JPH01123135A - Polarization analysis method - Google Patents

Abstract

PURPOSE:To make it possible to implement high accuracy, by making the wavelength and the incident angle of a light beam, which is inputted in the surface of a sample, variable, performing the measurement under a plurality of measuring conditions, inputting all the measured values at the same time by a least square method, and analyzing the physical properties of the surface film layer of the sample. CONSTITUTION:A light beam from a light source 1, in which a plurality of wavelengths can be switched, is inputted into a sample 4 through a polarizer 2. An incident angle 10 is made variable. A reflected light beam 8 is detected with a detector 6 through a rotary analyzer 5. The result is analyzed in a computer. In the analysis of the sample having multilayered films, the parameters of the reflectivity of a substrate and the film thickness and the reflectivity of each layer are defined. The initial values of the suitable parameters are imparted. The parameters of a structure are computed by using a nonlinear least square method. The known parameter among the structure parameters are fixed, and the unknown parameters are optimized. Thus the improved values of the structure parameters are obtained. In this way, the physical properties of the sample can be analyzed highly accurately.

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Application Field] The present invention relates to an ellipsometry method suitable for measuring physical properties of multilayer film samples.

[Conventional technology]

Ellipsometry is a method for determining the physical properties of a sample by measuring changes in the state of polarization when polarized light passes through or reflects the sample. The basic properties include the film thickness and optical constants of the thin film sample, and the optical constants of the substrate. These are collectively referred to as the structural parameters of the sample.

This method has the highest accuracy as a method for measuring film thickness, and has the advantage of being non-destructive. Quantify the condition. As measurement conditions, the incident angle of the light beam, the wavelength of the light beam, etc. are set to appropriate values.

This method has a long history and has been studied since the end of the last century, and many analysis methods have been proposed depending on the sample to be measured.

The methods that have been commonly used are mainly one
This method is aimed at analyzing layered film samples.

From the two measured values Δ and ψ measured under a single measurement condition, two unknown quantities such as the thickness and refractive index of a single layer film can be obtained by solving simultaneous equations. R, M, Ni, Azam (R, M, A.

Azgam) and N, M, Bashara (N, M, B
"Ellipsometry and Polarized Light" (Ellipsometry and Polarized Light) co-authored by (aahara) North Holland Publishing Company Amsterdam 197°7
&! l(L polariz@dlight',
North-Ho1land publishing
Co.

Am5t@rlam, 1977) - there is much literature for example.

However, the above method cannot determine three or more structural parameters and is unsuitable for analysis of multilayer film samples. - In a simple equation, a solution can only be found if the number of measured values is greater than or equal to the number of unknowns. Quantifying the structure of a multilayer film sample requires a large number of parameters (K, which quantitatively represents the structure of a multilayer film with m layers, requires at least (3m+2) parameters). It was necessary to obtain measured values, and the method described below was invented.

Journal of Applied Physics Volume 60 5
Pages 293 to 5302 (PG, Snyder et al.
e: J.

AIIPl, Phys, 60, 329s-5
SE method spectroscopic repsometry (Sp*otros) described in
(abbreviation for aopic ellipsomstry), the incident angle is fixed, measurements are taken using a large number of different wavelengths, and the multilayer structure parameters are determined from the plurality of measured values by the least squares method.

Shin Solid Films Volume 28, Page 167, Page 17
Page 7 (J., Saracitus and J. 21.

Spiridellis (J, 5arakinos anl J
, 3pyrideli, s: Th1n 5oz1a
Films, 28, 167-177, 197
5)) MAI (Multiple Angle Op Incident)
ofInailenae) method uses a single wavelength light source,! ! The multilayer structure parameters are determined by the method of least squares from the plurality of measured values obtained by measuring at several incident angles.

[Problem that the invention seeks to solve]

In the first example, the SE method, the incident angle is fixed and measurements are made using a number of different wavelengths to determine the multilayer structure parameters.

However, among the multilayer structure parameters, the refractive index takes a different value for each wavelength, so there is a problem in that only samples and analyzes for which the wavelength dependence of the refractive index is known in advance can be performed.

