Spettroscopie elettroniche Con la spettroscopia si può caratterizzare un materiale rispetto a: composizione chimica, stati elettronici e magnetismo, eccitazioni elettroniche, roto-vibrazionali e magnetiche.

Fotoemissione ed elettroni Auger forniscono principalmente informazioni sulla superficie del materiale. La composizione di volume può essere ottenuta erodendo il campione mediante bombardamento ionico (depth profiles).

L’informazione EELS riguarda eccitazioni elettroniche mentre l’HREELS (EELS ad alta risoluzione) riguarda eccitazioni vibrazionali. Contrariamente ad AES e fotoemissione l’informazione è per lo più qualitativa. La profondita di informazione dipende dall’energia degli elettroni.

Determinazione della composizione chimica: ) Elettroni secondari: AES (Auger Electron Spectroscopy) ) Fotoemissione XPS (X-rays Photoemission Spectroscopy) o ESCA (Electron Spectroscopy for Chemical Analysis), UPS (Ultraviolet Photoelectron Spectroscopy), Fotoemissione inversa o Bremsstrahlung Isocromat Spectroscopy ) Spettroscopia di perdita di energia: EELS (Electron energy loss Spectroscopy)

Two-Hole Final State

One-Hole Initial State

De-Excitation Auger Process

e- e-

Ground State

K 1s

L1 2s

L2,3 2p

M1 3s

M2,3 3p VB

Evac

EF

Ekin

spettroscopia AES:

Electron In: Il cristallo è colpito da un fascio di elettroni primari

differenziando lo spettro si elimina il fondo dovuto agli elettroni secondari

Electron Out: 1) Elettroni riflessi elasticamente 2) Elettroni riflessi anelasticamente 3) Elettroni secondari generati dalla

creazione di coppie elettrone-buca 4) Elettroni secondari Auger

AES

1s K

3d M4,5

3p M2,3

Auger Electron

Auger Process

3s M1

2p L3

2s L1 2p L2

Fermi

Level

X-Ray Fluorescence

Nel processo di diseccitazione l’emissione Auger compete con la fluorescenza. Il processo Auger domina per piccoli numeri atomici, la fluorescenza per grandi numeri atomici

3s M1

2p L3

1s K

2s L1 2p L2

Fermi

Level

Photon

3d M4,5

3p M2,3

Computing the kinetic energy of Auger electrons: XYZ Process, One-Particle Scheme, Energy Conservation

Ekin XYZ Eb X Eb Y Eb Z

Eb X

Eb Y

Eb Z

Ekin XYZ Kinetic Energy of the Auger Electron

Binding Energy of the X-Level

Binding Energy of the Y-Level

Binding Energy of the Z-Level

Work Function

Usually additional terms must be included accounting for the two-hole final state correlation interaction and the relaxation effects

Ekin XYZ Eb X Eb Y Eb Z F R F Two-Hole Final State Correlation Energy R Relaxation Energy

Principal Auger Lines while Spanning the Periodic Table of the Elements

KL1L2 … L1M1M2 Auger Processes L1L2M1 Coster-Kronig Process (the initial hole is filled by an electron of the same shell)

CCC Transition Core-Core-Core

CCV Transition Core-Core-Valence

CVV Transition Core-Valence-Valence

L-S-coupling Intermediate coupling

J-J-coupling

Origin of the multiplets Relative energies within the KLL Auger series while changing the atomic number. Differing coupling of the final state multiplet terms while spanning over Z

Rela

tive

Ene

rgie

s

Z 20 40 60 80 100

Gas vs. Solid Auger Emission from Mg:

Very similar lines for CCC transitions, except for: an almost rigid energy shift (relaxation) some additional features related to many-body effects in solids (e.g. energy losses due to plasmons)

Primary Electron Beam Energy Dependence of the X-Level Ionization Cross-Section by Electron Impact

The maximum is achieved at Ep ≈ (3÷4) EAX EAX appearance threshold

Comparison between electron in electron out and photon in electron out 1s Ionization Cross-Section for Selected Elements by Electron Impact and by X-Ray Excitation

Auger Electron Spectroscopy

Semi-Quantitative Analysis

One can determine the atomic concentration (Ci) of the atomic species present in the near-surface region of a solid sample

Ci

IisiIisii

Ci Atomic Concentration of the i-th species Si Orbital Sensitivity Factor of the i-th species Ii Spectral Intensity Related to the i-th species

Fragments of Theory

K 1s

L1 2s

L2,3 2p

M1 3s

M2,3 3p VB

Evac

EF

Ekin

The Auger process fulfills 1) Energy Conservation 2) Angular Momentum Conservation 3) Parity Conservation

M if f e2

riji j

i

The process is governed by the Coulomb interaction between the electrons and related selection rules

Mif 3 p 3 p e2rij

i j

2s

Often |i > and |f > are expressed in terms of single-particle hole vector states, provided the total wave function is antisymmetric (Slater determinant)

Thereby the initial and final S, L, M, J and S’, L’, M’, J’ values are defined in terms of the s, l, m, j of the two holes in the each initial and in the final states.

Auger Process Fragments of Theory

The transition probability of the Auger process can then be written as

if 2D E

2 E f

(Ef) Density of final states conserving the energy D Direct matrix element E Exchange matrix element

Core-Valence-Valence (CVV) Auger Transitions 1) To a zero-th order approximation (i.e. no final state effects and assuming the matrix elements constant all over the transitions), the Auger emission is expected to mimic the self-folded DOS N(E), i.e. the Transition Density of States D(E) 2) Thereby, its width should be twice the value of G(width of the one-particle state distribution)

I E D0E N E N E E d

Core-Valence-Valence (CVV) Auger Transition

To a more refined level, one has to take into account possible final state effects. Schematically speaking two limits are expected: 1) Pure Band-like Limit No final state effects are present 2) Atomic-like Limit The two final states holes are not effectively screened The band picture (i.e. the delocalized character of the valence wave functions along with the Bloch theorem) does not hold any more. The two holes left behind behave as sources of an impurity term in the Hamiltonian and atomic-like multiplet effects are expected. Since the overall energy of the process is conserved, the Auger electron does not have the kinetic energy expected in the pure band-like scheme. Within a Hartree-Fock picture, Correlation and Exchange Potentials must be appropriately taken into account.

Experiment

Self-folded DOS

C KVV Auger Lines from a Variety of C-based Systems sensitivity to the chemical binding

Si L2,3VV Auger Line from Solid Silicon: Experiment vs. Theory

Experiment

Theory

CMA vs CDA

• Accettanza angolare ampia (elemento

conico ±3° attorno a 42° dall’asse 1

sterad).

• pass energy variabile.

• Resolving power E0/DE ~200 per diam

150 mm.

• E0/DE dipendente da E0

• Accettanza angolare piccola (~5° dall’asse

10-2 sterad).

• Lenti ritardanti prima della apertura di

ingresso pass energy costante.

• Resolving power E0/DE =1000-2000 per

diam 150 mm.

• E0/DE indipendente da E0

Alta efficienza in conteggi con limitata

risoluzione e ridotta distanza di lavoro. Ridotta efficienza in conteggi ma alta

risoluzione e distanza di lavoro.

V-shaped Filament

Extractor

Deflecting Plates

Backscattered Electrons

Primary e- Beam

Sample

Image Display

Auger Scanning Electron Microscopy

Applicazioni

Auger Spectra as Measured at Selected Points of the Self-organized Agglomerated Au/Si(111) Interface

Flat region

Island

Si L2,3VV Au N6,7VV