Surface Science 162 (1985) 585-590 North-Holland, Amsterdam
I N T E R F A C I A L S T R E S S E S IN T H I N M E T A L L I C F I L M S
C. CHEFI, F. H I L A and A. EL H I L l lztboratoire de Microscopie Electronique, Dbpartement de Physique. Facultb de.~ Scwnces de Tunts, Carnp,~ Untversttaire, Turns. Tumsie
and M. G I L L E T Laboratotre de Mtcroscopie et Diffracttons Electroniques, Equtpe de Recherche assoctbe au UA 797. Faculti" des Sciences et Techniques de Saint Jbrbme, Rue ttenri PoincarC F- 13397 Marsetlle Cedex 13, France
Received 1 April 1985; accepted fi~r publication 30 May 1985
This work is an experimental contribution to the study of stresses in interfaces between a thin film and its substrate. Two systems were investigated Cu/Mo and Ti/Mo. During the deposit, the deflections of the system deposit-substrate are measured as a function of deposit thicknesses by means of an optical system and the interfacial stresses are calculated with the stress-deflecLion relations established by Stoney (m~xiified by Brenner and Hollond). The results are discussed in relation of the misfit and the interracial configuration.
1. Introduction It is well k n o w n that the structure and the properties of thin films deposited on a substrate are affected by the interface between the deposit and the substrate. Lattice a c c o m m o d a t i o n mechanisms cause internal stresses at the interface. These stresses can be relaxed in different ways, one of which is the macroscopic d e f o r m a t i o n of the substrate and its coating resulting in the b e n d i n g of the system in an analogous m a n n e r to that observed in a bimetallic system. This p h e n o m e n o n can be used for investigating the stresses in metallic couples. If the substrate is a flexible ribbon, the b e n d i n g due to the deposit can be related to the stresses giving a simple experimental method for measuring these stresses. The internal stresses in thin films generally result from two p h e n o m e n a : the first one results from the different thermal expansion coefficients of the substrate and the deposit, the second one results from the a c c o m o d a t i o n of the deposit on its substrate. 0 0 3 9 - 6 0 2 8 / 8 5 / $ 0 3 . 3 0 '~; Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)
C. ('heft et al. / Interracial stresses in thin metalhc films
In this work, we study the mechanical stresses which a p p e a r in the interface d u r i n g the d e p o s i t growth of c o p p e r and t i t a n i u m on a m o l y b d e n u m substrate. Stresses p r o d u c e d by the thermal effect are negligible in c o m p a r i s o n of the g r o w t h stresses.
2. Experimental procedure and stress calculations C o p p e r and t i t a n u m are v a p o r - d e p o s i t e d on a flexible M o s u b s t r a t e (length L = 9 cm, width / = 0.5 cm and thickness t = 0.01 cm). T h e deposit thicknesses vary in a range of 5 0 - 1 0 0 0 ,h,. C r y s t a l l o g r a p h i c a l and mechanical characteristics of substrate and deposits are given in table 1 [8,9]. T h e M o substrates are previously cleaned in dilute solution of a m m o n i a , then heated in v a c u u m at 500 K for 30 min, a n d before the e v a p o r a t i o n cooled to r o o m temperature. The m o l y b d e n u m is e x p o s e d to a metallic flux either of Cu or of Ti at a 1 , ~ / s rate in a v a c u u m of 10 -6 Torr. T h e d e p o s i t e d quantities are c o n t r o l l e d with an oscillating quartz. T h e flexible s u b s t r a t e of M o is fixed at one end, the other one is free. W i t h an optical system, the position xqj of the free end is noted before the e v a p o r a t i o n ; after c o n d e n s a t i o n , the system (substrate + deposit) is bent and the free end of the substrate takes the p o s i t i o n x (above or below x~} d e p e n d i n g on the metal to evaporate). The deflection o is then m e a s u r e d for each d e p o s i t e d thickness, by the shift ( x - x o ) . The stresses in thin films were studied for the first time by Stoney  in the case of films d e p o s i t e d by electrolysis technique on a flexible substrate; the presence of stresses was e x p e r i m e n t a l l y i n d i c a t e d by the curvature 1 / r of the d e p o s i t - s u b s t r a t e system. The stresses as function of the deflection o were established a n d discussed by several a u t h o r s [2-7]. The stress in the d e p o s i t at the interface plane and in the direction parallel to the length of the substrate is give by the formula.
1 --~, 3L 2 d" where E is Y o u n g ' s m o d u l u s of the substrate, p Poisson's ratio of the substrate, a n d d the d e p o s i t thickness.
