Ultrasonic Harmonic Generation in Piezoelectric Semiconductors

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Abstract
Second‐harmonic generation of ultrasound in piezoelectricsemiconductors is investigated using a quantum treatment which is valid at high frequencies and in strong magnetic fields. The effects of collisions are neglected so that our treatment is valid only for ql≫1. It is shown that the amplitude of the second harmonic can be expressed in terms of the fundamental using the linear and nonlinear conductivity tensors. The latter quantities are related to the current densities which are linear and nonlinear in the piezoelectric fieldsgenerated by the ultrasound. The linear and nonlinear conductivities are calculated using the parabolic and nonparabolic models for the energy bands of a semiconductor. It is found that only those sound waves which induce longitudinal electric fields will contribute appreciably to second‐harmonic generation. For waves propagating parallel to a magnetic field, we find that the amplitude of the second harmonic is independent of the magnetic field for the parabolic model. It is also found that the acoustic flux in the second harmonic will peak at sound wave vectors of the order of the Debye wave vector. In contrast, for the nonparabolic model it is found that the amplitude of the second harmonic depends upon magnetic field. The results of the calculation are applied to n‐type InSb, and the magnitude of the second‐harmonic generation is estimated for ultrasonic frequencies in the microwave region. It is found that the magnitude of the second harmonic is considerably enhanced using the nonparabolic model over what would be predicted using the parabolic model.