Communication
`
`by Erik Klokholm
`
`Delamination
`and fracture
`of thin films
`
`The fracture and delamination of tliin films is a
`relatively common occurrence, and prevention of
`these mechanical failures is essential for the
`successful manufacture of thin-film devices.
`Internal elastic stresses are an inherent part of
`the thin>film deposition process, and are largely
`responsible for the mechanical failures of thin
`films. However, it is not the magnitude of the
`film stress S which governs film fracture or
`delamination, but the elastic energy U stored in
`the film. It is the intent of this presentation to
`show that the mechanical stability of the film
`and the substrate requires that U be less than a
`critical value U^ and that U^ is dependent upon
`the surface energy y.
`
`Introduction
`The elastic stress present in thin films is an inherent part of
`the deposition process, and can be either tensile or
`compressive. The sign and the magnitude of the film stress
`are for the most part determined by the deposition
`parameters, i.e., substrate temperature, kind of substrate,
`deposition rate, and method of deposition. Stresses of about
`iO'-iO'" dynes/cm are often observed [1, 2], and it has been
`commonly found that these stresses cause film fracture,
`delamination, and occasionally substrate fracture. However,
`the important criterion for the mechanical stability turns out
`not to be the magnitude of the stress, as commonly believed,
`but the elastic energy stored in the film.
`
`^Copyright 1987 by international Business Machines Corporation.
`Copying in printed form for private use is permitted without
`payment of royahy provided that (1) each reproduction is done
`without alteration and (2) the Journal reference and IBM copyright
`notice are included on the first page. The thle and abstract, but no
`other portions, of this paper may be copied or distributed royalty
`free without further permission by computer-based and other
`information-service systems. Permission to republish any other
`portion of this paper must be obtained from the Editor.
`
`Elastic energy and surface energy
`Whatever its origins, the elastic stress in thin films is only
`sustained by the mechanical constraint of the substrate.
`Separation of the film from the substrate relieves the film
`stress entirely; stress relief also occurs with film fracture and
`occasionally by fracture of the substrate surface due to the
`film stress. These stress relief modes come about because, as
`film thickness increases, the elastic energy stored in the film
`eventually becomes so large that the film catastrophically
`fails.
`(It is also possible in some cases, for instance, in materials
`that melt at very low temperatures, such as Bi, Cd, Sb, to
`relieve film stress by plastic deformation; however, in the
`discussion that follows we will not concern ourselves with
`this stress-relief mode.)
`The elastic energy U stored in a film of unit surface area
`and of thickness S is expressed by
`
`t,= 5 ^ I i ^,
`
`(1)
`
`where E is Young's modulus and v is Poisson's ratio [3]. The
`stress S in Equation {1) is assumed to be biaxial and
`isotropic in the plane of the film. Often, but not always, S is
`constant and independent of &, so that U increases linearly
`with 5. Figure 1 shows a section of film of thickness 5 and of
`unit surface area, i.e., unit length and width. The energy U is
`effectively the energy per unit area, as shown by the shaded
`section at the right of the figure. This presentation will show
`that the mechanical stability of the film and substrate
`requires that U be less than a critical value U^ and that U^ is
`determined by the surface energy y. The surface energy y for
`film fracture is illustrated in Figure 1, where the two new
`surfaces formed by the fracture contribute an increase of 27
`(ergs/cm ) to the total surface energy.
`
`IBM J. RES. DEVELOP. VOL. 31 NO. 5 SEPTEMBER 1W7
`
`ERIK KLOKHOLM
`
`S85
`
`MICRON ET AL. EXHIBIT 1046
`Page 1 of 7
`
`

`
`Td = 7s + Tf.
`
`(2)
`
`where the subscripts refer to delamination, substrate, and
`film, respectively, and y^ is the increase in surface energy
`upon delamination.
