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Younes Sina, Ion Channeling



Ion channeling, Younes Sina, The University of Tennessee, Knoxville

Ion channeling, Younes Sina, The University of Tennessee, Knoxville



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  • Full Name Full Name Comment goes here.
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  • hello
    thanks so much,mr sina
    my mail is manikian34@yahoo.com
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  • KIAN34,

    I need your email address. I can send you a lot of useful books.
    Are you sure you want to
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  • I am a graduate student that work in application of RBS-C in semi –conductor but I don’t have any refrences except one book (ion beam for material analysis by bird) because unfortunately in my country limited number of persons work in about. so I want from you help me that:
    Whence I started my project?
    Which s books or articles read?(I read only bird books because I don’t have other book such as(Handbook of Modern Ion Beam Materials Analysis by tesmer and nastasi and other books ……)
    Also I want work about the porous material like silicon and…I want to know this subject is well or in other words what is top subject in this field?
    In the last I than you so much for your time and your help
    Good luck
    Are you sure you want to
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    thanks so much mr sina
    I was be happy when a compatriot ,accept my appeal
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  • KIAN 34,

    I'll be happy to answer your question. Please ask your question by email.

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     Younes Sina, Ion Channeling Younes Sina, Ion Channeling Presentation Transcript

    • Ion Channeling
      A course of professor McHargue
      Presented by Younes Sina
    • Introduction
      Ion channeling is a powerful tool for characterization of crystalline solids. The method is based on the channeling effect.
    • Introduction
      When the He+ ion beam is properly aligned with the crystalline axis of a single crystal sample, the backscattering signal drops dramatically.
      If the crystal contains defects involving atoms that are displaced from the atomic rows, close-encounter collisions with these displacements will increase the yield. The yield can be used to precisely calculate the defect densities in imperfect crystals.
    • Introduction
    • Theory of Channeling
      An energetic ion that is directed at a small angle,ψ, to close-packed rows or planes of atoms in a crystal is steered by a series of gentle collisions with the atoms so that it is channeled into the regions between these rows or plans.
      • Steering of the ions through the open channels can result in ranges several times the maximum range in no-steering directions or in amorphous materials.
      • Electronic losses determine the range and there is very little straggling.
      • When a low-energy ion goes into a channel, its energy losses are mainly due to the electronic contributions. This implies that a channeled ion transfers its energy mainly to electrons rather than to the nuclei in the lattice.
    • Theory of Channeling
      Basic assumption for ion channeling
      • The scattering angles are small
      • successive collisions are strongly correlated (because ions passing close to an atom in a string must also come close to the next atom.)
      • The collisions are elastic two-body encounters.
      • A real crystal can be approximated by perfect strings of atoms in which the atomic spacing , d, is uniform.
    • Atomic configuration in the diamond cubic structure
    • The ion can be considered to move in a transverse potential, VT.
      Distance traveled along the string
      Distance of the ion from the string of atoms
      If the string consists of different atomic species, the potentials for each atom are different, and an average potential is used.
    • Two-body potential V(r) is generally taken to have the Tomas-Fermi form:
      Electronic charge
      Nuclear separation distance
      Tomas-Fermi screening function
      Atomic numbers of ions at the string
    • Molière approximation for
      Tomas-Fermi screening function
    • String potential
    • Modified Bessel function
      Molière screening function
      Lindhard screening function
    • Example 1
      Calculation of fL and fM for 4He+ incident along a <110> channel in Si.
      a=0.0157 nm
    • A plot of FRS(x′) versus x′, where FRS(x′) is the square root of the Molière string potential fM and x′ = 1.2u1/a
    • Incident energy
    • Example2:
      Calculation of for 2 MeV 4He+ along a <110> channel in Si
    • For mixed strings of different atoms, Z2 is an arithmetic average of the atomic numbers of the atoms in the string.
      Calculation of interatomic spacing d and interplanar spacing dp for GaP(zinc blende structure)
    • If the crystal contains defects, even slightly displaced from atomic rows, the string potential is disturbed, and ions will be dechanneled.
    • If a near surface layer of the crystal is completely disordered(amorphized),backscattering yield are significantly enhanced, and the close-encounter probability becomes equal to that obtained in the non-channeling mode.
    • Normalization was achieved by dividing the aligned yields by the random yield.
