View
215
Download
1
Embed Size (px)
Citation preview
1
Fiber Textures: application to Fiber Textures: application to thin film texturesthin film textures
27-750, Spring 2008
A. D. (Tony) Rollett
CarnegieMellon
MRSEC
Acknowledgement: the data for these examples were provided by Ali Gungor; extensive discussions with Ali and his advisor, Prof. K. Barmak are gratefully acknowledged.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
2
Lecture ObjectivesLecture 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.• Discuss the phenomenon of axiotaxy - orientation relationships
based on plane-edge matching instead of the usual surface matching.
• 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
3
SummarySummary• Thin films often exhibit a surprising degree of texture, even when deposited on an
amorphous substrate.• The texture observed is, in general, the result of growth competition between
different crystallographic directions. In fcc metals, e.g., the 111 direction typically grows fastest, leading to a preference for this axis to be perpendicular to the film plane.
• Such a texture is known as a fiber texture because only one axis is preferentially aligned whereas the other two are uniformly distributed (“random”).
• Although vapor-deposited films are the most studied, similar considerations apply to electrodeposited films also, which are important in, e.g., copper interconnects.
• Especially in electrodeposition, many different fiber textures can be obtained as a function of deposition conditions (current density, chemistry of electrolyte etc., or substrate temperature, deposition rate).
• Even the crystal structure can vary from the equilibrium one for the conditions. Tantalum is known is known to deposit in a tetragonal form (with a strong 001 fiber) instead of BCC, for example.
• Thin film texture should be quantified with Orientation Distributions and volume fractions, not by deconvolution of peaks in pole figures, or pole plots. The latter approach may look straightforward (and similar to other types of analysis of x-ray data) but has many pitfalls.
4
Example 1: Example 1: Interconnect LifetimesInterconnect 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
5
SiO2W
linerSiNx
ILD via
Inter-Level-Dielectric
M2
Si substrate
SiO2
M1ILD
Silicide Silicide
A MOS transistor (Harper and Rodbell, 1997)
Interconnects provide apathway to communicatebinary signals from onedevice or circuit to another.
Issues:- Performance- Reliability
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
6
Promote electromigrationresistance via microstructurecontrol:
• Strong texture• Large grain size(Vaidya and Sinha, 1981)
Reliability: Electromigration Resistance
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
7
Special transport properties on certain lattice planes cause void faceting and spreading
Voids along interconnect direction vs. fatal voids across the linewidth
Grain Orientation and Electromigration VoidsGrain Orientation and Electromigration Voids
(111)
Top view
(111)_
(111)_
e-
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
Slide courtesy of X. Chu and C.L. Bauer, 1999.
8
Aluminum Interconnect LifetimeAluminum Interconnect Lifetime
H.T. Jeong et al.
Stronger <111> fiber texture gives longer lifetime, i.e. more electromigration resistance
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
9
ReferencesReferences• 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).
• Barmak K, Gungor A, Rollett AD, Cabral C, Harper JME. 2003. Texture of Cu and dilute binary Cu-alloy films: impact of annealing and solute content. Materials Science In Semiconductor Processing 6:175-84.
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
-> YBCO textures
10
Fiber TexturesFiber 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
11
Research on Cu thin films by Research on Cu thin films by Ali Gungor, CMUAli Gungor, CMU
substratesubstrate
filmfilm
C
2 copper thin films, vapor deposited:e1992: mixed <100> & <111>; e1997: strong <111>
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
See, e.g.: Gungor A, Barmak K, Rollett AD, Cabral C, Harper JME. Journal Of Vacuum Science & Technology B 2002;20:2314.
{001} PF for strong <111> fiber
12
Epitaxial Thin Film TextureEpitaxial Thin Film TextureFrom work by Detavernier (2003): if the unit cell of the film material is a sufficiently close match (within a few %) the two crystal structures often align.
13
Axiotaxy - NiSi films on SiAxiotaxy - NiSi films on Si
Spherical projection of {103}:
Detavernier C, Ozcan AS, Jordan-Sweet J, Stach EA, Tersoff J, et al. 2003. An off-normal fibre-like texture in thin films on single-crystal substrates. Nature 426: 641 - 5.
