Institute of Metals Division - A Simplified Method of Evaluating Various Piezoelectric Semiconductors for Use in an Ultrasonic Amplifier

The basic principles and assumptions involved in D. L. White's solution5 for ultrasonic wave amplification in piezoelectric semiconductors are summarized. If the gain per unit length is maximized at each frequency without regard to the drift-field power density, the gain increases linearly with frequency. Therefore it would seem that very high gain is possible for frequencies in the hundreds of megacycles. However, with present materials the resulting drift-field power density is so large that cooling would be a major problem. For this reason it is more realistic to judge the capabilities of an ultrasonic amplifier in terms of the gain that is possible with a specified power density. In this case the gain at high frequencies does not increase but decreases more rapidly than l/f. The calculation of the gain us frequency at a fixed power level involves the repeated solution of a cubic equation and is therefore tedious. For the purpose of comparing different materials, sufficient accuracy can be obtained from an approximate solution which may easily be plotted as three straight lines on logarithmic graph paper. This method is used to compare the Performances of CdS, CdSe, ZnO, and GaAs. At a power density of 10 watts per cu cm, the first three give maximum gains of 60 to 80 db per cm in the vicinity of 60 megacycles. At the same power density, GaAs has a maximum gain of about 7 db per cm near 150 megacycles. Although an increase in mobility usually increases the gain for a specified power density, it is shown that there is an optimum mobility above which the gain decreases. An approximate expression for the optimum mobility is established. It is well-known that the interaction between charged particles and an electromagnetic wave can be used to amplify the electromagnetic wave. In the conventional traveling-wave tube, electrons in a vacuum are caused to move at a velocity slightly greater than the wave velocity, thereby coupling energy into the wave.' In principle, the same effect would be evident in a solid except that repeated collisions prevent the electrons from attaining a velocity greater than that of an electromagnetic wave. However, the drift velocity of electrons can be made to exceed the velocity of an acoustic wave in a solid. In 1956, weinreich2 noted that the deformation potential provided one means of coupling energy from drifting electrons into an acoustic wave, but the effect was too small to be of any practical importance. It was not until 1961 that White and Hutson demonstrated that the piezoelectric effect provided a strong enough coupling to give appreciable amplification of an ultrasonic wave and awakened wide interest in electron-phonon interactions. Qualitatively the effect may be described as follows. An acoustic wave propagating through a piezoelectric material is accompanied by an electric-field wave. If the vibrations are properly oriented with respect to the crystal axes of a piezoelectric semiconductor, the local electric fields are axially directed and cause bunching of the charged carriers. If the drift velocity of these carriers is less than the velocity of sound, they tend to be dragged along by the acoustic wave. This electroacoustic effect results in a net potential appearing across the material and in attenuation of the acoustic wave. On the other hand, if the drift velocity exceeds the velocity of sound, energy is coupled from the carriers to the acoustic wave and amplification results. Related effects which are being investigated include ultrasonic amplification in semimetals6-' and semi-conductor, and current saturation in piezoelectric semiconductors.'4-17 There are various problems which hinder the immediate application of ultrasonic amplification in a practical device. First, there are the traditional problems encountered in the design of acoustic delay lines: attenuation in the electromechanical transducers, reflected waves (which can lead to self-oscillation in an amplifying device), mechanical tolerances necessary to maintain phase coherence, and so forth. Second, there is the problem of selecting the best material from among the various piezoelectric semiconductors as they become available in single-crystal form with a wide choice of characteristics. This paper deals with the second problem and shows that the most realistic way of comparing materials is in terms of the gain which can be obtained without exceeding a