Определена система уравнений тепло-, массопереноса Навье-Стокса для диффузии компонент смеси газов и найдено приближенное аналитическое решение, описывающее стационарную стадию процесса роста монокристаллов карбида кремния для диодов и светодиодов. Получены распределения температур и концентраций компонент смеси в ростовой камере. Определены радиальные профили скорости роста кристаллов на начальной и конечной стадиях роста.Оценка значений скорости роста кристалла согласуется с результатами численных расчетов других авторов и данных опытов. A system of Navier-Stokes heat and mass transfer equations for the diffusion of gas mixture components has been determined and an approximate analytical solution has been found that describes the stationary stage of the growth process of silicon carbide single crystals for diodes and light-emitting diodes. The distributions of temperatures and concentrations of the mixture components in the growth chamber have been obtained. The radial profiles of the crystal growth rate at the initial and final stages of growth have been determined. The estimate of the crystal growth rate is consistent with the results of numerical calculations by other authors and experimental data.

Предлагаемые авторами ускоренные технологические режимы синтеза ВТСПкерамики и теоретическая обработка полученных результатов в значительной мере решают задачу реализации ускоренной производственной технологии получения ВТСП-материалов. Приведены результаты разработки и оптимизации ускоренных режимов технологии (6-10 часов вместо 50-60) получения массивных образцов Tl (Bi) ВТСП-керамики с рекордными параметрами (температурами сверхпроводящего перехода (Tc) до 205 К, плотностью транспортного критического тока (Jc) вплоть до десятков тысяч и более А/см2 ). Показана возможность получения образцов с Tc до 150-205 К и выше. Приведены сведения по практическому применению массивных образцов ВТСП-керамики: таблетки, массивные образцы, изделия. Общая себестоимость изделий из новых ВТСП-материалов при серийном производстве будет существенно ниже, чем у ВТСП-материалов 2-го поколения. По нашим оценкам, только производство 1 км транспортного силового кабеля, изготовленного по этой технологии, в 700-800 раз дешевле аналогичного по физическим параметрам кабеля, изготовленного по «сэндвичной» технологии. Нужно учесть и дешевизну эксплуатации кабеля, работающего при температуре «сухого льда», по сравнению со стоимостью обслуживания силового кабеля, изготовленного по технологии ВТСП-материалов 2-го поколения и работающего при температуре жидкого азота. The accelerated technological modes of synthesis of HTS-ceramics proposed by the authors and the theoretical processing of the results obtained largely solve the problem of implementing an accelerated production technology for obtaining HTS-materials. The paper presents the results of the development and optimization of accelerated modes of the technology (6-10 hours instead of 50-60 hours) of obtaining massive samples of Tl (Bi) HTS-ceramics with record parameters (superconducting junction temperatures (Tc) up to 205 K, the density of transport critical current (Jc) up to tens of thousands or more A/sm2 ). The possibility of obtaining samples from Tc up to 150-205 K and above is shown. Information on the practical application of massive samples of HTS ceramics is given: tablets, massive samples, products. The total cost of products from new HTS-materials in mass production will be significantly lower than that of HTS-materials of the 2nd generation. According to our estimates, only the production of 1 km of transport power cable manufactured using this technology is 700-800 times cheaper than a similar cable in terms of physical parameters, made using "sandwich" technology. It is necessary to take into account the cheapness of operating a cable operating at the temperature of "dry ice" in comparison with the cost of servicing a power cable made using the technology of HTS-materials of the 2nd generation and operating at a temperature of liquid nitrogen ВТСП-керамикин синтезан сихйина технологин раж а, хиллачу жамIийн теорех пайдаэцар а ВТСП материалаш царах йахарехь гIуллакх муха до гойту авторша. ХIокху балха тIехь жамIаш далийна, уьш довза а довзийтина Tl кепара хIуманаш раж сихйаран технологешца (50-60 сахьтийн меттана 6-10 сахьтехь) TI (Bi) ВТСП-керамика лаккхарчу параметрашца температура токан иттанаш эзарнаш, цул сов А/см2 ). Йаккхар. Тс тIера 150-205 К а, цул лакхара а кепаш йахаран таро а гайтина. Керлачу ВТСП-материалех даьхначу сурсатийн йуккъерчу барамехь мах дуккха а лахара хир бу алсам уьш арахецарехь 2-гIачу чкъуран ВТСП-материалел а. Оха биначу талламашца, оцу технологешца арахецна 1 км транспортни ницкъан кабель 700-800-зIа механа йораха хуьлу «сэндвични» технологин кепехь кечйинчул а.

