IonIon BeamBeam AnalysisAnalysis inin MaterialsMaterials ScienceScience (Rutherford(Rutherford backscatteringbackscattering andand relatedrelated techniques)techniques)
Kin Man Yu Electronic Materials Program, Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
(510) 486-6656 [email protected]
1 Outline
Introduction: General aspects of ion beam analysis Equipment Rutherford backscattering spectrometry (RBS) Introduction-history Basic concepts of RBS Kinematic factor (K) Scattering cross-section Depth scale Quantitative thin film analysis Pitfalls Particle induced x-ray emission (PIXE) Hydrogen Forward Scattering Non-Rutherford scattering and nuclear reaction analysis Ion channeling Minimum yield and critical angle Dechanneling by defects Impurity location
2 K. M. Yu November 2008 References
Books: Backscattering Spectrometry, Wei-Kan Chu, James W. Mayer and Marc-A. Nicolet, (Academic Press, New York 1978). Handbook of modern ion beam materials analysis, edited by J.R. Tesmer and M. Nastasi (MRS, pittsburgh, 1995). Materials Analysis by Ion Channeling, L. C. Feldman, J. W. Mayer and S. T. Picraux, (Academic Press, New York 1982). Ion Beam Materials Analysis, edited by J. R. Bird and J. S. Williams, (Academic Press, Australia 1989). Fundamentals of Surface and Thin Film Analysis, L. C. Feldman and J. W. Mayer (Elsevier Science, New York 1986). Encyclopedia of Materials Characterization, edited by C. R. Brundle, C. A. Evans, Jr., S. Wilson, (Butterworth-Heinemann, Stoneham, MA 1992). Review Articles: W-K. Chu, J. W. Mayer, M-A. Nicolet, G. Amsel, T. Buck, and F. H. Eisen, “Principles and applications of ion beam techniques for the analysis of solids and thin films,” Thin Solid Films 17, 1 (1973). L. C. Feldman, “ MeV ion scattering for surface structure determination,” C. R. C. Crit. Rev. Solid State and Mater. Sci. 10, 143 (1981). D. David, “New trends in ion-beam analysis,” Surf. Sci. Rep. 16, 333 (1992). W. K. Chu and J. R. Liu, “Rutherford backscattering spectrometry: reminiscences and progresses,” Mater. Chem. Phys. 46, 183 (1996).
http://www.eaglabs.com/en-US/references/tutorial/rbstheo/cairtheo.html
3 K. M. Yu November 2008 Ion Beam Analysis: General
Low energy Medium energy High energy regime
SIMS 102 Ar ERA
10 LEIS NR
Ion Mass (amu) A PI RBS, CH, HFS GE He MEIS PI PIXE XE
1 H PIGE, PIXE, NRA 1 10 102 103 104 Energy (keV)
CH -Channeling PIGME -Particle Induced Gamma-ray Emission ERA -Elastic Recoil Analysis SIMS -Secondary Ion Mass Spectrometry RBS -Rutherford Backscattering MEIS -Medium Energy Ion Scattering NRA -Nuclear Reaction Analysis LEIS -low energy ion scattering PIXE -Particle Induced X-ray Emission HFS -hydrogen forward scattering
4 K. M. Yu November 2008 MeV Ion Beam Techniques
Particle induced x-ray emission Rutherford backscattering spectrometry (PIXE) (RBS) hν MeV H+, 4He+ E1=k(m,M,θ)E0 m, Eo Particle induced γ-ray emission (PIGE) m, E1 θ M1>M2>m>M3
M1 M2 M3
Elastic recoil detection (ERA) Hydrogen forward scattering (HFS)
5 K. M. Yu November 2008 Ion Beam techniques
