Misfit Strain Relief Beyond the Critical Thickness Using Curvature Measurements and in Situ Characterization of the Magn
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lao - aI
17= •
al
,
(1)
where as and ar are the bulk equilibrium lattice parameters of the substrate and film, respectively. In the case of Ni/Cu, rI = 0.026. The most significant way in which this strain is relieved is through the formation of dislocations at the interface. These dislocations act to relieve misfit strain such that the overall film strain is equal to: b' e --o--•, 265 Mat. Res. Soc. Symp. Proc. Vol. 356 © 1995 Materials Research Society
(2)
where b' is the magnitude of the component of the Burgers vector in the plane of the interface and perpendicular to the dislocation line and S is the spacing between dislocations. Strain relief through misfit dislocation formation has been described by several authors[ 1,2,3], based on a model by Matthews and Blakeslee.[1] The model is based on an energy balance between elastic strain energy within the film and dislocation energy and therefore is a description of the thermodynamic equilibrium state of the system. This paper is concerned with behavior beyond the critical thickness at which misfit dislocations begin to form. As the film thickness increases, more dislocations move toward the interface to relieve misfit strain. The equilibrium dislocation spacing can be calculated by minimizing the total energy of the system. The following equation results [3]: S =~- n( 1 +
-Ln
(3 )
where h is the film thickness and v is Poisson's ratio. In practice, the equilibrium strain relief is rarely observed due to kinetic limitations to dislocation nucleation and motion. EXPERIMENT All films for this work were grown in a Perkin-Elmer MBE system using electron-beam evaporation. All films were deposited at room temperature. The focus of our attention is the (100) Ni/Cu interface. In order to obtain a single crystal Cu substrate, we deposited Cu on Si (100) wafers to a thickness of 2000A. The film was fully relaxed at this thickness as determined using x-ray diffraction and wafer curvature measurements. Ni films of thickness ranging from 15 to several hundred Angstroms were deposited on the Cu surfaces. Magnetic anisotropy was measured in situ by MOKE.[4] Some typical M-H loops are shown in Figure 1. Ex situ structural analysis consisted of two measures of misfit relaxation conducted in tandem. The first was measurement of substrate curvature; the second was made using plan-view TEM to measure the average spacing between misfit dislocations. Curvature measurements were made using a WYKO optical interferometer. In this device, light is reflected simultaneously off the wafer and an internal reference flat. The resulting optical interference pattern is used to determine the optical path length difference between the wafer and the flat, giving a profile of the wafer surface. This profile is then fit to a sphere to give a radius of curvature of the wafer. The change in curvature of a wafer can be related to the strain in the film using a modified version of the equation originally developed by Stoney: [5] M, h2AK 6 = M- h.A "(4) Mm 6hm' where Mtli and M~i are the biaxial
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