Laboratory Course in Condensed Matter Physics Prof. Mario Rocca AA 2013-2014

Laboratory Course in Condensed Matter Physics
                 Prof. Mario Rocca AA 2013-2014
Prerequisites: concepts of solid state physics like direct and reciprocal space

The progress in Physics is strictly connected with the Advancements in the
methods of experimental investigation, disclosing new areas of research.
E.g. : Superconductivity was discovered by serendipity when scientists
        understood how to reach extremely low temperatures.
        Surface Science developed following the establishment of ultra high
        vacuum technologies

The course deals with the principal methods of crystallographic and spectroscopic
investigation available today to recover information at atomic as well as
nanoscopic scale, both in the bulk and at the surface of a specimen.

•How to determine the crystallographic, electronic and magnetic structure in the
bulk and at surfaces and interfaces.
•How to determine the dynamical properties: vibrational, electronic and magnetic
excitation spectra
•How to modify and manipulate such properties following gas adsorption,
chemical reactions and nanostructuring.

Probe particles for Surface Science Investigations

The experimental information is mediated by probe particles.
For their choice we have to consider:
1) the depth of the desired information
2) the interaction cross section (elastic as well as inelastic)
          e.g. for magnetic properties the probe particle must have a magnetic moment
          as it is the case for photons, neutrons and electrons
3) the desired time resolution
4) the availability and the intensity of the sources in the lab or in great scale facilities

For bulk properties:
              photons and X Rays, neutrons, swift electrons and ions
For surface properties: grazing incidence photons and X Rays,
       chemically inert atoms at thermal energy, slow electrons,
       low and medium energy ions

 Ultrarapid phenomena can be studied only with photons

Condition over l
The necessary condition to see an object is
that the wavelength l of the probe
particle is comparable or smaller than the
dimension of the object.
For the crystallographic structure what
matters is the lattice spacing (0.2 nm).

This condition determines the
energy scale of the probes

 10   keV        photons (X rays)
100   eV         electrons (low energy electrons)
100   meV        neutrons (thermal neutrons)
 20   meV        He atoms (thermal He beams)
This energy scale is important to estimate the influence of the probe
particle on the sample

Cristallography and Microscopy
Accurate crystallographic information can only be retrieved from scattering
experiments. Energy transfer is undesired.
The smallest observable size is determined by the wavelength of the probe particle.
The largest by the transfer width of the instrument.

Choice of probe particles:
Volume: X Rays, neutrons, swift electrons
Surfaces: grazing incidence X Rays (XRD), thermal He atoms (HAS o TEAS),
          slow electrons (LEED) or swift electrons at grazing incidence (RHEED),
          low and medium energy ions.

Alternatively one can use microscopy tools:
1)   By image formation whereby the resolution is determined by probe particle
     wavelength and by the aberrations of the lenses
2)   By scanning probe techniques: a beam is focussed on a small area and a
     macroscopically integrated response is assigned to it

Transfer width
The transfer width w corresponds to the size of the area over which the wave associated
with the incident particles is coherent (it has a well defined phase relationship
  q||=kf||-ki ||             transferred momentum
  q||= k |sinf-sin i|
  w=2/q||                  with q|| uncertainty over q|| (width of diffraction spots)
  q||=(q|| /E) E+(q||/) 

  one obtains two contributions:
  w=2/(kcosi i)
  wE=2 2 k/(E |sinf -sini|)

  For low energy electron diffraction (LEED)
  k 0.51 E (Ǻ-1) for E given in eV
  In LEED E 100 eV and f 10-2 rad w  100 Å

coherent sources
   Small area

   Far away
   Monochromatic

Radiography using a laboratory
X-Ray source

Radiography
using Synchrotron Radiation

Spectroscopy
In spectroscopic studies a given amount of energy is transferred to the
    sample obtaining information on the fundamental as well as on the
    excited electronic states and on the roto-vibrational levels and the
    chemical composition of the sample.