 ФИЗИКО-МАТЕМАТИЧЕСКИЕ НАУКИ  СТАТЬИ УДК 548.

The article describes the methods for producing thin films and structures based on SiC, GaN and their SiC – AlN and Al – GaN solid solutions, as well as mathematical models of film growth and properties-behavior of the I–V characteristics of heterostructures. Two models were developed for producing thin films and heterostructures based on SiC, GaN and their solid solutions. The first model makes it possible to determine the sputtering coefficient when producing films by high-frequency magnetron sputtering. In the second quantum-mechanical model, the equation for the gap of the mean field of condensate was built and the growth rate of a film on the crystalline substrate was determined. The current-voltage characteristic of the transistor based on the AlGaN / GaN heterosystem was provided. The models for the growth of heterostructure films made it possible to modify the technologies for producing perfect SiC crystals and SiC – AlN solid solutions. It was possible to offer a pilot plant for growing SiC crystals with improved control over the modes of induction high-temperature heating of the growth crucible.

The paper presents models of bands (levels) in solid (SiC) 1-x (AlN) x luminescence centers and n-SiC/p-(SiC) 1-x (AlN) x heterostructures (light-emitting diodes). The diagram of (SiC) 1-x (AlN) x energy gaps shows the positions of luminescence levels, subject to x. A SiC/SiC–AlN series of electroluminescence bands, for the first time, is found to have a continuous relationship between the positions of short-wave and long-wave band maxima in a K-minimum conduction band, respectively, as continuous functions of contact current density.

The 4H-SiC monocrystals and SiC-AlN solid solutions are described. Models of a series of strips (levels) of solid solutions of Silicon carbide SiC - AlN and hetero-structures (light-emitting diodes) n-SiC/p-(SiC) 1-x (AlN) x as a function of x composition are proposed. The SiC/ 1-x (AlN) x diagram defines the positions of the glow center levels, depending on x. In the series of electroluminescence bands of the light-emitting diodes SiC/SiC-AlN, continuous dependences of the positions of short-wave and long-wave bands in the K-minimum conductivity zone are defined, respectively, as continuous functions of the density of current through contact. This is very important for the wide practical application of the resulting light-emitting diodes with the ability to select radiation throughout the visible spectrum when changing the composition of x solid silicon carbide solution.

Temperature behavior calculation of the anomalous conductivity of the A4B6-type ferroelectric semiconductors (GeTe, SnTe and A(x–1) B(x)C) of Tc near-phase transitions is carried out in the paper. The proposed integrable (analytical) model is applicable both for describing the temperature behavior of the conductivity of GeTe multivalley semiconductors and SnTe-type systems. The influence of the structural phase transition on the systems' conductivity is analyzed. The proposed analytical model of the conductivity behavior of ferroelectrics-semiconductors allows considering compounds with various spectra and compositions. The model is applicable both for the kinetic properties of multivalley semiconductors and for analyzing the effect of external influences on these properties: x composition and T temperature, as well as the presence of a structural phase transition in the system at Tc(x). It is shown that the graph can have the form of a break or the form of a smooth asymmetric maximum, depending on the value of the effective relaxation rate of carriers on soft phonons and the intervalley splitting of the anomalous conductivity near Tc in A4B6 systems. The calculation results are consistent with the experimental data. The dependence of the phase transition temperature Tc(x) on x composition is obtained.

The Schottky barrier heights in the М/n-(SiC) 1–x (AlN) x systems are obtained on the assumption of a high density of surface states in the region of the metal (M) – SiC–AlN-solid solution contact. Current–voltage (I–V) characteristics of the Al/n-(SiC) 1–x (AlN) x diodes are calculated. It is shown that at moderate concentrations of surface states (c ≈ 4–8), the Schottky barrier height Ф x B ( с ) of these diodes is close to the heterojunction potential barrier Ф x g , which is the reason for the known similarity in the behavior of the corresponding I–V characteristics. The role of the ideality factors in the behavior of the I–V characteristics is analyzed. The obtained values of the Schottky barrier heights are in accordance with experimental data.

Abstract The main methods for producing 4H-SiC single crystals and films of its solid solutions are considered. A new technique for producing single crystals of SiC polytypes is described. A new nonlinear model of the Schottky barrier height (BS) has been developed, and the current-voltage characteristics of Schottky diodes have been obtained, their comparison with the I–V characteristics of silicon-based diodes has been made.

