by current-carrier drift in semiconductors, the phenomenon whereby an ultrasonic wave passing through a semiconductor crystal is amplified when the drift velocity of current carriers in the direction in which the wave propagates exceeds the phase velocity of the wave.
The physical nature of ultrasonic amplification is most easily understood by considering the example of a piezoelectric semiconductor (seePIEZOELECTRICITY). As a result of the piezoelectric effect, an elastic wave passing through such a crystal is accompanied by an electric field, which interacts with current carriers—electrons and holes—in the semiconductor. The interaction leads to the redistribution of the carriers in space and the formation of a region of enhanced carrier concentration, that is, the formation of a space charge. If an electric field Ed that produces a space-charge drift with a velocity greater than the phase velocity c of the elastic wave is applied to the specimen, the current carriers will impart energy to the wave as they overtake it, thereby amplifying the ultrasonic wave. A similar process occurs in a traveling-wave tube.
In semiconductors that do not exhibit the piezoelectric effect, an elastic wave interacts with current carriers by way of the deformation potential, that is, directly by means of the interaction of electrons and phonons that characterizes the change in the energy of conduction electrons when the lattice is subjected to elastic deformation. The force exerted on an electron by the strained lattice is proportional to the square of the wave frequency ω. Therefore, ultrasonic amplification in conventional semiconductors is effective only at hypersonic frequencies ω > 109 hertz (seeHYPERSOUND).
At low frequencies, where the mean free path l of current carriers is much less than the ultrasonic wavelength λ, ultrasonic amplification is caused by the space charge, that is, by the supersonic motion of a localized bunch of current carriers of the same sign; the bunch is formed by the wave itself. However, if l/λ ≫ 1, the electrons or holes are nearly free, no space charge is formed, and amplification results from the coherent emission of phonons by individual current carriers. In this case, the amplification process is similar to the two-stream instability in a gas-discharge plasma.
For ultrasonic amplification in a piezoelectric semiconductor crystal, the crystal symmetry and the direction in which the elastic wave propagates should be such that an elastic wave with a given polarization is accompanied by a longitudinal electric field, since the current carriers in the semiconductor interact most effectively with the longitudinal component of the wave’s electric field vector. Both longitudinal and transverse waves may be amplified in CdS, CdTe, ZnO, GaAs, and CdSe piezoelectric crystals.
In practice, the main difficulty in the use of ultrasonic amplification is the overheating of specimens during amplification. To avoid this problem, experiments are usually performed in the pulse mode by applying a drift field to a specimen only during an ultrasonic pulse. Very high levels of ultrasonic amplification may be achieved in piezoelectric semiconductors; however, nonlinear effects that limit the amplification become substantial.
Ultrasonic amplification may be used in practice to develop active ultrasonic delay lines, to amplify microwave oscillations (with the use of double acoustoelectric conversion), and to produce hypersonic radiators and receivers. The study of the effect of ultrasonic amplification in semiconductors—especially in a strong magnetic field—makes it possible to evaluate and measure a number of characteristic parameters and constants of solids; in particular, Fermi surfaces may be investigated.
REFERENCESSee references under ULTRASOUND.
V. I. PUSTOVOIT