Technique Typical Applications Elements Depth Depth lateral Detection Quanti- Depth detected probed resolution resolution limit tative profiling RBS •thin film composition and B-U 1-2μm 20-200Å 0.5-1mm 1-10 at.% Yes Yes thickness Z<20 •impurity profiles 0.01-1 at.% •thin film interactions and 0.01-0.001at.% interdiffusions Z>70 PIXE •element identification Al-U up to poor 0.5-1mm 0.001 at.% Yes No •impurity analysis 10μm HFS •hydrogen or deuterium in H, d 1μm 500Å 2-3 mm 0.01 at.% Yes Yes thin films non-RBS •Composition of thin B, C, N, up to 200Å 0.5-1 mm 0.1 at.% Yes Yes oxide, nitride, carbide O, Si 10μm films NRA •profiling of light H, B, C, up to a 500- 0.5-1mm 0.001-1 at.% Yes Yes elements in heavy matrix N, O, F few μm 1000Å Channeling •crystalline quality of thin B-U 1-2μm 20-200Å 0.5-1mm 0.0001 at.% Yes Yes films •lattice location of impurity in single crystal •strains in pseudomorphic thin films •implantation damage analysis
6 K. M. Yu November 2008 Experimental Setup
7 K. M. Yu November 2008 An Ideal IBA Laboratory
Arizona State University
8 K. M. Yu November 2008 A compact RBS System
NEC MAS1000
9 K. M. Yu November 2008 Rutherford Backscattering Spectrometry (RBS)
10 Rutherford Backscattering Spectrometry (RBS)– a brief history The original experiment
Alpha particles at a thin gold foil experiment by Hans Geiger and Ernest Marsden in 1909.
1) Almost all of the alpha particles went through the gold foil 2) Some of the alpha particles were deflected only slightly, usually 2° or less. 3) A very, very few (1 in 8000 for platinum foil) alpha particles were turned through an angle of 90° or more. "We shall suppose that for distances less that 10-12 cm the central charge and also the charge on the alpha particle may be supposed to be concentrated at a point." (1911)
11 K. M. Yu November 2008 RBS: The Surveyor V experiment
Surveyor V, first of its spacecraft family to obtain information about the chemical nature of the Moon's surface, landed in Mare Tranquillitatis on September 11, 1967.
"Surveyor V carried an instrument to determine the principal chemical elements of the lunar-surface material," explained ANTHONY TURKEVICH, Enrico Fermi institute and Chemistry Department, University of Chicago. "After landing, upon command from Earth, the instrument was lowered by a nylon cord to the surface of the Moon …”
12 K. M. Yu November 2008 General applications of RBS
Quantitative analysis of thin films thickness, composition, uniformity in depth Solid state reactions interdiffusion Crystalline perfection of homo- and heteroepitaxial thin films Quantitative measurements of impurities in substrates Defect distribution in single-crystal samples Surface atom relaxation in single crystals Lattice location of impurities in single crystals
13 K. M. Yu November 2008 Strengths of RBS
Simple in principle Fast and direct Quantitative without standard Depth profiling without chemical or physical sectioning Non-destructive Wide range of elemental coverage No special specimen preparation required Can be applied to crystalline or amorphous materials Simultaneous analysis with various ion beam techniques (PIXE, PIGE, channeling, etc.)