`For film-substrate cotnbinations where the adhesion is
`not perfect, as shown schematically in Figure 3, 7^ requires
`further definition. In this instance there is assumed to be a
`surface energy y^ already expended, which is a measure of
`the degree of adhesion [4]. For instance, if 7; = 0, then the
`adhesion is for the film-substrate of Figure 1; on the other
`hand, if tj = T, + tf. then 7^ = 0, since in this case no
`"new" surface energy is formed because the film and
`substrate were never physically joined. So, for imperfect
`adhesion,
`
`7d = % + 7 f- 7i.
`
`(3)
`
`Values of 7 (in ergs/cm ) range from =5000 for diamond
`and =1000-3000 for metals to =500 for glasses
`A section of film of thickness 5 and of unit surface area, i.e., of unit
`length and width. The shaded area at the right of the figure indicates the
`(or glass-like materials) [5].
`elastic energy per unit area U. A cracli is shown which contributes ly to
`For the tensile fracture of thin films, the well-known
`the total surface energy via the formation of two new surfaces.
`Griffith fracture theory will be used [5]. A less well-known
`theory, that of Barenblatt, will be applied to the conditions
`for delamination [6]. In the derivations, v is neglected since
`its omission will not significantly affect the results. Although
`the derivations are phenomenological, and imperfect in
`detail, they have the advantage of being simple in concept
`and application.
`
`Film
`
`Substrate
`
`A perfect film-substrate interface having maximum film-substrate
`adherence.
`
`For film-substrate delamination the definition for the
`surface energy requires modification. Consider Figure 2,
`where the film and the substrate form a contiguous and
`perfect joint at the interface; if the film delaminates from the
`substrate (Figure 6, shown later), then the surface energy
`gained is
`
`5i6
`
`Film fracture
`Figure 4 shows schematically a film fracture for a film firmly
`bonded to the substrate; the crack is essentially
`perpendicular to the film plane and does not penetrate, or
`cause film separation fi-om, the substrate at the intersection
`of the crack and the substrate. Cracks of this kind are caused
`by tensile stress. The relation between the critical film
`fracture stress S^ normal to the crack plane and the Griffith
`crack length h [5] for the geometry of Figure 1 is
`
`lEy
`h
`
`(4)
`
`The probability of film fracture increases as S^
`approaches and exceeds the value defined by the parameters
`on the right side. By squaring both sides and rearranging
`terms, Equation (4) becomes
`
`= 27.
`
`E
`
`The critical energy U^ for fracture is therefore
`
`Slh
`l / = -^ = 27.
`
`(5)
`
`(5a)
`
`For the crack shown in Figure 1, it is intuitively plausible
`that i = h, and substituting 5 for h in Equation (5a) yields
`the following relation;
`
`ERIK KLOKHOLM
`
`IBM J. RES. DEVELOP. VOL. 31 NO. 5 SEPTEMBER 1987
`
`MICRON ET AL. EXHIBIT 1046
`Page 2 of 7
`
`

`
`Table 1 s.
`for two values of 7 and S.
`
`7
`
`500
`2000
`
`d^ at ; o'
`(Mm)
`
`10
`40
`
`i^atlO"
`(/iffl)
`
`0.1
`0.4
`
`a^q.u,.
`
`(6)
`
`Equation (6) demonstrates the supposition that the
`criterion for film fracture is U> t/,, and t/, is governed by
`the magnitude of the surface energy y while U is dependent
`upon the product 5S . There is, then, for U, when 5 is
`constant and independent of 5, a critical film thickness 5^ at
`which U exceeds [/,. We therefore define 5^ by the condition
`U — t/,, and 5^ is then given by the following equation:
`
`2Ey
`
`&.="
`
`(6a)
`
`Film fracture will occur when 5 S 8^.
