B. K. Ridley
- Published in print:
- 2017
- Published Online:
- April 2017
- ISBN:
- 9780198788362
- eISBN:
- 9780191830280
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198788362.003.0008
- Subject:
- Physics, Condensed Matter Physics / Materials
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 ...
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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
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.
Brian K. Ridley
- Published in print:
- 2017
- Published Online:
- April 2017
- ISBN:
- 9780198788362
- eISBN:
- 9780191830280
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198788362.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
Crystalline semiconductor nanostructures have special properties associated with electrons and lattice vibrations and their interaction, and this is the topic of the book. The result of spatial ...
More
Crystalline semiconductor nanostructures have special properties associated with electrons and lattice vibrations and their interaction, and this is the topic of the book. The result of spatial confinement of electrons is indicated in the nomenclature of nonostructures: quantum wells, quantum wires, and quantum dots. Confinement also has a profound effect on lattice vibrations and an account of this is the prime focus. The documentation of the confinement of acoustic modes goes back to Lord Rayleigh’s work in the late nineteenth century, but no such documentation exists for optical modes. Indeed, it is only comparatively recently that any theory of the elastic properties of optical modes exists, and the account given in the book is comprehensive. A model of the lattice dynamics of the diamond lattice is given that reveals the quantitative distinction between acoustic and optical modes and the difference of connection rules that must apply at an interface. The presence of interfaces in nanostructures forces the hybridization of longitudinally and transversely polarized modes, along with, in polar material, electromagnetic modes. Hybrid acoustic and optical modes are described, with an emphasis on polar-optical phonons and their interaction with electrons. Scattering rates in single heterostructures, quantum wells, and quantum wires are described and the anharmonic interaction in quantum dots is discussed. A description is given of the effects of dynamic screening of hybrid polar modes and the production of hot phonons. The book is structured into three parts: basics, hybrid modes, and the electron-phonon interaction.Less
Crystalline semiconductor nanostructures have special properties associated with electrons and lattice vibrations and their interaction, and this is the topic of the book. The result of spatial confinement of electrons is indicated in the nomenclature of nonostructures: quantum wells, quantum wires, and quantum dots. Confinement also has a profound effect on lattice vibrations and an account of this is the prime focus. The documentation of the confinement of acoustic modes goes back to Lord Rayleigh’s work in the late nineteenth century, but no such documentation exists for optical modes. Indeed, it is only comparatively recently that any theory of the elastic properties of optical modes exists, and the account given in the book is comprehensive. A model of the lattice dynamics of the diamond lattice is given that reveals the quantitative distinction between acoustic and optical modes and the difference of connection rules that must apply at an interface. The presence of interfaces in nanostructures forces the hybridization of longitudinally and transversely polarized modes, along with, in polar material, electromagnetic modes. Hybrid acoustic and optical modes are described, with an emphasis on polar-optical phonons and their interaction with electrons. Scattering rates in single heterostructures, quantum wells, and quantum wires are described and the anharmonic interaction in quantum dots is discussed. A description is given of the effects of dynamic screening of hybrid polar modes and the production of hot phonons. The book is structured into three parts: basics, hybrid modes, and the electron-phonon interaction.
B. K. Ridley
- Published in print:
- 2017
- Published Online:
- April 2017
- ISBN:
- 9780198788362
- eISBN:
- 9780191830280
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198788362.003.0011
- Subject:
- Physics, Condensed Matter Physics / Materials
Nanostructures in which the electrons are confined in two directions and unconfined in the third are known as quantum wires. Theories of electron confinement and phonon spectrum in quantum wires have ...
More
Nanostructures in which the electrons are confined in two directions and unconfined in the third are known as quantum wires. Theories of electron confinement and phonon spectrum in quantum wires have focused on two simple geometries: wires with rectangular cross section and wires with circular cross section. This chapter covers: scalar and vector potentials in cylindrical coordinates; ionic displacement components for longitudinally polarized modes, and for transversely polarized modes, and for interface modes; hybrid LO modes; energy normalization; acoustic stresses and strains; particle displacements for LA, TA1, and TA2 modes; and free surface.Less
Nanostructures in which the electrons are confined in two directions and unconfined in the third are known as quantum wires. Theories of electron confinement and phonon spectrum in quantum wires have focused on two simple geometries: wires with rectangular cross section and wires with circular cross section. This chapter covers: scalar and vector potentials in cylindrical coordinates; ionic displacement components for longitudinally polarized modes, and for transversely polarized modes, and for interface modes; hybrid LO modes; energy normalization; acoustic stresses and strains; particle displacements for LA, TA1, and TA2 modes; and free surface.
