Dislocations in thin metal films observed with X-ray diffraction
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Dislocations in thin metal films observed with X-ray diffraction Léon J. Seijbel1 and Rob Delhez2 1 Netherlands Institute for Metals Research, Rotterdamseweg 137, 2628 AL Delft, Netherlands 2 Laboratory for Materials Science, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, Netherlands email: [email protected] ABSTRACT X-ray diffraction has been used to measure the stress, the crystallite size and the dislocation distribution in thin metal layers. By measuring two orders of a reflection, the contribution of the size distribution to the diffraction line broadening can be eliminated. A model equation is fitted to the strain Fourier coefficients of the diffraction line from which the dislocation arrangement can be obtained. For untextured nickel on steel or on silicon the dislocation densities have been obtained. It is demonstrated that for highly textured layers more information can be obtained than for untextured layers. It was found that a heated molybdenum layer on oxidized silicon showed only inclined screw dislocations.
INTRODUCTION Thin metallic films are used for many purposes. They almost invariably contain high, internal stresses. These stresses play an important role in the quality of these layers and may even lead to premature failure of the layer. However, the internal stresses may relax by the movement of dislocations. X-ray diffraction can be used for the determination of dislocations in thin films. Due to the imperfections in the lattice and due to the finite dimensions of the crystallites in the layer, the diffraction lines are broadened. Because dislocations are line shaped crystallographic defects and their motions are related to the crystal structure, the lattice deformation is different for different crystallographic directions. In the XRD-experiment this leads to reflection (HKL) dependent line broadening. In this paper we present a method to obtain both the dislocation distribution parameters and the average crystallite dimensions. As examples we use three different types of specimen: nickel layers sputtered on a silicon wafer, molybdenum layers sputtered on a silicon wafer, and steel with an electrolytic nickel coating.
THEORY The volume density E of the elastically stored energy in a crystal is generally written in the form [1]: Re E = CVGb 2 r ln (1) r0 where C is a parameter depending on the type of dislocation, V the crystal volume, G the shear modulus, b the Burgers vector, ρ the dislocation density, r0 the inner cutoff radius and Re the
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outer cut off radius belonging to the dislocation. When a diffraction line is broadened as a consequence of the presence of dislocations only, then it can be described in terms of Re and ρ. Denoting A as the Fourier transform of the diffraction profile, it is found that [2] A L = AS L AD L , (2) with AS the order independent particle size broadening and AD describing the order dependent strain (or distortion) broadening. Expressions for these coefficients as function of the correlation distance L are given b
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