JPH0672844B2 - Crystal orientation analysis method - Google Patents

Description

TECHNICAL FIELD The present invention relates to a crystal orientation analysis method, and more particularly to a crystal orientation analysis method utilizing polarization characteristics of Raman scattered light.

[Prior Art] The principle of crystal orientation analysis utilizing the polarization characteristics of Raman scattered light is described in, for example, Applied Physics, Volume 55, No. 1, 1986, No. 73.
-80 pages. First, an outline of this principle will be described. The relationship between the Raman scattering intensity I and the polarization of the incident light and the polarization of the scattered light is expressed by the following equation (I).

here, Represents the polarization vector of the incident light and the scattered light respectively, and Rj represents the Raman tensor. This Raman Sol Rj is
As known to those skilled in the art, it is determined depending on the crystal orientation.

With reference to FIG. 1, a relationship between incident light and scattered light and crystals in a Raman microscopic measurement is schematically illustrated. Incident light 1 is condensed on the sample crystal 5, and Raman scattered light 3 is scattered from the crystal. In this case, the incident light 1 has a polarization direction 2 rotated by a polarization ψ ₁ from the polarization reference direction ψ ₀ , and the Raman scattered light 3 has a polarization angle ψ ₀ from the polarization reference direction ψ _0.
It has a polarization direction 4 rotated by ₂ . The component of this polarization direction 4 is taken out by the analyzer, and its scattering intensity I
Is measured. The three-dimensional orientation of the crystal 5 with respect to the axis of the incident light 1 can be determined by fitting the scattering intensities measured in various polarization directions to the theoretically obtained scattering intensities in the above equation (1) and fitting. .

An apparatus used for such a crystal orientation analysis method is schematically illustrated with reference to FIG. The laser light beam 12 emitted from the laser source 11 is passed through a filter spectroscope 13 to remove natural light other than laser light. Next, the laser beam 12 selected to have an arbitrary polarization direction by the polarization rotator 1 is expanded in beam diameter by the beam expander 15, then changed in direction by the half mirror 16, and then focused on the sample crystal 5 by the range 17. Be matched. At this time, light having energy different from that of the original laser light 12 is emitted from the crystal 5 as Raman scattered light. lens
The scattered light 19 collected by 17 is redirected by a mirror 20, only the scattered light having a certain polarization direction is taken out by an analyzer 21, passes through a depolarizing plate 22, and then a spectroscope 24 by a lens 23. It is focused on the slit. Then, the dispersed light scattered is detected by the detector 25, and the computer 26 processes the data to analyze the crystal orientation.

Conventionally, in such a crystal orientation analysis method, the polarization characteristic of the Raman scattered light is measured by the polarization rotator 14 or the analyzer 21.
Either one of them is rotated, or both polarization directions are matched and simultaneously rotated.

[Problems to be Solved by the Invention] Conventionally, in the measurement of the polarization characteristics of Raman scattered light, either one of the polarization directions of incident light and scattered light is changed, or both are changed at the same time. ing.
In this case, when the incident light is incident along a certain axis of the crystal, the Raman scattering intensity may be constant despite the change in the polarization direction. At this time, there is a problem that the orientation of the crystal axis in the plane perpendicular to the incident light cannot be determined, that is, the three-dimensional orientation of the crystal cannot be determined.

An object of the present invention is to solve such a problem and to easily and promptly analyze the three-dimensional orientation of the crystal whose orientation is to be analyzed, whatever orientation the incident light has. It is to provide a crystal orientation analysis method.

[Means for Solving the Problems] A crystal orientation analysis method utilizing the polarization characteristics of Raman scattered light according to one aspect of the present invention is a method of changing the scattering intensity while changing the polarization directions of incident light and scattered light so as to match each other. The first step of measuring the change, and only when one of the polarization directions of the incident light and the scattered light is fixed and the other is changed only when it is detected that the scattered intensity does not change in the first step A second step of measuring the change in scattering intensity,
And a third step of determining the three-dimensional orientation of the crystal by comparing the change in the measured scattering intensity with the change in the scattering intensity obtained by theoretical calculation.