    • Notation for normalized yield at channeling
      χ = normalized yield= (aligned yield)/(random yield)
      χh = normalized yield from host atoms
      χs = normalized yield from solute atoms
      χh<uvw> ,χs<uvw> , = normalized yields from host and solute atoms, respectively for alignment along <uvw> axial channels
      χh{uvw} ,χs{uvw} = normalized yields for host and solute atoms, respectively, for alignment along {hkl} planar channels
    • The normalized yield χh<uvw>, for alignment along an axial channel<uvw>, according to the continuum model (Lindhard):
      Screening length:
      Atomic density
    • The experimental χh<uvw>value is increased appreciably if the divergence of the ion beam exceeds 0.1° or if oxides or other impurities are present on the surface of the crystal.
    • The half-with of the channeling dip,ψ1/2, defined as the angle at which the normalized yield from host atoms χh, reaches a value halfway between its minimum value and the random value.
    • Given in Fig.A17.2
      Unchanneled ion
      Channeled ion
    • Reason for difference of calculated and experimental data above ψ1/2:
      That ions that are incident at angles slightly larger than ψ½ ,have a higher –than- average probability of collision with atoms in the string.
      Calculated data --------
      Experimental data
    • Flux distribution and trajectories of channeled ions
      Because of the steering action of channeling, ions are directed toward the center of a channel, resulting in an enhanced ion flux there. In order to calculate ion trajectories and, thus, the spatial distributions of channeled ions within a given channel, it is usually assumed that the transverse component E┴, of the ion energy is conserved (energy loss are neglected).
      Initial incident angle when the ions strike the crystal
      Ion transverse energy
      Distance between the atomic row and the initial striking position
    • In analytical calculations, it is assumed that ions are uniformly distributed within an accessible area specified by the equation:
      The ions are excluded from an area πρA2 close to the string.
      Cross-sectional area of the channel
      Normalized flux at the jth potential contour
      Accessible area at the potential lower than that of the jth potential contour
    • Equipotential contours (eV) for He+ ions in Al for one-quarter of a <110> channel
      Cell of string
      14 string of atoms
      First cell
      second cell
    • Example 4:
      Calculation of Fj
      The areas outside the strings enclosed by the 20 eV potential contours are  0.6 of the total .
      Accessible area at the potential lower than that of the jth potential contour
    • Equiflux contours for 1 MeV He+ ions in Al at 30K for one-quarter of a <110> channel
      Analytical calculation
      Monte Carlo simulation ---------
    • The ion flux not only varies across a channel but also exhibits strong depth oscillation. This occurs because of the rather regular movement of channeled ions from one side of channel to the other. Thus, peaks in the mid-channel flux (and minima in the flux at the channel walls) occur at /4
       is the wavelength of the channel ion’s path
      Unchanneled ion
      Channeled ion
    • wavelength of the channel ion’s path
      Lindhard characteristic angle
      Constant taken as 31/2
      Number of atomic strings bordering the channel
      Distance from a string to the center of the channel
      Unchanneled ion
      Channeled ion
    • Depth variation of the calculated mid-channel flux of 1 MeV He+ ions in a <100> axial channel of Cu
      No multiple scattering included
      multiple scattering, energy losses, thermal vibration(T=273K), and beam divergence of 0.06° included
      multiple scattering, energy losses, thermal vibration(T=273K), and beam divergence of 0.23° included
    • The depth oscillations are less regular for axial channels than for planar channels, because axially channeled ions can move to neighboring channels more easily than planar channeled ions can.
    • Picture of different types of lattice defects
      a) Interstitial impurity atom,
      b) Edge dislocation
      c) Self interstitial atom,
      d) Vacancy
      e) Precipitate of impurity atoms
      f) Vacancy type dislocation loop,
      g) Interstitial type dislocation loop
      h) Substitutional impurity atom
    • Damage to a crystal involves displaced lattice atoms:
      • Strain
      • Point defects
      • Dislocations
      • Stacking faults
      • Twins
      • Defect clusters
      • Small precipitates
      • Amorphous regions
      Damage produced by ion beam :
      • Frenkel pairs(a vacant lattice site+ the self-interstitial atom rejected from the site)
      • Clusters of vacancies and self-interstitials
      • Voids or dislocation loops
      • Amorphous regions
    • Displaced atoms can effect channeling in two qualitative ways:
      • By dechanneling (gradual deflection of the channeled ions out of channels)
      • By direct backscattering of channeled ions
      In practice, a combination of these two process usually occurs.
