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Figure 7. Electron miniband energies at T and t points in a superlattice. Reprinted with permission from [205], J. L. Marin et al., in "Handbook of Advanced Electronic and Photonic Materials and Devices" (H. S. Nalwa, Ed.). Academic Press, San Diego, 2001. © 2001, Academic Press.

Figure 7. Electron miniband energies at T and t points in a superlattice. Reprinted with permission from [205], J. L. Marin et al., in "Handbook of Advanced Electronic and Photonic Materials and Devices" (H. S. Nalwa, Ed.). Academic Press, San Diego, 2001. © 2001, Academic Press.

Finally, Eq. (52) for the envelope function can be generalized as h2 d 1

2.5.2. Quasi-One-Dimensional System

Let us consider a quasi-one-dimensional system with finite length and width formed by A and B materials; in general, the wavefunction can be written as

We will also consider that the quasi-one-dimensional system is a quantum well wire of rectangular or circular cross-section, where the z direction coincides with the free direction of the carrier motion; that is, the confinement direction is in the cross section.

The envelope function for both cases can be written as fA,B(7) = exp(ikzz)xA'B(l± )

where xA,B(^± ) depends on the cross section symmetry, yA,B

xtlOYnAmiy)

rectangular quantum well wire

circular quantum well wire h2 d 1

2 dz m*(z) dz where l, m are integer numbers and (r,9,z) are the cylin-(57) drical coordinates. For convenience we will omit the band index n in the following treatment.

The differential equations for the envelope functions are now

2m* (y) dy2 b , for rectangular symmetry. In this case the barrier potential is vrr =

0 0

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