Complex images for electrostatic field computation in multilayered media

Chow, Y.L.; Yang, Jian; Howard, Gregory

doi:10.1109/22.85378

Cited by 84 publications

(30 citation statements)

References 8 publications

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“…24 The various Green's functions are expressed in terms of a spectral domain kernel, which can be numerically approximated by using Prony's method, and the spatial Green's function are obtained by using the complex image method. 22 The threelayered Green's functions are listed below. …”

Section: Appendix B: the Green's Functions For The Silicon And Silicomentioning

confidence: 99%

“…To tackle the second problem, we use the multilayered Green's functions and solved an integral equation by the moment method. 21 We use the complex image method 22 to calculate the spatial domain Green's functions from the spectral domain multilayered Green's functions, and this enables us to consider more realistic, arbitrary shape, and threedimensional ͑3D͒ structured A gates. Using the corrected wave functions and the numerical values of potential distribution, we are able to formulate a first-order perturbation theory for the perturbed system under the influence of an electric field.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical method for determination of the NMR frequency of the single-qubit operation in a silicon-based solid-state quantum computer

Hui

2006

Phys. Rev. B

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A numerical method is introduced to determine the nuclear magnetic resonance frequency of a donor ͑ 31 P͒ doped inside a silicon substrate under the influence of an applied electric field. This phosphorus donor has been suggested for operation as a qubit for the realization of a solid-state scalable quantum computer. The operation of the qubit is achieved by a combination of the rotation of the phosphorus nuclear spin through a globally applied magnetic field and the selection of the phosphorus nucleus through a locally applied electric field. To realize the selection function, it is required to know the relationship between the applied electric field and the change of the nuclear magnetic resonance frequency of phosphorus. In this study, based on the wave functions obtained by the effective-mass theory, we introduce an empirical correction factor to the wave functions at the donor nucleus. Using the corrected wave functions, we formulate a first-order perturbation theory for the perturbed system under the influence of an electric field. In order to calculate the potential distributions inside the silicon and the silicon dioxide layers due to the applied electric field, we use the multilayered Green's functions and solve an integral equation by the moment method. This enables us to consider more realistic, arbitrary shape, and three-dimensional qubit structures. With the calculation of the potential distributions, we have investigated the effects of the thicknesses of silicon and silicon dioxide layers, the relative position of the donor, and the applied electric field on the nuclear magnetic resonance frequency of the donor.

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Section: Appendix B: the Green's Functions For The Silicon And Silicomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical method for determination of the NMR frequency of the single-qubit operation in a silicon-based solid-state quantum computer

Hui

2006

Phys. Rev. B

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“…Due to environmental and safety considerations, the engineers are also interested in the temperature field in the ground surrounding the electrode Detailed research has been reported in the literature on calculating current and temperature fields for HVDC grounding electrodes. Generally speaking, the complex image method has a high accuracy and is simple in operation [9]. However, this method requires vertically stratified soil and is not applicable when the soil resistivity varies in all directions.…”

Section: Introductionmentioning

confidence: 99%

Calculating current and temperature fields of HVDC grounding electrodes

Zhang

2015

J. Mod. Power Syst. Clean Energy

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Current field calculation based on the resistance network method (RNM) and temperature field calculation based on the finite volume method (FVM) can be used to evaluate the performance of high-voltage direct-current (HVDC) grounding electrodes. The main idea of the two methods is to transform an electric and temperature field problems to equivalent circuit problems by dividing the 3D soil space near the grounding electrode into a suitable number of contiguous and non-overlapped cells. Each cell is represented as a central node connecting to the adjacent cells. The resistance network formed by connecting all the adjacent cells together can be solved to calculate the current field. Under the same conditions, the results calculated by the RNM are consistent with the result by CDEGS, a widely used software package for current distribution and electromagnetic field calculation. Based on the finite volume method, the temperature field results are also calculated using time domain simulation.

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“…To accomplish this, a closed-form Green's function for such media is required. Chow et al [23] have derived a closedform approximation to the Green's function utilizing a finite number of complex images. Oh et al [24] accomplish the same by using only real images.…”

Section: Introductionmentioning

confidence: 99%

Multipole‐accelerated capacitance computation for 3‐D structures in a stratified dielectric medium using a closed‐form Green's function

Jandhyala

Michielssen

Mittra

1995

Int. J. Microw. Mill.‐Wave Comput.‐Aided Eng.

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In this article, the capacitance matrices of three-dimensional conducting structures embedded in a stratified dielectric medium are computed by using the fast multipole method in conjunction with a closed-form approximation of the appropriate Green's function. Image charges that result from the employment of this Green's function are incorporated into the fast multipole method. This technique is used to accelerate the iterative generalized minimal residual-based solution of the system of equations generated by the method of moments. This yields the charge distributions on the conductors and thereby the required capacitance matrix. It is shown that the use of this technique typically results in a speedup of more than an order of magnitude over iterative and direct methods without a compromise of the numerical accuracy. 0 1995 John Wiley & Sons, Inc.

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Complex images for electrostatic field computation in multilayered media

Cited by 84 publications

References 8 publications

Numerical method for determination of the NMR frequency of the single-qubit operation in a silicon-based solid-state quantum computer

Numerical method for determination of the NMR frequency of the single-qubit operation in a silicon-based solid-state quantum computer

Calculating current and temperature fields of HVDC grounding electrodes

Multipole‐accelerated capacitance computation for 3‐D structures in a stratified dielectric medium using a closed‐form Green's function

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