Nano-technology and Nano-electronics by pmv64896

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									Nano-technology and
  Nano-electronics
  Department of Electrical and
    Computer Engineering,
     University of Tehran
       Measurement in Nano
•   Electron microscopes, diffraction,
•   Transmission electron microscopes,
•   Scanning electron microscopes,
•   Tunneling microscopes,
•   Scanning positioning microscopes,
•   Atomic force microscopy,
•   Optical microscopes,
•   Dark field phase microscopes,
•   Depth of focus, poor for electron microscopes,
•   Small apertures, loss of electron beam
            First TEM




• Ruska and Knoll, 1930!
Fundamental of TEM
    Diffraction of electrons
• Matter-wave nature
  of electrons,
• λ=h/p where
  – h: Planck’s constant
  – p: momentum, (mv)
  – λ:wavelength of
    electrons,
• E=1/2 (m0v2) or
  – λ= h/(2m0eV)0.5
• or λ=
 h/[2m0eV(1+eV/(2m0c2))]0.5
        Relativistic effects
• V: accelerating voltage, non-relativistic
  – 100kV 0.0038nm,
  – 200kV 0.0035nm
  – 400kV 0.0023nm
• Relativistic wavelength
  – 200kV 0.0033nm, 2*108m/s
  – 400kV 0.0016, 2.5*108m/s
  – Increase in mass m/m0= 1.78
• High speeds, close to speed of light
• Microscopes with ultra-high resolution,
  V=1MV!!
Various effects
          Electron scattering
• Interaction of electron with a
  single isolated atom,
• Scattering angle (θ) small
• Solid angle, , steradian(sr)
• σ=πr2 , cross-section,
• d=2πsinθ dθ
• dσ/d = 1/(2πsinθ) dσ/dθ
   – Differential cross section
• σ=πrelast2 , relast = Ze/Vθ
• σt= σelas + σ inelas
             Diffraction of light




•   The scattered waves are in-phase when the path difference is a nλ
•   L=d sinθ, d: spacing of slits
•   Detector is placed far away at angle of θ
•   Two wavelets traveling in direction (r) are out of phase by 2πL/λ
•   This difference is called a “phasor”
       Diffraction patterns
• Five-slit aperture,
• If phasors are
  360/5 (o) apart,
  the resultant
  vector is zero-
  magnitude.
• Second zero
  happens at 144o,
  etc.
Finite width slit
          Airy diffraction
• Visible light
  diffraction
  produced by
  0.5mm diameter
  circular
  aperture,
• Airy rings:
  resulted from
  diffraction from
  small aperture.
Angles in TEM
              scattering
• Coulomb scattering
  from atoms and
  electrons,
• Higher energy
  electrons, less
  scattering,
• r=Ze/Vθ
• Smaller distances,
  more scattering
• Higher energies, less
  scattering
Wave scattering
• Two waves traveling,
  incident and scattered.
• Incident wave,
  Ψi(r)=exp(iKIr),
• Incident wave could be set
  at Z-axis
• Reflected (scattered) wave:
  Ψsc(r)= Ψ0 f(θ)/r exp(ikr)
• Summation of both waves
  must be valid in SE.
• Ψt(r)= Ψ0{exp(iKIr) +if(θ)/r
  exp(ikr)}
                  Atomic factor
• |f(θ)|2= dσ(θ)/d
• dσ(θ)/d =e4Z2/(16E02sin4θ/2)
• Where E0 in eV, is the incident
  energy of electrons
• dσ(θ)/d
   λ4Z2/(64π4a02(sin2θ/2 + θ02/2)2)
• a0=h2ε/(πm0e2), Bohr radius,
  around 0.5Ǻ
• θ0 describes the electron-electron
  scattering, about 2 degrees,
• When θ bigger than θ0 nuclear
  scattering is dominant.
                 diffraction




• Diffraction of waves in terms of reflection of a
  plane wave at an angle of “theta”.
• The path difference is AB+BC,
• Under Brag condition this path difference is a
  multiple of wavelength.
Brag diffraction




        • K in this image is
          the same as “g” in
          other notations.
Real image, diffraction
       Diffraction patterns




• Single crystals, regular patterns,
• Poly-crystals, dotted pattern
• Many-crystals, rings
        TEM in Electronics




• Top: TEM image of 500nm,
  silicon epitaxy, the
  bending lines are evident
• Right: image of small
  transistors
            Ewald sphere
• Reciprocal Lattice,
  Condition: Exp(iK.R)=1
• K.R=2nπ, R: translation
  vector, K defines the RL.
• FCC BCC, SCSC
• Incident beam, k=1/λ
• Smaller λ, larger radius,
• Brag conditions, ki-kd=g
• “g” a vector in reciprocal
  lattice.
           Finite specimen




• Extinction error (s) or deviation parameter.
• Diffraction occurs even without Brag’s condition
• When ki-kd=g+s, the intensity of the diffraction
  spots depends on the value of “s”.
                 Finite thickness



• Kinetic theory, specimen thickness is split into slices of atomic
  foils.
• Diffraction from solid is the summation of all slices.
• Similar to diffraction from slit with a limited width,
• Ig(s)=(π/ξg)2 (sin(πts)/πs)2 where ξg is the extinction distance.
    – Ig is the intensity of the diffracted beam.
• Thinner specimens, more deviation from an ideal crystal or Brag
  diffraction
• More chance of electron penetration through the specimen to
  measure the diffracted beam
          Diffraction patterns




• Diffraction patterns of silicon along 110 direction.
• By increasing the sample thickness, DP becomes hazier.
Images
Convergent beam
Image formation
Energy losses
                AES
• Auger electron,
  secondary electron
• Emission from
  L:shell
• Characteristics of
  the material.
• High adsorption
• Surface effect
      Inelastic scatterings
• Phonon, lattice
  vibration,
• High Z atomic systems
• Mean free path,
  350nm
• Hamper diffraction
  patterns,
• Cooling the specimen
  for better imaging.
• Plasmon, longitudinal
  electron wave
• Resulted from impact
  of high energy
  electrons,
• Similar to acoustic
  waves
• Electron gas in highly
  conductive metals,
• Mean free path about
  100nm
      Cathedoluminescence
• Incident electron leads
  to a promotion of
  electrons from V.B to
  C.B.
• The return on this
  electron leads to a band-
  to-band recombination.
• For a direct gap
  semiconductor, a
  radiative recombination
  is observed.
• Photons with the value
  of the B.G. are emitted.
     Electron guns in TEM
• Tungsten hair-pin
  tip: easy to use,
• Low vacuum
  conditions, high
  temperature
  operation,
• Thermionic
  emission,
• Low current
      Crystalline sources
• LaB6 crystal
  sources.
• Undersaturated
  emission, mostly
  from corners,
• Saturated, a
  uniform and
  coherent emission.
         Field-Emission guns
•   Coherent and high current density
•   Two anodes to extract and converge the beam.
•   Need for ultra-high vacuum technologies,
•   Applications in SEM.
        Various definitions
• Depth of focus:
  depth of sharpness
  in the image plane,
• Depth of field: depth
  of sharpness in the
  object space
• αim=dim/Dim
• βob=dob/Dob
• It can be shown
  that:
Dim=dob/ βob MT2
       TEM images of nano-
            particles
• TEM of nickel
  particles on silicon
  oxide
• (a) Bright field
  image, (b) Diff.
  pattern
• (c) aperture
  filtered, (d)
  improved aperture
• (e) processed
  image, (f) oxide
  layer.

								
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