A crystal orientation analysis method using the polarization characteristic of Raman scattered light according to another aspect of the present invention is characterized by using a microscopic Raman spectroscope.

[Operation] In the measurement of the Raman scattering intensity in the crystal orientation analysis method of the present invention, the scattering intensity is measured while changing the polarization directions of both the incident light and the scattered light in the first step in order to reduce the analysis parameter. However, the second step is introduced only when the scattering intensity does not change due to the change of the polarization direction in the first step, and the change is made by changing the polarization direction of only one of the incident light and the scattered light. Since the scattering intensity is measured, it is possible to easily and quickly perform a three-dimensional orientation analysis of a crystal having any orientation with respect to the incident light.

[Example] In this example, the orientation analysis of a silicon crystal will be described as an example. First, for the convenience of explanation of the curve showing the theoretical polarization characteristic of Raman scattered light, the reference direction of polarization is determined as shown in FIG. Lines 1 and 3 are the optical axes of incident light or scattered light. φ is the angle formed by the straight line obtained by projecting the optical axes 1 and 3 on the (001) plane of the crystal and the [100] time of the crystal, and θ is the optical axis 1 and 3 and [00
1] The angle with the axis. e indicates a polarization direction perpendicular to the optical axes 1 and 3, and its polarization angle ψ is defined as an angle formed between the optical axes 1 and 3 and a plane including the [001] axis. In other words, θ, φ, ψ
If is determined, the three-dimensional orientation of the crystal with respect to the optical axes 1 and 3 is determined.

Referring to FIG. 4, there is shown a polarization characteristic curve of scattered light calculated in the equation (1) when incident light is incident in the <110> direction of the crystal. In this case, the polarization direction ψ ₁ of the incident light is fixed and only the polarization direction ψ ₂ of the scattered light is changed. The horizontal axis represents the polarization angle ψ ₂ of the scattered light, and the vertical axis represents the scattered light intensity I at that polarization angle. As can be seen from the figure, different polarization characteristic curves are obtained for each polarization angle ψ ₁ of the incident light. That is, when analyzing a crystal with an unknown orientation, since the polarization angle ψ ₁ of the incident light is unknown, the measured polarization characteristics are compared with various logical curves by a computer to determine the crystal axis orientation perpendicular to the optical axis. I have to decide. In addition, the polarization angle of incident light ψ ₁ = 0
In the vicinity of °, even if the polarization angle ψ ₂ of the scattered light is changed, the scattered light intensity I does not change at all or hardly changes.
Therefore, even if the measured polarization characteristics are compared with the theoretical results, it is difficult to accurately determine the polarization angles ψ ₁ and ψ ₂ . That is, it is difficult to accurately determine the axis orientation of the crystal perpendicular to the optical axis.

Referring to FIG. 5, the incident light is <11 as in the case of FIG.
Although the light is incident in the 0> direction, the polarization characteristic curve obtained from the calculation of the equation (1) is shown when the polarization angles ψ ₁ and ψ ₂ of both the incident light and the scatter are changed while matching. Has been done. In this case, only one curve is obtained.
That is, ψ ₁ = ψ ₂ , and the parameter in the azimuth analysis is decreased by one. Therefore, the polarization angles ψ ₁ and ψ ₂ can be easily obtained by comparing the measured polarization characteristic curve with one theoretical curve, and the crystal axis direction perpendicular to the incident optical axis can be easily determined. The incident light is <
The same applies to the case of incidence in the 100> direction, and the formula (1)
The polarization characteristic curve obtained from is shown in FIG.

Referring to FIG. 7, incident light is incident in the <111> direction,
The polarization characteristic curve obtained from the equation (1) is shown when the polarization angles ψ ₁ and ψ ₂ of both the incident light and the scattered light are changed while being matched. In this case, as is clear from the figure, the scattered light intensity is constant regardless of changes in the polarization angles ψ ₁ , ψ ₂ . Therefore, the polarization angles ψ ₁ and ψ ₂ cannot be determined at all even if the measured polarization characteristics are compared with the theoretical results.

