Nuclear Instruments and Methods in Physics Research B 267 (2009) 1737–1739
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Simulation and fitting of high resolution Rutherford backscattering spectra Christian Borschel a,*, Martin Schnell b,1, Carsten Ronning a, Hans Hofsäss b a b
Institute for Solid State Physics, University of Jena, Max-Wien-Platz 1, 07743 Jena, Germany II. Institute of Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
a r t i c l e
i n f o
Article history: Available online 30 January 2009 PACS: 07.05.Kf 82.80.Yc Keywords: RBS Data analysis Computer simulation
a b s t r a c t A computer program for the analysis of high resolution Rutherford backscattering spectra (HR-RBS), which can be recorded with an electrostatic energy analyzer (ESA) and a resolution of about 1 keV, has been developed. The use of an ESA results in various differences compared to conventional RBS spectra, motivating the development of a new algorithm for simulation for these spectra. We present a Monte Carlo based diffusion-like fit approach for evaluation of the HR-RBS spectra, which is in particular useful for fitting concentration gradients. Examples for the application of the algorithm are shown to demonstrate its functionality. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction
2. Recording ESA spectra
A variety of ion beam analysis software, that can be used for simulation and fitting of Rutherford backscattering (RBS) spectra, is available [1–6]. A comparison of the most used programs has recently been made by Barradas et al. [7]. However, there are different reasons for the development of a new simulation and fitting program for high resolution RBS spectra. We use an electrostatic analyzer (ESA) for high resolution RBS analysis of thin films and their interfaces, providing an energy resolution of about 1 keV, which roughly translates to a depth resolution of down to 1 nm at perpendicular incidence. The ESA spectra exhibit various differences compared to conventional RBS spectra, necessitating special care in the data analysis. In particular, the energy resolution DE scales with the energy E and the charge state distribution of backscattered ions becomes important. Additionally, the high depth resolution requires accurate calculation of energy straggling. In principal, these differences could easily be included in other codes. However, as the analysis of concentration gradients on the nanometer scale is an interesting application of high resolution RBS, we put more emphasis on fitting concentration gradients instead of fitting layer thicknesses or stoichiometry. Therefore, a Monte Carlo fit algorithm, representing a diffusion process and suitable to find complex concentration gradients was developed.
In order to achieve an excellent energy resolution in RBS spectra, we use a 90° cylindrical capacitor as an electrostatic analyzer (ESA) for determining the energy of backscattered ions. Ion beam transport simulations were made in order to optimize the ESA geometry: the backscattering angle is fixed to 127°, the mean radius is 300 mm and the plates are 6 mm apart. The resulting resolution of the ESA is about DE/E 0.3%. Considering typical stopping powers and the charge state distribution of backscattered ions, optimum primary beam energies are around 450–500 keV for our setup. This corresponds to a typical energy resolution of about 1 keV for the backscattered ions, which – depending on the target material – translates approximately to a depth resolution of 1 nm at perpendicular incidence. This high depth resolution can only be reached within the first few nanometers of the sample, the energy straggling puts the major limit on the depth resolution in greater depths. The ESA setup is connected to the HVEE ion implanter ‘‘IONAS” in Göttingen, which provides several lA of He+ beam up to 500 keV with an energy spread well below 1 keV (details are described elsewhere [8]).
