volume | PIER Journals

Abstract

The paper presents the faster, simpler, and accurate algorithm to solve time independent Schrodinger equation based on transfer matrix method. We can thus calculate all bound and quasi bound energy and the corresponding probability density. A central part of this paper deals with the solving of Schrodinger equation for quantum well structure. Our results show that the transfer matrix method is accurate, it is easier to implement. The increase in well width increases the FWHM from 5.4 nanometer to 9.4 nanometer, while the increase in the Aluminum concentration the FWHM decreases from 8.98 to 5.4.

1. Samuel, E. P. and D. S. Patil, "Effect of aluminum mole fraction and well width on the probability density spreading in GaN/AlGaN quantum well," Optoelectronics and Advanced Materials-Rapid Communications, Vol. 8, 394, 2007. Google Scholar

2. Chiu, C. H., H. C. Kuo, C. E. Lee, C. H. Lin, P. C. Cheng, H. W. Huang, T. C. Lu, S. C. Wang, and K. M. Leung, "Fabrication and characteristics of thin film InGaN-GaN light emitting diodes with TiO₂/SiO₂ omnidirectional reflectors," Semiconductor Science and Technology, Vol. 22, 831, 2007. Google Scholar

3. Chen, C.-N., K.-F. Yarn, W.-J. Luo, et al. "Effects of giant optical anisotropy in R-plane GaN/AlGaN quantum wells by valence band mixing," PIERS Online, Vol. 2, 562, 2006. Google Scholar

4. Ahmed, I. and A. R. Baghai-Wadji, "1D canonical and perturbed quantum potential wave problem: A universal approach," PIERS Online, Vol. 3, 481, 2007. Google Scholar

5. Chen, C.-N., W.-C. Chien, K.-F. Yarn, S.-H. Chang, and M.-L. Hung, "Intrinsic optical anisotropy in Zinc-blende semiconductor quantum wells," Progress In Electromagnetics Research Symposium, 223, Hangzhou, China, August 22-26, 2005. Google Scholar

6. Brubach, J., A. Y. Silov, J. E. M. Haverkort, W. van der Vleuten, and J. H. Wolter, "Carrier capture in ultrathin InAs/GaAs quantum wells," Physical Review B, Vol. 61, 136833, 2000. Google Scholar

7. Peng, L.-H., C.-M. Lai, C.-W. Shih, C.-C. Chuo, and J.-I. Chyi, "Boundary effects on the optical properties of InGaN multiple quantum wells ," IEEE J. of Selected Topics in Quantum Electronics, Vol. 9, 708, 2003. Google Scholar

8. Baro, M., H. Chr. Kaiser, H. Neidhardt, and J. Rehberg, "Dissipative Schrodinger-Poisson systems," J. of Mathematical Physics, Vol. 45, 21, 2004. Google Scholar

9. Gmachl, C., D. L. Sivco, R., F. Colombelli, F. Capasso, and A. Y. Cho, "Ultra-broadband semiconductor laser," Letters to Nature, Vol. 415, 883, 2002. Google Scholar

10. Samuel, E. P., K. Talele, U. Zope, and D. S. Patil, "Semiclassical analysis of capture in Gallium Nitride quantum wells," Optoelectronics and Advanced Materials-Rapid Communications, Vol. 5, 221, 2007. Google Scholar

11. Shwetanshumala, S. Jana and S. Konar, "Propagation of a mixture of modes of a laser beam in a medium with saturable nonlinearity," J. of Electromagn. Waves and Appl., Vol. 20, 65, 2006. Google Scholar

12. Mora-Ramos, M. E., R. Perez-Alvarez, and V. R. Velasco, "The electrostatic potential associated to interface phonon modes in Nitride single heterostructures," Progress In Electromagnetics Research Letters, Vol. 1, 27, 2008. Google Scholar

13. Hori, A., D. Yasunaga, A. Satake, and K. Fujiwara, "Temperature and injection current dependence of electroluminescence intensity in green and blue InGaN single quantum well light emitting diodes," J. of Applied Physics, Vol. 93, 3152, 2003. Google Scholar

14. Schwarz, U. T., E. Sturm, W. Wegscheider, V. Kummler, A. Lell, and V. Harle, "Excitonic signature in gain and carrier induced change of refractive index spectra of (In,Al)GaN quantum well lasers," Applied Physics Letters, Vol. 85, 1475, 2004. Google Scholar

15. Chern, G. D., H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, "Unidirectional lasing from InGaN multiple quantum well spiral-shaped micropillars," Applied Physics Letters, Vol. 83, 1710, 2003. Google Scholar

16. Mamishev, A. V., K. S. Rajan, F. Yang, Y. Du, and M. Zahn, "Interdigital sensors and transducers," Proceedings of the IEEE, Vol. 92, 808, 2004. Google Scholar

17. Srivastav, R., S. Pati, and S. P. Ojha, "Enhancement of omnidirectional reflection in photonic crystal heterostructures," Progress In Electromagnetics Research B, Vol. 1, 197, 2008. Google Scholar

18. Walpita, L. M., "Solutions for planar optical waveguide equations by selecting zero elements in a characteristic matrix," J. Opt. Soc. Amer. A, Vol. 2, 595, 1985. Google Scholar

19. Brennan, K. E. and C. J. Summers, "Theory of resonant tunneling in a variably spaced multiquantum well structure: An airy function approach," J. Appl. Phys., Vol. 61, 614, 1987. Google Scholar

20. Ghatak, A. K., K. Thyagarajan, and M. R. Shenoy, "A novel numerical technique for solving the one-dimensional Schrodinger equation using matrix approach application to quantum well structures," IEEE J. Quantum Electron., Vol. 24, 1524, 1988. Google Scholar

21. Lu, J., B. I. Wu, J. A. Kong, and M. Chen, "Guided modes with a linearly varying transverse field inside a left-handed dielectric slab," J. of Electromagn. Waves and Appl., Vol. 20, No. 5, 689, 2006. Google Scholar

22. Gaggero-Sager, L. M., N. Moreno-Martinez, I. Rodriguez-Vargas, R. Perez-Alvarez, V. V. Grimalsky, and M. E. Mora-Ramos, "Electronic structure as a function of temperature for Si δ-doped quantum wells in GaAs," PIERS Online, Vol. 3, No. 6, 851, 2007. Google Scholar

23. Gaggero-Sager, L. M. and I. Rodriguez-Vargas, "p-n-p δ-doped QuantumWells in GaAs," PIERS Online, Vol. 3, No. 6, 855, 2007. Google Scholar

24. Chen, C.-N., K.-F. Yarn, W.-C. Chien, S.-H. Chang, and M.-L. Hung, "Interface heterobond effects in (hkl) InAs/GaSb superlattice solved by bond orbital model," Progress In Electromagnetics Research Symposium, 318, Hangzhou, China, August 22-26, 2005. Google Scholar

25. Jancewicz, B., "Plane electromagnetic wave in PEMC," J. of Electromagn. Waves and Appl., Vol. 20, No. 5, 647, 2006. Google Scholar

26. Wu, C.-J., "Transmission and reflection in a periodic superconductor/dielectric film multilayer structure," Progress In Electromagnetics Research Symposium, 164, Hangzhou, China, August 22-26, 2005. Google Scholar

Dr. Edmund Samuel

Dr. Dyneshwar Patil