Background: Bragg Equation

The common XRD method for surface orientation determination is based on the Bragg equation:

2⋅d⋅sin(θ) = n⋅λ

which describes the relation between X-ray wavelength λ, lattice plane distance d, and the reflection glance angle θ. n indicates the diffraction order of the reflection.

Features of Theta-scan

pro:

  • allows to measure all crystalline materials, polytypes & orientations

contra:

Theta Scan of the (0 0 12) reflection of a c-sapphire wafer; the barycenter of the peak is at 0.065° tilt.

Advantages of this method are the relatively simple diffractometer alignment and its flexibility. The disadvantages are the rather long measurement time (some minutes) and the problem of finding enough reflections.

Successful Theta Scans on at least two different lattice planes are needed to determine the complete crystal orientation. The reflections should be accessible to the diffractometer without moving the sample.

Measurment procedure

The angle between X-ray beam and detector is set to the reflection condition for a certain lattice plane that is given by the Bragg equation. To find the reflection, both X-ray and detector are moved coupled and simultaneously the sample is rotated. The direction of the lattice plane’s perpendicular is then calculated from the position of the reflection peak. There is no specific name for this method, thus we call it the "Theta-scan".