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`Physics of Thin Films
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`Advances in Research and Development
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`VOLUME 3
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`CONTRIBUTORS TO THIS VOLUME
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`KLAUS H. BEHRNDT
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`D. E. Boo:
`
`L. V. GREGOR
`
`R. W. HOFFMAN
`
`LEON I. MAISSEL
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`A. Vscnr
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`Physics of Thin Films
`
`Advances in Research and Development
`
`Edited by
`
`GEORG HASS
`
`Night Vision Laboratory
`U. S. Army Elecrronics Command
`Fort Belvoir, Virginia
`
`and
`
`RUDOLF E. THUN
`
`International Business Machines Corporation
`Owego, New York
`
`VOLUME 3
`
`1966
`
`@
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`ACADEMIC PRESS
`
`New YORK AND LONDON
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`SAMSUNG ET AL. EXHIBIT 1044
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`1;(,7<>S$"s3
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`Corvmcnr © 1966, BY ACADEMIC Pmass INC.
`ALL moms am:-znvm.
`NO PART or mus noox MAY BE REPRODUCED IN ANY FORM,
`BY pHo1'osrA'r, MICRO!-‘ILM, on ANY mum MEANS, wnuour
`wIu1'rEN PERMISSION mom THE runusmans.
`
`ACADEMIC PRESS INC.
`Ill Fifth Avenue, New York, New York 10003
`
`United Kingdom Edition published by
`ACADEMIC PRESS INC. (LONDON) LTD.
`Berkeley Square House, London W.l
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`PRINTED [N THE UNITED STATES OF AMERICA
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`67.
`68.
`69.
`70.
`71.
`72.
`73.
`74.
`75.
`76.
`
`77.
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`Ws
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`21
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`0
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`A. vacm‘
`
`63
`
`. A. Rose, “Concepts in Photooonductivity and Allied Problems." Wiley (Interscience),
`New York, 1963.
`64.
`H. K. Henisch, “Electroluminesoenoe.” Pergamon Press, New York, 1962.
`65.
`H. K. Henisch, Rept. Progr. Phys. 27, 369 (1964).
`66.
`H. F. lvey, Electroluminesoenoe and Related Effects, Suppl. 1, in “Advances in Eleo-
`tronics and Electron Physics." Academic Press, New York, 1963.
`“Photoeondu¢tivity" (H. Levinstein, ed.). Pergamon Press, New York, 1961.
`A. Vecht and B. W. Ely, Vacuum 14, I22 (1964).
`Y. Sakai and H. Okimura, Japan. J. Appl. Phys. 3, 144 (1964).
`K. Weiss, Z. Natutforsch. 2a, 650 (I947).
`J. E. Jacobs and C. W. Hart, Proc. Nat. Electron. Conji I1, 592 (I955).
`P. Goercke, Ann. Telecom. 6, 325 (I951).
`W. Ehrenberg and J. Franks, Prac. Phys. Soc. (London) B66, 1507 (1953).
`D. E. N. King, J. Television Soc. 10, 2 (1962).
`C. Feldman, J. Soc. Motion Piclure Television Engrs. 67, 455 (1958).
`A. Bril, in “Luminescence of Organic and lnornanic Materials" (H. P. Kallman and
`G. M. Spruch, eds.), p. 479. Wiley, New York, 1962.
`D. A. Cusano, Pro. Image Inteuslfer Symp., Fort Belvoir, Va., Oct. 24-26, 1961, p. II9.
`USAEROL, Fort Belvoir, Virginia.
`78
`. W. A. Thornton, J. Electraclrem. Soc. 108, 636 (1961).
`79.
`_
`W. A. Thornton, Phys. Rev. 123, I583 (I961).
`80
`. H. F. Ivey, Pt. I, IRE Dans. Electron. Devices 6, 203 (1959); Pt. 11, J. Electrochem.
`Soc. 108, 590 (1961); Pt. llI.J. Eleclrochem. Tech. I, 42 (1963).Pt. IV Ibid., 3, 137 (I965).
`. D. A. Cusano, in “Luminescence of Organic and Inorganic Materials” (H. P. Kallman
`and G. M. Spmch, eds.), p. 494. Wiley, New York, 1962.
`. P. Goldberg and J. W. Nickerson, J. Appl. Phys. 34, I601 (I963).
