Test of Marcus Theory Predictions for Electroless Etching of Silicon

Rational design of stain etchants has led to greatly improved control of porous silicon formation and thicker, more uniform layers. It has also facilitated the quantitative evaluation of the hole injection probability per collision of various oxidants (VO 2 +, Fe 3+, Ce 4+, and IrCl 6 2– ) with a silicon surface, the absolute rate constant, and direct comparison to the predictions of Marcus theory. The absolute rate constants vary roughly from 10 –33 to 10 –31 m 4 s –1, which indicates a maximum rate constant of 1 × 10 –25 m 4 s –1 for VO 2 + but only 1 × 10 –27 m 4 s –1 for Fe 3+, 6 × 10 –28 m 4 s –1 for Ce 4+, and 7 × 10 –29 m 4 s –1 for IrCl 6 2– . Therefore, the charge transfer step that limits the rate of etching induced by VO 2 + is well described by a Marcus theory description of an outer shell electron transfer process with a matrix element for coupling between the oxidant and the valence band roughly equal to the upper limit previously determined by Lewis and co-workers. However, for Fe 3+, Ce 4+, and IrCl 6 2– coupling is much weaker, indicating that system specific calculations of the values of the reorganization energy, the coupling matrix element, and the tunneling range parameter are required to determine the extent of kinetically significant dynamical corrections for the description of electrochemical reactions at the liquid/semiconductor interface.