Novel method to determine effective length of quantum confinement using fractional-dimension space approach

Li, Hua; Liu, Bingcan; Shi, Bingxin; Dong, Shikui; Tian, Qiang

doi:10.1007/s11467-015-0472-2

Cited by 8 publications

(3 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Polaron effects in these systems can be studied simply by using the fractal dimension framework with good accuracy. [1][2][3][4][5][6][7] In the past few years, the fractal dimension method has aroused a lot of interest. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] The fractal dimension method proposed by He [1] has been successfully applied to model excitons, [7][8][9][10][11] polarons, [12] and impurities [13][14][15][16] in semiconductor materials.…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7] In the past few years, the fractal dimension method has aroused a lot of interest. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] The fractal dimension method proposed by He [1] has been successfully applied to model excitons, [7][8][9][10][11] polarons, [12] and impurities [13][14][15][16] in semiconductor materials. Among these materials, core-shell nanowires are extensively regarded as the next frontier in the applications of numerous optoelectronic and electronic equipments.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Polaron effects in cylindrical GaAs/Al _x Ga _{1–
x} As core-shell nanowires ^*

Sun

Liu²,

Tian

2017

Chinese Phys. B

Self Cite

View full text Add to dashboard Cite

By the fractal dimension method, the polaron properties in cylindrical GaAs/Al x Ga 1−x As core-shell nanowire are explored. In this study, the polaron effects in GaAs/Al x Ga 1−x As core-shell nanowire at different values of shell width and aluminum concentration are discussed. The polaron binding energy, polaron mass shift and fractal dimension parameter are numerically worked out each as a function of core radius. The calculation results show that the binding energy and mass shift of the polaron first increase and then decrease as the core radius increases, forming their corresponding maximum values for different aluminum concentrations at a given shell width. Polaron problems in the cylindrical GaAs/Al x Ga 1−x As core-shell nanowire are solved simply by using the fractal dimension method to avoid complex and lengthy calculations.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Polaron effects in cylindrical GaAs/Al _x Ga _{1–
x} As core-shell nanowires ^*

Sun

Liu²,

Tian

2017

Chinese Phys. B

Self Cite

View full text Add to dashboard Cite

show abstract

“…24,25 The axiomatic basis of spaces with fractional dimension had been introduced by Stillinger, 24 where he described the integration on a space with non-integer dimension, and provided a generalization of second order Laplace operators. This approach has been widely applied in quantum field theory, 18,26,27 general relativity, 28 thermodynamics, 29 mechanics, [30][31][32] hydrodynamics, 33 and electrodynamics. 20,[34][35][36][37][38][39][40][41][42][43] To expand the range of possible applications of models with fractional-dimensional spaces, a complete generalization of vector calculus operators has been reported recently.…”

Section: Introductionmentioning

confidence: 99%

Fractional-dimensional Child-Langmuir law for a rough cathode

Zubair

Ang

2016

Physics of Plasmas

View full text Add to dashboard Cite

This work presents a self-consistent model of space charge limited current transport in a gap combined of free-space and fractional-dimensional space (Fα), where α is the fractional dimension in the range 0 < α ≤ 1. In this approach, a closed-form fractional-dimensional generalization of Child-Langmuir (CL) law is derived in classical regime which is then used to model the effect of cathode surface roughness in a vacuum diode by replacing the rough cathode with a smooth cathode placed in a layer of effective fractional-dimensional space. Smooth transition of CL law from the fractional-dimensional to integer-dimensional space is also demonstrated. The model has been validated by comparing results with an experiment.

show abstract