Depth Profiling of Multilayer Thin Films Using Ion Beam Techniques

Abstract

Functional properties of thin film structures depend a lot on the thickness and chemical composition of the layer stack. There are many analytical techniques available for the identification and quantification of chemical species of thin film depositions on substrates, down to a few monolayers thickness. For the majority of these techniques, extending the analysis to several tens of nanometres or more requires some form of surface sputtering to access deeper layers. While this has been done successfully, the analysis tends to become quite complex when samples analysed consist of multilayer films of different chemical composition. Ion beam analysis (IBA) techniques using projectile ions of energies in the MeV range have a demonstrated advantage in the study of multilayer thin films in that the analysis is possible without necessarily rupturing the film, up to over 500 nm deep in some cases, and without the use of standards. This chapter looks at theoretical principles, and some unique applications of two of the most widespread IBA techniques: Rutherford Backscattering Spectrometry (RBS) and Elastic Recoil Detection Analysis (ERDA), as applied to multilayer thin film analyses.

1. Introduction

Structure-property studies of thin films underpin research and development of new functional materials from fundamental experimental investigations right up to device fabrication stage. This is, to a large extent, made possible by the availability of specialised analysis tools able to probe materials at the nano/micrometre levels. Examples of analytical tools found in typical materials research labs include Atomic Force Microscopy (AFM), Scanning Electron Microscopy (SEM) for surface morphology, X-ray Photoelectron Spectroscopy (XPS), Auger Electron Spectroscopy (AES) for elemental and chemical state information, X-ray Diffraction (XRD) for crystal structure determination, Raman Spectroscopy and Fourier Transform Infrared Spectroscopy (FTIR) for molecular identification, and so on [1, 2]. Thin film coatings of up to a few 100nm thickness abound in many advanced technological applications, including sensor devices designed for a whole range different stimulus [3]. These thin film structures derive their functional properties from their physical dimensions and chemical makeup. Film thickness, for instance, plays a key role in semiconductor solar radiation detectors, in determining the fraction of solar radiation that is absorbed in the active region of the detector [4]. The concentration and depth distribution of dopant species in semiconductor materials is key to the operation of sensor devices based on thin film diode and/or transistor structures. The aforementioned analytical techniques can readily provide surface and structural properties of a film but not so much thickness and elemental depth profile information. Ion beam analysis techniques using MeV energy beams have a demonstrated capability to provide this information, without the use of standards in most instances [5]. At the highest level of performance, standard-free analysis at 1% traceable accuracy has been reported [6].

Multilayer structures present unique challenges for elemental depth profiling analytical techniques. In sputter depth profiling using any of XPS, AES, or Secondary Ion Mass Spectrometry (SIMS) there is a need for standards for calibration of the sputter etch rate to a depth scale. On the other hand, the interaction depth/range of MeV ions allows for probing films to depths of up to 1 micrometre or more depending on the probing ion species and energy, without necessarily sputtering the material. For a film comprising different layers the ion-matter interaction parameters change in a way that makes it possible to distinguish the different layers, again without recourse to a reference standard. This chapter begins with a look at how these fundamental interactions are exploited in two widely used ion beam analysis techniques; Rutherford Backscattering Spectrometry (RBS) and Elastic Recoil Detection Analysis (ERDA). The discussion then progresses to description of a typical experimental set up before looking at practical multilayer film analysis examples that showcase the unique strengths of IBA techniques.

2. Ion-matter interactions at MeV energies

When a swift ion penetrates solid matter a number of interactions may take place between the ion and the target atomic nuclei and electrons. These include elastic and inelastic scattering, nuclear reactions, excitation and ionisation, photon emission, etc. The extent of the interaction between a beam of ions and the target atoms depends largely on the particular collision cross section σ (E, Z₁, Z₂), which in many instances is a function of both the ion energy and atomic numbers of the incident and target atoms. The cross-section gives the probability of a given type of ion-atom interaction taking place. If the cross section for a particular ion-atom combination is known, then detecting, counting and sorting the products of an interaction in some systematic way can provide information about the nature of target atoms. This information could be any of the identity, concentration and depth distribution of a particular atomic species in a film. Therein lies the core of ion beam analysis techniques, and indeed other similar ‘probe-and-measure’ analytical techniques. Within the kaleidoscope of possible interactions that may occur when an ion beam strikes a solid target material, there are three main physical parameters that underpin the application of ion beams in materials analysis. These are described hereunder.

