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Fiber Textures: application to thin film textures. 27-750, Spring 2007 A. D. (Tony) Rollett, A. Gungor & K. Barmak. Acknowledgement : the data for these examples were provided by Ali Gungor; extensive discussions with Ali and his advisor, Prof. K. Barmak are gratefully acknowledged.

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fiber textures application to thin film textures

Fiber Textures: application to thin film textures

27-750, Spring 2007

A. D. (Tony) Rollett, A. Gungor & K. Barmak

Acknowledgement: the data for these examples were provided by Ali Gungor; extensive discussions with Ali and his advisor, Prof. K. Barmak are gratefully acknowledged.

example 1 interconnect lifetimes
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

slide3

Interconnects provide a

pathway to communicate

binary signals from one

device or circuit to another.

Issues:

- Performance

- Reliability

A MOS transistor

(Harper and Rodbell, 1997)

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

slide4

e-

extrusion

void

vacancy diffusion mass diffusion

Reliability: Electromigration Resistance

  • Promote electromigration
  • resistance via microstructure
  • control:
    • Strong texture
    • Large grain size
    • (Vaidya and Sinha, 1981)

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

slide5

Top view

(111)

_

_

-

(111)

(111)

e

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 X. Chu and C.L. Bauer, 1999.

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

al interconnect lifetime
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

references
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

lecture objectives
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

fiber textures
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

source research by ali gungor cmu
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

method 1 experimental pole figures e1992
Method 1:Experimental Pole Figures: e1992

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

recalculated pole figures e1992
Recalculated Pole Figures: e1992

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

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

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

sod e1992 polar plots note similarity of sections
SOD: e1992: polar plots:note similarity of sections

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

crystallite orientation distribution e1992
Crystallite Orientation Distribution:e1992

1. Lines on constant Qcorrespond to rings inpole figure

2. Maxima along top edge = <100>;

<111> maxima on Q= 55° (f = 45°)

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

sample orientation distribution e1992
Sample Orientation Distribution: e1992

1. Self-similar sections

indicate fiber texture:lack of variation withfirst angle (y).

2. Maxima along top edge -> <100>;

<111> maxima on Q= 55°, f = 45°

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

experimental pole figures e1997
Experimental Pole Figures: e1997

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

recalculated pole figures e1997
Recalculated Pole Figures: e1997

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

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

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

sod e1997 polar plots note similarity of sections
SOD: e1997: polar plots:note similarity of sections

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

crystal orientation distribution e1997
Crystal Orientation Distribution: e1997

1. Lines on constant Qcorrespond to rings inpole figure

2. <111> maximumon Q= 55° (f = 45°)

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

sample orientation distribution e1997
Sample Orientation Distribution: e1997

1. Self-similar sections

indicate fiber texture:lack of variation withfirst angle (y).

2. Maxima on <111> on Q= 55°, f = 45°,only!

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

fiber locations in sod
Fiber Locations in SOD

[Jae-Hyung Cho, 2002]

<100>fiber

<110>fiber

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

<111>fiber

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

inverse pole figures e1997
Inverse Pole Figures: e1997

Slight in-plane anisotropy revealed by theinverse pole figures.Very small fraction of non-<111> fiber.

Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

inverse pole figures e1992
Inverse Pole figures: e1992



<111>

<11n>

<001>

<110>

F

TransverseDirectionTD

NormalDirectionND

RollingDirectionRD

Electromigration Weak StrongIPF VolumeFraction PolePlot Deconvolution

method 1 volume fractions from ipf
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 = SI() sin() dd
  • Partition the IPF according to components of interest.
  • Integrate intensities over each component area (i.e. choose the range of  and ) and calculate volume fractions:Vi = SiI()sin() dd

Electromigration Weak StrongIPF VolumeFraction PolePlot Deconvolution

method 2 pole plots
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 StrongIPFVolumeFraction PolePlot Deconvolution

slide28

Intensityalong aline fromthe centerof the {001}polefigureto theedge(any azimuth)

e1992: <100> & <111>

e1997: strong 111

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

high resolution pole plots
High Resolution Pole plots

e1997: pure <111>; very small fractions other?

e1992: mixture of <100>and <111>

∆tilt = 0.1°

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

volume fractions
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 StrongIPFVolumeFraction PolePlot Deconvolution

example for thin cu films
Example for thin Cu films

<100>

<111>

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

log scale for intensity e1997
Log scale for Intensity: e1997

NB: Intensities not normalized

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

area under the curve
Area under the Curve

• Tilt Angle equivalent to second Eulerangle, q F• Requirement: 1 = S I(q)sin(q) dq; qmeasured in radians.

• Intensity as supplied not normalized.

• Problem: data only available to 85°: therefore correct for finite range.• Defocusing neglected.

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

extract random fraction
Extract Random Fraction

Mixed <100>and <111>,e1992

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

normalized
Normalized

Randomcomponentnegligible~ 4%

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

deconvolution
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 StrongIPFVolumeFraction PolePlot Deconvolution

slide37

{111} Pole Plot

<111>

<100>

<110>

A3

A2

A1

q

Ai = Si I(qsinq dq

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

slide38

{111} Pole Plot: Comparison of Experiment with Calculation

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

100 pole figure pole multiplicity 6 poles for each grain
{100} Pole figure: pole multiplicity:6 poles for each grain

<100> fiber component

<111> fiber component

North Pole

South Pole

3 poles on each of two rings, at ~55° from NP & SP

4 poles on the equator;1 pole at NP; 1 at SP

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

100 pole figure pole figure projection
{100} Pole figure: Pole Figure Projection

(010)

The number of poles present in a pole figure is proportional to the number of grains

(-100)

(100)

(001)

(001)

(100)

(010)

(0-10)

<100> oriented grain: 1 pole in the center, 4 on the equator

<111> oriented grain: 3 poles on the 55° ring.

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

111 pole figure pole multiplicity 8 poles for each grain
{111} Pole figure: pole multiplicity:8 poles for each grain

<100> fiber component

<111> fiber component

1 pole at NP; 1 at SP3 poles on each of two rings, at ~70° from NP & SP

4 poles on each of two rings, at ~55° from NP & SP

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

111 pole figure pole figure projection
{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 StrongIPFVolumeFraction PolePlot Deconvolution

111 pole figure pole plot areas
{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 v100of <100> oriented material compared to a volume fraction v111 of <111> fiber,3A2 / 4A3 = v100 /v111and,A2 / {A1+A3} = v100 /v111

Electromigration Weak StrongIPFVolumeFraction PolePlot Deconvolution

intensities densities in pfs
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 StrongIPFVolumeFraction PolePlot Deconvolution

high temperature superconductors an example
High Temperature Superconductors: an example

Theoreticalpole figuresfor c & a 

ybco 123 on various substrates
YBCO (123) on various substrates

Various epitaxialrelationshipsapparent fromthe pole figures

dependence of film orientation on deposition temperature
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 tothe electrical properties of the film.

summary fiber textures
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).
summary other issues
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).
example 1 calculate intensities for a 100 fiber in a 100 pole figure
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}
example 2 equal volume fractions of 100 111 fibers in a 100 pole figure
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}