1 Fiber Textures: application to thin film textures , 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.

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 (~10 6 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 A MOS transistor (Harper and Rodbell, 1997) Interconnects provide a pathway to communicate binary signals from one device or circuit to another. Issues: - Performance - Reliability Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

4 e-e- extrusionvoid vacancy diffusion mass diffusion Promote electromigration resistance via microstructure control: Strong texture Large grain size ( Vaidya and Sinha, 1981) Reliability: Electromigration Resistance Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

5  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 Voids (111) Top view (111) _ _ e - Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution Slide courtesy of X. Chu and C.L. Bauer, 1999.

6 Al Interconnect Lifetime H.T. Jeong et al. Stronger fiber texture gives longer lifetime, i.e. more electromigration resistance 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 (Nov/Dec 2002). Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution -> YBCO textures

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 and mixed and. Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

10 Source: research by Ali Gungor, CMU substrate film CC 2 copper thin films, vapor deposited: e1992: mixed & ; e1997: strong 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: e Lines on constant  correspond to rings in pole figure 2. Maxima along top edge = ; maxima on  Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

16 Sample Orientation Distribution: e Self-similar sections indicate fiber texture: lack of variation with first angle (  ). 2. Maxima along top edge -> ; maxima on  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: e Lines on constant  correspond to rings in pole figure 2. maximum on  Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

22 Sample Orientation Distribution: e Self-similar sections indicate fiber texture: lack of variation with first angle (  ). 2. Maxima on on  only! Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

23 Fiber Locations in SOD fiber, and fibers [Jae-Hyung Cho, 2002] 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- fiber. Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

25 Inverse Pole figures: e1992   Normal Direction ND Transverse Direction TD Rolling Direction 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 =  I(    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: V i =  i I(    sin(  ) d  d    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 line from the center of the {001} pole figure to the edge (any azimuth) e1992: & e1997: strong 111 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

29 High Resolution Pole plots e1992: mixture of and e1997: pure ; very small fractions other? ∆tilt = 0.1° 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 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

32 Log scale for Intensity: e1997 NB: Intensities not normalized Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

33 Area under the Curve Tilt Angle equivalent to second Euler angle,    Requirement: 1 =  I(  sin(  ) d   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 Mixed and, e1992 Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

35 Normalized Random component negligible ~ 4% 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 A1A1 A2A2 A3A3  A i =  i I(  sin  d  Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

38 {111} Pole Plot: Comparison of Experiment with Calculation Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

39 {100} Pole figure: pole multiplicity: 6 poles for each grain 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

40 {100} Pole figure: Pole Figure Projection (100) (010) (001) (100) (010) (-100) (0-10) oriented grain: 1 pole in the center, 4 on the equator 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

41 {111} Pole figure: pole multiplicity: 8 poles for each grain fiber component 1 pole at NP; 1 at SP 3 poles on each of two rings, at ~70° from NP & SP 4 poles on each of two rings, at ~55° from NP & SP fiber component Electromigration Weak Strong IPF VolumeFraction PolePlot Deconvolution

42 {111} Pole figure: Pole Figure Projection (001) oriented grain: 4 poles on the 55° ring 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

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 oriented material, we have 3A 1 = A 3 ; for a volume fraction v 100 of oriented material compared to a volume fraction v 111 of fiber, 3A 2 / 4A 3 = v 100 / v 111 and, A 2 / {A 1 +A 3 } = v 100 / v 111 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, , and declination (from NP), , area, dA = sin  d  d . 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 ∆  = 0.5°, ∆  = 0.2° Tilt  Azimuth, 

48 Dependence of film orientation on deposition temperature Impact: superconduction occurs in the c-plane; therefore c  epitaxy is highly advantageous to the 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 YBa 2 Cu 3 O 7-d as a function of deposition temperature. J. Mater. Res., 7,

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 fiber in a {100} pole figure Choose a 5°x5° grid for the pole figure. Perfect 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°] = Area within 5° of equator = 2π*[cos 85°- cos 95°] = {intensity at NP} = (1/4)*(0.1743/ ) = 11.5 * {intensity at equator}

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