2.1 Kinematics of ion-atom collisions

As a swift ion moves through solid matter, it interacts with both the electron cloud and the atomic nuclei of the target material. Collisions with target nuclei provide the basis for identification of the target atom species according to their mass. This is achieved through treating the interaction as a binary elastic collision between the two particles. In the ideal case the effects of the electron sub-system and the neighbouring nuclei are ignored, thereby simplifying the mathematical treatment [7]. Figure 1 shows a representation of the ion-atom collisions relevant to (a) RBS and (b) ERDA. The backscattering and recoil angles are defined with respect to the incident beam direction by the orientation of the detectors employed for the measurement.

Figure 1.

Collision kinematics for (a) RBS and (b) ERDA techniques. In RBS an incident ion of mass m_i with energy E_i is backscattered through an angle 0 < θ < 90 with an energy E_B, and in ERDA target atoms of different masses m_R, are forward recoiled at an angle 90^o < φ < 180^o with different energies E_R. The actual values of θ and φ are defined by the orientation of the RBS and ERDA detectors.

For RBS, applying the principle of conservation of kinetic energy and momentum in elastic collisions leads to the following equation that gives the backscattering energy E_b, of the incident ion of mass m_i, after collision with a target atom of mass m_t:

$$\frac{E_b}{E_i}=k_b={\left(\frac{-m_{i}cos\theta \pm \sqrt{m_t^2-m_i^2{sin}^2\theta }}{m_i+m_t}\right)}^2$$E1

where k_b is known as the backscattering kinematic factor, with the plus sign in Eq. (1) holding for m_i < m_t. A similar consideration for Figure 1b leads to:

$$\frac{E_r}{E_i}=k_r=\frac{4m_i{m}_r}{{\left(m_i+m_r\right)}^2}{cos}^2\varphi$$E2

where, k_r is referred to as the recoil kinematic factor describing the ratio of the recoil atom energy E_r, to the incident ion energy E_i, and m_r is the mass of the recoil atom. The angles θ and φ are as defined in Figure 1. In principle then, for a given experimental configuration, measurement of the energy of the backscattered ion in RBS or that of the recoiled atom in ERDA can be used to determine the mass of the target or recoil atom, respectively.

2.2 Collision cross section

The quantitative capability of ion beam analysis techniques is a direct consequence of the physical concept of cross section(σ) in ion-target interactions. The cross section describes the probability of a backscattering or recoil event occurring in a given direction, defined by the detector solid angle (Ω), and is a function of the interaction potential associated with the collision. Continuing with the concept of point charge interactions used in kinematics, quantitation in both RBS and ERDA techniques is based on a Coulomb interaction potential. For a pure Coulomb potential the RBS or Rutherford scattering cross section is given by [7, 8].

$${\left(\frac{d\mathrm{\sigma }}{d\mathrm{\Omega }}\right)}_{\mathit{\text{scattered}}}={\left(\frac{Z_i{Z}_t{e}^2}{2E_i}\right)}^2\frac{{\left(\sqrt{m_t^2-m_i^2{sin}^2\theta }-m_{2}cos\theta \right)}^2}{m_t{sin}^4\theta \sqrt{m_t^2-m_i^2{sin}^2\theta }}$$E3

similarly the recoil cross section is given by

$${\left(\frac{d\mathrm{\sigma }}{d\mathrm{\Omega }}\right)}_{\mathit{\text{recoil}}}={\left(\frac{Z_i{Z}_r{e}^2}{2E_i}\right)}^2{\left(1+\frac{m_i}{m_r}\right)}^2\frac{1}{\left({-cos}^3\varphi \right)}$$E4

