On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires
Само за регистроване кориснике
2016
Аутори
Topalović, DušanArsoski, Vladimir
Pavlović, Suncan
Čukarić, Nemanja A.
Tadić, Milan Ž.
Peeters, François M.
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrodinger equation. The accuracy of the solution is explored as it varies with the range of the numerical domain. The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires. Also, the model of a linear harmonic oscillator is considered for comparison reasons. It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range, which is thus considered to be optimal. This range is found to depend on the number of mesh nodes N approximately as alpha(0) log(e)(alpha 1) (alpha N-2), where the values of the constants alpha(0), alpha(1), and alpha(2) are determined by fitting the numerical data. And the optimal range is found to be a weak function of the diffusion length. Moreover, it was demonstrated that a domain range adaptation to the optimal value leads to substantial improv...ement of accuracy of the solution of the Schrodinger equation.
Кључне речи:
intermixing quantum well / quantum wire / Schrodinger equation / finite element / adaptiveИзвор:
Communications in Theoretical Physics, 2016, 65, 1, 105-113Финансирање / пројекти:
- Ministry of Education, Science, and Technological Development of Serbia, Flemish fund for Scientific Research (FWO Vlaanderen)
Колекције
Институција/група
VinčaTY - JOUR AU - Topalović, Dušan AU - Arsoski, Vladimir AU - Pavlović, Suncan AU - Čukarić, Nemanja A. AU - Tadić, Milan Ž. AU - Peeters, François M. PY - 2016 UR - https://vinar.vin.bg.ac.rs/handle/123456789/974 AB - We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrodinger equation. The accuracy of the solution is explored as it varies with the range of the numerical domain. The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires. Also, the model of a linear harmonic oscillator is considered for comparison reasons. It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range, which is thus considered to be optimal. This range is found to depend on the number of mesh nodes N approximately as alpha(0) log(e)(alpha 1) (alpha N-2), where the values of the constants alpha(0), alpha(1), and alpha(2) are determined by fitting the numerical data. And the optimal range is found to be a weak function of the diffusion length. Moreover, it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrodinger equation. T2 - Communications in Theoretical Physics T1 - On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires VL - 65 IS - 1 SP - 105 EP - 113 UR - https://hdl.handle.net/21.15107/rcub_vinar_974 ER -
@article{ author = "Topalović, Dušan and Arsoski, Vladimir and Pavlović, Suncan and Čukarić, Nemanja A. and Tadić, Milan Ž. and Peeters, François M.", year = "2016", abstract = "We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrodinger equation. The accuracy of the solution is explored as it varies with the range of the numerical domain. The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires. Also, the model of a linear harmonic oscillator is considered for comparison reasons. It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range, which is thus considered to be optimal. This range is found to depend on the number of mesh nodes N approximately as alpha(0) log(e)(alpha 1) (alpha N-2), where the values of the constants alpha(0), alpha(1), and alpha(2) are determined by fitting the numerical data. And the optimal range is found to be a weak function of the diffusion length. Moreover, it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrodinger equation.", journal = "Communications in Theoretical Physics", title = "On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires", volume = "65", number = "1", pages = "105-113", url = "https://hdl.handle.net/21.15107/rcub_vinar_974" }
Topalović, D., Arsoski, V., Pavlović, S., Čukarić, N. A., Tadić, M. Ž.,& Peeters, F. M.. (2016). On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires. in Communications in Theoretical Physics, 65(1), 105-113. https://hdl.handle.net/21.15107/rcub_vinar_974
Topalović D, Arsoski V, Pavlović S, Čukarić NA, Tadić MŽ, Peeters FM. On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires. in Communications in Theoretical Physics. 2016;65(1):105-113. https://hdl.handle.net/21.15107/rcub_vinar_974 .
Topalović, Dušan, Arsoski, Vladimir, Pavlović, Suncan, Čukarić, Nemanja A. , Tadić, Milan Ž., Peeters, François M., "On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires" in Communications in Theoretical Physics, 65, no. 1 (2016):105-113, https://hdl.handle.net/21.15107/rcub_vinar_974 .