Transient response of hot electrons in narrow-gap semiconductors at low temperatures in the presence of a longitudinal quantizing magnetic field

Transient response of hot electrons in narrow-gap semiconductors to a step electric field in the presence of a longitudinal quantizing magnetic field has been studied at low temperatures using displaced Maxwellian distribution. The energy and momentum balance equations are used assuming acoustic phonon scattering via deformation potential responsible for the energy relaxation and elastic acoustic phonon scattering together with ionized impurity scattering for momentum relaxation. The calculations for the variation of drift velocity and electron temperature as functions of time are made for n-Hg_0.8Cd_0.2 Te in the extreme quantum limit at 1.5 K and 4.2 K. The momentum and energy relaxation times are found to be of the same order of magnitudes as with the experimental values. The magnetic field and lattice temperature dependences of the relaxation rates have been investigated.One of the authors, Suchandra Bhaumik, acknowledges the Council of Scientific and Industrial Research (New Delhi) for financial support.     

Tight-binding approach to field desorption: N2 ON Fe(111)

We present a tight-binding cluster calculation including interatomic Coulomb repulsion for field-induced adsorption and desorption. For electric field strengths F up to the desorption threshold $\text{F ～ 1.5}\text{V}\text{A}\text{?}$ for N₂ on Fe(111) we calculate total potential energy surfaces. The variation of the Schottky barrier and of the N₂ vibrational frequency is extracted as a function of F.     

Phonon heating by hot electrons in n-InSb in quantizing magnetic fields

The effect of the phonon “narrow throat” was experimentally found in n-InSb in crossed electrical and quantizing magnetic fields at temperatures 1.6—4.2°K. The phenomenon of energy relaxation by hot electrons on phonons was detected with $\text{T}\text{S}\text{?}\text{h}\text{?}\text{λ}{}^{\mathrm{?1}}$ in the case of absence of a phonon thermal tank (S is sound velocity, λ is magnetic length, T is temperature). The value of a critical electric field (E_cr) on the S-type current-voltage characteristic (CVC) was measured as a function of temperature and the magnetic field.     

Influence of Cr3+ doping on photoelectronic processes of La2Ti2O7 pyrochlore and La23TiO3 perovskite anodes

Photoelectrical properties of La₂TiO₂O₇ and La_{$\text{2}\text{3}$}TiO₃ anodes undoped and Cr³⁺—doped have been investigated. The onset of photocurrent for both the undoped and Cr³⁺ doped pyrochlore is at 400 nm while for undoped perovskite it is at 420 n.m. A shift of the spectral photoresponse down to 550 n.m. is observed for the Cr-doped perovskite. The experimental data have been analyzed according to the Schottky barrier model of the semiconductor-electrolyte junction. This analysis has allowed us to propose a photoconduction mechanism.     

Effects of electric field and size on the electron-phonon interaction in a spherical quantum dot with impurity

The effects of electric field and size on the electron-phonon interaction with an on-center impurity in a Zn_1?x Cd _x Se/ZnSe spherical quantum dot are studied, taking into account the interactions with confined, half-space and surface optical phonons. In addition, the interaction between impurity and phonons has also been considered. The results show that the electron-confined, electron-half-space, and electron-surface optical phonon interaction energies are all negative. The electron-confined optical phonon interaction energy is weakened by the electric field, but the electron-half-space and electron-surface optical phonon interaction energies are strengthened by it. In particular, the electron-surface optical phonon interaction depends strongly on the electric field, and it will vanish when the electric field is absent. It is also found that the electron-confined optical phonon interaction and electron-impurity “exchange” interaction energies reach a peak values as the quantum dot radius increases and then gradually decrease, but the electron-half-space optical phonon interaction energy exponentially quickly approaches 0 as the quantum dot radius increases.     

A convergent expansion about mean field theory: I. The expansion

We give a convergent expansion for nearly Gaussian quantum field theory in the multiphase region. The expansion combines (1) an expansion in phase boundaries, (2) a cluster expansion, and (3) a perturbation expansion to isolate dominant behavior. We study in detail the ground state of the $\text{P}$(φ)₂ = (λφ⁴ ? φ² ? μφ)₂ model, with ∥ μ ∥ ? λ² ? 1. The ground state is close to the classical free field, obtained by replacing $\text{P}$(φ) by the quadratic mean field polynomial $\text{P}$_c(φ), tangent to $\text{P}$ at a global minimum. Selecting one minimum gives a pure phase (ergodic ground state) satisfying the Wightman-Osterwalder-Schrader axioms with a positive mass. We also establish analyticity in λ for μ = 0 in the sector ∥ Im λ ∥ < ? Re λ ? 1, for ? ? 1.     