`On the other hand for constant b there is a critical value
`of film stress at which film fracture will take place as S
`approaches and exceeds S^; namely. Equation (4). In practice
`S tends to be independent of 5 [2], and therefore S is
`generally the critical variable for film fracture. We can
`calculate the relative magnitudes of 5^, by using Equation (6a)
`with two typical values of 5—10 and 10 dynes/cm (which
`cover the range of observed film stresses) and for 7 = 500
`and 2000 ergs/cm . We further assume that £ = lO'
`dynes/cm . The results of the calculations are shown in
`Table 1. These results illustrate that, at constant S, 5^ is
`directly proportional to 7. For the typical values of 7 used,
`6^ varies from 10 to 40 /nm for 10 d/cm , but for lO' d/cm
`the &^ are 1/100 of the values for the smaller stress. This is
`due to the dependence of i^ upon 5 . If we assume that
`8^ = 1 Mm, then 5^ is = 3 • lO' and 6 • lO' for 7 = 500 and
`2000 ergs/cm , respectively.
`The values assumed for E, 7, and S are typical of many
`thin-film materials, so the data of Table 1 are fair
`approximations for the limits of mechanical stability of
`various films and substrates [7].
`The photographs of Figure 5 illustrate the critical
`dependence of the film fracture criterion upon 8 [8]. The
`upper photograph is a top view and the lower an oblique
`view. These permalloy films were deposited in the same
`pump-down by an electron gun evaporation source through
`a shuttered mask. Note the severe film fractures from
`column a to column d, and that even in column e there are
`indications of film cracking. The adhesion of these films to
`the substrate is very strong and, after film fracture, substrate
`fracture also occurred underneath the films in columns a, b.
`
`Imperfect film-substrate interface with imperfect film-substrate
`adhesion; adhesion exists only in contact areas.
`
`A "Griffith" film crack. The crack does not penetrate the substrate
`and is essentially normal to the film-substrate interface.
`
`c, and d. The film thicknesses are as follows: column a,
`8= 1.2 iim; column b, 5 = 1 fim; column c, 5 = 0.8 fim;
`column d, 5 = 0.6 fim; column e, 6 = 0.4 Mm; and column f,
`8 = 0.2 fitn. The tensile stress in all of these films is =5 • lO'
`d/cm , and from Figure 5 the critical 8 appears to be at
`column e, where 8 = 0.4 ^m. Substituting these in Equation
`(6a) indicates that 7 =: 1000 ergs/cm^, which is in fair
`agreement with the preceding discussion.
`
`587
`
`IBM J. RES. DEVELOP. VOL. 31 NO. 5 SEPTEMBER 1987
`
`ERIK. KLOKHOLM
`
`MICRON ET AL. EXHIBIT 1046
`Page 3 of 7
`
`

`
`mm mm
`H pgmmm
`
`fi! ill Si ll«.rHi •1
`'Msji-^'Mmm^
`
`mmmm
`frmmM
`
`Fracture and delamination of permalloy films: the upper photograph
`is a top view; the lower, an oblique view. The film thicknesses (in
`[xm) are 1.2 in column a, 1 in column b, 0.8 in column c, 0.6 in
`column d, 0.4 in column e, and 0.2 in column f. (Photographs
`courtesy of K. Y. Ahn, IBM Thomas J. Watson Research Center.)
`
`Film delamination
`The separation of the film from the substrate, as illustrated
`in Figure 6, is also a fracture phenomenon; however, the
`Barenblatt [6] rather than the Griffith fracture model is more
`appropriate. In the Griffith model the crack tip has a small
`but finite radius of curvature, while in the Barenblatt picture
`the crack has the shape of a cusp, and is very much Uke that
`of the delamination "crack" in Figure 6. The basic
`parameter in the Barenblatt model is a modulus of cohesion
`K and is defined by the energy
`
`delamination crack formation. The constant K [6] is
`approximately defined by
`
`K'^
`
`irEy
`(1 - A'
`(In the following v will again be neglected.)
