Etching of Oxides - Electrochemistry of Silicon and Its Oxide - page 163

concentration of adsorbed fluoride and (2) it increases the pH and this decreases [SiF].
At low

the fluoride concentration effect predominates and etch rate increases

with whereas at relatively high the pH effect dominates and a decline

in etch rate is observed.
According to Monk et al ., 451,800 it is difficult to use the rate equations that are
based on the concentrations of the ionic or complex species in the solutions because of
the uncertainties in the equilibrium data for high concentrations of HF. It is more con-
venient to describe the etch rate equations only as a function of HF in the mathemati-
cal forms using simply the concentration of HF. Depending on the specific etching
systems, etch rate equations can be expressed as follows:

Non-first-order kinetics

Freundlich adsorption isotherm kinetics

Langmuir-Hinshelwoodkinetics

Data fitting to Eq. (4.24) gives n = 1.37-1.5 for etching of thermal oxides at
high HF concentrations and n = 0.75-1.07 at low concentrations as well as in BHF
solutions. For low-temperature CVD films, it is in the range of 1.6-2.0 in HF solutions
and 0.5-1.0 in buffered solutions. The dependence of etch rate on HF concentration,
according to Monk et al ., 451 is due to the two-step etch reaction. In the first step, hydro-
gen ions break up the siloxane bonds to form silanol species on the surface, and in the
second step the fluorinated species attack the silicon in the silanol species. At low con-
centrations, because of the limited supply of the reactants the silicon bonds are broken
in series resulting in a first-order reaction. However, at higher HF concentrations, more
reactant species will be available so the rate-limiting reaction may take place with two
reactants simultaneously resulting in a second-order reaction.

4.7.3 . Effect of Oxide Structure
The many etch rate equations described above are empirical in nature even
though mechanistic arguments are made in each specific case. One important omis-
sion in these quantitative formulations on the etching kinetics is the lack of con-
sideration of the effect of the structure of silicon oxides. As shown in Fig. 4.40, etch
rate can vary over more than three orders of magnitude for different types of oxides.
It increases with increasing disorder of the oxide structure with the most ordered
oxide, that is, quartz, having the lowest etch rate. The structural disorder of the silicon
oxide can be due to impurities, partial oxidation of the silicon atoms, and degree of
crystallinity.
Qualitatively, the effect of oxide composition has been considered in many inves-
tigations, particularly those related to the etching of doped glasses. Tenny and Ghezzo 148
suggest that the etch rate of doped glasses is limited primarily by the dissolution of the
in the glasses since the etch rate increases with increasing dopant concentration
for phosphosilicate and arsenosilicate glasses in BHF and for borosilicate glasses in
dilute BHF. According to Brown and Kennicott, 425 the fact that

glasses