1. Postfach 510119, D-01314 Dresden, Germany
Slow positron implantation spectroscopy – a tool to characterize vacancy-type damage in solids
G. Brauer
Institut für Ionenstrahlphysik und Materialforschung, Forschungszentrum Dresden-Rossendorf
Postfach , D Dresden, Germany
See also:
# G.Brauer W. Anwand, P.G. Coleman, W. Skorupa
Slow positron annihilation spectroscopy – a tool to characterize vacancy-type damage in ion-implanted 6H-SiC
Vacuum 78 (2005)
# R.I. Grynszpan, W. Anwand, G. Brauer, P.G. Coleman
Positron depth profiling in solid surface layers
Annales de Chimie - Science des Materiaux (2007, in press) (18 pp)

2. Where do positrons come from ? - (1) radioactive decay
- (2) Bremsstrahlung / pair production
Institut für Ionenstrahlphysik und Materialforschung

3. - pair production: Eγ 2 m0c²
β+-decay: p  n + e+ + ν
22Na
Emean = 225 keV
Emax = 542 keV
n(E)dE
Emean E
- pair production: Eγ 2 m0c²
Institut für Ionenstrahlphysik und Materialforschung

4. Distribution of positrons from ²²Na in solids (experiment)
G. Dlubek, PhD 1975, U Halle
ρLi = 0,535 g cm-3
ρSiC = 3,217 g cm-3
In good approximation holds for e+ from ²²Na
r zeff = 100 mg cm-2 ρ zmax = 200 mg cm-2
Example: ρFe = 7,841 g cm-3
zeff = 128µm zmax = 255 µm
Institut für Ionenstrahlphysik und Materialforschung

5. Positron energy vs. Time
Institut für Ionenstrahlphysik und Materialforschung

6. Positron trapping by open volume defects
increasing preference
vacancy agglomerate
grain boundary
edge dislocation
monovacancy
Institut für Ionenstrahlphysik und Materialforschung

7. TRAPPING MODEL rate equation approach (vacancies, dislocations)
Method
Parameter DB AC LT
S , W H
t , tmean
sensitivity
range
defect concentration Nd
0,1 – 200 ppm
1012 – 1015 m-2
monovacancies
dislocations
In metals:
larger sizes seen:
– 50
agglomerated mono-
vacancies
TRAPPING MODEL
rate equation approach (vacancies, dislocations)
diffusion-limited approach
(vacancy agglomerates, shape of the trapping site!)
k = µdefect Nd
k = 4p D+ Nd
Institut für Ionenstrahlphysik und Materialforschung

8. Principal methods of Positron Annihilation Spectroscopy (PAS)
Institut für Ionenstrahlphysik und Materialforschung

9. Definition of the line shape parameters S and W in DB
Eg = m0c² c x pparallel
pparallel ... electron momentum component parallel to
emission direction of g-quantum
S = A1 / A
W= (B1 + B2) / A
low electron momentum parameter, annihilation with valence electrons
high electron momentum parameter,annihilation with
core electrons
Institut für Ionenstrahlphysik und Materialforschung

10. Cartoon of a slow positron beam
Institut für Ionenstrahlphysik und Materialforschung

11. Cartoon of a positron moderator
E ~ 3eV
W (110), negative workfunction for positrons, ~ 3eV
Institut für Ionenstrahlphysik und Materialforschung

12. Slow POsitroN System Of Rossendorf
„SPONSOR“
Slow POsitroN System Of Rossendorf
direction of
fast e+
γ-rays
Positron energy: eV keV
Beam diameter: ~ 4 mm at all energies
Since 1999:
(1,09 ± 0,01) keV FWHM
Institut für Ionenstrahlphysik und Materialforschung

13. „SPONSOR“
Institut für Ionenstrahlphysik und Materialforschung

14. Depth distribution of thermalized positrons in SiC
“natural” positrons from 22Na (b) mono-energetic positrons of
energy E as indicated
N(z) is the distribution function obtained by P(E,z) is the distribution function of positrons
integration of P(E,z) over all energies having the energy E
(0-542 keV) of positrons from 22Na.

15. Goal of Slow Positron Implantation Spectroscopy (SPIS)
depth (nm)
Institut für Ionenstrahlphysik und Materialforschung

16. First step: from S(E) to S(d) plot
Institut für Ionenstrahlphysik und Materialforschung

17. First step: from S(E) to S(d) plot (mathematical background)
Numerical solution of the positron diffusion equation (one dimensional)
(Software „VEPFIT“: van Veen u.a. in AIP Conf. Proc. 218 (1990) 171)
D+ … Diffusion coefficient keff ... Part of the positrons annihilating in defects
n(z) ...Positron density at depth z
Makhovian distribution of the implanted positrons
z0 = zmean/Γ/(1/m+1)
zmean = A/ρ*En ... mean penetration depth of positrons
A, m, n ... experimental parameters
Mean positron depth
zmean : nm
ρ : g cm-3
E : keV
Institut für Ionenstrahlphysik und Materialforschung

