JPH04320904A - Method for measuring refractive index and thickness of thin films - Google Patents

Abstract

PURPOSE:To measure the refractive index and the film thickness of a thin film of a monoaxial crystal simultaneously by calculating the refractive index and the film thickness for a wavelength according to prescribed computation by using values of angles of incidence at the time when energy reflectivities of S polarization and P polarization obtained by making monochromatic lights of different wavelengths enter the thin film of the monoaxial crystal with the angles of incidence varied become extremes. CONSTITUTION:A monochromatic light of a wavelength lambda is made to enter a thin film 11 of a monoaxial crystal on a substrate 12 with an angle of incidence changed variously, energy reflectivities of S polarization and P polarization for each angle of incidence are measured respectively, and the angle of incidence at the time when each of the reflectivities becomes an extreme is determined. Next, a monochromatic light of a wavelength lambda' is made to enter the thin film 11 of the monoaxial crystal with the angle of incidence changed variously, the energy reflectances of the S polarization and the P polarization for each angle of incidence are measured respectively, and the angle of incidence at the time when each of the reflectances becomes the extreme is determined. Using values of the angles of incidence at the time when the energy reflectances of the S polarization and the P polarization thus determined become the extremes and according to prescribed computation, the refractive indexes nY and nZ of the thin film 11 of the monoaxial crystal for the wavelength lambda, the refractive indexes nY' and nZ' thereof for the wavelength lambda' and the film thickness d1 thereof are calculated.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring the refractive index and thickness of thin films that can be applied to optical evaluation of semiconductor devices, optical devices, etc.

0002

[Prior Art] Conventionally, LASER-VAMFO (Var
iable-Angle Monochromatic
There is a known method called Fringe Observation (I
B.M.J. Res. Develop. 8, pp. 43-
51 (1964)).

0003

[Problem to be solved by the invention] However, the above LASE
R-VAMFO requires the use of a monochromator, which has the disadvantage that the device is large-scale and measurement takes time. Therefore, the present inventor proposed a method to measure the refractive index and film thickness of a thin film by measuring the incident angle at which the reflectance reaches an extreme value using incident light of two wavelengths (hereinafter, this method will be referred to as (called the VAMFO method). However, this two-wavelength VAMFO method can only measure isotropic films, and is not suitable for measuring the refractive index and film thickness of uniaxial crystal thin films (hereinafter referred to as anisotropic films). The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a novel method for measuring the refractive index and thickness of a thin film.

0004

[Means for Solving the Problems] The present invention is a method for measuring the refractive index and film thickness of an anisotropic film formed on a substrate, in which the normal direction perpendicular to the substrate surface is the Z axis, and the When the directions parallel to the plane and perpendicular to each other are defined as the X and Y axes, find the principal refractive index nZ in the normal direction of the thin film, the principal refractive index nY in the tangential direction, and the film thickness d1 of the thin film. In the measurement method, ■ First, monochromatic light of wavelength λ is applied to the anisotropic film at an incident angle of φ0.
The energy reflectance Rs(φ0) of S-polarized light for each incident angle was measured by changing the incident angle in various ways.
) is the extreme value, the incident angle φ01, φ02,..., φ
0m (m is the number of extreme values), ②Next, let monochromatic light of wavelength λ enter the above anisotropic film while varying the incident angle θ0,
Energy reflectance Rp of P-polarized light for each incident angle (θ0
), and the incident angle θ when the Rp(θ0) reaches the extreme value is
01, θ02, ..., θ0M (M is the number of extreme values), and then monochromatic light of wavelength λ'(λ≠λ') is applied to the anisotropic film at various angles of incidence φ0'. The energy reflectance Rs'(φ0') of S-polarized light for each incident angle is measured, and the incident angle φ01 when Rs'(φ0') becomes the extreme value is determined.
', φ02', ..., φ0m''(m' is the number of extreme values)
.Next, monochromatic light with wavelength λ' is incident on the anisotropic film at various incident angles θ0', and P for each incident angle is calculated.
The energy reflectance Rp'(θ0') of polarized light is measured, and R
Incident angle θ01', θ0 when p'(θ0') becomes the extreme value
Find 2',...,θ0M''(M' is the number of extreme values),
■After calculating the above ■■■■, φ01, φ02,...,
Using the values of φ0m, φ01', φ02', ..., φ0m'', calculate nY and nY of the anisotropic film according to a predetermined calculation.
' and d1, then θ01, θ02,..., θ
Using the value of 0M and the obtained value of nY, the value of nZ of the anisotropic film is calculated according to a predetermined calculation, and then θ01'
, θ02', . ', nZ' are refractive indices with respect to wavelength λ').

