Abstract
Keywords
1. Introduction
Lithium niobate (, LN) is a well known and commercially available material of great importance for integrated optics—“the silicon of photonics,” due to its excellent characteristics: a wide transparency window of 0.35–5.5 µm, high Curie temperature , and electro-optical coefficients . LN is widely used for the manufacture of LN-on-insulator (LNOI) components[
For all these applications, the important role is not of the bulk properties of LN but of its near-surface layer, because the ridge or buried waveguides and electrodes are created on the surface of the crystal. Some authors[
It is well known that electro-optical properties of LN are sensitive to the intrinsic defects and impurities. Structure defects in LN crystals can be roughly divided into two types: internal, related to the crystal growth, and external, related to the wafer dicing and polishing. The defect structure of a congruent LN consists of Li vacancies, -antisites, oxygen vacancies, polarons, bound polarons, and bi-polarons[
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External or technological defects arise during the cutting and polishing of LN. Despite the high quality of the optical surface, which is obtained during cutting and polishing, the number of defects increases[
The structure of the damaged near-surface layer in LN has a deformation nature with the multiplication of the dislocation density[
The aim of this work is to analyze experimentally and theoretically the dislocation density of the near-surface layer of LN as a function of the thermal annealing temperature.
2. Materials and Methods
The samples used for the investigations were congruent X-cut LN 1-mm-thick wafers by Fomos Materials (Russia). The wafers were cut into pieces, where the short side coincided with polar axis Z of the crystal.
Thermal annealing (treatment) of LN was performed at temperatures of 400°C, 500°C, and 600°C in air atmosphere. The samples were heated by 10°C/min to the required temperature, then for 4 h they were annealed, and after that they were slowly cooled in the furnace. In addition, there was a reference sample without annealing. Thermal annealing is required to reduce internal stresses, absorption[
The dislocation density on the surface of LN was estimated by the method of identifying etching pits by using wet selective etching in the melt of KOH with 35% NaOH for 5 min at a temperature 200°C. Detection of etching pits was carried out using the optical microscope Leica DMi8 in reflected light and a bright field. All samples were cleaned sequentially in isopropyl alcohol and distilled water for 3 min in an ultrasonic bath.
The topology of the etch pits was studied using atomic force microscopy (AFM) in the semi-contact mode (NT-MDT NTEGRA Prima Corp.). Analysis and quantitative calculation of AFM images were carried out using the program Nova 1.1.1 NT-MDT.
The dislocation density was also experimentally estimated using the X-ray method based on the account of an extinction effect in imperfect single crystals, using a model of randomly distributed dislocations. X-ray diffraction (XRD) was carried out by using a precise double-crystal spectrometer. The monochromator was a dislocation-free Si crystal, set in the position corresponding to the reflection -line of Co-radiation (, 1 Å = 0.1 nm) from the crystallographic plane (111). Integrated intensities were obtained for the first and second orders of the X-ray reflections with indices (110) and (220), respectively. The integral intensity of X-ray peaks was calculated by numerical integration with Simpson’s rules.
3. Results
3.1. Wet selective etching
The real structure of LN was revealed by the wet selective etching method, which can be used to analyze the dislocation density. Many etching pits appear on the surface with selective etching, which are the emergence of dislocations caused by cutting and grinding of a monocrystalline wafer. Also, the authors[
Figure 1.Etching pits of LiNbO3 (a) after thermal annealing at 500°C and (b) in pristine state.
The near-surface layer of the crystal was treated by thermal annealing to reduce the density of dislocations and stresses. The dislocation etching pits on the surface before and after thermal annealing were detected with an optical microscope (Fig. 1). The calculated dislocation density is presented in Fig. 2 for treated and reference samples. Each point is the result of averaging 10 sections of the wafer. Etching pits were counted manually due to the low contrast of transparent materials and many artifacts.
Figure 2.Dependence of the dislocation density N determined by wet selective etching on the annealing temperature T.
For determination of the etching depth some samples were studied using AFM. The distribution profiles of the pits by their depth were obtained. One of these profiles is shown in Fig. 3. The etching pit depth varies from 5 to 100 nm. This means that the etching rate is from 1 to 20 nm/min.
Figure 3.AFM image of etch pits and the profile of etching pits (line 146).
3.2. X-ray diffraction results: theory and experiment
When considering XRD on single crystals, it is necessary to take into account the dynamic extinction effects, which lead to a decrease in the integral reflection coefficients of X-rays in comparison with the calculation of a kinematic theory[
The value of depends on the type of distribution and density of defects of the crystal structure. In the case of a chaotic distribution of dislocations in a single crystal, the extinction effect is related to the fact that there is a strongly distorted region of the crystal around each dislocation, scattering in accordance to the kinematic theory. The remaining volume of the crystal scatters X-rays according to the dynamic theory. Kinematic volumes can be represented as straight circular cylinders of radius , drawn around each dislocation line.
The radiation scattered by kinematic volumes is incoherent among instances and with the radiation scattered by the rest of the (dynamic) crystal. Then, the integral component of the reflection of the crystal volume is equal to
Considering the two types of polarization and [
Here, , where is a parameter that accounts for the polarization of radiation when reflected from a monochromator crystal at an angle ; is the Bragg’s angle corresponding to reflection (). For both types of components of the integral reflection coefficient according to the kinematic and dynamic scattering theory taking into account Eq. (2), we have
Therefore, an integral reflection coefficient and an extinction parameter are equal to
The value of can be found as[
In the case of Bragg’s angle, the extinction depth is[
Here, is the wavelength of X-ray; is the volume of the unit cell of LN; is the classical radius of the electron; is a multiplier taking the value of one for polarization () and for -polarization (); is the real part of the structural amplitude of LN.
