**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.

**Keywords:** thin film, multilayer, ion beam analysis, ERDA, RBS, depth profiling

### **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

#### **Figure 1.**

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

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.

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 *Eb*, of the incident ion of mass *mi*, after collision with a target atom of mass *mt*:

$$\frac{E\_b}{E\_i} = k\_b = \left(\frac{-m\_i \cos \theta \pm \sqrt{m\_t^2 - m\_i^2 \sin^2 \theta}}{m\_i + m\_t}\right)^2 \tag{1}$$

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

$$\frac{E\_r}{E\_i} = k\_r = \frac{4m\_i m\_r}{\left(m\_i + m\_r\right)^2} \cos^2 \phi \tag{2}$$

where, *kr* is referred to as the recoil kinematic factor describing the ratio of the recoil atom energy *Er*, to the incident ion energy *Ei*, and *mr* 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].

$$\left(\frac{d\sigma}{d\Omega}\right)\_{\text{scattered}} = \left(\frac{Z\_i Z\_t e^2}{2E\_i}\right)^2 \frac{\left(\sqrt{m\_t^2 - m\_i^2 \sin^2\theta} - m\_2 \cos\theta\right)^2}{m\_t \sin^4\theta \sqrt{m\_t^2 - m\_i^2 \sin^2\theta}}\tag{3}$$

similarly the recoil cross section is given by

$$
\left(\frac{d\sigma}{d\Omega}\right)\_{recoil} = \left(\frac{Z\_i Z\_r \varepsilon^2}{2E\_i}\right)^2 \left(1 + \frac{m\_i}{m\_r}\right)^2 \frac{1}{(-\cos^3\phi)}\tag{4}
$$

where *Zi, Zt* and *Zr* 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 *mi* < *mt* 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:

$$
\Delta \mathbf{x} = \int \frac{1}{\mathcal{S}(E)} dE \tag{5}
$$

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.

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 *Depth Profiling of Multilayer Thin Films Using Ion Beam Techniques DOI: http://dx.doi.org/10.5772/intechopen.105986*

#### **Figure 2.**

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

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

**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]).*

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].