The principle of the present invention will be explained in detail below. The purpose here is to measure the refractive index and film thickness of the anisotropic film 11 on the substrate 12 as shown in FIG. Note that the anisotropic film targeted by the present invention is directed in the normal direction of the thin film (Z
It is a uniaxial crystal thin film whose optical axis is axial direction), and the principal refractive index of such a thin film is nZ in the normal direction and n in the tangential direction.
It is given by Y. In addition, in the above uniaxial crystal thin film,
The refractive index nX for a light beam having a wavefront in the axial direction and the refractive index nY for a light beam having a wavefront in the Y-axis direction are equal. Therefore, in the present invention, the refractive indices nZ, nY and the film thickness d1 are determined. First, as shown in Figure 1, monochromatic light of wavelength λ is
0 to the anisotropic film. Then, since the X-Z plane becomes the plane of incidence, the refractive index for S-polarized light is nY
The equation expressing the Fresnel reflection coefficient for S-polarized light can be established as is by simply replacing the refractive index of the film in the case of an isotropic thin film with nY. Therefore, when S-polarized monochromatic light with a wavelength λ is incident on an anisotropic film at an incident angle φ0, the reflectance reaches a maximum or minimum value when the following equation is satisfied. 2d1√(nY2-n02sin2φ0)=m
λ
...(1) (n0 is the refractive index of the incident medium, m is the order of interference and is an integer or a half-integer) However, in the case of P-polarized light,
Since the electric field component is in the X-Z plane, when monochromatic light of the wavelength λ is incident at an incident angle θ0, the reflectance becomes maximum or minimum when the following equation is satisfied. 2d1nY√{1-(n02sin2θ0/n
Z2)}=Mλ ・
...(2) (M is the order of interference and is an integer or a half-integer)

[0006] Here, as a result of changing the incident monochromatic light of wavelength λ to S-polarized light and making it incident on the above-mentioned anisotropic film and measuring the reflectance by changing the angle of incidence, minimum values appeared at angles φ01 and φ02. do. Next, it is assumed that as a result of similarly measuring the reflectance of P-polarized light, minimum values appear at angles θ01 and θ02. Furthermore, as a result of measuring the reflectance by changing the incident angle of incident monochromatic light with wavelength λ'(λ'≠λ) to S-polarized light, minimum values appeared at angles φ01' and φ02', and P
As a result of measuring the reflectance by changing the angle of incidence with polarized light,
Suppose that the minimum values appear at angles θ01' and θ02'. In addition, in general, the refractive index has wavelength dispersion, so the wavelength λ'
Let nY' and nZ' be the refractive indexes for the wavelength λ (nY and nZ are the refractive indexes for the wavelength λ). Then, the following equation holds from equations (1) and (2). 2d1√(nY2−n02sin2φ01)=
m1λ
...(3) 2d1√(nY2-n02
sin2φ02)=m2λ
...(4) 2d1
nY√{1-(n02sin2θ01/nZ2)}=M
1λ...(5)
2d1nY√{1-(n02sin2θ02/nZ
2)}=M2λ...
(6) 2d1√(nY'2−n02sin2φ
01')=m1'λ'
...(7) 2d1√(nY'2-n
02sin2φ02')=m2'λ'
...(8) 2d
1nY'√{1-(n02sin2θ01'/nZ'2
)}=M1'λ'...(9)
2d1nY'√{1-(n02sin2θ02'
/nZ'2)}=M2'λ'...
・(10) Also, the formula for calculating nY from formulas (3) and (4) is as follows. nY=n0√{(m12sin2φ02−m2
2sin2φ01)/(m12-m22)}
...(11) Therefore, assuming the order m1 (or m2), (11
), and by substituting the value into equation (3) (or equation (4)), the film thickness d1 is calculated. Further, the formula for calculating nZ from formulas (5) and (6) is as follows. nZ=n0√{(M12sin2θ02−M2
2sin2θ01)/(M12-M22)}
(12) Furthermore, the formula for calculating nZ' from formulas (9) and (10) is as follows. nZ'=n0√{(M1'2sin2θ02'-M
2'2sin2θ01')/(M1'2-M2'2)}
...(13)