Stokes and anti-stokes excitation of the resonance emission band of crystal phosphors

Anti-Stokes laser excitation has been induced by one photon absorption transitions in the resonance band of the following crystal phosphors: a natural diamond crystal in which the line structure of the spectrum is quite important, a ZnS:Mn crystal in which the line spectrum is easily observed but its intensity is smaller than that of the wide band emission, and halo-complexes of manganese in which the zero phonon line can hardly be observed. In all cases the emitted spectrum has the same shape as while using Stokes excitation; the intensity depends on temperature by means of a Boltzmann factor. Such a result is easily accounted for by the theory; however, except perhaps in the case of diamond, experiment is not in agreement with the simple theoretical model which concludes that the activation energy W involved in the excitation process is equal to the difference E₀ - hv between the energy of the zero phonon line E₀ and the exciting laser energy hv.     

To the problem of Hall “mobility” in polycrystalline thin films with potential barriers

The peculiarities of the potential shape in polycrystalline films were considered. It was shown that the barrier height (φ_B) in sites (the place where three or more crystallites are connected) with respect to the concentration of boundary states (BS) was higher or coincided with the barrier height (φ_A) at the crystallite boundaries (CB). That is why the sites for majority charge carriers in films were “blocked down” and current transport along CB was not realized. If inversion of the conductivity type at CB was absent, the Hall potential was generated in quasi-neutral regions of crystallites and in barrier regions perpendicular to the current lines. If $\text{φ}{}_{\mathrm{A}}\text{+ E}{}_{\mathrm{F}}\text{<}\text{1}\text{2}\text{E}{}_{\mathrm{g}}$ the Hall potential coefficient (R_H) of the film is determined by the carrier concentration n₀ in quasi-neutral regions. In this case the activation energy of the Hall mobility was equal to the activation energy of the conductivity (σ_A). In the opposite case the inversion conductivity type takes place on CB. When the inversion regions are present near the barrier tops and conductivity is realized along CB, R_Hp ～ (N_cN_v/n₀)^-1 exp (E_g?φ_B/kT) and μ_Hp ～ exp (?φ_B?φ_A/kT), where E_g is the band gap, N_c, N_v are the effective density of states in the conduction and valence bands.     

Diffusion of electrons by coherent wavepackets

The momentum transfer and velocity diffusion of electrons periodically interacting with a coherent longitudinal wavepacket is considered. Applying the resonance overlap criterion, we establish the threshold for intrinsic stochasticity and the width of the stochastic region Δv_stoch in velocity space. Direct numerical integration of the single-particle dynamics and an approximate discrete mapping are used to corroborate the resonance overlap results and to find the short- and long-term momentum transfer and diffusion in the field. After the onset of stochasticity, we find a net induced current j ≈ Δv_stoch and in the weak-field regime (autocorrelation time ? bounce time) an initial rate of change of the variance 〈πv²〉 /2t equal to the quasilinear-theory diffusion coefficient. In the strong-field regime momentum transfer and stochasticity persist owing to non-adiabatic transitions between trapped and untrapped states as the electron traverses the wavepacket. The diffusion coefficient substantially deviates from the quasilinear (≈E²) as well as from resonance broadening ($\text{≈E}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$) scaling, while the scattering in velocity space tends to lose the local, diffusive nature characteristic of weak fields.     

Failure of length scaling in Wilson's ϵ expansion

We show that length scaling of the four-point scattering amplitude in Wilson's ? expansion is not consistent in the order of ?³. However, in conformity with conformal invariance at the critical point, momentum scaling in a given channel is consistent. This latter method permits us to calculate the dimension of the field φ² at the critical point without recourse to length scaling and one finds $\text{d}{}_{\mathrm{\phi }}\text{2 =}\text{d}\text{2}\text{?}\text{1}\text{ν}\text{to O}\text{(?}{}^2\text{)}$ as if length scaling were true. However, this does not imply Kadanoff's relation 2?α = νd which is predicted on length scaling. Indeed the above-mentioned inconsistency makes impossible the determination of α by these methods.     

