RU2071049C1 - Method for curvature measurement of monocrystalline plates - Google Patents

Abstract

FIELD: crystal analysis. SUBSTANCE: method is related to X-ray diffraction analysis of crystals, in particular, of residual mechanical stresses and structural perfection of semiconductor plates-substrates, homo- and heterocompositions after various technological operations when manufacturing discrete devices and integrated microcircuits in solid-state microelectronics. Method includes forming two parallel monochromatic X-rays directed on to examined plate. Determination of difference of reflection angles of these rays from different points located at specified distance from each other on curved surface is performed by successive bringing them into reflecting position by turn of plate about rotational axis perpendicular to plane holding incident and reflected rays, and located in the middle between points of incidence of rays on to reflecting surface. Third central ray parallel to first two rays and arranged at equal distances from each of them is formed simultaneously with them and is directed on to examined surface. It is used to orient plate before measurement of curvature. Determination of difference of angles of rays reflection noncoinciding with central one is conducted before and after turns of plate through 180 deg about rotational axis lying in plane of ray passage and matching normal to surface at point of reflection of central ray. Curvature is found by formula $$$, where K is curvature of plate ($$$, R is radius of curvature); S is distance between rays on reflecting surface; $$$ and $$$ are correspondingly differences of reflection angles before and after turn of plate through 180 deg about normal to surface at point of reflection of central ray. EFFECT: higher efficiency. 2 dwg, 2 tbl

Description

The invention relates to X-ray diffraction analysis of crystals, namely, methods for determining the bending strain of crystals, and can, in particular, be used to control residual mechanical stresses and structural perfection of semiconductor wafers, homo and heterocompositions after various technological operations in the manufacture of discrete devices and integrated circuits in solid state microelectronics [1]
A known method of measuring the curvature of single crystal plates by the X-ray method on a three-crystal spectrometer by recording the broadening of the diffraction maxima of the rays reflected from curved crystals [2]
The disadvantage of this method is the low accuracy of determining the curvature due to errors introduced into the general broadening of diffraction maxima by the azimuthal beam divergence and azimuthal misorientation of the crystal under study, and they are also inhomogeneous in the distribution profile of the residual strain of the crystal lattice in the surface reflecting layer.

где S расстояние между точками на поверхности исследуемого кристалла, от которых отражаются составляющие дублета.A known method of measuring the curvature of single crystals on an x-ray double-crystal spectrometer [3] is that the primary x-ray beam is directed to a crystal-monochromator, on which two rays are obtained components K _α1 and K _{α2 of the} most intense K _α- doublet. These rays are directed to the crystal under study, and if it is bent, then the rays K _α1 and K _α2 are not reflected from it simultaneously, but only after rotation through a certain angle ΔΦ associated with the curvature (K) or radius of curvature (R = 1 / K) by the formula

where S is the distance between points on the surface of the investigated crystal, from which the components of the doublet are reflected.

This method is more accurate compared to [2] However, it also has disadvantages, namely:
low sensitivity to small bends (K≅10 ^-2 m ^-1 ) due to the limited spatial separation of the rays of the K _α doublet;
low accuracy in determining the curvature of plates having a nonuniformly deformed (along the surface) surface layer, when the increments of the reflection angles K _α1 and K _α2 are associated not only with bending, but also with the difference in the lattice periods in the regions reflecting these rays.

