Semiconductor heterostructures are suitable for the design and fabrication of terahertz (THz) plasmonic devices, due to their matching carrier densities. The classical dispersion relations in the current literature are derived for metal plasmonic materials, such as gold and silver, for which a homogeneous dielectric function is valid. Penetration of the electric fields into semiconductors induces locally varying charge densities and a spatially varying dielectric function is expected. While such an occurrence renders tunable THz plasmonics a possibility, it is crucial to understand the conditions under which propagating resonant conditions for the carriers occur, upon incidence of an electromagnetic radiation. In this manuscript, we derive a dispersion relation for a p–n heterojunction and apply the methodology to a GaAs p–n junction, a material of interest for optoelectronic devices. Considering symmetrically doped p- and n-type regions with equal width, the effect of certain parameters (such as doping and voltage bias) on the dispersion curve of the p–n heterojunction were investigated. Keeping in sight the different effective masses and mobilities of the carriers, we were able to obtain the conditions that yield identical dielectric functions for the p- and n-regions. Our results indicated that the p–n GaAs system can sustain propagating resonances and can be used as a layered plasmonic waveguide. The conditions under which this is feasible fall in the frequency region between the transverse optical phonon resonance of GaAs and the traditional cut-off frequency of the diode waveguide. In addition, our results indicated when the excitation was slightly above the phonon resonance frequency, the plasmon propagation attained low-loss characteristics. We also showed that the existence or nonexistence of the depletion zone between the p- and n- interfaces allowed certain plasmon modes to propagate, while others decayed rapidly, pointing out the possibility for a design of selective filters.
Probing dynamic behavior of electric fields and band diagrams in complex semiconductor heterostructures
