In this paper the overview of the most important approximate methods for the optical characterization of inhomogeneous thin films is presented. The following approximate methods are introduced: Wentzel–Kramers–Brillouin–Jeffreys approximation, method based on substituting inhomogeneous thin films by multilayer systems, method based on modifying recursive approach and method utilizing multiple-beam interference model. Principles and mathematical formulations of these methods are described. A comparison of these methods is carried out from the practical point of view, ie advantages and disadvantages of individual methods are discussed. Examples of the optical characterization of three inhomogeneous thin films consisting of non-stoichiometric silicon nitride are introduced in order to illustrate efficiency and practical meaning of the presented approximate methods.
Dispersion models are necessary for precise determination of the dielectric response of materials used in optical and microelectronics industry. Although the study of the dielectric response is often limited only to the dependence of the optical constants on frequency, it is also important to consider its dependence on other quantities characterizing the state of the system. One of the most important quantities determining the state of the condensed matter in equilibrium is temperature. Introducing temperature dependence into dispersion models is quite challenging. A physically correct model of dielectric response must respect three fundamental and one supplementary conditions imposed on the dielectric function. The three fundamental conditions are the time-reversal symmetry, Kramers-Kronig consistency and sum rule. These three fundamental conditions are valid for any material in any state. For systems in equilibrium there is also a supplementary dissipative condition. In this contribution it will be shown how these conditions can be applied in the construction of temperature dependent dispersion models. Practical results will be demonstrated on the temperature dependent dispersion model of crystalline silicon.
Between 2010 and 2011 a field survey dedicated to Dracaena cinnabari (DC) population was conducted in Firmihin, Socotra Island (Yemen). It’s main goal was to collect data that would make it possible to unbiasedly estimate main characteristics of the local DC population. Our motivation was to provide reliable information to support decision-making processes as well as other research activities. At the same time we were not aware of a survey which could provide this kind of statistical-sound estimates for the whole population covering an area of almost 700 ha.
This article describes how the survey has been planned and carried out in practice. In addition, we also provide a set of preliminary estimates of the main DC population figures - totals and per hectare densities of stems, overall and partitioned according to predicted crown age. Among estimated parameters there are also mean crown age and proportions of predefined age classes on the total number of living DC stems. These estimates provide an explicit information on age structure of the whole DC population in Firmihin.
Although we collected data on more than one hundred randomly located plots, the reported accuracy of our estimates is still rather limiting. We discuss several possibilities to obtain more accurate results or at least to approach the supposedly lower true variance that can’t be calculated by approximate techniques applied here.
The design and concept of our survey makes it possible to evaluate changes over time on stem by stem bases and to generalize these stem-level details to the whole population. Mortality, regeneration and even change of population’s mean crown age can be estimated from a future repeated survey, which would be extremely useful to draw firm conclusions about the dynamic of the whole DC population in Firmihin.