Modelling of micro- and nanodomain arrays recorded in ferroelectrics-semiconductors by using atomic force microscopy

The thermodynamical theory of nanodomain tailoring in ferroelectrics-semiconductors allowing for semiconducting properties, screening and size effects is presented. The obtained analytical results prove that domains appearance is similar to the first order phase transition and completely agree with experimentally observed threshold nanodomains recording in Pb(Zr,Ti)O₃ and LiTaO₃ thin films. The realistic dependence of equilibrium nanodomain radius over applied voltage in BaTiO₃ LiNbO₃ ferroelectric-semiconductors, LiTaO₃ and Pb(Zr,Ti)O₃ thin films have been calculated. These results will help researchers both to achieve the reliable understanding of physical process taking place during nanoscale polarization reversal in the ferroelectric-semiconducting media and to determine the necessary conditions in order to record stable nanodomains with optimum lateral sizes and configuration to increase recording density and create various profiled microstructures

The resolution function and effective response of piezoelectric thin films in Piezoresponse Force Microscopy

The elastic Green function and resolution function in Piezoresponse Force Microscopy (PFM) of thin piezoelectric film capped on the rigid substrate are derived. The extrinsic size effect on the resolution function is demonstrated

Domain structure formation by using Scanning Probe Microscopy: equilibrium polarization distribution and effective piezoelectric response calculations

In the paper we adopt the analytical Landau-Ginzburg-Devonshire theory to describe the ferroelectric domain structure formation using Scanning Probe Microscopy. We calculate the effective local piezoresponse of the domain structure within the decoupling approximation using the conventional relation between piezoelectric tensor components and the spontaneous polarization vector. The depth profile of the polarization distribution was derived from the nonlinear Landau-Ginzburg-Devonshire equation. We demonstrate that depending on the material parameters such as the intrinsic domain wall width and probe apex geometry, the shape of the nucleating nanodomains induced by the probe can be either oblate or prolate. The derived analytical expressions for the polarization redistribution caused by the biased probe are valid for both first and second order ferroelectrics

Modeling of information recording and selective etching processes in inorganic resists