`. J. W. Nickerson and P. Goldberg, in “Tenth National Symposium on Vacuum Tech-
`nology Transactions, 1963" (G. H. Bancrofl, ed.). Pergamon Press, New York, 1963.
`. W. A. Thornton, J. Appl. Phys. 33, 3045 (I962).
`. P. A. Jackson, Hull Conference on Luminescence, 1964, to be published.
`. M. Shiojiri and E. Suito, Japan. J. Appl. Phys. 3, 314 (I964).
`. H. Berger, Phys-ica Status Solidi 1, 739 (1961).
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`The Mechanical Properties of Thin Condensed Films
`R. W. HOFFMAN
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`Department ofPhysics, Case Institute of Technology, Cleveland, Ohio
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`I. Introduction .
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`11. Structural Considerations
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`l. Nucleation and Growth
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`2. Stnicture .
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`3. Surface Structure
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`Ill. Internal Stresses .
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`1. Experimental Techniques
`2. Summary of Experimental Results for Various Metals and Nonmetals
`3. Models for the Origin of Internal Stress
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`4. Anisotropic Stress
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`IV. Tensile Properties
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`l. Experimental Techniques
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`2. Summary of Experimental Results
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`3. Models for Strength .
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`References
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`I. Introduction
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`The mechanical properties of thin films have been studied from several
`points of view. The large internal stresses, first found in electroplated films,
`have been an annoying feature often leading to film fracture and peeling,
`although there exist a few examples where the planar stress has been useful
`in producing a desired pseudosingle crystal symmetry for certain film pro-
`perties. Early observations of films exhibiting an unexpectedly high structural
`strength provided another motivation for the study of the mechanical pro-
`perties of films. More recently, the correlation of structure and mechanical
`properties is leading to a better understanding of condensed films, but a
`quantitative theory of film mechanics seems to evolve only slowly.
`Although the literature concerning the mechanical properties of films is not
`so extensive as in the case of the electricaland magnetic properties, we still
`cannot review every paper in detail. We shall set as our goal, then, to give d
`summary of the major research trends, together with a discussion of the
`physical models proposed to explain the experimental results. For the most
`part we shall be concerned with films of metals formed by evaporation tech‘-'
`niques under various deposition conditions. Nonmetals will be considered
`when the corresponding information for metallic films is lacking, or where
`the different properties of such substances can give an insight
`into the
`particular physical mechanism studied. Films formed by sputtering and by
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`electroplating will not be discussed in detail, since the information is generally
`lacking for the former and too dependent on bath complications for the latter.
`As the correlation between structural details and mechanical properties un-
`folds, it will become increasingly clear that these properties do not depend on
`the particular mode of film formation, but only on the resultant structural
`order and impurity content.
`
`ll. Structural Considerations
`
`The association of physical properties with structural details has been the
`objective of much of recent solid-state science. In the case of films, the high-
`resolution electron microscope has been perhaps the most important tool.
`Results have been discussed in a number of detailed reviews: “Structure and
`
`Properties of Thin Films,” (Wiley, 1959), “Thin Films" (American Society
`for Metals, I964), and the multivolume “Physics of Thin Films” (Academic
`Press, 1963112) deal with the present knowledge of the condensation process,
`and with crystal growth, textures, and epitaxy. In scanning the literature, it
`becomes apparent that most of the detailed structural infomiation comes from
`epitaxial films condensed on substrates at elevated temperatures, whereas
`most of the mechanical data has been obtained from polycrystalline films
`condensed on ambient-temperature glass-like substrates. A critical review of
`the present status of film-structure research thus seems in order, if the proper
`correlations to the mechanical properties of films are to be achieved.
`
`l. NUCLEATION AND Gnowru
`
`Thun (I), Neugebauer (2), and Walton (3) have recently discussed the
`nucleation and growth of very thin layers, and several authors (4, 5, 6) have
`examined in particular the growth of Au, Ag, and Pb films under electron-
`microscope observation. They found the now well-known “liquid-like”
`behavior, in which the density of crystallization nuclei decreases, during depo-
`sition, by the coalescence of such nuclei. The nuclei are usually rounded, but
`exhibit sudden changes in shape when two join together in the early stages of
`growth. The mass-transport mechanism is believed to be surface diffusion.
`Reorientation of two crystallites has also been noted at this stage (7). As the
`growth continues, the nuclei become larger and grow together to form a
`network with many open areas.
