Dielectric Properties of Semiconductors at Low Temperatures

The dielectric constant κ′ and the dielectric loss κ″ of p-type, n-type, and compensated Si have been studied at frequencies from 103 to 109 Hz and temperatures from 4.2 to 300 °K. At frequencies above 107 Hz, the κ′ decreases with temperature from 12.1 at 4.2 °K to 11.94 at 300 °K. In this frequency region, electronic polarizability of Si only is observed. At frequencies below 107 Hz the atomic polarizability of dopants (or impurities) is predominant. In this frequency range the κ′ and κ″ show strong variation with temperature and depend on the matrix material, the dopants, and frequency. At lowest temperatures the dopants are inactive and the κ′ corresponds to that at high frequency. By increasing the temperature, dipoles are activated and correspondingly, κ′ and κ″ are changed. Within about 10 °K, the κ′ reaches a maximum value and then remains constant, while the κ″ shows a relatively sharp maximum at the temperature where the κ′ curve goes through inflection. The temperature of κ″ maxima are for Sb, 18.0, 19.5, 21.5, and 23.5 °K; for B, 22, 24, 27, and 29 °K; for P, 25, 29, 33, and 38 °K; for B + P (compensated), 27, 31, 36, and 42 °K. The °K numbers correspond to the frequencies 103, 104, 105, and 106 Hz. The variation of κ′ and κ″ with frequency and temperature is explained by the Debye relaxation theory. From the relation of frequency and temperature of κ″ maxima, the following activation energies have been obtained: for Sb, 0.0431 eV; for B, 0.0410 eV; for P, 0.0427 eV; for B + P, 0.0431 eV. Our activation energy data correspond quite closely to the published data obtained by optical activation for the same dopants. In a very pure sample, 30 000 Ω cm, three κ″ maxima have been observed which may correspond to three excited levels. Some preliminary results for Ge, GaAs, and CdS are also given. Our results indicate that dielectric measurements are very suited for the study of semiconductors.