Ion Beam Analysis (IBA)

1. Ion Beam Analysis (IBA) IBA IBA uses incident ions to probe the sample SIMS RBS Gives composition vs. depth ERD NRA IIX Channeling

2. IBA • 2 ways in which ions interact with matter and lose energy Elastic Collisions Inelastic Collisions • Coulomb interaction • between ion and • nuclear cores • (Rutherford scattering) • Produces recoil atoms • Ion interacts with atomic electrons in solid and loses energy

3. IBA • Elastic collisions : • Interaction between ion and nuclear core (Rutherford scattering) • Described as binary collision Before collision M0, E0 Mr After collision Mr, Er q f M0, Es

4. IBA • Incident ion transfers kinetic energy to recoiling particle • Conservation of energy and momentum : • Er = 4 E0 MoMrcos2q/(M0+Mr)2 • Can measure energy of recoiling particle (principle of SIMS & ERD) After collision Mr, Er M0, E0 q M0, Es f

5. IBA • Incident ion loses energy as it propagates through sample • Conservation of energy and momentum (for elastic collisions): 2 Es = E0 (Mr2 – M02sin2f)½ + M0cosf M0 + Mr • Can measure energy of scattered incident ion (principle of RBS) After collision Mr, Er M0, E0 q M0, Es f

6. IBA • Inelastic collisions : • Due to interaction of ions with electrons Total rate of energy loss: dE/dx = - N [ Se(E) + Sn(E) ] target atom density [cm-3] stopping power [eV/Å] nuclear stopping cross-section [eV cm2] electronic stopping cross-section [eV cm2] • e.g., for 1 keV Ar+ ions in Al • dE/dx = 39 eV/Å

7. IBA dE/dx nuclear elastic scattering electronic inelastic scattering E ~ MeV’s ~ 1 keV RBS ERD IIX NRA SIMS • Detection of scattered ions (incident or recoil) and their energies gives information on sample

8. SIMS • Secondary ion mass spectrometry • Incident ion beam • 1 – 20 keV • Ar+, Cs+, O+ • Sputtered atoms are sorted by mass (mass analyzed) • Sputtered surface recedes • Gives composition versus depth mass analyzer incident ion (e.g., Ar+) sputtered atoms sample

9. SIMS • Static SIMS vs Dynamic SIMS • Compositional mapping achieved by scanning incident ion beam across the sample surface • Lateral resolution ~ 100 mm from Feldman and Mayer, Fig. 4.7, p. 81

10. SIMS • Applications : • Determine presence and location (depth and lateral position) of impurities or dopants (dopant profiling) • Measures the dopant profile not the carrier density From LaPierre, Ph.D. thesis O C 2H

11. SIMS • Depth calibration • Measure ion current • Use calibration layers • Measure etch pit depth (e.g., stylus profilometry) • Errors • At large depths (long sputtering times) bottom of crater can become rough • Sputtering of crater walls • Ion-induced mixing/implantation

12. SIMS • Depth resolution • ~ 5 – 10 Å = depth from which sputtered atoms are emitted from Stradling and Klipstein, Fig. 2, p. 89

13. SIMS Quantification Y = # sputtered (ejected) target atoms # incident ions [Y] = atoms/ion Typical sputtering yields are between 0.1 and 4 From Ohring, Table 3-4, p. 113

14. SIMS Quantification • In SIMS, charged ions are detected and mass analyzed • Y+ = secondary ion yield = # sputtered ions # sputtered atoms [Y+] = ions/atom

15. SIMS Quantification Y+ ~ 10-4 - 1 from Feldman and Mayer, Fig. 4.13(a), p. 86

16. SIMS Quantification • A general theory to explain Y+ does not exist • Y+ depends on many factors • Surface conditions (e.g., oxidation) • Ion species being sputtered • Sputtered ion energy • Sample composition • Positive ion yield frequently enhanced when using O2- beams • Negative ion yield frequently enhanced when using Cs+ beams