`These holes ultimately fill in and may be the source of the large dislocation
`density found in most epitaxed films (8). Twins, stacking faults, and other
`defects have been noted in large numbers for thicker (continuous) single-
`crystal films. These films have all been deposited on substrates held at elevated
`temperatures to reduce film contamination and to achieve epitaxy. Under
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`MECHANICAL PROPERTIES or THIN oonmsnsen FILMS
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`these conditions and with the materials so far studied, a high mobility is
`expected.
`It is not clear whether the same pattern governs the nucleation and growth
`of polycrystalline films at lower temperatures on glassy substrates, but some
`information is available. Pashley er al. (6) indicate that a similar liquid-like
`coalescence occurs in polycrystalline films, and that large orientation changes
`and recrystallization take place as the growth proceeds. The resulting grain
`size of the deposit is large compared with the initial separation of the nuclei,
`since as many as I00 initial nuclei may contribute to each grain. The grain
`size is thus determined primarily by the recrystallization process rather than
`the density of initial nuclei. The details of recrystallization have not been
`worked out, but since a dependent: of the crystallite size upon deposition
`rate has been noted, the final deposit may reflect to a degree the initial
`nucleation.
`
`a. Preferred Nucleation. A characteristic of the mechanisms just discussed
`is the appearance of initial nuclei at an average thickness of a few angstroms.
`These nuclei may lie along the cleavage steps of a single-crystal substrate,
`they may be located at the intersections of dislocations with the surface, or
`they can form at point defects, or impurities (4). Prenucleation of the sub-
`strate with another extremely thin evaporated layer changes the growth con-
`siderably in the case of Zn, Sn, and Pb. Jeppesen and Caswell (9), for instance,
`prenucleated a NaCl substrate maintained at room temperature with 10 A of
`Cu, Ag, or Au, and examined the resulting 300-A Pb film by transmission
`microscopy and X-ray diffraction. The unnucleated lead film consisted of
`isolated grains with rounded edges. The Cu and Ag nucleation yielded similar
`open patches between grains, except that almost all the grains were connected
`by bridges. The Au nucleation, in contrast, produced an almost continuous
`film with much smaller crystallites. It was felt that the formation of a Au-Pb
`intermetaliic compound was important in the nucleating process.
`Similar fine-grained iron films on formvar substrates have been observed
`without prenucleation (10). In this case no well-defined isolated nuclei were.
`found for films of IO to 20 A average thickness, but rather a “fuzzy” two-
`dimensional maze-like structure. These maze formations were 50 to 100 A
`wide and appeared to consist of iron crystallites 10 to 20 A in size. An iron
`diflraction pattern was obtained, albeit broadened by strain and particle size.
`Conditions of low mobility resulting in continuous films of small crystallite
`size are probably more common than is generally realized.
`The recent Mossbauer measurements on layered films of iron and SiO
`have shown that the internal field is the same as bulk for films down to 5 A,
`indicating a continuous film in this thickness range. In addition, Lee et al.
`(I0a) found a two-line spectrum for thinner films, demonstrating a narrow
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`distribution of crystallite sizes. 25-A-thick films were examined by electron
`microscopy and found to be continuous.
`b. Angle-of-Incidence Eflecn. Smith et at. (11) have found that chains of
`crystallites oriented perpendicular to the plane of incidence are developed
`when the incident vapor beam forms a large angle with the substrate nonnal.
`_Direct confirmation by electron microscopy was available for thinner films,
`and optical dichroism as well as magnetic measurements suggested that these
`chains are also present at greater film thickness. Resistivity anisotropies also
`resulted, according to Pugh er al. (12) and Smith et al. (13), from large angles
`of incidence. The mechanism for this chain formation is a geometric “self-
`shadowing” in which the initial random nuclei shield the substrate from the
`vapor beam. As the film grows, vacant areas remain on the substrate, but the
`crystals ultimately grow together to form long chains. It is felt that this con-
`dition would hold only for films evaporated under conditions of low mobility,
`but this is disputed by Behmdt (86a). Although these effects would clearly
`be important for very thin films, their role may be less pronounced for a con-
`tinuous film unless anisotropic growth is obtained. Both maze and chain-like
`structures were found in electron micrographs of iron deposited at 36 degrees
`incidence (I0). Chains both parallel and perpendicularto the plane ofincidence
`were found at depositions between 100 and 150°C, but only.a random maze
`at lower substrate temperatures.
