Steady-state oxide thickness

Steady-State Oxide Thickness. The steady-state etching rate (R = S/M) does not contain any of the kinetic parameters thus it does not contain any information about the kinetics of the oxidation process. In contrast, the steady-state oxide thickness is determined by the kinetics of the transport and oxidation processes thus one can learn about these processes by studying the steady-state oxide thickness. The silicon material balance (Eq. 9)... 

Most theories of droplet combustion assume a spherical, symmetrical droplet surrounded by a spherical flame, for which the radii of the droplet and the flame are denoted by and respectively. The flame is supported by the fuel diffusing from the droplet surface and the oxidant from the outside. The heat produced in the combustion zone ensures evaporation of the droplet and consequently the fuel supply. Other assumptions that further restrict the model include (/) the rate of chemical reaction is much higher than the rate of diffusion and hence the reaction is completed in a flame front of infinitesimal thickness (2) the droplet is made up of pure Hquid fuel (J) the composition of the ambient atmosphere far away from the droplet is constant and does not depend on the combustion process (4) combustion occurs under steady-state conditions (5) the surface temperature of the droplet is close or equal to the boiling point of the Hquid and (6) the effects of radiation, thermodiffusion, and radial pressure changes are negligible. 

Figure 4 shows the application (6) of potentials to the Pt and Au electrodes of the sandwich (vs. a reference electrode elsewhere in the contacting electrolyte solution) so that they span the E° of the poly-[Co(II/I)TPP] couple (Fig. 4B). There is a consequent redistribution of the concentrations of the sites in the two oxidation states to achieve the steady state linear gradients shown in the inset. Figure 4C represents surface profilometry of a different film sample in order to determine the film thickness from that the actual porphyrin site concentration (0.85M). The flow of self exchange-supported current is experimentally parameterized by applying Fick s first law to the concentration-distance diagram in Fig. 4B ...

Figure 11. Steady-state current density as a function of imposed voltage at a o constant thickness of a barrier-type oxide, in log versus E and log versus El/2 coordinates. (Based on data from Ref. 5.)...

The capacitance determined from the initial slopes of the charging curve is about 10/a F/cm2. Taking the dielectric permittivity as 9.0, one could calculate that initially (at the OCP) an oxide layer of the barrier type existed, which was about 0.6 nm thick. A Tafelian dependence of the extrapolated initial potential on current density, with slopes of the order of 700-1000 mV/decade, indicates transport control in the oxide film. The subsequent rise of potential resembles that of barrier-layer formation. Indeed, the inverse field, calculated as the ratio between the change of oxide film thickness (calculated from Faraday s law) and the change of potential, was found to be about 1.3 nm/V, which is in the usual range. The maximum and the subsequent decay to a steady state resemble the behavior associated with pore nucleation and growth. Hence, one could conclude that the same inhomogeneity which leads to pore formation results in the localized attack in halide solutions. 

Figure 3.12 (a) Steady state values of A and 1 as a function of potential. Platinum in aqueous sulphuric acid. (b> Dependence of oxide film thickness on potential. Platinum in aqueous sulphuric acid. From Reddy et a . (1968). 

Following this initial period of polyimide development, interest reached a steady-state and remained there until the late 1970s. During this time a major impetus to the polyimide area was provided by the aerospace industry. The need for composite matrix resins as well as structural adhesives with excellent oxidative and thermal stability appeared to be at least partially met by polyimide type resins. Ultimately, requirements of high flow and low void content in relatively thick parts directed these efforts into different directions. Another upswing occurred in the early 1980s with the potential application of... 

Fig. 1. Top Reference spectra for femtosecond transient absorption measurements S-S abs. in solution (thin solid lines), oxidized dye (dye+) abs. in solution (thick solid line), fluorescence for solution (dotted line), steady-state absorption ofNKX-2311/ZnO (dotted-dashed line), and absorption of electrons in the conduction band (dashed line). Bottom Transient absorption spectra of NKX-23ll/ZnO in the spectral range between 600 and 1350 nm at the 2 (thick solid line), 10 (dotted line), 100 ps (thin solid line) delay times after excitation at 540 nm by the femtosecond pulse with the intensity of about 10 pJ.

For a finite flux jA, there is a (steady state) shift of the AX crystal towards the side with the higher pXi. jx does not lead to such a shift. The shift velocity is / A-Vm(AX). Equation (4.104) can also be used to quantify the basic (one dimensional) metal oxidation experiment A+1/2X2 = AX shown in Figure4-4. In terms of thickness growth, one obtains from Eqn. (4.104) the expression... 

Several definitive experiments have shown that during the thermal oxidation of silicon the oxidizing species (some form of oxygen) diffuses through the oxide layer and reacts with the silicon to produce more oxide at the Si-Si02 interface (70, 71). For oxidation to occur, three consecutive oxidant fluxes must exist (1) transport from the furnace ambient to the outer oxide surface, (2) diffusion through the oxide layer of thickness x0, and (3) reaction with silicon at the interface. At steady state, all three fluxes are equal. 

Solving this equation in a steady state, 3C/3t = 0, leads to the thickness concentration profile, C = f(x), and the local oxidation rate... 

In this section we discuss the model predictions for the ketone ethyl acetoacetate (1). With the ketone absent ([Ket]x = 0 mM), the extended model reproduces all previous results with oscillations of all system variables above [Glc]xo > 18.5 mM [53]. Figure 3.6 shows the system s response to a fixed glucose concentration [Glc]xo at 30 mM and an increase of [Ket]x to 1 mM. The oscillations vanish at [Ket]x = 0.23 mM in a supercritical Hopf bifurcation and the steady state is stable for [Ket]x > 0.23 mM. Figure 3.6a shows the minimum and maximum concentrations of NADH as two thick curves, while in all other panels the time averages of the plotted variables are shown, not the minimum and maximum values. Since the addition of ketone provides an alternative mode of oxidation of NADH, the concentration of NADH is decreasing in Fig. 3.6a whereas the fluxes of carbinol production are increasing in Fig. 3.6b. 

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