17. SIMS Quantification • Comparison with known sample required for absolute quantitative analysis • But, SIMS is highly sensitive, ~ 1016 cm-3

18. RBS • Rutherford Backscattering Spectrometry • Light, 1-3 MeV ions (e.g., 4He) backscatter from target atoms (Rutherford scattering) • Measure energy of backscattered ions • Gives composition versus depth Transmitted beam from Chu et al, Fig. 2.4, p. 28

19. RBS from Chu et al, Fig. 6.1, p. 154 • Ions detected by solid state (Si) detector, similar to EDX detector

20. RBS From Ohring, Fig. 6-23, p. 293

21. RBS • Elastic collisions : • Interaction between ion and nuclear core (Rutherford scattering) • Described as binary collision Before collision M0, E0 M2 Mr After collision M0, E0 Mr, Er q M0, Es f

22. RBS K = kinematic factor = Es/E0 = (Mr2 – M02sin2f)½ + M0cosf 2 M0 + Mr • Incident ion: M0, E0 known • Detection angle fixed: f known • K measured for backscattered ion • Can determine Mr (atomic components of sample) After collision M0, E0 Mr, Er q M0, Es f

23. RBS • Example: impurities on a surface Eo Carbon Substrate Es1 (Au) Es2 (Si) Es3 (O) Es4 (C) from Chu et al, Fig. 5.1, p. 124

24. RBS • K increases with M2→ peak position identifies element from Feldman and Mayer, Fig. 2.2, p. 16 from Chu et al, Fig. 5.1, p. 124

25. RBS • Ions scattered throughout depth of film • Ions lose energy during transit in film primarily due to inelastic electron scattering After collision Mr, Er M0, E0 q M0, Es f M0, Es - DE

26. RBS From Ohring, Fig. 6-21, p. 290

27. RBS Typical RBS spectrum From Ohring, Fig. 6-21, p. 290

28. RBS From Ohring, Fig. 6-24, p. 295

29. RBS • Energy of leading edge gives element identification From Ohring, Fig. 6-21, p. 290

30. RBS • Width of peak related to film thickness • Can convert energy scale to depth scale From Ohring, Fig. 6-21, p. 290

31. RBS Depth Scale From Ohring From Ohring, Fig. 6-21, p. 290 • Ions lose energy at the rate dE/dx (stopping power) • Incident path, x = - ∫ dE / (dE/dx) • Outgoing path, x = - ∫ dE / (dE/dx) E2 E1 E4 E3 • Stopping power, dE/dx, varies with energy, E

32. RBS Depth Scale • dE/dx varies with energy dE/dx nuclear elastic scattering electronic inelastic scattering E ~ keV’s ~ MeV’s

33. RBS Depth Scale • Approximation (valid for thin films) : • (dE/dx)incident path ~ dE/dx at E1 • (dE/dx)outgoing path ~ dE/dx at E4 From Ohring, Fig. 6-21, p. 290

34. RBS Depth Scale • Incident path: • x = - ∫ dE / (dE/dx)E1 • = - (E2 – E1) / (dE/dx)E1 • Outgoing path: • x = - ∫ dE / (dE/dx)E4 • = - (E4 – E3) / (dE/dx)E4 • = - (E4 – KE2) / (dE/dx)E4 • Can eliminate E2 and solve for x E2 E1 E4 E3

35. RBS Depth Scale • x = (KE1 – E4) / [ K (dE/dx)E1 + (dE/dx)E4 ] • E1 , (dE/dx)E1, (dE/dx)E4 are known • Measure E1, E4 • Can determine x • Depth resolution ~ 10-20 nm (determined by energy resolution of MCA ~ few keV) From Ohring, Fig. 6-21, p. 290

36. RBS • Height of peak gives amount of element present From Ohring, Fig. 6-21, p. 290

37. RBS Quantification • The number of backscattered ions gives the composition • # scattered particles : • Y = Q (Nt) (ds/dW) W detector solid angle total # of incident ions # atoms per unit area Differential scattering cross-section = scattering cross-section per unit solid angle, W • ds/dW given by famous Rutherford scattering formula : • ds/dW~ (Z1Z2e2 / 4Eo)2 sin-4(f/2)