Closest to the proposed one is a method for measuring curvature, including the formation of two parallel monochromatic x-rays, for example, K _α1 , directed to the plate under study, and determining the difference in the reflection angles of these rays ΔΦ from different points of the curved surface spaced from each other at a given distance S at a sequential bringing them into a reflective position by turning the plate around an axis of rotation perpendicular to the plane containing incident and reflected rays, and located way between points of incidence on the reflective surface. In this case, the radius of curvature is also determined by the formula R = S / ΔΦ [4]
This method, adopted as a prototype, has a higher sensitivity to small bends compared to the method [3] since the spatial separation of the rays is limited only by the size of the focus of the x-ray source. It can be further enhanced by using an asymmetrically reflecting monochromator, as in the method [2]
The disadvantage of the method [4] is that during its implementation, as well as in the cases of [2, 3], measurement errors caused by inhomogeneous deformation of the crystal lattice of the surface layer of the test sample cannot be ruled out or numerically evaluated. The latter introduces an additional change in the difference in the angles of reflection of the rays, proportional to the quantity (ε ₁ -ε ₂ ) tgθ, where ε ₁ and ε _2, respectively, are the deformations of the lattice regions from which the first and second rays are reflected; θ Bragg angle. Thus, the disadvantage of the method [4] is the low accuracy of determining curvature.

где K кривизна пластины (

, R радиус кривизны);
S расстояние между лучами на отражающей поверхности;
ΔΦ_o и ΔΦ₁₈₀ соответственно разность углов отражения до и после поворота пластины на 180^o вокруг нормали к поверхности в точке отражения центрального луча.The objective of the invention is to increase the accuracy of measurements of the curvature of single crystal plates by eliminating the error due to the inhomogeneous distribution of the deformation of the crystal lattice along the reflective surface. To do this, in a method for measuring the curvature of single-crystal plates, including the formation of two parallel monochromatic x-rays directed to the test plate, and determining the difference in the angles of reflection of these rays from different points of the curved surface spaced from each other by sequentially bringing them to the reflecting position by rotation of the plate around the axis of rotation perpendicular to the plane of incident and reflected rays and located in the middle between points n rays of radiation on a reflecting surface, simultaneously with the first two rays, in parallel and at an equal distance from each of them, a third central beam is formed and directed to the surface to be studied, the reflection of which is first oriented to the plate before the curvature measurements, and the subsequent determination of the difference in the reflection angles of the rays that do not coincide with central, conducted twice before and after the rotation plate 180 ^o about a rotation axis lying in a plane passing beams and coincides with the normal to the surface at the reflection prices eral beam, and determining the curvature of the formula

where K is the curvature of the plate (

, R is the radius of curvature);
S is the distance between the beams on a reflective surface;
ΔΦ _o and ΔΦ _180, respectively, the difference in the angles of reflection before and after rotation of the plate 180 ^o around the normal to the surface at the reflection point of the central beam.

где K кривизна пластины;
S расстояние между лучами на отражающей поверхности;
ΔΦ_o и ΔΦ₁₈₀ соответственно разность углов отражения до и после поворота пластины на 180^o вокруг нормали в точке отражения центрального луча.A new, not found in the analysis of patent and scientific and technical literature, a set of features in the inventive method for measuring curvature is that simultaneously with the first two (measuring) beams, a third central beam is formed and directed to the surface to be studied simultaneously and at an equal distance from each of them , the reflection of which is first oriented to the plate before measuring the curvature, and the subsequent determination of the difference in the angle of reflection of the rays that do not coincide with the central one is carried out twice before and after rotation Lastin 180 ^o about a rotation axis lying in a plane passing beams and coincides with the normal to the surface at the reflection point of the central beam and the curvature is determined by the formula

where K is the curvature of the plate;
S is the distance between the beams on a reflective surface;
ΔΦ _o and ΔΦ _180, respectively, the difference in the angles of reflection before and after rotation of the plate 180 ^o around the normal at the reflection point of the central beam.

 This combination of features is new, distinguishing the claimed method from known technical solutions.