where Z_i, Z_t and Z_r are the atomic numbers of the incident, target and recoil ions, respectively, and e is the electron charge. The angles θ and φ are again as defined in Figure 1. The concentration of a given atomic species in a sample is then obtained from the experimental yield, which is directly proportional to the cross section, in the energy spectrum associated with that element. Real collisions approximate this simplified approach in cases where the incident particle is totally stripped of its electrons and can thus be regarded as a point charge. Corrections are nonetheless needed to account for deviations from the ideal case scenario in instances where the incident ion energy is low, to a point that screening by orbital electrons cannot be neglected. Anderson and co-workers [9] reviewed the energies at which this deviation occurs and these are now fairly well known. Deviation also occurs at the high-energy side when the distance of closest approach of the nuclei is within the range of nuclear forces and the interaction potential is no longer a simple Coulomb potential. Bozoian et al. [10] have determined the energies at which nuclear force field effects become significant.

Additional parameters that are needed for concentration evaluation are the incident beam dose and the detector solid angle. Eqs. (3) and (4) both show that for a given experimental geometry, the experimental yield is directly proportional to the square of the Z-values and inversely proportional to the square of the incident beam energy. This fact underpins the preference of low energy heavy ions in the case of ERDA, as this favours good measurement statistics within a relatively short measurement time. For RBS, while the cross section is higher for heavier and slower incident ions, the requirement that m_i < m_t precludes their use in many applications. This limitation is generally countered through delivering fairly high beam doses of light element projectiles to get acceptable spectral yields.

2.3 Energy loss rate: Stopping force

Depth analysis in ion beam analytical techniques follows directly from the energy lost by the projectile and the target atoms traversing the target sample [11]. In RBS for example, the energy loss of the incident ion as it enters and exits the target sample gives the location of the scattering atom below the surface, whereas in ERDA it is the total energy lost by the projectile ion as it enters and the recoil atom as it exits the target sample that gives a similar indication. The energy loss per unit depth, or the stopping force, is a fundamental ion-atom interaction parameter that is the key linkage between an energy spectrum and the thickness of a target layer. In basic terms the energy width dE in a measured energy spectrum depends on the thickness Δx of a target layer according to:

$$\mathrm{\Delta }x=\int \frac{1}{S\left(E\right)}\mathit{dE}$$E5

where S(E) is the energy dependent stopping force. The energy loss of the incident ion traversing a target material arises from two types of interactions which are dependent on the ion velocity [12]. At low energies (below about 1 keV/u) the energy loss is mainly due to elastic collisions with target nuclei. This is referred to as nuclear energy loss. As energy increases, interaction with the electron cloud becomes more dominant as the ion speed approaches that of the orbital electrons in target atoms. The energy loss is then mainly through inelastic collisions with the target electrons of the system. This is referred to as electronic energy loss and for the typical ion energies used in IBA, this is the dominant mode of energy loss.

Stopping force is also dependent on the Z-values of the colliding particles. For a fixed target, the stopping force increases with the projectile ion charge at the same velocity. This points to better depth resolution when heavy ions are used, according to Eq. (5). This, however, is at the expense of ion range or analytical depth since heavy ions would have a shallower range because of the higher stopping force. There are several theoretical formulations that are of semi-empirical [13] or ab initio [14, 15] origin that are used to calculate S(E) for a wide range of ion-atom combinations and energy ranges. It goes without saying that the accuracy of the stopping force data that is used in the energy-to-depth calculations is one of the major contributing factors to the accuracy of layer thickness and depth profile measurements.

3. Analytical software

The three physical concepts of binary collisions, collision cross section and stopping force discussed above constitute the theoretical foundation of ion beam analysis techniques. Practical implementation of the techniques requires taking into account many other additional effects that lead to deviations from the ideal situation. Software codes have been devised over the years to aid the interpretation of energy spectra obtained in a measurement. These can be broadly classified into two categories. The first category encompasses codes that calculate concentration profiles directly from experimental energy spectra using modified analytical calculations [16, 17]. These modifications could include for instance screened Rutherford cross sections, where the effect of the electron cloud on the pure Coulomb interaction is taken into account in ion-atom collisions. One advantage of these codes is that they are unlikely to generate more information about the sample than the data actually contain. The main drawback is that the profiles derived are, strictly speaking, not real concentration depth profiles since they still have the energy resolution convoluted with effects of the actual sample structure and so one has to live with the limited depth resolution given by the experimental and sample conditions.