      Limiting cases:
      • Distortion-type defects
      • Obstruction-type (amorphous region)
    • Limiting cases:
      • Distortion-type defects
      -Because they involve small displacements of host atoms into the channels
      -Lattice vibrations can be considered to be another example of distortion-type defects
      • Obstruction-type (amorphous region)
      Because they occupy central positions in the channels
    • The effect of lattice defects on channeling can be described most simply by considering that the ion beam consists of a channeled fraction that is backscattered only from displaced atoms
      and a dechanneled fraction that is backscattered from all atoms in the same way as randomly directed.
    • Channeled ions gradually become dechanneled (deflected out of the channel) by multiple collisions with electrons and with displaced atoms, including thermally vibrating atoms and lattice defects.
      In backscattering geometry, the normalized yield,χh, is equal to the dechanneled fraction of the beam plus the yield arising from the backscattering of the channeled ions from displaced atoms
      Χh :
    • Normalized ion flux for site i
      Geometric factor for site i
      Dechanneled fraction of ions
      Displaced atom for site i
      Channeled fraction of ions
    • Because of the lack of knowledge about a stable configuration of displacements, it is usually assumed that, for single, randomly displaced atoms, the defect scattering factor is given by:
      Defect density at the depth of x
      Calculated by χhD
      Total atomic density
    • Dechanneling by point defects
      As ion penetrate a crystal their transverse energy component, E┴, gradually increases because of multiple collisions with electrons and displaced atoms. This effect eventually causes ions to be deflected out of channels ( dechanneled) ,producing an increase in the yield, χh<uvw>,and a decrease in the channel half-with, ψ1/2, as the ions penetrate deeper in to the material.
    • For shallow depth, where χ<0.2 , dechanneling is caused mainly by nuclear multiple collisions with thermally vibrating atoms and with lattice defects, whereas multiple electronic collisions become increasingly important at greater depths.
    • Defect density
      Effective defect cross section for dechanneling
      Effect of thermal vibration
    • Value for undamaged crystal
    • An ion is assumed to be dechanneling when its transverse energy exceeds a critical value, E┴C.
      Distribution of transverse ion energy as a function of depth
    • Cross section for dechanneling by point defects
      Cross section for dechanneling by point defects
      Critical angle
    • Dechanneling by dislocation loops
      Under the condition that direct scattering is negligible:
      Defect density
      Cross section for dischanneling
    • Magnitude of the Burgers vector of the dislocation loop
      Dechanneling by dislocation loops
      Atomic density in the plane
      A constant dependent on the dislocation orientation and type
      Planar dechanneling cross section per unit dislocation length
    • Cross section for dischanneling
      Defect density
      Planar dechanneling cross section per unit dislocation length
      If σd=λp
      Total projected length of dislocation lines per unit volume at a depth of x.
    • Dechanneling by dislocation loops
      Analysis of phosphorous-diffused by Si
      A misfit dislocation network is observed at a depth of 450 nm
      Backscattering spectra for 2.5 MeV He+ along {110}planar and <111> axial channels
      Energy dependence of planar dechanneling
    • Energy dependence of dechanneling
      Dechanneling can be used to identify the type of defects, because it has an energy dependence behaviors.
      Expected energy dependence:
      E0 for stacking faults
      E1/2 for dislocations
      E-1 to E-2 for point defects and defect clusters
    • Dechanneling by heavily damaged regions
      Channeling is commonly used to measure the epitaxial regrowth of materials that are amorphized by ion implantation.
      Si implanted by Si in order to amorphize the surface layer without introducing foreign atoms.
      Implantation energy=50-250 keV
      Depth of amorphization=460 nm
      He+ energy = 2 MeV
    • Epitaxial growth is linear with time
      Regrowth rate is lower and nonlinear
    • Energy loss of channeled and random ions
      The energy loss of channeled ions and random ions can be significantly different.
      Channeled ions with a typical ion flux distribution peaked in the middle of channel, have small probability of a close encounter with atom rows and, consequently, have reduced interactions with inner-shell electrons of target atoms. Therefore, channeled ions usually have a stopping power less than that of random ions.
      Unchanneled ion
    • Energy loss of channeled and random ions
      Energy loss of He+ as a function of the incident ion energy for <100>,<111>, and<110> channeling directions of silicon.
