We present a systematic investigation of calculating quantum dots （QDs） energy levels using finite element method in the frame of eight-band k · p method. Numerical results including piezoelectricity, electron ...We present a systematic investigation of calculating quantum dots （QDs） energy levels using finite element method in the frame of eight-band k · p method. Numerical results including piezoelectricity, electron and hole levels, as well as wave functions are achieved. In the calculation of energy levels, we do observe spurious solutions （SSs） no matter Burt Foreman or symmetrized Hamiltonians are used. Different theories are used to analyse the SSs, we find that the ellipticity theory can give a better explanation for the origin of SSs and symmetrized Hamiltonian is easier to lead to SSs. The energy levels simulated with the two Hamiltonians are compared to each other after eliminating SSs, different Hamiltonians cause a larger difference on electron energy levels than that on hole energy levels and this difference decreases with the increase of QD size.展开更多
In this paper we analyze a long standing problem of the appearance of spurious,non-physical solutions arising in the application of the effective mass theory to low dimensional nanostructures.The theory results in a s...In this paper we analyze a long standing problem of the appearance of spurious,non-physical solutions arising in the application of the effective mass theory to low dimensional nanostructures.The theory results in a system of coupled eigenvalue PDEs that is usually supplemented by interface boundary conditions that can be derived from a variational formulation of the problem.We analyze such a system for the envelope functions and show that a failure to restrict their Fourier expansion coeffi-cients to small k components would lead to the appearance of non-physical solutions.We survey the existing methodologies to eliminate this difficulty and propose a simple and effective solution.This solution is demonstrated on an example of a two-band model for both bulk materials and low-dimensional nanostructures.Finally,based on the above requirement of small k,we derive a model for nanostructures with cylindrical symmetry and apply the developed model to the analysis of quantum dots using an eight-band model.展开更多
This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamical system in which t...This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamical system in which the step-size acts as a parameter. We present a unified approach to look for bifurcations from the steady solutions into spurious solutions as step-size varies.展开更多
基金Project supported by the National High Technology Research and Development Program of China(Grant No.2006AA03Z401)'One-Hundred Talents Program' of the Chinese Academy of Sciences,and the National Natural Science Foundation of China (Grant No.60876033)
文摘We present a systematic investigation of calculating quantum dots （QDs） energy levels using finite element method in the frame of eight-band k · p method. Numerical results including piezoelectricity, electron and hole levels, as well as wave functions are achieved. In the calculation of energy levels, we do observe spurious solutions （SSs） no matter Burt Foreman or symmetrized Hamiltonians are used. Different theories are used to analyse the SSs, we find that the ellipticity theory can give a better explanation for the origin of SSs and symmetrized Hamiltonian is easier to lead to SSs. The energy levels simulated with the two Hamiltonians are compared to each other after eliminating SSs, different Hamiltonians cause a larger difference on electron energy levels than that on hole energy levels and this difference decreases with the increase of QD size.
文摘In this paper we analyze a long standing problem of the appearance of spurious,non-physical solutions arising in the application of the effective mass theory to low dimensional nanostructures.The theory results in a system of coupled eigenvalue PDEs that is usually supplemented by interface boundary conditions that can be derived from a variational formulation of the problem.We analyze such a system for the envelope functions and show that a failure to restrict their Fourier expansion coeffi-cients to small k components would lead to the appearance of non-physical solutions.We survey the existing methodologies to eliminate this difficulty and propose a simple and effective solution.This solution is demonstrated on an example of a two-band model for both bulk materials and low-dimensional nanostructures.Finally,based on the above requirement of small k,we derive a model for nanostructures with cylindrical symmetry and apply the developed model to the analysis of quantum dots using an eight-band model.
基金The work of this author is supported in part by E-Institutes of Shanghai Municipal Education Commission （No. E03004）, Shanghai Science and Technology Commission （No.03QA14036）, Shanghai Leading Academic Discipline Project （No. T0401）, Science Foundation of Shanghai （No. 04JC14062） and Special Funds for Major Specialties of Shanghai Education Commission.Acknowledgement. The authors wish to thank the anonymous referees for their carefully correcting the preliminary version of the manuscript.
文摘This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamical system in which the step-size acts as a parameter. We present a unified approach to look for bifurcations from the steady solutions into spurious solutions as step-size varies.