Theoretical consideration and computer modeling of information pit recording and etching processes in chalcogenide vitreous semiconductors are proposed, namely we demonstrate how to record and develop information pits with the necessary shape and sizes in the inorganic resist using focused Gaussian laser beam and selective etching. It has been shown that phototransformed region cross-section could be almost trapezoidal or parabolic depending on the resist material optical absorption, recording beam power, exposure, etchant selectivity and etching time. Namely, during the laser illumination and thermal heating caused by it, photosensitive material is the quasi-equilibrium microscopic mixture of the transformed and nontransformed phases with different optical absorption coefficients: temperature dependent near the absorption edge «transformed» coefficient бe and almost independent coefficient α0 . If αe ≤ α0 e after thermal heating, the photo-transformed region «bleaches» and the pit depth increases more rapidly under the following laser power increasing. If αe > α0 , the phototransformed region «darkens» and the pit depth increases sub-linearly or even saturates under the following laser power increasing. Thus, almost parabolic or flattened pits appear when αe ≥ α0, whereas the pits with elongated tops appear when αe << α0. After illumination, the spatial distribution of photo-transformed material fraction was calculated using the Kolmogorov-Awrami equation. Analyzing obtained results, we derived a rather simple approximate analytical expression for the dependence of the phototransformed region width and depth on the recording Gaussian beam power, radius and exposure time. Then the selective etching process was simulated numerically. The obtained results quantitatively describe the characteristics of pits recorded by the Gaussian laser beam in thin layers of As₄₀S₆₀ chalcogenide semiconductor. Our model open possibilities how to select the necessary recording procedure and etching conditions in order to obtain pits with the optimum shape and sizes.Запропоновано теоретичний розгляд та комп’ютерне моделювання процесів запису інформації та селективного травлення в халькогенідних напівпровідниках. Змодульовано процес одержання інформаційних питів необхідної форми та розміру у неорганічному резисті, використовуючи сфокусований гаусівський лазерний пучок та селективне травлення. Показано, що переріз фототрансформованої області змінюється від майже трапецієвидного до параболічного в залежності від коефіцієнта оптичного поглинання, потужності лазерного пучка, експозиції, селективності травника та часу травлення. Просторовий розподіл долі фототрансформованого матеріалу розраховано з рівняння Колмогорова-Аврами. Проаналізовано одержані результати й виведено досить простий наближений аналітичний вираз для залежності ширини та висоти фототрансформованої області від потужності лазерного пучка, його радіусу, часу експонування та селективності травника. Одержані результати добре описують характеристики пітів, записаних у тонких шарах халькогеніду As₄₀S₆₀. Модель відкриває реальну можливість добору умов запису та травлення резисту, необхідних для одержання пітів з оптимальними розмірами.Предложено теоретическое рассмотрение и компьютерное моделирование процессов записи информации и селективного травления в халькогенидных полупроводниках. Смоделирован процесс получения информационных питов необходимой формы и размеров в неорганическом резисте, используя сфокусированный гауссовский лазерный пучок и селективное травление. Показано, что сечение фототрансформированной области может изменяться от практически трапециевидного до параболического в зависимости от коэффициента оптического поглощения, мощности лазерного пучка, экспозиции, селективности травителя и времени травления. Пространственное распределение доли фототрансформированного материала рассчитано из уравнения Колмогорова-Аврами. Проанализированы полученные результаты и выведено достаточно простое приближенное аналитическое выражение для зависимости ширины и высоты фототрансформированной области от мощности лазерного пучка, его радиуса, времени экспонирования и селективности травителя. Полученные результаты хорошо описывают характеристики питов, записанных в тонких слоях халькогенида As₄₀S₆₀. Модель открывает реальную возможность выбора условий записи и травления резиста, необходимых для получения питов с оптимальными размерами

Theoretical consideration of pits recording and etching processes in chalcogenide vitreous semiconductors

We propose theoretical consideration and computer modeling of information pit recording and etching processes in chalcogenide vitreous semiconductors. We demonstrate how to record and develop information pits with the necessary shape and sizes in chalcogenide photoresists using gaussian laser beam and selective etching. It has been shown that phototransformed region cross-section could be almost trapezoidal or parabolic depending on the photoresist material optical absorption, recording beam power, exposure, etchant selectivity and etching time. After illumination, the spatial distribution of photo-transformed material fraction was calculated using the Kolmogorov-Awrami equation. Analyzing obtained results, we derived a rather simple approximate analytical expression for the dependence of the photo-transformed region width and depth on the recording gaussian beam power, radius and exposure time. Then the selective etching process was simulated numerically. The obtained results quantitatively describes the characteristics of pits recorded by the gaussian laser beam in thin layers of As40S60 chalcogenide semiconductor.Comment: 14 pages, 1 scheme, 9 figure

Modelling of pyroelectric response in inhomogeneous ferroelectric-semiconductor films

We have modified the Landau-Khalatnikov approach and shown that the pyroelectric response of inhomogeneous ferroelectric-semiconductor films can be described using six coupled equations for six order parameters: average displacement, its mean-square fluctuation and correlation with charge defect density fluctuations, average pyroelectric coefficient, its fluctuation and correlation with charge defect density fluctuations. Coupled equations demonstrate the inhomogeneous reversal of pyroelectric response in contrast to the equations of the Landau-Khalatnikov type, which describe the homogeneous reversal with the sharp pyroelectric coefficient peak near the thermodynamic coercive field value. Within the framework of our model, the pyroelectric hysteresis loop becomes much smoother, thinner and lower as well as the pyroelectric coefficient peaks near the coercive field completely disappear with increase in disordering caused by defects. This effect is similar to the well-known "square to slim transition" of the ferroelectric hysteresis loops in relaxor ferroelectrics. Also the increase of defect concentration leads to the drastic decrease of the coercive field typical for disordered ferroelectrics. Usually pyroelectric hysteresis loops of doped and inhomogeneous ferroelectrics have typical smooth shape without any pyroelectric coefficient peaks, and the coercive field values much lower than the thermodynamic one. Therefore, our approach qualitatively explains available experimental results. A rather well quantitative agreement between our modelling and typical Pb(Zr,Ti)O₃ film pyroelectric and ferroelectric loops has been obtained

