Bulk Longitudinal Optical Phonons Research Articles

The effective mass of a slow-moving surface polaron in a semi-infinite crystal

There is weak bulk but strong surface coupling between electrons and phonons in a semi-infinite crystal. Here some properties of the surface polaron in a semi-infinite crystal, weak coupling with bulk longitudinal optical (BO) phonons and strong coupling with surface longitudinal optical (SO) phonons, are studied. The effective Hamiltonian of a slow-moving surface polaron in a semi-infinite crystal is derived using an improved linear combination operator and perturbation method. If we consider the interaction between phonons of different wave vectors in the recoil process, the influence of this interaction on the effective Hamiltonian, the induced potential and the effective mass of the surface polaron are discussed. Numerical calculations for an AgBr crystal, as an example, are performed, and some properties of the surface polaron in a semi-infinite crystal are discussed.

Interface Polaron Within Parallel Electric and Magnetic Fields11The project supported by the Higher Education Bureau of Guangdong Province

A combinative method of variational wavefunction and harmonic oscillator operator algebra is used to treat the interface polaron in a semi-infinite polar crystal within parallel electric and magnetic fields perpendicular to the interface. Both the bulk longitudinal optical phonon and the interface optical phonon together with the anisotropic mass of the electron are included. The energy level correction up to the second-order perturbation, cyclotron-resonance frequency and cyclotron mass are expressed as functions of the electric and magnetic fields and a parameter characterizing the mean distance of the polaron from the interface. This theory is used to calculate numerically the single heterostructure AlAs/GaAs, when the electron is at the X high-symmetry point of the conduction band of AlAs. The results show that the magnetic field greatly enhances the polaronic correction of the electron energy levels while the electric field only increases the correction of their surface optical phonon part but obviously decreases that of their bulk optical mode part and thus the total energy correction decreases as the electric field increases. The change of red shift due to the electron-phonon interaction with electric and magnetic fields is also obtained.

Influence of the electron-electron and electron-phonon interaction on the cyclotron resonance of 2DEG in GaAs

The resonant polaron effect was investigated for cyclotron transitions N → N + 1 in magnetic field regimes where the Landau levels N = 2 and 3 cross with the level N = 0 plus one bulk longitudinal optical phonon. The experiment is analyzed in the framework of the improved Wigner-Brillouin perturbation theory taking into account band-coupling phenomena, a finite thickness of the inversion layer in the growth direction, and coupling of the cyclotron transitions due to electron-electron interactions. From the cyclotron mass enhancements, a Fröhlich coupling constant α = 0.06 to 0.07 was obtained.

Properties of the surface magnetopolaron in polar crystals

There is weak bulk but strong surface coupling between the electron and phonons for polar crystals in a magnetic field. In this paper, the influences of the electron interaction with both the weak-coupling bulk longitudinal optical phonons and the strong-coupling surface optical phonons on the properties of the surface polaron in a magnetic field are studied. The effective Hamiltonian of the surface polaron is derived by using a linear-combination operator method. Numerical calculations on the AgCl crystal, as an example, are performed, and some properties of the vibration frequency and the effective interaction potential of the surface polaron in a magnetic field are discussed.

Effect of Strong Electron-Phonon Interactions on an Interface Polaron

The present work deals with an electron interacting strongly with both bulk longitudinal optical (LO) phonons and interface (IF) optical phonons in which we adopt and generalize the Tokuda's variational method for studying the interface polaron properties in polar crystals at zero temperature, In our approach, we can reduce the Hamiltonian equation of the system to a pair of integro-differential equations in two variational parameters of the electron wavefunction from which we can calculate various physical properties of an interface polaron including the ground state energy, average numbers of interacting phonons, the average distance from the interface and the anisotropic effective masses of the interface polaron. Numerical results are obtained explicitly for LiF crystal interfaced with NaF crystal as well as other similar systems with varying physical constants, which show the typical trends of variations for the effects of strong electron-phonon interactions on different physical properties of an interface polaron.

Theory of photoluminescence of magnetopolarons in quantum wells containing high densities of electrons.

We present a theory of photoluminescence in the presence of a quantizing magnetic field for a quasi-two-dimensional electron gas interacting with the lattice assuming a weak Fr\"ohlich interaction with bulk longitudinal optical (LO) phonons. Unlike in the conventional cyclotron resonance, the calculated photoluminescence spectrum for high electron concentrations exhibits strong renormalization due to the resonant electron-phonon coupling between two quasiholes in conduction Landau levels whenever the LO-phonon energy is close to the energy difference between any two occupied Landau levels. The high electron concentration is necessary to push the Fermi energy well above that of LO phonons. The screening of the electron-phonon interaction was included within the static random-phase approximation and the finite extent of the electron wave function in the quantum well was accounted for. The calculated spectra are in excellent agreement with experimental photoluminescence data for GaAs/${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$As quantum wells.