]'able 1 Crystallographical and mechanical characteristics of substrate and deposits Metal
Lattic parameters (,~.)
Young's modulus E (mean value) ( lOII dyn/cm 2)
Poisson's ratio J,
Mo Cu Ti
cc fcc hc
a = 3.140 a = 3.608 a = b = 2.951
34 12.7 11.6
0.305 0.324 0.34
c. Chefi et al. / Interfacial stresses in thtn metallK" filrrt~" 3. E x p e r i m e n t a l
Fig. 1 represents the variation of the deflection as a function of the film thickness d, respectively, for T i / M o and C u / M o . we note that for these systems, the variations of o have o p p o s i t signs. In both cases, the deflection o
_~ l l l l l •
~" ~ T ' ~
Fig. I. Variation of the deflections with deposit thickness d: (a) Ti/Mo, (b) Cu/Mo.
('. ('heft et al. / Interfact.I stresses in thin metallic Xtlms
varies linearly versus d. o varies more rapidly for T i / M o (fig. la) than for C u / M o (fig. lb). For T i / M o , the measurements are not possible with our optical system, when d exceeds 500 ,,~. For the couple C u / M o , we note a slope change for d > 400 A; the variation o = f ( d ) become then very weak and one can measure an average deflection nearly constant (o = 0.2 mm, for d > 600).
S ( l o m d y n e s / c m 2)
essa,| esSai 2
L _ °
Fig. 2. Variation of the stress S with deposit thickness d: (a) " l i / M o . (b) Cu/Mo.
C Chefi et al. / Interracial stresses in thin metalhcfilms
The internal stress S given by the relation (1) and calculated from deflection o is represented in fig. 2. For the couple T i / M o (fig. 2a), the stress S is extensive and decrease from 4 x 101° d y n / c m 2 to 3.25 × 101° d y n / c m 2 for 350 A, above this thickness, S is approximatively constant. In the case of the couple C u / M o (fig. 2b), the stress is compressive and increases with the thickness d. For d > 400 ,~, the change in the stress is very slow and this stress tend towards a limit value of about 0.5 × 101° d y n / c m 2.
The stresses developed in the two thin films deposited on the same substrate are of different kinds: extensive for T i / M o and compressive for C u / M o . This different behaviour can be qualitatively understood in terms of the accomodation of crystalline lattices at the interface. During the deposit growth, the deposit-substrate accommodation depends on several factors such as the structure of the materials in contact and their elastic constants and their interfacial bounding parameters . Other parameters may influence the generation of stresses: lattice imperfections, grain boundaries, electric forces and surface impurities . Nevertheless, stresses which appear in the thin films originate essentially from the accomodation of the two lattices at the interface. It has been established that up to a critical misfit this adaptation includes two stages [11 -13]: First, the deposit is strained elastically so that to accommodate the substrate (by compression or by extension according to the sign of the misfit). Then, the misfit accommodation is realized essentially by the generation of interfacial dislocations. Thus, the deposit grows with a nearly bulk crystalline parameter. In this mechanism, the adaptation deposit-substrate depends qualitatively on their interfaciai structure and their elastic constants. In both cases studied, Young's moduli are nearly equal and the phenomena can be related to the interfacial configuration. In our experiments, the substrate is a polycrystalline ribbon of Mo, but for the most part, it grains have a (001) plane parallel to their surface with  axis parallel to the length of the substrate and their sizes are about several microns, then we can consider that this substrate acts as a monocrystal oriented (001). In the case of Ti deposit, the growth is so that the plane (01.1) is parallel to the (001) plane of Mo with TilJMo and TillMo  the misfit is - 6 % and - 12%, respectively in the M o and M,, directions so accommodation of the deposit lattice on the substrate gives extensive stresses in the deposit. In the case of Cu deposit, the growth is so that the (001) plane is parallel to
('. ('heft et al. / Interfaoal ~tresses m thin metallic ftlms
(001)Mo and Cu I[Mo . The misfit is positive so the stresses in the deposit are compressive. Thus the experimental results agree well qualitatively with the interracial configuration resulting from the growth. In the first stage of the growth, the stresses are important and induce an elastic deformation of the deposit. Then they tend towards a limit when the interfacial misfit is mainly accomodated by interfacial dislocations. So interfacial dislocations play an important role in relaxing the internal stresses which occur in thin films grown on a substrate. They maintain the coherency between the substrate and the deposit by reducing the interfacial energy. It is expected that the stresses are quantitatively dependent of the deposit-substrate boundings which strongly influences the interfacial dislocation formation. Different boundings in T i / M o and C u / M o can explain the differences in the measured stresses in these two systems.
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