    • Energy loss of channeled and random ions
      α and β are fitting parameters
      E is the ion energy
      Reduction in stopping power for channeled ions is a phenomenon that depends on ion penetration depth. For shallow penetration depth (a few hundred nanometers), the stopping power is close to the random stopping power because of a nearly uniform ion flux distribution. At deep depth, the stopping power approaches the random value as a result of significant dechanneling.
    • Data Analysis
      Typical detector used in RBS analysis
      Channel-energy conversion
      An evaporated thin layer of gold
      The number of electron- hole pairs created in the depletion region is proportional to the particle energy loss in this region.
      A diode whose depletion region increases with bias voltage
    • Data Analysis
      Channel number
      The created electrons and holes cause a pulse of charge. The height of the pulse can be converted to channel number after amplifying and analyzing.
      Energy of the particle
      c and ΔE/Δn can be determined by linear fitting of the equation using a calibration sample that contains at least 2 different elements on the surface.
      Kinematic factor for the calibration elements
    • Data Analysis
      Energy-depth conversion
      Incident particle
      final energy
    • Data Analysis
      Separation of dechanneling fraction
      To analyze displacement profiles quantitavely, the backscattering of channeled particles from displaced atoms needs to be separated from the backscattering of dechanned particles from lattice atoms. There are 3 approaches for this separations:
      Line approximation
      Iterative procedure
      Double- iteration procedure
    • Data Analysis
      Separation of dechanneling fraction
      Line approximation
      The easiest way to separate the dechanneling component. The line connects 2 points corresponding to
      A minimum yield after the surface damage peak
      A minimum yield after the damage peak
    • Data Analysis
      Separation of dechanneling fraction
      2. Iterative procedure
      In a standard iterative procedure, the substrate is divided into multiple layers. The analysis starts from the surface layer by assuming χhD(x)=0 in the following Equation:
      Density of displaced atoms
      Total atomic density
      In the first layer, nD is calculated fist. Then, the amount of dechanneling in the next layer is calculated by the following equation and then used in the above equation to obtain the number of defects in the second layer.
      Aligned yield at depth x for a virgin crystal
    • 2. Iterative procedure
      The disorder profiles of H ion implanted Si obtained after different times of iterative processes. The profile from the line approximation is also compared.
    • Data Analysis
      2. Iterative procedure
      Separation of dechanneling fraction
      This iterative procedure requires that the dechanneling cross section, σD, must first be known.
      The calculation did not consider the lattice distortions around defects. The strain relaxation around defects can enhance dechanneling significantly.
    • 3. Double-iteration procedure
      This method requires no knowledge about σD. The double-iteration approach requires selecting a point at depth x1 giving nD(x1)=0. x1 can be any point beyond which direct backscattering centers diminish to zero.
    • For any point x<x1
      Where m represents the number of cycles of the iterative calculation.
    • Data Analysis
      3. Double-iteration procedure
      This result is used, in turn, to calculate the additional amount of dechanneling in the next layer . The procedure is continued until the defect density drops to zero at a depth beyond the disordered region.
    • The channeling RBS spectra in comparison with the calculated dechanneling component after different times of iterative processes.
    • Analytical versus Monte Carlo analysis
      Angular scan
      Statistical equilibrium approximation for the ion flux
      Analytical calculation with multistring Moliere-type potentials to calculate equipotential contours and ion fluxes
    • Numerical method to calculate angular scans
      The angular dependence of backscattering yields can be calculated numerically by using continuum approximation:
      The transverse potential as a function of location across the channel
      The probability distribution of the transverse energy of the ions
      The ion flux across the channel
      Angular distribution of the backscattering yields
    • Transverse potential
      The axial channel can be divided into tiny square regions of area ΔA. The potential for each square is calculated by adding potential contributions from multi-atom rows. Considering periodic boundary conditions, an appropriate unit cell should be selected.
    • A group of 12-atom rows with a square unit cell is appropriate for the calculations associated with displacements close to the channel center.
      A group of 9-atom rows with a circular unit cell is appropriate for the problems associated with the small displacements from the atom row.
    • The potential for each small area ΔA is calculated and listed in a table in order from the smallest to largest.
    • Probability distribution of transverse energy
      For an ion hitting an area with a potential of ui, the transverse energy is given by E┴,i=Eψ2+ui. Therefore, the possibility of obtaining the value E┴,i is given by:
    • Ion flux distribution
      The allowed area for channeled ions with transverse energy E┴,i, is the area having a potential equal to or less than E┴,i.
