of the surface of a metal at high temperature in an oxidizing environment is critically dependent on the adherence and diffusion-inhibiting properties of the oxide scale on its surface. Four different computer programs which have been developed to deconvolute RBS spectra are examined and their relative strengths and weaknesses in their ability to characterize the oxide and its interface with the underlying alloy are discussed in this paper.
* Paper presented at the 15th InternationalConferenceon MetallurgicalCoatings, San Diego, CA, U.S.A.,April 11-15, 1988.
0040-6090/88/$3.50
© ElsevierSequoia/Printedin The Netherlands
202 2.
J. SAULITIS, G. R. JOHNSTON, J. L. COCKING
RUTHERFORD BACKSCATI'ERING SPECTROMETRY
The technique involves the measurement of the energy and number of elastically scattered ions which result from the impact of a beam of monoenergetic megaelectron-volt ions with a solid. The number of elastically scattered ions detected is proportional to the number of atoms present in the volume of material irradiated. The energy loss of an ion in penetrating and backscattering from a solid is related to the mass of the atom which it struck, the angle through which the collision took place and the depth at which the scattering event occurred. Thus backscattered energy spectra contain much useful information concerning the type and concentration of atoms within the first few microns of a surface. The equations used to generat e theoretical Rutherford backscattering spectra have been well documented 1-8 and will not be repeated here. 3.
COMPUTER PROGRAMS
The first computer program, of the four to be discussed, will be designated PROFILE. It was developed in 1974 at BRL by J. E. Youngblood. This program was modified by A. Niiler, R. Birkmire, J. Gerrits and G. H. Swope 7 and was written in FORTRAN 77. It contains 1870 lines of code and has been modified so that it can run on the Materials Research Laboratory VAX-11/780 computer. The second program, designated SCATT, was developed by J. F. Ziegler, R. F. Lever and J. K. Hirvonen at IBM 8. It was originally written in APL, but has been translated into FORTRAN IV. The latter program included improvements, such as the introduction of Coulomb scattering and straggling. The program used contains 1986 lines of code and has been adapted for use on the Materials Research Laboratory VAX- 11/780 computer. The third program, designated RUMP, was developed by L. Doolittle and others in 19859. The version used was designed for the VAX-11/780. A version is also available for use on IBM personal computers. RU MP occupies more memory space than the other three programs. The fourth program, designated CALC, was developed by J. W. Butler4. It was written in BASIC 3.0 with language extensions and designed to run on the series 200 Hewlett-Packard computer. This program contains about 2500 lines of code and it has not been translated for use on the VAX-11 system. Each of the programs differs in its approach. The comparative advantages and disadvantages of each program are discussed with respect to the research program in progress at the Materials Research Laboratory. 4.
THE MODELLING PROCESS
The programs are used to deconvolute the RBS spectra by a process of successive simulations. The user must arrive at an inspired first estimate of the structure of the surface of the samples as a function of depth. Some prior knowledge of this structure, from some other form of surface analysis technique, is often useful if specific experience with the behaviour of the sample is lacking. In general,
COMPUTER MODELLING PROGRAMS FOR RBS ANALYSIS OF OXIDIZED SURFACES
203
characterization of the sample is made by dividing the sample into a composition matrix. The matrix is made up of layers, in which each layer is assigned a composition. In each of the four programs the assumption is made that the composition within each layer is uniform. The individual layers may be varied in thickness in order to reflect the variation in composition with depth. When the model of the sample is formulated, units for depth and concentration must be assigned. In RBS analysis the apparent thickness used is the areal density and not the more commonly understood dimension of length. Since, to a first approximation, the sizes of the atoms of all elements are the same, a monolayer of atoms contains about 1015 atoms cm-2. This is often taken to be the natural unit to be used in RBS analysis. In order to convert from the dimensions of atoms per area to a length unit, such as hngstr6ms, the density of the material in the region of interest must be known. The use of ~mgstr6ms as a descriptive unit is attractive since it gives an easily visualized model for the characterization of the material. Unfortunately, it carries with it the corollary that the appropriate relative density must be known. Differences between estimated and actual densities will lead to errors when the theoretical spectra are generated by the computer. The four programs use different units for describing depth in the simulation model. CALC, SCATT and R U M P can use areal density, with units of atoms per square centimetre. SCATT and R U M P can also formulate the depth in hngstr6ms. P R O F I L E originally used micrograms per square centimetre, but a conversion routine was added so that units of hngstr6ms or atoms per square centimetre could be incorporated. Concentrations are usually expressed in atomic or weight per cent. SCATT, CALC and R U M P can also use the ratio of relative concentrations of atoms within a designated layer. CALC is usually run with normalized atom fractions, but also accepts normalized weight per cent. The maximum dimensions of the composition matrix differ for each program. The composition matrix for SCATT is 5 elements in 55 layers. Thus SCATT can simultaneously model up to five elements in forming a spectrum. CALC can offer a matrix of 8 elements and 55 layers. P R O F I L E offers a matrix of 10 elements and 100 layers, while R U M P uses a maximum of 20 elements and 20 layers. All but SCATT can further divide the layers into sublayers. Once the model of the sample has been assigned, the program calculates a spectrum. This calculated spectrum is compared with the experimental spectrum and the model is modified until, after a series of iterations, the model matches the experimental spectrum. 5. STRENGTHS AND WEAKNESSES OF THE PROGRAMS
