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Figure 51. Donor binding energy as a function of the impurity position for infinite GaAs-(Ga,Al)As quantum dots with distinct dot radii. From top to bottom, r0 = 50, 100, 200, 1000 Á. Reprinted with permission from [205], J. L. Marín 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 51. Donor binding energy as a function of the impurity position for infinite GaAs-(Ga,Al)As quantum dots with distinct dot radii. From top to bottom, r0 = 50, 100, 200, 1000 Á. Reprinted with permission from [205], J. L. Marín et al., in "Handbook of Advanced Electronic and Photonic Materials and Devices" (H. S. Nalwa, Ed.). Academic Press, San Diego, 2001. © 2001, Academic Press.

minimum as the donor position is equal to the radii of the quantum dot. The absorption probability w(m, R) for an infinite quantum dot with one single impurity as a function of h(ú — sg is shown in Figure 52. In Figure 52a, we present the absorption probability for an infinite GaAs quantum dot of radius r0 = 3000 Á. We observe that there is a noticeable peak structure associated with a single impurity located at the center of the dot, which is much larger than the structure associated with a single impurity next to the edge of the dot, meaning that we have essentially reached the bulk limit. Our results for an r0 = 1000 Á and r0 = 500 Á quantum dots are shown in Figure 52b; the structure associated with a single impurity located at the center of the dot is smaller than the structure associated with a single impurity at the edge of the dot.

In Figure 53, we display the total absorption probability for an infinite GaAs quantum dot with a homogeneous distribution of impurities. For a quantum dot of r0 = 3000 Á the total absorption probability as a function of h ( — sg is shown in Figure 53a. An absorption edge associated with transitions involving impurities at the center of the well and a peak related with impurities next to edge of the dot are observed. The peak associated with impurities located next to the edge of the dot is much larger than the peak associated with impurities located next to the center of the dot. This behavior is quite different from that found for GaAs quantum wells and quantum well wires of comparable dimensions. This is a consequence of the quantum confinement and the homogeneous distribution of the impurities in the quantum dot.

When the radius of the quantum dot decreases we observe that the peak associated with impurities located next to the center diminishes (see Fig. 53b), which may be understood by means of the behavior of the density of the states as a function of the binding energy (see Fig. 3 in [135]). In this figure, it is seen that for small radii the density of the states r o 3

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