`
`2. STRUCTURE
`
`A correlation of mechanical properties and structure requires knowledge
`of the distributions of crystallite size and orientation, as well as the density of
`planar, linear, and point defects in the films as deposited and after subsequent
`annealing. It is thus appropriate to discuss some of these structural features
`as they are found in polycrystalline and single-crystal films.
`a. Polycrystalline Films. The crystallite size increases as the substrate tem-
`perature is raised. Fleet (14) has carried out a detailed study of nickel films
`condensed on glass or fused silica at condensation rates of 3 to 12 A/sec. For
`room-temperature substrates the crystallites had diameters of about 60 A,
`and the films were several crystallites thick. At substrate temperatures of
`about 350°C, large flat crystals measuring about 1000 A across and extending
`through the film were surrounded by regions several crystallites thick and 500
`A in diameter. At still higher temperatures the film became one crystallite
`thick throughout and the crystallites measured several thousand angstroms
`across. Figure 1 indicates the average crystallite size as a function of substrate
`temperature for 500-A-thick nickel films, showing the onset of the large
`crystallites at about 350{C_.
`The condensation rate also effects the crystal size. Thun (I) gives son1e data
`for 1000-A chromium films at various substrate temperatures. For 25°C sub-
`
`.1
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`3000
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`2000
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`AVERAGECRYSTALLITESIZEANGSTROMS §0
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`SUBSTRATE TEMPERATURE ‘C
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`I000
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`FIG. 1. Crystallite size in 500-A nickel films as a function of substrate temperature.
`[Data from Fleet (14).)
`
`strate temperature the grain diameter was independent of the rate between
`the limits of 10 and 500 A/sec, whereas higher substrate temperatures resulted
`in a constant grain size only up to a threshold rate at which the grain size
`began to decrease rapidly with increasing rate. This behavior indicates
`that the crystal size became limited by a process in which the high-mobility
`surface atoms were buried before they could reach an ordered lattice site.
`Campbell et al. (15) also observed, for gold and lithium fluoride, smaller
`crystals at larger evaporation rates, similar to earlier measurements by Sennett
`and Scott (16), who found more agglomeration in silver at low evaporation
`rates.
`
`For a fixed condensation rate and substrate temperature the crystallite size
`depends on the average fiJrn thickness. Figure 2 presents Fleet's results for
`nickel at a substrate temperature of l50°C. Up to a thickness of 250 A grain
`size increases almost linearly, and then decreases slowly to a constant mean
`diameter of about 100 A. This implies that either new crystals are nucleated
`as the film continues to grow, or that existing crystals are broken up. Lithium
`fluoride behaves similarly. Its crystallite size increases up to a film thickness
`of about 100 A, and then decreases slowly to an average area of 2 x 10‘ A2
`for thicknesses greater than 200 A. As a result of these ‘observations, Campbell
`et al. (15) developed a specific model for the nucleation and growth of LiF.
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`Gold shows also an initially increasing crystallite size, at least up to an average
`film thickness of I00 A.
`
`It is not clear whether the crystallites extend through the thickness of the
`film. Columnar growth is well known in electroplated films at particular
`current densities and temperatures, and with certain additions to the bath.
`Nickel films are, according 10 Fleet (/4), several crystallites thick when de-
`posited at lower substrate temperature, but consist of only a single layer of
`thick crystallites when condensed ata high temperature. Blakely (I 7) indicates,
`on the other hand, that polycrystalline gold films deposited at only 40°C consist
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`300
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`200
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`I00
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`AVERAGECRYSTALLITESIZEANGSTROMS
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`FILM THICKNESS ANGSTROMS
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`I000
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`Fla. 2. Crystallitc size in nickel films evaporated at approximately 10 A/sec on substrate
`at 150°C as a function of film thickness. [Data from Fleet (l4).]
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`usually of grains which extend from one surface to the other. He found a mean
`grain diameter of about 200 A, much less than the 800-A thickness of the gold
`films.