5.1. Thickness limits
While none of the programs places a limit on the thickness of the sample that can be analysed, in practice two of the programs have difficulty with thick samples. At thicknesses of around 7000 ~ SCATT fails under certain configurations, such as when many elements are being modelled. Prior to failure the run times increase from the normal condition of about 16-20 s central processing unit time to 30min and more. P R O F I L E begins to malfunction at thicknesses around 700 lag c m - 2, which is
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J. SAULITIS, G. R. JOHNSTON, J. L. COCKING
equivalent to around 5500 A for a sample whose composition is Co-28wt.%Cr7wt.~Al. At these thicknesses the run times are of the order of 20-30 min. CALC and R U M P do not experience difficulty with thick samples. For example, with CALC the run time is only about 1 min for a 2 ~tm thick sample which has been divided into 50 layers. In each program the dimension of a layer determines the integration step size for the calculation. If the energy spread corresponding to each layer is much greater than the detector resolution, the spectrum generated will assume a stepped appearance. SCATT overcomes this problem by having the operator input the appropriate integrating depth step in hngstr6ms. CALC and P R O F I L E solve this problem by subdividing the layers into sublayers, the number of which is left to the discretion of the operator. 5.2. Ease o f use
R U M P , with its interactive program package, is the most versatile program. It offers the useful feature of being able to exit from R U M P to use the features of the VAX and then to return to continue the analysis without loss of previous work. R U M P commands can be gathered together in a MACRO file which can speed up an operation which has a long set of fixed instructions. CALC is the easiest program to use. CALC and R U M P are the only programs which incorporate some degree of error recovery in the event of having input incorrect parameters. Both have optionally preset default conditions. CALC make much use of the programmable key features of the Hewlett-Packard series 200 (HP9836A) computer to speed up and simplify its use. It uses on-screen editing graphics, in colour, and provides a convenient on-screen overlay plot of the concentration vs. depth profile for the elements used. SCATT and P R O F I L E were oriented for use in mainframe computers and have a more rigid structure, which requires a preformed ASCII file containing all the data for the simulation. These programs were modified at the Materials Research Laboratory to interact with control programs to form control files and to perform the calculations. The data-forming modifications include interacting prompts for the input parameters. The drawback of this arrangement is that the programs are specifically VAX oriented and take up more memory. In addition, this arrangement does not provide a fully rounded software package which R U M P , in contrast, does. SCATT is very sensitive to the size and configuration of its run parameters. Run-time errors occur under some combinations of parameters, even though the individual parameters have not exceeded their operating ranges. The result is that the program can easily generate a state where access violations can occur because the bounds of the arrays are exceeded. This is a fundamental fault in the program. This fault can cause failure of the program from things as diverse as the size of the channel width or the interpolation of the step size. For example, SCATT will run successfully for four elements with a channel width of 3.9 keV for the multichannel analyser. If an extra element is introduced the program will 0nly run if the channel width is increased to 5.0 keV or more. Another example shows that even apparently unrelated descriptors can interact to cause program failure. SCATT is nominally capable of using 55 layers. The program will run successfully if a combination of 20 layers at a detector collection angle of 150° is used. However, if the collection angle is
COMPUTER MODELLING PROGRAMS FOR RBS ANALYSIS OF OXIDIZED SURFACES
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reduced to 120° the program will only run successfully if the number of layers is reduced to 13, while at the same time ensuring that the total thickness of the model is within 7000/~. 5.3. Presentation of data With the exception of RUMP, the level of sophistication of the output depends on the peripherals of the computer system used. PROFILE and SCATT rely for their graphics on the VDU and the digital plotters as driven by the Materials Research Laboratory graphics package 1°. CALC and RUMP have the visual display integrated with the program. All programs can give their yield output in counts, but RUMP and PROFILE can also use normalized yields which is more convenient in analysis. The original SCATT output was in the form of a line printer histogram. This was modified to also give visual graphics. All programs give hard copy spectral outputs of yield vs. channel, but PROFILE and RUMP can also give various additional outputs. PROFILE as originally received included a comprehensive graphics capability. Since the graphics software was not supported by the Materials Research Laboratory VAX-11 system, PROFILE was modified to use the Materials Research Laboratory graphics package. 