Quantum Confinement Model

Quantum Confinement Model. To account for the formation of micropores of less than a few nanometers formed on p-Si, Lehmann and Gosele in the early 1990s postulated that instead of the depletion layer, which is involved in macropores, quantum carrier confinement is responsible for the formation of the micropores on p-Si. The confinement occurs due to an increase in band-gap energy and energy barrier caused by the quantum size porous structure, which prevents the carriers from entering the wall regions of the PS as illustrated in Fig. 8.61. Due to the quantum confinement the pore walls are depleted of carriers and thus do not dissolve during the anodization. 

The quantum confinement model was extended by Frohnhoff etal to account for the wide distribution of pore diameters of the PS formed on p-Si. Tunneling of holes through silicon crystallites was proposed as a process also involved in the formation of the quantum size porous structure. The tunneling current oscillates with the crystallite size which was considered to be responsible for the uneven pore size distribution and for the stability of very small crystallites in the PS. The quantum confinement model 

The quantum confinement model reasonably explains the formation of crystallites of a few nanometers in size. However, it does not provide an explanation of what determines pore diameter. If quantum confinement, which is not related to doping type and concentration, were to occur, it should also occur on all types of silicon substrates. However, quantum size PS is not found in many types of PS, e.g., the PS formed on n-Si in the dark. 

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The effect of pressure on the ground-state electronic and structural properties of atoms and molecules have been widely studied through quantum confinement models [53,69,70] whereby an atom (molecule) is enclosed within, e.g., a spherical cage of radius R with infinitely hard walls. In this class of models, the ground-state energy evolution as a function of confinement radius renders the pressure exerted by the electronic density on the wall as —dEldV. For atoms confined within hard walls, as in this case, pressure may also be obtained through the Virial theorem [69] ... 

The optical gain observed in Si-NC embedded in SiC>2 formed by different techniques [24-27] has given a further impulse to these studies. Interface radiative states have been suggested to play a key role in the mechanism of population inversion at the origin of the gain [24,25,28]. However many researchers are still convinced of the pure quantum confinement model and they are focusing their efforts mainly on the self trapped excitonic effects [29,30] in order to explain the differences between their results and the experimental outcomes. 

Ignored in the above quantum confinement model is the fact that when an electron is excited into the conduction band and a positive hole is left behind in the valence band, the hole and electron are coulombically attracted. The pair can be treated as a well-defined qnasiparticle called an exciton, a hydrogen-like system for which a bulk exciton Bohr radius = tfKeJ nfj.f- can be defined. Here k is the dielectric constant (10.2 for bulk CdSe ) and bq is the permittivity of space (8.854 X 10 The quantity a is a... 

Why does a material with indirect and relatively small band gap of 1.1 eV (corresponding to photons in the near infrared) emit efficiently visible light The original explanation of Canham [6], which is nowadays called the quantum confinement model, is based on the theoretical prediction, according to which the band gap increases and becomes direct with decreasing crystallite size. 

One of the great issues in the field of silicon clusters is to understand their photoluminescence (PL) and finally to tune the PL emission by controlling the synthetic parameters. The last two chapters deal with this problem. In experiments described by F. Huisken et al. in Chapter 22, thin films of size-separated Si nanoparticles were produced by SiLL pyrolysis in a gas-flow reactor and molecular beam apparatus. The PL varies with the size of the crystalline core, in perfect agreement with the quantum confinement model. In order to observe an intense PL, the nanocrystals must be perfectly passivated. In experiments described by S. Veprek and D. Azinovic in Chapter 23, nanocrystalline silicon was prepared by CVD of SiH4 diluted by H2 and post-oxidized for surface passivation. The mechanism of the PL of such samples includes energy transfer to hole centers within the passivated surface. Impurities within the nanocrystalline material are often responsible for erroneous interpretation of PL phenomena. 

CO2 laser pyrolysis of silane in a gas flow reactor and the extraction of the resulting silicon nanoparticles into a cluster beam apparatus has been shown to offer an excellent means for the production of homogeneous films of size-separated quantum dots. Their photoluminescence varies with the size of the crystalline core. All observations are in perfect agreement with the quantum confinement model, that is, the photoluminescence is the result of the recombination of the electron-hole pair created by the absorption of a UV photon. Other mechanisms involving defects or surface states are not operative in our samples. 

Since the discovery of the intense red photoluminescence of porous silicon [1,2], much work has been devoted to this particular nanostructured material [4, 5] and, in the meantime, also to silicon nanoparticles [6, 7]. An important issue of current studies is the influence of the surface passivation on the photoluminescence properties. It has already been said that, in the quantum confinement model, it is essential that the surface is well passivated to avoid any dangling bonds [8]. Being middle-gap defects, these dangling bonds will quench the PL. On the other hand, the surface itself may lead to surface states that can be the origin of another kind of photoluminescence [9,10]. 

The conclusion that can be drawn from the experiments just discussed is that, except for the very small particles, the photoluminescence of our Si nanocrystals, which are produced by CO2 laser-assisted pyrolysis of silane and which are gently oxidized in air under normal conditions, can be perfectly explained on the basis of the quantum confinement model, that is, by the radiative recombination of electron-hole pairs confined in the nanocrystals [15]. In order to obtain high quantum yields, the nanoparticles must be defect-free in particular, they must be perfectly monocrystalline and all dangling bonds must be passivated, for example by a silicon oxide layer. Indeed, high-resolution electron microscopy (HREM) studies have shown that our Si nanoparticles are composed of a perfect diamond-phase crystalline core and a surrounding layer of SiO [19]. 

The early research on the electrical transport properties of porous silicon carried out in the 1980s revealed that the resistivity of the porous silicon layer was a few orders of magnitude higher than the original substrate (Beale et al. 1985). While quantum confinement model has been successfully used to explain the luminescence properties of PS, applying it to explain the transport properties of PS has... 

Lee etal. (1996) Nanoporous membrane Al/PS (CP) Quantum confinement model... 

Additionally, near-field scanning optical microscopy (NSOM) has been successfully applied to the imaging of topography and locally induced photoluminescence of porous silicon (Rogers et al. 1995). The experimental results are, as in previous cases, consistent with the quantum confinement model. 

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