      Accessible area
    • Ions are allowed to be uniformly distributed over the accessible area, the ion density at rh(the position corresponding to potential uh) is given by:
      Ion flux at rh is contributed by only those ions with E┴≥uh
    • Under the condition that:
      Ion flux is given by:
    • Angular distribution
      When ions are incident with an angle of ψ, the yield of close encounters is given by:
      Displacement probability
      Selecting ψ=0°,0.1°,…., the angular distribution is obtained by repeating the above calculation procedure. The angular distribution can be normalized by the yield with ψ ≈ 5ψ1.
    • Surface studies
      Basic consideration
      In a good channeling direction, a clearly resolvable surface peak in the backscattering yield can be observed because the ion beam is scattered from the exposed surface atoms with the same intensity as from a random array of atoms, that is, the surface atoms are not shadowed.
      Shadow cone
    • Surface studies
      Radius cone
      The shadow cone radius for a Au layer on Ag:
      For a 1 MeV He beam on Au, Z1=2, Z2=79, d<110>=0.288 nm, e2=1.44×10-13 cm, E=1 MeV
      Thus, Rc=0.0162 nm, which can be compared with u2=0.012 nm.
    • Lattice sites of solute atoms
      One of the most frequently used applications of channeling has been to determine lattice sites of impurity atoms in crystals.
      Impurity atoms that project into axial or planar channels are “seen” by the ion beam, causing an increased backscattering yield from the solute atoms, χs, as compared to that from the host atoms, χh.
    • Lattice sites of solute atoms
      Χs<100> >1
      Χs<110> ≈1
      Χs<111> =Χh<111>
    • Lattice sites of solute atoms
      Angular scans of backscattering yields
    • Unchanneled ion
      The numbers on the curves are the displacement value in angstroms.
      Channeled ion
      1 MeV He+ in a <110> channel of Al at 30 K at the depth of 100 nm (beam divergence=0.048°)
      Calculated yields in a <110>axial channel for atoms displaced along the <100> direction as a function of the incident angle ψ, normalized to the Linhard characteristic angle ψ1.
    • Solute atoms associated with point defects
      The Al- 0.02 at% In sample was irradiated with 1 MeV He + at 35 K and then annealed for 600 s at 220 K before each of the angular scans. The yields measured at 35 K for a depth interval of 50-280 nm from the surface.
      <100> angular scans for irradiated Al-0.02 at.% In
    • Surface studies
      Channeling can be used to measure lateral reconstruction, surface relaxation, vibration amplitudes, and premelting of atoms in the surface and near surface planes.
      Schematic illustration of measurements of channeling surface peaks to study displacements of surface atoms
    • Surface studies
      Channeling can also be used to measure:
      Surface relaxation
      Surface impurities
      Interface structures
    • Surface relaxation
      An illustration of the method to study surface relaxation experimentally, based on channeling and blocking.
      The scattering plane coincides with the crystallographic plane. A displacement of the first layer results in different angular position of the blocking cone for surface and bulk atoms.
    • An energy scan of backscattered ions detected at an angle θ by means of an electrostatic energy analyzer.
    • Angular scans of backscattered intensities from surface and bulk atoms. The displacement caused by the relaxation effect causes a shift, Δθ, in the surface blocking minimum.
    • Blocking minimum for 0.1 MeV protons scattered from bulk and surface Ni atoms for a clean(110) surface and for an oxygen coverage of one-third of a monolayer. The Ni yield was normalized by the Rutherford cross section, σR.
    • Interface structures
      Measured densities of Si and O atoms for a Si(110) surface that was covered by oxides of varying thickness. The straight line corresponds to stoichiometric SiO2 plus 8.6×1015 atoms cm-2of excess Si. A contribution of 6.4×1015 unshadowed Si atoms per cm2 from the Si substrate is indicated.
    • Epitaxial layer and strain
      The quality of epitaxial layers and the strain in such layer or in multilayers can be determined by channeling measurement at normal incidence or at oblique angles.
      In general, good epitaxy can be achieved only when the lattice parameters of the substrate and overlayer are almost the same. For a small lattice-parameter mismatch, perfect epitaxy can be accommodated by vertical elastic strain in the overlayer. When the stress in the strained epilayer exceeds the elastic modulus, the strain is accommodated by the reaction of “misfit” dislocation.
    • The channeling directions [100] and [110] are shown. The displacements, xn, of the Ge atoms from the substitutional sites are indicated.
