Dopant equilibrium

Defect and dopant equilibrium with discrete formation... 

It is important to know that the defect equilibria that apply to the pure material, and the associated equilibrium constants, also apply to the doped material. The only additional information required is the nature and concentration of the dopant. To illustrate the construction of a diagram, an example similar to that given in Chapter 7 will be presented, for a nonstoichiometric phase of composition MX, nominally containing M2+ and X2- ions, with a stoichiometric composition MXl 0. In this example, it is assumed that the relevant defect formation equations are the same as those given in Chapter 7 ... 

In general, differences in chemical bonding and electron configuration between carbon atoms and dopants mandate the deviation from the geometric and electronic equilibrium structure of the aromatic layers in CNTs. As a consequence, topological defects such as Stone-Wales defects are formed with increased probability [37]. 

In this chapter, we review the current status of doping of SiC by ion implantation. Section 4.2 examines as-implanted depth profiles with respect to the influence of channeling, ion mass, ion energy, implantation temperature, fluence, flux, and SiC-polytype. Experiments and simulations are compared and the validity of different simulation codes is discussed. Section 4.3 deals with postimplant annealing and reviews different annealing concepts. The influence of diffusion (equilibrium and nonequilibrium) on dopant profiles is discussed, as well as a comprehensive review of defect evolution and electrical activation. Section 4.4 offers conclusions and discusses technology barriers and suggestions for future work. 

Frequently, growth of crystals from melt involves more than one component, such as impurities, intentionally added dopants, etc., in addition to the major component. In these cases, it is essential to know the distribution of the second component between the growing crystal and the melt. This distribution occurs according to the phase diagram relating the equilibrium solubilities of the second component (impurity) in the liquid and the solid phases. 

Figure 2-2. a) Fraction /Vp of defect pairs (e.g., [B.V] in Schottky-disordered AX) as a function of the normalized temperature (R/ AGp )-T for various dopant concentrations Nb) NP as a function of at given T. The parameter Ks denotes the Schottky equilibrium constant FVv-A )-... 

Purification of Solution. An approximate model for the purification of the solution can be developed by assuming that a stagnant melt initially contains an impurity at a uniform concentration, Cf°, and loss of dopant occurs by evaporation at the top surface. The rate of evaporation is assumed to be directly proportional to the difference in concentrations at the top surface and at equilibrium. If the proportionality constant is z, the diffusion coefficient of the impurity in the melt is D v and the depth of the melt is Z, then the following expression for the impurity concentration in the melt,... 

The equations used to describe dopant incorporation are identical to those used to describe the deposition of the semiconductor. Thus equations 12-14 are applicable to a diflusion-limited model, with the number of components, n, increased by the number of dopants added. The equilibrium distribution coefficient, ki9 is defined as... 

Point Defect Models of Diffusion in Silicon. Under conditions of thermal equilibrium, a Si crystal contains a certain equilibrium concentration of vacancies, C v°, and a certain equilibrium concentration of Si self-interstitials, Cz°. For diffusion models based on the vacancy, Cv° Cf and the coefficients of dopant diffusion and self-diffusion can be described by equation 27 (15)... 

On the other hand, the ability of a semiconductor to donate or accept electrons is uniquely related to the energy of the electron in its Fermi level EF. The transfer of fractional charge 8e can be viewed as a redox equilibrium between the dopant and the matrix in which the role of the electron donor and of the electron acceptor is relative and governed by the difference between % and EF, respectively. 

We now use A as the total primary dopant concentration (e.g., the donor) and link it to the charge transfer from the gas molecules through the electron-exchange equilibrium. The ionization equilibrium involving this level is... 

Recently, it was shown that equilibrium amorphous films also exist at interfaces between metals (Ni and Cu) and alumina, via model experiments based on nanocomposites. Cu-A1203 and Ni-Al203 nanocomposites were prepared using high-purity alumina powder to which predetermined amounts of Ca and Si dopants were added.25... 

One can measure the equilibrium constant for defect association between a dopant ion and its charge compensation by measuring the relative concentrations of the paired and dissociated probe ion concentrations over a range of dopant concentrations. 

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