a X-Ray scattering: X-Ray Diffraction (XRD) and X-Ray Reflectivity (XRR) 59 

When X-Rays go through a material, they interact with its atomic electron cloud. For inorganic materials constituted of regularly spaced series of atoms, scattering of the incident X-Rays occurs: due to the interaction between radiation and matter, incident photons are forced to change direction while keeping the same energy according to the principle of Rayleigh scattering. Since the wavelength of X-rays is close to lattice inter-plane distances (a few Angstrom), constructive and destructive interference between scattered rays can occur as well. Depending on the angular direction, both of those alternatively occur, yielding either high (for constructive interferences) or low (for destructive interferences) X photon flux. The angular spacing between directions of high flux is determined by a simple Bragg law and therefore constitutes a direct indication of the inter-atomic distances in the direction normal to the sample surface. X-Ray scattering techniques use this phenomenon to quantitatively infer the properties of pure, mono and polycrystalline material since each material (in its crystallographic form) has a unique lattice parameter. When a sample is constituted of several, heterogeneous materials layers, the different orders of reflexion n of the rays on the interfaces may also show oscillations with a given wavelength (similar to Fabry-Pérot effect), which contain information on the thickness of the layers. XRD or XRR spectra are obtained by illuminating a sample with an X-ray monochromatic beam and then rotating the sample. X- Ray source is fixed while both sample and detector are moved in such a way that the angle of incidence of the X-Rays is always equal to the angle of the measured scattered rays. This way one obtains a scan of intensity of scattered X-Rays as a function of their incident angle, as shown in Figure II.12 [26]. The difference between both settings consists in their angular range: while XRD measurements are obtained using rather wide incident angles (typically 30- 40 degrees), XRR measurements are obtained at shallow angles (0-5 degrees) since the intensity of reflected X-Rays exponentially decreases with the incident angle (as seen on Figure II.12.B). Using XRD, the overall spectrum is dominated by the intense and narrow substrate peak, the other well-defined features are attributed to the overlayer peak (second peak in intensity) and its thickness fringes (smaller peaks). The angular separation between substrate and overlayer peaks corresponds to a given x content for the overlayer material alloy. Similarly, regular fringe spacing yields a given thickness for this layer. Attenuation of the oscillations around the overlayer material peak can suggest a non-uniform composition of the layer (see Figure II.12.A). Using XRR, an intensity plateau is obtained at low angles, corresponding to total reflection of the beam on the sample surface. The critical angle for intensity drop is characteristic of the material density. Once again, angular spacing between two peaks contains information about layer thickness, while attenuation and modulation of the oscillations with increasing incident angle allow quantitative measurement of interface roughness and of the presence of surface (or interfacial) layers (see Figure II.12.B). Such ω- 2θ scans, so-called “double-axis rocking curves” are easily simulated using fundamental X- ray scattering theory. By fitting composition, number of layers, thickness and composition of the overlayer(s) in XRD or density, thickness and interfacial roughness in XRR one can fit experimental data to theoretical spectra and therefore quantitatively infer interface roughness, layer crystalline quality (in particular strain state or degree of relaxation) and presence of potential thin layers such as surface native oxides. In the case of multiple overlayers, the main features of the scans remain unchanged but spectra are more complex, due to the presence of multiple order diffraction (or reflection) peaks. For a more comprehensive overview or X-Ray scattering techniques principles and applications particularly concerning Si and SiGe epitaxial layers, please refer to references [26-31]

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Solutions explored to answer ToF-SIMS characterisation needs

60

Both of these techniques are therefore very useful for precise determination of epitaxial, defect-less layer properties. Since these techniques are non-destructive they would preferably be used prior to any other measurement. Precisely, we are interested in the following parameters which can be provided by XRD and XRR:

- Absolute layer thickness (quantitative)

- Precise epitaxial alloy composition (quantitative)

- Interfacial roughness (qualitative)

- Layer strain state (qualitative)

- Layer crystalline quality (qualitative)

The absolute determination of layer thickness constitutes an interesting property for us since it allows direct determination of ToF-SIMS profile depth scale for both single or multiple heterogeneous material layers samples. Interfacial roughness measurement is also quite useful since it can be used to understand interface width obtained in a depth profile or to understand depth resolution worsening effects after sputtering through multiple interfaces. Finally, indications on layer strain state and crystalline quality can help in understanding of some effects observed on sputter rates or ionisation yields in particular materials.

II. 4. b- Spectrosopic ellipsometry

Light is composed of a wide variety of electromagnetic waves differing in phase and amplitude. The electric fields of these waves can be decomposed into two components, orthogonal to each other and always normal to the light’s propagation direction.

Figure II.13Measurement principle of ellipsometry. Extracted from [32].

This results in an electric field orientation, which is random (and varying in a stochastic manner) for natural light. However also this field can also have a preferential orientation (polarized light), and can be either linear (if component waves are equal in phase and in amplitude), circular (if component waves are opposed in phase but equal in amplitude) or elliptic (composed of waves of random phase and amplitude), the latter being the most common as it is the natural state of light. When light hits a surface of different refraction index, it is partly reflected, and its polarisation is modified. Ellipsometry measures the change in polarisation occurring at such events. To achieve such a measurement, one has to produce polarised light through the use of a polariser, which is then directed to a sample. The linearly polarised light reflects on the sample surface, becomes elliptically polarised, and travels through an analyser usually composed of a continuously rotating polariser. The polarisation change is represented as the amplitude ratio, tan(Ȍ), and the phase difference, ǻ, as shown in

CHAPTER II

Solutions explored to answer ToF-SIMS characterisation needs

Figure II.13 [32]. The measured response depends on optical properties and thickness of individual materials. Thus, ellipsometry is primarily used to determine film thickness and optical constants through comparison with theoretical calculations using Fresnel’s equations. However, it can also be used to characterise composition, crystallinity, roughness, doping concentration, and other material properties associated with a change in optical response. The film thickness is determined by interference between light reflecting from the surface and light traveling through the film. Depending on the relative phase of the reflected light, interference can be constructive or destructive. The interference involves both amplitude and phase information. The phase information from ǻ is very sensitive to films down to sub- monolayer thickness [32].

In our study, we have only used this technique to obtain precise layer thickness measurements for thin (<10 nm) to ultra thin (~nm) layers. Compared to X-Ray scattering techniques, ellipsometry has the double advantage of precise measurement even for ultra-thin layers combined with efficiency on any type of material, be it crystalline, amorphous or even for organic materials.

Accurate thickness measurements on ultra-thin layers are often measurable only by ellipsometry. Based on these thicknesses one can either assess the accuracy of the depth scale of a ToF-SIMS profile or, more simply, directly infer sputter rates in single or double overlayer systems by affecting ellipsometry measured experimental thicknesses to ion intensity half signals or particular peaks characteristics of interfaces.