Etch rate calculation

Solution Using Equation 5.18 and the etching rates calculated from the previous two examples, we have... 

A local etch rate can be calculated once n2 is determined. The change in thickness corresponding to one complete oscillation is known as the thickness period, dp,... 

Srinivasan etal.,64 in a phenomenological development, split the etch rate into thermal and photochemical components and used zeroth-order kinetics to calculate the thermal contribution to the etch rate. An averaged time-independent temperature that is proportional to the incident fluence was used to determine the kinetic rate constant. The photochemical component of the etch rate was modeled using, as previously discussed, a Beer s law relationship. The etch depth per pulse is expressed, according to this model, in the form... 

From a knowledge of the absorption coefficient aeff and the threshold fluence Fth, the value of the photochemical contribution to the etch rate, Fph0to> can calculated and subtracted from the measured hole depth for any given fluence. The difference, which according to this model is the thermal etch rate Fthermai will be modeled by Eq. (5) by rewriting it as... 

Silicon etch rates in alkaline solutions commonly increase monotonically with temperature. For KOH, for example, the etch rate r can be calculated according to ... 

Fig. 9.17 Calculated growth rates of macropores for nv=2 and nv=4 (lines) and experimentally obtained initial macropore etch rates rp (squares) versus the HF concentration Chf of the electrolyte (J/JPS = 0.2S, 1015 crrT3 n-type, RT, square pattern). After [Le9],...

Fig. 22. Sequence of in-situ STM images showing n-Si(l 11) etching in 2 M NaOH (t/j = -1.65 V/ SCE, / s = -150 M-A/cm ). Frames are 1270 A x935 A and were recorded 45 s apart. In image (f) the hatched area is the surface of terraces removed during the sequence. Its value divided by the surface area under observation is used to calculate the local etch rate (after [20]).

FIGURE 5.51. Dependence of the period of oscillation on the calculated etch rate as a function of pH in different NH4F solutions. (Reprinted from Lewerenz and Aggour, 1993, with permission from Elsevier Science.)... 

Ablation at High Fluences (0.5-10 ] cm 2). The etch rates (etch depth/pulse) at high fluences were calculated from linear plots of the etch depths vs pulse number at a given fluence. All plots were linear, showing no incubation behavior as expected for highly absorbing polymers. 

Fig. 3. a Measured etch rates as a function of natural logarithm fluence at high fluences (0.5 to 10 J cm-2), b Calculated etch rates of all polymers at 2,000 mj cm-2. REPRINTED WITH PERMISSION OF [Ref. 82], COPYRIGHT (2001) American Chemical Society... 

The calculated etch rates (Eq. 1) at 2000 mj/cm2 of polymers are shown in Fig. 3b. The ablation rates were calculated from ablation plots, such as Fig. 3a, for identical fluences to allow a direct comparison of different polymers. 

To calculate the horizontal etch rate, it is reasonable to assume that bombarding ions strike the substrate surface at normal incidence. The ion flnx incident on a vertical trench sidewall in this case is equal to zero. Then expression (8-20) can be rewritten for the horizontal etch rate as... 

At 720°C diamond will burn in an oxygen jet. It is often stated in the literature that oxidation starts at 600°C. The theoretical onset of oxidation should be well below 600°C, because from the etching rates of Evans [44] for the lll)-plane in 1 bar oxygen a well below zero (w 0.02) is calculated. Linear extrapolation would give T w 340°C for = 0. However, in analogy with graphite there may be an accumulation of C-O complexes at the surface, which is faster then their removal between 300°C and 500°C [49]. Surface graphitization at F > 600°C points in this direction. 

This can be further converted into an etching rate (i.e., the decrease in the thickness of the Ti solid per unit time, dx/dt) via some simple algebraic transformations using the density and molecular weight of the Ti. Consider first that the number of moles of Ti (%i) in a Ti plate of thickness x and area A can be calculated as... 

Finally, inserting the Ti reaction rate law (Equation 5.9 ) into this expression allows for the etching rate to be calculated as a function of the heterogeneous reaction rate... 

Question (a) Calculate the etching rate of a Ti surface undergoing active gas corrosion in HCl(g) assuming that the surface reaction is rate controlling, (b) Under these conditions, how much time would be required to etch 1 mm deep into a Ti plate The following information is provided ... 

Thus, the etching rate under the assumption that diffusion limits the kinetics is almost the same as that calculated assuming the surface reaction is rate limiting. As we will see in the next section, the similarity between the surface reaction and diffusion rates in this situation means that both must be considered simultaneously to accurately determine the overall total etching rate under these conditions. 

Question As we learned from Examples 5.2 and 5.3, for the active gas corrosion of Ti by HCl at T = 1500 K the surface reaction rate and diffusion rate are approximately equal. Considering both processes operating in series, calculate the actual overall etching rate for Ti under this situation. 

Thus, the actual etching rate in this situation, taking into account both reaction and diffusion, is about half the rate calculated assuming that only one process... 

Since intergranular corrosion is limited to corrosion at or immediately adjacent to grain boundaries and is detectable at the microstructural level, simple corrosion rate calculations using weight loss measurements provide no information. Standard ASTM tests, such as the oxalic acid etch test... 

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