  We have studied the effect of annealing temperature on the statistical
properties of $WO_3$ surface using atomic force microscopy techniques (AFM). We
have applied both level crossing and structure function methods. Level crossing
analysis indicates an optimum annealing temperature of around 400$^oC$ at which
the effective area of the $WO_3$ thin film is maximum, whereas composition of
the surface remains stoichiometric. The complexity of the height fluctuation of
surfaces was characterized by roughness, roughness exponent and lateral size of
surface features. We have found that there is a phase transition at around
400$^oC$ from one set to two sets of roughness parameters. This happens due to
microstructural changes from amorphous to crystalline structure in the samples
that has been already found experimentally.

Data Analysis, Statistics and Probability