The article deals with the methods for producing silicon carbide (4H-SiC) mono-crystals and films using the Schottky barrier. A nonlinear model of the Schottky barrier height and a composite model for the CVC of the total emission current were developed. An induction heating method for producing SiC monocrystals at 2000-25000С was developed. On the basis of the full-scale model of this method, a patented unit for producing perfect SiC monocrystals was designed [1]. Models of thin SiC film growth were analyzed.

A modified Schottky-barrier model, which is nonlinear in terms of the surface-state concentration and contains a local quasi-Fermi level at the interface induced by excess surface charge, is proposed. Such an approach makes it possible to explain the observed similarity of the I–V characteristics of diodes with the Schottky barrier M/(SiC)1–x(AlN) x and those of heterojunctions based on SiC and its solid solutions taking into account Φg ≈ ΦB. The results of calculations of the Schottky-barrier heights are consistent with the experimental data obtained from measurements of the photocurrent for metals (M): Al, Ti, Cr, and Ni. The I–V characteristics in the composite–additive model of charge transport agree with the experimental data for the n-M/p-(SiC)1–x(AlN) x and n-6H-SiC/p-(SiC)0.85(AlN)0.15 systems.

AbstractA modified Schottky-barrier model, which is nonlinear in terms of the surface-state concentration and contains a local quasi-Fermi level at the interface induced by excess surface charge, is proposed. Such an approach makes it possible to explain the observed similarity of the I–V characteristics of diodes with the Schottky barrier M/(SiC)_1– x (AlN)_ x and those of heterojunctions based on SiC and its solid solutions taking into account Φ_g ≈ Φ_B. The results of calculations of the Schottky-barrier heights are consistent with the experimental data obtained from measurements of the photocurrent for metals (M): Al, Ti, Cr, and Ni. The I–V characteristics in the composite–additive model of charge transport agree with the experimental data for the n -M/ p -(SiC)_1– x (AlN)_ x and n -6 H -SiC/ p -(SiC)_0.85(AlN)_0.15 systems.

Proposed nonlinear defect concentration model of metal-semiconductor contact.It is shown that taking into account nonlinear dependence of the Fermi energy EF defect concentration leads to higher barrier Schottky in 15-25 %.Calculated Volt-Amper characteristics of the diodes are consistent with experiment.

A simple but nonlinear model of the defect density at a metal–semiconductor interface, when a Schottky barrier is formed by surface defects states localized at the interface, is developed. It is shown that taking the nonlinear dependence of the Fermi level on the defect density into account leads to a Schottky barrier increase by 15–25%. The calculated barrier heights are used to analyze the current–voltage characteristics of n-M/p-(SiC)1–x (AlN) x structures. The results of calculations are compared to experimental data.

Предлагается простая нелинейная по концентрации дефектов модель контакта металл–полупроводник, когда барьер Шоттки формируется поверхностными дефектными состояниями Ei, локализованными на границе раздела. Показано, что учет нелинейной зависимости энергии Ферми ЕF от концентрации дефектов ведет к повышению барьера Шоттки на 15–25%. Рассчитанные значения высоты барьера используются для анализа вольтамперных характеристик структур M/(SiC)1 - x(AlN)x. Результаты расчета сопоставляются с экспериментальными результатами.

A simple model of the metal–semiconductor contact that is nonlinear in the concentration of defects when the Schottky barrier is formed by the surface defect states E i localized at the interface has been proposed. It has been shown that taking into account the nonlinear dependence of the Fermi energy E F on the concentration of defects results in an increase in the Schottky barrier height by 15 to 25%. The calculated values of the Schottky barrier height have been used for the analysis of the current-voltage characteristics of M/(SiC)1–x (AlN) x structures. The theoretical results have been compared with the experimental data.

Поскольку в одноосных совершенных «идеальных» кристаллах происходит подавление флуктуаций поляризации (кулоновскими дальнодействующими силами), то в них происходит расширение области применимости около Тк термодинамической теории Ландау-Гинзбурга. С другой стороны, в очень узком интервале температур вблизи Тк проявляются аномальное поведение и крайне резкие скачки тепловых характеристик кристаллов. В работе с единых позиций на основе микроскопической модели мягкой моды рассчитаны и дано объяснение аномальному около Тк поведению диэлектрической проницаемости теплоемкости и коэффициента теплового расширения совершенных кристаллов ТГС. Определены значения важных параметров теории: температурная зависимость мягкой моды, величина скачка теплоемкости около Тк, поведение теплоемкости в широком интервале температур и величина скачка коэффициента теплового расширения около Тк. Результаты расчетов согласуются с соответствующими экспериментами.