14 K. M. Yu November 2008 Radiation Damage of RBS
2 MeV 4He+ in Si
15 K. M. Yu November 2008 Basic concepts of RBS
Kinematic factor: elastic energy transfer from a projectile to a target atom can be calculated from collision kinematics ¾ mass determination Scattering cross-section: the probability of the elastic collision between the projectile and target atoms can be calculated ¾ quantitative analysis of atomic composition Energy Loss: inelastic energy loss of the projectile ions through the target ¾ perception of depth
These allow RBS analysis to give quantitative depth distribution of targets with different masses
16 K. M. Yu November 2008 Kinematic factor: K
Conservation of energy : Conservation of momentum:
1112 22 mv111=+ mvcosθ mv 22 cosφ mv11122=+ mv mv 222 mv11sinθ = mv 2 2 sinφ θ 2 ⎡ 2 2 2 ⎤ E1 (m2 − m1 sin ) + m1 cosθ K = = ⎢ ⎥ = Kmm(θ ,,21) m2 E ⎢ (m + m ) ⎥ o ⎣ 2 1 ⎦
17 K. M. Yu November 2008 Kinematic Factor θ 2 ⎡ 2 2 2 ⎤ E (m − m sin ) + m cosθ K = 1 = ⎢ 2 1 1 ⎥ m2 E ⎢ (m + m ) ⎥ o ⎣ 2 1 ⎦ 2 ⎡(m − m )⎤ K (θ = 180o ) = 2 1 m2 ⎢ ⎥ ⎣⎢(m2 + m1)⎦⎥ (m − m ) K (θ = 90o ) = 2 1 m2 (m2 + m1)
When m2>>m1: K (θ = 180o ) ~ 1 m2
18 K. M. Yu November 2008 Element identification
2.5 MeV He ion with θ=170o
K(197Au) = 0.923 K(109Ag) = 0.864
K(107Ag) = 0.862 K(65Cu) = 0.783 K(63Cu) = 0.777
19 K. M. Yu November 2008 Mass Resolution, δm2
2 E ⎡(m − m )⎤ For 180o scattering: K = 1 = 2 1 m2 ⎢ ⎥ E0 ⎣(m2 + m1)⎦ 3 2 ()mm21+ δ E1 δ E1 ()mm21− = ∴δ m2 = 2 ()E E ()4mm12− m 1 0 0 δ mm12+
For a fixed δE1/E0 (~0.01), heavier projectiles result in better mass resolution
However, δE1 for heavier projectiles is higher
20 K. M. Yu November 2008 Mass Resolution: Examples
With system energy resolution δE = 20keV and E0=2MeV (40 + 4)3 20 For m =40 δm2 = • = 1.48a.m.u. 2 4× 4(40 − 4) 2000 (70 + 4)3 20 For m = 70 δm = • = 3.84a.m.u. 2 2 4× 4(70 − 4) 2000 Isotopes of Ga (68.9 and 70.9 a.m.u.) cannot be resolved
4 MeV 3 MeV 2 MeV 1 MeV
21 K. M. Yu November 2008 RBS Quantification
Backscattering Yield For a given incident number of particles Q, a greater amount of an element
present (Ns) should result in a greater number of particles scattered. Thus we need to know how often scattering events should be detected (A) at a characteristic energy (E =
KE0) and angle θ, within our detector’s window of solid angle Ω.
22 K. M. Yu November 2008 Scattering cross-section
σ
Rutherford cross-section:θ θ 2 2 2 θ2 1 / 2 2 d ⎛ Z 1 Z 2 e ⎞ [cos + (1 − A sin ) ] m1 = ⎜ ⎟ A= d Ω 2 E 4 ⎛ ⎞ 2 2 1 / 2 m ⎝ o ⎠ sin ⎜ ⎟ (1 − A sin θ ) 2 ⎝ 2 ⎠
23 K. M. Yu November 2008 Scattering Yield
σθ
1/2 2 2 ⎡ 22 ⎤ Example: 2 cosθθ+−() 1A sin ⎛⎞ZZe12 ⎣⎢ ⎦⎥ Yield,Y ∝∴ ()= ⎜⎟ 2E 4221/2 ⎝⎠0 sinθ() 1− A sin 2 Z1Z1 2 ∝ ( ) ~ 10−24 cm2[barn] θ E0
Mixed Si and W target analzed by a 2MeV He ion beam at 165o scattering angle. σ(Si)=2.5x10-25cm2/str σ(W)=7.4x10-24cm2/str Total incident ions Q=1.5x1014 ions Ω=1.8mstr Area under Si, A(Si)=200 counts Area under W, A(W)=6000 counts 15 2 (Nt)Si=3x10 atoms/cm 15 2 (Nt)W=3x10 atoms/cm
24 K. M. Yu November 2008 Deviation from Rutherford scattering
Correction factor F, which describes the deviation from pure Rutherford scattering due to electron screening for He+ scattering from atoms,
Z2, at variety of incident kinetic energies.
At very high energy and very low energy, scattering will deviate from the Rutherford type. At low energy : screening of e- must be considered At high energy : nuclear short range force will enhance the cross-section, the so-called “resonance scattering.”
