Redistribution of Solutes During Thermal Oxidation of Silicon

Abstract

During thermal oxidation of silicon, the solute in the original silicon is redistributed between the oxide formed and the unoxidized silicon. The redistribution depends on the segregation coefficient of the solute between the oxide and the silicon, the growth rate constant of the oxide, and the diffusion coefficients of the solute in the oxide and in the silicon. It also depends on the boundary condition existing at the oxide-free space interface. The concentration profile of the redistributed solute is analyzed mathematically and exact solutions are obtained for two cases. In the first case, there is no gain or loss of the solute by the oxide-silicon system through the oxide surface. In the second case, the oxide is in equilibrium with the ambient gas so that the concentration of the solute is a constant at the oxide surface. The results are discussed with special attention to the two most common solutes, boron and phosphorus.

A Thermodynamic Approach to Guide Reactive Element Doping: Hf Additions to NiCrAl

“…The equilibrium calculation failed to predict the local HfO 2 formation observed in the γ-γ alloys. In examining this discrepancy, we note that while the Hf tolerance is calculated based on equilibrium phase compositions, i.e., on the composition of the alloy surfaces prior to oxidation, the composition of an alloy at the metal/oxide interface changes as oxidation proceeds, due to selective Al removal to form Al 2 O 3 (if scale growth is parabolic, a constant interfacial composition is reached at steady state [26][27][28][29]). An obvious manifestation of this change is the dissolution of γ below the scale.…”

Semiconductor measurement technology

“…9-11) associated with the oxide. Equation 7is believed to be more appropriate in certain Ku [37] has found a closed-form solution to the uniform redistribution problem with the assumption that eq (7), with C =0, holds at P the oxygen-oxide interface. His work suggests that the solution to the uniform redistribution problem in the case of zero flux between the oxide and air should possess two qualitative features: (i) that the value of the concentration in the silicon at the moving front be independent of time and (ii) that the concentration in the oxide be spatially uniform and independent of time.…”

Impurity Redistribution in a Semiconductor during Thermal Oxidation

“…This condition is expressed as C1 (0, t) = Cs [5] (B) If the impurity concentration in the ambient gas is such that an appreciable time is required for the equilibrium impurity concentration, Cs, to be established at the oxide surface, the rate of loss or gain of impurities through the outer oxide surface can be assumed proportional to the difference between the surface impurity concentration, Cl(0,t) at any time t in the oxide, and the equilibrium concentration Cs. This condition is expressed as C1 (0, t) = Cs [5] (B) If the impurity concentration in the ambient gas is such that an appreciable time is required for the equilibrium impurity concentration, Cs, to be established at the oxide surface, the rate of loss or gain of impurities through the outer oxide surface can be assumed proportional to the difference between the surface impurity concentration, Cl(0,t) at any time t in the oxide, and the equilibrium concentration Cs.…”

“…It is interesting to note that the solution of the diffusion equation, with the boundary condition described by Eq. [5]. [5].…”

“…Equations [1] and [2] with conditions described by [3], [4], [5], [6], [7], and [8] can be solved by letting ul = y/2 (Di t)1/~ [9] and us : x/2 (D2 t) 1/2 [10] The solutions can then be written as 4 Equations [1] and [2] with conditions described by [3], [4], [5], [6], [7], and [8] can be solved by letting ul = y/2 (Di t)1/~ [9] and us : x/2 (D2 t) 1/2 [10] The solutions can then be written as 4…”