Structural Properties
Several experimental procedures can be implemented to study the microstructural, compositional, and thermal degradation of thin films. These procedures may be classified as X-ray diffraction (XRD) analysis, scanning electron microscopy (SEM), transmission electron microscopy (TEM), thermogravimetry analysis (TGA), etc. However, for organic semiconductors, one important analysis is IR spectra where molecular bonding phenomena are accurately studied. XRD analysis is one of the main tools to analyze the structures of any materials. Using this XRD technique, the nature of any material can be identified, whether it is amorphous, crystalline, or polycrystalline. The lattice constants, reflections of crystalline planes, particle size, composition, defects, stress, and strain, etc. can also be studied using this XRD technique (Kalita et al. 2000, De et al. 1996 & De and Mishra 1997).
Bragg (Dekker 1996) considered X-ray diffraction from the crystalline material as a problem of reflection from atomic planes and analyzed a set of parallel atomic planes of Miller indices (hkl), the spacing between successive planes being dhkl. When an X-ray beam reflected by an atomic plane, the condition for reflection or diffraction from the said considered plane is given by Bragg’s law.
(3.1)Here, n is the order of reflection having values of 0,1,2,3…, d is the inter-planner distance of particular crystalline plane, λ is the X-ray wavelength, and θ is the angle of diffraction or Bragg’s angle. This condition shows for a given value of dhkl and λ and n having integer values; only a particular angle θ would produce such a reflection. Thus, it can be concluded that when a beam of monochromatic X-rays incident on a crystal with an arbitrary angle θ is in general not reflected. Also, because sinθ ≤ 1 and d ~10-8 cm, reflection or diffraction can be observed only for λ of the order of 10-8 cm or less.
Lattice Constant/Parameter
The lattice constants/parameters are the features of a crystal and defined as the distances of the neighboring unit cells in three dimensions generally denoted by ‘a’. For a cubic lattice, the distance between successive planes is given by equation 3.2 (Dekker, 1996):
(3.2)Here, hkl are the Miller indices, and dhkl is the inter-planar spacing. The precise measurement of lattice constant (a) can be affected by many factors viz. deviation of the X-ray beams, deflection and absorption of X-rays by the specimens, etc. Therefore, accurateness of determination of lattice constant is dependent upon the accurateness in the measurement of the inter-planar spacing (d). From Bragg’s law,
(3.3)The Nelson-Riley curve is plotted for precise measurement of lattice constant at θ = π/2 where the curve plotted between the calculated lattice constant ‘a’ for different planes and the error function (Nelson & Riley, 1945) which is given as:
(3.4)The lattice constant/parameter can accurately be measured by intercepting the plot, as mentioned above with the x-axis.