      Schematic diagram of the structure of a strained epitaxial film of Ge capped with the substrate material, Si.
    • Channeling angular scan of Ge/Si structure, using 1.8 MeV He+
      Scan through the [1-10] axial direction in the (100) plane for an epitaxial structure consisting of Si(100)/Ge[6 monolayer]Si(20 nm)
    • Scan through the [110] axial direction in the (100) plane for an epitaxial structure consisting of Si(100)/Ge[6 monolayer]Si(20 nm)
    • Channeling angular scan of Ge/Si structure, using 1.8 MeV He+
      Scan through the [100](crystal normal) channeling direction in the (100) plane for an epitaxial structure consisting of Si(100)/Ge[6 monolayer]Si(20 nm)
    • Scan through the [110] channeling direction in a sample of Si(100)/Si0.99Ge0.01(100 monolayer) /Si(13.6nm) Si(100)/Ge[6 monolayer]Si(20 nm)
    • Experimental methods
      Channeling equipment
      A beam divergence of 0.1° or less
      Two-axis goniometer
      Rotation about the crystal normal
      0.3-2.5 MeV light ion
      from electrostatic accelerator
      Rotation about the vertical axis
    • Comparison of RBS, PIXE, and NRA methods
      For lattice site measurements, careful attention must be paid to the cross section for a particular reaction and the depth information of the element (that is suppose to be analyzed).
    • choice of ion species and energy
      For most channeling applications, the use of 4He+ beams (at 1-2 MeV) is suitable because of the moderate mass resolution, beam damage, channel width, and depth resolution.
      If one desires to probe more deeply into the sample, 1H+ beams are suitable for probing the distribution of deep damage, such as that caused by high –energy implantations to ~1μm.
    • choice of ion species and energy
      Use of heavier ions such as C increases the mass resolution and the sensitivity for detection of small quantities of heavy elements in a light-element host material.
      However, the depth resolution is not improved when surface-barrier Si detectors are used because of the decrease in detector resolution. In addition, the damage introduced by heavier ions is much greater .
    • choice of ion species and energy
      The choice of ion energy is determined by consideration of cross section and mass resolution. The cross section for backscattering generally decreases with increasing energy. However at higher energies (e.g., above 2 MeV 4He+ on light element such as O, N, and C), the cross section for backscattering can increase by a factor of up to 10 because of non-Rutherford behavior. In addition, several resonances in (α,α) reaction occur at higher He energies.
    • Ion damage
      The damage caused by energetic ions is mainly due to elastic collisions with target atoms. Damage from the analyzing beam can interfere with the results of channeling analysis, especially for studies of low levels of implantation damage or lattice location studies of low concentrations of impurities.
      Methods for minimizing damage:
      • Increasing the detector solid angle
      • Analyzing only near channeling direction
      • Moving the analyzing spot frequently
      • Using high-energy and low-mass ions
    • Ion damage
      The simplest ways to increase detector solid angle are to use larger detectors and to move the detector closer to the target.
      Disadvantages of these methods:
      Loss of depth resolution
      Loss of mass resolution
      Methods of reducing that loss:
      • Using multiple detectors or specially constructed detectors
      • Using coincident techniques (suitable only for low-mass elements and uniform thin foil target)
      At coincident technique energies of the scattered ion and the recoiled target atom are measured in coincidence
    • Obtaining channeling spectra
      Stereographic projection
      {100} poles of a cubic crystal
      The stereographic projection provides an accurate representation of the angles between the planes and axes of a crystal.
    • Obtaining channeling spectra
      Stereographic projection
    • A beam divergence of 0.1° or less
      Two-axis goniometer
      Rotation about the crystal normal
      0.3-2.5 MeV light ion
      from electrostatic accelerator
      Rotation about the vertical axis
    • random
      Scattering yield (counts)
      Alignment of a Si (110) crystal for channeling
      RBS spectra for a randomly oriented crystal
      and aligned crystal
    • φ
      Yield (counts)×103
      Alignment of a Si (110) crystal for channeling
      RBS yield as a function of azimuthal angle φ
      for a tilt angle of 6°
    • Yield (counts)×103
      Polar plot of the planar minima from panel of yield- azimuth angle
    • Precise determination of the value of θ for
      <110> alignment, with φ set at 60°
    • Theta scan of my sample in AAMURI
    • Thank you
      Tomb of Diako (the king of Madia) about 1000 B.C