The second category (mainstream codes are in this group) includes codes that tackle the problem from the opposite viewpoint; a hypothetical sample structure is assumed and a theoretical energy spectrum calculated either analytically, as in SIMNRA [8], or by Monte Carlo (MC) methods [17, 18] and compared with the experimental one. This sample structure is altered until a best fit is obtained between the simulated and the experimental- spectra [18]. This iterative simulation approach uses analytical functions to convolute the ideal energy spectrum so as to consider most of the physical limitations that include the detector resolution, energy loss straggling, multiple scattering and sample roughness [11] among others.

Monte Carlo simulation-based codes such as MCERD, that is in-built in Potku [17] and CORTEO [18] stand apart from the deterministic codes in the sense that MC methods principally include all the important phenomena involved in ion-target interactions. The approach employed here is that the calculation follows individual ion trajectories to negligible energies, based on analytical functions that describe ion stopping and collision cross sections with the necessary correction (e,g. screening functions) implemented. In this way complex physical processes such as multiple scattering and the interaction between ions and the detector system are taken into account in a natural way, without the approximations that analytical codes involve. The one drawback of analytical and Monte Carlo simulation codes is that they may include phantom structural details that lead to a good fit to experimental data but not necessarily reflecting the true sample structure. Good practice in IBA then dictates using both direct calculation and iterative simulation codes to get a more accurate interpretation of the measurement data.

4. IBA instrumentation

Ion beam techniques are based on high energy ion beams generated from particle accelerators. Typical IBA accelerators vary in size, from small compact tandetrons of 2.0 MV terminal voltage to fairly huge tandem accelerators of up to 20 MV [19]. These machines deliver particles of energies ranging from 0.1–to 10 MeV/u, depending on particle mass. In brief, specific ions are injected from the ion source into the accelerator column where particle acceleration is due to a huge electrostatic field. On exiting the acceleration stage, a magnetic field is used to select ions of a specific charge to mass ratio, or energy, to filter through to the experimental end station or scattering chamber. The schematic in Figure 2 shows the general set up for both RBS and ERDA analysis techniques. There are of course additional accessory systems such as beam diagnostics, beam focusing elements, vacuum systems and high voltage power supplies, and so on that make up a complete accelerator system.

Figure 2.

Basic set up for RBS and ERDA ion beam analysis techniques.

As pointed out in the introduction, functional exploitation of ion-matter interactions in ion beam analysis depends on the positioning and type of particle and/or photon detectors to detect and count the relevant products of ion-atom collisions. In RBS for instance, solid state semiconductor detectors are generally used to count the number of incident ions backscattered through a particular angle and to measure their energy as well. Raw data is collected in the form of an energy spectrum of backscattered particles. It is this energy spectrum that is fitted using analytical software like SIMNNRA [8] to extract sample properties such as elemental depth profiles.

In the case of ERDA, two detector variants are available. The simplest or conventional set up, mostly used for hydrogen analysis, consists of a solid-state detector with a filter foil in front of it to stop all other atomic species besides hydrogen. It is possible though, to select the incident beam species, energy and filter foil in such a way that other ions heavier than hydrogen can be analysed—if hydrogen itself is not one of the constituent elements of the target sample. The limitation of the conventional set up is quite apparent. If the object of analysis is the depth distribution of several elements in a sample then this configuration cannot be used. Mass dispersive detector systems such as time-of-flight (ToF) telescopes [20] become quite useful in this regard. In a ToF detector set up the energy of recoil atoms is measured simultaneously with their transit time over a known distance—leading to mass identification or separation. Figure 3 is a schematic of the ToF detector system used at the iThemba LABS ERDA set-up, where the flight path is 0.6 m long. Raw data generated from such a detector set up consists of 2-D scatter plots of ToF vs. energy (Figure 4) from which elemental energy spectra can be extracted and fed into analytical software for either direct depth profile calculation [16, 17] or simulation [8, 21].

Figure 3.

The time-of-flight detector set up for heavy ion ERDA at iThemba LABS.

