5 Rutherford Back Scattering – IV
Dr. Ajit K. Mahapatro
Learning Objectives:
From this module students may get to know about the following:
i. Back scattering for thin film analysis
ii. Single and multi component thin film analysis
iii. Single and multilayer thin film analysis
1. Introduction
Thin film plays an important role in making devices and also in many analytical works including analysis of organic-inorganic interface, role of substrate in thin film deposition, low level doping determination with the other elements etc. The main feature of such a spectrum is that both the front surface and the interface can be probed with better accuracy by this technique unlike in thick sample where only front surface is recognizable. Two independent parameters can be extracted from both the outer surface and the inner interface of the sample in a backscattering signal, (i) the interface gives an energy difference ΔE between the adjacent edges of the signal (ii) the total number of counts A contained in all channels of the signal between these edges. From these one can calculate the number of atoms per unit area contained in the thin film. The back scattering spectrum contains more than one signal for each element present in the sample and elemental analysis can be done with ease.
2. Energy spectrum of a thin elemental film
In order to analyze the energy spectrum of a thin film, we assume that the thin film contains Nt atoms of a single element per unit area. It also contains thin film with element of higher atomic mass than the substrate itself. A typical spectrum is shown in the figure below with the suppression of the background signal. The two quantities of interest are the energy width ΔE of the signal and A, the total number of counts added over all channels in the signal. Both the quantities are directly related to the number of atoms per unit area contained in the film.
Figure 1: Schematic representation of the back scattering processes in thin film and corresponding backscattering signal.
3. Energy Width ΔE between High- and Low-Energy Edges of the Signal
As is shown in Fig. 1, particles backscattered particles from the surface of the thin film has a kinetic energy KE0; those backscattered from atoms at the rear produce counts at an energy E1,t. The energy difference ΔE = KE0 — E1,t is related to the number of atoms per unit area in the film, given by the equation,
∆?= [?]̅ ?t (1)
When the film is very thin, the surface approximation for [?]̅ is adequate. From the measured value ΔE and the knowledge of [?]̅, we can determine the number of atoms per unit area Nt in the film.
4. Total number of counts in the Signal
Moreover, apart from the above, other quantity that one can be extracted from the backscattering spectrum of a thin film is the total number of counts and given by the equation,
?= ∑??? (2)
Summed over all channels i of the signal. If Hi is expressed in terms of E1,i, the summation becomes unwieldy. The reason is that scattering cross sections are given as a function of the energy Ei immediately before the scattering. This energy is most readily arrived at by computing the energy that the particle loses along its incident path, which is ( ???/cos ?1) ?(E̅in)and subtracting it from the incident energy E0:
5. Energy spectrum of multilayered elemental filmsNow we would discuss the backscattering spectra of a sequence of elemental thin films. The analysis of the spectrum is divided into two parts. The first part is the top layer. The backscattering spectrum of this layer remains unaffected by the layers underneath. Therefore the analysis of this layer can be done by the preceding section, where the analysis of elemental film is discussed. The other part of the elemental analysis consists of the layer that is underneath the top layer. For the films that lie beneath the top layer, the incoming incident particle has a lower kinetic energy than that falls on the surface layer. This is because the top surface Layer acts an absorber and hence the energy is reduced considerably. The particles that also reach after back scattering from the second layer also has lower energy than the back scattered particle of the top layer. A qualitative discussion of this problem is illustrated in Fig.2. The thin sample shown in figure consists of a film ‘A’ sandwiched to a film ‘B’ on the top and both rest on elemental substrate S. For backscattering spectrometry, the most favorable situation is when element A is heavier than B, and B is heavier than S, i.e., Ks < KB < KA. The backscattering energy spectrum for this particular case is sketched in Fig. 2a. The signal of A reaches to the edge KAE0 of A, but the signals of B and of S are shifted to energies below their respective edges KBE0 and KSE0 because of the energy loss in the outer layer A. To illustrate this point, Fig.2b represents a spectrum of a sample without layer B. Since there is no layer, the particles reaching the substrate has lower energy than that of A. The signal would have a higher energy. The signal of A is unchanged, because the spectrum of a surface layer is not influenced by the underlying material. This is so because both A and B act as energy absorbers for S; the removal of B reduces the absorbing layer to the thickness of A only. The high-energy edge of the signal of B now appears at KBE0 because B is at the surface. To a first approximation, the signals of B and S are both shifted toward higher energies by an amount that roughly equals the width of the absorber signal A.
Figure 2: (a) Schematic representation of the backscattering spectrum of a bilayered film on a substrate S. The monoisotopic element A is the heaviest, B is intermediate, and S is the lightest, (b) Spectrum for a sample without the intermediate layer B. (c) Spectrum for a sample without the top layer A.
6. Energy spectrum of a homogeneous thin film containing more than one element (compound film)
We will focus on the analysis of a thin film which is composed of many elements. This is different than the single element thin films in many ways. Firstly, due to the presence of different constituent atoms, the energy of the incident particle decreases as there are many interactions with the other elements of the film. As a result, the stopping cross section depends on the composition of the film and is therefore initially this quantity is unknown. Similarly, the back scattered electron also carry different kinetic energy due to the presence of dissimilar atoms. This mass is different for the various elements in the film. The stopping cross section varies with energy, so that the energy of the scattered particles would depend on the type of atom it interacts during the collision. Suppose that the film contains two elements A and B in the atomic ratio AmBn. The backscattering spectrum of such a homogeneous film with two elements is sketched in Fig. 3. Two signals are observed, corresponding to scattering from the heavy atom A and the light atom B.