Next, assuming the following films, nY, nZ
We will explain how to calculate d1 and d1. Refractive index of the incident medium n0=1.000, refractive index of the substrate 12 n2*=
3.858-0.018i, when wavelength λ = 6328 Å, nY = 1.470, nZ = 1.700, when wavelength λ' = 5941 Å, nY' = 1.471, nZ'
= 1.701, film thickness d1 = 32000 Å, and as a result of calculating the reflectance of the anisotropic film 11 using Fresnel's formula, in the case of S-polarized light with a wavelength of 6328 Å, φ01 =
38.01°, φ02=52.73° Wavelength 63
For P polarized light at 28 Å, θ01=45.41°, θ
02=66.98° In the case of S-polarized light with a wavelength of 5941 Å, φ01'=36.40°, φ02'=50.
38° In the case of P-polarized light with a wavelength of 5941 Å, θ
The minimum values appear at 01'=43.33° and θ02'=62.97°, respectively. 1) First, substitute the values of φ01 and φ02 into equation (11), assume various values for the order m1, calculate the value of nY, and substitute that value into equation (3) to obtain d1. Table 1 shows the results of calculating the values of (Since φ01 and φ02 are adjacent minimum values, the order m1 of φ01 is the order m2 of φ02.
one larger than).

[0008]

[Table 1] However, it is not possible to determine which set of nY and d1 is the true value based only on the results in Table 1.

2) Next, by transforming equation (7), we get
nY'=√{(m1'2λ'2/4d12)+si
n2φ01'}
...(7') Therefore, in equation (7'), φ01'=36.40°, λ'=
Substituting 5941 Å and the data in Table 1 for d1, the order is the same as that assumed in Table 1, the order is +1, and the order is +2.
The results of calculating nY' for the orders are shown in Tables 2 and 3.
, shown in Table 4.

0010

[Table 2]

[0011]

[Table 3]

0012

[Table 4] Looking at Table 2, the value of nY is larger than the value of nY' in any order. Also, in Table 4, the value of nY is nY
' is smaller than the value of ' in any order. However,
In Table 3, starting from the highest order, m1=13.
5, the value of nY' becomes larger than the value of nY for the first time, and thereafter the difference gradually increases. In the case of general dielectric materials, when the wavelength becomes shorter in the visible light region,
The refractive index for that wavelength becomes slightly larger (Sellmeyer's dispersion equation). Therefore, nY (refractive index for wavelength 6328 Å) is 1.46975, nY' (wavelength 59 Å).
The refractive index relative to 41 Å) can be determined to be 1.47076. Also, correspondingly, the film thickness d1 is 32006
．． It can be determined to be 8 Å.

3) Next, substitute the values of θ01 and θ02 into equation (12), assume various values of the order M1, calculate the value of nZ, and use the value of nZ and 1) and 2). The calculated nY
Table 5 shows the results of calculating the value of d1 by substituting the value of d1 into equation (5).

[0014]

[Table 5] Looking at Table 5, when M1 = 13.5, the value of d1 is 3
It is 2005.8 Å, which is closest to the value of d1 determined in 1) and 2). Therefore, the value of nZ at this time is 1.699
97 can be determined as the value of nZ.

