Vacancy concentration charge state

The vacancy is very mobile in many semiconductors. In Si, its activation energy for diffusion ranges from 0.18 to 0.45 eV depending on its charge state, that is, on the position of the Fenni level. Wlrile the equilibrium concentration of vacancies is rather low, many processing steps inject vacancies into the bulk ion implantation, electron irradiation, etching, the deposition of some thin films on the surface, such as Al contacts or nitride layers etc. Such non-equilibrium situations can greatly affect the mobility of impurities as vacancies flood the sample and trap interstitials. 

Multiple-Charge-State Vacancy Model. On the basis of the previous discussion, diffusion depends upon the concentration of point defects, such as vacancies or self-interstitials, in the crystal. Therefore, diffusion coefficients can be manipulated by raising or lowering the concentration of point defects. 

The presence of high concentrations of implanted dopants influences the epitaxial growth rate. As shown in Fig. 10.7, concentrations of phosphorus at levels greater than 0.1 atomic percent (5 x 1019 cm3) cause an increase in the growth rate. This increase is similar to the increase in the diffusion coefficient of dopants, which is attributed to an increase in the vacancy concentration in heavily doped Si, where the Fermi level is near the conduction or valence-band edges. The concentration of vacancies in Si depends on the charge state of the vacancy. The neutral vacancy concentration [Vx] (Mayer and Lau 1990) is given by... 

There is a significant difference between the defects (vacancies and interstitials) in semiconductors and those in metals that is, defects in a semiconductor can be charged electrically, whereas defects in a metal are considered neutral. Since they can be charged (or ionized), the concentration of these defects becomes a function of the Fermi level position in the semiconductor. Consider the charged states of vacancies in Si as an example. It is generally accepted that the single vacancy in Si can have fom charge states (Van Vechten 1980) V, F, and F , where + refers to a donor state, x a neutral species,... 

In a previous study of non-stoichiometiy in ScS, [30] an analysis of the charge densities and partial densities of states for a series of low-energy structures with increasing vacancy concentration revealed very clearly the mechanism of intrinsic non-stoichiometry in that system. Despite the very obvious similarities of the ground states in these two systems compared to those of ScS, the details of the mechanism for non-stoichiometry appears to be different. An analysis of the partial densities of states(not shown here) for non-stoichiometric TiC and TiN did not reveal a mechanism for vacancy formation similar to that found for ScS—a somewhat puzzling result given the fact that the ground states in ScS are so closely related to those in TiC/N. At this point, we have not been able to determine the electronic mechanism that drives the formation of vacancies in TiC and TiN. This topic is a focus of our current research and will be discussed in a future publication. 

A more highly-charged defect such as +2 would be determined by the same formula but the ratio would be with respect to the concentration of the less charged (e.g. -1-1) defect rather than the neutral vacancy. The total number of vacancies in the material is then the sum over all charge states. 

To illustrate the effect of Equations 7.6 and 7.7 on the vacancy concentration, let us consider the case of undoped and doped Si. Here vacancies can occur in three charge states, -1-1, -1, and -2, with energies 1.0 eV below the conduction band, and 0.6 and 1.05 eV above the valence band at 300 K, respectively. The overall energy gap of Si is 1.12 eV. The energy of formation of a neutral vacancy is 2.4 eV, the vibrational entropy change per added vacancy is 1.1 ke, and the site density in the Si lattice is 5x10 2 cm [3]... 

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