`Substituting for K in Equation (7), then,
`
`U,
`
`T-
`
`(8)
`
`(9)
`
`For the delamination model, substitute y^ for y in Equation
`(9), and then the critical energy for delamination is defined
`by
`
`t/„
`
`-Yd-
`
`(10)
`
`Equation 10 is the delamination analog of Equation (5a) for
`fracture. As the film elastic energy U approaches and exceeds
`[/,j, the probability of film delamination becomes
`increasingly greater; hence, the criterion for delamination is
`
`U-
`
`E
`
`«"
`
`The critical thickness for delamination is then
`
`and similarly the critical delamination stress is
`
`(11)
`
`(11a)
`
`(lib)
`
`K\\
`
`v)
`
`VK =
`
`ET
`
`588
`
`required to initiate separation of the two surfaces by
`
`(7)
`
`S
`
`Equations (11), (11a), and (1 lb) are of the same form as
`Equations (6), (6a), and (6b) for fracture; however.
`
`ERIK KLOKHOLM
`
`IBM J, RES. DEVELOP. VOL. 31 N O. 5 SEPTEMBER 1987
`
`MICRON ET AL. EXHIBIT 1046
`Page 4 of 7
`
`

`
`Equations (11), (1 la), and (1 lb) contain the important
`variable 7-. As mentioned previously, 7; depends upon the
`degree of adhesion of the film to the substrate, and is 0 for
`perfect adhesion (cf Figure 2), but is a maximum =^yf + 7^
`when adhesion of the film to the substrate is very poor.
`Moreover, 7. is not necessarily a material constant, but is
`largely dependent upon the physical and chemical nature of
`the substrate, namely, substrate surface cleanliness,
`smoothness, ambient deposition conditions, etc.
`
`Discussion
`From Equation (6) and (11) some general inferences with
`regard to film fracture and delamination can be drawn. If
`U^(U^= U^), then film fracture and delamination could
`occur simultaneously, as in Figure 7. For U^ > U^,
`delamination will probably occur before fracture, and if
`U^ < t/^j, the films will fracture before delamination. These
`considerations depend upon the relative values of 7 and 7^.
`For a given film material 7 is essentially a known constant,
`but 7j depends upon the degree of adhesion as determined
`by 7i, in Equation (3). For films that adhere strongly,
`7j = 27 probably satisfies the conditions for simultaneous—
`or nearly simultaneous—fracture and delamination. There is
`some evidence for this in Figure 5. Films that adhere weakly
`(for instance, Al, Cu, or Au on glass or sihcon substrates)
`delaminate long before film fracture occurs. Metallic films
`for the most part delaminate before fracture, while dielectric
`films, glass, quartz, etc., tend to fracture before
`delamination.
`For films in compression, a common mechanical
`instability is "blistering," as illustrated in Figure 8 [5]. The
`blisters are often circular and of uniform size and
`distribution. Occasionally, film fracture occurs at the
`periphery of the blister. The criterion for blistering is
`described by Equation (11). For distributed bhstering, 7^,
`must be smaller inside the blister areas than outside,
`therefore U> U^, but outside of the blisters, U< U^. The
`lack of adhesion in the interior of the blister can be caused
`by the presence of a foreign substance, substrate
`imperfections, etc.
`If 7j values are equal to 27 of Table 1, then similar d^
`would be obtained for the same range of S. Hence, the same
`conclusions as drawn for fracture can be applied to
`delamination.
`The application of the simpler aspects of fracture theory
`shows that the criterion for film-substrate mechanical
`stability is governed by 7, 7^, S, and S, and that the
`equations which describe the criteria for fracture and
`delamination have the same form. The surface energy 7 of
`film and substrate materials is approximately known, but y^
`may not be known a priori since it is dependent upon
`7;—an unknown quantity. There is also a dependence of
`t/, upon E, but the variation off among common materials
`is only from about 0.5 to 2 • lO'^ d/cm^ and a value of
`
`Simultaneous fracture and delamination.
`
`Blister formation by compressive film stress.