4) Next, set the values of θ01' and θ02' to (1
3) Substitute into the equation and assume various values of the order M1' to calculate nZ
Table 6 shows the results of calculating the value of d1 by substituting the value of nZ' and the value of nY' obtained in 1) and 2) into equation (9).

[0016]

[Table 6] Looking at Table 6, when M1'=14.5, the value of d1 is
It is 32005.8 Å, which is closest to the value of d1 determined in 1) and 2). Therefore, the value of nZ' at this time is 1.70
095 can be determined as the value of nZ'.

[0017]

[Operation] As explained above, according to the refractive index/film thickness measuring method of the present invention, the principal refractive index nZ (nZ') in the normal direction of an anisotropic film (uniaxial crystal thin film) and the principal refractive index nZ (nZ') in the tangential direction Principal refractive index nY
(nY') and the film thickness d1 can be measured.

[0018]

[Examples] Examples of the present invention will be described below. This example shows the results of measurements on a ZnO thin film formed by sputtering on a glass substrate (refractive index: 1.530). Figure 2 shows the configuration of the measurement system. Figure 2
, symbol 8 is the θ-2θ rotation system, and this θ-2
The θ rotation system has a mechanism in which when the measurement sample 7 rotates θ, the photodetector 6 rotates by 2θ, and the power of the reflected light is detected by the photodetector 6 by continuously changing the incident angle. In addition, the dichroic mirror 4 has a higher transmittance for the light from the He-Ne laser 1 with a wavelength λ=6328 Å, so that λ'=
It is designed to have a higher reflectance for the light from the 5941 Å He-Ne laser 2, and by switching the shutters 3a and 3b, the incident light on the measurement sample 7 can be set to 6328 Å or 5941 Å. It looks like this. In addition, the polarizer 5 uses a Glan-Thompson prism in this example, and by changing the direction of this prism,
The polarization direction is set so that the incident light becomes S-polarized light or P-polarized light with respect to the plane of incidence. In addition, in the measurement method of the present invention, the incident angle at which the extreme value of the energy reflectance appears is determined and the refractive index and film thickness are calculated using that value, so there is no need to measure the absolute value of the energy reflectance. . Therefore,
It is sufficient to detect the amount of reflected light and obtain the relative value of the energy reflectance for each incident angle, and there is no need to detect the amount of incident light. However, this is the case when the power fluctuation of the incident light during the measurement time is very small. Also, the incident angle is 0° or 90°.
It is difficult to accurately measure the amount of reflected light in areas close to 100°, and it is also difficult to determine the extreme value of reflectance. Therefore, in order to obtain a highly accurate refractive index and film thickness, it is better not to use an incident angle that gives an extreme value as close to 0° or 90° as possible.

Now, as a result of measuring the amount of reflected light using the above method, extreme values appeared at the following angles. λ=6328Å, S polarization, φ0
1=25.77°, φ02=50.16°
λ=6328Å, P polarization, θ01=26.
00°, θ02=50.71° λ'=5
941Å, S polarization, φ01'=31.43°,
φ02'=53.40° λ'=5941Å
, P polarized light, θ01'=31.71°, θ02'
=54.02°Here, first, according to the steps 1) and 2) above, using φ01, φ02, φ01', the order m1,
nY, d1, nY' calculated by assuming various m1'
The combinations are shown in Table 7.

[0020]

[Table 7] Looking at Table 7, the value of nY' becomes larger than the value of nY for the first time when m1=18.5, and thereafter the difference gradually increases. Therefore, wavelength λ=6328
The refractive index for Å is nY=1.99927, wavelength λ'=
The refractive index for 5941 Å is nY'=2.00027
It can be determined that Further, the film thickness can be determined as d1=29995.5 Å.

Next, according to the procedure 3) above, θ01, θ
Table 8 shows the results of calculating the values of nZ and d1 by assuming various values of the order M1 using the value of 02 and the obtained value of nY.