25 K. M. Yu November 2008 Energy Loss
Electronic dE stopping dx ele
Nuclear dE Stopping dx nucl When an He or H ion moves through matter, it loses energy through interactions with e- by raising them to excited states or even ionizing them. Direct ion-nuclei scattering Since the radii of atomic nuclei are so small, interactions with nuclei may be neglected dE dE dE dE = + ≈ dx total dx ele dx nucl dx ele
26 K. M. Yu November 2008 How to read a typical RBS spectrum
A thin film on a light substrate Most projectile ions experience electronic stopping that results in a gradual reduction of the particle’s kinetic energy (dE/dx). At the same time a small fraction of projectile ions come close enough to the nucleus for large- angle scattering (KE). A detected backscattered particle has lost some energy during initial penetration, then lost a large fraction of its remaining energy during the large-angle scattering event, then lost more energy in leaving the solid.
27 K. M. Yu November 2008 Depth Scale
E1 = K(E0 − ΔEin ) − ΔEout dE dE t E = K(E − •t) − ( • ) 1 0 dx dx cosθ E0 KE0
KEo Total energy loss ΔE=KE0-E1 θ K dE 1 dE ΔE = ( • + • ) • t = [S ]• t cos dx cosθ dx o 1 E0 2 KE0
E1 KE ΔE 0 [So] is the effective stopping power Stopping cross-section
1 dE eV cm3 eVcm2 ε =θ ε : = N dx cm atom atom θ ε ⎛ K 1 ⎞ ΔE = ⎜ • N + • N ⎟ • t = N[ε ]• t E ⎜ in out ⎟ o ⎝ cos 1 cos 2 ⎠
28 K. M. Yu November 2008 Depth scale: thin film
180o-θ Thickness of film: Eo
KEo dE E dE dx KE 1 ΔE = (K + 0 ) •t = [S ]•t t dx cosθ o E0
E KE ΔE ΔE 1 o t = = []So N[ε o ]
ΔE ε obtained from TRIM code or empirical energy loss data fitting
E
29 K. M. Yu November 2008 Example: layer thickness
consider the Au markers
ΔEAu=EAuF -EAuB
= [KAu dE/dx⎮Eo + 1 / (cos10º) • dE/dx⎮ EAuB ] • t
dE/dx⎮ 3MeV = NAl εAl⎮ 3MeV = 6.02x1022 • 36.56x10-15 = 2.2x109eVcm-1
dE/dx⎮ EAuB = NAl εAl⎮ 2.57MeV = 6.02x1022 x 39.34x10-15 = 2.37x109 eVcm-1 t = 3945Å
ΔEAl = 165keV consider the Al signals ΔEAl = [KAl dE/dx⎮Eo + 1 / (cos10º) • dE/dx⎮ KEo ] • t ΔΕAu = 175keV
KAu = 0.9225 t = 3937Å
KAl = 0.5525
30 K. M. Yu November 2008 Energy Loss: Bragg’s rule
For a target AmBn, the stopping cross- section is the sum of those of the constituent elements weighted by the abundance of the elements.