`
`£• == 10 is a reasonable approximation for a wide range of
`materials. The equations which describe the criteria for
`fracture and delamination can be combined into a single
`equation as follows:
`
`1
`
`10"
`
`27
`where S is in units of 10 dynes/cm . By substituting for S
`values of 'A, V2, 1, 2, 4, 7, 10, Equation (12) can be plotted
`on a log-log scale, as shown in Figure 9. The result is a
`straight Une which covers the common range of 5 in thin
`films as well for 7, and is a universal curve describing the
`
`(12)
`
`589
`
`IBM J. RES. DEVELOP. VOL. 31 NO. 5 SEPTEMBER 1987
`
`ERIK KLOKHOLM
`
`MICRON ET AL. EXHIBIT 1046
`Page 5 of 7
`
`

`
`27 SS 7^ SS i(X)0 ciis/cm . This shows that film-substrate
`adhesion of Fe/Ni films deposited at =25°C is somewhat
`better than Al, Cu, and Au, but y^ is somewhat smaller than
`anticipated. However, for films deposited at substrate
`temperatures of =a200'C, the films fracture at (Si) = lO' at
`6 = 1 iim—S « 10 • 10' (see Figure 5), Again from Figure 9,
`7 = 5000 ei^/cm^, and since the film fractured, the
`adhesion was very good; namely, 7^ is laiie and y^ very
`small. These observations have phenomenological
`consequences; i.e., films of metals with melting temperatures
`<1500°K do not adhere as well as metals with melting
`temperatures >1500*K when deposital omo substrates at
`=25°C; however, increasing the substrate temperature
`improves film-substrate adhesion.
`
`«r-
`
`0.10
`
`1.0
`
`10
`
`Critical stress (10 dynes / cm j
`
`Figure 9
`
`Critical stress S^ plotted against the ratio of the critical thickness 8^ to
`twice the surface energy y.
`
`^^^mm
`
`^ ^ ^^
`
`Conclusion
`By using the simpler aspects of fracture theory, it has been
`shown that the criterion for film-substrate mechanical
`stability is governed largely by 7 and/or 7^. These surface
`energies are dependent upon the nature of the film and
`substrate materials; 7, and 7, are essentially known
`quantities; however, y^ may not be known a priori since it is
`dependent upon 7^—an unknown quantity.
`From another viewpoint, film-substrate instabilities are
`caused by film stresses which more often than not are nearly
`independent of film thickness. Therefore, the elastic eneiBy
`stored in films increases linearly with film thickness.
`Eventually, this energy becomes so large that it cannot be
`contained by the internal bonds of the film material and/or
`the bonds that hold the film to the substrate. These bonds
`then part catastrophically with concomitant stress relief. The
`surfacx energies, 7,. tr(and 7^), are a measure of these bond
`strengths—the larger the 7, the greater the bond strength.
`To avoid catastrophic film failure (S^&} must be reduced
`conditions for the mechanical instabihty of thin films
`in some manner. Reducing S seems obvious, but the means
`deposited on substrates. (For delamination, y^ = 27.) In this
`may not be available or practical. There may be instances
`figure, when S = 1, the ordinate value is also = 1 (in units of
`when fracture or delamination cannot be avoided and
`10"''), and from this we can determine 6^ for 7 = 500 and
`alternative manufacturing methods and/or materials for a
`2000, and these &^ are of course identical to those in Table 1.
`given thin-film device must be determined.
`It has been the author's observation [3], from the in situ
`measurement of stress in thin ilms deposited (by
`evaporation at 25'C substrate temperature) on glass
`substrates, that Al, Cu, Au films delaminated at values of
`the product of the stress and film thickness (SS) of about
`10"* dynes/cm at 5 ==: 0.1 nm. From Figure 9, SJ2y =
`0.25 • 10"*, which indicates that y^ = 40. Since the
`maximum y^ should be = 1500,7j» 7^ + 7^, which is
`indicative of the poor adhesion in these films. On the
`other hand, thin films of Fe, Ni, Co, and alloys of these
`metals, deposited by evaporation (at =25°C substrate
`temperature), delaminated at (Sd) = lO' dynes/cm at
`5 =s 0.1 ^m—5 = 10 . 10' dynes/cm . From Figure 9, for
`(Sa)= 10*;5 = 0.!^m;
`S
`27 = 10'
`
`References
`1. For a review of stress in thin fllms see R. W. Hoffman,
`Mechanical Properties of Non-Metallic Thin Films, Nato
`Advanced Study Institutes, Series B, Plenum Publishing Co.,
`New York, 1976, Vol. 14, pp. 273-354.
