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Bloch-like surfaces that describe all possible spin states and, therefore, can be used to visualize spin precession and spin dynamics in external fields are presented for HgTe, a material with inverted energy bands. The spin and orbital surfaces for both free electrons and holes are shown, in general, to be spheroids, with the rotational axis parallel to a charge-carrier wave vector. The lengths of the principal axes of the spheroids depend on the energy band index and wave vector magnitude. At some wave vectors the surfaces may reduce to a line or a disc in the spin space. The corresponding graphs are presented.

Spin properties of free charge carriers in PbTe and PbSe are analysed using for this purpose the concept of spin surface, which in the simplest case reduces to the Bloch sphere. It is shown that in lead chalcogenides the spin surfaces are ellipsoids, the principal axes of which depend on the charge carrier wave vector, spin–orbit interaction strength, and the basis functions used to construct the Hamiltonian. The present results may be useful in the study of dynamics of the polarized charge carriers injected electrically or optically into the volume of PbTe, PbSe or PbS.

The scattering of hole spin during hole intra- and intervalence band transitions due to optical deformation potential interaction in tetrahedral semiconductors is considered. Matrix elements for transitions mediated by longitudinal and transverse optical phonons are presented. It is shown that for this type of scattering, the spin relaxation time can be found from hole momentum scattering time.

Intercollisional dynamics of hole spin, when free holes are subjected to an external electric field, is considered. Coherent evolution of spin projections and the population in valence bands is presented for dc and harmonic fields. Spin operators in the band representation are found and it is shown that there appears an uncertainty related with band degeneracy. The results obtained may be useful in the simulation of simultaneous spin and charge transport in p-type semiconductors, for example, by the Monte Carlo method.

Intervalence band dynamics of free holes in infrared fields is studied. A realistic valence band structure is used to simulate simultaneous excitation of split-off, heavy- and light-mass bands by femtosecond duration pulses. The decoherence due to phonon and ionized impurity scattering is taken into account in a quantum-mechanical density matrix. The excitation patterns in the Brillouin zone and hole distribution dynamics are presented. It is shown that it is possible to obtain high excitation levels in the valence band and dynamical inversion even in presence of dissipation, if femtosecond pulses are properly tailored.

The shift of resonance energy in direct optical interband transitions is evaluated. The case of hole transitions between heavy and light mass valence bands is considered, using the full form of the Luttinger-Kohn Hamiltonian. In addition to anisotropy, very large Bloch-Siegert shift, of the order of 100%, was found at high IR light intensities in the teraherz frequency range. The shift is related to a periodic hole motion in the Brillouin zone.

Dynamical electrical breakdown in the depleted region of diodes has been investigated in the nanosecond timescale. A persistent conductivity due to Si-related DX centre impact ionization in high electric fields was observed after the onset of the breakdown. From the present investigation it follows that DX centre breakdown begins at electric fields of ( and is related to impact ionization of DX centres by free hot carriers.

Dissociation of free excitons into electrons and holes, due to collisions between the excitons and charge carriers accelerated by an in-plane electric field in a multiple quantum well structure, is considered. We found that at normally used 2D excitonic concentrations the impact ionization process is rather strong and dominates over the exciton formation process at electric fields of the order of a few hundred V .

The effect of lattice vibrations on the field ionization dynamics of shallow donors in pure germanium is investigated by transient tunnelling spectroscopy in the temperature range from 4.2–6.5K. In this range the excited donor levels are populated and the free electron concentration in the conduction band is negligible. The increase of the tunnelling rate, when the lattice temperature is raised, is observed. The experimental results are explained by acoustic phonon assisted and activated tunnelling mechanisms. Both mechanisms are shown to enhance the tunnelling rate. The importance of excited donor states in the dissipative tunnelling is stressed.

