Calculated Solubilities of Oxygen in Liquid and Solid Silicon

Abstract

By a thermodynamic approach, several equilibria for the silicon‐oxygen system, important for silicon crystal growth, were derived. The solid solubility of oxygen in silicon in equilibrium with SiO2 was calculated with good agreement with experimental literature data. Equilibrium data for liquid silicon, which has never been measured although of great importance for the control of oxygen in Czochralski crystal growth, were also obtained.

Thermodynamics and phase stability in the Si–O system

“…It should be noted though, that all these extrapolations to the low temperature range are based on the consistent thermodynamic description of the entire Si-O system, which improves their reliability. The own results are distinctly different from those of Ekhult and Carlberg [112,155]. While x liquid O at the eutectic with cristobalite was given just 22% below the present value, it was claimed that the liquidus line of SiO(am) is located at lower concentration compared to the liquidus of SiO 2 (cristobalite) and that at even lower oxygen concentration a liquidus line of crystalline ÔSiO(cr)' appears [112].…”

“…The fact that there is no evidence for the existence of bulk crystalline silicon monoxide had been detailed above. These completely different results are due to the kind of thermodynamic derivation suggested by these authors [112,155]. The main problem with that derivation is not that it uses only linear approximations for the temperature dependency of Gibbs energy of reactions, which merely results in neglecting the differences in heat capacities, as shown by the term C in Table 8.…”

“…Another major problem is in the derivation of the oxygen solubility in solid silicon, Eq. (7) in [155] and Eq. (12b) in [112].…”

“…That equation was obtained from the oxygen solubility in liquid silicon, Eq. (6) in [155], by simply Ôcombining it with the free energy of solidification of silicon'. This, however, only changes the reference state; it does not give any information on how the solute will dissolve in the entirely different structures of the liquid or solid solvents.…”

“…A correlation of oxygen solubilities in different liquid elements has been assessed by [153], whose estimated equation is quite good compared to the measured data. The assessed equations of [154,155] are not taken into account, as discussed later. The available data points are presented in Fig.…”