Random Layer Thickness Research Articles

Yield analysis of multilayer optical coatings

Yield is defined as the ratio of the number of devices that satisfy a particular technical specification to the total number of devices produced. For coated optical devices, random layer thickness variations decrease the yield. Variations in refractive index can also affect yields, but in this work we assume that changes in index are not as important as changes in thickness. A graphic method of yield analysis for optical coatings is presented. This method probes the sensitivity of the device performance against thickness variations and translates it into yield figures. Five examples of this analysis are provided including spectral and nonspectral applications.

Layer thickness variations and x-ray diffraction patterns: A general treatment

Using a columnar approximation, the effect of random layer thickness variations in a compositionally modulated material on the x-ray diffraction pattern is expressed in terms of their distribution function. It is demonstrated that the Fourier transform of this distribution function appears in a function describing the effective phase relations between the individual layers. Features of multilayer diffraction patterns, such as the presence or absence of superlattice peaks, are explained. It is also shown that when the Fourier transform of the thickness variation distribution changes sign from positive to negative, the superlattice peaks change position from integral to half-integral order. The effects of thickness variations are compared with those of interface roughness.

CHARACTERISTICS OF ELECTRONIC WAVE FUNCTIONS IN SUPERLATTICES WITH RANDOM LAYER THICKNESS

The wave functions of electrons in superlattices with random layer thicknesses are studied. They are localized in the direction perpendicular to the layers characteristic of one-dimensional systems and extended in the plane of the leyers. Numerical results of computation of localization lengths are given.

Optical properties of very thin, nonideal multilayer superlattice stacks

In this study, the theory of very thin, nonideal multilayer stacks is developed, and the computed wavelength variation of the transmissivity and reflectivity is compared with that measured on experimentally prepared silver-silicon monoxide layer stacks. The model imputes a step-function character to the complex index of refraction along the layer structure, and nonideality is accounted for by allowing for the likely presence of interfacial layers between each primary layer pair and also for the possibility that the thickness of the individual layers may vary randomly within some limit of error. Abeles's transfer matrix technique is used to arrive at the characteristic matrix of the stack, and additive corrective matrices are derived to account for the effects due to interfacial layers and the random layer thickness variation.