18. Second step: theoretical calculation of positron lifetimes
positron lifetime - specific for bulk and every defect
- independent from defect concentration
see e.g.
G. Brauer, W. Anwand, P.G. Coleman, A.P. Knights, F. Plazaola, Y. Pacaud, W. Skorupa, J. Störmer,
P. Willutzki, Positron studies of defects in ion implantated SiC, Phys. Rev. B54 (1996)
Institut für Ionenstrahlphysik und Materialforschung

19. Problems
to identify a defect by positron lifetime in a compound semiconductor
Experiment:
- already native (grown in) defects can exist on both sublattices
- defects may be charged
mostly impossible to create a certain defect on one sublattice only,
e.g. by irradiation
Theory:
- calculations performed so far for neutral defects only
- different approaches to include electron-positron interaction available
- adjustment of calculation to reality somehow necessary
- possible lattice relaxation around a defect
Theoretical methods in use:
ATSUP (atomic superposition method):
rigid lattice positions, large defects, gives positron binding energy
(b) LMTO (linear muffin tin orbital method):
ab initio calculation, small defect configurations only, gives positron affinity and positron binding energy

20. Third step: lifetime measurements (pulsed positron beam, Munich)
Result: scaling curve S(N)
see e.g.
W. Anwand, G. Brauer, P.G. Coleman, W. Skorupa, MRS Proc. Vol. 504 (1998)
Institut für Ionenstrahlphysik und Materialforschung

21. Fourth step: defect size depth distribution N(d)
W. Anwand, G. Brauer, P.G. Coleman, R. Yankov,
W. Skorupa, Appl. Surf. Sci. 149 (1999)
W. Anwand, G. Brauer, W. Skorupa,
Appl. Surf. Sci. 184 (2001)
depth d (nm)
Institut für Ionenstrahlphysik und Materialforschung

22. Evolution of ion implantation-caused vacancy-type defects in 6H-SiC
Motivation:
ion beam synthesis of a buried (SiC)1-x(AlN)x layer
layer between 80 nm and 210 nm with x~0.2
to adjust the band gap between 3.0 eV (6H-SiC) and 6.2 eV (2H-AlN)
Experimental details:
{0001}-oriented, n-type 6H-SiC wafer
Fourfold implantation necessary:
Al+ implantation: 100 keV (5.0x1016 cm-2) and 160 keV (1.3x1017 cm-2)
N+ implantation: keV (5.0x1016 cm-2) and 120 keV (1.3x1017 cm-2)
substrate temperature during implantation: 800°C
Institut für Ionenstrahlphysik und Materialforschung

23. Results of TRIM / SRIM calculations
F. Ziegler, J.P. Biersack, The stopping and range of ions in matter,
Al+ 100 keV
Al+ 160 keV
Institut für Ionenstrahlphysik und Materialforschung

24. Results of TRIM / SRIM calculations
F. Ziegler, J.P. Biersack, The stopping and range of ions in matter,
N+ 65 keV
N+ 120 keV

25. 6H-SiC ion-implanted (800°C) + annealed (1.200°C, 10 min)
Institut für Ionenstrahlphysik und Materialforschung

26. 6H-SiC ion-implanted (800°C) + annealed (1.650°C, 10 min)
? Incomplete defect annealing – a surface problem ?
Institut für Ionenstrahlphysik und Materialforschung

27. Detection capabilities for various microprobe techniques
(a) defect concentration
(b) defect size
(PAS refers to all positron annihilation techniques)

28. Further improvements needed...
Solved...
more and more sophisticated data collection possible
ambitious theoretical calculations available
Further improvements needed...
increase of available positron beam intensity
depth dependant positron lifetime measurements routinely
combination of PAS results with those from other methods
State – of – the – art in this field was reviewed at SLOPOS – 10
Doha / Qatar, March 19 – 25, 2005.
Results see at: Applied Surface Science, Vol. 252 (Feb 2006)
Next meeting: SLOPOS – 11 at Orleans / France, July 9 -13, 2007
Institut für Ionenstrahlphysik und Materialforschung

29. Coincidence Doppler Broadening measurements
Principle
Institut für Ionenstrahlphysik und Materialforschung

30. CDB – results
Institut für Ionenstrahlphysik und Materialforschung

31. Institut für Ionenstrahlphysik und Materialforschung

32. EPOS scheme For a description of the project, see also:
R. Krause-Rehberg, S. Sachert, G. Brauer,
A. Rogov, K. Noack
Appl. Surf. Sci. 252 (2006) 3106

33. The End
Institut für Ionenstrahlphysik und Materialforschung

42. Detection capabilities for various microprobe techniques
(a) defect concentration
(b) defect size
(PAS refers to all positron annihilation techniques)

43. EPOS scheme For a description of the project, see also:
R. Krause-Rehberg, S. Sachert, G. Brauer,
A. Rogov, K. Noack
Appl. Surf. Sci. 252 (2006) 3106

44. Fourth step: defect size depth distribution N(d)
see e.g.
W. Anwand, G. Brauer, W. Skorupa, Appl. Surf. Sci. 149 (1999)
Institut für Ionenstrahlphysik und Materialforschung

45. Depth distribution of thermalized positrons in SiC
“natural” positrons from 22Na (b) mono-energetic positrons of
energy E as indicated
N(z) is the distribution function obtained by P(E,z) is the distribution function of positrons
integration of P(E,z) over all energies having the energy E
(0-542 keV) of positrons from 22Na.