`
`During the growth of polycrystalline films on carbon substrates at about
`400°C, Pashley (6, 8) has observed large reorientation effects when the nuclei
`coalesce. The orientation difference between adjacent crystallites, however,
`covers a range including large angles. Some information on this point is
`available from the work of Palatnick era]. (18) using electron-diffraction micro-
`beam techniques on aluminum films of 60 to 200 A thickness which had been
`condensed on cool substrates. They found that the small crystallites or “block
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`crystallites" extended through the thickness of the film. Reduction of the
`aperture and hence the difiracting volume reduced the number of spots in a
`given ring and increased the average angle between spots, indicating that most
`blocks have a large orientation difference with their neighbors. If the blocks
`were assumed to be cubes, the average length would be greater than the film
`thickness, but even so, the block crystallite size was felt to be determined by
`the thickness of the film.
`
`The crystallite size may undergo large changes upon annealing. Palatnik
`et al. indicate that the random dilfraction ring tends to disappear, leaving
`only isolated spots as a proof of the microrecrystallization which takes place.
`Upon further heating, the number of spots decreases, indicating that the larger
`crystallites grew at the expense of those which are smaller and more randomly
`distributed. Grain growth in iron during heating has been qualitatively ob-
`served by Vesely and Hoffman (10) in the electron microscope. Their study
`confirms the fact that the extremely small crystals (< 100 A) in a condensed
`film undergo rapid changes and increase in size by a factor of 5 to l0. The
`recrystallization seems to stop rather suddenly at a crystallite size many times
`larger than the thickness of the film. This final structure contains voids between
`some crystallites. Recrystallized grain diameters of about 1000 A can befound
`in films of an average thickness of about 50 A. It is not yet known whether
`this growth pattern is similar to the recrystallization by coalescence observed
`in cold-rolled foils by Hu (I9). Blakely has observed the microstructure
`changes in annealing carbon-coated gold films on at 600°C hot stage in the
`electron microscope. His observations indicate that aggregation occurs in two
`stages: first, recrystallization to a stable grain structure, and then separation
`of individual grains along the stationary grain boundaries. It is suggested
`that a diffusion process is responsible for this behavior.
`Gimpl er a1. (I9a) have recently annealed continuous nickel and gold films
`to high temperatures and studied the resulting recrystallization and island
`fonnation. They observed amorphous NiO as well as an unidentified amor-
`phous gold film occupying the area between the islands, in contrast to previous
`workers who have interpreted such structureless areas on micrographs as
`cracks in the films.
`
`Bachmann et al. (1%) finally have studied the morphological changes in
`copper films during annealing and oxidation, and in particular examined very
`thin (10 to 50 A) deposits on both carbon and SiO substrates. For carbon
`substrates they found at 500°C a large increase in crystallite size approaching
`l000 A in diameter, whereas little or no change was noted for the films on
`Si0 substrates. Thicker (100 to 200 A) deposits, although still not continuous
`showed a growth on Si0 substrates only if the original deposit consisted of
`large, interconnected islands. The authors suggest that for the thicker con-
`tinuous films the mass transport occurs by self-diffusion of copper, whereas
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`R. w. HOFFMAN
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`for island films the copper must migrate over the substrate surface. This
`surface diffusion is indeed slower for SiO than for carbon substrates.
`The internal structure of individual crystals in a polycrystalline film is
`similar to those observed in epitaxial films, but has not yet found detailed
`interpretation. It is probably safe to assume that dislocation densities will be
`at least as high as those found in epitaxial films, and other imperfections are
`undoubtedly present as well. We shall not consider allotropic transitions
`except to remark that such changes will be reflected in the mechanical as well
`as other properties.
`b. Films with Preferred Orientation. Fiber textures have been noted in films
`for a long time [see, for instance Evans and Wilman (20)]. Mixed textures are
`common, as well as a partial texturing together with some random crystallites.
`The texture axis is perpendicular to the film for atoms arriving perpendicular
`to the substrate, and is usually inclined toward the vapor stream for other
`angles of incidence. Since none of the models for the mechanical properties
`are sufficiently detailed to take account of any local orientation differences,
`we face the same interpretation problems as for the random-oriented poly-
`crystalline films. A film with a strong fiber texture would normally have
`different elastic constants for the texture axis and the axis normal to it, but
`these differences cannot account for the anisotropic stresses actually ob-
`served. For the case of an inclined fiber axis, the elastic constants would be
`an intricate function of the angle between the direction of measurement and
`the texture axis. These anisotropies would probably not be large. since most
`fiber textures are not well developed. It is also not clear that an anisotropy in
`the elastic constants of the film would be reflected in a measurement of the
`internal stress, because it is really the strain in the substrate which is measured,
`and from which the stress in the film is inferred. Hence at the moment we need
`not treat textured films as being particularly different from random-oriented
`films.
