The dependence of current density on the electric field strength in homopolar semi-conductors

The distribution function is derived for conduction electrons in a semi-conductor under the effect of a homogeneous electric field, on the basis of which one can explain the deviations from the validity of Ohm's law in strong electric fields or at low temperatures in homopolar semiconductors as well as the temperature dependence of the mobility.     

A derivation of Manin's formula

The formula of Manin for the bosonic string measure is derived using elementary methods.     

Another derivation of Weinberg's formula

To investigate how quantum effects might modify special relativity, we will study a Lorentz transformation between classical and quantum reference frames and express it in terms of the four-dimensional (4D) momentum of the quantum reference frame. The transition from the classical expression of the Lorentz transformation to a quantum-mechanical one requires us to symmetrize the expression and replace all its dynamical variables with the corresponding operators, from which we can obtain the same conclusion as that from quantum field theory (given by Weinberg's formula): owing to the Heisenberg's uncertainty relation, a particle (as a quantum reference frame) can propagate over a spacelike interval.     

On microscopical derivation of Lorentz-Lorenz formula

Lorentz-Lorenz formula may be derived microscopically by the analytical inversion of the dielectric matrix (DM) in the limit of tightly bound electrons. Exchange and correlation effects are to be taken into account and atomic polarisability is to be defined correctly in terms of the atomic susceptibility instead of the polarization operator. A wrong definition was the origin of usual contradictions between microscopical calculations and classical formula. The inversion of the DM diminishes dielectric constant in comparison with the diagonal element of DM but this procedure takes into account only a part of the local field effects caused by rapidly oscillating fields. Another part is connected with exchange interaction and increases the diagonal element of DM in comparison with dielectric constant without any local field effects, hence all local field effects do increase the dielectric constant.     

Hall mobility of hot electrons in CdS

Photo-Hall effect of hot electrons in a pure single crystal of CdS was observed, for the first time. The measurement was carried out for electric fields up to 4,300 V/cm in magnetic fields up to 40 kOe at 4.2 K. The saturation of the drift velocity V_d of electrons due to optical phonon emission was observed. The saturated value of V_d is found to be about 1.7 × 10⁷ cm/sec.     

Drift mobility of electrons in TlSbS2

The time-of-flight technique has been used to study the transport of electrons in TlSbS₂ in the perpendicular direction with respect to the cleavage planes. The transport of electrons is non-dispersive and can be considered an activated process with an activation energy of 0·40 eV. The value of 1·68 eV has been found for the energy gap of TlSbS₂ at room temperature.     

The mobility of electrons in strained silicon

The development of Si and Si_1−xGe_x layer growth by molecular beam epitaxy has enabled heterostructures and HEMT devices to be made with Group IV semiconductors. Strain is very important in determining the electronic behaviour of this system and as an initial step towards understanding mobility in SiGe HEMT structures a Monte Carlo technique has been used to simulate electron transport in bulk Si, strained by commensurate growth on a (001) Si_1−yGe_y buffer. The in-plane mobility initially increases with increasing strain but then falls at higher strains and fields. Results are presented for both undoped and 10¹⁷ cm⁻³ n-type Si, fields of 10² to 10⁴ Vcm⁻¹ and strain levels up to the equivalence of growth on a Si_0.25Ge_0.75 buffer. The results are explained by the splitting of the degenerate conduction band minimum and the transition probability between the two-fold and four-fold split minima.     

A new derivation of the drift-diffusion equations for electrons and phonons

A new model, based on an asymptotic procedure for solving the generalized kinetic equations of electrons and phonons, is proposed. The linearized equations turn out to be solvable and lead naturally to the displaced Maxwellian approximation. The constitutive laws for the electric and thermal currents are derived and the Onsager relations are verified. The balance equations for the electron number and the total energy density for the whole system constitute now, together with the Poisson equation, a system of three equations for the electron chemical potential, the temperature of the system, and the electric potential.     

用不变速度推导卢瑟福散射公式

通过横向速度变换得到两种不变速度，由此推出卢瑟福散射公式。     

Theory of forward glory scattering for chemical reactions: New derivation of a uniform semiclassical formula for the scattering amplitude

The theory of forward glory scattering is investigated for a state-to-state chemical reaction whose scattering amplitude can be written as a Legendre partial wave series. Legendre series occur in the exact quantum theory of reactive scattering when the initial and final helicity quantum numbers are zero, as well as in many approximate theories of chemical reactions. The starting point for the semiclassical theory is a two-dimensional integral representation for the scattering amplitude. A uniform semiclassical approximation is derived that is valid for angles both on, and off, the axial caustic associated with the glory. The derivation is the first application to a concrete problem in molecular physics of a method outlined by J. N. L. Connor and H. R. Mayne in 1979 for the uniform semiclassical evaluation of multidimensional integrals. The approach exploits the theory of singularities of differential mappings. The key step in the derivation is an exact one-to-one change of variables in the neighbourhood of the stationary phase points that locally reduce the two-dimensional phase of the integrand to a non-polynomial canonical form. The derivation complements a different semiclassical glory analysis reported in a companion paper.     

A superspace normal coordinate derivation of the density formula

Using normal coordinate expansions we derive by purely superspace methods the density formula giving the component action corresponding to a superspace supergravity-matter action.     

Geometrical derivation of a new ground state formula for the n-electron Friedel resonance model

The n-electron ground state of the Friedel resonance model can be written as a single Slater determinant of n s-electrons plus d-electron-s-hole companion. This new formula is derived geometrically in the Hilbert space. The derivation uses the fact that a n-electron Slater determinant, built from N band states, corresponds to a n-dimensional subspace in the N-dimensional Hilbert space. Received: 4 November 1997 / Accepted: 19 November 1997     

Negative dynamic mobility of electrons in silicon in the far-infrared range

We performed Monte Carlo simulation of electron response to a strong pumping wave (443 GHz) and weak signal harmonic waves (886 and 1329 GHz) in silicon. A negative dynamic conductivity is found to arise for 1329 GHz above a threshold value of the pumping wave amplitude and below a maximum value of the signal wave amplitude in a limited range of phase difference between the waves.     

The derivation of explicit solutions to Wannier–Stark resonances for electrons on coupled chains

Electrons on infinite coupled chains with nearest neighbour couplings under uniform electric and magnetic fields can be expressed as conditionally solvable systems, which concerns both discrete coordinate and wavenumber representations. We then have to account for multiparameter extra-conditions relying on the single chain phase of the system, which amounts to perform a suitable selection of parameters. The implicit plots provided by such conditions exhibit both regular and irregular patterns. This results in the onset of a finite number of Wannier–Stark resonances, now by performing rescalings needed. However, this time the resonance width is sensitive to the quantum number characterizing the Stark-ladder. Bound-state limits, rescalings and approximations proceeding irrespective of the wavenumber have also been presented.