The Effect of Spin-Dependent Donor Cluster Polarizabilities on the Magnetocapacitance of N-Type Silicon
Abstract
Magnetocapacitance studies have been employed to determine the variation of the donor polarizability contribution to the dielectric constant in n-type silicon with magnetic field, temperature, and donor concentration. Silicon samples with phosphorus concentrations ranging from 9 x 10('16)/cc to 1.0 x 10('18)/cc, as well as Si:As samples with 1.4 x 10('17)donors/cc and 2.5 x 10('18)donors/cc, were studied in the temperature range from 30 mK to 4.2 K at fields up to 19 tesla. Experimental results show the donor contribution varying as B('2) at low fields and B('n) at high fields, with n varying with concentration between .5 and 1.2. The low-field region shows a 1/T('n) dependence with n ranging from 1 to 3, with a much weaker temperature dependence at high fields. The magnitude of the field dependence is larger than expected for diamagnetic effects, isotropic, and smaller in Si:As than in Si:P at comparable concentrations, fields, and temperatures. A donor pair model, utilising spin-dependent polarizabilities, is presented which predicts a low-field (B/T)('2) region, weakening temperature dependence as the field increases, and high-field behavior determined by cluster diamagnetic effects. The calculation is extended to clusters of three donors. The question of donor cluster statistics has been studied using ESR donor cluster spectra in Si:P (3 x 10('16)/cc < N(,D) < 4.8 x 10('17)/cc) and Si:As (1.4 x 10('17)/cc < N(,D) < 1.0 x 10('18)/cc). The ratio of the integrated intensity of the outer hyperfine lines to the total integrated intensity is found to vary exponentially with donor concentration, consistent with the predictions of Poisson statistics. By partitioning a system of computer generated donors, requiring each donor in a cluster interact "strongly" with at least one other donor in the cluster, topological and cluster -cluster interaction effects are explored. Results of ESR studies allow explicit results to be calculated from the cluster polarizability expressions, with good qualitative agreement. Direct observation of spin-dependent effects in donor polarizabilities was attempted by monitoring changes in capacitance in Si:P samples as relative spin-state populations were changed via saturation of ESR lines. Results are discussed in terms of relaxation effects and pair polarizability contributions.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- June 1984
- Bibcode:
- 1984PhDT........29N
- Keywords:
-
- ESR;
- RESONANCE;
- SEMICONDUCTOR;
- Physics: Condensed Matter