Modelling of Electron States in Conical Quantum Dots
This paper is devoted to the study of solutions of the stationary Schrodinger equation for the case of a conical quantum dot (CQD). We obtained wave numbers and functions, probability density, and energy eigen values for s-electrons, and studied how they depend on the geometrical parameters of a CQD...
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| Видавець: | Кам'янець-Подільський національний університет імені Івана Огієнка |
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| Дата: | 2019 |
| Автори: | , , , , |
| Формат: | Стаття |
| Мова: | Ukrainian |
| Опубліковано: |
Кам'янець-Подільський національний університет імені Івана Огієнка
2019
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| Онлайн доступ: | http://mcm-math.kpnu.edu.ua/article/view/189000 |
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Репозиторії
Mathematical and computer modelling. Series: Physical and mathematical sciences| Резюме: | This paper is devoted to the study of solutions of the stationary Schrodinger equation for the case of a conical quantum dot (CQD). We obtained wave numbers and functions, probability density, and energy eigen values for s-electrons, and studied how they depend on the geometrical parameters of a CQD (diameter D and height H). We used the Wentzel-Kramers-Brillouin method to calculate the energy eigen values. We used the wave function normalization condition to obtain the wave function amplitude for electron stationary states. The energy eigen states of a stationary electron in the effective mass approximation depends on z-coordinate in case of a CQD, unlike the case of a cylindrical quantum dot. We consider the z-coordinate limits for respective energy eigen values for a CQD with D = 8 nm and H = 10 nm. We plot 3D distribution of the electron probability density in a CQD for axial and radial wave function modes. We also consider the standing electron waves in a CQD with energy eigen values obtained using the Bohr-Sommerfeld quantization condition (0th approximation of the Wentzel-Kramers-Brillouin method). The spatial probability density discrete modelling is performed in MathCad and Scilab environment. Computer and mathematical simulations have been widely employed in modern engineering.Based on the results of this research we developed a computer modelling laboratory work «Modelling of electronic states in a conical quantum dot». Quantum dots have found various applications in nanoelectronics, for example QLED screens, semiconductor lasers for fiber optics, sensors etc. Therefore, the development of simplified models of finite movement of charge carriers in a quantum dot is the promising direction of a laboratory course «Physical fundamentals of modern information technologies» for «Computer sciences» students. |
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