Furthermore, in order to analyze the structure of a multilayer film sample, there is an optimal incident angle for K for each wavelength and for each structure of the multilayer film to be measured. This angle of incidence will be referred to as a characteristic angle of incidence. For analysis of multilayer structures, it is important to measure K near the characteristic angle of incidence. However, in the SE method, measurements are taken at a single angle of incidence for vI wavelengths, so k
, there is a problem that the measurement accuracy decreases.

In the second example, the MAI method, the multilayer structure parameters are determined by measuring at a single wavelength and at a large angle of incidence. Since only the measured values near the characteristic angle of incidence are important for determining the parameters, sufficient information cannot be obtained even if a large number of measured values are obtained by the MAI method. Furthermore, since a single wavelength is used, there is a problem in that only a plurality of solutions can be obtained due to the phase difference between the light beams. Furthermore, among the multilayer structure parameters, the film thickness and the refractive index have a large correlation, so there is a problem that both cannot be determined simultaneously with high accuracy.

An object of the present invention is to analyze the physical properties of a multilayer film sample with high precision.

[Means for solving problems]

The above purpose is to perform measurements under multiple measurement conditions in which the wavelength and angle of incidence of the light beam incident on the sample surface are variable in the ellipsometry method, and to simultaneously input all of the obtained measurement values into the least squares method. This is achieved by optimizing the structural parameters that describe the physical properties of the surface layer.

[Effect]

In order to obtain sufficient information to determine the structural parameters of the multilayer film sample, independent ellipsometry measurements are performed under the measurement conditions of v1't&. By measuring at multiple angles of incidence, it is possible to obtain information around the characteristic angle of incidence necessary for determining the parameter, and by measuring at multiple wavelengths, it is possible to obtain information about the characteristic angle of incidence necessary to determine the parameter. Can solve numerical problems.

〔Example〕

Hereinafter, one embodiment of the present invention will be described in detail using the drawings.

(1) Measurement FIG. 2 is a schematic diagram of the polarization analyzer used in this example, FIG. 3 is a schematic diagram of the optical system, and FIG. 4 is a block diagram of the polarization analyzer. Although this example shows an example of a reflection polarization analyzer using a rotating analyzer method, similar measurements can be made using other polarization analyzers. 1 is a light source that can switch and generate a plurality of wavelengths. light source 1
The generated light beam passes through the polarizer 2 and becomes incident light II7.

The incident light @7 is incident on the surface of the sample 4. At this time, the angle between the incident light beam 7 and the vertical line on the sample surface is the incident angle 10. The incident light ts7 is reflected on the surface of the sample 4, and the reflected light 1s
It becomes 8. When the light beam is reflected, the state of polarization changes depending on the physical properties of the sample 4. The reflected light ls8 passes through a rotating analyzer 5 controlled by a computer 20, enters a detector 6, and is detected. Detection strength is Combiator 2
It is analyzed from 0 K to obtain measured values Δ and ψ.

In this embodiment, for example, light beams with wavelengths of 655 mm and 700 nm are used, and measurement is performed at an incident angle of 70 degrees to 84 degrees in increments of 2 degrees at each wavelength. - Assuming that boat fishing is carried out under one different measurement condition, the first measurement condition will be expressed by λ1 and φ1. However, λ1 is the wavelength of the first measurement, and φ1 is the incident angle of the first measurement. At this time, a set of measured values (Δ1, Δ2..., ΔJ, φ1, ψ2, .
..., ψz) (1) is obtained.

(2) Structure of multilayer film In order to measure the physical properties of a multilayer film sample, it is necessary to clearly define the structure of the multilayer film.

FIG. 5 shows a model of the m-layer multilayer film used in this example. The film interface is a parallel plane with an infinite area, and the refractive index changes discontinuously at the interface. The refractive index n8 of the substrate, the film thickness d,1 of each layer, and the refractive index nj are taken as parameters representing the physical properties of this model for light of a certain wavelength. Note that bean j is a complex refractive index, and the refractive index n
It is expressed by two equations using j and an extinction coefficient of 5.

