Quantum films

Figure JO Electronic band structures of SimH and GemH quantum films of about 1.0 nm thickness for different orientations (m and n refer to the number of Si(Ge) and H layers in the considered film) (a) S17H4 (1 0 0) (b) Ge7H4 (1 0 0) (c) Sii0H4 (1 1 0) (d) Ge10H4 (1 1 0) (e) Si6H2 (1 1 1) (f) Ge6H2 (1 1 1).

Figure 31 Calculated imaginary part of the dielectric function of Si and Ge quantum films for different orientations and thicknesses. The curves are convolved with Lorentzian broadening of 0.1 eV.

The effect of quantum confinement is also pronouncedly seen in the real parts of the dielectric function. The characteristics versus photon energy behavior for all considered Si and Ge quantum films are presented in Figure 32. One can observe the reduction of the maximum value of ei as well as its value at zero energy (static dielectric constant) when going to the thinner films. The calculated values of the static dielectric constant (ei(0)) for the films considered are considerably smaller than that of bulk material. Moreover, for the same film thickness ei(0) appears to be higher for the Si structures as compared to the Ge ones, despite the fact that for bulk the Ge value is higher than the Si one. Even if, as stated above, the data shown for the dielectric functions are those relative to the supercell calculation, for films of similar width, at least, semi-quantitative comparison is possible, since the ratio between the volume occupied by the isolated layer and the supercell volume is almost constant in these cases. 

Quantum films (multiple quantum wells and superlattices) (1-D quantisation)... 

Figure 3.7 Density of states for bulk semiconductors, quantum films, quantum wires and quantum dots.

In light of the above discnssion, the optical absorption spectrum of a quantum film is expected to consist of a series of steps, with the position of these steps corresponding to the transitions between heavy or light hole quantum states and electron quantum states following the selection rule An = 0. Furthermore, since the widths of the wells are commonly smaller than the calculated diameter of an exciton, the exciton binding... 

However, carriers in the space-charge layer at the surface of a heavily doped semiconductor are only confined in one dimension, as in a quantum film. This... 

Nho K., and Manousakis, E. (2003). Commensurate—incommensurate transitions in quantum films submonolayer molecular hydrogen on graphite, Phys. Rev. B, 67, 195411-1-7. 

Charge carriers in semiconductors can be confined in one spatial dimension (ID), two spatial dimensions (2D), or three spatial dimensions (3D). These regimes are termed quantum films, quantum wires, and quantum dots as illustrated in Fig. 9.1. Quantum films are commonly referred to as single quantum wells, multiple quantum wells or superlattices, depending on the specific number, thickness, and configuration of the thin films. These structures are produced by molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition (MOCVD) [2j. The three-dimensional quantum dots are usually produced through the synthesis of small colloidal particles. 

Some fundamental differences exist for the three types of quantization. In particular, the densities of electronic states (DOS) as a function of energy are quite different, as illustrated in Fig. 9.2. For quantum films the DOS is a step function, for quantum dots there is a series of discrete levels and in the case of quantum wires, the DOS distribution is intermediate between that of films and dots. According to the distribution of the density of electronic states, nanocrystals lie in between the atomic and molecular limits of a discrete density of states and the extended crystalline limit of continuous bands. With respect to electrochemical reactions or simply charge transfer reactions. 

Quantum films are usually produced in a periodic sequence of sandwich type of two semiconductors, one with a small, the other with a large bandgap, as illustrated in Fig. 9.7a. They can be produced with much higher precision than quantum dots of a narrow... 

Quantum films represent a beautiful physical example of the particle in the box problem. The energy levels of the conduction band electrons in the electron well (MQW) can be easily calculated using the envelope function or the effective mass approximation [6]. The electron wave function is then [29-31]... 

A further theoretical analysis of the quantum film shows that the density of states (DOS) is given by [2]... 

Semiconductor nanoparticles that arise due to the confinement of electrons/holes in zero spatial dimension are called quantum dots. Quantum wires and quantum films or wells arise when the charge carriers in the corresponding semiconductor are confined in one or two spatial dimensions. These dimensional confinements and corresponding density of states are illustrated in Figures 9.10 and 9.11, respectively. 

Figure 9.2 Density of states (DOS) functions for quantum films, quantum wires, and quantum dots (after [2]).

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