The challenge of parasitic bulk doping in Bi-based 3D topological insulator materials is still omnipresent, especially when preparing samples by molecular beam epitaxy (MBE). Here, we present a heterostructure approach for epitaxial BSTS growth. A thin n-type Bi$_2$Se$_3$ (BS) layer is used as an epitaxial and electrostatic seed which drastically improves the crystalline and electronic quality and reproducibility of the sample properties. In heterostructures of BS with p-type (Bi$_{1-x}$Sb$_x$)$_2$(Te$_{1-y}$Se$_y$)$_3$ (BSTS) we demonstrate intrinsic band bending effects to tune the electronic properties solely by adjusting the thickness of the respective layer. The analysis of weak anti-localization features in the magnetoconductance indicates a separation of top and bottom conduction layers with increasing BSTS thickness. By temperature- and gate-dependent transport measurements, we show that the thin BS seed layer can be completely depleted within the heterostructure and demonstrate electrostatic tuning of the bands via a back-gate throughout the whole sample thickness.
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