εAmBn = m εA + n εB
Example: Al2O3 the stopping cross-section ε of Al2O3. Given: εAl = 44 x 10-15eVcm2 εO = 35 x 10-15eVcm2 εAl2O3 = 2/5 x εAl +3/5 x εO = (2/5 x 44 + 3/5 x 35) x 10-15 = 38.6 x 10 -15 eV-cm2/atom Al2O3 22 -15 dE/dx(Al2O3)=Nε =(1.15x10 )(38.6x10 )eV/cm =44.4 eV/Å
31 K. M. Yu November 2008 Quantitative analysis: composition and thickness
AA=σA•Ω•Q•(Nt)A
AB=σB•Ω•Q•(Nt)B A σ (Nt) Z m A = ( A ) •( A ) = ( A )2 • A σ (Nt) n B B B ZB m A Z = ( A ) •( B )2 n AB Z A
(ΔE) (ΔE) t = A = B AmBn AmBn [So ]A [So ]B (εΔE) (ΔE) t = A = B AmBn AmBn N[ o ]A N[εo ]B
32 K. M. Yu November 2008 Example: As implanted Si
KAs=0.809; KSi=0.566 ε Si −15 2 [ o]Si = 92.6x10 eV − cm / atom Si −15 2 [εo]As = 95.3x10 eV − cm / atom
Si ΔEAs = 68keV (FWHM )As = 60keV ε ΔE Si R = As = 1420Å p Si N[ o]As (FWHM ) ΔR = As = 540Å p Si 2.355• N[εo]As
Total As dose: AAs (Nt)As = (σ As •Ω •Q)
33 K. M. Yu November 2008 Quantitative Analysis
When Y(t) corresponds to the yield for δt t one energy division in the RBS spectrum: Y(t)=H(E) H(E)=σ•Ω•Q•Ν•δt
=σ•Ω•Q•Ν•δE/[So] =σ•Ω•Q•Ν•δE/N[εo] where δE is the energy/channel in the RBS spectrum KE o Considerσ the As implanted Si example: Y(t) AAs=σAs•Ω•Q•(Νt)As δ E H = •Ω •Q • N Si Si Si Nε [ o]Si As Z (Nt) As = ( As )2 • As δ Si H Si ZSi E /[εo]Si
δE Independent of Q and Ω
34 K. M. Yu November 2008 Thin film analysis
YxBayCuzO
YBCO y HY ZBa 2 ε[ o]Y y A Z 2 = •( ) • = Y •( Ba ) x H Z [ε ]YBCO x A Z Ba Y o Ba Ba Y H Z ≈ Y •( Ba )2 H Ba ZY
35 K. M. Yu November 2008 RBS simulation
36 K. M. Yu November 2008 Example: silicide formation
2MeV 4He+ Si Pd Before reaction
After reaction
37 K. M. Yu November 2008 RBS application: silicide formation
Reaction kinetics:
K. N. Tu et al. Thin Solid film 25, 403 (1975).
K. N. Tu et al. Japn, J. Appl. Phys. Suppl. 2 Pt 1 669 (1974). J. O. Olowolafe et al. Thin Solid film 38, 143 (1976).
38 K. M. Yu November 2008 RBS Application: impurity profile
Ge inplanted region 1.95 MeV 4He+
Si SiO2
I. Sharp et al., LBNL (2004)
39 K. M. Yu November 2008 Pitfalls in IBA
Charge Integration Accurate charge integration is important for absolute quantitative measurements Good faraday cup design
40 K. M. Yu November 2008 Pitfalls in IBA (cont.)
Deviation from Rutherford cross-section:
2 b=distance of closest approach=Z1Z2e /E 1/3 -5 rn= nuclear radius=1.4Z2 x10 rK=atomic K-shell radius=0.5/Z2
In order to miminize electron screening and maintain a point charge approximation: For typical RBS: Rutherford 0.5rK>b>3rn cross section is valid (~4%)
41 K. M. Yu November 2008 Pitfalls in IBA (cont.)
Insulating samples: charging effect
Severely distort the RBS spectrum
• Provide a supply of low-E electrons from a small, hot filament located nearby
• Coating the surface with a very thin layer of conducting material
42 K. M. Yu November 2008 Pitfalls in IBA (cont.)
Target non-uniformity Surface roughness and interface roughness cannot be distingusihed Target non-uniformity will resemble diffusion
Campisano et al., 1978
43 K. M. Yu November 2008 Weaknesses of RBS
Poor lateral resolution (~1mm) Moderate depth resolution (~100Å) No microstructural information No phase identification Poor mass resolution for target mass heavier than 70amu Detection of light impurities in a heavy matrix difficult (e.g. C, O, B in Si)