The donor impact-ionization coefficient is calculated using the Boltzmann transport equation. It is shown that impact-ionizing collisions of free electrons with shallow donors induce strong cooling of the hot-electron distribution function. From the obtained results it is found that in the analysis of impurity breakdown or related processes the approach based on phenomenological equations is valid only for small changes of electron concentration. Corresponding graphs for the impact-ionization coefficient are presented for n-InP and n-GaAs.

Experimental studies on shallow acceptor and donor field ionization dynamics in MBE-grown GaAs epitaxial layers are presented. The experiments have been carried out with a new non-resonant spectroscopic technique, transient tunnelling spectroscopy. It has been found that intense hole tunnelling from shallow acceptors begins at electric fields higher than 6000 V cm-1, while electron tunnelling from shallow compensating donors to the conduction band occurs at much lower electric fields, of the order of 500 V cm-1. The dependence of the acceptor to valence band tunnelling time on the electric field strength has been measured for the first time, From the analysis of the experimental results it is concluded that initially the acceptor to valence band tunnelling dynamics is dominated by a light-hole mass.

A new fast transient method is developed to study free and bound exciton formation and decay dynamics in semiconductors. The method uses two time-scales, slow and fast. In the slow time-scale the excitonic system, after its creation, is allowed to evolve freely in time, while in the fast one the detection of the state of the system due to tunnel dissociation of excitons is performed in a fast swept electric field. The principle of the proposed method is demonstrated by measuring free and bound exciton lifetimes in the n region of silicon p+nn+ structures. diffusion to p+n and nn+ junctions is found to limit the free-exciton lifetime at temperatures lower than 14 K, whereas at higher temperatures exciton thermal dissociation is found to dominate.

The ionization dynamics of shallow donors in stepped electric fields is investigated in the nanosecond time-scale by monitoring the current transients in InP and GaAs epitaxial layers. Electron multiplication in the conduction band is analysed within the rate equation formalism, taking into account the ground state as well as the first excited state of the donor atom. Various ionization and recombination mechanisms, which can influence the dynamics of impact ionization, are considered. The dependence of the impact ionization and excitation coefficients on electric field strength has been deduced from a comparison of the experimental and theoretical current transients.

Tunnelling dynamics of electrons from isolated phosphorus atoms into the conduction band of silicon have been investigated experimentally at low temperatures and high electric fields. The impurity-band tunnelling times in the (111), (110) and (100) crystallographic directions were measured with the help of the recently developed transient tunnelling spectroscopy. The largest tunnelling time was observed in the (111) direction. Tunnelling times were found to be equal when the electric field was parallel to the (110) and (100) directions. The source of tunnelling anisotropy in many-valley semiconductors is briefly discussed.

Spin and pseudospin properties of monolayer graphene, when both the exchange and extrinsic spin–orbit (SO) interactions are taken into account, are analyzed within a framework of geometric algebra. The rotor equations for even and odd parts of electron bispinor are constructed in three-dimensional (3D) Euclidean space thus providing clear geometrical interpretation to the problem. It is shown that in the presence of combined action of exchange and SO interactions the spin and pseudospin fields in a monolayer graphene from two-dimensional become 3D, with spin and pseudospin components pointing out of the graphene plane. Also, the effect of both interactions on the Berry phase is considered analytically.

Properties of spin and pseudospin in monolayer graphene are investigated in terms of geometric algebra (GA). Specifically, Cl algebra that describes Minkowski relativistic spacetime is used for this purpose. Influence of exchange and spin–orbit (SO) interactions on spin and pseudospin are discussed in detail. It is shown how the eigenvalue problem can be depicted by GA rotors in 3D Euclidean space and solved geometrically. In this first part, the connection between Cl algebra and the Hilbert space formulation is established and spin/pseudospin properties in the presence of either exchange or SO interaction are studied. In the second part (2015 Phys. Scr. 90 025808) the effect of simultaneous action of both SO and exchange interactions on spin, pseudospin and Berry phase will be considered within the framework of GA.

