Quantum Wells

  • Weng W. Chow
  • Stephan W. Koch


We continue the development of the previous chapter to include the bandstructure modifications in quantum wells resulting from the quantum-confinement geometry. Section 6.1 shows how the envelope approximation method incorporates confinement effects into the k · p theory. The influence of quantum confinement on the valence band structure can be quite significant mixing especially the top two bulk semiconductor valence bands, i.e. the heavyhole and light-hole bands. We show in Sect. 6.2 how this mixing is treated in the context of the Luttinger Hamiltonian. Section 6.3 introduces the concept of elastically strained systems and shows how strain effects may be incorporated into the band-structure calculations. In order to compute gain and refractive index, we need the dipole matrix elements, which we derive in Sect. 6.4. Up to that point, the hole band-structure calculations are based on the bulk-material 4 x 4 Luttinger Hamiltonian, which ignores the effects of the additional split-off hole states with total angular momentum j = 1/2. Section 6.5 describes how these states can be included in the band-structure calculations. Reasons for doing so involves laser compounds based on phosphides and nitrides, where the spin-orbit energies are smaller than those of the arsenides. The nitride based compounds exist in the cubic and hexagonal crystal structures. Section 6.6 shows the modifications of the Luttinger Hamiltonian which are necessary in order to be applicable to the hexagonal geometry.


Heavy Hole Hole State Envelope Function Light Hole Diagonal Matrix Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


The Hamiltonian for strained semiconductors has been derived by

  1. Bir, G. L. and G. E. Pikus (1974), Symmetry and Strain-Induced Effects in Semiconductors, Wiley & Sons, New York.Google Scholar
  2. Pikus, G. E. and G. L. Bir (1960), Sov. Phys. — Solid State 1, 1502 [Fiz. Tverd. Tela (Leningrad) 1, 1642 (1959)]Google Scholar
  3. Kittel, C. (1971), Introduction to Solid State Physics, Wiley & Sons, New York; Kittel, C. (1967), Quantum Theory of Solids, Wiley & Sons, New York.Google Scholar
  4. Landolt-Börnstein (1982), Numerical Data and Functional Relationships in Science and Technology, ed. K. H. Hellwege, Vol. 17 Semiconductors, edited by O. Madelung, M. Schulz, and H. Weiss, Springer-Verlag, Berlin.Google Scholar

For papers and reviews dealing with bandstructure calculations and optical properties of strained superlattices see, e.g.

  1. Ahn, D. and S. L. Chuang (1988), IEEE J. Quantum Electron. 24, 2400.ADSCrossRefGoogle Scholar
  2. Chuang, S. L. (1991), Phys. Rev. B43, 9649. Dawson, M. D. and G. Duggan (1993), Phys. Rev. B47. ADSGoogle Scholar
  3. Duggan, G. (1990), SPIE 1283, 206.ADSCrossRefGoogle Scholar
  4. Marzin, J. Y. (1986), Heterojunctions and Semiconductor Superlattices, eds. G. Allan, G. Bastard, and M. Voos, Springer, Berlin, p. 161.CrossRefGoogle Scholar
  5. Chuang, S. L. (1995), Physics of Optoelectronic Devices, Wiley & Sons, New York.Google Scholar

For references on the composition dependence of the In1_xGaxP bandgap see, e.g.,

  1. Adachi, S. (1982), J. Appl. Phys. 53, 8775.ADSCrossRefGoogle Scholar
  2. Stringfellow, G. B., P. F. Lindquist, and R. A. Burmeister (1972), J. Electron. Mater. 1, 437.ADSCrossRefGoogle Scholar

For the wurtzite group-III nitrides see, e.g.,

  1. Pearton, S. J., Ed. (1997), GaN and Related Materials, Vol. 2, (Gordon and Breach, Netherlands)Google Scholar
  2. Nakamura, S., et al. (1996), Appl. Phys. Letts. 69, 4056 (1996)ADSCrossRefGoogle Scholar
  3. Miles K. and I. Akasaki, Eds. (1998), GaN- Based Lasers: Materials, Processing, and Device Issues, IEEE Journal of Selected Topics in Quantum Electronics 4. Google Scholar
  4. Chuang, S. L. and C. S. Chang (1996), Phys. Rev. B54, 2491.ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Weng W. Chow
    • 1
  • Stephan W. Koch
    • 2
  1. 1.Sandia National LaboratoriesAlbuquerqueUSA
  2. 2.Fachbereich Physik und Wissenschaftliches Zentrum für MaterialwissenschaftenPhilipps-Universität MarburgMarburgGermany

Personalised recommendations