In many applications in solid-state catalysis, as well as in fabrication of solar panels and microelectronic devices, surface characteristics indicate key performance features. The performance in many instances is controlled by the surface nanostructure. Thus, in order to create an application of desired features, one needs to understand the surface characteristics and characterization based on surface phenomena is essential. If the surface characteristics can be controlled during fabrication, then desired specifications can be implemented. Characterization based on imaging techniques is fast, cheap and can be implemented online. In order to characterize nanostructured surfaces with microscopic images, a multi-resolution multi-scale methodology can be used. This requires an analytical and computational framework.

The surface structure of different applications which is created by molecular deposition on the surface due to surface kinetics and surface diffusion governs the behavior of the material. Thus the key to control fabrication of applications whose performance matrix is governed by its surface feature is to characterize the surface and use those characteristic features as control parameter.

Microscopy images provide qualitative information about surface features. In order to characterize the surface, we need to make a quantitative description of surface morphology. Microscopy image processing techniques can be used for the purpose of characterizing the surfaces. This is done by making a multi-resolution multi-scale analysis of the image using wavelet transformation (WT). One can analyze different layers of the surface at different scales (frequency). Various statistical measures like flatness factor (kurtosis), skewness factor, Hurst exponent etc can be used as surface characterizing features. These features can be calculated at different frequencies using multiscale analysis of the image. Imaging techniques like Scanning Electron Microscopy (SEM), Atomic Force Microscopy (AFM) etc. can be used to obtain the image of the surface.

Although a multiscale analysis can be done with Fourier transformation, wavelet transformation has the advantage of spatial localization along with frequency localization. Furthermore in determining characteristic feature like Hurst exponent when data at only few frequencies are available, the wavelet method is more accurate than the Fourier method.

In microelectronic fabrication, lithography is used for pattern transfer in the substrate. A line edge roughness (LER) is created in the transferred pattern due to roughness of the resist polymer. This causes a loss of efficiency for the microelectronic device. LER can determine the performance of the device. In this paper, the characterization of this roughness of the photoresists is carried out by evaluating parameters like sigma value, roughness exponent and correlation length. Experimental images are obtained and LER detection based on those images of the surface are performed using wavelet analysis. A molecular simulation of the surface also gives the characteristic parameters. Molecular simulation of the surface complements the experimental work by comparing the simulation results with the experimental ones.