A. R. Hutson

A plane elastic wave propagating in a piezoelectric crystal may be accompanied by longitudinal electric fields which provide an additional elastic stiffness. When the crystal is also semiconducting, these fields produce currents and space charge resulting in acoustic dispersion and loss. A linear theory of this effect is developed, taking into account drift, diffusion, and trapping of carriers for both extrinsic and intrinsic semiconductors. Conductivity modulation sets an upper limit on strain amplitude for a linear theory. The directional characteristics and the magnitude of the effects are illustrated for CdS and GaAs. The Appendix treats the interaction of an arbitrary acoustic plane wave with the electromagnetic fields in a piezoelectric crystal (based on a treatment by Kyame [J. J. Kyame, J. Acoust. Soc. Am. 21, 159 (1949); 26, 990 (1954).]) and further shows explicitly that only the effects of longitudinal electric fields need be considered.

Radiofrequency waves at 15 and 45 Mc are transduced into pressure waves at the same frequencies, and are applied to a CdS crystal. The waves are then converted by a second transducer into a r-f output wave. The signal amplification is found as a function of the illumination intensity on the crystal, and the electric field parallel to the pressure waves. Positive gain may be attained for suitable values of the electric field. (T.F.H.)

Measurements of the Hall coefficient and the electrical conductivity of single-crystal specimens of $n$-type ZnO at temperatures between 55\ifmmode^\circ\else\textdegree\fi{}K and 300\ifmmode^\circ\else\textdegree\fi{}K are reported. An analysis of carrier concentration vs temperature indicates that "as-grown" crystals contain more than one active donor. Crystals with low initial donor concentrations were doped with H or interstitial Zn or Li, allowing a single-donor-level analysis. Doping was accomplished by interstitial diffusion followed by a rapid quench. Each of the added donors gives rise to a hydrogen-atom-model donor center whose ionization energy is ${E}_{D}=0.051$ ev for ${N}_{D}<5\ifmmode\times\else\texttimes\fi{}{10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. Lithium was also found to introduce a small concentration of acceptors, presumably due to an exchange between interstitial and substitutional positions. The quantity ${(\frac{{m}^{(N)}}{m})}^{\frac{3}{2}}{D}^{\ensuremath{-}1}$, where ${m}^{(N)}=\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\ensuremath{-}\mathrm{o}\mathrm{f}\ensuremath{-}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}''$ effective mass and $D=\mathrm{donor}\mathrm{degeneracy}$, was found to be about 0.19 for all three donors, indicating that if $D=2$ then ${m}^{(N)}=0.5$. The low-frequency dielectric constant of ZnO was redetermined as $\ensuremath{\kappa}=8.5$. The effective mass associated with the electron found in a hydrogen-like orbit is then ${m}^{(H)}=0.27m$, and the observed decrease of ${E}_{D}$ with increasing ${N}_{D}$ corresponds to the overlap of these large orbits.The Hall mobility is 180 ${\mathrm{cm}}^{2}$ ${\mathrm{volt}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ at 300\ifmmode^\circ\else\textdegree\fi{}K and increases with decreasing temperature. It has been analyzed for lattice and impurity scattering. The optical-mode scattering mobility has been calculated from both the perturbation and intermediate-coupling theories making use of the effective mass, ${m}^{(H)}$, so that no adjustable parameters were included. The two theories agree for ZnO since it turns out to have a polar-mode electron coupling constant of $\ensuremath{\alpha}=1$. The mobility so obtained is in good agreement with experiment and indicates that optical-mode scattering is important above 200\ifmmode^\circ\else\textdegree\fi{}K. Some acoustical-mode scattering also appears to be present. At low temperatures the mobility appears to be limited by impurity scattering.

Piezoelectric scattering of conduction electrons by acoustical phonons is discussed for ZnO and CdS, and approximate values of the mobilities determined by this mechanism alone are derived. The phonon drag contribution to the Seebeck effect in ZnO is assumed to arise from crystal-momentum exchange between electrons and acoustical phonons by way of the piezoelectric interaction alone. Comparison of the results of this assumption with the data has led to the discovery of strong piezoelectric phonon scattering from neutral donor states. These two piezoelectric scattering mechanisms and an effective electron mass of about 0.32m, derived from other experiments, provide a model for phonon drag in ZnO which agrees with the temperature dependence and ``impurity'' dependence of the data and gives the correct magnitude of the effect to within the uncertainties of the approximations employed.