Surface polaronic effect on donor-impurity states of a wurtzite nitride nanowire: Two-parameter variational approach

2011 ◽  
Vol 110 (1) ◽  
pp. 013712 ◽  
Author(s):  
Li Zhang ◽  
J. J. Shi ◽  
P. M. Shao
Keyword(s):  
Variational Approach ◽  
Donor Impurity ◽  
Impurity States ◽  
Two Parameter

Electronic and shallow donor impurity states in GaAs‐Ga1−xAlxAs quantum‐well wires: Effects of dielectric mismatch

1994 ◽  
Vol 75 (11) ◽  
pp. 7389-7393 ◽  
Author(s):  
Zhen‐Yan Deng ◽  
Ting‐Rong Lai ◽  
Jing‐Kun Guo ◽  
Shi‐Wei Gu
Keyword(s):  
Quantum Well ◽  
Shallow Donor ◽  
Donor Impurity ◽  
Impurity States ◽  
Quantum Well Wires ◽  
Dielectric Mismatch

Variational Approach to Beams Resting on Two-Parameter Tensionless Elastic Foundations

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
A. Nobili
Keyword(s):  
Variational Formulation ◽  
Variational Approach ◽  
Multiple Solutions ◽  
Numerical Solutions ◽  
Bernoulli Beam ◽  
Scaling Invariance ◽  
Two Parameters ◽  
Euler Bernoulli Beam ◽  
Two Parameter ◽  
Nonlinear Nature

This paper presents a Hamiltonian variational formulation to determine the energy minimizing boundary conditions (BCs) of the tensionless contact problem for an Euler–Bernoulli beam resting on either a Pasternak or a Reissner two-parameters foundation. Mathematically, this originates a free-boundary variational problem. It is shown that the BCs setting the contact loci, which are the boundary points of the contact interval, are always given by second order homogeneous forms in the displacement and its derivatives. This stands for the nonlinear nature of the problem and calls for multiple solutions in the displacement, together with the classical result of multiple solutions in the contact loci position. In particular, it is shown that the Pasternak soil possesses an extra solution other than Kerr’s, although it is proved that such solution must be ruled out owing to interpenetration. The homogeneous character of the BCs explains the well-known load scaling invariance of the contact loci position. It is further shown that the Reissner foundation may be given two mechanical interpretations, which lead to different BCs. Comparison with the established literature is drawn and numerical solutions shown which confirm the energy minimizing nature of the assessed BCs.

Influence of Al Composition on Donor Impurity States in Self-Formed GaAs-AlxGa1-xAs Quantum Rings

2013 ◽  
Vol 380-384 ◽  
pp. 4284-4289
Author(s):  
Guang Xin Wang ◽  
Xiu Zhi Duan
Keyword(s):  
Binding Energy ◽  
Electric Field ◽  
Growth Direction ◽  
Uniform Electric Field ◽  
Donor Impurity ◽  
Impurity States ◽  
Quantum Rings ◽  
Mass Approximation ◽  
Donor Binding Energy ◽  
Special Value

Based on the the effective mass approximation and variational approach, the donor impurity states confined in self-formed GaAs/AlxGa1-xAs quantum rings (QRs) are investigated theoretically. A uniform electric field is applied along the growth direction of the QR. The different effective masses in the different regions of the GaAs/AlxGa1-xAs QR are taken into consideration. Numerical results show that the binding energy of a donor impurity increases gradually, reaches a maximum value, and then decreases quickly to the special value as the QR height decreases. Given a fixed QR size, the binding energy increases for the impurity located at the center of the QR when the Al composition increases. In addition, it can also be found that when the applied electric field strength increases, the donor binding energy increases for impurities localized at the negative z axis of the QR; however, the donor binding energy decreases slightly for impurities located at the center and positive z axis of the QR.

scholarly journals Spin splitting of X-valley-related donor impurity states in an AlAs barrier

2005 ◽  
Vol 71 (19) ◽  
Author(s):  
E. E. Vdovin ◽  
Yu. N. Khanin ◽  
L. Eaves ◽  
M. Henini ◽  
G. Hill
Keyword(s):  
Spin Splitting ◽  
Donor Impurity ◽  
Impurity States ◽  
Related Donor
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