Applying X-Ray Diffraction in Material Analysis Dr. Ahmed El-Naggar

Introduction X-Ray diffraction techniques Some X-Ray diffraction applications Summary Outline

I) Introduction

II) X-Ray diffraction techniques I- High-resolution Mostly used for near-perfect epitaxial thin films and single crystals. 2- Medium resolution Primarily used for thin films that are textured epitaxial, textured polycrystalline. Also can be used for polycrystalline and amorphous materials. 3- Low resolution Mostly used for polycrystalline as well as amorphous materials

6 motorized movements of the Sample

Low Resolution applications: Texure analysis, Stress analysis, and ω-2θ scan, phase analysis Medium Resolution applications: ω-2θ scan, phase analysis, Stress analysis, and Reflectivity. High Resolution applications: Rocking curve (ω-scan), Reciprocal space map, ω-2θ scan, phase analysis, Stress analysis, and Reflectivity

III) Some X-Ray diffraction applications ω/2θ-scan, phase analysis

From ω-2θ (θ -2θ) scan the ensemble of d- spacings (" d" s) (Using Bragg's law to get them) and intensities (" I" s) is sufficiently in order to identify phases Phase determination can be performed by a comparison of a set of experimental d's and I'swith a database of d-I files Database of d-I files were named Powder Diffraction File (PDF) database (started 1919 and was containing 4000 compounds), but from 1978 the name changed to be International Center for Diffraction Data (ICDD) which contains about 300,000 pattern

Indexing and lattice constants determination

N.B. The unit cell volume V( for Cubic) = a 3, for tetragonal = a 2 c, and for hexagonal = a 2 c

Reflectivity It is proceeded at low angles of incidence (θ) to study the surface only (GIXRD)

Reciprocal Space Maps

From reciprocal space mapping (RLM): composition, thickness (at least 50 nm), mismatch, mosacity, and defects profile.

Rocking curve measurement; composition and thickness determination

HRXRD (004) Rocking curve for sample 1683 of In0.53Al0.47As on InP substrate

For example: To measure layer composition for InyAl1-yAs we need only ∆θ B (difference between Bragg angle of the substrate and epilayer) and use the following relation (comes from Vegard's law) for symmetric measurements : Symmetric measurement is only sensitive to the lattice mismatch perpendicular to the substrate/layer interface Where, for symmetric measurements :

Also, one can use The layer thickness can be determined from the relation :

The best way to determine layer compositions and thicknesses : is to compare the experimental rocking curve to simulated curves. There are some commercial programs for that purpose (i.e. RADS (Rocking curve Analysis by Dynamical Simulation)

Summary XRD is the main method for crystallographic characterization for both bulk and thin film materials The diffraction pattern is like a finger print of the crystal structure. From the diffraction pattern of ω-2θ (θ -2θ) scan : phase analysis From rocking curves: composition, thickness ( nm), mismatch. From reciprocal space mapping(RLM): composition, thickness (at least 50 nm), mismatch, mosacity, and defects profile. From Reflectivity measurements: composition, thickness (5-150 nm), and interface roughness. From Pole figures: Composition, orientation with respect to substrate and phase analysis