Deep Levels and High Concentrations of Impurities in Silicon

Citation

Lee, Tsu-wei Frank (1975) Deep Levels and High Concentrations of Impurities in Silicon. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/j2rb-3s97. https://resolver.caltech.edu/CaltechTHESIS:10122021-201307143

Abstract

A study of the electronic levels associated with the divacancy in silicon is reported. The extended Hückel theory is shown to reproduce the band structure of silicon near the energy gap. The electronic levels of the divacancy are calculated by considering a periodic array of large unit cells each containing 62 atoms; a 64 atom perfect cell with 2 atoms removed to form the divacancy. The results are found to be in qualitative agreement with the results of EPR and infrared absorption measurements.

A theory of the variation of conduction electron density with the temperature for various impurity concentrations is presented. In addition to previously noted effects of conduction band edge lowering and screening of the impurity potential by the conduction electrons, the influence of a finite energy transfer integral and spatial fluctuation in the potential are included. The results show that for N_D ≲ 10¹⁷ cm^-3 silicon one must not view the activation as occurring between a single impurity level and a well defined conduction band edge, but must include the broadening of the impurity level and tailing of the conduction band density of states, Calculations for the shallow donors P, Sb, and As in Si are found to be in satisfactory agreement with experiment.

Hall and sheet resistivity measurements as a function of temperature combined with layer removal have been used to study Si implanted with Te at energies up to 220 KeV. At low doses (≲ 4 x 10¹² cm^-2), Te has a donor level with 140 meV activation energy. The activation energy decreases at higher Te doses and is approximately equal to zero for Te doses ≳ 10¹⁵ cm^-2. At high dose levels, the number N_s of conduction electrons is more than an order of magnitude below the number of Te cm^-2. High temperature anneal treatments followed by quenching did not produce a substantial increase in N_s suggesting that the formation of Te clusters was not responsible for the low value of N_s. Also channeling measurements indicated a high substitutional fraction. Based on differential Hall measurements on P-implanted samples, with and without Si pre-damage, we conclude that residual radiation damage is not a major factor. A theoretical calculation, which includes the effect of decrease of activation energy with increasing impurity concentrations, indicated that the number of conduction electrons could be much less than the number of implanted Te even though the apparent activation energy is almost zero. Although the results of theoretical calculation do not give quantitative agreement with the experimental results, they do confirm the changes in apparent activation energy with concentration.

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