This paper presents a review of models of the current transport in different kind of heterojunctions (HJs) and their characteristics. In order to effectively deduce the dominant electron transport for the HJs based on ZnO or Zn_1−xMg_xO layers grown on Si substrate by MBE a comparison is performed – which type of the HJ exhibits better electrical properties. The current–voltage characteristics for the studied HJs were measured within 280–300 K. The transport properties of the HJs are explained in terms of Anderson model with reference to aforementioned current transport models. It is found, that the mechanisms of current transport for all of the studied HJs are similar. At a low forward voltage bias the tunneling current dominates while at medium voltage bias (0.5–1 V) multitunneling capture-emission prevails with the electron trap located at 0.1–0.25 eV below the bottom of a ZnO (Zn_1−xMg_xO) conduction band. Beyond this voltage bias space charge limited current governs the current transport.

The review of peculiarity of growth and experimental results of the magneto-transport measurements (longitudinal magneto-resistance R_xx and the Hall resistance R_xy) over a wide interval of temperatures for several samples of Hg_1−xCd_xTe (x ≈ 0.13–0.15) grown by MBE is presented in this paper. An amazing temperature stability of the SdH-oscillation period and amplitude is observed in the entire temperature interval of measurements up to 50 K. Moreover, the quantum Hall effect (QHE) behaviour of the Hall resistance was shown in the same temperature interval. These peculiarities of the R_xx and R_xy for strained thin layers are interpreted using quantum Hall conductivity (QHC) on topologically protected surface states (TPSS). In the case of not strained layers it is assumed that the QHC on the TPSS contributes also to the conductance of the bulk samples. The experimental results on magneto-transport (QHC and SdH) obtained for the strained 100 nm thickness Hg_1−xCd_xTe layer are interpreted on the basis of the 8 × 8 kp model and an advantage of the Hg_1−xCd_xTe as topological insulators is shown. This article is an expanded version of the scientific reports presented at the International Conference on Semiconductor Nanostructures for Optoelectronics and Biosensors 2016 ICSeNOB2016, May 22–25, 2016, Rzeszow, Poland.