`
`c. Single-Crystal Films. As compared to other structures, we probably
`know most about the growth and structure of single crystals and least about
`their mechanical properties. The growth conditions for single-crystal films
`are now reasonably well known, and in any event do not concern us here.
`A reorientation of the joining nuclei is common during film growth [see
`Bassett (7) for the case of silver on molybdenite]. Once a continuous film is
`fonned, a second twinned layer may develop, according to Jacobs and
`Pashley (21). (The boundaries between the two twin-related orientations
`possible in silver or gold on mica are at first perpendicular to the plane of the
`film; but after the film becomes continuous, parallel boundaries develop.)
`in silicon stacking faults develop at the boundaries of the joining grains (22).
`It is found that the dislocation density in epitaxial films is large, perhaps l0‘°
`to 10“/cm’; many twins and stacking faults are found also (6). Dot-like
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`MECHANICAL pnopenr or "r1-rm CONDENS FILMS
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`
`features tentatively identified as vacancy aggregates or small dislocation loops
`were later seen to arise during the exposure to the electron beam, probably
`as a result of surface contamination (23). Annealing of single-crystal films
`does not seem to reduce the dislocation concentration appreciably, a behavior
`which is in contrast to that of bulk material, although annealing experiments
`with films free of the constraint of a substrate may add new information.
`
`3. SURFACE Srnucruiu-:
`
`As discussed in some detail by Thun (I), the density of a film may be con-
`siderably smaller than that of the bulk material. X-ray diffraction diagrams
`indicate, however, that the density within the crystallites is near normal.
`This implies that the low over-all density of films arises from voids between
`islands when the films are discontinuous or from high concentrations of oxide
`or other impurities, as well as vacancies at the grain boundaries for con-
`tinuous films. Surface-area measurements [see Beeck et al. (24), for example]
`also indicate that the surface is anything but smooth on an atomic scale.
`Allen el al. (25) found that copper films deposited at low temperatures have
`a surface area linear with mass. This implies a film consisting of loosely
`packed particles. At higher substrate temperatures this linear relation is no
`longer observed.
`Even in high vacuum a surface oxide or nitride layer will form in rather
`short times. Since all tensile measurements and some of the stress measure-
`
`ments have been made outside a vacuum system, we expect that these
`measurements include contributions from such chemical changes, and thus
`may not represent data characteristic for pure films. As these surface layers
`are generally quite thin, any contribution is expected to be small for thick
`films.
`
`Ill. Internal Stresses
`
`Since the work of Stoney on electroplated films in l909 (26), the existence
`of large internal stresses has been known. Evaporated films were studied in
`the l950's with the aim of understanding the origin of these stresses. In the
`following sections we shall review the measurement techniques, summarize
`the experimental results, and present models for their origin.
`
`1. EXPERIMENTAL TECHNIQUES
`
`a. Bending-Plate Methods. The stress has commonly been determined by
`observing the deflection of the composite of film and substrate during or afier
`film deposition. For most of the” experiments a long thin beam was used,
`either clamped at one side for an observation of the deflection of the free
`end, or held on knife edges for measuring the center deflection. In the case
`
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`

`
`220
`
`R. w. HOFFANM
`
`of the cantilever beam, the deflection has been observed optically (27-29),
`through a capacitance change (30), or mechanically by using a surface-
`analyzer probe (31). An electromechanical (32, 32a) or magnetic restoration
`(33) of the null position in combination with a measurement of the restoration
`force has also been used. Some of these methods are sufliciently sensitive to
`permit stress measurements during the stage of initial film growth.
`Table I compares the sensitivities of various techniques for measuring the
`
`TABLE I
`
`SENSITIVFIY or STRESS-MEASURING Tecimiouas
`
`Method of
`observing deflection
`
`Type of plate“
`
`Detectable force per unit
`width, dyne/cm
`
`Optiml
`Capacitance
`Optical
`Magnetic restoration
`Electromechanical restoration
`Mechanical
`Electromechanical
`Interferometric
`lnterferomet ric
`Ferromagnetic resonance
`X-ray
`
`B
`C
`C
`C
`C
`C
`C
`C
`P
`
`800
`500
`250
`250
`150
`I
`1
`0.5
`I 5
`I000‘
`500°
`
`Ref.
