Effective mass model

Values of AEG calculated on the basis of the effective mass model are sensitive to the height of the barrier present at the surface of the confined structures [De4, Xu2]. For the case of oxidized PS, it is obvious that the silicon crystallites are embedded in a wide-gap material. In the case of a hydrogen termination of the crys-... 

Fig. 3.5.1 The minimum of the first derivative of UV/visible absorbance spectra of CdS particles as a function of the particle diameter. The data points have been collected from literature sources where particle sizes were determined by EM or XRD. If specific data about the minimum of the first derivative were not expressly provided, they were estimated from spectra supplied. The estimated error in this technique is less than 5 nm. For clarity, only data from groups with the greatest number of data points have been used here. A curve has been fitted to the data using a theoretical relationship between particle diameter and wavelength using the effective mass model (6). Inset Absorbance spectra of colloidal CdS produced by exposure of a CdAr film, or a Cd2+/HMP solution, to H S. The minima of the first derivative (380 nm in film, 494 nm in solution) correspond to particle sizes of approximately 2.5 nm and 6.0 nm, respectively. (From Ref. 5.)...

There are many theoretical models to correlate the increase in semiconductor bandgap with crystal size. However, for our purposes we will show only the original model, known as the effective mass model, since this is the easiest to understand, in spite of its limited accuracy. 

The effective mass model is based on the energy of the lowest-energy par-ticle-in-a-box configuration, taking into account that the relevant mass term is given by a reduced effective mass, p, where p, is given by... 

The effective masses of electrons (md) and holes (m ) represent the masses that these charges appear to have when moving in the solid rather than in free space, and these vary from material to material. (In the size quantized regime, they can also vary with crystal size, particularly for small quantum dots, hence the limitations of the effective mass model). 

If the Hamiltonian with variable reduced mass is used, the dependence of the reduced mass on coordinate will be a function of to. On the other hand, if the constant effective mass model is used, the reduced mass can be evaluated from Eqs. (3.1) to (3.10) for an infinitesimal displacement from the planar conformation. The constant effective reduced mass derived in this fashion is independent of to, and thus, no knowledge of to is needed to use the Hamiltonian Eq. (3.22) conversely, no information about the value of to can be determined from the vibrational data and Eq. (3.22). 

Effective Mass Model. The effective mass description of an impurity (donor) state requires that the electron orbit extend over many lattice distances. This permits the use of the macroscopic dielectric constant to describe the electronic motion. With these conditions satisfied, the impurity energy state can be approximated by the hydrogenic form with the electron mass replaced by an effective mass m ... 

It is clear that the effective mass model must be modified in order to account for different chemical donors. The FTIR experiment monitors the n = 1 to n = 2 transition. For shallow donors in many of the III-V compounds the 2s and 2p states are degenerate for all practical purposes. The resolution is improved by applying a magnetic field. The magnetic field separates the orbital angular momentum states. The magnetic field also compresses the wave function which sharpens the transitions, it also separates transitions due to different chemical impurities ( ). 

The effective mass model can be used in conjunction with the UVA isible spectrum of the CdS colloid to determine the approximate particle size (13). In this model, the effective mass of electrons and holes is determined by their interactions with other electrostatic charges within the lattice. Eqnation 2 shows how the semicondnctor band gap is related to the particle size ... 

It can be used to measure the photoluminescence (PL) emission of rare earth ions, noble metal NPs, and semiconductor quantum dots. For quantum dots, based on their fluorescence spectra, the particle size can be evaluated, using the Brus effective mass model [21]. 

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