DETERMINATION OF DISLOCATION DENSITY AND CORRELATION LENGTH OF Si, Ti, Au and ZnO on Ge by PEAK PROFILE

In this study, X-ray diffraction peaks of Si, Ti, Au and ZnO grown on Ge substrate with thickness of 500 nm by using sputtering method are analyzed to determine correlation length and dislocation density. It is seen that in most dense region of peaks, peak behaviour is in accordance with Gauss function. Right and left tails of peaks are in good accordance with q3 law. For randomized dislocations, obeying q3 law is typical and they can be monitored with w-scans by using open detectors. Whole profile is fitted with a limited dislocation dispersion. Edge dislocation density and correlation length are determined in the degree of 10 10 cm -2 and 10 3 nm, respectively. In order to gain these values, semi-experimental equations in Kragner method are used. For making a good fit, fit iteration step is taken as 9x10 6 .

Because, these structures are not influnced by edge dislocations. Also, edge dislocations produce defects in lattice planes parallel to surface, but they do not effect peak positions along layer normal. The highest value of edge dislocations is gained by diffraction patterns formed by lattice planes normal to surface. In this diffraction geometry X-ray reaches sample by sweeping the surface [4].
In order to determine the problem absolutely, it is good to give fundamentals of subject here.
Alternative geometry that can easily be performed in labrotary is asymmetric (screw) geometry. This geometry (incident and refracted waves have the same angle towards surface) is shown in  Incident wave K in and diffracted wave K out makes the same  angle with sample surface. Scattering vector Q makes  angle with sample surface [5].
Lattice planes normal to surface can be determined by measuring diffraction reflections with increasing tilt of lattice plane. Scanning curve can be gained by focusing wide tilts to odd reflections. Circular diffractometer is needed for symmetric geometry, because sample is tilted according to normal of surface. Asymmetric planes on circular diffractometer are less sensitive to edge dislocations and they have connection with lattice parts normal to surface [5]. Full width at half maximum (FWHM) of diffraction peak is not dependent on dislocation density but dependent on correlation among dislocations. FWHM is also dependent on natural orientations of scattering vector, dislocation path orientation and direction of Burgers vector [5,6].
In this study, shape of peaks and especially tail regions of peaks are analyzed in whole diffraction profile. Dislocation densities are determined by using Kragner's q-3 law. In this method, Fourier transform is applied to correlation function numerically and dislocation densities, dislocation correlation lengths are determined [5].

Experimental
Sputtering is a common system to grow thin films on substrates in which atoms are detached from target material in vacum medium. In this system, reactive ions such as Ar+ are accelerated in high potential difference and target material is bombed with these ions. Molecules detached from target material are deposited on substrate. The best advantage in this system is that it permishes deposition operation at low temperatures. With this advantage, any desired material can be deposited on the substrate.
Sputtering technique used for growth of Au, Si, Ti and ZnO structures on Ge substrate includes removal of atoms from target by applying high voltage to metal in high vacum medium.
Conductive material is used as anode and metal is used as cathode. Sample is coated in high vacum. After forming an atmosphere of an inert gas such as Ar+ in the tube with anode and cathode, there forms a plasm atmosphere at high voltage. At desired voltage value an electrical arc comes out. Sputtering systems are applied as radio frequency (RF), magnetic field, triode, direct current (DC) and ion beam sputtering.
In this study, Si, Au, Ti and ZnO are grown on high crystallized Ge with D.C sputtering method.
In D.C sputtering method, coating material is inserted in cathode and substrate is inserted in anode. As Ar+ is put in the coating medium and anode-cathode system is exposed to D.C voltage there forms the plasm atmosphere. As Ar+ ions are accelerated and hit the target material, atomsa re detached from target material. At the end of this operation surface of substrate is coated. In order to gain highest X-ray diffraction peak, Ge is coated with Au, Si, Ti and ZnO with thickness of 500 nm under 10 -3 mbar pressure.

Results&Discussion
In diffraction peak profile analysis, limited moments of intensity distribution is calculated by using q-3 asymptode. But, in randomized and limited dislocations wieving length can not be gained from asymptothic part of peak. Fit of whole peak profile maintains both dislocation distribution density and wieving length parameters. Numerical calculation of peak profile includes 1-D Fourier integral. By using this integral calculation can be made rapidly. Using q-3 asymptode is a more reliable way to determine dislocation density because q-3 asymptode is not effected among dislocations and it is in accordance with scattering in the region near to dislocation lines. Asymptothic part of intensity distribution does not include X-ray diffraction studies. Determination of dislocation density is related with FWHMs. If peak is effected by both bulk and defects, sum of Gaussian and Lorentz functions (Psevdo-Voigt) are fitted.
FWHM of Gaussian is used for determining dislocation density. Width of symmetric and asymmetric reflections are effected from dislocation densities and they change shape of the peak. It is likely that dislocation distribution is similar in similar film coating and growth. For films those have partly dislocations, width of given peak reflection is not only dependent on dislocation density, it is also dependent on limited randomized dislocation density and correlation length.
In this study, peak shape analysis is width of correlation length at the same time. Simple thought of peak width gives hand to determination of dislocation density. Peak shape analysis shows that X-ray diffraction profile is Gaussian at the center of peak. Peak tails obeys q-3 law in Xray diffraction with randomized dislocations. When omega curves with analyser crystal obeys q-4 behaviour, omega curves are measured with an open detector detecting q-3 behaviour [5]. It is very convenient to study omega curves with an open detector both experimentally and theorically because diffraction density is more and wider. Diffraction density is described by converting 1-D Fourier transform of peak profiles to correlation function. q-3 peak tails maintains determination of dislocation densities more accurately and they are denser with correlations among dislocations.
All diffraction profiles are fitted to main equation with suitable parameters. These parameters are dislocation density (ρ), wieving length and crystallite size (L). Next term is in accordance with Burgers vector equal to zero and average crystallite volume [5]. In order to compare  Structure is face centered cubic. Gold peak center is at 66.017 degree and it corresponds to (400) peak PDF-4-784 XRD database. Lattice constant is a=4.079 Å. This structure is also face centered cubic.          Because ZnO structure has good crystal quality it has sharp peaks.

Conclusion
In this study, profile fit of Au, Si, Ti and ZnO thin films grown on Ge substrate by sputtering method is made after XRD scans. As the result of fit, dislocation density and correlation lengths are determined. Comparison of these results can be made with Figure 10. According to these results dislocation densities are found almost at the same level (~10 10 ). Here the biggest dislocation density value belongs to Ti and biggest crystal length belongs to Si.  Crystallite size