44 K. M. Yu November 2008 Particle Induced X-ray Emission (PIXE)
45 Paricle Induced X-ray Emission (PIXE)
46 K. M. Yu November 2008 PIXE: Light impurity in heavy matrix
GaAs 2 MeV 4He+
Ga Mn As RBS 1-x x PIXE
K. M. Yu et al. 2002.
47 K. M. Yu November 2008 PIXE Application: Geology, Art, Archeology, Biology External Beam
48 K. M. Yu November 2008 Hydrogen Forward Scattering (HFS) (Elastic Recoil Detection Analsyis ERDA)
49 Hydrogen Forward Scattering (HFS)
Generally known as Elastic Recoil Detection (ERD)
Charles Evans and Assoc., RBS APPLICATION SERIES NO. 3
• Quantitative hydrogen and deuterium profiling • Good sensitivity (~0.01at% of H) • Can be perform simultaneously with RBS and PIXE • Profiling with any light element in solid (using heavy ion beam, ERD)
50 K. M. Yu November 2008 HFS: H implanted Si
Channeling-RBS HFS
300 200 100 0 600 depth (nm) Si random Reference
105°C
400 200°C 400°C Counts
200
0 300 500 700 900 1100 1300 1500 Energy (keV)
Rp
17 2 [Nt]H=2.1x10 /cm Rp=280 nm ΔR=140 nm
51 K. M. Yu November 2008 HFS: a-Si:H film
RBS
HFS
52 K. M. Yu November 2008 HFS: a-SiN:H film
Energy (MeV) 0.4 0.6 0.8 1.0 1.2 25
20 RBS 15
10 Normalized Yield
5 177 nm SiN1.15H0.013
0 100 200 300 400 500 600 700 Channel Energy (MeV) 0.5 0.6 0.7 0.8 0.9 1.2
1.0 Si
0.8
HFS 0.6
0.4 Normalized Yield
0.2
0.0 Courtesy: F. Hellman group, 2008 200 250 300 350 400 450 500 Channel
53 K. M. Yu November 2008 Non-Rutherford Scattering and Nuclear Reaction Analysis
54 Non-Rutherford Scattering
Non-Rutherford elastic scattering cross sections appear when the ion energy is so high that the ion starts penetrate the Coulomb barrier of the target atom. When the ion penetrates the Coulomb barrier of the target atom, the scattering is from the target atom’s nuclear potential and the effect of the nuclear forces for the scattering then become significant.
For MeV ion beams, this phenomenon can be observed in low Z projectile/target system where the Coulomb barrier is small. The cross-section for such nuclear resonance scattering can be many times greater than the Rutherford values. Such non-Rutherford scattering has been used to some extent for the detection of light elements (C, N, O, Si) in heavy matrixes
55 K. M. Yu November 2008 Non-Rutherford Cross-Sections
56 K. M. Yu November 2008 Non-Rutherford Cross-Sections (cont.)
57 K. M. Yu November 2008 Non-Rutherford Cross-Sections (cont.)
58 K. M. Yu November 2008 Non-Rutherford cross sections
59 K. M. Yu November 2008 Non-Rutherford scattering: Example 1: SiO2 K. M.Yuetal.,Nucl.Instrum. Meth. SiO GaAs 2 B30 (1988) 551-556
60 K. M. Yu November 2008 Non-Rutherford scattering: Example 1: SiC K. M.Yuetal.,Nucl.Instrum. Meth. SiC Si B30 (1988) 551-556
61 K. M. Yu November 2008 Nuclear Reaction Analysis (NRA)
14N (d,p) 15N
When the incident beam energy exceeds a certain threshold value, other energetic particles appear in the spectrum. The detection of these particles usually provide information which is not obtainable from RBS. The NRA technique is very useful as a tool for the detection and profiling of light elements in heavy matrix. In many cases such particle-particle NRA can be carried out in a RBS setup with only minor modifications.