In FIG. 1 shows a diagram of an X-ray double-crystal spectrometer in which rays from the focus of an X-ray source F are incident on a crystal-monochromator M, where the most intense rays (for example, the doublet K _α ) are extracted; of which three parallel beams are formed using a slit device: 1 and 2 beams, on which the curvature of crystal K is measured, and beam 3 is central, along which the studied plate K is adjusted before measuring curvature before and after turning the plate 180 ^o around an axis coinciding with the normal N to the surface reconstructed at the point of reflection of this ray. Rays 1, 2, and 3 reflected from the test surface are detected by detector D. FIG. 1, the following notation is also used: Dv is the difference between the angles of reflection of rays 1 and 2 when the plate K is rotated, having a radius of curvature R about the axis O, perpendicular to the plane in which the incident and reflected rays lie, and passing through the reflection point of ray 3; Dq ₁ and Δθ _2, respectively, the increments of the reflection angles of rays 1 and 2, due to the difference between the lattice periods of the crystal K in the regions reflecting these rays, and also their difference from the lattice period of the monochromator: Δθ _i = -ε _i tgθ, where ε _{i is the} deformation of the lattice corresponding area (i = 1,2); θ is the Bragg angle.

In FIG. 2 shows a diagram of the path of the rays and the orientation of the plate, the curvature of which is measured on beams 1 and 2, before and after its rotation through 180 ^o around the axis coinciding with the normal to the curved surface N at the point of incidence of the central beam 3. Shaded areas correspond to differently deformed zones, reflecting rays 1 and 2, the reflection angles of which consequently change to Dq ₁ = ε ₁ tgθ and Δθ ₂ = ε ₂ tgθ. The total recorded difference in the angles of reflection due to bending and deformations, before and after the rotation of the plate by 180 ^{o is} indicated by ΔΦ ₁ and ΔΦ _2, respectively.

определяют кривизну пластины из формулы

где S расстояние между лучами на отражающей поверхности пластины.The method is implemented as follows. Three parallel monochromatic rays are formed from the X-ray beam coming from the source F (Fig. 1) using a monochromator M and a slot device S, on two of which 1 and 2 measure the curvature of the crystal K under study, and the third beam (3) is central, is a reference for the adjustment of the plate before measuring the curvature before and after its rotation through 180 ^o around the axis that coincides with the normal to the surface of the plate, restored at the point of incidence and reflection of the beam 3. At the beginning of the measurements, the studied plate is oriented so that the radiation detector D, the maximum reflection intensity of the central ray 3 is recorded. Then, by successively turning the plate K around the axis of rotation, perpendicular to the plane in which the incident and reflected rays lie and which passes through point O, the reflections of rays 1 and 2 are found and the difference in their reflection angles ΔΦ _{o is} fixed = Φ $\genfrac{}{}{0ex}{}{\text{o}}{\text{1}}$ -Φ $\genfrac{}{}{0ex}{}{\text{o}}{}$$\genfrac{}{}{0ex}{}{}{\text{2}}$ where Φ $\genfrac{}{}{0ex}{}{\text{o}}{}$$\genfrac{}{}{0ex}{}{}{\text{1}}$ and Φ $\genfrac{}{}{0ex}{}{\text{o}}{\text{2}}$ the angles between the tangents to the surface, drawn at the points of incidence and reflection of rays 1 and 2. Next, the plate is rotated 180 ^o around an axis lying in the plane of the rays and coinciding with the normal to the surface of the plate at point O, reflecting the central beam 3. When turning, the correctness the orientation of the plate is controlled by the maximum intensity of reflection of the beam 3, which eliminates the error in measuring the difference in the angles of reflection of the rays due to possible mismatch (for example, due to backlash of the goniometric device) about SI rotation with the middle of the distance between the beams 1 and 2 on the surface of the plate. After 180 ^° rotation, the reflections from the plate of rays 1 and 2 are again sequentially found and the difference in the reflection angles ΔΦ ₁₈₀ = Φ $\genfrac{}{}{0ex}{}{\text{180}}{\text{1}}$ -Φ $\genfrac{}{}{0ex}{}{\text{180}}{\text{2}}$ . By measured increments

determine the curvature of the plate from the formula

where S is the distance between the beams on the reflective surface of the plate.

