1 Fiber Textures application to thin film textures

1 Fiber Textures: application to thin film textures 27 -750, Spring 2008 A. D. (Tony) Rollett 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 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 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 Volume. Fraction Pole. Plot Deconvolution

3 Summary • • 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 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: 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 Volume. Fraction Pole. Plot Deconvolution

5 Interconnects provide a pathway to communicate binary signals from one device or circuit to another. A MOS transistor (Harper and Rodbell, 1997) Issues: - Performance - Reliability Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

6 Reliability: Electromigration Resistance Promote electromigration resistance via microstructure control: • Strong texture • Large grain size (Vaidya and Sinha, 1981) Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

7 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 Top view (111) _ (111) e- Slide courtesy of X. Chu and C. L. Bauer, 1999. _ (111) Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

8 Aluminum Interconnect Lifetime Stronger <111> fiber texture gives longer lifetime, i. e. more electromigration resistance H. T. Jeong et al. Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

9 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). • 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. -> YBCO textures Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

10 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 Volume. Fraction Pole. Plot Deconvolution

11 Research on Cu thin films by Ali Gungor, CMU C See, e. g. : Gungor A, Barmak K, Rollett AD, Cabral C, Harper JME. Journal Of Vacuum Science & Technology B 2002; 20: 2314. film substrate 2 copper thin films, vapor deposited: e 1992: mixed <100> & <111>; e 1997: strong <111> {001} PF for strong <111> fiber Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

12 Epitaxial Thin Film Texture From 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 - Ni. Si films on Si Detavernier C, Ozcan AS, Jordan-Sweet J, Stach EA, Tersoff J, et al. 2003. An offnormal fibre-like texture in thin films on single-crystal substrates. Nature 426: 641 - 5. Spherical projection of {103}:

14 Plane-edge matching Axiotaxy C. Detavernier

15 Possible Orientation Relationships

16 Fiber Textures: Pole Figure Analysis: Example of Cu Thin Film: e 1992 Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

17 Recalculated Pole Figures: e 1992 Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

18 COD: e 1992: polar plots: Note rings in each section Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

19 SOD: e 1992: polar plots: note similarity of sections Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

20 Crystallite Orientation Distribution (COD): e 1992 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 Volume. Fraction Pole. Plot Deconvolution

21 Sample Orientation Distribution (SOD): e 1992 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 Volume. Fraction Pole. Plot Deconvolution

22 Experimental Pole Figures: e 1997 Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

23 Recalculated Pole Figures: e 1997 Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

24 COD: e 1997: polar plots: Note rings in 40, 50° sections Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

25 SOD: e 1997: polar plots: note similarity of sections Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

26 Crystal Orientation Distribution (COD): e 1997 1. Lines on constant Q correspond to rings in pole figure 2. <111> maximum on Q= 55° (f = 45°) Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

27 Sample Orientation Distribution (SOD): e 1997 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 Volume. Fraction Pole. Plot Deconvolution

28 Fiber Locations in SOD [Jae-Hyung Cho, 2002] <100> fiber <111> fiber <100>, <111> and <110> fibers Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

29 Inverse Pole Figures: e 1997 Slight in-plane anisotropy revealed by the inverse pole figures. Very small fraction of non-<111> fiber. Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

30 Inverse Pole figures: e 1992 <11 n> <001> <110> Normal Direction ND Transverse Direction TD Rolling Direction RD Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

31 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 • • 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 = Si I( ) sin( ) d d 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 pop. LA 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. • 1 = S I( ) sin( ) d d Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

32 Volume 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 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°x 5° pole figures, e. g 0. 1°. • High resolution inverse PF preferable but not measurable. Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

34 {001} Pole plots Intensity along a line from the center of the {001} pole figure to the edge (any azimuth) e 1992: <100> & <111> e 1997: strong 111 Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

35 High Resolution {111} Pole plots e 1992: mixture of <100> and <111> ∆tilt = 0. 1° e 1997: pure <111>; very small fractions other? Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

36 Volume fractions • Pole plots (1 D 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 Volume. Fraction Pole. Plot Deconvolution

37 {111} Pole plots for thin Cu films E 1992: mixture of 100 and 111 fibers E 1997: strong 111 fiber <100> <111> Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

38 Log scale for Intensity NB: Intensities not normalized Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

39 Area under the Curve • Tilt Angle equivalent to second Euler angle, q • 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 Volume. Fraction Pole. Plot Deconvolution

40 Extract Random Fraction Mixed <100> and <111>, e 1992 Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

41 Normalized Random component negligible ~ 4% Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

42 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 Volume. Fraction Pole. Plot Deconvolution

43 {111} Pole Plot <111> <100> <110> A 1 Ai = Si I(q sinq dq A 3 A 2 q Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

44 {111} Pole Plot: Comparison of Experiment with Calculation Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

45 {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; 1 pole at NP; 1 at SP 3 poles on each of two rings, at ~55° from NP & SP Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

46 {100} Pole figure: Pole Figure Projection The number (-100) of poles present in a (001) pole figure is proportional to the number of grains (0 -10) (010) (100) (001) <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 Volume. Fraction Pole. Plot Deconvolution

47 {111} Pole figure: pole multiplicity: 8 poles for each grain <100> fiber component 4 poles on each of two rings, at ~55° from NP & SP <111> fiber component 1 pole at NP; 1 at SP 3 poles on each of two rings, at ~70° from NP & SP Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

48 {111} Pole figure: Pole Figure Projection (-111) (1 -11) (001) (111) (-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 Volume. Fraction Pole. Plot Deconvolution

49 {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 3 A 1 = A 3; for a volume fraction v 100 of <100> oriented material compared to a volume fraction v 111 of <111> fiber, 3 A 2 / 4 A 3 = v 100 / v 111 and, A 2 / {A 1+A 3} = v 100 / v 111 Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

50 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), q, area, d. A = sinq dq d. Electromigration Weak Strong IPF Volume. Fraction Pole. Plot Deconvolution

51 YBCO High Temperature Superconductors : an example Theoretical pole figures for 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 YBa 2 Cu 3 O 7 -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 epitaxies 102 peaks close to equator [-102] [001] 102 peaks close to center [102] [001] [102] a c Superconduction occurs in this plane

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

54 Scan with ∆a = 0. 5°, ∆b = 0. 2° Azimuth, b Tilt a

55 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 YBa 2 Cu 3 O 7 -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.

56 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; 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 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 for a <100> fiber in a {100} pole figure • Choose a 5°x 5° 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> & <111> fibers in a {100} pole figure • Choose a 5°x 5° 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}