ABSTRACTThis work was concerned with comparing the relative effects of boron and phosphorus impurities on the solid phase epitaxial (SPE) regrowth rate of self-ion amorphized layers in silicon wafers with (100) orientation. We used previously reported data measured by in situ, high precision, cw laser interferometry during isothermal annealing for temperatures from 450°C to 590°C, and concentrations in the range from 7.8×1018 cm-3 to 5×l020 cm-3 for boron (NB), and from 5×l017 cm-3 to 3×1020 cm-3 for phosphorus (Np) impurities. The basis for the comparison was a recently developed model that extends the Spaepen-Turnbull model for silicon recrystallization to include ionization enhanced processes.The experimental data for bom boron and phosphorus exhibited the linear variation in regrowth rate expected for low concentrations of implanted hydrogenic impurities having a concentration-independent fractional ionization in amorphous silicon. In the linear range the relative enhanced regrowth rate produced by these impurities can be expressed as a product of their, relative fractional ionizations, and the relative amount the rate constant for reconstruction is altered by localizing an electron, or a hole, at the reconstruction site. Assuming that a localized hole and electron equally softened the potential barrier for reconstruction, the experimental results indicated that boron had an ?40 meV lower barrier to ionization in amorphous silicon than phosphorus.The variations in the SPE regrowth rates with higher concentrations of both implanted boron and phosphorus were well fit by quadratic equations, but with different curvatures (+ and - for B and P respectively). This result was interpreted to indicate that SPE regrowth was further enhanced by localized hole pairs, but retarded by localized electron pairs.
Analysis of Students’ Error in Solving Quadratic Equations Using Newman’s Procedure
