Text optional: Institute Prof. Dr. Hans Mousterian www.fzd.de Mitglied der Leibniz-Gemeinschaft Light element IBA by Elastic Recoil Detection and Nuclear Reaction Analysis R. Heller
IBA Techniques slide 2
Contents Elastic Recoil Detection Analysis Basic Properties / Kinematics / Cross Sections Energy Loss / Stopping Straggling Experimental Setup(s) Examples Nuclear Reaction Analysis Principle 15 N Method for H profiling Further nuclear reactions Non-Rutherford Backscattering slide 3
Basic properties Commonly used surface / near surface analysis technique Gives information on (light) elemental composition & on particular element s depth profiles Non-destructive (in most cases) Quantitative method that does not require any standard Very sensitive to light elements Needs energetic (usually MeV) ions as probe need for accelerator slide 4
Basic properties A heavy MeV ion hits the surface with energy E a under a small angle α Ion penetrates the sample and is scattered at a target atom in depth x under a certain scattering angle θ Recoil ion is detected by an mass and energy dispersive detection system Detected energy reveals depth profile of a certain element in the sample Detector E x E in x E out x Energy to depth conversion: k E E x E x p in out Energy loss of the incident ions on the way in Energy loss of the recoils or scattered ions on the way out x slide 5
Kinematics Elastic scattering in pure coulomb potential no excitation Energy and momentum conservation E 1,v 1 M 1, v 0, E 0 E 0 = E 1 + E 2 M 2 E 2, v 2 M 1 v 1 cos Q M 1 v 1 sin Q ( ) + M 2 v 2 cos( F) = M 1 v 0 ( ) - M 2 v 2 sin( F) = 0 slide 6
Kinematics E 1 = k S E 0 æ k S = ç ç è M 2 2 - M 1 2 sin 2 ( Q) + M 1 cos( Q) M 1 + M 2 ö ø 2 E 1,v 1 M 1, v 0, E 0 M 2 E 2 = k R E 0 k R = 4M M 1 2 cos2 M 1 + M 2 ( ) 2 ( F) E 2, v 2 slide 7
Kinematics E 2 = k R E 0 k R = 4M M 1 2 cos2 M 1 + M 2 ( ) 2 ( F) Highest sensitivity (biggest slope of k) for small recoil mass and heavy ion mass K. Mizohata, Thesis, 2012 slide 8
Cross sections ds R dw = æ e 2 Z 1 Z ç 2 è8pe 0 E 0 ö ø 2 ( 1+ M 1 M 2 ) cos 3 F K. Mizohata, Thesis, 2012 slide 9
Shielded cross sections Shielding by shell electrons at low projectile velocities Described by shielding factor F ( E,Q) s ( E,Q) = F( E,Q)s R ( E,Q) Shielding factor is obtained by solving scattering equations for the screened inter-atomic potential: V( r) = Z 1Z 2 e 2 r j æ ç r ö è a ø F ( E,Q) j screening function Thomas Fermi / Lens Jensen a screening radius a 0 Bohr radius a = 0.885a ( 2 2 0 Z 3 1 + Z 3 ) 1 2 2 slide 10
Shielded cross sections L Ecuyer et al. (1979) Wenzel & Whaling (1952) s =1-0.049Z Z 4 3 1 2 s R E CM s =1-0.0326Z Z 7 2 1 2 s R E CM Andersen et al. (1980) s s R = æ 1+ 1 V 1 ö ç è 2 E CM ø ìï 1+ V é 1 V + 1 ù í ê ú îï E CM ë2e CM sinq CM 2û 2 ( ) 1 2 V 1 = 0.04873 Z 1 Z 2 Z 1 2 3 + Z 2 2 3 2 üï ý þï 2 slide 11
Energy loss and stopping Electronic stopping o Andersen, Ziegler (1977): H, He in all elements o Ziegler, Biersack, Littmarck (1985): All ions in all elements o Several SRIM-versions since then o Additional work by Kalbitzer, Paul, o Accuracy: 5% for H, He 10% for heavy ions Nuclear stopping o Only important for heavy projectiles and for low velocities o Ziegler, Biersack, Littmarck (1985): All ions in all elements using ZBL potential slide 12
