Fiber Textures application to thin film textures by pzk16293

VIEWS: 5 PAGES: 52

									1




        Fiber Textures: application to
              thin film textures

                 27-750, Spring 2007
                A. D. (Tony) Rollett,
               A. Gungor & K. Barmak
    Carnegie
     Mellon        Acknowledgement: the data for these examples
    MRSEC          were provided by Ali Gungor; extensive
                   discussions with Ali and his advisor, Prof. K.
                   Barmak are gratefully acknowledged.
2



               Example 1: Interconnect
                     Lifetimes
      • Thin (1 µm or less) metallic lines used in
        microcircuitry to connect one part of a
        circuit with another.
      • Current densities (~106 A.cm-2) are very
        high so that electromigration produces
        significant mass transport.
      • Failure by void accumulation often
        associated with grain boundaries
    Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
3




                                                                      Interconnects provide a
                                       M2
                                                                      pathway to communicate
     Inter-Level-Dielectric
                                                                      binary signals from one
     ILD                              via

     ILD                      liner
                                             M1
                                                               SiNx
                                                                      device or circuit to another.
                                                       SiO2
                          W
                                                       SiO2


           Silicide
                                                Si substrate

                                            Silicide
                                                                      Issues:
                                                                            - Performance
           A MOS transistor                                                 - Reliability
      (Harper and Rodbell, 1997)



    Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
4


     Reliability: Electromigration Resistance
                                                                      Promote electromigration
      extrusion            void                  e-
                                                                      resistance via microstructure
                                                                      control:
                                                                          • Strong texture
                                                                          • Large grain size
            vacancy diffusion                 mass diffusion             (Vaidya and Sinha, 1981)

            (111) Al-Cu


                                  Cu



          1 um

         < 1995           2001                    70 nm ~ 500 atoms



                  Sub-250 nm dimensions
                    Finite number of atoms
                    Proximity of interfaces
                    Limited space for microstructure development

    Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
5



     Grain Orientation and Electromigration Voids
       Special  transport properties on certain
        lattice planes cause void faceting and
        spreading
       Voids along interconnect direction vs. fatal
        voids across the linewidth
                                                           Slide courtesy of
                                  Top view                 X. Chu and C.L.
                                                           Bauer, 1999.
                                       (111)

                           _                                   _
                        (111)          e-                   (111)


    Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
   6



                     Al Interconnect Lifetime
    Stronger <111> fiber texture gives longer lifetime,
    i.e. more electromigration resistance



H.T. Jeong et al.




       Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
7


                              References
      • H.T. Jeong et al., “A role of texture and orientation
        clustering on electromigration failure of aluminum
        interconnects,” ICOTOM-12, Montreal, Canada, p 1369
        (1999).
      • D.B. Knorr, D.P. Tracy and K.P. Rodbell, “Correlation of
        texture with electromigration behavior in Al
        metallization”, Appl. Phys. Lett., 59, 3241 (1991).
      • D.B. Knorr, K.P. Rodbell, “The role of texture in the
        electromigration behavior of pure Al lines,” J. Appl.
        Phys., 79, 2409 (1996).
      • A. Gungor, K. Barmak, A.D. Rollett, C. Cabral Jr. and
        J.M. E. Harper, “Texture and resistivity of dilute binary
        Cu(Al), Cu(In), Cu(Ti), Cu(Nb), Cu(Ir) and Cu(W) alloy
        thin films," J. Vac. Sci. Technology, B 20(6), p 2314-
        2319 (Nov/Dec 2002).
                                                               -> YBCO textures

    Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
8




                      Lecture Objectives
      • Give examples of experimental textures of thin copper
        films; illustrate the OD representation for a simple case.
      • Explain (some aspects of) a fiber texture .
      • Show how to calculate volume fractions associated with
        each fiber component from inverse pole figures (from
        ODF).
      • Explain use of high resolution pole plots, and analysis of
        results.
      • Give examples of the relevance and importance of textures
        in thin films, such as metallic interconnects, high
        temperature superconductors and magnetic thin films.

    Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
9




                          Fiber Textures
      • Common definition of a fiber texture:
        circular symmetry about some sample axis.
      • Better definition: there exists an axis of
        infinite cyclic symmetry, C, (cylindrical
        symmetry) in either sample coordinates or
        in crystal coordinates.
      • Example: fiber texture in two different thin
        copper films: strong <111> and mixed
        <111> and <100>.
    Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
10



        Source: research by Ali Gungor,
                     CMU
               C
                                                          film




                                                         substrate
2 copper thin films, vapor deposited:
e1992: mixed <100> & <111>; e1997: strong <111>
     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
11


                    Method 1:
         Experimental Pole Figures: e1992




     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
12


             Recalculated Pole Figures:
                       e1992




     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
13


               COD: e1992: polar plots:
               Note rings in each section




     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
14


               SOD: e1992: polar plots:
               note similarity of sections




     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
15


        Crystallite
       Orientation
       Distribution:
          e1992
 1. Lines on constant Q
 correspond to rings in
 pole figure
 2. Maxima along top
 edge = <100>;
 <111> maxima
 on Q= 55 (f = 45)
     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
16
        Sample
      Orientation
      Distribution:
         e1992
 1. Self-similar sections
 indicate fiber texture:
 lack of variation with
 first angle (y).
 2. Maxima along top
 edge -> <100>;
 <111> maxima
 on Q= 55, f = 45
     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
17




         Experimental Pole Figures: e1997




     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
18

             Recalculated Pole Figures:
                       e1997




     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
19

            COD: e1997: polar plots:
           Note rings in 40, 50° sections




     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
20

               SOD: e1997: polar plots:
               note similarity of sections




     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
21

         Crystal
       Orientation
       Distribution:
          e1997
     1. Lines on constant Q
     correspond to rings in
     pole figure
     2. <111> maximum
     on Q= 55 (f = 45)

     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
22

           Sample
         Orientation
         Distribution:
            e1997
      1. Self-similar sections
      indicate fiber texture:
      lack of variation with
      first angle (y).
      2. Maxima on <111>
      on Q= 55, f = 45,
      only!
     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
23




                 Fiber Locations in SOD
                                                             [Jae-Hyung Cho, 2002]


        <100>                                                       <110>
         fiber                                                       fiber


                                                                   <100>,
                                                                   <111>
        <111>                                                        and
         fiber                                                     <110>
                                                                    fibers

     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
24




            Inverse Pole Figures: e1997




      Slight in-plane anisotropy revealed by the
      inverse pole figures.
      Very small fraction of non-<111> fiber.
     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
25




             Inverse Pole figures: e1992

                        <111>                                   f
        <11n>




      <001>           <110>
                                                           F
             Normal           Transverse        Rolling
            Direction          Direction       Direction
               ND                 TD              RD
     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
26


                     Method 1:
              Volume fractions from IPF
       • Volume fractions can be calculated from an inverse pole
         figure (IPF).
       • Step 1: obtain IPF for the sample axis parallel to the C
         symmetry axis.
       • Normalize the intensity, I, according to
                                1 = S I(F,f) sin(F) dFdf 
       • Partition the IPF according to components of interest.
       • Integrate intensities over each component area (i.e. choose
         the range of F and f) and calculate volume fractions:

                                Vi = Si I(F,f) sin(F) dFdf 

     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
27




                 Method 2: Pole plots
     • If a perfect fiber exists (C, aligned with the
       film plane normal) then it is enough to scan
       over the tilt angle only and make a pole
       plot.
     • High resolution is then feasible, compared
       to standard 5°x5° pole figures, e.g 0.1°.
     • High resolution inverse PF preferable but
       not measurable.
 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
28

Intensity
along a                                 <100>                  <111>
                                  500
line from
the center                        400
of the {001}
pole                              300
                      Intensity



figure
to the                            200

edge
(any azimuth)                     100


e1992: <100> & <111>                0
                                        0       15   30   45       60   75    90
e1997: strong 111
                                                      Tilt (°)
     Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
29




           High Resolution Pole plots




e1992: mixture of <100>                        e1997: pure
and <111>                                      <111>; very
                                               small fractions
     ∆tilt = 0.1°                              other?
 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
30