`
`63
`30
`27
`33
`32
`31
`32a
`
`41
`49
`35
`
`' B, beam supported on both ends; C, cantilever beam; and P, circular plate.
`" Approximate equivalent; a force is not measured.
`
`deflection following Blackburn and Campbell (31) and Klokholm (32a). The
`sensitivity values quoted are a measure of the smallest detectable force per unit
`width using the conventional substrate geometry for the particular method.
`For thicker films any method will sufiiec, although those amenable to auto-
`matic recording might be preferred. For studies of the initial stages of growth,
`a sensitivity of at least the interferometric method is needed. The sensitivities
`may be increased by a factor of about five by choosing thinner substrates,
`but limitations in the validity of the usual plate equations represent a serious
`constraint. The methodical details of each approach can best be found by
`consulting the original papers.
`The deflection of a circular plate has also been used for stress measurements
`(34, 35). The change in the optical fringe system between the plate and an
`optical flat is here used to measure the deflection of the plate. Because of the
`limited flatness of available substrates, the substrate profile is remeasured
`after the film has been dissolved and then used as a reference profile. (Fused
`
`SAMSUNG ET AL. EXHIBIT 1044
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`

`
`MICIIANICAL PROPERTIES or THIN CONDFNSED FILMS
`
`221
`
`quartz StIl)xtratesz<1rc generally flatter than glass, but. on the other hand. have
`more severe thickness gradients.) The fringe technique is illustrated in Fig. 3.
`and the phomgrzlph of an actual Fringc pattern is shown in Fig. 4. It can be
`sccn that the circular plate 0iTL‘.l"S thc }'I<)S‘s‘iblli‘.y of observing stress aniso-
`tropies. Anisotropy has also bccn observed by Pricst er al. (36) by using two
`orthogonal cantilever beams.
`SUBSTRATE,
`FlLM SIDE DOWN
`
`- OPTlCAL FLAT
`
`
`
`
`PARTIALLY!
`SILVERED.
`MIRROR 4'
`
`ll —‘} ' “"
`L
`
`SODIUM
`
`VAPOR
`IJM9
`
`i
`
`—
`
`7
`TO CAMERA
`
`INTERFERENCE APPARATUS
`
`lenses may be needed if
`Fin. 3. Schcmatic dr:1\4.ing of circular fringe apparatus.
`apparatus is used in vacuor [After ltncgan and Itoflman (¢I).]
`
`Tu. 4 (’)hser\=cd fringe paucrns. The circular fringes are observed {or film L-vapoqatcd
`3| 0 angle of incidence and thc elliptical rings correspond to :1 bcam incident from the top
`im‘]i:1n.-d 22.5 IO the substrate n(u'nv..1l. [After l incgan and Hvifmun (4/).]
`
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`R. w. HOFFMAN
`
`In both the beam and the plate methods, it is elastic theory which yields
`the film stress as a function of the measured deflection. It is assumed that the
`
`film strains the substrate, which bends until equilibrium is reached, and that
`the film-substrate bond is strong enough to suppress slippage, a condition
`that seems to be fulfilled in practice. Since the film stress is computed from
`the observed substrate strain only, it is apparent that the elastic constants of
`the film are not taken into consideration in this approximation.
`The equation derived by Stoney is
`
`¢r=—
`
`(l)
`
`where a is the stress in the film, E Young’s modulus for the substrate, d the
`substrate thickness, I the thickness of the film, and r the radius of curvature
`of the bent strip. This equation can easily be transformed to an expression
`relating the stress to the deflection of a cantilever or otherwise supported
`beam. The stress is defined as tension if the plate bends in a way decreasing
`the film length, and compression if the film tends to expand. Brenner and
`Senderofi" (37) pointed out that Eq. (l) neglects some important features.
`First, it ignores the stress change in the film as the substrate curvature changes
`during condensation. This change induces a stress relief, which in turn de-
`pends on the total amount of deflection. A second error arises from the fact
`that the beam is really a composite structure of film and substrate, and that
`this results in a different equation if the elastic moduli of film and substrate
`differ. A correction can be obtained by replacing the composite beam with
`an equivalent T beam, where the widths of substrate and film are proportional
`to their moduli. The neutral axis and stiffness can now be calculated by stan-
`dard beam theory. Brenner and Senderoff have further distinguished between
`three experimental cases during the deposition of the film: rigid constraint
`so that neither contraction nor