Mathematical Methods of Planning and Optimization Processes Growing of Thin Films and Nanostructures AIIBVI and AIVBVI from the Vapor Phase

Abstract

It is known that semiconductors groups AIIBVI and AIVBVI have unique features number that allows them to apply for production of photodetectors and lasers with spectral range of 3-50 microns. Advances for reduce the size of photonic devices closely related with the use of controlled growing of epitaxial thin layers. Despite numerous studies of thin films and nanostructures compounds of AIIBVI and AIVBVI, still not fully clarified the impact of growing conditions on the electrical parameters of thin-layer material. In this paper, using the method of mathematical planning of multifactor experiments received the dependence of the electrical properties of thin layers and nanostructures of PbTe from technological factors of growing from vapor phase by the method of hot wall. As substrate used fresh chips (111) of crystal BaF2. To describe the dependence of the electrical parameters of thin layers from technology factors were constructed global polynomial models in 3-factor hyperspace using mathematical modeling. For factors which vary (k=3) were selected substrate temperature (TS), evaporator temperature (TV) and chamber walls temperature (TC) technologically acceptable change range of which are respectively: 473 К £ ТS £ 623 К, 758 К £ ТV £ 878 К, 833 К £ ТС £ 983 К. Optimization parameters are: charge carrier mobility (m), concentration (n), Seebeck coefficient (a), conductivity (s), thermoelectric power (a2s), and value: Z=μ/μmax +(n/nmin)–1 + (α2s)/(α2s)max, which is a complex optimization parameter. Choosing the latter option due to the need of researchers to obtain thin layers with maximum values mmax, (a2s)max and minimum concentration nmin. Optimization was performed for summary values: μ = μ/μ0, where μ0 = 104sm2 × V-1 × s-1, n' = n/n0, where n0 = 1017sm-3, s = s/s0, where s0 = 102Ohm-1 × sm-1, α' = α/α0, where α0 = 102В1 × К-1, (α2s)' = (α2s)/(α2s)0, where (α2s)0 = 102W × К-2 × sm-1. In describing the dependence of the electrical parameters from technological factors identified models of a different order. Borders of adequacy model are defined as the cube which inscribed in hypersphere of planning with radius R=a, were a - magnitude shoulder of star. The data presented in the table and shown in the form of hypersurfaces of response.