Dramatización como estrategia didáctica interactiva

X-ray diffraction (XRD) is a very powerful technique for the characterization of epitaxial layers and has been extensively used throughout this thesis work, in particular to measure the composition, thickness, and defect density of the epilayers grown by MOVPE. The instrument used is a Brucker New D8 Discovery. The principle of XRD is shown in Fig. 3.2. In XRD, an X-ray beam is generated by an X-ray tube and is sent to the sample, which diffracts the beam. A mobile X-ray detector collects the diffracted beam and measures its intensity. The instrument used in this work is furthermore equipped with an X-ray mirror for focusing the incident beam and with a set of monochromators for increased resolution. Both the sample and the detector can be moved. In particular, the sample can be tilted around theω axis while the detector is moved in order to change theθ angle. Fig. 3.2 shows, together with the sample and the instrument’s X-ray source and detector, the reciprocal space of the crystal under study and the incident (k0), diffracted (kh) and scattering (S) vectors. k0and khhave magnitude 1/λ, where

λ is the wavelength of the X-rays used (λ = 1.54 Å in our case). S = kh− k0. The detector will

register a non zero signal when the Bragg diffraction condition is fulfilled, i.e. when S points to a reciprocal space node or, equivalently, when nλ = 2d sinθ, where n is an integer and d is the separation between the planes of atoms corresponding to the diffraction spot observed. Several types of XRD measurements can be performed.ω scans are measurements where the detector is kept fixed, while the sample is rotated around theω axis. Such measurement config- uration allows to explore the broadening of the diffraction spots in a direction perpendicular to the scattering vector. For (000l ) reflections, the FWHM of the diffraction peak is related to the tilt angle (βt i l t) between the grains constituting the crystal, while For¡l 0¯l0¢ reflections it

is related to the twist angle (βt w i st) between the grains. The broadening of other reflections

Figure 3.3: (a)ω − 2θ spectra of the (0002) reflection of an InAlN/GaN heterostructure on sapphire with 8 nm total (AlN + InAlN) barrier thickness. (b) X-ray reflectivity spectra of the same layer.

dislocation densities (DD) can be extracted using the formulas of Dunn and Kogh [136]:

[Screw DD] = β 2 t i l t 4.35b2s £Edge DD¤ =β 2 t wi st 4.35b2e (3.1)

where bs= 5.185 Å and be= 3.189 Å are the Burgers vector lengths for edge and screw dislo-

cations, respectively. We will see in Sec. 3.3.2 a rigorous method for the extraction of the tilt and twist angles. However, this method has the drawback of being quite time consuming and furthermore the recording of¡l 0¯l0¢ω scans requires a dedicated instrument for in plane XRD. These measurements have been performed at the University of Magdeburg in the group of prof. Alois Krost. Alternatively, we verified experimentally that a very good approximation of βt i l tandβt wi st are given by the FWHM of the (0002) and (2¯1¯12) reflections, respectively. This

method has been thus employed to obtain a quick and reliable estimation of the dislocation densities.

A second type of XRD measurement areω − 2θ scans, which consist in varying simultaneously and by the same amount theω and the θ angles. This kind of measurement allows exploring the reciprocal space in the direction parallel to the scattering vector, as shown in Fig. 3.2. During this work,ω−2θ scans have been recorded only for the (0002) reflection. The result of a scan over an InAlN/GaN heterostructure on sapphire having 8 nm total (AlN + InAlN) barrier is shown in Fig. 3.3(a). The spectra is composed of several peaks, corresponding to the various materials constituting the multilayer. The GaN and AlN peaks are easily distinguished and their separation is due to the difference in c lattice parameters. InAlN, on the other hand,

3.2. Growth of InAlN alloys

gives rise to a broad peak with several interference fringes on both sides. These fringes, called Pendellosüng fringes, are due to the the low thickness of the barrier. From the period∆θ of the fringes the total thickness T of the barrier can be calculated:

T = λ

2∆θ cosθ (3.2)

The average composition of the barrier can be on the other hand obtained from the position of the main peak, in particular from its distance to the GaN peak. The GaN buffer can be indeed considered in most cases relaxed, and is taken thus as a reference for the calculation of the InAlN c parameter, from which the composition is extracted using Vegard’s law (Sec. 1.1.1). The last kind of measurement performed in this work is X-ray reflectivity. This measurement can be thought as anω − 2θ scan of the (0000) peak. The θ angle is therefore scanned around very low values, usually from 0◦to 5◦. The X-ray reflectivity spectra for the same InAlN/GaN heterostructure of Fig. 3.3(a) is shown in Fig. 3.3(b). For angles higher than the angle of total internal reflection, interference fringes can be observed. These fringes are due to the finite thickness of the barrier stack and their period∆θ can be used to determine the barrier thickness:∆θ = λ/2T . There might be however a difference between the barrier thickness determined from the period of the Pendelosüng fringes and the one determined from X-ray reflectivity. The former corresponds indeed to just the thickness of the crystalline material, while the latter comprises any layer on top of the GaN buffer, crystalline or amorphous. By comparing the two thicknesses we can thus detect the presence of amorphous layers at the surface. We will see examples of this in chapter 4.