Influence of Defects on the Splitting of the Acceptor Ground State in Silicon
The distribution of strain fields from specified defects in otherwise pure silicon crystals is reflected in the resulting distribution of splittings E of the partially orbitally degenerate г8 ground state of effective mass acceptors. The spectral density N(E) can be probed by resonant scattering of hv = E ultrasonic  or 3.8 kT ≅ E thermal phonons . The results of both methods (in the following: α (v) and κ (T)) are compared for Si (B) and Si (In) crystals containing definite amounts of C and 0 [Tab.1]. Monte Carlo calculations (M.C.) for point defects and for 60° dislocations in Si (isotropic approximation) have been made to obtain N(E) as well as D1 (E), the latter being the mean coupling constant of a specified phonon (L,T1,T2, , , ) to splittings at E. This average coupling for all 9 types of phonons practically does not depend on E and therefore presumably also for the thermal phonons. Thus, though in both experiments D 1 2 (E)·N(E) is measured the form of N(E) is preserved and D1 can be estimated by integrating over the whole distribution normalizing with na=∫N(E)dE. The calculated distribution for point defects derives from Lorentzians and from Gaussians for dislocations. Fig.1 shows D 1 2 ·N(E)/ na for Si (B) crystals with various concentrations of point defects from α (v). Analysis shows that only for the crystal with the highest concentration of point defects (S 80) D 1 2 ·N(E)/ na can be fitted by the calculated “Lorentzian”.
KeywordsPoint Defect Monte Carlo Calculation Calculated Distribution Resonant Scattering Isotropic Approximation
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