Acoustoelectric Effect inn-Type Germanium

Abstract

Theory and experiment are presented for the drag exerted on electrons in a solid by a traveling ultrasonic wave. After a discussion of the reasons why the effect is generally very small, it is shown that under certain conditions in $n$-type germanium it may be quite appreciable, and that its size directly indicates the intervalley scattering rate. Experimental data are given for arsenicdoped germanium ranging in impurity content from ${10}^{14}$ to ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$, at temperatures from 20 to 160°K. These yield the absolute value of the "uniaxial" deformation potential constant (16 ev) and the intervalley scattering rate as a function of temperature and doping. The interpretation of the results ascribes intervalley scattering action both to phonons and to impurities. The phonon contribution yields the frequency of the $〈100〉$ longitudinal phonon (6.6×${10}^{12}$ ${\sec }^{-1\mathrm{}}$) and the size of the appropriate coupling parameter; the impurity contribution yields intervalley scattering cross sections for neutral and ionized donors as a function of temperature. The two cross sections are explained as, respectively, being due to exchange scattering events and to compound capture-reemission processes. Further analysis gives a lower limit to the valley-orbit splitting of the arsenic donor ground state (1.7×${10}^{-3\mathrm{}}$ ev). The experiment verifies that the conduction-band valleys lie on $〈111〉$ axes at the Brillouin zone edge. Ultrasonic attenuation due to intervalley scattering is discussed and is shown to be too small to be easily measurable.