The silicon integrated-circuits chip is built by contiguously embedding, butting, and overlaying structural elements of a large variety of materials of different elastic and thermal properties. Stress develops in the thermal cycling of the chip. Furthermore, many structural elements such as CVD (chemical vapor deposition) silicon nitride, silicon dioxide, polycrystalline silicon, etc., by virtue of their formation processes, exhibit intrinsic stresses. Large localized stresses are induced in the silicon substrate near the edges and corners of such structural elements. Oxidation of nonplanar silicon surfaces produces another kind of stress that can be very damaging, especially at low oxidation temperatures. Mismatch of atomic sizes between dopants and the silicon, and heteroepitaxy produce another class of strain that can lead to the formation of misfit dislocations. Here we review the achievements to date in understanding and modeling these diverse stress problems.

The phenomena of the formation of stacking faults and the enhanced diffusion during the oxidation of silicon are shown to be closely related and to have a common cause. A model is presented which at once can consistently explain various aspects of both phenomena; in particular, it is capable of explaining the crystal-orientation dependence of these phenomena and the parabolic growth of stacking faults. The model envisages a small incompleteness (∼ 10−3) of oxidation, producing silicon interstitials. A concept is introduced that these excess interstitials, as they supersaturate the lattice, will undergo surface regrowth. The rate of interface regrowth is proportional to the density of surface kinks, which is in turn dependent on the surface orientation. The dependence is described. Quantitative analyses are given for the excess interstitials, the growth of stacking faults, and the enhancement of diffusion. The analyses also show that the stacking-fault embryos are formed within a very short time of the start of oxidation, usually less than 1 sec, consequently leading to uniform stacking-fault size. The occasionally observed variation in the size of bulk stacking faults is attributed to a continuous formation of stacking-fault nuclei (e.g., oxide clusters and precipitates). The absence of a surface regrowth would predict a 1/4 power law of stacking-fault growth, in contradiction of the experiments.

The problem of film-edge-induced stress in substrates has been analyzed self-consistently by allowing a distributed force in the film. The distributed force arises from the relaxation of the film strain, which is complementarily coupled to the substrate strain under the film force. The results are compared to those from a concentrated-edge-force approximation.

It is shown that the infrared absorption band at 1230 cm−1, observed under certain conditions of oxygen precipitation in silicon, is the LO mode of SiO2. The LO mode, which is normally infrared inactive, becomes infrared active under the condition of polarization of small (<0.36 μm) platelets in an appropriate dielectric matrix (silicon). Infrared absorption spectra of SiO2 particles of various shapes, imbedded in silicon, have been calculated. For platelet SiO2 precipitates, the spectrum shows an absorption band at 1215 cm−1, which is reasonably close to the observed band at 1230 cm−1. For SiO2 precipitates of other shapes the spectra do not exhibit this absorption band. Instead, they exhibit a slightly weaker primary absorption band at 1095 cm−1, the TO mode, and a very weak band at 1170 cm−1, which is a mixed mode of longitudinal and transverse optical phonons.

Two-dimensional infrared correlation spectroscopy as a probe of sequential events in the diffusion process of water in poly(ε-caprolactone)A multitype random sequential processThe effect of an internal electric field and the variation of equilibrium lattice vacancy concentration was incorporated into the continuity equations for the treatment of impurity diffusion in semiconductors. After the explanation of dominant mechanisms involved in the interactions, formulations of the sequential diffusion process and its solution are outlined and numerical results are given. It is shown that the base impurity profile generally experiences a strong retardation by the internal field, resulting in a pro£le much different from what is generally conceived. Important physical and process parameters of this effect are the extrinsicity factor a (defined as the ratio of impurity surface concentration to twice the intrinsic carrier concentration), the base to emitter diffusivity ratio, and the relative diffusion distance of the base initial profile and the emitter profile. Effect of interaction on the emitter profile is mainly due to the variation of vacancy concentration with doping concentration. In the cases considered, comparisons are made between interacting and noninteracting impurity profiles. One implication particularly emphasized is that sequentially diffused transistor profiles constructed by the superposition method can involve large errors even with accurate experimental data on the single diffused emitter and base profiles. The computed transistor profiles from a boron-arsenic sequential diffusion process, based on the model combining the effect of internal field and vacancy concentration variation, agreed well with the experimental results.