Chapter 6 Electric-Field Effects on the Dielectric Function of Semiconductors and Insulators

Aspnes, D. E.; Bottka, N.

doi:10.1016/s0080-8784(08)62836-7

Cited by 63 publications

(63 citation statements)

References 81 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…However, for degenerate bands, the existence of singularities in the coordinate matrix has led most authors to abandon the Bloch representation and search for other ways of treating such problems (Wannier (1960), appendix I; Roth (1962); Blount (1962), p 319; Aspnes and Bottka (1972), p 501). These singularities lead directly to a poor localization of Wannier functions (Blount 1962, Zak 1985, and much effort has gone into finding alternative definitions for Wannier functions with better localization properties (des Cloizeaux 1963, 1964a, b, Kohn 1973, Zak 1985.…”

Section: Discussionmentioning

confidence: 99%

“…One is of course free to include an arbitrary k-dependent phase factor, in which case the diagonal elements (3.14) are likewise arbitrary and may be set equal to any real value (Blount 1962, Lax 1974. The existence of singularities in ξ nn (k) means that the Bloch representation is ill suited for the analysis of degenerate bands in external fields (Wannier (1960), appendix I; Roth (1962); Blount (1962), p 319; Aspnes and Bottka (1972), p 501). To eliminate the singularities, one must use basis functions that are analytic functions of k. The best-known example is the Luttinger-Kohn representation, which was used in the construction of the pseudo-Bloch functions mentioned above.…”

Section: Singularities In ξ Nn (K) At a Degeneracymentioning

confidence: 99%

See 1 more Smart Citation

Theory of the effective Hamiltonian for degenerate bands in an electric field

Foreman¹

2000

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Abstract.Recent experiments have generated a renewed interest in the properties of the degenerate valence states in semiconductors under the influence of a uniform external electric field. In response, a number of authors have proposed that the standard Luttinger-Kohn effectivemass Hamiltonian should be modified to include the energy of interaction between the electric field and the dipole matrix elements of the relevant zone-centre Bloch functions. This article examines these proposals by comparing the proposed dipole interaction with rigorous derivations of the fielddependent Hamiltonian in the Bloch and Luttinger-Kohn representations. It is shown that the dipole matrix element of a unit cell is not a suitable foundation for a Hamiltonian because it depends on the choice of unit cell, which is arbitrary. Moreover, the correct Luttinger-Kohn Hamiltonian has no wave-vector-independent matrix elements that are linear in the applied field E, except for small terms of relativistic origin. Therefore, the proposed modifications to the Luttinger-Kohn theory are not valid. The correct form of the Luttinger-Kohn Hamiltonian is derived here through terms of order k 3 , kE, and E 2 , along with the momentum matrix to first order in k and E. In addition, the recent discovery of field-induced mixing at the Brillouin zone boundary in the Luttinger-Kohn representation is studied in detail.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Singularities In ξ Nn (K) At a Degeneracymentioning

confidence: 99%

Theory of the effective Hamiltonian for degenerate bands in an electric field

Foreman¹

2000

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…O sinal da amostra #1 é constituído de uma estrutura em torno de 1,42 eV, relacionada à transição do "gap" fundamental (E 0 ) do GaAs, seguida por oscilações rapidamente amortecidas, provavelmente devidas ao efeito Franz-Keldysh (SHEN;DUttA, 1995). Seguindo a teoria desenvolvida por Aspnes (ASPNES, 1980), a posição em energia do n-ésimo extremo dessas oscilações obedece à relação O espectro da amostra #2 (Fig. 2-(b)) é composto de estruturas provenientes de várias transições, e as três de menor energia estão centradas em 1,421 eV, 1,479 eV e 1,510 eV, e são relacionadas com a transição E 0 da camada buffer do GaAs e com as transições envolvendo o primeiro nível de energia do elétron e os primeiros níveis de buraco pesado (e1-hh1) e leve (e1-lh1) no poço quântico, respectivamente.…”

Section: Resultados Experimentais E Discussãounclassified

Diodos emissores de luz como fonte de bombeio em fotorefetância.

et al. 2008

View full text Add to dashboard Cite

“…[12]. We use the Maxwell-Garnett effective medium approximation (EMA) [13] applying the non-linear least square fitting procedure [14], where the goodness of fit is estimated by the parameter 2 defined elsewhere [13,15]. The EMA model has been used satisfactorily to determine the dielectric function of the middle layer containing the Ge-NCs, which are embedded between the a-Al 2 O 3 films.…”

Section: Methodsmentioning

confidence: 99%

“…To cancel the influence of the substrate and to maximise the information of the Ge-NCs embedded between Al 2 O 3 thin films, the second derivative of the pseudo-dielectric function with respect to the energy h"i 00 was taken and then fitted ( 2 ¼ 1.083572). The line shapes in the derivative spectra of the CPs were modelled with the Lorentz oscillators described as [15],…”

mentioning

confidence: 99%

Microstructure and dielectric functions of Ge nanocrystals embedded between amorphous Al₂O₃films: study of confinement and disorder

Nayak

Bhunia

2012

Journal of Experimental Nanoscience

View full text Add to dashboard Cite

Ge nanocrystals (6-9 nm) embedded between amorphous Al 2 O 3 films were produced in a cluster beam deposition system. The microstructural evaluation and compressive stress experienced by the Ge nanocrystals due to the presence of an oxide layer, nanoparticle size distribution and their changes due to thermal annealing were studied by X-ray diffraction, HRTEM and Raman spectroscopy. Spectroscopic ellipsometry was used to measure the dielectric functions of the deposited films. A multilayer model based on the effective medium approximation was used to analyze the variation of percentage of defects and the extent of disorder with particle size of the nanocrystals. The correlation between the microstructural characteristics and optical properties was established by evaluating standard sum rules. Germanium nanocrystals show visible photo luminescence at room temperature around 3.0 and 2.8 eV. However, a peak shift towards lower energies with increasing particle size due to thermal annealing was not detected. The experimentally observed luminescence is presumably originated due to the presence of oxiderelated defect centers at the interface between the germanium nanocrystals and the embedded oxide layers.

show abstract

Chapter 6 Electric-Field Effects on the Dielectric Function of Semiconductors and Insulators

Cited by 63 publications

References 81 publications

Theory of the effective Hamiltonian for degenerate bands in an electric field

Theory of the effective Hamiltonian for degenerate bands in an electric field

Diodos emissores de luz como fonte de bombeio em fotorefetância.

Microstructure and dielectric functions of Ge nanocrystals embedded between amorphous Al₂O₃films: study of confinement and disorder

Contact Info

Product

Resources

About

Chapter 6 Electric-Field Effects on the Dielectric Function of Semiconductors and Insulators

Cited by 63 publications

References 81 publications

Theory of the effective Hamiltonian for degenerate bands in an electric field

Theory of the effective Hamiltonian for degenerate bands in an electric field

Diodos emissores de luz como fonte de bombeio em fotorefetância.

Microstructure and dielectric functions of Ge nanocrystals embedded between amorphous Al2O3films: study of confinement and disorder

Contact Info

Product

Resources

About

Microstructure and dielectric functions of Ge nanocrystals embedded between amorphous Al₂O₃films: study of confinement and disorder