Silicon diffusion coefficient

The technology of silicon and germanium production has developed rapidly, and knowledge of die self-diffusion properties of diese elements, and of impurity atoms has become reasonably accurate despite die experimental difficulties associated widi die measurements. These arise from die chemical affinity of diese elements for oxygen, and from die low values of die diffusion coefficients. 

It will be noted that because of the low self-diffusion coefficients the numerical values for representations of self-diffusion in silicon and germanium by Anhenius expressions are subject to considerable uncertainty. It does appear, however, that if this representation is used to average most of the experimental data the equations are for silicon... 

Examples of this procedure for dilute solutions of copper, silicon and aluminium shows the widely different behaviour of these elements. The vapour pressures of the pure metals are 1.14 x 10, 8.63 x 10 and 1.51 x 10 amios at 1873 K, and the activity coefficients in solution in liquid iron are 8.0, 7 X 10 and 3 X 10 respectively. There are therefore two elements of relatively high and similar vapour pressures, Cu and Al, and two elements of approximately equal activity coefficients but widely differing vapour pressures. Si and Al. The right-hand side of the depletion equation has the values 1.89, 1.88 X 10- , and 1.44 X 10 respectively, and we may conclude that there will be depletion of copper only, widr insignificant evaporation of silicon and aluminium. The data for the boundaty layer were taken as 5 x lO cm s for the diffusion coefficient, and 10 cm for the boundary layer thickness in liquid iron. 

Fig. 3.1.7 The surface diffusion coefficient / surface of cyclohexane (squares) and acetone (circles) in porous silicon with 3.6-nm mean...

Fig.3.1.9 (a) The adsorption-desorption isotherm (circles, right axis) and the self-diffusion coefficients D (triangles, left axis) for cyclohexane in porous silicon with 3.6-nm pore diameter as a function of the relative vapor pressure z = P/PS1 where Ps is the saturated vapor pressure, (b) The self-diffusion coefficients D for acetone (squares) and cyclohexane (triangles) as a function of the concentration 0 of molecules in pores measured on the adsorption (open symbols) and the desorption (filled symbols) branches. 

Just as in the case of (16), an equation of the form (20) applies to any other association-dissociation reaction in which one of the dissociated species is mobile, the other fixed. When the two species are distinct but both mobile, as for hydrogen combining with, say, an interstitial silicon, a similar line of reasoning, whose details we omit, leads to equations of the same form as (16) and (20) but with D+ replaced by the sum of the diffusion coefficients of the two species. When the two mobile species are the same, as for the reaction H° + H° 5H2, it turns out that nA and n+ should each be replaced by the monatomic density n, D+ by the monatomic diffusion coefficient, and 4ir by 8tt in (16) but not in (20). 

Fig. 11. High-temperature behavior of the solubility s of hydrogen in silicon and of its diffusion coefficient D. Squares are from the measurements of Van Wieringen and Warmholtz (1956) on H2, fitted by the full lines (80) and (81), respectively. Crosses are measurements of s using 3H2, by Ichimiya and Furuichi (1968), fitted by the dotted line(82). 

Fig. 16. Panorama of values in the literature for diffusion coefficients of hydrogen in silicon and for other diffusion-related descriptors. Black symbols represent what can plausibly be argued to be diffusion coefficients of a single species or of a mixture of species appropriate to intrinsic conditions. Other points are effective diffusion coefficients dependent on doping and hydrogenation conditions polygons represent values inferred from passivation profiles [i.e., similar to the Dapp = L2/t of Eq. (95) and the ensuing discussion] pluses and crosses represent other quantities that have been called diffusion coefficients. The full line is a rough estimation for H+, drawn assuming the top points to refer mainly to this species otherwise the line should be higher at this end. The dashed line is drawn parallel a factor 2 lower to illustrate a plausible order of magnitude of the difference between 2H and H.

For completeness it should be mentioned that the passivation of gold, presumably via the same AuH complex, has also been studied in p-type silicon, where it is the donor rather than the acceptor level of gold that is active (Hansen et al., 1984). Though no profiles were reported in this work, apparent hydrogen diffusion coefficients inferred by these authors are of the same order as the Pearton (1985) points of Fig. 16 at temperatures 110°C and below. 

DIFFUSION COEFFICIENT ACTIVATION ENERGY AND PREEXPONENTIAL FACTOR FOR UNDOPED AMORPHOUS SILICON... 

It is important to note that Eqs. 5, 8, and 9 were derived entirely from a silicon material balance and the assumption that physical sputtering is the only silicon loss mechanism thus these equations are independent of the kinetic assumptions incorporated into Eqs. 1, 2, and 7. This is an important point because several of these kinetic assumptions are questionable for example, Eq. 2 assumes a radical dominated mechanism for X= 0, but bombardment-induced processes may dominate for small oxide thickness. Moreover, ballistic transport is not included in Eq. 1, but this may be the dominant transport mechanism through the first 40 A of oxide. Finally, the first 40 A of oxide may be annealed by the bombarding ions, so the diffusion coefficient may not be a constant throughout the oxide layer. In spite of these objections, Eq. 2 is a three parameter kinetic model (k, Cs, and D), and it should not be rejected until clear experimental evidence shows that a more complex kinetic scheme is required. 

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