Self-capacitance of a quantum dot: Dependence on the shape of the confining potential

Ranjan, V.; Pandey, Rakesh Kumar; Harbola, Manoj K.; Singh, Vijay A.

doi:10.1103/physrevb.65.045311

Cited by 13 publications

(14 citation statements)

References 33 publications

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“…Note that the HS scheme accounts for self-interaction correction while the local density approximation (LDA) does not. This formalism has been employed earlier [13] to study the Coulomb blockade and the quantum capacitance of quantum dots. In this scheme the binding energy of a positive donor can be written as…”

Section: Df-emt Modelmentioning

confidence: 99%

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Defects in semiconductor nanostructures

2008

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Impurities play a pivotal role in semiconductors. One part in a million of phosphorous in silicon alters the conductivity of the latter by several orders of magnitude. Indeed, the information age is possible only because of the unique role of shallow impurities in semiconductors. Although work in semiconductor nanostructures (SN) has been in progress for the past two decades, the role of impurities in them has been only sketchily studied. We outline theoretical approaches to the electronic structure of shallow impurities in SN and discuss their limitations. We find that shallow levels undergo a SHADES (SHAllow-DEep-Shallow) transition as the SN size is decreased. This occurs because of the combined effect of quantum confinement and reduced dielectric constant in SN. Level splitting is pronounced and this can perhaps be probed by ESR and ENDOR techniques. Finally, we suggest that a perusal of literature on (semiconductor) cluster calculations carried out 30 years ago would be useful.

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Section: Df-emt Modelmentioning

confidence: 99%

“…For a hydrogenic impurity, Z = 1, m * is the effective mass of the electron inside the QD in units of m e , the free electron mass. We model the external potential as [13,14] V ext (r) =…”

Section: Emt Modelmentioning

confidence: 99%

Defects in semiconductor nanostructures

2008

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“…We call it the "Hubbard U". 11,12 For a one orbital system the last two terms in the Eq. (5) cancel each other in the HS scheme but they do not cancel within the LDA.…”

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Shallow–deep transitions of neutral and charged donor states in semiconductor quantum dots

2004

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We carry out a detailed study of neutral ͑D 0 ͒ and charged ͑D − ͒ impurity states of hydrogen-like donors in spherical semiconductor quantum dots. The work is carried out within the effective mass theory, treating many-body effects within the local density approximation and the Harbola-Sahni schemes. We observe that the donor level undergoes shallow to deep transition as the dot radius is reduced. On further reduction of the dot radius it becomes shallow again. This suggests the possibility of carrier "freeze out" for both D 0 and D − . Further, our study of the optical gaps also reveals a nonmonotonic shallow-deep behavior.

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“…4 Theoretical studies of a QD involve multielectron effects. Review of earlier work in this direction maybe found in the recent work of Jiang et al 5 and Ranjan et al 6 In this work, we investigate the behavior of the direct Coulomb and the exchange correlation with the shape of the confinement potential and size of the quantum dot. Before we discuss the motivation behind this work, we define a few relevent terms.…”

Section: Introductionmentioning

confidence: 97%

Scaling of Coulomb and exchange-correlation effects with quantum dot size

2003

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The role of many-body effects in quantum dots is of both academic and practical interest. We study the electron-electron interaction within a simplified spherical quantum dot using the local spin-density approximation. We experiment with a variety of confining potentials ͑triangular, harmonic, square well, etc.͒ and with a varying number of electrons (Nϭ2 to 20͒. We carry out a detailed study of the scaling behavior of the ''Hubbard U'' potential, which is a measure of the capacitive energy, with quantum dot size R (Uϳ1/R ␤ ). We find that the scaling exponent ␤ is Ϸ1/2 for harmonic confinement and equal to 1 for the square-well confinement. The dependence of the scaling exponents on the confining potential and the number of electrons N is elucidated. We also examine the relative importance of Coulomb, exchange, and correlation terms in the Hubbard U potential and find that correlation plays a relatively more important role at a larger size. We provide a partial explanation for the value of the exponent in the Appendix.

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Self-capacitance of a quantum dot: Dependence on the shape of the confining potential

Cited by 13 publications

References 33 publications

Defects in semiconductor nanostructures

Defects in semiconductor nanostructures

Shallow–deep transitions of neutral and charged donor states in semiconductor quantum dots

Scaling of Coulomb and exchange-correlation effects with quantum dot size

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