The role of stress and diffusion in structure formation in semiconductors
Résumé
This dissertation addresses two aspects of the theory and simulation of stress-diffusion coupling in semiconductors. The first part is a study of the role of kinetics in the formation of pits in stressed thin films. The second part describes how atomic-scale calculations can be used to extract the thermodynamic and elastic properties of point-defects.
Recently, pit nucleation has been observed in a variety of semiconductor thin films. We present a model for pit nucleation in which the adatom concentration plays a central role in controlling the morphological development of the surface. Although pits relieve elastic energy more efficiently than islands, pit nucleation can be prevented by a high adatom concentration. Three-dimensional islands act as adatom sinks and the lower adatom density in their vicinity promotes pit nucleation. Thermodynamic considerations predict several different growth regimes in which pits may nucleate at different stages of growth depending on the growth conditions and materials system. When kinetics are taken into account, the model predicts a wide range of possible morphologies: planar films, islands alone, island nucleation followed by pit nucleation, and pits alone. The model shows good agreement with experimental observations in III-V systems given the uncertainties in quantifying experimental parameters such as the surface energy.
The same stresses which lead to the nucleation of surface features can have a significant effect on the stability of dopant profiles by altering diffusivities and by inducing chemical potential gradients. We perform an extensive set of empirical calculations regarding a simple model point-defect, a vacancy in the Stillinger Weber model of silicon. In the context of these calculations we devise a method to extract the strength of the elastic relaxation in the vicinity of the defect. This quantity is extracted from the leading order term which must be evaluated sufficiently far from the defect and the boundaries. It is also directly related to the formation volume, the thermodynamic quantity that couples the defect free energy to the externally applied stress. We propose that this method of extracting the formation volume is more accurate than a direct measurement of the surface relaxation for large system sizes.
Recently, pit nucleation has been observed in a variety of semiconductor thin films. We present a model for pit nucleation in which the adatom concentration plays a central role in controlling the morphological development of the surface. Although pits relieve elastic energy more efficiently than islands, pit nucleation can be prevented by a high adatom concentration. Three-dimensional islands act as adatom sinks and the lower adatom density in their vicinity promotes pit nucleation. Thermodynamic considerations predict several different growth regimes in which pits may nucleate at different stages of growth depending on the growth conditions and materials system. When kinetics are taken into account, the model predicts a wide range of possible morphologies: planar films, islands alone, island nucleation followed by pit nucleation, and pits alone. The model shows good agreement with experimental observations in III-V systems given the uncertainties in quantifying experimental parameters such as the surface energy.
The same stresses which lead to the nucleation of surface features can have a significant effect on the stability of dopant profiles by altering diffusivities and by inducing chemical potential gradients. We perform an extensive set of empirical calculations regarding a simple model point-defect, a vacancy in the Stillinger Weber model of silicon. In the context of these calculations we devise a method to extract the strength of the elastic relaxation in the vicinity of the defect. This quantity is extracted from the leading order term which must be evaluated sufficiently far from the defect and the boundaries. It is also directly related to the formation volume, the thermodynamic quantity that couples the defect free energy to the externally applied stress. We propose that this method of extracting the formation volume is more accurate than a direct measurement of the surface relaxation for large system sizes.
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