Dispersion and bandgap feature of coupled Bloch waves in one-dimensional piezoelectric semiconductor phononic crystal with PN junction

The dispersion, attenuation and bandgap feature of coupled Bloch waves in one-dimensional piezoelectric semiconductor phononic crystal are studied in the present work. In particular, the influences of PN junction are emphasized. Different from the Bloch waves in the piezoelectric phononic crystal, the Bloch wave in piezoelectric semiconductor phononic crystal is attenuated. Moreover, the existence of the carrier fields brings forth more modes of Bloch waves due to the coupling of multiple physical fields. Using the state transfer equation method, the transfer matrix of the unit cell in a one-dimensional piezoelectric semiconductor phononic crystal is derived. Combining this with Bloch theory for periodic structures, the dispersion equation for multi-field coupled Bloch waves is obtained. The dispersion, attenuation and bandgap characteristics of the coupled Bloch waves are then plotted in the complex wave number domain. It is found that the influences of the PN junction are evident and thus provide an enlightenment that the propagation feature of Bloch waves can be adjusted by the control of the PN junction.