】KOLjaIlnj-1kj...φcurvature...e-(
2) Set the structural parameters of the sample for a certain − wavelength to (3+
n+2) It is assumed that the original vertical vector C is expressed as in equation 3.

From now on, vertical letters and kutle will be expressed in lowercase bold letters, but due to space limitations, they will be written horizontally.

0 ”” (ml l ”' y ”m + ”B +
kl r ”' y 1cm t kl rdl,・
...,dITl) -(.t t 0.' t.3In+,)000600
0. (3) Since the refractive index and extinction coefficient have different values depending on the wavelength, the structural parameters of the sample for two wavelengths are (
5m+4) is expressed as the original vertical vector C' as in equation 4.

"" = (nl y "・+ "m + "8 v
kl * ”' * km * kl znl,
−,”m, !II!, kl, −,ky,
, , kg.

dl,..., 6) -(cl,..., 0 glaze 14)...
・ ・ (4) Although this embodiment shows an example for two wavelengths, the same can be considered when using three or more types of wavelengths.

(3) Analysis In order to analyze multilayer film samples, we need to understand the structure of the multilayer film.

It is necessary to find the relationship between the structure and the measured value. measured value.

Δ1 and ψ1 are the structural parameter C′ and the measurement conditions (wavelength λ
1 and the angle of incidence φ1).

△t-f'(λ1.φ1;C')3f'i(C')...
・(5) ψ1−f(λ1.φ1: o')Ef (C
)''・(6)(1-1~J-) The functions f, f are described as examples in "Ellipsometry and Polarization" above.

As a method for calculating structural parameters from a large number of measured values under a large number of measurement conditions, a nonlinear least squares method is applied.

The estimated value of the structural parameter is C, and the calculated value for C is △1-f' (δ) (t -1~1)...
・ (7) ψ1-f (8) (1-1~A) ・・
... Expressed as (8), and the residual rl is defined as in Equation 9.

rl-C(△1-△1)/σ (Δ1)+(ψ1-ψ1
)/σ (φ1)] ・ ・(9) However, σ (△
1) and σ (ψ1) are the measured film deposition values of the first measured values Δ1 and ψ1, respectively.

The least squares condition is a condition that minimizes the residual sum of squares Q.

When appropriate initial values of parameters are given, a set C of parameters satisfying the least squares condition can be determined by the non-M-type least squares method. In this example, the iterative improvement method using linear approximation (G
An example of the auss-Newton method is shown below. Regarding the least squares method, for example, see Koyanagi's "Experimental Data Analysis Using the Least Squares Method" (University of Tokyo Press, 1999).
82) K has been described.

If the next estimated value of the parameter t-o, the improved parameter is 0, and the correction vector is σC, then 11
The formula holds true.

(k+1) (k) (k)o
'+1110 +δ0 ・・・ ・・・
(11) The correction vector can be obtained using the following equation.

, a(h) , (X(k) wl A(h)+5(
k) w' B(k))-t, (λ(k) wl, ,
1 (k) +1(k) w2 , yz(k)),,
, (12) (k) (k) A , B is a matrix with 1 row and m columns and is called a Jacobian matrix, and its 'tj components Aij , Bi, j
is the partial differential coefficient of the function '1111 with respect to the parameter oj, as shown in the following equation.

(1-1~1s J -i~J!1) -(k) -(k) (k) (k)A
, B are the transposed matrices of A , B .

δ 1(k) δ ffi (k) is a 1-element vertical vector, and its 1 components δy 1 and δy 1 are given by Equations 15 and 16.

δ7 1-Δx-f't (a(k)) ,,,
,, (1s)1(k) 2(k) δy 1−ψx −f'i (c(k)) ---
---(16) (z-1 to 1) W and W are called weight matrices and are diagonal matrices with 1 row and 1 column. The first diagonal components of W′ and W2 are 1/σ, respectively.
(Δ1) and 1/σ (ψ1).

The Gauas-Newton method has poor stability when the initial value is far from the true value or when the objective function has a large non-S shape. Therefore, as a stabilizing method, a reduction factor α (0 × α≦1) is introduced into the correction vector. If Q increases due to the improved value of the parameter, a correction vector that decreases Q can be obtained by decreasing α.

