When solids are reduced to the nanometer scale, they exibit new and exciting behaviours which constitute the basis for a new generation of electronic devices.Nanotechnology for Microelectronics and Optoelectronics outlines in detail the fundamental solid-state physics concepts that explain the new properties of matter caused by this reduction of solids to the nanometer scale. Applications of these electronic properties is also explored, helping students and researchers to appreciate the current status and future potential of nanotechnology as applied to the electronics industry.
Based on the zone folding concept, one can fabricate superlattices of GaAs and AlAs with direct and indirect gaps, respectively, which show quasi-direct optical transitions. Another example is that of the SinGem superlattices based on SiGe heterostructures (Section 5.3.2). In these superlattices, which are constructed usually symmetrical (n = m), the minimum of the Si conduction band close to the band edge can be brought close to k = 0 by successive zone-folding. Evidently, the higher the number of monolayers (n), the behaviour of the superlattice would better resemble that of a direct bandgap semiconductor structure. It is interesting to note that due to the small widths of the minigaps and minibands in superlattices, as well as the quasi-direct type of transitions which might show, they nd many applications in infrared optics. In addition they can show new interesting properties like WannierStark localization and Bloch oscillations (Section 8.5).
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Semiconductor Quantum Nanostructures and Superlattices 5.5.3. Tight binding approximation of a superlattice In this section we will deduce a series of properties of the band diagram of a superlattice from the tight binding approximation for solids (section 2.5.2), in a similar manner to the previous section by using the KronigPenney model. For this purpose we consider the superlattice as a set of N quantum wells along the z-direction that are weakly coupled, in analogy with the potentials felt by electrons in solids. For instance, the Bloch wave function in the ground state of the superlattice g.s. should be a linear combination of the wave functions of each quantum well (z nd) of potential energy V (z nd), where we are supposing that each well is centred at locations z = nd g.s. = 1 N (cid:3) n
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Solving the perturbation problem, within the nearest neighbour approximation, one gets following the same method as for the derivation of Eq. (2.49): E(q) = E0 + s + 2t cos qd
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(Figure 5.14(a)), which is similar to Figure 2.6 for bands in solids . Note also from Eq. (5.16) that the band width is (cid:1)E = 4 |t|, i.e. depends on the transfer integral t, which takes into account the coupling between nearest neighbours and depends on the superlattice parameters. Figure 5.14(b) shows the dependence of the bandwidth on the barrier thickness. As expected, when the barriers between wells get thicker, and therefore t 0, we should have the same result as for multiquantum wells with single levels for the energy. One interesting point that should be emphasized is related to the periodicity of the superlattice in the z-direction, since in reality superlattices are three-dimensional structures. Therefore, the expression of the total energy should also take into account the kinetic energy of electrons for their motion along the (x, y) planes. The total energy of the electrons in the i subband should be equal to the kinetic term plus the e
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