A positive effect in the implementation of the proposed method is achieved due to the fact that measuring the difference in the angles of reflection of the rays before and after turning the plate 180 ^o in its own plane eliminates the error in determining the curvature due to the difference in the periods of the crystal lattice of the areas of the plate, reflecting rays, by which the curvature is fixed. In this case, the selection and use of the third central beam to orient the plate before measurements (before and after turning it 180 ^° ) and to control its reflective position during rotation in its own plane provides a symmetrical arrangement of the rays on which the curvature is measured relative to the intersection of the axis of rotation of the plate , which also eliminates the error associated with inhomogeneous deformation, since before and after rotation of the plate, ray reflections are formed in the same regions of the crystal lattice (f Ig. 2). In addition, as already indicated, control of the reflecting position of the plate for the central beam when rotating through 180 ^o allows you to avoid errors caused by the mismatch of the axis of rotation due to inaccuracies in the manufacture of the goniometer, as a result of which it is possible to form reflections of rays from different parts of the surface that do not match for conditions for measuring the curvature before and after the rotation of the sample by 180 ^o .

, при последовательном отражении лучей 1 и 2 соответственно; Δθ₁ и Δθ₂ приращения углов отражения (брэгговских углов) лучей 1 и 2, связанные с относительными приращениями периодов кристаллической решетки пластины в отражающих областях ε₁ и ε₂(ε₁≠ε₂) формулами Δθ₁= -ε₁tgθ и Δθ₂= -ε₂tgθ, где θ брэгговский угол недеформированного кристалла.To derive a formula that determines the curvature of the plate through the angular increments ΔΦ _o and ΔΦ ₁₈₀ , measured before and after turning it in its own plane by 180 ^o , we turn to the diagrams in FIG. 2. Before the plate rotates 180 ^o around the axis coinciding with the normal N to the surface, the measured difference in the reflection angles of rays 1 and 2 will be
ΔΦ _o = Φ ₁₀ -Φ ₂₀ + Δθ ₁ -Δθ ₂ , (1) (1)
where Φ ₁₀₀ and Φ ₂₀ are the rotation angles of the plate due to its pure bending, i.e., determining the curvature

, with successive reflection of rays 1 and 2, respectively; Δθ ₁ and Δθ ₂ increments of the reflection angles (Bragg angles) of the rays 1 and 2, associated with the relative increments of the periods of the crystal lattice of the plate in the reflecting regions ε ₁ and ε ₂ (ε ₁ ≠ ε ₂ ) by the formulas Δθ ₁ = -ε ₁ tgθ and Δθ ₂ = -ε ₂ tgθ, where θ is the Bragg angle of the undeformed crystal.

получим расчетную формулу для определения кривизны

В эту формулу не входят соответствующие приращения брэгговских углов, обусловленные деформациями ε₁ и ε₂, т. е. результат измерения кривизны не отягощен неконтролируемой погрешностью. Это реализуется только в том случае, если во время поворота пластины на 180^o в собственной плоскости не происходит ее линейного перемещения в той же плоскости в направлении, нормальном к обеим осям вращения, т.е. лучи 1 и 2 попадают после поворота на те же области (соответственно, на ε₂ и ε₁, см. фиг. 2), от которых они отражались до поворота (соответственно ε₁ и ε₂). Контроль отсутствия такого перемещения пластины осуществляют по постоянству угла отражения центрального луча 3, неизменность которого должна сохраняться независимо от величины деформации кристаллической решетки в области, где формируется отражение этого луча, т. е. заявляемый способ реализуется и в случаях ε₁≠ ε₂≠ε₃, где ε₃ деформация решетки в области падения центрального луча.After turning the plate 180 ^o in its own plane, the measured difference in the angle of reflection of the rays 1 and 2 will change and become equal
ΔΦ ₁₈₀ = Φ $\genfrac{}{}{0ex}{}{\text{o}}{\text{1}}$ -Φ $\genfrac{}{}{0ex}{}{\text{o}}{\text{2}}$ + Δθ ₂ -Δθ ₁ . (2) (2)
Summing up the expressions (1) and (2) and considering that

