Piezoelectric stiffening and attenuation of ultrasonic waves inn-type GaSb doped with sulfur

Abstract

Measurements of the velocity and attenuation of [110] [001] ultrasonic waves and of the velocity of [100] [001] waves have been made on single-crystal samples of sulfur-doped $n$-type GaSb down to liquid-helium temperatures. (The first and second set of digits in brackets give the crystallographic indices of the propagation and polarization directions of the waves, respectively.) It is found that the [110] [001] waves exhibit an attenuation maximum and an additional increase in velocity as the temperature is lowered sufficiently. The additional velocity increase begins at a temperature which depends on the sample involved and the measuring frequency, but the total increase is not dependent on these factors. Both the additional velocity increase and the attenuation maximum are understandable in terms of the decreased screening of piezoelectric fields as electrons freeze out of the conduction band into impurity levels. (Evidence for such freeze out is provided by resistivity and Hall-effect measurements we have made at a few temperatures.) Theoretical formulas of Hutson and White are found to fit our most accurate velocity and attenuation versus temperature data almost exactly when a semiempirical expression is used for the resistivity which suggests that the conductivity at low temperatures is controlled by levels closer to the conduction band than is the sulfur level whose ionization dominates the electrical behavior above 77 K. Comparison of the theoretical formulas with the velocity enhancement observed at lowest temperatures and the amount by which the maximum attenuation exceeds a small background value yields values of 0.170 \ifmmode\pm\else\textpm\fi{} 0.005 and 0.160 \ifmmode\pm\else\textpm\fi{} 0.016 C/${\mathrm{m}}^{2}$, respectively, for the magnitude of the piezoelectric constant. Both of these values are larger than that obtained previously by others using a different method. However only the 0.170-C/${\mathrm{m}}^{2}$ value exceeds the previous value by more than the sum of the quoted experimental errors. Possible reasons for the discrepancy are discussed, but no definitive one is identified.