                     Volume fractions
     • Pole plots (1D variation of intensity):
       If regions in the plot can be identified as
       being uniquely associated with a particular
       volume fraction, then an integration can be
       performed to find an area under the curve.
     • The volume fraction is then the sum of the
       associated areas divided by the total area.
     • Else, deconvolution required.
 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
31




                  Example for thin Cu films
                   15




                                        Strong <111>
                  10                    Mixed <111> & <100>
      Intensity




                                          <100>
                   5                                <111>



                   0
                       0   20      40         60       80       100
                                   Tilt Angle (°)
 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
32


        Log scale for Intensity: e1997
                                100

NB:                                             Strong <111>
Intensities                      10
                                                Mixed <111> & <100>

not
normalized
                    Intensity


                                  1



                                 0.1



                                0.01
                                       0   20    40         60        80   100
                                                 Tilt Angle (°)
 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
33



                Area under the Curve
     • Tilt Angle equivalent to second Euler
     angle, q  F
     • Requirement: 1 = S I(q) sin(q) dq;
                      q measured in radians.
     • Intensity as supplied not normalized.
     • Problem: data only available to 85°:
         therefore correct for finite range.
     • Defocusing neglected.

 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
34



            Extract Random Fraction         e1992.111PF.data
                           2
                                         Fiber components
Mixed <100>
            1.5
and <111>,
e1992
              Intensity




                           1
                                    Random Equivalent


                          0.5



                                          Random Component = 18%
                           0
                                0   20         40             60   80
                                             Tilt Angle (°)
 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
35
                                         Intensity
                                         Normalized + 2.5
     Normalized
            100
                                         re-Normalized Intensity
                                         Normalized Intensity

                                         random
                                                      <100> fiber

                          10
             Intensity




                           1
                                                  ?

Random                    0.1
component
negligible
~ 4%                     0.01
                                0   15    30          45        60   75   90
          e1997.111PF.data                     Tilt Angle (°)
 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
36




                        Deconvolution
     • Method is based on identifying each peak in
       the pole plot, fitting a Gaussian to it, and
       then checking the sum of the individual
       components for agreement with the
       experimental data.
     • Areas under each peak are calculated.
     • Corrections must be made for multiplicities.

 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
37


                                   {111} Pole Plot
                             140
                                       [111] Cu(Ir) - 400C-5hrs and Gauss Fit of Data

                             120
                                                             <111>
                             100                      <100>
                 Intensity




                                                 <110>
                             80
                                                                               A3
                             60


                             40
                                       A1                            A2
                             20


                              0
                                   0            20           40
                                                                     q    60            80


         Ai = Si I(q)sinq dq
                                                              Tilt




 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
38

     {111} Pole Plot: Comparison of
     Experiment with Calculation
                         140
                                              Cu(Ir) - 400C-5hrs

                         120
                                                  Convolution
                                                  Raw Data <111>
                         100
             Intensity




                         80


                         60


                         40


                         20


                          0
                               0   10   20   30    40      50      60   70   80
                                                    Tilt
 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
39


 {100} Pole figure: pole multiplicity:
       6 poles for each grain
        <100> fiber component               <111> fiber component
                       North Pole




                       South Pole
        4 poles on the equator;             3 poles on each of two rings,
        1 pole at NP; 1 at SP               at ~55° from NP & SP
 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
40

                 {100} Pole figure:
               Pole Figure Projection
     The number                               (010)
     of poles       (-100)
     present in a
     pole figure         (001)              (100)
     is
     proportional
     to the                                                    (001)
     number of                                    (100)
     grains          (0-10)         (010)

     <100> oriented grain: 1 pole in the center, 4 on the equator
     <111> oriented grain: 3 poles on the 55° ring.
 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
41


 {111} Pole figure: pole multiplicity:
       8 poles for each grain
     <100> fiber component                  <111> fiber component




                                             1 pole at NP; 1 at SP
     4 poles on each of two rings,           3 poles on each of two rings,
     at ~55° from NP & SP                    at ~70° from NP & SP
 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
42

                 {111} Pole figure:
               Pole Figure Projection

                           (-111) (111)
                       (-111)        (1-11)
                               (001)
                               (111)
                         (-1-11)
                                  (1-11)
                                   (-1-11)

