Analysis of crystal defects by simulation of x-ray section topographs

Abstract

This thesis is concerned with the simulation of the contrast in X-ray section topographs due to the strains induced in silicon single crystals by various types of technologically relevant crystal defect. A general introduction to the field of X- ray topography is presented, illustrating that this technique is well suited to the characterisation of defect induced strain in highly perfect crystals. A review of X-ray dynamical theory is given, culminating in Takagi's equations for a crystal containing a defect. Techniques for simulating X-ray section topographs, based on Takagi's equations, are discussed. Computer simulation of section topographs has been used throughout this work to deduce the microscopic strains from the X-ray topographic images. The volume of oxygen precipitates in MCZ silicon was found to increase linearly as lnT, where T is the annealing temperature of the sample. Results suggest that the vast majority of precipitates which survive to maturity are nucleated at approximately the same time, subsequently growing at the same rate. An industrial role for simulation in conjunction with experiment is proposed, in the evaluation of the precipitate depth and the deformation parameter, C, representing the precipitate strain magnitude. The technological relevance of these two quantities is discussed. The effect of surface relaxation on the structure of images due to precipitates has been investigated. The critical depth (_z(_crit)) at which the effect of surface relaxation became negligible was found to increase linearly with lnC. Simulations have been generated for crystals containing oxygen precipitate distributions, with denuded zones. Characteristic image features have been discussed. Studies on precipitate resolvability revealed that the critical separation for two precipitates to be just resolved increases linearly as lnC. An extensive study of intrinsic gettering has been undertaken, in terms of decorated dislocations. The strain distribution due to precipitate decoration was modelled by the cylindrical inclusion model. It was shown that even for very low precipitate strains, precipitate decoration is distinguishable from the associated dislocation by section topography. Hence, an industrial role is proposed for simulation, in conjunction with experiment, in the parameterisation of the strain induced by decorated dislocations. To fully explore the use of the cylindrical inclusion model in this way, the variation in the inclusion strain magnitude was determined as a function of the precipitate strain and density, and the size of the precipitate distribution. It was found that the strain magnitude of the equivalent cylindrical inclusion must increase more rapidly relative to the precipitate deformation parameter for low-order reflections than for high-order reflections. Decorated dislocations have been shown to be resolvable by section topography even in the most dislocation-rich sihcon samples. The industrial usefulness of this characteristic is discussed. A study was made of the critical deformation parameter, C(_crit), for decorated dislocations to be just resolved, as a function of the separation, k, of the dislocations. For k greater than about 45µm, the variation of In(C(_crit) with k was linear. For smaller separations, the linearity breaks down because of the increasingly important strain contribution due to the dislocations. The strains induced by oxide films and devices in the silicon substrates onto which they are formed have been investigated. Experimental section topographs of oxide edge regions and devices on silicon have been simulated, and the visibility of the extra set of fringes found in simulations by another worker has been examined. The variation in image structure with device position on the entrance and exit surfaces has been investigated. An absolute minimum on device width detectable by section topography of lµm has been found. However, this minimum was found to depend on device-induced strain, and for values of strain characteristic of contemporary devices, the minimum detectable device width was found to be at least 3.5µm. This is above the limits set by the geometric and other constraints of the experimental technique. A thorough study has been made of the cancellation of opposing strains due to opposite edges of a device. The total distortion induced by the device was found to be minimised by reducing the device width and increasing the force per unit length, 5, along the device edges. Quantitative information has been obtained on this process. It was found that the fractional increase in lattice parameter at a fixed point, due to device-induced strain, increases linearly with S, with increasing gradient for increasing device width. It was shown that the narrower the device, the faster the relative fall-off in fractional increase in lattice parameter with increasing displacement from one edge of the device.