C(k+□> am C(k)+αδC・・・・・・
(17) (k) (4) Analysis procedure An example of analysis using the Gauaa-Newton algorithm described above will be explained with reference to chart 70 in FIG.

In step 100, 21 measured values measured under one type of measurement condition are input. In step 1o1, the initial value (#1 constant value) of the structural parameter c(Q)t-is manually calculated. In step 102, the least squares cycle ff
Enter iIcMAX and select the parameters to optimize. In the above-mentioned Qau Law Newton algorithm, all elements of the structural parameter vector C are simplified and described as being iteratively improved, but in reality, the structure and
It is sufficient to fix the known structural parameters and optimize only the unknown parameters. Hereinafter, in order to avoid complicating the equation, a vector consisting only of parameters to be optimized will be expressed as C.

In step 103, the cycle number IC and the reduction factor α't
-ty Set to initial value 1. In step 104, the initial value of the parameter is substituted into C in equation (7) $ (8), and A1. Calculate $t(1-1~1). Step 10
5, the calculated value Δ1. ψ1 and measured value Δ1゜ψ1 (1-1
~j) is substituted into (9) 2, the residual r1 (1-1 to 1) is calculated, and Q (c (0°) is calculated by (10) 2.

In step 101, partial differential coefficients of the functions f and f with respect to the harameter are calculated (15).

(k) (k') (1 Calculate A and (B according to 2. Also, (
15) and (16) to calculate δY and δ2(0). The results obtained above are substituted into equation (12) to calculate the correction vector δC (step 112).

This δC is substituted into (17) 2 to obtain the improved value C of the structural parameter (step 113).

After adding 1 to the IC3) value in step 114, the process proceeds to the next cycle, and after 0, which returns to step 104, the same process continues. If the number of cycles exceeds the limit value ICMAX, the process ends (step 106). If the cycle number IC is neither 1 nor ICMAX, step 1 determines whether Q has increased from the previous cycle.
oe), if it is increasing, then α is made smaller (step no), and if it is decreasing, α is made larger (step 109).

Although the most basic example of implementing the present invention using the Gauss-Newton method has been shown above, there are many other nonlinear least squares algorithms that can obtain similar results.

〔Effect of the invention〕

As described above, in the method of the present invention, in order to obtain sufficient information to determine the structural parameters of a multilayer film sample,
Perform independent ellipsometry measurements under multiple measurement conditions. By measuring at multiple incident angles, it is possible to obtain information around the characteristic incident angle necessary for determining the parameter,
Furthermore, by measuring at multiple wavelengths, it is possible to solve the problem of gaps between multiple solutions caused by phase differences between light beams. Thereby, physical properties such as film thickness and refractive index of the multilayer film sample can be determined with high precision.

[Brief explanation of the drawing]

FIG. 1 is a flowchart showing one embodiment of the processing procedure of the present invention, FIG. 2 is a schematic diagram of the polarization analyzer according to the present invention, and FIG. 3 is a schematic diagram of the optical system of the polarization analyzer according to the present invention. FIG. 4 is a block diagram of the polarization analyzer according to the present invention, and FIG. 5 is a diagram showing the structure of the multilayer film sample measured by the present invention. 1...Multiple emission light source, 2...Polarizer, 3...1/
4 wavelength plate, 4...sample, 5...rotating analyzer, 6...
・Detector, 7... Incident ray, 8... Reflected ray, 9.
...Sample position drive mechanism, 10...Incidence angle. ′, 1, ′ Patent attorney Masaru Ogawa Ogawa 2 Figure 3 Saigo front armpit ΔSesekatsu? Ninori 1 ring mocking koku 3 figure 4 Test Pi-7 people village Saki sea bream (10th figure 5 figure

Claims (1)

[Claims] 1. A step of reflecting a polarized light beam on a sample or transmitting it through the sample, and analyzing the polarization state of the light beam reflected by the sample or transmitted through the sample; The method is characterized by performing measurements under multiple measurement conditions with variable incidence angles and inputting all measured values obtained in this process simultaneously into the least squares method to analyze the physical properties of the sample. and ellipsometry.