Figure 4.

ToF vs. energy scatter plots from the analysis of an Al₂O₃-Ti bi-layer stack on a silicon substrate before annealing (a) and after annealing (c) in vacuum at 800°C. the resultant depth profiles are shown in (b) and (d), respectively. Channels in (a) and (b) refer to as yet uncalibrated time and energy axes. (reproduced with permission from ref. [20]).

5. Application examples

The examples of analyses below have been selected from the literature to highlight some of the relative strengths (and weaknesses) of the two IBA techniques discussed in this chapter.

5.1 ERDA analysis of an alumina-titanium layer stack

Figure 4 shows results of ERDA depth profiling of an Al₂O₃/Ti/Al₂O₃/Ti/Si bi-layer film annealed at 800°C in vacuum [20], to study the Al₂O₃-Ti solid state reaction. The measurement was carried out using a 26.1 MeV ⁶³Cu⁷⁺ beam, with a time-of-flight (ToF) recoil detector mounted at 30^o (φ = 150^o in Figure 1) to the incident beam direction. Further details of the measurement set-up are given in Msimanga et al. [20]. Coincidence measurement of the ToF and energy of atoms recoiled from the target sample allows for their separation according to mass. The 2-D scatter plots in Figures 4a and c show all the elements detected from each target sample, as well as the forward scattered incident ⁶³Cu beam. The shape of the scatter plots derives from the simple inverse relationship between the ToF and kinetic energy E_r of the recoil atoms; $\mathit{ToF}=\sqrt{m_r/2E_r}\bullet L$, where m_r is the recoil atom mass and L is the length of the flight path. For a given atomic species, atoms recoiled right from the surface will be detected with higher energy (i.e. shorter ToF) than those from deeper layers due to energy loss of the latter as they move through, and out of the sample. And for a given energy E_r, the ToF increases as the particle mass increases, i.e. heavier atoms move slower, hence the observed separation of recoil atoms in terms of mass.

The depth profile of the as-prepared sample is shown in Figure 4b and that of the annealed one in Figure 4d. To get a sense of the analytical depth shown, if the depth scale is converted to units of nanometres using known atomic densities of the Al₂O₃ and Ti, the Ti/Si interface is about 150 nm from the surface in Figure 4b and shifts to just under 140 nm in Figure 4d, indicating silicide formation at the interface. The advantage of such ‘raw’ depth profiles, calculated using the direct energy-to-depth conversion code KONZERD [16] is that they give a quick visual description of the layer structure, with no need for a standard or reference sample. This provides a good starting point for further, more detailed analysis through MC simulation codes as described in ref. [20].

5.2 RBS analysis of Ti_0.7Al_0.3N/MoN and CrN/MoN multilayer films

Bin Han et al. [22] report of the analysis of Ti_0.7Al_0.3N/MoN and CrN/MoN multilayer films on Si(001) substrates using RBS. The incident ions used were 2.42 MeV and 1.52 MeV Li²⁺ ions at varying incident angles. The RBS data was supplemented by XPS, SEM and HR-TEM. The measurement using the 2.42 MeV energy beam at 0^o incidence was able to resolve the Ti and Mo signals from first seven pairs of bi-layers of 44 nm Ti_0.7Al_0.3N and 32 nm MoN. Figure 5 shows the experimental and SIMNRA simulated spectra for extracting the depth profiles [22]. For Al this was possible only for the first three bilayers—beyond which the overlap of the Al signal with that of Ti and Mo from deeper layers precluded Al analysis. A pertinent observation that Bin Han and co-workers make from their results is that the low energy incident beam gave a much a higher backscattering yield (an indication of enhanced sensitivity—see Eq. (3)) and better depth resolution, but for a shallower analytical depth. For a fixed beam energy, increasing the tilt angle improved the depth resolution but again at the expense of the analytical depth. Another important observation that highlights a chink in the armoury of RBS is that while the surface sensitive XPS confirmed nitrogen in the topmost layers, it also pointed out presence of oxygen in those layers. RBS could not, because of the ‘shadowing’ effect of the (heavier) substrate element signal on that of light elements.

Figure 5.

