Semiconductor solid-liquid equilibrium

Solid-Liquid Equilibrium in Ternary Group III-V Semiconductor Materials... 

Several excellent reviews of liquid-phase epitaxy have appeared in the literature over the past 15 years (1-12). The discussion in this chapter will be limited in scope but will supplement the material discussed in previous reviews. In particular, issues that can be analyzed by traditional methods of chemical engineering are addressed for this chemical process. Because the growing solid-liquid interface is near equilibrium, the calculation of multicomponent compound-semiconductor phase diagrams will be emphasized. 

Heteroepitaxy. Heteroepitaxy (e.g., deposition of Al Ga As on GaAs) is somewhat different, because the solid and liquid cannot initially be in equilibrium, that is, a chemical potential difference exists across the solid-liquid interface. In compound semiconductors, the chemical potential of each element is constrained by compound stoichiometry. For example, for a ternary solid (A B C) in equilibrium with a ternary liquid, the conditions of equilibrium are given by equations 8 and 9 ... 

Analysis of the growth process by LPE usually stipulates an equilibrium boundary condition at the solid-liquid interface. The solid-liquid phase diagrams of interest to LPE are those for the pure semiconductor and the semiconductor-impurity systems. Most solid alloys exhibit complete mis-... 

A general formulation of the problem of solid-liquid phase equilibrium in quaternary systems was presented and required the evaluation of two thermodynamic quantities, By and Ty. Four methods for calculating Gy from experimental data were suggested. With these methods, reliable values of Gy for most compound semiconductors could be determined. The term Ty involves the deviation of the liquid solution from ideal behavior relative to that in the solid. This term is less important than the individual activity coefficients because of a partial cancellation of the composition and temperature dependence of the individual activity coefficients. The thermodynamic data base available for liquid mixtures is far more extensive than that for solid solutions. Future work aimed at measurement of solid-mixture properties would be helpful in identifying miscibility limits and their relation to LPE as a problem of constrained equilibrium. 

As already discussed in Section 3.2 the potential across a single solid-liquid interface cannot be measured. One can only measure the potential of an electrode vs. a reference electrode. It has already been shown in Section 3.2 that a certain potential is produced at a metal or semiconductor electrode upon the addition of a redox system, because the redox system equilibriates with the electrons in the electrode, i.e. the Fermi level on both sides of the interface must be equal under equilibrium. It should be emphasized here that the potential caused upon addition of a redox couple to the solution occurs in addition to that already formed by the specific adsorption of, for instance, hydroxyl ions. A variation in the relative concentrations of the oxidized and reduced species of the redox system leads to a corresponding change of the potential across the outer Helmholtz layer, as required by Nernst s law (see Eq. 3.47), which can be detected by measuring the electrode potential vs, a reference electrode. However, there still exists a potential across the inner Helmholtz layer which remains unknown. 

In Fig. 17(a), the energetics of a typical interfacial region between an n-type semiconductor and an electrolyte solution is shown (see also Sect. 2.1.2.2). Electronic equilibrium exists between the semiconductor and a redox system present in the solution the electrochemical potential of electrons /Xg in the solid is equal to that in the liquid phase, and does not change with the spatial coordinate x, perpendicular to the solid/liquid interface. The electrochemical potential of the electrons is also equal to the electron Fermi level, denoted as and can be written as... 

The major application of vapor-liquid equilibrium (VLE) is distillation. The uses of liquid-liquid equilibrium (LLE), liquid-solid equilibrium (LSE), and gas-solid equilibrium (GSE) are much more diverse. They include extraction (both solid and liquid), decantation as a phase separation, vapor-phase deposition (the heart of the semiconductor business), and a host of environmental applications. In all of these applications the equilibrium state and the rate of approaching it are both important. This book discusses only the equiUb-rium state, normally asking what are the compositions of the equilibrium phases when the system has minimized its Gibbs energy, subject to the external constraints and the starting conditions. As with VLE, the working criterion for LLE, LSE, and GSE is that the fugacity of any individual species must be the same in aU the phases at equilibrium (Eq. 7.4). 

Equilibrium between the two phases at a semiconductor-electrolyte interface, solid and liquid, can only be achieved if their electrochemical potential is the same, that is ... 

Source Considerations. Many CVD sources, especially sources for or-ganometallic CVD, such as Ga(CH3)3 and Ga(C2H5)3, are liquids at near room temperatures, and they can be introduced readily into the reactor by bubbling a carrier gas through the liquid. In the absence of mass-transfer limitations, the partial pressure of the reactant in the gas stream leaving the bubbler is equal to the vapor pressure of the liquid source. Thus, liquid-vapor equilibrium calculations become necessary in estimating the inlet concentrations. For the MOCVD of compound-semiconductor alloys, the computations have also been used to establish limits on the control of bubbler temperature to maintain a constant inlet composition and, implicitly, a constant film composition (79). Similar gas-solid equilibrium considerations govern the use of solid sources such as In(CH3)3. 