* Corresponding author. Tel.: +49 3641 947358; fax: +49 3641 947302. E-mail address:
[email protected] (C. Borschel). 1 Present address: Asociación CIC nanoGUNE, Tolosa Hiribidea, 76 20018 Donostia – San Sebastian, Spain. 0168-583X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2009.01.084
3. Simulation and fitting of ESA spectra The general simulation procedure is similar to many other codes [9]: The concentration profile of the sample is represented as many thin layers, each of these layers having a homogeneous composition of arbitrary elements and isotopes. In contrast to other codes, all thin layers have the same thickness, which is set to a value around the depth resolution of the experiment (typically
C. Borschel et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1737–1739
4. Applications High resolution RBS was applied to samples of self-organized carbon/metal multilayers prepared by mass selected ion beam deposition. During hyperthermal ion deposition, metal nanoclus-
ters form within a tetrahedral amorphous carbon (ta-C) matrix, where these clusters congregate in metal-rich layers leaving metal-deficient layers in between (details in [16]). HR-RBS measurements were performed on carbon/gold multilayers in order to extract the depth distribution of the deposited Au utilizing the MC fit routine (completely random, no diffusion). Evaluation of these multilayers is in a sense straightforward as the backscattering spectra are unambiguous (ambiguity of RBS data is discussed in detail in [17], Section 8). The measured ESA spectrum, the fitted spectrum and the resulting concentration profile are illustrated in Fig. 1. To verify the functionality of the simulation and the fit with an independent method, a cross sectional transmission electron microscopy (TEM) image of the ta-C/Au sample is illustrated inside Fig. 1(b) for comparison. The Au-rich layers (dark) coincide with the peaks in the Au concentration profile found by the fit to the ESA spectrum. Additionally, an energy dispersive X-ray (EDX) line scan applied within the TEM is depicted in Fig. 1(b) along with the profile found by the Monte Carlo algorithm. The profiles are in general agreement, small differences are due to the facts, that firstly the EDX line scan measures the concentration profile locally, while RBS averages over the complete beam spot with a size of about 1 mm2 and secondly the EDX intensities may be distorted by thickness variations of the TEM specimen. The results from the fit to the HR-RBS are reasonably consistent with the TEM and EDX analysis, indicating correct functionality of the fit approach. The second application of HR-RBS together with our algorithm is the analysis of the interface in gadolinium/nickel bilayers. These bilayers, deposited by molecular beam epitaxy onto Al2O3 sub-
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1 nm). This way, concentration gradients can be represented appropriately according to the resolution. The energy spectrum is generated by tracing the way of ions into and out of the sample layer by layer: summing energy loss and energy straggling as well as simulating backscattering events by calculating the Rutherford cross-section. For the calculation of stopping power, we use polynomial fits to tables generated by the SRIM code [10] (version 2006.02), energy straggling (Gaussian-shaped) is calculated using empirical formulae provided by Yang et al. [11] with the effective charge factor for He ions taken from Ziegler et al. [10]. In contrast to detecting with Si detectors, the charge state distribution (CSD) of the backscattered He ions needs to be taken into account when using an electrostatic analyzer for detection. We use Armstrong’s empirical formulae to calculate the equilibrated fractions of He0, He+, and He++ exiting the sample as a function of energy [12]. The program allows accounting for (gamma-distributed) surface roughness by superimposing spectra of different layer thickness, as proposed by Mayer [13]. Comparisons to simulations made by the RUMP code [3], version 4.00 and a comparison to one of the IAEA intercomparison spectra [14] (calculation no. 1) serve as a test to verify the basic functionality of the simulation procedure. Simulations of different samples are in close agreement, which excludes major bugs in the simulation procedure. We are aware, as our program does not take into account several phenomena (i.e. plural and multiple scattering, pile-up, or other effects), that in fitting normal RBS spectra it cannot compete with some modern codes like NDF [4] or SIMNRA [5]. However, the high resolution of ESA spectra is most interesting close to the sample surface, because in greater depth the resolution is limited by energy straggling anyway. Multiple and plural scattering mostly influence the backscattering spectra at lower energies corresponding to greater depths in the sample [15]. Pile-up background on high energy signals does not exist in ESA spectra since the energy is determined by the voltage applied to the ESA plates and not the pulse-height of the detector signal. Additionally, since only a small energy window is detected at a time, count rates are very low. We conclude that most ignored effects do not pose a severe problem when analyzing ESA spectra with our code. In order to fit concentration profiles to measured spectra, a Monte Carlo (MC) approach is used together with the simulation procedure. The square deviation between measured and simulated spectrum is minimized by accepting or discarding random changes in the virtual concentration profile. For typical samples, a few 1000 of these cycles are necessary for minimization. The way how random changes of the concentration profile are applied, calls for some attention. A simple way is to randomly select one of the many thin layers of the virtual sample and change the relative concentrations of two elements a little. An alternative method to perform ‘‘random” changes, which we term Monte Carlo Diffusion, turned out to be quite useful in some cases: in a randomly selected depth, some material is swapped between two adjacent layers, which resembles a diffusion-like step, conserving quantity from the previous concentration profile. As one may expect, this MC diffusion approach turns out to be particularly useful to find concentration profiles of samples with multiple thin layers and diffuse interfaces in between.