The part of the kinematic volume at the dislocation density is equal to[
For X-cut samples, the observation plane of etching pits is a prismatic sliding plane. It is equivalent from the point of view of symmetry to the planes and . X-cut planes in LN correspond to the directions of dislocation lines and . Note that the dislocation with the Burgers vector is a partial dislocation from the full dislocation with the Burgers vector , which was considered in Ref. [28] when studying small-angle boundaries in single crystals of LN:
These Burgers vectors are located on the basis plane (0111), i.e., it should be considered for a Z-cut. Therefore, we will consider the sliding directions and .
Calculating the weight factor for the considered directions in the X-cut plane gives a value of 2/3 for reflections (110) and (220).
An expression of the integral reflection coefficients , corresponding to two different reflection orders, in terms of the dislocation density is obtained:
Here, the index “(1)” refers to the first-order reflections (110), and the index “(2)” refers to the second-order reflections (220), , and .
Equation (10) allows us to construct a theoretical dependence of the ratio of the integral reflection coefficients corresponding to two reflection orders to the density of chaotically distributed dislocations, shown in Fig. 4. To determine the density of dislocations in single crystals, the left branch of the presented curve should be used. That is because LN is a brittle material in which it is impossible to create conditions corresponding to large dislocation densities during plastic deformation.
Figure 4.Dependence of ρ110/ρ220 for a single crystal of X-cut LN on the density of chaotically distributed dislocations N, X-ray Co-λβ-radiation.
Table 1 shows the results of measuring the ratio of integral reflection coefficients corresponding to two reflection orders for the studied samples of different manufacturers. Using the results shown in Table 1 and the calculated curve in Fig. 4, the dislocation density for the studied samples was determined. The dependence of dislocation density on treatment temperature is shown in Fig. 5.
Figure 5.Dependence of the dislocation density N (determined by the results of XRD) on the thermal annealing temperature T.
Thermal Annealing | Sample |
---|---|
Pristine | 3.17 |
400°C – 4 h | 3.26 |
500°C – 4 h | 3.57 |
600°C – 4 h | 3.55 |
Table 1. The Experimental Ratio of the Integral Reflection Coefficients
4. Discussion
Dislocations characterize the imperfect structure of materials. In this paper, we present results of dislocation density measurement in crystal as a function of thermal annealing.
It is known that etching pits do not cover all surface areas of the wafer, but are located in positions where dislocations appear[
Figure 1 shows the decrease in the density of etching pits for treated samples and an increase in their size at a temperature of 500°C. These pictures were chosen because the thermal annealing temperature of 500°C is the most optimal and demonstrates minimum density of etching pits (see Fig. 2). The increase in linear size of etching pits in Fig. 1(a) can be explained by the duration of etching. But, the experimental conditions had to be identical. The etching pits were not ranked by size while being counted. The number of pieces per unit area was counted directly.
is a material with a low dislocation density 103−105 cm−2. Our results agree in the order of magnitude with literature data. At a temperature of 400°C, the number of etching pits on the surface of LN increases. This can be explained by the existence of damaged near-surface layers in LN[
A slight increase in the number of defects at 600°C (Fig. 5) indicates the beginning of deformation processes associated with the restructuring of the LN crystal lattice due to the high mobility of the ions at high temperatures. The X-ray method for determining the dislocation density is based on the measurement of integral intensity of the reflection lines of two orders. It is known that the integral intensity is affected by any change in the crystal structure[
Note that etching of single crystals makes it possible to estimate the density of defects on the surface of studied images, and the second method using the X-ray allows the estimation of the density of dislocations to be distributed over the depth of the samples. The volume was determined by the penetration depth of the X-rays. In our case, this was of the order of 15 µm, which is approximately equal to the depth of the defect layer, as reported earlier[
In addition, we note that the proposed extinction model of crystals with random dislocation distribution allows us to measure dislocation density ranging from to . For large dislocation densities (more than ), we usually use the methods based on the analysis of the physical broadening of XRD lines[
Thus, the treatment of LN crystals repairs the damaged layer by reducing the density of dislocations. These results are most important from the point of view of increasing the homogeneity of the structure of the near-surface layer and formation of more stable optical waveguides, integrated-optical circuits, and LNOI components/devices. For example, the creation of ridge waveguides for LNOI is performed by diamond blade dicing with subsequent polishing[
5. Conclusion
This work is dedicated to the study of the dislocation density of the near-surface layer of X-cut LN crystals, depending on thermal annealing in the range of 400°C–600°C.
Firstly, the experimental method of wet selective etching was applied to determine the dislocation structure of LN before and after treatment. Secondly, a method was proposed to determine the dislocation density by using XRD based on the account of the extinction effect in imperfect single crystals, using a model of randomly distributed dislocations (theory and experiment). These two methods were used to analyze the dislocation structure of crystals. This is enough to establish a relation between the treatment and the real structure of the LN crystal. It has been experimentally proved that thermal annealing of LN samples at a temperature of 500°C is accompanied by a decrease in the density of dislocations in the near-surface layer.
The obtained results are applicable to other optical materials as well. In addition, the found LN treatment regimen can improve the properties of Ti-diffused, proton-exchanged, and ridge waveguides for various optical systems.
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