The longitudinal magnetophonon effect in semiconductors containing magnetic impurities

The dependence of longitudinal magnetoresistance on magnetic field in semiconductors containing magnetic impurities is investigated theoretically. The calculation takes into account the scattering of electrons on magnetic impurities and on optical phonons. The inelastic optical phonon scattering itself is responsible for magnetophonon oscillations of the magnetoresistance, the extremes of these oscillations occuring when energy distance between Landau levels is equal to the energy of optical phonon, $\text{h}\text{?}$ω₀. The scattering on magnetic impurities may lead to spin flip electronic transitions. The spin flip electronic transitions manifest themselves as additional minima on the oscillatory picture of magnetoresistance. These new minima occur when the energy separation between spin-split Landau levels is equal to $\text{h}\text{?}$ω₀.     

Low-energy e4 compton scattering of spin-12 targets without C,P and T invariances

We have studied the low-energy e⁴ Compton scattering on $\text{spin}\text{-}\text{1}\text{2}$ targets without assuming C, P and T invariances. It is shown that the scattering amplitude has a term ω³ ln ω (ω is the energy of incident photon in the lab frame), whose coefficient is determined entirely by the charge, mass, magnetic dipole moment, and electric dipole moment of the target. To derive the result, we calculate the second-order (in ω) terms of the e² Compton scattering amplitudes. When the electric dipole moment (whose existence violates P and T but conserves PT) is set to zero, the result reduces to that obtained before by Lin assuming C, P and T invariances.     

Free carrier absorption in quantizing magnetic fields: Nonpolar optical phonon scattering

A quantum theory of free carrier absorption in nondegenerate semiconductors and in strong magnetic fields which was previously developed to treat the case when acoustic phonon scattering dominates the free carrier absorption process [1] is extended to treat the case when nonpolar optical scattering is important. When the electromagnetic radiation field is polarized parallel to the direction of the applied magnetic field, results are obtained which are similar to those when acoustic phonon scattering is dominant. The free carrier absorption is an oscillatory function of the magnetic field which on the average increases in magnitude with the magnetic field. However, more structure in the free carrier absorption occurs when nonpolar optical phonon scattering dominates. This is due to the fact that there are two periods in the oscillatory magnetic field dependence associated with the emission or the absorption of optical phonons during the intraband transitions. When the cyclotron frequency exceeds the sum of the photon and optical phonon frequencies, i.e. ω_c > θ + ω_o, the free carrier absorption is predicted to increase linearly with magnetic field when ?ω_c? k_BT. The magnetic field dependence of the free carrier absorption can be explained in terms of phonon-assisted transitions between the various Landau levels in a band involving the emission and absorption of optical phonons.     

Large electric-field-induced enhancement of resonant Raman scattering of a single quantum well

The electric-field enhancement of the resonant Raman efficiency of confined optical phonon modes in a single quantum well has been observed in an asymmetrical n-type triple-barrier GaAs/AlAs resonant tunneling structure. The measurement takes advantage of an outgoing resonance with the e₂-hh₁ exciton transition confined to the wide quantum well, and according to the polarization properties, the Fröhlich interaction dominates the scattering mechanism. A fifteenfold increase is found from zero field to 7.5 × 10⁴ V/cm, which results from break-down of the parity selection rules for the photon-exciton and the exciton phonon coupling mechanisms.     

Optical properties of a hydrogenic impurity in a confined Zn1−xCdxSe/ZnSe spherical quantum dot

The effect of longitudinal optical phonon field on the ground state and low lying-excited state energies of a hydrogenic impurity in a Zn_1−xCd_xSe/ZnSe strained quantum dot is investigated for various Cd content using the Aldrich-Bajaj effective potential. We consider the strain effect considering the internal electric field induced by the spontaneous and piezoelectric polarizations. Calculations have been performed using Bessel function as an orthonormal basis for different confinement potentials of barrier height. Polaron induced photoionization cross section of the hydrogenic impurity in the quantum dot is investigated. We study the oscillator strengths, the linear and third-order nonlinear optical absorption coefficients as a function of incident photon energy for 1s-1p and 1p-1d transitions with and without the polaronic effect. It is observed that the potential taking into account the effects of phonon makes the binding energies more than the obtained results using a Coulomb potential screened by a static dielectric constant and the optical properties of hydrogenic impurity in a quantum dot are strongly affected by the confining potential and the radii. It is also observed that the magnitude of the absorption coefficients increases for the transitions between higher levels with the inclusion of phonon effect.     

Correlation inequalities and the mass gap inP (φ)2

We consider the infinite volume Dirichlet (or half-Dirichlet)P(φ)₂ quantum field theory withP(X)=aX ⁴+bX ⁴+bX ²?μX(a>0). If μ≠0 there is a positive mass gap in the energy spectrum. If the gap vanishes as μ → 0, it goes to zero no faster than linearly yielding a bound on a critical exponent.