Document Details

Document Type : Thesis 
Document Title :
Quantum Dots in Hiezenberg Model
النقاط الكمية في نموذج هايزنبرج
 
Subject : Girls' College of Education in Jeddah 
Document Language : Arabic 
Abstract : Quantum Dots (QDs) are semiconductor-nanostructure materials which are also called artificial atoms. Their sizes range from 1 - 10 nm. A QD may contain few hundred or few thousands of atoms .It may also contain a single electron or few thousands of electrons. QDs are classified as ferromagnetic material. Recently experimentalists have succeeded to fabricate QDs from metals, such as: gold and silver. QDs are characterized by the phenomenon of Quantum confinement; where electrons are confined in three dimensions. Theoretically, Heisenberg model is regarded as a good model in describing these QDs. We used the above mentioned model to explore the physical properties of these materials, such as ground state energy, excitation energy and magnetization with the help of Spin Wave Theory. It has easy mathematical calculations, quick in getting results compared with other methods and works well for the case of ferromagnetic materials. In this research, we apply Heisenberg Hamiltonian to QDs containing unlimited number of electrons subjected to an external magnetic field. Spin wave theory is applied to the system followed by Holtsin-Primakoff transformation and Bogoliubov transformation to get the diagonal Hamiltonian. Mathematical expressions for the physical quantities are then computed. Linear as well as non-linear spin wave they were used in this calculation. We found that linear spin wave theory gives satisfactory results. We found that the ground state energy increases with the external magnetic field as E ~ ( B)1/2. A point of transition from a singlet to a triplet state at B ~ 1 T was observed in agreement with previous studies. Ferromagnetic materials are gapless in their excitation spectrum at K = 0. QDs show the same behavior in the absence of external magnetic field B = 0 T. But as soon as the magnetic field is switched on a gap appears in the spectrum and increases linearly with B. Magnetization curve shows an increase to a saturated value with B - as expected- since the magnetic field forces the spins to align in its direction. This increase goes as M ~ ( B)0.3. We also observe a transition point around B ~ 1 T. We can take advantages of these results in practical applications of the QDs where they enter in many medical applications, security, industry, computer logic gates and other applications. 
Supervisor : Dr. Aiman Alomari 
Thesis Type : Master Thesis 
Publishing Year : 1430 AH
2009 AD 
Added Date : Saturday, February 6, 2010 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
ريم عبد الله المطيريAlmotiri, Reem AbdullahResearcherMaster 

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