Applying X-Ray Applying X-Ray Diffraction in Material Diffraction in Material

AnalysisAnalysis

Dr. Ahmed El-NaggarDr. 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 applicationsω/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) = a3, for tetragonal = a2c, and for hexagonal = 0.866 a2c

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 ∆θB (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 (30- 1000 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