we get the calculation formula for determining the curvature

This formula does not include the corresponding increments of the Bragg angles due to strains ε ₁ and ε ₂ , i.e., the result of the measurement of curvature is not burdened by an uncontrolled error. This is realized only if during the rotation of the plate through 180 ^o in its own plane does not occur its linear movement in the same plane in the direction normal to both axes of rotation, i.e. rays 1 and 2 fall after the turn into the same areas (respectively, to ε ₂ and ε ₁ , see Fig. 2), from which they were reflected before the turn (respectively, ε ₁ and ε ₂ ). The absence of such movement of the plate is controlled by the constancy of the angle of reflection of the central beam 3, the invariance of which should be maintained regardless of the magnitude of the deformation of the crystal lattice in the region where the reflection of this beam is formed, i.e., the claimed method is also implemented in the cases ε ₁ ≠ ε ₂ ≠ ε ₃ , where ε _{3 is the} deformation of the lattice in the region of incidence of the central beam.

 Example 1

The X-ray double-crystal spectrometer measured the curvature of silicon wafers of the KDB-10 grade with a thickness of 450 μm with the [111] surface orientation after irradiation with 40 keV argon ions at doses of 1 • 10 ¹⁴ and 6 • 10 ¹⁴ ion / cm ² on the ILU-3 accelerator. The curvature measurements were carried out according to the prototype method [4] on two beams with a distance between them of 5 mm and according to the claimed method, using a slit device located after the monochromator, a central beam spaced at equal distances of 2.5 mm from the rays at which the curvature was measured, and also using the rotation of the plate through 180 ^o in its own plane while recording a reflection detector of the central beam. The radiation of the spectral component CuK _α1 from the BSV-8 tube was used. All measurements were performed in the third order of reflection from the (111) planes parallel to the surface of the plates. As a control of the increment of the Bragg angle associated with the relative increment of the lattice period of the samples in the reflecting regions, we used the results of measurements on a three-crystal spectrometer, where silicon crystals of the same KDB-10 (111) type were used as the reference and analyzer. The accuracy of reading the angles on both spectrometers was 0.5 angles. from. The measurements were carried out on two batches of 12 pieces irradiated with the indicated doses. samples in each. The average values of the curvature and increments of the Bragg angles (recorded on a three-crystal spectrometer) are given in table. 1. The negative sign of curvature in the table corresponds to the convexity of the side of the plate irradiated with ions.

From the table. 1 it is seen that the curvature of the plates, recorded using the proposed method, after irradiation with ions is greater than that measured by the prototype method, and corresponds (within the accuracy of measuring angular increments ± 0.5 arc.s.) to the calculated data according to formulas (1) and (2) taking into account the increments of the Bragg angles obtained on a three-crystal spectrometer, due to the inhomogeneous deformation of the irradiated layer during scanning of the ion beam. In addition, as follows from the data table. 1, the prototype method may give incorrect information about the sign of curvature, and therefore about the magnitude and sign of the residual mechanical stresses in the deformed layer (see the result of irradiation with a dose of 1 • 10 ¹⁴ ion / cm ² ).

Зная расстояние S между измеряющими лучами (1 и 2 на фиг. 2), легко определить градиент изменения деформации вдоль поверхности

