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The planar waveguide

Peter Blood

in Quantum Confined Laser Devices: Optical gain and recombination in semiconductors

The planar waveguide controls the overlap of the laser mode with the gain material, which drives the stimulated emission process and determines the divergence of the beam on leaving the laser, ... More

The planar waveguide controls the overlap of the laser mode with the gain material, which drives the stimulated emission process and determines the divergence of the beam on leaving the laser, important for coupling into external elements such as fibres. Through the optical confinement factor and the optical mode width, the waveguide provides the connection between the gain generated by the gain medium (the material gain) and the amplification experienced by the laser mode (the modal gain). Starting with Maxwell’s equations, this chapter provides an introduction to optical modes of transverse electric and transverse magnetic polarisation in a passive, planar waveguide in the weak guiding approximation. The chapter ends with a short introduction to the internal mode loss in a waveguide.Less

Non-Polar Slab

B. K. Ridley

in Hybrid Phonons in Nanostructures

Hybrid modes exist as a consequence of acoustic and optical waves having to satisfy the boundary conditions at an interface or at a surface. The author begins the description of hybrid modes in ... More

Hybrid modes exist as a consequence of acoustic and optical waves having to satisfy the boundary conditions at an interface or at a surface. The author begins the description of hybrid modes in nanostructures with an account of modes in a non-polar, free-standing slab. This chapter includes long-wavelength assumption decouples acoustic and optical modes; isotropy decouples LO and TO modes; s and p modes; acoustic hybrid modes: Love waves, Lamb waves, guided modes, Rayleigh waves; the boundary condition u = 0 for optical modes; the sTO mode; double hybrid: LO and pTO modes; and energy normalization.Less

Dynamic screening

B. K. Ridley FRS

in Quantum Processes in Semiconductors

Electrons in a semiconductor undergo polar scattering due to charged impurities, piezoelectric modes, holes, other electrons, and optical phonons — all of which are susceptible to electrical ... More

Electrons in a semiconductor undergo polar scattering due to charged impurities, piezoelectric modes, holes, other electrons, and optical phonons — all of which are susceptible to electrical screening by the mobile electron gas. Because the frequencies of acoustic phonons which can interact with electrons are quite low, the screening of the piezoelectric interaction can be adequately described by static screening. When the density of the electron gas is high, dynamic screening and plasma effects become inextricably mixed and must be treated together. This chapter focuses on the dynamic screening of electrons in semiconductors, first by considering polar optical modes, plasma modes, and coupled modes. It then discusses the Lindhard dielectric function, fluctuations, and four regimes of dynamic screening effects.Less

Polar Modes in Zinc Blende

B. K. Ridley

in Hybrid Phonons in Nanostructures

Continuing on from the second chapter, here, the polar elements that occur in III–V compounds are added. Chapter 3 covers: piezoelectricity and ionic charge, relation between electric field and ionic ... More

Continuing on from the second chapter, here, the polar elements that occur in III–V compounds are added. Chapter 3 covers: piezoelectricity and ionic charge, relation between electric field and ionic displacement for polar optical modes, the dielectric function, effects of lattice dispersion, interface electromagnetic modes, and ionic mass entering connection rules in nanostructures.Less

Optical Modes

B. K. Ridley

in Hybrid Phonons in Nanostructures

A continuum theory of long-wavelength non-polar acoustic and optical modes arising out of a microscopic model of the lattice dynamics is described. The chapter covers: microscopic model of the ... More

A continuum theory of long-wavelength non-polar acoustic and optical modes arising out of a microscopic model of the lattice dynamics is described. The chapter covers: microscopic model of the diamond lattice, equations of motion for acoustic and optical modes, decoupling of acoustic and optical modes, relation of elastic constants to bond strengths, lower symmetry for optical modes, and connection rules in nanostructures for acoustic modes different from those for optical modes.Less

Semi-classical transport

B. K. Ridley FRS

in Quantum Processes in Semiconductors

In order to provide a comprehensive account of the response of electrons in semiconductors to external fields, their quantum nature must be taken into account. However, there are cases in which the ... More

In order to provide a comprehensive account of the response of electrons in semiconductors to external fields, their quantum nature must be taken into account. However, there are cases in which the behaviour of electrons can be treated semi-classically, with quantum effects entering only through scattering and band structure. The electron is assumed to be in one of the Bloch states of the conduction band with a well-defined energy and a well-defined wavevector. This chapter examines the semi-classical transport of electrons in semiconductors, first by looking at the Boltzmann equation and weak electric fields. It then discusses electron–electron scattering, hot electrons and their distribution functions, scattering by non-polar acoustic phonons and non-polar optical modes, and the drifted Maxwellian approach to the hot-electron problem.Less

The Interaction between Electrons and Polar Optical Phonons in Nanostructures: General Remarks

B. K. Ridley

in Hybrid Phonons in Nanostructures

In the study of transport phenomena in semiconductor nanostructures the interaction between electrons and phonons assumes a central significance because of its intrinsic nature. In principle, ... More