Figure 3: Schematic representation of the backscattering process in a self-supporting compound thin-film sample, and the resulting backscattering spectrum. The figure also shows the meaning of the symbols used in the text.
7. Energy Width ΔE between High- and Low-Energy Edges of the Signals
The energy widths ΔEA and ΔEB generally differ by as much as 10% in spite of the fact that there is only one film thickness i, because, generally, [?]??/? ≠ [?]??/?. Since the depth-to-energy conversions are not the same for the two signals, hence the difference in energy is created. Hence, the number of molecules per unit area (or molecular units per unit area in the case of a mixture) can be found in two different ways:
8. Total Number of Counts in the Signals
The composition of the film is generally unknown. This means that [?]]??/? and [?]??/? cannot be computed, even when the elements A and B are known, because m and n are not known. Equations (5) and (6) also cannot determine the number of molecules (or molecular units) per unit area in the film. However, the total number of counts in a signal is related to the number per unit area of the atoms in the target that generate the signal. The ratio AA/AB of the total number of counts AA and AB in the spectrum of Fig. 2 is therefore related to the ratio m/n. The connection between the total numbers of counts AA and AB in signals A or B and the number NABAt and NABAt of atoms per unit area in the film thus constitutes the point of main interest in the backscattering spectrum of Fig. 3. This relationship is investigated next. The energy immediately before the collision is
9. Ratio of Signal Heights in Surface Energy Approximation
The ratio m/n of the relative concentrations m and n of the elements A and B in a homogeneous bielemental film can also be obtained from the heights HA,o and HB,o of the signals of A and B (see Fig. 3). Scattering from the top surface layer of such a sample is the same as for a bulk sample. There are therefore two different ways of finding the ratio m/n. One approach uses the total number of counts in the signals of A and of B, and the stopping cross section factors need not be known. The other approach uses the height of the signals at their high-energy edge. In this case, the ratio [?]AB/A / [?]AB/B of the stopping cross section factors enters into the result. That ratio is usually close to unity, and can be attained by iteration. From the knowledge of m/n, the relative compositions m and n follow with the condition that m + n = 1. It is not possible, however, to state that the sample is composed of the chemical compound Am Bn, even if m and n are fractions of small integers. Backscattering spectra only provide information on relative atomic composition. How these atoms are combined, i.e., the chemical constitution of the sample, must be deduced from other experiments, such as chemical analyses or x-ray diffraction.
10. Energy spectrum of multilayered films containing more than one element (layered compound films)
This section combines the subject of multilayered elemental films with that of compound film having more than one element. The combinations are many, e.g., multilayer plus compound film, compound film on an elemental film, the heaviest element being either in the top layer or underneath it. The formulas describing the spectrum of all these examples will be different in each case, but the concepts from which they are derived are the same in every case. We shall therefore give a detailed treatment of one particular case only to demonstrate the procedure through that example. In general, the spectrum of a multilayered sample with compound films is complex because the signals of the various elements in the layers overlap. To identify certain features of the spectrum with signals generated from a specific element in a specific layer of the target is usually a nontrivial task. This job is greatly facilitated if several spectra of the same sample are taken under different experimental conditions (sample normal and tilted with respect to the incident beam, several incident energies, etc.). We are not concerned here with these questions of proper interpretation of a spectrum. Rather, we assume that the subdivision of the spectrum in its individual signals has been accomplished already. It is then convenient for the discussion to assume that the signals of the various elements do not overlap. The top layer of a multilayered sample can be analyzed as described above if it is a compound film, since the underlying layers do not affect the spectrum of the top layer, other than possibly an overlap of signals. There the top layer is assumed to be elemental, but, as was pointed out in the end of that section, the treatment is the same for a compound absorber. After the second layer has been analyzed, the first two layers together are considered as one absorber to the third layer. The analysis of that layer is undertaken next, and the process is iterated as necessary until all layers have been analyzed. Although this process is logically simple, its execution and the formulas rapidly become long and cumbersome. A comparison with numerically computed spectra may be easier. In this section, this process is demonstrated in detail for the particular case of a sample composed of a thin film of element A on top of a compound film of composition AmBn. This situation is encountered when a thin film of A reacts at the interface with the substrate B and starts to form a compound AmBn. A schematic diagram of the backscattering energy spectrum of such a sample is shown in Fig. 4. For simplicity, A is assumed to be the heavier element of the two, and the total amount of A is taken to be small enough so that no signals overlap. In the superscripts, the compound AmBn is abridged to AB. Note that superscripts identify the medium and that subscripts give the element to which the quantity refers. The succeeding subsections discuss the main quantities of interest in this spectrum.
Figure 4: Schematic representation of the backscattering process in a sample composed of a thin surface film of a monoisotopic heavy element A, a substrate of a monoisotopic light element B, and a compound layer AmBn between, and the resulting backscattering spectrum. The figure also shows the meaning of the symbols used in the text.
Summary
In this section we have briefly described the elemental analysis of a thin film by back scattering spectrum. Various compositions of thin films including single layer, multi layer, single and multi elemental thin films have been described in detail. It gave an idea about how to analyze the back scattering spectrum in case of thin film with composite structure.
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References
1. Ziegler, J. F., Lever, R. F. and Hirvonen, J. K. (1976). In Ion Beam Surface Layer Analysis” (O. Meyer, G. Linker, and F. Käppeler, eds.), Vol. 1, p. 163. Plenum Press, New York