Au concentration [a.u.]
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Depth [nm] Fig. 1. (a) Open circles: ESA spectrum of carbon/gold multilayers. (The CSD and the scaling energy window both reduce counts at low energies, making it impossible to record a significant carbon signal.) The solid line shows the simulated spectrum resulting from the fit routine. (b) The Au concentration profile fitted by the program and an EDX line scan for comparison. (Due to uncertain carbon density and nonabsolute X-ray signals, the EDX result is adjusted to the MC fit result.) The inset shows a cross sectional TEM image.
C. Borschel et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1737–1739
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5. Conclusion
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A program for the analysis of high resolution Rutherford backscattering spectra has been developed. The program simulates spectra recorded with an electrostatic analyzer with nm resolution. In order to fit concentration profiles to measured spectra, a Monte Carlo fit is employed. In the Monte Carlo diffusion approach, material is swapped randomly between adjacent layers to match simulated and measured spectra. The functionality of the simulation and the fit routine are demonstrated on two different sample systems. The depth distribution of gold in self-organized carbon/gold multilayer structures was extracted from an ESA spectrum using a totally random Monte Carlo fit approach. The resulting Au profile is in reasonable agreement with results from an EDX line scan in a TEM measurement. For the analysis of the interface at Gd/Ni bilayers, the Monte Carlo diffusion approach was utilized. The profile of the interface was extracted and allows determination of interface roughness with resolution close to 1 nm. Users interested in obtaining the program are welcome to contact the authors!
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Fig. 2. (a) ESA spectrum of Au-covered Gd/Ni bilayers, the solid line shows the simulation; (b) fitted concentration profiles, solid lines to ‘‘guide the eye”.
strates, are particularly interesting due to their magnetic properties [18]. The samples are covered with a thin gold layer in order to avoid oxidation. Fig. 2(a) illustrates the experimental ESA spectrum along with the resulting simulation from the fit program, both being in nice agreement. The fitted concentration profile is plotted in Fig. 2(b). In analyzing this sample, a distinction of the MC diffusion approach from other random algorithms is revealed: a completely random search algorithm could for example also reproduce the measured Gd and Ni signals by adding gold in deeper layers; to avoid this, constraints for elemental concentrations in certain depths have to be defined. The MC diffusion approach conveniently avoids the necessity of defining such constraints. It can be observed that the interface between the Gd and the Ni layer is not sharp but stretches over a depth of almost 10 nm. Because RBS averages over the large beam spot of 1 mm2, it is not possible to determine the lateral scale of the roughness directly. Due to the largely different energy loss per length of He in Gd and Ni, we learn from the broadness of the low energy Gd edge, that the Gd/Ni interface is morphologically rough and not diffuse on an atomic scale, (the influence of roughness on RBS spectra is discussed in detail in [19]). The results on the interface roughness from the fit algorithm were confirmed by other methods, i.e. scanning tunneling microscopy (STM) measurements, which were performed in between Gd and Ni deposition and Auger electron spectroscopy (AES) applied during deposition [18].
Acknowledgements We would like to thank Günter Schatz and Alexander Barth (University of Konstanz) for the Gd/Ni bilayers, Inga Gerhards (now at Fraunhofer Institut für zerstörungsfreie Prüfverfahren) for the carbon/metal multilayer samples, and Michael Seibt from the University of Göttingen for the TEM image. References [1] [2] [3] [4] [5] [6] [7]
[8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
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