5.4. Energy straggling The phenomenon of energy straggling places a finite limit on the precision to which the energy losses, and hence depths, can be resolved. Straggling is an energydependent process Lll'1z that requires a considerable amount of computation to predict its effect. All four programs incorporate energy straggling, based on the Bohr model, as an option. In addition PROFILE and SCATT give the option of using further refinements to improve the effectiveness of the energy loss calculations. Straggling is only a second-order effect and its omission is not vital to the general analysis. Its implementation, however, may more than double the computation time. 5.5. Hardware effects Analysis by RBS does not require standards to be quantitative. The application of experimental conditions enables the resolution of the system to be determined. Quantitative analyses can be obtained directly from the experimental results. The parameters for evaluating the energy resolution of the system differ for each program; PROFILE is the most comprehensive while SCATT has the least sophistication. The uncertainty in the experimental beam energy can lead to ambiguities of several hundred ~mgstrrms in the generated depth profile which cannot be compensated for by the programs. 5.6. General There are many difficulties in constructing a model which is representative of a sample. Several of these have been mentioned above. In addition to those none of the programs makes provision to account for voids, gas bubbles, small precipitates, uneven spalling of the oxide or uneven growth of oxide, e.g. down grain boundaries or over different phases within an alloy. Of the four programs only RUMP
206
J. SAULITI$, G. R. JOHNSTON, J. L. COCKING
incorporates any means of manipulating the input data, such as subtracting the background. In addition, only RUMP has a routine for automatically varying parameters to yield the best fit. PROFILE includes a curve fit by the least-squares method and gives the option, as does RUMP, of using a five-point smoothing routine on the experimental spectrum before manual fit to the calculated spectrum is made. CALC also includes an option in which the experimental spectrum is smoothed. SCATT incorporates a thermal interdiffusion calculation feature, which provide an additional means of investigating the structure of ion-implanted specimens that have undergone high temperature oxidation. SCATT can calculate the thermal interdiffusion of two or more layers of the sample allowing for a simple generation of graded concentrations. RUMP allows a composition gradient to be automatically assigned by selection of any of seven equations from a menu. This option obviates the need for the operator to assign manually small changes in composition to a large number of sublayers to achieve a good fit of a sample which has a regular composition gradient. In order to obtain increased depth resolution, the target can be tilted so that the total path length required to reach a given point below the surface is increased ~a, 14. All four programs have been designed to be capable of calculating spectra for different detection angles. SCATT, however, begins to malfunction at angles less than 135°. 6. EXAMPLES The samples used in these examples are coupons of Co-22wt.%Cr-1 lwt.%A1 which were polished on one side to a 1/4 ~tm diamond paste finish. To allow direct comparisons of the effects of implanted species on oxidation mechanisms, one-half of the polished face on each sample was implanted with hafnium ions. The samples were oxidized at 700°C in air for 1 h. Previous investigations~s showed that the microstructure of the non-implanted Co-Cr-A1 prior to oxidation consisted of a matrix of t-CoAl and irregularly shaped precipitates of an ~-Co solid solution, which were between 5 and 20 pm in diameter. PROFILE, CALC and RUMP produced calculated spectra which were in better agreement with the experimental spectra than SCATT. An example of the spectra obtained from RUMP is presented in Fig. 1. Deconvolution of the experimental spectrum, which was collected on a microprobe with a spatial resolution of around 10 ~n, showed that the oxide that formed on the fl phase had an outer oxide which was a mixture of CoO, Cr203 and A120 a over a layer of AI20 a. The hafnium resides near the outer part of the A1203 layer. Deconvolution of the same spectrum using PROFILE (Fig. 2) using different units for the analysis (micrograms per square centimetre rather than atoms per square centimetre) produced a fit which was not quite as good in the fine details but which produced a composition matrix which was essentially the same. All programs produced spectra which diverged from the experimental spectra at the low energy end. Because SCATT uses only a limited number of layers the calculated spectra were not always as smooth as those produced by the other programs. In addition,
COMPUTER
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the samples stretched the operating parameters of the program to their limits. During analysis of oxidized samples, the simultaneous accommodation of the oxygen edge (at the low energy end of the spectrum) and the hafnium edge (at the high energy end)just spanned the normal operating range of the program. ENERGY (MeV] 1,0
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208
J. S A U L I T I S , G . R. J O H N S T O N , J. L. C O C K I N G
If the oxidized sample was ideal, i.e. the oxide formed in a layer of even thickness over the surface, the models of the spectra calculated by both the backward and glancing collection angles should result in identical composition matrices. The samples in these experiments were composed of two phases which
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COMPUTER MODELLING PROGRAMS FOR RBS ANALYSIS OF OXIDIZED SURFACES
209
oxidized differently. In those experiments in which the spectra were collected from an instrument whose beam diameter was greater than 1 m m it was not possible to generate a single composition matrix for the two collection angles. An example of this is shown in Fig. 3 for spectra generated by CALC. A reasonable fit was generated for the spectrum collected at 150 ° . When the same concentration profile was used to generate a spectrum at 130 ° the fit was poorer.