In the study of transport phenomena in semiconductor nanostructures the interaction between electrons and phonons assumes a central significance because of its intrinsic nature. In principle, scattering due to impurities, lattice defects, and interface roughness can be eliminated. In practice, technical innovation regarding purification and crystal growth can make non-phonon scattering subordinate in many structures at room temperature, and likely to be dominant only at low temperatures, where the excitation of lattice vibrations is weak, Even there, the electron-phonon interaction cannot be ignored when the electrons become hot in high electric fields. The only other scattering mechanism that is not readily amenable to ideal crystal growth is that due to alloy fluctuations. Otherwise, in unalloyed binary semiconductors, the electron-phonon interaction is of central importance. This chapter includes: a brief history; discussion on the role of lattice dispersion for optical modes; and coupled modes and hot phonons.Less

Single Heterostructure

B. K. Ridley

in Hybrid Phonons in Nanostructures

The single heterostructure is one of the most technologically versatile devices, being the structure of field-effect transistors and Schottky-effect devices, to say nothing of its capability of ... More

The single heterostructure is one of the most technologically versatile devices, being the structure of field-effect transistors and Schottky-effect devices, to say nothing of its capability of exhibiting the quantum Hall effect at low temperatures. Here, the focus is on a heterostructure composed of III–V compounds such as AlAs/GaAs at room temperature and above, where optical waves are readily excited. This chapter covers: hybrid model for optical modes: LO, pTO, IF; ionic displacement and associated electric fields; fields in the barrier layer – remote phonons; mechanical boundary condition u = 0; energy normalization; reduced boundary conditions; acoustic hybrids: sTA, pTA, pLO; and interface acoustic modes.Less

Quantum Dot

B. K. Ridley

in Hybrid Phonons in Nanostructures

Experimental determination of the properties of semiconductor quantum dots is bedevilled by the spread in sizes of dot in the population. Nevertheless, interest in their optical properties and their ... More

Experimental determination of the properties of semiconductor quantum dots is bedevilled by the spread in sizes of dot in the population. Nevertheless, interest in their optical properties and their dependence on the degree of confinement of electrons, holes, and lattice waves has stimulated a considerable literature. In particular, the excitation of electrons and holes, the nature of the exciton, the interaction with phonons, and the anharmonic effects associated with the Stokes shift have received considerable attention. The common approach to the electron-phonon interaction has been via the DC model. This chapter focuses on the confinement of lattice waves and in particular, of polar optical modes and their hybridization. The chapter covers: scalar and vector potentials in spherical coordinates; ionic displacements for LO and TO modes; polar double hybrids; quantum disc and quantum box.Less

Quantum Well

B. K. Ridley

in Hybrid Phonons in Nanostructures

Assumptions: long-wavelength, isotropy, u = 0 for optical modes. This chapter considers a slab of polar material bounded in the z direction at z = ±L/2 and unbounded otherwise. It covers: triple ... More

Assumptions: long-wavelength, isotropy, u = 0 for optical modes. This chapter considers a slab of polar material bounded in the z direction at z = ±L/2 and unbounded otherwise. It covers: triple hybrid model for optical modes; energy normalization; reduced boundary conditions; barrier modes; dispersion and wave patterns; acoustic hybrids; sTA and p modes; families of guided p modes; and interface acoustic waves.Less

Boundary Conditions

B. K. Ridley

in Hybrid Phonons in Nanostructures

An immediate problem that presented itself in the physics of nanostructures, formed from two semiconductors, was to describe conditions at their interface. In principle, band-structure and ... More

An immediate problem that presented itself in the physics of nanostructures, formed from two semiconductors, was to describe conditions at their interface. In principle, band-structure and lattice-dynamical calculations could be performed to give the eigenvalues and eigenstates of the whole heterostructure, but any result along these lines would refer only to the special case considered, and would provide little in the way of providing criteria for predicting the properties of the huge number of structures that were conceivableThis chapter will outline classical connection rules for acoustic modes, detailed connection rules for optical modes, and electromagnetic interface conditions.Less

Scattering Rate in Quantum Wires

B. K. Ridley

in Hybrid Phonons in Nanostructures

The scattering rate associated with hybrid optical modes in a cylindrical quantum wire is derived.

Threshold and the light–current characteristic

Peter Blood

in Quantum Confined Laser Devices: Optical gain and recombination in semiconductors

The light–current characteristic is the most basic measurement that can be made of the performance of a laser diode, giving its threshold current and external efficiency. For conventional laser ... More

The light–current characteristic is the most basic measurement that can be made of the performance of a laser diode, giving its threshold current and external efficiency. For conventional laser diodes a threshold in this characteristic is usually adequate evidence that laser action has been achieved. The contributions to the threshold current of real devices by current spreading, non-radiative recombination by Shockley–Read–Hall (SRH) and Auger processes, and carrier leakage over heterobarriers are described. These are not usually included in theoretical calculations of gain–current characteristics. The information that can be extracted from the threshold current density alone is limited; however, systematic measurements as a function of cavity length can give greater insight into operation of the device, for example in certain circumstances analysis of the differential quantum efficiency provides a value for the optical mode loss. Analysis of the characteristics of quantum dot and well devices is described.Less