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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}