40 research outputs found
Electron dynamics in crystalline semiconductors
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 , whereas the acceleration mass is not a scalar. Important
applications of the velocity mass are indicated. A two-band {\bm k}\cdot {\bm
\hp} 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.Comment: 7 pages; 1 figur
Spin-flip reflection of electrons from a potential barrier in heterostructures
Spin-conserving and spin-flip opaque reflections of electrons from a
potential barrier in heterostructures are described. An electric field of the
barrier is considered to be the only source of energy spin splitting in the
presence of spin-orbit interaction and its form is calculated in the
three-level {\kp} model for a nontrival case of unbound electrons. Reflection
angles and amplitudes are calculated for oblique incoming directions. It is
shown that the system can serve as a source or filter of spin-polarized
electron beams. Two unexpected possibilities are pointed out: 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.Comment: 10 pages, 3 figure