Evaluation of energy vs. depth Energy in depth x? E( x) = E( 0) + de + 1 d 2 E dx x=0 2 x2 + 1 d 3 E dx 2 6 x3 dx +... 3 x=0 de dx = -S d 2 E dx = d 2 dx -S d 3 E dx 3 ( ) = - ds de =... = -S''S2 - S' 2 S de dx = S'S ( ) E( x) = E 0 - xs+ 1 2 x2 SS'- 1 6 x3 S''S 2 + S' 2 S E 0 x x must be small enough!! S, S and S evaluated at x = 0 slide 13
Energy straggling Stopping of ions in solids is a statistical process that leads to a spread of the beam energy energy straggling Electronic energy loss straggling due to statistical fluctuations in the transfer of energy to the electronic sub-system Nuclear energy loss straggling due to statistical fluctuations in the nuclear energy loss Geometrical straggling due to finite detector solid angle and finite beam spot size Multiple small angle scattering Surface and interlayer roughness slide 14
Energy straggling Electronic energy loss straggling Fluctuations in the transfer of energy to the target electrons lead to fluctuations in the energy loss After passing a layer of thickness Δx: E = E 0 - SDx 10% Vavilov theory low number of ion-electron collisions 10-20% Bohr theory large number of ion-electron collisions 20-50% Symon theory non-stochastic broadening almost Gaussian 50-90% Energy below stopping power maximum non-stochastic squeezing due to stopping non-gaussian slide 15
Energy straggling Bohr theory Bohr 1948 (N. Bohr, Mat. Fys. Medd. Dan. Vid. Selsk. 18 (1948) ) Valid for intermediate energy losses o large number of ion-electron collisions o Gaussian energy distribution with tail towards low energies Approximations: o Ions penetrating a gas of free electrons o Ions are fully ionized o Ion velocity >> electron velocity stationary electrons o Stopping power effects are neglected 2 s Bohr = 0.26Z 1 2 Z 2 Dx slide 16
Multiple (small angle )scattering Small angle scattering has high cross sections Path length differences on ingoing and outgoing paths energy spread Spread in scattering angle energy spread of starting particles P. Sigmund and K. Winterbon, Nucl. Instr. Meth. 119 (1974) 541 E. Szilagy et al., Nucl. Instr. Meth. B100 (1995) 103 slide 17
Multiple (large angle) scattering Same scattering angle but different energies Most prominent at very low velocities W. Eckstein and M. Mayer, Nucl. Instr. Meth. B 153 (1999) 337 slide 18
Roughness Two different cases of roughness Rough layer on smooth substrate Smooth layer on rough substrate Different path length for incoming and outgoing projectile different energies broadening d p(d) From SIMNRA User s Guide, M. Mayer slide 19
Experimental setup Bragg Ionization-Chamber Si-Det.-Telescope +Al or Mylar-foil E E Rotating vane 35 MeV Cl 7+ TOF-Telescope Sample Start Monitordetector Stop Ionization Chamber slide 20
Experimental setup BIC Chamber Ion beam Load lock TOF E-detector slide 21
Recoil detection using a Bragg chamber Particle identification in Bragg ionization chamber by Pulse shape discrimination K FG A i e de dx Z 1 Z 2 Scatt. ions Recoils x t -3000V +600V =100 ns BP Z E = 3 s Entrance window: Si 3 N 4 Thickness: 350 nm Gas: 99.95% Isobutene Pressure: 50 200 mbar slide 22
Concentration (at%) Elastic Recoil Detection Example I 2D-intensity map data evaluation Depth profile 80 Sample: C:Co (30) 300 C 70 60 50 40 30 20 C Co O Si 10 0 H 0 50 100 150 200 250 300 Depth (nm) slide 23
Example II A. Blazevic et al. HMI Berlin slide 24
Recoil detection using a Time of Flight detector K. Mizohata, Thesis, 2012 slide 25
Example III K. Mizohata, Thesis, 2012 slide 26