Possible measurements:
       Appearance spectroscopies
       Absorption spectroscopies (flux removed from the primary beam)
       Energy Loss Spectroscopy and Inelastic Scattering
       (energy and angle distribution of primary reflected or transmitted particles)
       Secondary particle analysis
       (e.g. Auger Electrons or Photons emitted by fluorescence)

The information is mediated by the penetration depth of the primary
   particles and by the extraction depth of the secondary particles. The
   latter can be of the same sort as the primary ones or different
   (e.g. electron in - electron out or photon in - electron out)

• volume:

 absorption of photons of given frequency:
     IR: roto-vibrational properties,
     UV o raggi X: electronic properties

 inelastic scattering of weakly interacting particles
      neutrons or X Rays (through Raman effect),

 inelastic scattering of energetic particles :
      swift electrons (50 keV- 1 MeV), swift ions (1 MeV)

surfaces:
Rotovibrational properties:
       Absorption of IR photons (if the volume is inactive)

Electronic preoperties :

       Photoemission induced by UV o soft X Rays

       inelastic scattering of strongly interacting particles:
               atoms or slow electrons for vibrational properties
               low energy ions (keV) for the chemical analysis

Chemical composition:         emission of secondary ions and
                              electrons or Auger electrons

Electrons as Probe particles
                                        Electrons play a particularly
                                           important role in surface
                                           science studies since:
                                        1) They are easy to produce and detect.
                                        2) The information depth depends on their
                                            kinetic energy:
                                            10 eV

sonde spettroscopiche per superficie

assorbimento IR in riflessione (se il volume è inattivo)
                             proprietà rotovibrazionali
scattering anelastico          elettroni lenti (10-100 eV)
                               elettroni veloci (1-10 keV) radenti
               alta risoluzione proprietà vibrazionali (0-0,5 eV)
               bassa risoluzione proprietà elettroniche (1-100 eV)
fotoemissione indotta da raggi UV o X molli sfruttando il limitato
              libero cammino medio degli elettroni fotoemessi
              (XPS o ESCA e UPS) struttura elettronica
scattering anelastico di ioni di qualche keV composizione chimica
emissione di ioni secondari SIMS             composizione chimica
emissione di elettroni secondari ed Auger composizione chimica

sonde spettroscopiche per volume e superficie

  interfacce nascoste e composizione in profondità:

  con tecniche di superficie rimuovendo, nel corso della misura,
  gli strati più esterni del materiale.

  con fotoni emessi o assorbiti solo all’interfaccia (ottica non
  lineare)

  con metodi di volume tagliando il materiale in fette di
  spessore di poche centinaia di nanometri disposte
  verticalmente all’interfaccia con un Focussed Ion Beam (FIB)
  e studiando quindi il campione con microscopia di
  trasmissione di elettroni (TEM)

Cristallografia e Morfologia
Le informazioni cristallografiche si possono ottenere mediante esperimenti di
scattering elastico. La cessione di energia al corpo deve essere minimizzata per non
alterarne le caratteristiche. La dimensione massima dei dettagli visualizzati dipende
dalla coerenza delle particelle sonda, quella minima dalla lunghezza d’onda.
   La scelta della particella sonda dipende dalla proprietà in studio:
   Volume:              raggi X, neutroni, elettroni ad alta energia
   Superficie:          raggi X radenti (XRD), atomi di He termici (HAS o TEAS),
                        elettroni lenti (LEED) o elettroni energetici radenti (RHEED),
                        scattering di ioni.

  Alternativamente l’informazione si ricava mediante microscopia usando la
      particella sonda più conveniente.
  1)   con ricostruzione di immagini mediante lenti.
            La risoluzione raggiungibile è determinata dalle aberrazioni delle lenti e dalla
            lunghezza d’onda della sonda.
  1)   con misure in scansione, in cui il fascio delle particelle sonda viene focheggiato su
            un’area piccola misurando un segnale di risposta ad esso associabile

  Per migliorare il contrasto nelle immagini è utile la combinazione della
      microscopia con metodi spettroscopici (Spettromicroscopie).

Microspie e Spettromicroscopie
condizione necessaria per vedere un oggetto è che

       1) la sonda abbia lunghezza d’onda
       (λ=h/mv per particelle, λ=c/ν per i fotoni)
       paragonabile o inferiore alle dimensioni dell’oggetto stesso.

       2) che vi sia contrasto

       3) che la sonda sia coerente spazialmente e temporalmente