Metamaterial-based optoelectronic devices including Terahertz filters play a definitive role in advancement of THz technology. In this article we present a design procedure to obtain voltage-dependent carrier density control in a GaN-based heterostructurc with a Schottky gate configuration which serves as the substrate for a THz bandpass filter (BPF). The introduced structure consists of a cross shaped metallic layer on the AlGaN/GaN heterostructures. Then, we investigate tuning of transmission properties and the tunability of the filter. An overall tun-ability of about 103 GHz in the resonance frequency was obtained by varying the applied voltage from -8 V to 2 V. Also, a plasmonic metamaterial based on the graphene cross-shaped structure is studied and a comparison has been performed between the optical properties of graphenc-based cross-shaped structure and the original structure.
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