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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The quantum model of quasi-one-dimensional generalized Fibonacci semiconductor superlattice with the mass of charge carriers depending on the position in superlattice is formulated. The Landauer electrical conductance σ_{L} of generalized Fibonacci semiconductor superlattice is studied analytically and numerically. The dynamical maps allowing us to calculate σ_{L} of the studied systems are presented. It is shown that σ_{L} as a function of incident energy E of charge carriers oscillates strongly and exhibits the resonant character. We have verified numerically that σ_{L}(E) reaches its local maximum for energies E corresponding to energy eigenvalues of charges in superlattice.
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New efficient numerical methods of computing eigenvalues and eigenvectors of quasi-one-dimensional effective-mass Hamiltonian with arbitrary coordinate dependence of charge carrier mass are presented. Within the proposed approach the effective-mass equation is replaced by a nonsymmetric or symmetric matrix eigenproblem which can be analysed numerically with the help of existing computer routines. The presented methods are verified in special semiconductor heterostructure cases that are solvable within other approaches. A generalization of the presented methods for nonparabolic materials is also discussed.
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Polarization-resolved photoluminescence from two-dimensional GaAs/GaAlAs heterostructures doped with acceptors was studied in high magnetic fields. Measurements were carried out in low temperatures up to 2 K and magnetic field up to 21 T. Experiments performed in the Faraday configuration enabled to resolve hole states with different spin orientation. We observed a nonlinear behavior of valence-band g factor in strong magnetic fields. To explain obtained results, a detailed theoretical calculation was carried out based on the Luttinger model for valence-band states. We examined the spin splitting of hole levels under the influence of both external magnetic field and built-in electric field existing in doped heterostructures. Changes of hole g factor with the width of the structure and the density of two-dimensional carriers are discussed.
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