SU1081490A1 - Method of determination of elastic deformation in epitaxial systems - Google Patents

Abstract

A METHOD FOR DETERMINING ELASTIC DEFORMATION IN EPITAXIAL SYSTEMS, including irradiating a sample and recording Bragg reflections for planes, the normal to which is - 0–90 with normal to the sample surface, In order to simplify the method and increase its rapidity, a series of 6-28 curves are recorded for reflections of equally oriented in an unstressed state of the crystallographic planes of the film and substrate, and before each subsequent curve is recorded, the counter slit is shifted In the diffraction vector, the misorientation angle of the crystallographic planes is calculated by the formula. (,) where сГ2б and are the measured samples of the angular displacement of the slit, corresponding to the maximum intensity of 9 to 26 reflections of the film (I) and the substrate (P), and the lattice deformation is determined by the formula g 5S t .2 ko LP: r ig where e, and Ej, crystalline A strain, and; lattice of the film and the substrate along the b i – axis of the orthogonal basis, axes 1 and 2 of which are. pogo lie in the interfacial plane ,, 00 f Poisson's ratio And the film and the substrate. four;

Description

The invention relates to X-ray structural analysis, namely, to regenerative strain measurement of epitaxial layers, and can be used in non-ferrous metallurgy and electronics industries. A known method for determining strains in epitaxial systems based on the bending strength of a bicrystal tlJ This method does not allow determining the residual lattice deformation if the systems at least partially had a stress relaxation process. There is also known a method for determining the deformation in epitaxial systems, which includes irradiating a sample and detecting Bragg reflections for planes r the normal to which the angle V 0 is 90 with the normal to the surface of the sample. Deformations of the crystal lattice are determined by the position of the Bragg reflections from different (hkl) 2J planes. The known method is very laborious and to improve the accuracy of the analysis requires precise recording of reflections with a large Bragg angle b. In addition, because of the tetragonal lattice distortions in elastically stressed epitaxial systems, standard surveys — 9–20 scanning or a Bond-type scheme — cannot be used to analyze them. The aim of the invention is to simplify the method and increase the speed of the analysis. This goal is achieved by the fact that according to the method of determining elastic deformation in epitaxial systems, including sample irradiation, recording Bragg reflections for planes, the normal to which makes an angle V О -90 ° with normal to the surface of the sample, a series of Q - 20 curves for reflections is recorded equally oriented in the unstressed state of the crystallographic planes of the film and the substrate, and before registering each subsequent curve, the slit of the counter along the diffraction vector is displaced, the misorientation angle of the crystallographic planes, by the formula (.4V where (G2b and (/ 2U- are measured samples of the angular displacement of the slit, corresponding to a maximum intensity of 9-20 film reflections (1). and substrate (H), and by the amount of misorientation) lattice deformation according to the formula v where EJ. and jj are the crystal lattice deformation of the film and the substrate along the i-th axis of the orthogonal basis, axes 1 and 2 of which lie in the plane of the interphase boundary, 1, and the Poisson ratio of the film and the substrate. The method is based on measuring the misorientation of the crystallographic planes of the film and the substrate, resulting from tetragonal distortions of the crystal lattice caused by macrostrains in the epitaxial system. The method is carried out as follows. - When irradiating a bicrystal mounted on a goniometer, for example,. the X-ray beam is pre-made its standard alignment and is reflected at an angle close to 45 °. Then, rotating the sample around the main axis of the goniometer with a stationary counter (u) —an scan preliminarily finds the intensity of reflection from the (h jk | -ji--) substrate planes. After that, a narrow slit is placed in front of the counter and the counter is determined with a stationary sample. the position corresponding to the maximum scattered intensity. With a large width of the swing curve due to inhomogeneity of the interplanar distances, with a fixed counter with a narrow slit, the swing curve is recorded and the angle of rotation of the sample corresponding to the determined counter position is determined from the position of its maximum. Such a circuit makes it possible to sharply reduce the width of the swing curve and improve the accuracy of determining the angle of rotation of the sample. By fixing the angles of rotation of the sample and the counter corresponding to the highest intensity, a similar procedure is carried out for the corresponding crystallographic planes of the epitaxial layer (hjkjlj), which, in the absence of stresses, are parallel to the planes (hkjflj) of the substrate. Then, the difference in the angles of rotation of the sample is calculated for the reflections of the substrate and the epitaxial layer, leading them to the same value of the angle of rotation of the counter by Q - 26 scanning. A precise determination of the difference in the angles of rotation of the sample corresponding to the desired misorientation of the planes (hjkjlj) and {h, 7k (ilj-) is made by shooting seryib-20 curves, varying the position (L 29 of a narrow slit in front of the counter. caused by misorientations, and the angle

the reorientation of the planes of the film and the substrate is found using the formula 4 1/2 (r2ej.-cG20 ji), where and {/ -26.7 samples of the angular displacement of the slit, corresponding to a maximum intensity of 0-26 reflections from the film (I) and the substrate (P ).

An example. A residual strain analysis was performed. in the Mgg system,. The measurement results proposed and in a known manner () are presented in the table.

To determine the magnitude in a known manner, it was necessary, with careful alignment, to register the reflexes of the substrate: (008) Cu-Kd, 0 ° (135) Cu-Kot, H --- 32, (424) Cu-K, V 48; (442) Cu-Kv, V 70 j and films: (OODb) Cu-K.z, if 0; (2BDO) C-C C) 3-2, (848) C-C, 4 (884)

, 4 70. The X-ray imaging of a single sample on the diffractometer requires about 10 hours. Using the proposed method, the angular misorientation was determined by cordoning the table with the counter manually and did not require any X-ray imaging at all. The measurement time is determined mainly by the time it takes to search for a reflex from one type of inclined planes and does not exceed several minutes.

Thus, in comparison with the known, the proposed method significantly reduces the complexity and laboriousness of the analysis and increases its expressiveness due to the possibility of determining stresses by expressly registering only one pair of film and substrate reflexes.

(26,10)

(135)

(848) (424)

(26,10) (135)

4 (442)

(884) (424)

(848)

18 25 (424)

(848)

(884) (442)

0.10

2.9

3.0

0.11

2.9

-0.01

-0,3

-0.01

-0.02

0.10

2.6

2.45

3.1 2.7-2.9

0.12

0.06

2.6

Claims (2)

(54) METHOD FOR DETERMINING ELASTIC DEFORMATION IN EPITAXIAL SYSTEMS, including irradiating the sample and recording Bragg reflections for planes whose normal angle is Ψ 0-90 ° with the normal to the surface of the sample, which is why that, in order to simplify the method and increase its expressivity, a series of Θ - 2 6 curves are recorded for the reflections of the crystallographic planes of the film and the substrate equally oriented in the unstressed state, and before the registration of each subsequent curve, the counter slit is shifted along diffraction vector, the angle of disorientation of the crystallographic planes is calculated by the formula (<Γ2Θ _Τ ΔΨ = --------- 2 'where & 2Θ and are the measured readings of the angular displacement of the gap corresponding to the maximum intensity θ - 2Θ of the reflections of the film (I) and the substrate (P), the misorientations are determined by the lattice by the formula g and the strain is 4V g h - Γε _τ is the deformation of the crystal lattice of the film and the substrate along the i-axis of the orthogonal basis, the axes 1 and 2 of which are. · Rogos lie in the plane of the interface; - Poisson's ratio of the film and the substrate.