However, in such a case, if the polarization angle of either the incident light or the scattered light is fixed and only the other polarization angle is changed as in the case of FIG. 4, for example, as shown in FIG. The polarization characteristic curve as described above is obtained from the equation (1). Therefore, the polarization angles ψ ₁ and ψ ₂ can be determined by comparing the polarization characteristic curve measured in the same manner with the theoretical curve as shown in FIG. That is, the crystal axis orientation perpendicular to the incident optical axis can be determined,
The three-dimensional azimuth is determined.

As described above, in the present invention, in the first step, the polarization characteristics are measured while changing the polarization directions of both the incident light and the scattered light so as to reduce the parameters in the azimuth analysis. Only when it is detected that the scattered light intensity does not change in the second step, the polarization characteristic is measured by changing the polarization direction of only one of the incident light and the scattered light as the second step.

[Effects of the Invention] As described above, according to the present invention, the case where both the polarization directions of incident light and scattered light are changed to match and the case where one of the polarization directions is changed is appropriately combined. Since the polarization characteristics are also measured together, the three-dimensional orientation of the crystal can be uniquely determined easily and quickly no matter which direction the incident light enters the crystal.

[Brief description of drawings]

FIG. 1 is a diagram schematically showing the relationship between the polarization directions of incident light and scattered light and the crystal whose direction is analyzed. FIG. 2 is a diagram schematically showing an apparatus used in the crystal orientation analysis method of the present invention. FIG. 3 is a diagram for explaining the relationship between the crystal axial direction and the polarization reference direction. FIG. 4 shows a polarization characteristic curve of scattered light when the polarization angle of the incident light is fixed and the polarization angle of the scattered light is changed when the incident light direction is <110>. FIG. 5 is a diagram showing the polarization characteristics when the incident light direction is <110> but the incident light and scattered light are both changed in the same polarization angle. FIG. 6 is similar to FIG. 5, but the incident light direction is <100
It is a figure which shows the polarization characteristic curve in case of>. FIG. 7 is a diagram showing polarization characteristics of scattered light when the incident light direction is <111> and the polarization angles of both the incident light and the scattered light are changed so as to match. FIG. 8 is a diagram showing a polarization characteristic curve when the incident light direction is <111> but only the polarization angle of scattered light is changed. In the figure, 1 is the incident light, 2 is the incident light polarization direction, 3 is the scattered light, 4 is the scattered light polarization direction, 5 is the sample crystal, ψ ₀ is the reference direction of polarization, and ψ ₁ is the polarization angle of the incident light. , Ψ ₂ indicates the polarization angle of scattered light.

Claims (4)

[Claims] 1. A method for analyzing a crystal orientation by utilizing a polarization characteristic of Raman scattered light, which comprises a first step of measuring a change in scattering intensity while changing the polarization directions of incident light and scattered light so as to match each other. Measuring the change in the scattering intensity while fixing one of the polarization directions of the incident light and the scattered light and changing only the other, only when it is detected that the scattering intensity does not change in the first step. A crystal orientation comprising the following two steps: a third step of determining the three-dimensional orientation of the crystal by comparing the change in the measured scattering intensity with the change in the scattering intensity obtained by theoretical calculation. analysis method. 2. The crystal orientation analysis method according to claim 1, wherein the crystal is silicon. 3. A method for analyzing a crystal orientation from a polarization characteristic of Raman scattered light by using a microscopic Raman spectroscope, in which a change in scattering intensity is measured while the polarization directions of incident light and scattered light are changed so as to match each other. 1 and only when it is detected that the scattering intensity does not change in the first step, the scattering intensity changes while fixing one of the polarization directions of the incident light and the scattered light and changing only the other. And a third step of determining the three-dimensional orientation of the crystal from the comparison between the change in the measured scattering intensity and the change in the scattering intensity obtained by theoretical calculation. And the crystal orientation analysis method. 4. The crystal orientation analysis method according to claim 3, wherein the crystal is silicon.