14
Plane-edge matching Plane-edge matching Axiotaxy Axiotaxy
C. Detavernier
15
Possible Orientation RelationshipsPossible Orientation Relationships
16
Fiber Textures: Pole Figure Analysis:Fiber Textures: Pole Figure Analysis:Example of Cu Thin Film: Example of Cu Thin Film: e1992e1992
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
17
Recalculated Pole Figures: Recalculated Pole Figures: e1992e1992
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
18
COD: COD: e1992e1992: polar plots:: polar plots:Note rings in each sectionNote rings in each section
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
19
SOD: SOD: e1992e1992: polar plots:: polar plots:note similarity of sectionsnote similarity of sections
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
20
Crystallite Crystallite Orientation Orientation Distribution Distribution
(COD):(COD):e1992e19921. Lines on constant correspond to rings inpole figure2. Maxima along top edge = <100>;<111> maxima on
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
21
Sample Orientation Sample Orientation Distribution Distribution
(SOD): (SOD): e1992e1992
1. Self-similar sectionsindicate fiber texture:lack of variation withfirst angle ().2. Maxima along top edge -> <100>;<111> maxima on
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
22
Experimental Pole Figures: Experimental Pole Figures: e1997e1997
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
23
Recalculated Pole Figures: Recalculated Pole Figures: e1997e1997
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
24
COD: COD: e1997e1997: polar plots:: polar plots:Note rings in 40, 50° sectionsNote rings in 40, 50° sections
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
25
SOD: SOD: e1997e1997: polar plots:: polar plots:note similarity of sectionsnote similarity of sections
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
26
Crystal Crystal Orientation Orientation Distribution Distribution
(COD): (COD): e1997e1997
1. Lines on constant correspond to rings inpole figure2. <111> maximumon
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
27
Sample Sample Orientation Orientation Distribution Distribution
(SOD): (SOD): e1997e19971. Self-similar sectionsindicate fiber texture:lack of variation withfirst angle ().2. Maxima on <111> on only!
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
28
Fiber Locations in SODFiber Locations in SOD
<100>fiber
<111>fiber
<110>fiber
<100>,<111>
and<110>fibers
[Jae-Hyung Cho, 2002]
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
29
Inverse Pole Figures: Inverse Pole Figures: e1997e1997
Slight in-plane anisotropy revealed by theinverse pole figures.Very small fraction of non-<111> fiber.
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
30
Inverse Pole figures: Inverse Pole figures: e1992e1992
<111><11n>
<001> <110>
NormalDirection
ND
TransverseDirection
TD
RollingDirection
RDElectromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
31
Method 1: Method 1: Volume fractions from IPFVolume 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 = I( sin() dd• 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 = i I() sin() dd
• Caution: many of the cells in an IPF lie on the edge of the unit triangle, which means that only a fraction of each cell should be used. A simpler approach than working with only one unit triangle is to perform the integration over a complete quadrant or hemisphere (since popLA files, at least, are available in this form). In the latter case, for example, the ranges of and are 0-90° and 0-360°, respectively.
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
32
Volume fractions from IPFVolume fractions from IPF• How to measure distance from a component in an inverse pole
figure?- This is simpler than for general orientations because we are only comparing directions (on the sphere).- Therefore we can use the dot (scalar) product: if we have a fiber axis, e.g. f = [211], and a general cell denoted by n, we take f•b (and, clearly use cos-1 if we want an angle). The nearer the value of the dot product is to +1, the closer are the two directions.
• Symmetry: as for general orientations one must take account of symmetry. However, it is sensible to simplify by using sets of symmetrically related points in the upper hemisphere for each fiber axis, e.g. {100,-100,010,0-10,001}. Be aware that there are 24 equivalent points for a general direction (not coincident with a symmetry element).
33
Method 2: Pole plotsMethod 2: Pole plots
• If a perfect fiber exists then it is enough to scan over the tilt angle only and make a pole plot.
• A “perfect fiber” means that the intensity in all pole figures is in the form of rings with uniform intensity with respect to azimuth (C, aligned with the film plane normal).
• 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
34
Intensityalong aline fromthe centerof the {001}polefigureto theedge(any azimuth)
e1992: <100> & <111>e1997: strong 111
0
100
200
300
400
500
0 15 30 45 60 75 90
Tilt (°)
<100> <111>
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
{001} Pole plots{001} Pole plots
35
High Resolution {111} Pole plotsHigh Resolution {111} Pole plots
0
2
4
6
8
10
12
14
16
0 20 40 60 80 100
Tilt Angle (°)
0
1
2
3
4
5
6
0 20 40 60 80 100
TIlt (°)
e1992: mixture of <100>and <111>
e1997: pure <111>; very small fractions other?∆tilt = 0.1°
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
36
Volume fractionsVolume 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, which, unfortunately, is the usual case.
• In other words, this method is only reasonable to use if the only components are a single fiber texture and a random background.
