Scattering from rough surfaces

In the classical mechanics framework, a rough surface, such as a machined metal surface, randomizes the probability distribution function governing the incoming particles, leading to net momentum loss of the particle flux. ==Quantum description==

In the quantum mechanical framework, this scattering is most noticeable in confined systems, in which the energies for charge carriers are determined by the locations of interfaces. An example of such a system is a quantum well, which may be constructed from a sandwich of different layers of semiconductor. Variations in the thickness of these layers therefore causes the energy of particles to be dependent on their in-plane location in the layer. Classification of the roughness at a given position, \Delta_z(\mathbf{r}), is complex, but as in the classical models, it has been modeled as a Gaussian distribution by some researchers This assumption may be formulated in terms of the ensemble average for some given characteristic height, \Delta, and correlation length, \Lambda, such that :\langle\Delta_z(\mathbf{r})\Delta_z(\mathbf{r'})\rangle = \Delta^2\exp\left(-\frac{|\mathbf{r}-\mathbf{r'}|^2}{\Lambda^2}\right) == Types of Scattering ==

Selective Scattering : In selective Scattering scattering depends upon the wavelength of light. Mie scattering : Mie theory can describe how electromagnetic waves interact with homogeneously spherical particles. However, a theory for homogeneous spheres will completely fail to predict polarization effects. When the size of the molecules is greater than the wavelength of light, the result is a non-uniform scattering of light. Lambertian Scattering: This type of scattering occurs when a surface has microscopic irregularities that scatter light perfectly uniformly in all directions, causing it to appear equally bright from all viewing angles. Subsurface Scattering: This type of scattering occurs when light scatters within a material before exiting the surface at a different point. Isotropic crystal scattering (aka powder diffraction): This type of scattering occurs when every crystalline orientation is represented equally in a powdered sample. Powder X-ray diffraction (PXRD) operates under the assumption that the sample is randomly arranged such that each plane will be represented in the signal. ==Notes==