`2. (a) E. Klokholm and B. S. Berry, "Intrinsic Stress in Evaporated
`Metal Films," J. Electr. Soc. 118, 824 (1968). (b) E. Klokholm,
`"Intrinsic Stress in Evaporated Metal Films," /. Vac. Sci.
`Technol. 6,138 (1969). (c) E. Klokholm and W. C. Pritchett,
`"Residual Str^ses in SLT Thin Films," Research Report
`RC-1623, IBM Thomas J. Watson Research Center, Yorktown
`Heights, NY, 1966.
`3. J. J. Prescott, Applied Elasticity, Dover Publications, New York,
`pp.187, 188(1961).
`4. J. W. Matthews, E. Klokholm, and T. S. Plaskett, "Etefects in
`Magnetic Garnet Films," AIP Conf. Proc. 10, 276 (1973),
`5. A. Kelly, Strong Solids, Clarendon Press, Oxford, 1976.
`6. O. I. Barenblatt, "Mathematical Theory of Equilibrium Cracks in
`Brittle Fracture," Adv- Appl. Mech. 7, 55-131 (1962).
`
`590
`
`(13)
`
`ERIK KLOKHOLM
`
`IBM J. RES. DEVELOP. VOL. 31 NO. 5 SEPTEMBER 1987
`
`MICRON ET AL. EXHIBIT 1046
`Page 6 of 7
`
`

`
`7. For an example see J. W. Matthews and E. KJokholm, "Fracture
`of Brittle Epitaxial Films Under the Influence of Misfit Stress,"
`Mater. Res. Bull. 7, 213-222 (1972).
`8. K. Y. Ahn, "Magnetic Properties of Vacuum Evaporated Thick
`NiFe Films," Research Report RC-1470, IBM Thomas J. Watson
`Research Center, Yorktown Heights, NY, 1965.
`
`Received March 24, 1987: accepted for publication April 13,
`1987
`
`Erik Klokholm IBM Corporate Headquarters, 500 Columbus
`Avenue, Thornwood. New York 10594. Dr. Klokholm is currently an
`Associate Editor of the IBM Journal of Research and Development.
`He joined IBM at the Thomas J. Watson Research Center in 1962 as
`a Research staff member. Initially, he did research on
`superconducting thin films, and eventually worked on magnetic thin
`films for memory and thin-film head applications. As part of the
`latter work he developed instrumental techniques for the in situ
`measurement of film stress during deposition. This work led to a
`model which explained the origin of intrinsic stress in evaporated
`metal and alloy films. In 1973 he joined the Manufacturing Research
`Laboratory at Yorktown Heights, New York, as manager of the thin-
`film head group, and continued in that position until 1984, when he
`joined the Journal staff as an Associate Editor. Dr. Klokholm
`obtained an S.B. in physics from the Massachusetts Institute of
`Technology, Cambridge, in 1951 and a Ph.D. from Temple
`University, Philadelphia, Pennsylvania, in 1960. He received an IBM
`Outstanding Contribution Award for his work in bubble domain
`memory films and a fourth-level Patent Award. Dr. Klokholm is a
`member of the New York Academy of Sciences.
`
`IBM J. RES. DEVELOP. VOL. 31 NO. 5 SEPTEMBER 1987
`
`ERIK KLOKHOLM
`
`591
`
`MICRON ET AL. EXHIBIT 1046
`Page 7 of 7