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

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

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

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

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

dE/dx = - N [ Se(E) + Sn(E) ] IBA Inelastic collisions : Due to interaction of ions with electrons Total rate of energy loss: dE/dx = - N [ Se(E) + Sn(E) ] stopping power [eV/Å] target atom density [cm-3] 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

IBA RBS SIMS ERD IIX NRA dE/dx E ~ MeV’s ~ 1 keV 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

SIMS Secondary ion mass spectrometry Incident ion beam mass analyzer 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

RBS Eo Carbon Substrate Es1 (Au) Es2 (Si) Es3 (O) Es4 (C) 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

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

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

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

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

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

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

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

RBS Depth Scale Ions lose energy at the rate dE/dx (stopping power) 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

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

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

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

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

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

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)

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

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

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

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

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 Ns dE / (dE/dx)s (Nt)i = (Yi/Ys) (Zs/Zi)2 [Ns dE / (dE/dx)s]

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

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

ERD Mr, Er q After collision f M0, Es M0, E0 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

ERD detector Al foil Mr, Er q After collision f M0, Es M0, E0 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

ERD Mr, Er q After collision f M0, Es M0, E0 = 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

IIX After collision M0, E0 Mr M0, Es 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

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

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

energy released due to mass difference NRA Nuclear Reaction Analysis : Light MeV ions produce nuclear reaction with atomic species in target Detect reaction products X + a → Y + b + Q e.g., 12C + d → 13C + p + 2.722 MeV denoted as 12C(d, p)13C energy released due to mass difference target atom incident ion resulting atom reactant product

Before collision After collision NRA Use geometry similar to RBS Measure energy of particle b Before collision Ma, Ea a Mx X After collision Mb, Eb b Ma, Ea a q My, Ey Y f

NRA Eb = [ A ± (A2 + B)½ ]2 A = (MaMbEa)½cosq Mb + My B = MyQ + Ea (My – Ma) Q = (Mx+Ma)c2 – (My+Mb)c2 After collision Mb, Eb b Ma, Ea a q My, Ey Y f

Eb is characteristic of the reaction NRA Eb is characteristic of the reaction Can determine Mx (species in target sample) Use thin foil to block backscattered ions (Ma, Ea) detector Al foil After collision Mb, Eb b Ma, Ea a q My, Ey Y f

NRA Sensitivity ~ 10-3 at % from Mayer and Rimini, Table 4.2, p. 118

Channeling Ions incident along a major crystallographic orientation experience channeling effect RBS backscattering yield is reduced

Can detect light elements in larger mass matrix Channeling Can detect light elements in larger mass matrix from Chu et al., Fig. 8.21, p. 248

e.g., amorphous Si on crystalline Si Channeling e.g., amorphous Si on crystalline Si from Mayer and Rimini, Fig. 3.3, p. 78

Summary From Ohring, Table 6-3, p. 276