Self-energy of a magnetopolaron at the interface of polar crystals

The self-energy of an interface electron interacting with bulk longitudinal-optical phonons as well as interface optical (IO) phonons in a magnetic field of arbitrary strength is studied using the Green function method. Our results show that the absolute value mod Ee-ph(0) mod of the ground-state self-energy of the electron is a rapidly increasing function of the magnetic field in the weak magnetic-field region, but mod Ee-ph(0) mod is a slowly decreasing function of the magnetic field beyond a critical magnetic field Bc. For the excited states, mod Ee-ph(n) mod (n>or=1) is an increasing function of the magnetic field in the pre-resonant region, while Ee-ph(n) is a positive and decreasing function of the magnetic field beyond the resonant region. Numerical results show that the electron-IO phonon interaction contributes only when the mean distance of the polaron from the interface is small and in the extremely-weak-magnetic-field region.

Carrier energy relaxation time in quantum-well lasers

Carrier energy relaxation via carrier-polar optical phonon interactions with hot phonon effects in multisubband quantum-well structures is theoretically studied by using both bulk longitudinal optical phonons and confined longitudinal optical phonons. We find that the width and the depth of quantum wells only have moderate effects on carrier energy relaxation rates. Our results also indicate that the difference of energy relaxation rates between the quantum well and the bulk material is not significant. We investigate the effects of longitudinal optical phonon lifetimes on the carrier energy relaxation rate. Neglect of the finite decay time of longitudinal optical phonons will significantly underestimate the carrier energy relaxation time; this not only contradicts the experimental results but also severely underestimates the nonlinear gain coefficient due to carrier heating. The implications of our theoretical results in designing high-speed quantum-well lasers are discussed.

Ground state energy and effective mass of an interface polaron under strong electron-phonon interactions

For an electron interacting strongly with both the interface optical phonons and the bulk longitudinal optical (LO) phonons, the properties of a polaron bound at the interface between two semi-infinite polar crystals are studied. The important effect of the normally ignored electron-bulk LO phonon interaction is demonstrated.

Confined and interface phonon scattering in finite barrier GaAs/AlGaAs quantum wires

We report on the calculation of the total scattering rate in finite barrier GaAs/AlGaAs quantum wires based on the interaction Hamiltonian of confined longitudinal optical (LO) phonon and surface (SO) phonon modes. With multisubband processes being properly taken into account, our calculation indicates that for GaAs type of phonons the high-frequency symmetric (s+) branch plays an important role among all the other SO phonon branches; it can even dominate over confined LO phonons in highly confined quantum wires as observed by K. W. Kim, M. A. Stroscio, A. Bhatt, R. Mickevicius, and V. V. Mitin [J. Appl. Phys. 70, 319 (1991)]. Our results also demonstrate that the total contributions of confined LO and SO phonon scattering resemble closely to GaAs bulk LO phonon scattering. Selection rules between intersubband transitions for SO modes suggest the possibility of a bottle-neck effect for carrier relaxation in square wires compared with rectangular wires.

Temperature Dependence of the Interface Polaron in Polar Crystals

AbstractThere is weak bulk but strong surface coupling between the electrons and phonons for many polar crystals. Here some properties of the interface polaron in polar crystals, which is a weak coupling with bulk longitudinal optical (BO) phonons and a strong coupling with surface longitudinal optical (SO) phonon, are studied. The temperature dependence of vibration frequency, induced potential, image potential, the effective interaction potential, and mean number of interface polarons is obtained by using a linear‐combintion‐operator method proposed by Huybrechts. Numerical calculations, for the AgCl/Kl crystal interface, as an example, are performed and some properties of these quantities of the interface polarons in polar crystals are discussed.

Influence of Electron-Phonon Interactions on the Physical Properties of an Interface Polaron11The project partly supported by National Natural Science Foundation of China through Grant No. 39188006.

