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Electron Dynamics in Crystalline Semiconductors

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EN
Electron dynamics in crystalline semiconductors is described by distinguishing between an instantaneous velocity related to electron's momentum and an average velocity related to its quasi-momentum in a periodic potential. It is shown that the electron velocity used in the theory of electron transport and free-carrier optics is the average electron velocity, not the instantaneous velocity. An effective mass of charge carriers in solids is considered and it is demonstrated that, in contrast to the "acceleration" mass introduced in textbooks, it is a "velocity" mass relating carrier velocity to its quasi-momentum that is a much more useful physical quantity. Among other advantages, the velocity mass is a scalar for spherical but nonparabolic energy bands ϵ(k), whereas the acceleration mass is not a scalar. Important applications of the velocity mass are indicated. A two-band k·p^ model is introduced as the simplest example of a band structure that still keeps track of the periodic lattice potential. It is remarked that the two-band model, adequately describing narrow-gap semiconductors (including zero-gap graphene), strongly resembles the special theory of relativity. Instructive examples of the "semi-relativistic" analogy are given. The presentation has both scientific and pedagogical aspects.
EN
The density of states for ballistic electrons in the presence of an electric field of almost arbitrary shape is calculated for one, two, and three dimensions using the semiclassical quantization in a finite sample. The semiclassical results are compared with these of the complete quantum treatment for a constant electric field. The case of crossed electric and magnetic fields is also considered and it is demonstrated that in this configuration the density of states exhibits a transition between magnetic and electric types of motion. Implications of this transition for the quantum Hall effect are mentioned.
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2014
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vol. 126
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issue 3
820-827
EN
Reflection of electrons from a potential barrier in heterostructures is described. An electric field of the barrier causes spin splitting of electron energies via the spin-orbit interaction and its form is calculated in the three-level k·p model for a nontrivial case of unbound electrons. It is shown that if the potential barrier is the only source of the spin-orbit interaction, the spin-flip electron reflections are not possible. However, there appear two unexpected possibilities related to the spin-orbit interaction: (a) non-attenuated electron propagation in the barrier whose height exceeds the energies of incoming electrons, (b) total reflection of electrons whose energies exceed barrier's height. It is indicated that the system can serve as a source of spin-polarized electron beams.
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