Abstract
In this work, within the framework of the dynamic theory of the X-ray scattering, a model is constructed that describes the diffraction reflection curves obtained from the proton-exchange layers of a lithium niobate monocrystal subjected to the post-exchange annealing. Planar proton-exchange waveguides based on the X-cut of the lithium niobate monocrystal are obtained experimentally. It was shown that the proton implantation leads to the formation of the new crystalline phases with a larger lattice parameter. The structure changes (by the method of the diffraction structural analysis) and the optical properties (by the method of the mode spectroscopy) of the obtained waveguides are investigated in the various temperature regimes. The microstrain of the crystal lattice caused by еру proton implantation was estimated by the analysis of X-ray diffraction line broadening. It is shown the thickness of the waveguide layer and the number of new crystalline phases depend not only on the temperature regime of the proton exchange, but also on the duration of post-exchange annealing. The simulation of the experimentally obtained curves of the diffraction reflection is carried out within the framework of the described model. As a result of the modeling, the depth of the waveguide layer was determined, which is consistent with the data obtained by the method of the mode spectroscopy. The models of the assumed profiles of the crystal lattice deformation caused by proton implantation are presented. The average values of the lattice microstrain and the phase composition of proton-exchange lithium niobate layers are determined.
Highlights
В работе в рамках динамической теории рассеяния рентгеновских лучей построена модель, описывающая кривые дифракционного отражения, полученные от протонообменных слоев монокристалла ниобата лития, подвергнутых постобменному отжигу
Within the framework of the dynamic theory of the X-ray scattering, a model is constructed that describes the diffraction reflection curves obtained from the proton-exchange layers of a lithium niobate monocrystal subjected to the post-exchange annealing
The microstrain of the crystal lattice caused by еру proton implantation was estimated by the analysis of X-ray diffraction line broadening
Summary
Для описания процессов распространения рентгеновских лучей в кристаллической среде в самом общем случае, когда падающая и рассеянная волны взаимодействуют друг с другом, используют систему уравнений Максвелла [19], которая при некоторых преобразованиях может быть сведена к волновому уравнению: rot rot E. Волновое уравнение (1) описывает колебания электромагнитной волны с напряженностью электрического поля E E r, t в среде с поляризуемостью χ r в заданной радиус-вектором r точке кристалла. Здесь R e / m c 2.8 ∙ 10 см – классический радиус электрона (e и m – заряд и масса электрона, соответственно); λ длина электромагнитной (рентгеновской) волны; ρ r распределение электронной плотности в веществе. Волновое уравнение (1) имеет множество частных решений E r, t , E r, t , E r, t ,..., например, в виде плоских волн E r, t E e k∙r. Здесь ω – круговая частота, а волновой вектор k перпендикулярен фронту волны, его величина равна |k| k. . Вектор k характеризует направление распространения электромагнитной волны в вакууме. В случае распространения электромагнитной волны в среде следует учесть показатель преломления n √ε 1 χ 1.
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