62 K. M. Yu November 2008 Some useful particle-particle reactions
Nucleus Reaction Incident Energy Emitted Energy Approx. cross (MeV) (MeV) section (mb/sr) 2H 2H (d,p) 3H 1.0 2.3 5.2 2H 2H (3He,p) 4He 0.7 13.0 61 6Li 6Li (d,α) 4He 0.7 9.7 35 7Li 7Li (p,α) 4He 1.5 7.7 9 11B 11B (p,α) 8Be 0.65 5.57 (αo) 0.7 0.65 3.70 (α1) 550 12C 12C (d,p) 13C 1.2 3.1 35 15N 15N (p,α) 12C 0.8 3.9 15 18O 18O (p,α) 15N 0.73 3.4 15 19F 19F (p,α) 16O 1.25 6.9 0.5 23Na 23Na (p,α) 20Ne 0.592 2.238 4 31P 31P (p,α) 28Si 1.514 2.734 16
63 K. M. Yu November 2008 NRA Example: GaNAs dilute nitride
1.3 MeV deuterium ions 14N(d,p)15N and 14N(d,α)12C reactions
GaNAs film with ~4% N
T. Ahlgrena et al., Appl. Phys. Lett. 80, 2314 (2002).
64 K. M. Yu November 2008 Ion Channeling
65 Ion channeling
66 K. M. Yu November 2008 Ion Channeling
random Planar channel Axial channel
67 K. M. Yu November 2008 Ion Channeling
Kobelco Steel Group
68 K. M. Yu November 2008 Ion Channeling: minimum yield and critical angle
Two important parameters to characterize channeling results:
1. Minimum yield:
Ychanneled χmin = Yrandom ~0.02-0.06
2. Critical half-angle, ψ1/2 indicates presence of defects responsible for beam dechanneling
69 K. M. Yu November 2008 Ion Channeling: minimum yield and critical angle
Minimum Yield, χmin Critical half-angle, ψ1/2
1 2 1 2 χ 1 2Z1Z2e ⎧ Ca 2 ⎫ Y Ψc = ( ) 2 ⎨ln[( ) +1]⎬ channeled 2 Ed ρ min = ⎩ ⎭ Yrandom where d is the distance of atoms in a row, χ a is the Thomas-Fermi screeing distance, r π r 2 ≈ min ~ 0.02 − 0.05 is rms thermal vibration min 2 πro 2Z Z Ψ ~ Ψ ~ ( 1 2 )2 ~ 0.5 −1o 1/ 2 c E
70 K. M. Yu November 2008 Dechanneling by defects
Small angle dechanneling- line defects
Perfect crystal channeling
Direct scattering- point defects
71 K. M. Yu November 2008 Homo- and Heteroepitaxy
72 K. M. Yu November 2008 Channeling: Heteroepitaxy
500 nm
Z. Liliental-Weber ~530nm InN on 210 nm GaN
K. M. Yu et al., LBNL 2004.
73 K. M. Yu November 2008 Amorphous layer analysis
74 K. M. Yu November 2008 Channeling: Impurity Lattice Location
3 0.0 r 0.2
ro 2 0.4 Atomic row
Flux 0.6
ψ/ψ1 0.8 1 =1.0
Channel center
0 0.2 0.6 1.0
Distance from atom row, r/ro
75 K. M. Yu November 2008 Experimental techniques : combined channeling RBS/PIXE
Rutherford backscattering (RBS) Mn
Particle-induced x-ray emission (PIXE)
c-RBS: crystalline quality of film (from GaAs backscattering yields) c-PIXE: substitutionality of Mn atoms w.r.t. host GaAs
76 K. M. Yu November 2008 Channeling: Ga1-x-yBeyMnxAs
Channeling RBS/PIXE: -presence of interstitial Mn in GaAs
-[MnI] increases with Be doping -Mn reduces T <100> I C
<110>
<111>
K. M. Yu et al. 2003. 77 K. M. Yu November 2008 Examples of applications for IBA
Thin film analysis: composition and thickness Multilayer analysis: identification of reaction products; obtaining reaction kinetics, activation energy, and moving species Composition analysis of bulk garnets Depth distribution of heavy ion implantation and/or diffusion in a light substrate Surface damage and contamination Providing calibration samples for other instrumentation such as secondary ion mass spectroscopy and Auger electron spectroscopy Defect depth distribution due to ion implantation damage or residue damage from improper annealing Lattice location of impurities in single crystal Surface atom relaxation of single crystal Lattice strain measurement of heteroepitaxy layers or superlattices
78 K. M. Yu November 2008