Three-dimensional electrons and two-dimensional electric subbands in the transport properties of tin-doped n-type indium selenide: Polar and homopolar phonon scattering.

Abstract

Electron-scattering mechanisms in n-type indium selenide doped with different amounts of tin are studied by means of the Hall effect (30--300 K) and photo-Hall effect (300 K). The electron mobility at room temperature is found to increase with the free-electron concentration in samples with low tin content. The same behavior is observed when the electron concentration increases due to thermal annealing or photogeneration. That is explained through the presence of two kinds of free electrons contributing to the charge transport along the layers: high-mobility three-dimensional (3D) electrons in the conduction band, and low-mobility two-dimensional electrons in the electric subbands. These 2D subbands are proposed to exist in InSe due to size-quantization effects in thin layers located between two stacking faults. In these regions electron states become higher than conduction-band states. Electrons are transferred outside these regions and are confined in 2D subbands by the resulting electric field. In regard to the electron-scattering mechanisms, it is shown that LO polar phonons play an important role in the scattering of 3D electrons, whose mobility has been calculated by an iteration method. From a comparison with experimental results, we show that the coupling constant for the 3D electron-phonon deformation-potential interaction has been overestimated in previous calculations. The relaxation time for the scattering of 2D electrons by homopolar phonons is determined by using a variational wave function, and the calculated 2D mobility decreases when the localization of the 2D subbands along the c axis increases.