Nuclear Reaction Analysis Basics From http://physik2.unigoettingen.de/research/2_hofs/methods/nra/ Yield of reaction products proportional to concentration of reaction partner Commonly use for analysis of light elements as H, Li, Be, B, C, N, O, F, Na, Al and P Absolute measurement by use of standards Narrow resonances (100eV to some kev) can be use for depth profiling slide 27
Nuclear Reaction Analysis Hydrogen depth profiling by 15 N method 15 N + 1 H 12 C + 4 He + g-rays (4.43 MeV) incidence ion: beam current: 15 N, 6.385 to 12 MeV 10-50 na 8 nm Si beam spot: 1-25 mm 2 detector: detection limit: analysis depth: depth resolution: 4" x 4" BGO 0.1 at% 15 N 2+ beam up to 5 µm (depends on material) 6.385 MeV resonance energy ~ 8 nm (Si), min. 1 nm (grazing incidence) slide 28
Nuclear Reaction Analysis Hydrogen depth profiling by 15 N method 4-axis sample manipulator Transfer chamber Ion beam 15 N High voltage feed through BGO detector slide 29
Nuclear Reaction Analysis Hydrogen depth profiling by 15 N method Verification of fluence and profile for H implantation in Si slide 30
Hydrogen concentration (at.%) Nuclear Reaction Analysis Hydrogen depth profiling by 15 N method 7 6 5 Al 2 O 3 layers H 2 annealed N 2 annealed H depth profiling of Al 2 O 3 and ZrO 2 layers with nm resolution 4 3 2 ZrO 2 layers 1 0 0 2 4 6 8 10 12 14 16 Depth (nm) slide 31
Nuclear Reaction Analysis Further nuclear reactions And many more to be found in literature slide 32
Non-Rutherford Backscattering 12 C(α, α) 12 C Small cross sections at E < 3 MeV not suitable for BS High & smooth cross section around 4 MeV 4270 kev: o maximum sensitivity J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, MRS,1995 slide 33
Non-Rutherford Backscattering 14 N(α, α) 14 N Small cross sections at E < 3 MeV not suitable for BS Several useful resonances at higher energies J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, MRS,1995 slide 34
Non-Rutherford Backscattering 16 O(α, α) 16 O Widely used resonance at 3040 kev J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, MRS,1995 slide 35
Non-Rutherford Backscattering 27 Al(α, α) 27 Al and Si(α, α)si Many small resonances Small cross sections not suited for BS J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, MRS,1995 slide 36
Non-Rutherford Backscattering 12 C(p, p) 12 C High to very high cross section above 500 kev 1500 or 2500 kev: o smooth cross section o easy data evaluation, thick layers 1740 kev: o maximum sensitivity M. Mayer, 2003 slide 37
Non-Rutherford Backscattering 14 N(p, p) 14 N Partially very high cross section, but Large scatter in available cross section data M. Mayer, 2003 slide 38
Non-Rutherford Backscattering 16 O(p, p) 16 O High to very high cross section above 2 MeV 1500 or 2500 kev: o smooth cross section o Same as for C 3470 kev: o maximum sensitivity M. Mayer, 2003 slide 39
Non-Rutherford Backscattering 27 Al(p, p) 27 Al Small cross sections Many resonances Large scatter complicate spectrum not suitable for BS M. Mayer, 2003 slide 40
Non-Rutherford Backscattering Si(p, p)si Small cross sections suitable for background suppression if Si is bulk material 1500 or 1600 kev: o Small background 1670 & 2090 kev: o maximum sensitivity M. Mayer, 2003 slide 41
Summary ERD, NRA and Non-Rutherford BS deliver information on light elemental composition and depth profiles of light elements Sensitivity down to <0.1 at% possible Depth resolution of a few nm can be achieved Non-destructive (in most cases) Quantitative Accelerator needed Thank you for your attention! slide 42