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(b) Fig. 3. Rutherford backseattering spectra gathered at (a) 150 ° and (b)' 130 ° of oxidized hMniumimplanted C o . r - A 1 , using an instrument with a beam diameter of greater than I ram. Since the precipitate phase in the alloy was 5-20 lain in diameter, and since the oxides which grew on the two phases were of different thicknesses, it was not possible to match the experimental (e) and theoretical ( ) spectra with a unique composition matrix. In this example CALC was used; however, the problem is common to all four programs.
210
J. SAULITIS, G. R. JOHNSTON, J. L. COCKING
7. CONCLUSIONS (1) PROFILE, CALC and RUMP gave better agreement with experimental spectra than SCATT. (2) Of the programs examined, only CALC could be used after a brief introduction period by a non-specialist user of a computer. (3) CALC is oriented to Hewlett-Packard BASIC. To translate the program to a more common language that can be used on a system such as the VAX-11 is probably not practical. (4) SCATT and PROFILE in their original forms were slow and difficult to use. Their operation and control parameters assumed a great deal of knowledge that a person who was unfamiliar with computer programming was unlikely to have. The formulation of the control data and their running made them unsuitable for an interactive type of operation. (5) RUMP was comparatively easy to use, but required initial implementation by a computer expert. (6) SCATT and PROFILE could be adapted to run in smaller, dedicated computers. Their versatility could be increased in much the same fashion as was achieved with CALC. Considerable work would be needed to achieve this successfully. RUMP can be and has been implemented on PC systems. (7) SCATT and PROFILE had very long simulation cycle times. They are not practical for analysing large numbers of samples. (8) The oxides which form on alloys which have been oxidized at high temperatures may be too complex to be successfully analysed with the RBS technique alone, especially if the diameter of the incident beam is larger than the individual phases present in the sample. (9) For the samples analysed, mass resolution was not a problem and the use of straggling calculations did not visibly improve the analysis. ACKNOWLEDGMENTS
The authors wish to thank RMIT for RBS with the Tandetron accelerator and the University of Melbourne, Physics Department, for microprobe RBS with the Pelletron accelerator. REFERENCES 1 W.K. Chu, J. W. Mayer and M. A. Nieolet, Backscattering Spectrometry, Academic Press, New York, 1978. 2 W.K. Chu, J. W. Mayer and M. A. Nicolet, Thin Solid Films, 17 (1973) l~tl. 3 J.W. Mayer and E. Rimini (eds.), Ion Beam Book for MaterialAnalysis, Academic Press, New York, 1977. 4 J.W. Butler, M R L Rep. MRL-I040, 1987. 5 D . K . Briee, Thin SolidFilms, 19 (1973) 121-135. 6 M. Braun, Vacuum, 34 (1984) 1045-1052. 7 A. Niiler, R. Birkmire and J. Gerrits, Tech. Rep. A R E R L TR-02233, 1980. 8 J.E. Ziegler, R. F. Lever and J. K. Hirvonen, Ion Beam Surf. Anal., 1 (1976) 163-183. 9 L. Doolittle, Nucl. lnstrum. Methods B, 9 (1985) 344; 15 (1986) 227.
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S.R. Kennett, M R L Tech. Note 485, 1984. E. Bonderup and P. Hvelplund, Phys. Rev. A, 4 (1971) 562-569. P. Bcscnbaeh, J. U. Andersen and E. Bonderup, Nucl. Instrum. Methods, 168 (1980) 1-15. J.S. Williams, Nucl. In.strum. Methods, 149 (1978) 207-217. J. Schou, S. Steenstrup, A. Johansen and L. T. Chaderton, Ion Beam Surf. Anal., 1 (1976) 255-263. J.A. Sprague, G. R. Johnston, F. S. Smidt, Jr., S. Y. Hwang, G. H. Meier and F. S. Pettit, in S. C. Singhal (ed.), High Temperature Protective Coatings, Metallurgical Society ofAIME, Warrendale, PA, 1982, pp. 93-103.