Photonic crystals in biology

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Poster Session, Tuesday, June 15 Theme A1 - B702 Observation of the ground and excited states in a zero-dimensional semiconductor nanostructure under the magnetic field Saban Aktas, 1* Figen Karaca Boz 1 , Abdullah Bilekkaya 2 and Sevket Erol Okan 1 1 Department of Physics, Trakya University, Edirne 22030, Turkey 2 Department of Electronics, Trakya University Edirne Vocational College of Technical Sciences, Edirne 22100, Turkey Abstract— The ground and excited states in a zero–dimensional semiconductor nanostructure (quantum dot) have observed as a function of the dot radius under a magnetic field. The energies of the 1s, 1p, 1d and 1f states of a spherical quantum dot have been calculated using the fourth order Runge-Kutta method without magnetic field and the variational method with magnetic field within the effective mass approximation. It is shown that the energies in quantum dot with a small radius very small change with magnetic field, whereas energy changes with large radius are affected by the magnetic field. The experimental progress has made possible the fabrication of zero-dimensional semiconductor nanostructure (quantum dot) which impose quantum confinement in three directions to a charge carrier [1].The 1s-1s transition energies in spherically layered semiconductor quantum dots (QDs) were compared with the experimental results [2] and it was found that thick CdS outer layers prevent the charge carriers from escaping from the particles. Recently, the energies of electronic levels of the spherical QD has been presented by Özmen et al. [3,4]. Wenfang Xie found that the linear and nonlinear optical absorption coefficients are strongly affected by the confinement strength of QDs, and the external magnetic field [5,6]. In this work, we will focus on studying the energies of ground (1s), first (1p), second (1d), and third (1f) excited states of the spherical QD. The Hamiltonian of the QD in the effect of a magnetic field can be written in reduced units, 2 2b 1 2 2 2 H i r sin v( r) . (1) r 4 The above equation has been solved using the Runge–Kutta numerical method without the magnetic field (B=0). The Hamiltonian in the presence of the magnetic field has been calculated using the variational approach. The binding energy E B of the hydrogenic impurity is defined as the difference between the energies with and without the impurity. Namely, E n 0( b 0) and E ni ( b 1) are obtained from Eq.1. Thus, the impurity binding energy in the QD is E B E ( b . n0 0) E ni ( b 1) Fig. 1 shown the binding energies of 1s, 1p, 1d, and 1f states as a function of the magnetic field for R Dot = 2a* value. The barrier height is given as V=Q c 1.247x for the Al concentration x=0.25 in the unit of eV., where Q c is the conduction band offset parameter taken to be Q c =0.60. As seen from the figure, the binding energies increase with increasing the magnetic field. The character of the binding energy for 1s state is different than other states. E B (R*) 3,2 2,7 2,2 1,7 1,2 0 5 10 15 20 B(T) Figure 1: The binding energies of 1s, 1p, 1d, and 1f states as a function of the magnetic field for R Dot = 2a* value. In summary, we showed that the energies of the ground and excited states in zero-dimensional semiconductor nanostructure as a function of magnetic field for various the dot radius. For small dot radii, the contribution of the magnetic field is very small. The contribution to the energy of the magnetic field becomes dominant for large dot radii. These results are a good agreement with the results of our previous studies [6,7]. Our results might be useful for some devices in the future. This work was partially supported by Trakya University under Grant No. TUBAP 739-754-759-886-929- 2008(58). . *Corresponding author: sabana@trakya.edu.tr [1] M. A. Reed et al., Phys. Rev. Lett. 60, 535 (1988) [2] D. Schooss, A. Mews, A. Eychmüller, H. Weller, Phys. Rev B 49 17072 (1994). ( and references therein) [3] A. Özmen et al., Optics Comm., 282 3999 (2009). [4] B. Çakır et al., Superlattices and Microstructures, (In Press) [5] Wenfang Xie, Commun. Theor. Phys. 51, 923 (2009) [6] F. K. Boz et al. Appl. Surf. Sci. 255, 6561 (2009) [7] F. K. Boz et al. Appl. Surf. Sci. 256, 3832 (2010) 1s 1p 1d 1f 6th Nanoscience and Nanotechnology Conference, zmir, 2010 266
Poster Session, Tuesday, June 15 Theme A1 - B702 The electronic properties of the multilayered spherical quantum dot under a magnetic field S E Okan 1 , A.Bilekkaya 2 , F.K.Boz 1 and S.Aktas 1 1 Department of Physics, Trakya University, 22030 Edirne, Turkey 2 Department of Electronics, Trakya University Edirne Vocational College of Technical Sciences, Edirne 22100, Turkey Abstract— We investigate the binding energy of an impurity located at the center of multilayered spherical quantum dot (MSQD) is reported as a function of the dot and barrier thickness for different alloy compositions under the influence of a magnetic field. The binding energy has been calculated using the fourth order Runge–Kutta method without magnetic field within the effective mass approximation. With the advent of modern micro-fabrication technology, semiconductor quantum dot (QD) structures are of considerable interest in fundamental science and device applications. The impurity states in a quantum dot (QD), which play an essential role in technological applications, are studied for understanding the electron and the impurity states in the confined systems. [1,2] In this work we use the fourth order Runge– Kutta method without magnetic field within the effective mass approximation [3]. A variational approach has been employed if a magnetic field is present. Our results show that the structural confinement is very effective for thin MSQD, and the influence of magnetic field is more effective according to the geometric effect for thick MSQD. If the dot thicknesses are closer to the barrier thickness, the abrupt deviations of the binding energy can be observed by changing the strength of the applied external magnetic field [4]. In figure 1, we showed the binding energy as a function of equal dot and barrier thickness for different magnetic fields and alloy concentrations x = 0.20, 0.25, 0.30, respectively. E B (R*) 6,0 4,5 3,0 1,5 0,0 0,4 0,8 1,2 1,6 Figure 1: The binding energy as a function of equal dot and barrier thickness for different magnetic fields and alloy concentrations. Corresponding author: serolok@yahoo.com References R in =R out =R B (a*) x=0.20 x=0.25 x=0.30 B=5 T B=0 [1] J.-L. Zhu, J.-J. Xiong, B.-L. Gu, Phys. Rev. B 41 (1990) 6001 [2] N. Porras-Montenegro, S.T. Perez-Merchancano, Phys. Rev. B 46 (1992) 9780 [3] F.K. Boz, S. Aktas, A. Bilekkaya, S.E. Okan, Appl. Surf. Sci. 255 (2009) 6561. [4] F.K. Boz et al., Applied Surface Science 256 (2010) 3832– 3836 6th Nanoscience and Nanotechnology Conference, zmir, 2010 267
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