RBS spectra from the analysis of Ti_0.7Al_0.3N/MoN and CrN/MoN multilayer films using 2.42 MeV Li2+ ions at 0^o incidence angle (a) and at varying tilt angles (b). Similar spectra are shown in (c) and (d) respectively for a 1.52 MeV Li²⁺ incident beam. (taken from ref. [22], reproduced under the terms of the creative commons CC BY licence).

5.3 RBS and ERDA analysis of a solar thermal absorber stack

In A study of solar thermal absorber stack based on CrAlSiN_x/CrAlSiN_xO_y structure by ion beams, AL-Rjoub et al. [23] describe RBS and ERDA measurements of a four-layer solar absorber film stack. The RBS data leads to rather inconclusive findings due to extensive overlap of signals from the different layers. On the other hand, the mass dispersive detector of the ToF-ERDA system allows separation of all the elements in the layer stack according to mass. Depth profiles are then extracted from Monte Carlo simulation using the MCERD code [17].

Figure 6 shows, raw data from ToF and energy detectors, experimental and simulated energy spectra of oxygen recoils from different layers and, the depth distribution of oxygen in the layer stack. While the obtained profiles are rather unrealistic step functions, it is widely accepted that due to the one ion at a time nature of the treatment of ion-target collisions in MC simulations, they produce the closest description to reality of a target structure.

Figure 6.

Raw energy vs. ToF data (left), experimental and simulated oxygen energy spectra (Centre), and depth distribution of oxygen (right) in a SiAlO_x/CrAlSiN_xO_y/CrAlSiN_x/W layer stack. (reproduced with permission from ref. [23]).

5.4 Real-time RBS analysis of a hydrogen storage Pd/Ti/Pd layer stack

Another unique application of IBA techniques is the study of solid state reactions in real-time. This is a technique which has been pioneered by among other labs, the iThemba LABS (formerly known as the National Accelerator Centre) in South Africa [24]. Magogodi et al. [25] report of in-situ real-time RBS analysis of a 125 nm thick Pd/Ti/Pd film stack to investigate diffusion kinetics and stoichiometric evolution under different annealing environments. This formed part of a study aimed at developing hydrogen storage materials. The measurement described used 2 MeV He²⁺ ions to probe the layer structure as the samples were annealed in vacuum and in hydrogen environments, with the data taking starting from 160°C up to 600°C, at 30-second intervals.

Figure 7 is a 2-D plot of the colour coded spectral yield as the temperature increases. For the sample annealed in vacuum, Figure 7a, the authors surmise that there is complete reaction between the Pd and Ti layers by the time the sample temperature reaches 550°C, and for the one annealed in a H₂ environment, their conclusion is that the Ti-Pd reaction is, to a great extent, inhibited. The obvious advantage of such a measurement is that by monitoring the reaction in real-time, any intermediate phases that may form are also detected, and not just the end-point—thus facilitating the study of solid-state reaction mechanisms. Indeed this has been applied in, for example, studies of growth kinetics of Ni(Pt) silicides [26], where the analysis of the huge data generated was done using artificial neural networks.

Figure 7.

Contour plots comparing the onset of reaction between atomic species in Pd/Ti/Pd layers annealed in (a) vacuum and in (b) hydrogen environments. (reproduced with permission from ref. [25]).

6. Summary

Multilayer thin film structures have become ubiquitous in many device structures in the current era of nanotechnology driven advances in electronics, medicine, energy and other technological fields. Ion beam analysis techniques can readily generate invaluable structural information about multilayer films through standard-free analyses that are not possible with other analytical techniques. The physics behind RBS and ERDA techniques described in this chapter is well established and there are data analysis tools available to the materials analyst that can facilitate interpretation of experimental data with reasonably good accuracy. The selected applications described showcase the versatility of these analytical tools in addressing different problems from simple film thickness measurements to tracking solid state reactions in real-time.

Acknowledgments

The author would like to gratefully acknowledge financial and infrastructural support from the Tshwane University of Technology through the Photovoltaic Nanocomposites Research and Development Platform, and from NRF-iThemba LABS.

Conflict of interest

The author declares no conflict of interest.