[0022]

[Table 8] Looking at Table 8, when M1=18.5, the value of d1 is
It is 29996.2 Å, which is closest to the value of d1 determined in Table 7. Therefore, the value of nZ at this time is 2.01492
can be determined as the value of nZ.

Next, according to the procedure 4), θ01', θ0
Table 9 shows the results of calculating the values of nZ' and d1 by assuming various values of the order M1' using the value of 2' and the obtained value of nY'.

[0024]

[Table 9] Looking at Table 9, when M1'=19.5, the value of d1 is 29995.8 Å, which is closest to the value of d1 found in Table 7. Therefore, the value of nZ' at this time is 2.01604
can be determined as the value of nZ'.

[0025]

As explained above, according to the method for measuring the refractive index and film thickness of a thin film according to the present invention, the principal refractive index in the normal direction and the principal refractive index in the tangential direction of a uniaxial crystal thin film (anisotropic film) can be measured. refractive index,
and film thickness can be determined simultaneously and with high precision.

[Brief explanation of the drawing]

FIG. 1 is a diagram for explaining the principle of the present invention.

FIG. 2 is a schematic configuration diagram of a measurement system showing an embodiment of the present invention.

[Explanation of symbols]

1 He-Ne laser (wavelength λ=632
8 Å) 2 He-Ne laser (wavelength λ'
=5941Å) 3a, 3b Shutter 4 Dichroic mirror 5
Polarizer 6 Photodetector 7
Measurement sample 8 θ-2θ rotation system 11 Anisotropic thin film 12 Substrate

Claims (1)

[Claims] Claim 1: A method for measuring the refractive index and film thickness of a uniaxial crystal thin film (hereinafter referred to as an anisotropic film) formed on a substrate, wherein the normal direction perpendicular to the substrate surface is the Z-axis. , when the directions parallel to the substrate surface and orthogonal to each other are defined as the X and Y axes, the principal refractive index nZ in the normal direction of the thin film, the principal refractive index nY in the tangential direction,
In the method for measuring the refractive index and film thickness of a thin film to determine the film thickness d1, first, monochromatic light with wavelength λ is incident on the anisotropic film at various angles of incidence φ0, and the energy of S-polarized light for each angle of incidence is calculated. The reflectance Rs (φ0) is measured and the Rs (
Incident angles φ01, φ02,... when φ0) becomes the extreme value
, φ0m (m is the number of extrema), and then () make monochromatic light of wavelength λ incident on the anisotropic film at various incident angles θ0, and calculate the energy reflectance Rp of P-polarized light for each incident angle. (
θ0), find the incident angles θ01, θ02, ..., θ0M (M is the number of extreme values) when the Rp (θ0) becomes an extreme value, and then calculate the wavelength λ' (λ≠λ ') is incident on the anisotropic film at various incident angles φ0', and the energy reflectance Rs'(φ0') of S-polarized light for each incident angle is measured. ) is the extreme value of the incident angle φ
01', φ02', ..., φ0m''(m' is the number of extreme values), and then apply monochromatic light of wavelength λ' to the anisotropic film with various angles of incidence θ0'. The energy reflectance Rp'(θ0') of P-polarized light for each incident angle is measured, and the incident angle θ01' when Rp'(θ0') becomes the extreme value is determined.
After finding θ02',..., θ0M''(M' is the number of extreme values), and finding the above ■■■■, φ01, φ02,...
・, φ0m and φ01', φ02', ..., φ0m''
using the value of nY of the anisotropic film according to a predetermined calculation.
, nY' and d1, then θ01, θ02,...
・Using the value of θ0M and the obtained value of nY, calculate the value of nZ of the anisotropic film according to a predetermined calculation, and then calculate θ
The value of nZ' of the anisotropic film is calculated according to a predetermined calculation using the values of 01', θ02', ..., θ0M'' (however, nY and nZ are the refractive indexes for the wavelength λ). , nY', nZ' are refractive indexes for wavelength λ')
A method for measuring the refractive index and thickness of a thin film.