Необходимость оценивать степень неоднородности деформации (или градиента при варьировании расстояния S между лучами) возникает во многих практически важных задачах технологии, например, при определении однородности легирования полупроводников диффузией и особенно ионной имплантацией, при эпитаксии, механической обработке и т.д.This is a fundamental disadvantage of the prototype in cases where the data of curvature measurements are used to sort structures according to the degree of defectiveness in the technological route of manufacturing semiconductor devices. This is confirmed by the results presented in the following example. Here, one more advantage of the proposed method should be pointed out, which allows numerically assessing the degree of heterogeneity of the distribution of the strain profile of the crystal lattice along the reflecting surface. From formulas (1) and (2) from the difference ΔΦ _o -ΔΦ ₁₈₀ it is easy to obtain a relation for determining the inhomogeneity of the strain distribution
ΔΦ _o -ΔΦ ₁₈₀ = 2 (Δθ ₁ -Δθ ₂ ) = 2 (ε ₂ -ε ₁ ) tgθ
or

Knowing the distance S between the measuring beams (1 and 2 in Fig. 2), it is easy to determine the gradient of the deformation along the surface

The need to evaluate the degree of strain heterogeneity (or gradient when varying the distance S between the beams) arises in many practically important technology problems, for example, when determining the uniformity of doping of semiconductors with diffusion and especially ion implantation, during epitaxy, machining, etc.

 Example 2. Using the prototype method and the proposed method, the grading of gallium arsenide grades of the AHCHP-5 grade with a thickness of 600 μm was carried out with a surface orientation of [001] after cutting with diamond blades with an internal cutting edge on the machine model 24.05. The sorting was carried out in order to select the working (less defective) side of the wafers for subsequent technological operations of chemical etching, diamond and chemical-mechanical polishing and chemical-dynamic polishing of the working side, on which active regions of field-effect transistors with a Schottky gate should then be formed. The measurement results on a double-crystal spectrometer were controlled by direct measurements of the residual deformation of the surface layers on both sides of the plates on a three-crystal spectrometer. According to the results of determining the curvature, the concave side was considered as the working side of the plates, near which the concentration of crystallographic defects (dislocations, impurity-defect clusters) is lower than near the convex one. After cutting from the ingot all the plates were marked, the side of the plates was marked after the first cut (that is, before the plate was separated from the ingot), which according to the well-known ideas about the processes of defect formation during mechanical cutting of semiconductors (see, for example, [5]) than the side formed in the second cut. A total of 102 plates were measured.

 In the table. Figure 2 shows the number of plates in which, when measured in different ways, the concave (i.e., working) side coincides with the side of the first cut, i.e., it turns out to be less defective, and with the side of the second cut. The control data obtained on a three-crystal spectrometer for direct measurements of the residual strain near the surface of the plates from the first and second cuts are also presented here.

 As can be seen from the data table. 2, the proposed method gives results that completely coincide with the choice of the working less defective side in direct measurements of residual deformation on a three-crystal spectrometer. That is, the use of the proposed method as a means of sorting the backing material at the earliest stages of the technological route for the manufacture of devices will increase the yield of products in subsequent operations, including finishing.

 Thus, as the results shown in both examples show, when implementing the proposed method, an increase in the accuracy of measuring the curvature of single crystal plates is achieved by eliminating the error caused by the inhomogeneous distribution of the crystal lattice deformation along the reflecting surface.

Claims (1)

A method for measuring the curvature of single-crystal plates, including the formation of two parallel monochromatic x-rays directed to two points of the curved surface of the plate spaced apart from each other at a given distance S, and determining the difference of the reflection angles ΔΦ _{o of} these rays when they are subsequently brought into a reflective position by turning the plates around axis perpendicular to the plane of the incident and reflected rays lying in the middle between the points of incidence of the rays on the surface under study, about characterized by the fact that simultaneously with the first two beams, a third central monochromatic beam is formed and directed to the surface to be studied simultaneously and at the same distance from each of them to obtain reflection for rays that do not coincide with the central one, the single crystal is preliminarily oriented according to the maximum reflection of the central beam, after which the single crystal rotate 180 ^o around the axis coinciding with the normal to the surface, restored at the point of incidence of the central beam, and first repeat the orientation operation along the central beam, and then determining the difference in the reflection angles ΔΦ 180 ^o from two beams located on both sides of the central one, and determine the curvature K by the formula

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