1. Assessing Single Crystal Diamond Quality
Guangliang Yang
Glasgow University

2. Contents Introduction
Experimental set up for diamond rocking curve and topography measurements.
Detailed Results of the diamond rocking curve and topography measurements at CHESS.
Conclusions.

3. 1. Introduction
The angular spread of the mosaic blocks is usually called the mosaic spread. A large mosaic spread means a poor crystal quality.
Experimentally, we can estimate the value of the mosaic spread from the rocking curve width.
According to the mosaic model, an imperfect crystal is believed to be composed of large number of small mosaic blocks; within each block the distribution of atoms is perfect, but for different blocks, the crystal planes have different orientations.

4. Effects of mosaic spread on coherent bremsstrahlung
When the diamond crystal has a large mosaic spread, there is a variation in the direction of a given reciprocal lattice vector throughout the crystal, and hence the longitudinal component of the reciprocal lattice vector ql will be slightly different for different electrons. A different ql leads to a different xd, (the upper limit of the coherent peak ) and the averaged effect is that the edge of the coherent bremsstrahlung becomes broader

5. Techniques for assessing diamond crystal
Optical polaroid analysis,
Convenient, fast, low resolution;
X-ray topography,
High resolution, slow;
X-ray Rocking curve,
High resolution, slow, need special equipments.

6. Diamond 1532_3

7. 2. Experimental set up CCD detector
Asymmetric silicon 111 monochromator
Channel cut silicon 220 monochromator
Diamond sample
CCD detector
X ray source
Notes: 1. The distance from the x ray source to the first monochromator is 10.1 m.
2. The distance from the first monochromator to the second one is around 2 m.
3. The distance from the first monochromator to the diamond sample is 4.4 m.
4. The distance from the diamond crystal to the CCD detectors is 0.3 m.
5. The angle between the crystal surface and the 111 reflection plane is 6 degrees for
the first monochromator.
6. At the source position, the vertical size of the x ray beam is 1.39mm (FWHM).

8. Some pictures
CCD detector
Goniometer
Diamond
X ray beam

9. 3. Results. Bad 50 Hall b 20 microns Good 50
CCD images for three diamond radiators.

10. Rocking curves measured by ion chamber (blue) and CCD camera (black).

11. Rocking curves for isolated pixels
Rocking curve at radiation damaged region
The narrowest rocking curve from this measurement.
Note: The pixel size is roughly 20 microns by 20 microns

12. Rocking curves measured without (bottom) and
with (top) the second monochromator.

13. Results for the 20 microns thick diamond
Contour map of the rocking curve width (-220 scan)

14. Rocking curve peak position over the measured regions (-220 scan)

15. Contour map of the rocking curve width (220 scan)

16. Rocking curve peak position over the measured regions (220 scan)

17. crystal shape calculated by using the rocking curve peak position of each pixel.

18. Diamond rocking curves, a) measured result, b) simulated result.

19. Results for the Gwurg diamond

20. Rocking curve for a single pixel

21. Rocking curve peak position over the measured regions (-220 scan)

22. Rocking curve peak position over the measured regions (220 scan)

23. Rocking curves for the whole crystal (-220) and (2,-2,0) scans

24. crystal shape calculated by using the rocking curve peak position of each pixel.

25. Results for diamond 1532 A1

27. Rocking curve for the whole crystal

28. Rocking curve for a single pixel

29. Conclusions
X-ray topograph and rocking curve measurements are very useful techniques for assessing diamond crystal qualities.
2D map of rocking curve width and peak positions can be generated by using a pixel detector in X-ray rocking curve measurement.
For very thin diamond crystals, the curvature of diamond crystal plate has a big contribution to the crystal rocking curve width.
Further studies on crystal thinning and mounting methods are required.

30. X ray source
C1 Station Summary
Source:
e-s, Hard bend magnet HB5West, 6 mrad (horizonta) into C1
Source size
FWHM (horizontal) = mm, FWHM (vertical) = 1.39 mm
Distance to source:
14.5 m to center of hutch
Be windows:
0.030 inch into hutch
Cave slit sizes:
0 to 60 mm (horizontal), 0.25 to 3.0 mm (vertical)
White Beam:
1 horizontal mrad
Monochromators:
Double-bounce (with high resolution 4-bounce capability or side bounce)

31. Asymmetric monochromator
Why should we us an asymmetric monochromator?
Because the distance from x ray source to the diamond sample is short. It affects the beam size and beam divergence.
What does a asymmetric monochromator do?
Expand the beam size by a factor of b.
Reduce the beam divergence by a factor of b.
Where b is asymmetric factor, and b=sin(θ+α)/sin(θ-α). θ is the bragg angle of the reflection plane, α is the angle between the crystal surface and the reflection plane.
What did we use at CHESS?
A silicon 111 asymmetric monochromator.
The angle between the crystal surface and the 111 plane is 6 degrees, At 15 kev, the reflection angle of silicon 111 is 7.53 degree. That makes the asymmetric factor b to be 8.5.

32. Non dispersive geometry
The relative orientation of the monochromator crystal and the diamond crystal defines if the system is dispersive or a non dispersive geometry.
diamond
monochromator
monochromator
diamond θ2 θ1
Dispersive
Non dispersive
For the non dispersive setting, the contribution of wavelength spread of the beam to the sample rocking curve width which can be calculated by the following formula.
dω = (dλ/λ)*(tan(θ1)-tan(θ2)).
dλ/λ= sqrt(ωb*ωb + ωd * ωd) *cot(θ1).
In order to reduce this effect, the monochromator must be carefully selected according to their Darwin width and the reflection angle. In the future a silicon 331 or 333 asymmetric monochromator will be used.

33. Design of an asymmetric monochromator

34. Diamond 1482_2