  The effect of etching time on the statistical properties of the hydrophilic
surface of SiO_2/TiO_2/Glass nano bi-layer has been studied using Atomic Force
Microscopy (AFM) and stochastic approach based on the level crossing analysis.
We have created a rough surface of the hydrophilic SiO_2/TiO_2 nano bi-layer
system by using 26% Potassium Hydroxide (KOH) solution. Measuring the average
apparent contact angle assessed the degree of hydrophilicity and the optimum
condition was determined at 10 min etching time. Level crossing analysis based
on AF images provided deeper insight into the microscopic details of the
surface topography. For different etching time, it has been shown that the
average frequency of visiting a height with positive slope behaves Gaussian for
heights near the mean value and obeys power law for the heights far away from
the mean value. Finally, by applying the generalized total number of crossings
with positive slope, it was found that the both high heights and deep valleys
of the surface are extremely effective in hydrophilic degree of the
SiO_2/TiO_2/Glass nano bi-layer investigated system.
