Most common microdefects in Czochralski silicon, voids and dislocation loops, are formed by agglomeration of point defects, vacancies, and self-interstitials, respectively. Dynamics of formation and growth of the microdefects along with the entire crystal pulling process is simulated. The Frenkel reaction, the transport and nucleation of the point defects, and the growth of the microdefects are considered to occur simultaneously. The nucleation is modeled using the classical nucleation theory. The microdefects are approximated as spherical clusters, which grow by a diffusion-limited kinetics. The microdefect distribution at any given location is captured on the basis of the formation and path histories of the clusters. The microdefect type and size distributions in crystals grown under various steady states as well as unsteady states are predicted. The developed one-dimensional model captures the salient features of defect dynamics and reveals significant differences between the steady-state defect dynamics and the unsteady-state defect dynamics. The model predictions agree very well with the experimental observations. Various predictions of the model are presented, and results are discussed.
A study to understand the transport and kinetic effects in three-phase, acid-based wet etching of silicon has been accomplished. Reactants overcome the liquid-phase mass-transfer resistance and the kinetic resistance to complete the reaction. The gaseous bubbles formed by the reaction adhere to random sites on the surface and, thus, mask a fraction of the surface from the reactants. This bubble masking effect is modeled as the bubble transport resistance that acts in parallel with the liquid-phase mass-transfer resistance. These transport effects are lumped into an effective mass-transport resistance, which acts in series with the kinetic resistance. It is shown that the etched surface morphology is a function of the ratio of the effective mass-transport resistance to the kinetic resistance. A rough surface is a field of peaks and valleys. It is theorized that under mass-transfer influence, etch rates at peaks are higher than etch rates at valleys. Hence, the surface is chemically polished. It is shown that the polishing efficiency increases with increasing ratio of mass-transfer resistance to the kinetic resistance, reaches a maximum, and then decreases. Effects of mass-transfer and kinetics on the surface roughness and gloss are explained by both the developed phenomenological model and experimental data.
On page 176, Eq. 3 and the two sentences immediately following should read:µ ∝ e Ea µ /KT Since the viscosity is a transport property of the liquid, they claim that the temperaturen dependence of the viscosity can be a measure of the temperature dependence of mass-transfer rates. The argument can be valid in a limited context because the mass transfer rate decreases with increasing viscosity. However, the argument is not entirely valid because the mass-transfer coefficient is a function of many temperature dependent parameters other than viscosity.In addition, the descriptions of Fig. 4 and 6c given on pages 180 and 181, respectively, are in error. Correctly stated, they should be: Figure 4 shows the qualitiative dependence of the polishing efficiency (η pol ) on the ratio of the mass transfer resistance (R m,i ) to the kinetic resistance (R r,i ). The parameters (R m,i /R r,i ) and (R m,i /R r,i ) max , in general, should correspond to the same η pol . Figure 6c shows the qualitative dependence of the polishing efficiency on the ratio of the effective mass transfer resistance (Rm,eff,i) to the kinetic resistance (R r,i ). The parameters (R m,eff,i /R r,i ) and (R m,eff,i /R r,i ) max , in general, should correspond to the same η pol .
Microdefect distribution in a monocrystalline silicon wafer is identified by saturating the wafer with copper at a high temperature followed by copper precipitate growth through rapid cooling followed by surface polishing and subsequent microdefect-decorating etching. The decorated microdefect field consists of etch pits that are formed by the difference in the etching rates of the precipitate influenced region around microdefects, and the etching rate of the surrounding defect-free silicon. Interplay between liquid-phase mass-transport effects and surface kinetics plays a key role in the microdefect decoration. It is shown that the macrodecoration of microdefects is typically realized in the absence of significant effects of the liquid-phase diffusion. The developed phenomenological model leads to classification of etchants as either polishing or potentially decorating and to identification of conditions necessary for an efficient microdefect decoration. The competing effects of kinetics toward microdefect decoration and liquidphase transport toward surface polishing are quantified by theoretically derived solutions for the decorating efficiency and the polishing efficiency. Autoerosion of the microdefects by mildly polishing etchants is also quantified. Analytical expressions for the microdefect-decorating and microdefect-polishing conditions are presented. Finally, decorating and polishing etchants are experimentally identified from a group of etchants and the proposed theory is verified by experimental data.
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