The interaction parameter, ft, is a fitting parameter in the regular solution model that can be found from liquid-solid equilibrium data (93). With the DLP model, the interaction parameter is calculated from the lattice parameters of the binary compounds. For a compound semiconductor AiJB C, ft is computed from the lattice constants aAC and aBC of the binary compounds from the following expression... 

For gas-solid and liquid-solid systems, the interaction of a species with the solid surface depends on the chemical nature of the species and on the chemical and physical nature of the solid. For nonilluminated surface of semiconductor oxides, a thermodynamic equilibrium between a species and the solid is established only when the electrochemical potential of the electrons in the entire system is uniform. When the adsorption-desorption equilibrium is established, an aliquot of the species is located in an adsorbed layer, held at the surface by either weak or strong bonding forces. 

In the theory of non-equilibrium processes at solid state junction and also semiconductor-liquid interfaces, as developed in the previous section, frequently quasi-Fermi levels have been used for the description of minority carrier reactions [90, 91], A concept for a quantitative analysis for reactions at n- and p-type electrodes has been derived [92, 93], using the usual definition of a quasi-Fermi level (Eqs. (3a) and (3b)). Taking a valence band process as an example, the quasi-Fermi level concept can be illustrated as follows ... 

In ideal semiconductor/electrolyte junctions, the presence of an energetic barrier in the semiconductor phase, originated from the equilibrium of the Fermi level in the solid and liquid phases, can be approached by the semiconductor depletion layer capacitance or space charge capacitance, Cgc- Measurement of capacitance versus... 

Vapor pressure - The pressure of a gas in equilibrium with a liquid (or, in some usage, a solid) at a specified temperature. Varistor - A device that utilizes the properties of certain metal oxides with small amounts of impurities, which show abrupt nonlinearities at specific voltages where the material changes from a semiconductor to an insulator. 

The application of zone melting to the purification of semiconductor materials has been well established. In this technique a molten zone is passed along the length of a solid rod in one direction several times. Impurities more soluble in the molten metal i ill move in the direction in which the molten zone is moved while impurities less soluble in the liquid metal will be deposited in the solid metal and will tend to move in the opposite direction. Since the degree of purification depends on the solubility of the impurities in the solid metal, those impurities which are soluble in the solid cannot be removed to below the equilibrium concentration. Thus the interstitial impurities which are quite soluble in the solid rare earths just below their melting point cannot be completely removed. 

An electron-conducting material brought into contact with an ionically conducting phase establishes an electrode. In case of semiconductors in addition to electrons, holes may act as means of charge propagation. The ionically conducting phase may be an electrolyte solution composed of a dissociated electrolyte and a solvent, an ionic liquid, a molten salt, or a solid electrolyte. At the established interphase an equilibrium is established. Assuming at the instance of contact a non-equilibrium between both phases and the chemical potentials of the involved species, two ]u, possibilities may be considered one is depicted below (Fig. 1) ... 

Liquid-solid When all the constituents are present in both phases at equilibrium, we have the operation of fractional crystallization. Perhaps the most interesting examples of this are the special techniques of zone refining, used to obtain ultrapure metals and semiconductors, and adductioe crystallization, where a substance, such as urea, has a crystal lattice which will selectively entrap long straight-chain molecules like the paraffin hydrocarbons but will exclude branched molecules. 

Of the three categories of liquid-solid equilibria considered in Section 3.3.7.S and briefly considered above, a solid solution in equilibrium with a molten mixture has special importance in the purification of semiconductor materials such as silicon. Here, the bulk solid phase, as well as the molten mixture, consists essentially of silicon the concentrations of impurities are at a very low level. Therefore the area of focus is very close to either end of the type of phase diagram in Figures 3.3.6A for a given impurity-silicon system. Usually the solution being extremely dilute, the distribution coefficient Kb for the impurity i between the solid phase and the melt (see Example 1.4.3),... 

One of the observations about Czochralski growth is that the concentration of impurities in the solid is generally much different (and fortunately often much lower) than in the liquid. The ratio of the concentration in the solid to the concentration in the liquid is referred to as the segregation ratio. Typical values for segregation ratios of selected impurities are given in Table 4.1. Some of the more striking values are for O (which actually prefers to be in the solid phase) and Fe, which is in equilibrium when the liquid contains one hundred twenty five thousand times more Fe than does the sohd. The latter is particularly fortunate as Fe is a major problem for semiconductor devices. Detectable degradations in performance may be found at the part-per-billion Fe level. Consequently, effective methods, such as those discussed above, to remove Fe are particularly important. 

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