Polar properties and local piezoelectric response of ferroelectric nanotubes

We consider the polar properties of the ferroelectric nanotubes within the framework of Landau-Ginzburg-Devonshire phenomenology. The approximate analytical expression for the paraelectric-ferroelectric transition temperature dependence on the radii of nanotube, polarization gradient, extrapolation length, elastic stresses and strains arising from surface tension and thermal expansion mismatch, and electrostriction coefficient was derived. We calculated effective local piezoresponse of the ferroelectric nanotube within decoupling approximation of electric and elastic problem. Obtained results explain the ferroelectricity conservation in Pb(Zr,Ti)O₃ and BaTiO₃ nanotubes observed by using Piezoelectric Force Microscop

Partial polarization switching in ferroelectrics-semiconductors with charged defects

We propose the phenomenological description of ferroelectric disordering caused by charged defects in ferroelectric-semiconductors. The good agreement between the obtained experimental results for PZT films and theoretical calculations has been shown. We suppose that proportional to the averaged charge density of defects improper conductivity is sufficiently high to provide the screening of charge density random fluctuations drs in the absence of external field. When external electric field is applied, inner field fluctuations and induction fluctuations dD appear in the inhomogeneously polarized system “charged fluctuation + screening cloud”. We show that the macroscopic state of ferroelectric-semiconductor with random charged defects and sufficiently high improper conductivity can be described by three coupled equations for three order parameters. Averaged over sample volume induction determines the ferroelectric ordering in the system, its square fluctuation determines disordering caused by electric field fluctuations appeared around charged fluctuations drs, and reflects the correlations between the free carriers screening cloud and charged defects drs. For the first time, we derive the following system of three coupled equations: Also the obtained system of coupled equations qualitatively describes the peculiarities of polarization switching (footprint and minor hysteresis loops) in such ferroelectric materials with charged defects as PZT films with growth imperfections, PLZT ceramics and SBN single crystals doped with cerium

Optical recording of information pits in thin layers of chalcogenide semiconductors

The paper is devoted to the theoretical consideration of the question how to record pits with the necessary height profile in photosensitive materials by varying their heat conductivity, photosensitivity, optical absorption, as well as the recording gaussian beam intensity, radius and exposure time. A rather simple analytical expression for the height profile of pits has been derived. It has been shown that this profile depending on photosensitive material parameters and recording beam characteristics could be almost rectangular, flat with rounding edges, spherical or parabolic. The proposed model describes adequately the height profile of pits recorded in thin layer chalcogenide semiconductors by a gaussian laser beam

Recording the high efficient diffraction gratings by using He-Cd laser

High efficient holographic diffraction gratings with spatial frequencies from 600 to 3600 mm⁻¹ have been recorded using As₄₀S₆₀–хSeх (х = 0, 10, 20) photoresist layers and He-Cd laser operating at the wavelength λ = 440 nm. The investigation of the grating relief made by atomic force microscopy revealed that As₄₀S₆₀–хSeх resists allows one to record grating originals with profiles of various heights depending on the resist chemical composition, its etching and exposure times. We obtained typical spectral and angular dependences of the first order diffraction efficiency for the grating with the high modulation depth and groove profile close to the sinusoidal one. Comparing the recorded gratings with different spatial frequencies, exposure and etching times, we determined optimal recording conditions (exposure and etching times) in order to obtain gratings with the high diffraction efficiency