38. RBS Quantification • Example: impurities on a surface • Peak position identifies element • Peak height identifies amount of element Eo Carbon Substrate Es1 (Au) Es2 (Si) Es3 (O) Es4 (C) from Chu et al, Fig. 5.1, p. 124

39. RBS Quantification • Quantification • Method 1: Theoretical • Amount of impurity per unit area = • (Nt)i = Yi / [ Q(ds/dW)iW] • If geometry (W, f) is well known from Chu et al, Fig. 5.1, p. 124

40. RBS Quantification • Quantification • Method 2: Comparison with substrate peak • Substrate: • Ys = Q {Ns [dE/(dE/dx)s]} (ds/dW)sW depth, x, corresponding to dE One energy channel ~ few keV Ys from Chu et al, Fig. 5.1, p. 124

41. RBS Quantification • Quantification • Method 2: Comparison with substrate • Impurity Atom: • Yi = Q (Ni t) (ds/dW)sW Ys from Chu et al, Fig. 5.1, p. 124

42. RBS Quantification • Quantification • Method 2: Comparison with substrate • Ratio: • Yi / Ys = (dsi/dW)i (Nt)i • (dss/dW)s Ns dE/(dE/dx)s • ds/dW ~ Z2 • Yi / Ys = Zi2 (Nt)i • Zs2 NsdE / (dE/dx)s • (Nt)i = (Yi/Ys) (Zs/Zi)2 [Ns dE / (dE/dx)s]

43. RBS Quantification • Sensitivity • ~ 1012 – 1014 cm-2 • ~ 1 at % • Lateral resolution ~ mm to mm • MCA detects energy difference of a few keV → determines region of good mass resolution from Feldman and Mayer, Fig. 2.2, p. 16

44. RBS • Major advantage of RBS • Quantitative capability • Problem with RBS : • Difficult to detect light elements in a heavy mass substrate • Overlap produces small signal on large background • Problem solved by using ERD adapted from Chu et al., Fig. 8.21, p. 248

45. ERD • Elastic Recoil Detection : • Use light MeV ions at glancing incidence; e.g., 4He • Detect energy of recoiling atoms • Gives composition versus depth • Useful for light element detection in sample (e.g., H, D) Mr, Er q After collision f M0, Es M0, E0

46. ERD • Elastic Recoil Detection : • Al foil blocks backscattered (incident) ions (M0, E0); ds/dW ~ Z2 • Lighter recoil atoms (M2, E2) pass to detector detector Al foil Mr, Er q After collision f M0, Es M0, E0

47. ERD • = Er/E0 = [ 4M0Mr / (M0 + Mr)2 ] cos2q • Incident ion: M0, E0 known • Detection angle fixed: q known • g measured for backscattered ion • Can determine Mr (atomic components of sample) versus depth Mr, Er q After collision f M0, Es M0, E0

48. IIX • Ion Beam Induced X-ray Emission : • Light MeV ion causes inner shell ionization • Outer shell electron fills vacancy • Measure energy of characteristic x-ray emission → Identify atomic species • Similar to EDX After collision M0, E0 Mr M0, Es

49. IIX • Typical IIX Spectrum from Mayer and Rimini, Fig. 5.1, p. 315

50. IIX Quantification • Can determine amount of element present by measuring x-ray line intensity (same as EDX) • Solid state (Si) detector • Intensity of x-rays from a depth d is : • I = Q(d)cswx e-md/cosq e dW/4p • Q(d) = intensity of ion-beam at depth d • c = atomic concentration • s = ionization cross-section • wx = x-ray yield (fluorescence yield) • m = x-ray absorption coefficient • e = detector efficiency • dW = detector solid angle • q = detector angle wrt ion-beam