Taking into account the interactions of both bulk longitudinal optical (LO) phonons and surface optical (SO) phonons and using Haga's perturbation method, we derive an effective Hamiltonian for the interface magnetopolaron in polar crystals at zero temperature. We illustrate in details how to solve this effective Hamiltonian analytically and we obtain explicit formulae not on1y for the electron cyclotron mass associated with the Landau levels but also for the self-trapping energy of the magnetopolaron with respect to its first three quantum states in the direction normal to the interface of the system. Numerical results are calculated for some II-V and III-V semiconductor compounds, indicating that the bulk LO phonons and SO phonons do have different trends of effects on the electron in different quantum states.

The effect of electron-phonon interactions on the cyclotron mass and self-trapping energy of an interface polaron

Employing Haga's perturbation method the authors derive an effective Hamiltonian for the interface magnetopolaron in polar crystals at zero temperature, in which the interactions of both bulk longitudinal optical (LO) phonons and interface (IF) phonons have been taken into account. Solving this effective Hamiltonian analytically, they obtain explicit formulae not only for the electron cyclotron mass associated with the Landau levels but also for the self-trapping energy of the magnetopolaron with respect to its first three quantum states in the direction normal to the interface of the system. Numerical results are calculated for some II-VI and III-V compounds, revealing that the effects of the bulk LO phonons and IF phonons on the electron in different quantum states do show different trends.

The cyclotron mass and self-trapping energy of an interface polaron

We employ the Haga's perturbation method to obtain the self-trapping energy and the cyclotron mass of the electron interacting with both bulk longitudinal optical (LO) phonons and surface optical (SO) phonons in some interfaced systems of two semi-infinite polar crystals. Our results show that the bulk LO phonons and SO phonons have different trend of effects on the electron in different states.

The Shallow Donor Impurity State Near a Polar Crystal Surface

We report the results of a variational calculation for the ground state of a near surface hydrogenic donor interacting with both surface and bulk longitudinal optical (SO and BO) phonons in polar crystals. In calculation we also consider the effect of the image potentials. The variations of ground state energies and binding energies with R are given for some materials.

Weak-coupling magnetopolarons in a slab of a polar crystal.

Magnetopolarons in a polar-crystal slab are studied in the situation of weak electron-phonon coupling and a weak external magnetic field. The interactions between the electron and the bulk longitudinal-optical phonon and between the electron and the surface-optical phonon are included in this work. Formulas for the magnetopolaron energy levels in the slab are obtained by a perturbation method. The magnetopolaron cyclotron frequency is calculated numerically as a function of the slab thickness and the external magnetic field for several III-V and II-VI compounds. It is found that the renormalized cyclotron frequency increases with increasing slab thickness and with increasing magnetic field. The contributions of the bulk-optical phonons and the surface-optical phonons for the renormalization of the cyclotron frequency are also discussed.

The bound polaron in a polar slab

In the paper, for the polaron bound to a fixed Coulomb origin located at the centre of a polar slab, the energies of the ground state and the excited state as well as the effective mass are investigated by means of the Lee-Low-Pines variation technique. From consideration of the interactions between an electron and both the bulk longitudinal optical (LO) phonon and the surface optical (SO) phonon, the self-energy and the effective mass are derived as functions of slab thickness. Taking GaAs as an example, the authors discuss a number of interesting features.

A magnetopolaron in a slab of a polar crystal

The Hamiltonian of a magnetopolaron in a slab of a polar crystal, including bulk longitudinal optical phonons and surface optical phonons as well as the influence of the image potential, is derived. The relations between its ground and excited energies and the magnetic field and thickness of the slab are studied.

The effect of the electron-phonon interaction on the binding energy of hydrogen impurities in a quantum well

The authors use the method suggested by Huybrechts (1978) to study a bound polaron in a three-dimensional polar crystal. They assume the walls of the quantum well to be infinitely high and choose the variational wavefunction to be that used by Bastard (1981) in a study of the states of shallow donors in a quantum well. They investigate the effect of the interaction of electrons with phonons (the phonons include bulk longitudinal optical phonons and surface optical phonons) on the binding energy of shallow donors confined in a quantum well. They find that the effect of polarons increases the binding energy of shallow donors. For the GaAs-Ga1-xAlxAs quantum well, when the L/a0 ratio (where L is the width and a0 the effective Bohr radius) is decreased from 4 to 1, the binding energy increases from 0.3 to 1.3 meV.

Temperature dependence of the bound polaron in a polar crystal slab

In considering both the electron interaction with the bulk longitudinal optical (LO) phonon and the electron interaction with the surface optical (SO) phonon, we have obtained the temperature dependence of the ground state and the excited state energy and the effective mass of the bound polaron confined in a slab of polar crystal by using Lee-Low-Pines variational technique and perturbative variational method.