     <100> oriented grain: 4 poles on the 55° ring
     <111> oriented grain: 1 pole at the center, 3 poles on the 70° ring.
 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
43



                    {111} Pole figure:
                     Pole Plot Areas
     • After integrating the area under each of the peaks
       (see slide 35), the multiplicity of each ring must be
       accounted for.
     • Therefore, for the <111> oriented material, we
       have 3A1 = A3;
       for a volume fraction v100 of <100> oriented
       material compared to a volume fraction v111 of
       <111> fiber,
           3A2 / 4A3 = v100 / v111 and,
            A2 / {A1+A3} = v100 / v111

 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
44




           Intensities, densities in PFs
     •   Volume fraction = number of grains  total grains.
     •   Number of poles = grains * multiplicity
     •   Multiplicity for {100} = 6; for {111} = 8.
     •   Intensity = number of poles  area
     •   For (unit radius) azimuth, f, and declination (from
         NP), q, area, dA = sinq dq df.



 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
45




      High
  Temperature
Superconductors
  : an example

     Theoretical
     pole figures
     for c & a 
46


            YBCO (123) on various
                 substrates
     Various epitaxial
     relationships
     apparent from
     the pole figures
47



     Scan with ∆a = 0.5°, ∆b = 0.2°
                   Azimuth, b




 Tilt
 a
 48

           Dependence of film orientation
             on deposition temperature

Ref: Heidelbach, F., H.-R. Wenk,
R. E. Muenchausen, R. E. Foltyn,
N. Nogar and A. D. Rollett (1996),
Textures of laser ablated thin
films of YBa2Cu3O7-d as a
function of deposition temperature.
J. Mater. Res., 7, 549-557.




        Impact: superconduction occurs in the c-plane;
        therefore c epitaxy is highly advantageous to
        the electrical properties of the film.
49


           Summary: Fiber Textures
     • Extraction of volume fractions possible provided
       that fiber texture established.
     • Fractions from IPF simple but resolution limited
       by resolution of OD.
     • Pole plot shows entire texture.
     • Random fraction can always be extracted.
     • Specific fiber components may require
       deconvolution when the peaks overlap.
     • Calculation of volume fraction from pole
       figures/plots assumes that all corrections have
       been correctly applied (background subtraction,
       defocussing, absorption).
50




               Summary: other issues
     • If epitaxy of any kind occurs between a film and its
       substrate, the (inevitable) difference in lattice paramter(s)
       will lead to residual stresses. Differences in thermal
       expansion will reinforce this.
     • Residual stresses broaden diffraction peaks and may distort
       the unit cell (and lower the crystal symmetry), particularly
       if a high degree of epitaxy exists.
     • Mosaic spread, or dispersion in orientation is always of
       interest. In epitaxial films, one may often assume a
       Gaussian distribution about an ideal component and
       measure the standard deviation or full-width-half-
       maximum (FWHM).
51
      Example 1: calculate intensities
     for a <100> fiber in a {100} pole
                  figure
     • Choose a 5°x5° grid for the pole figure.
     • Perfect <100> fiber with all orientations uniformly
       distributed (top hat function) within 5° of the axis.
     • 1 pole at NP, 4 poles at equator.
     • Area of 5° radius of NP
       = 2π*[cos 0°- cos 5°] = 0.0038053.
     • Area within 5° of equator
       = 2π*[cos 85°- cos 95°] = 0.174311.
     • {intensity at NP} = (1/4)*(0.1743/0.003805) = 11.5 *
       {intensity at equator}
52



Example 2: Equal volume fractions of <100>
   & <111> fibers in a {100} pole figure
     • Choose a 5°x5° grid for the pole figure.
     • Perfect <100> & <111> fibers with all orientations
       uniformly distributed (top hat function) within 5° of the
       axis, and equal volume fractions.
     • One pole from <100> at NP, 3 poles from <111> at 55°.
     • Area of 5° radius of NP
       = 2π*[cos 0°- cos 5°] = 0.0038053.
     • Area within 5° of ring at 55°
       = 2π*[cos 50°- cos 60°] = 0.14279.
     • {intensity at NP, <100> fiber} = (1/3)*(0.14279/0.003805)
       = 12.5 * {intensity at 55°, <111> fiber}

								
To top