We present experimental results on the field ionization of beryllium acceptors in micrometre AlGaAs/GaAs structures on a nanosecond timescale. At liquid helium temperature, the tunnelling ionization of beryllium was found to switch on effectively at electric fields higher than .

Analytical expressions for spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and effective masses are different. This was achieved by Gr\"obner basis algorithm which allows to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation., Comment: 4 figures, Mathematica full calculation notebook

Application of Clifford algebra in the analysis of valence-band spin properties in semiconductors is considered. In the first part (Dargys A 2009 Phys. Scr. 80 065701), for this purpose the isomorphism between multivectors and their matrix representations was used to transform the problem to Clifford algebra. Here equivalence rules are established between the spinors of Hilbert space and basis elements of the five-dimensional Clifford algebra Cl4, 1. Then, the rules are applied to the total angular momentum components and the two-band hole Hamiltonian. The resulting biquaternionic Schrodinger equation for hole spin is solved as an example.

Recently the Clifford (geometrical) algebra was addressed to describe dynamical properties of electron spin in semiconductors (Dargys 2009 Phys. Scr. 79 055702). In this paper, the Clifford algebra is used to investigate heavy and light hole spins in valence bands of cubic semiconductors. Owing to strong spin–orbit interaction in the valence band, the precession trajectories of hole spin polarization are ellipses, or even lines, rather than circles as usually found in the case of electrons. The paper shows how one can investigate the valence band spectrum and free-hole spin precession trajectories within a framework of the Clifford algebra Cl 4, 1. General formulae that describe free heavy- and light-mass hole spin precession are presented.

Geometric algebra is a relatively new and powerful tool in mathematical physics that allows one to solve physical problems in a very elegant way. In the present paper, which also bears a pedagogical flavor, geometric algebra is applied to a simple problem of electron spin dynamics in the conduction bands of cubic semiconductors. It is shown that the spin-related multivector, which is a basic object of geometric algebra, is a more transparent and flexible physical object as compared with spinor eigenvectors in the standard formulation of the problem in Hilbert space. Using geometric algebra the general equation of motion for electron spin in A3B5 and A2B6 semiconductors in the presence of spin–orbit interaction is solved exactly for the first time.

This letter shows how the inversion of energy bands is reflected in spin properties of a free charge carrier in the narrow-gap semiconductor Hg1-xCdxTe. The concept of the spin surface (analogue of the Bloch sphere) is used to represent all possible spin states of a ballistic 2D carrier. It was found that the spin dynamics in HgTe/Hg1-xCdxTe quantum wells may take place on spherical, spheroidal, disk- or needle-like spin surfaces.

For pt.I see ibid., vol.1, no.48, p.9637 (1989). The Monte Carlo method described in paper I is used to find heavy- and light-hole distribution functions and inter-valence absorption cross sections at high infrared laser intensities. At such intensities a hole is burned out in the hole distribution function and, as a result, the p-type semiconductor becomes transparent. The graphs of inter-valence absorption cross sections as a function of NH3 and CO2 laser electric field strength inside the semiconductor are presented for p-type germanium at two lattice temperatures, T=300 and 77 K and compared with the available experimental results. The paper also demonstrates how the Monte Carlo method can be extended to include valence band warping and non-parabolicity.

This is the first of two papers that present general principles of Monte Carlo (MC) simulation of linear and non-linear infrared-radiation absorption due to hole inter-valence transitions in p-type semiconductors. In the MC model the heavy- and light-mass sub-bands are treated as a collection of two-level systems, wherein the hole due to excitations by lattice vibrations hops between different members of the system. The close analogy with the two-level system allows one to incorporate into the MC program such purely quantum-mechanical effects as Rabi oscillations and dephasing. In this paper the general principles are presented and used to calculate absorption cross section at weak laser intensities. High-intensity absorption will be treated in the second paper.

It is shown numerically that electron tunnelling probability out of a one-dimensional delta potential in an electric field is much larger than standard tunnelling theories predict.