Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-28T02:32:48.143Z Has data issue: false hasContentIssue false
  • English
  • Français

Wavefunction Engineering of Layered Quantum Semiconductor Structures: Recent Progress

Published online by Cambridge University Press:  01 February 2011

L. R. Ram-Mohan
L. R. Ram-Mohan*
Affiliation:
[email protected], Worcester Polytechnic Institute, Physics, 100 Institute Road,, Worcester, MA, 01609, United States, 5088315339, 5088315886
Get access

Abstract

A Lagrangian formulation for the valence bands of bulk zinc blende and wurtzite compound semiconductors provides a direct approach to determining derivative operator ordering at layer interfaces in the multiband k·P description of electronic states, in the envelope function approximation. The current continuity condition is obtained through a gauge-variation on the Lagrangian. The principle of least action together with the discretization of the action integral naturally leads into a finite element approach for the modeling and simulation of the multiband Schrödinger equations. Being a variational method, the wavefunctions and energy eigenvalues can be systematically improved with quadratic convergence. By including the Poisson Lagrangian, a self-consistent treatment of the Schrödinger-Poisson band-bending in arbitrarily doped structures is obtained. Numerical examples are presented for the valence band electronic states for quantum wells and superlattices. We have also coupled the finite element method with layer parameter optimizations to design heterostructures for lasers emitting at given wavelengths. It is in this sense that wavefunction engineering goes beyond the notion of bandgap engineering in providing the means for optimizing wavefunction localization in layers, selecting layer thicknesses, enhancing optical matrix elements, and laser gain.

Keywords

dielectric propertiessimulationelectronic structure
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 891: Symposium EE – Progress in Semiconductor Materials V – Novel Materials and Electronics and Optoelectronic Applications , 2005 , 0891-EE02-06
Copyright
Copyright © Materials Research Society 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Ram-Mohan, L. R., “Finite Element and Boundary Element Applications to Quantum Mechanics” (Oxford UP, Oxford, UK, 2002).Google Scholar
2. Löwdin, P. O., J. Chem. Phys. 19, 1396 (1951).Google Scholar
3. Kane, E. O., J. Phys. Chem. Solids 6, 236 (1958).Google Scholar
4. Foreman, B. A., Phys. Rev. B 48, 4964 (1993).Google Scholar
5. van Dalen, R. and Stavrinou, P. N. Phys. Rev. B 55, 15456 (1997).Google Scholar
6. Mireles, F. and Ulloa, S. E. Phys. Rev. B 60 13659 (1999).Google Scholar
7. Chuang, S. L. and Chang, C. S., Appl. Phys. Lett. 68, 1657 (1996); Phys. Rev. B 54, 2491 (1996).Google Scholar
8. Bir, G. L. and Pikus, G. E., Symmetry and Strain Induced Effects in Semiconductors (Wiley, New York, 1974).Google Scholar
Also see, Sirenko, Yu. M., Jeon, J. B., Kim, K. W., Littlejohn, M. A., and Stroscio, M. A., Phys. Rev. B 53, 1997 (1996).Google Scholar
9. Gell-Mann, M. and Levy, M., Il Nuovo Cimento 16, 53 (1960).Google Scholar
10. Ram-Mohan, L. R., Moussa, J., and Yoo, K. H., J. Appl. Phys. 95, 3081 (2004).Google Scholar
11. Ram-Mohan, L. R., Girgis, A. M., Albrecht, J.D., Litton, C. W., and Steiner, T. D., 27th International Conference on the Physics of Semiconductors, ed. Menendez, J. and Van de Walle, C. G., 941–942 (Am. Inst. Phys., Melville, NY, 2005);Google Scholar
Ram-Mohan, L. R., Girgis, A. M., Albrecht, J. D., Litton, C.W., Superlattices and Microstructures, to be published (2005).Google Scholar
12. Vurgaftman, I., Meyer, J. R., and Ram-Mohan, L. R., J. Quant. Electron. 34, 147 (1998).Google Scholar
Ram-Mohan, L. R., Dossa, D., Vurgaftman, I. and Meyer, J. R., in Handbook of Nanostructured Materials and Nanotechnology, Vol. 2, Ed. Nalwa, H. S., (Academic Press, New York, 1999), Chap. 15.Google Scholar