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
37
{111} Pole plots for thin Cu films{111} Pole plots for thin Cu films
0
5
10
15
0 20 40 60 80 100
Strong <111>Mixed <111> & <100>
Tilt Angle (°)
<100>
<111>
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
E1992: mixture of 100 and 111 fibersE1997: strong 111 fiber
38
Log scale for IntensityLog scale for Intensity
0.01
0.1
1
10
100
0 20 40 60 80 100
Strong <111>Mixed <111> & <100>
Tilt Angle (°)
NB: Intensities not normalized
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
39
Area under the CurveArea under the Curve
• Tilt Angle equivalent to second Eulerangle,
• Requirement: 1 = I( sin() dmeasured 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
40
Extract Random FractionExtract Random Fraction
0
0.5
1
1.5
2
0 20 40 60 80
e1992.111PF.data
Tilt Angle (°)
Random Component = 18%
Fiber components
Random Equivalent
Mixed <100>and <111>,e1992
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
41
Normalized Normalized
0.01
0.1
1
10
100
0 15 30 45 60 75 90
e1997.111PF.data
IntensityNormalized + 2.5re-Normalized IntensityNormalized Intensity
Intensity
Tilt Angle (°)
<100> fiberrandom
?
Randomcomponentnegligible~ 4%
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
42
DeconvolutionDeconvolution
• 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
43
<111>
<100>
<110>
{111} Pole Plot
A1A2
A3
Ai = i I(sin d
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
44
{111} Pole Plot: Comparison of Experiment with Calculation
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
45
{100} Pole figure: pole multiplicity:{100} Pole figure: pole multiplicity:6 poles 6 poles for each grainfor each grain
<100> fiber component <111> fiber component
4 poles on the equator;1 pole at NP; 1 at SP
3 poles on each of two rings, at ~55° from NP & SP
North Pole
South Pole
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
46
{100} Pole figure: {100} Pole figure: Pole Figure ProjectionPole Figure Projection
(100)
(010)
(001)
(001)(100)
(010)(-100)
(0-10)
<100> oriented grain: 1 pole in the center, 4 on the equator<111> oriented grain: 3 poles on the 55° ring.
The number of poles present in a pole figure is proportional to the number of grains
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
47
{111} Pole figure: pole multiplicity:{111} Pole figure: pole multiplicity:8 poles 8 poles for each grainfor each grain
<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
<100> fiber component
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
48
{111} Pole figure: {111} Pole figure: Pole Figure ProjectionPole Figure Projection
(001)
<100> oriented grain: 4 poles on the 55° ring<111> oriented grain: 1 pole at the center, 3 poles on the 70° ring.
(-1-11)
(1-11)(111)
(1-11)
(111)(-111)
(-1-11)
(-111)
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
49
{111} Pole figure: {111} Pole figure: Pole Plot AreasPole 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
50
Intensities, densities in PFsIntensities, 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, , and declination
(from NP), , area, dA = sin d d.
Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution
51
YBCO High YBCO High Temperature Temperature
SuperconductorsSuperconductors: an example: an example
Theoreticalpole figuresfor c & a films
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.
See also Chapter 6 in Kocks, Tomé, Wenk
52
Diagram of possible epitaxiesDiagram of possible epitaxies
[001]
[001]
[102][-102][-102]
[102]
c a
102 peaks close to equator
102 peaks close to center
Superconduction occurs in this plane
53
YBCO (123) on various YBCO (123) on various substratessubstrates
Various epitaxialrelationshipsapparent fromthe pole figures
54
Scan with ∆Scan with ∆ = 0.5°, ∆ = 0.5°, ∆ = 0.2° = 0.2°
Tilt
Azimuth,
55
Dependence of film orientation Dependence of film orientation on deposition temperatureon deposition temperature
Impact: superconduction occurs in the c-plane;therefore c epitaxy is highly advantageous tothe electrical properties of the film.
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.
56
Summary: Fiber TexturesSummary: 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; not advisable when more than one component is present (or, great care required).
• Calculation of volume fraction from pole figures/plots assumes that all corrections have been correctly applied (background subtraction, defocussing, absorption).
57
Summary: other issuesSummary: 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).
• Off-axis alignment is also possible, which is known as axiotaxy.
58
Example 1: calculate intensities Example 1: calculate intensities for a <100> fiber in a {100} pole for a <100> fiber in a {100} pole
figurefigure• 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}
59
Example 2: Equal volume fractions of <100> Example 2: Equal volume fractions of <100> & <111> fibers in a {100} pole figure& <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}