KR20230120699A - Mueller matrix ellipsometer - Google Patents

Abstract

The present invention does not rotate the phase retardant in a Mueller matrix ellipsometer (MME) using a phase retardant deviating from the 4-minute-wavelength phase retardation characteristic, and through a combination of the polarizer's azimuth angle and the polarizer-side phase retardant's azimuth angle, It relates to a Muller matrix measurement technique that optimizes the polarization state of incident light and determines the polarization state of reflected light through a combination of the azimuth angle of the analyzer and the azimuth angle of the analyzer-side phase retarder.
In the Muller matrix ellipsometer having the arrangement structure of the light source-polarizer-first phase retarder-sample-second phase retarder-analyzer according to the present invention, the first phase retarder and the second phase retarder have a quarter-wavelength phase A phase retarder deviating from the delay characteristic, and the azimuth angle of the polarizer and the first phase retarder is the incident light Muller matrix absolute value of Incident light Stokes vector such that is greater than 0.2 It is characterized in that it is set as a combination that satisfies.

Description

Muller matrix ellipsometer {Mueller matrix ellipsometer}

The present invention does not rotate the phase retardant in a Mueller matrix ellipsometer (MME) using a phase retardant deviating from the 4-minute-wavelength phase retardation characteristic, and through a combination of the polarizer's azimuth angle and the polarizer-side phase retardant's azimuth angle, It relates to a Muller matrix measurement technique that optimizes the polarization state of incident light and determines the polarization state of reflected light through a combination of the azimuth angle of the analyzer and the azimuth angle of the analyzer-side phase retarder.

Ellipsometry is widely used as a non-destructive measurement method in industrial fields using various thin films, and is particularly useful for non-destructively measuring the thickness of thin films in the semiconductor field.

The elliptic method is a method for determining factors such as density change, optical thickness, and complex refractive index, which are factors that change polarization, by injecting light having a specific polarization state into a sample and then measuring and analyzing the changed polarization state of the reflected light. is called an ellipsometer.

In the early days when ellipsometers were developed, short-wavelength ellipsometers operated at a single wavelength were used to precisely measure the thickness of a single thin film, but a spectroscopic ellipsometer (SE) was developed that acquires multiple elliptic constant values over a wide wavelength band. Since then, by modeling and analyzing many elliptic constant measurements, it has been possible to quickly, accurately, and nondestructively derive the structure and physical properties of multilayer thin film samples, making spectroscpic ellipsometry (SE) very useful in various industrial fields including semiconductors. It is being utilized.

However, a general ellipsometer is a technique for obtaining an elliptic constant by irradiating a sample with light in a certain polarization state and measuring a change in the polarization state of the reflected light, and measurement is impossible in an environment without polarization.

In particular, as semiconductors are being finely patterned, when light is scattered by fine patterns and devices on a substrate, some polarization components may be lost or a non-polarized state may occur.

In this way, the Mueller matrix ellipsometer is a technology designed to obtain elliptic constants even in an environment without polarization.

In a general ellipsometer, the polarization state is represented by a 1×2 Jones vector, the polarization action by a polarizer is represented by a 2×2 Jones matrix, and the elliptic constant is represented by Δ, ψ or two parameters corresponding thereto, whereas the Mueller matrix ellipse In the system, a 1×4 Stokes vector including a component related to the depolarization effect (lost polarization information) and a total light intensity component, which is a state in which polarization is lost, is used to express the polarization state, and the polarization action of the polarizer is 4×4 represented by the Mueller matrix.

The Muller matrix ellipsometer generally has an arrangement of polarizer-compensator-sample-compensator-analyzer (PC ₁ SC ₂ A), and the compensators placed before and after the sample, that is, each phase As the retarder, an ideal quarterwave phase retarder having a phase retardation value of 90 degrees and an electric field transmittance ratio between fast and slow axes of 1.0 is preferred.

However, it is relatively easy to obtain an ideal quarter-wavelength phase retarder when using a single wavelength light such as a He-Ne laser, but in a Mueller matrix spectroscopic ellipsometer (MMSE) that operates over a wide wavelength band There are practically no achromatic quarter-wavelength phase retarders that can be used.

Accordingly, in the conventional measurement technology using the Muller matrix ellipsometer, many methods for implementing a compensator in a form close to an ideal quarter-wavelength phase retarder have been proposed. There is a multi-channel spectroscopic ellipsometer with a compensator rotation method.

1. Korean Patent Registration No. 10-1698022 (Name: Achromatic optical element-rotational ellipsometer and method for measuring Muller-matrix of specimen using the same) 2. Korean Patent Registration No. 10-1509054 (Name: Optical element-rotating Muller-matrix ellipsometer and method of measuring the Muller-matrix of a sample using the same)

In the Muller matrix ellipsometer of the PC ₁ SC ₂ A arrangement structure using non-ideal quarter-wavelength phase delayers, the present invention does not rotate the phase delayers unlike the conventional double compensator rotation method, and the azimuth angle of the polarizer and the sample rotation The technical purpose is to provide a Muller matrix ellipse system that enables the optimal Mueller matrix to be determined through the combination of the azimuth angle of the phase retarder and the combination of the azimuth angle of the phase retarder and the azimuth angle of the analyzer after the sample.

According to one aspect of the present invention for achieving the above object, in a Mullerian matrix elliptic system having a layout structure of a light source-polarizer-first phase retarder-sample-second phase retarder-analyzer, the first phase delay The ruler and the second phase retarder are phase retarders that deviate from the 4-wavelength phase retardation characteristics, and the azimuth angles of the polarizer and the first phase retardant are the incident light Muller matrix absolute value of Incident light Stokes vector such that is greater than 0.2 There is provided a Muller matrix elliptic system, characterized in that set to a combination that satisfies.

,

), (±

, ±

), (O,±

) 중에서 설정되는 것을 특징으로 하는 뮬러행렬타원계가 제공된다.In addition, the combination (P, C) of the azimuth angle P of the polarizer and the azimuth angle C of the first phase retarder is (0,0), (

,

), (±

, ±

), (O, ±

) There is provided a Muller matrix elliptic system, characterized in that set in.

,

)조합에 대응되는 제1 그룹의 입사광 스톡스벡터와, (±

, ±

) 조합에 대응되는 제2 그룹의 입사광 스톡스벡터 및, (O,±

) 조합에 대응되는 제3 그룹의 입사광 스톡스벡터들을 이용하여 결정되는 것을 특징으로 하는 뮬러행렬타원계가 제공된다.In addition, the incident light Muller matrix is (0,0), (

,

) the incident light Stokes vector of the first group corresponding to the combination, (±

, ±

) the Stokes vector of incident light of the second group corresponding to the combination, and (O, ±

) is determined using the Stokes vectors of the third group of incident rays corresponding to the combination.

In addition, the Stokes vector of the incident light of the first group is , the incident light Stokes vector of the second group is , the Stokes vector of the incident light of the third group is In addition, the Mullerian matrix elliptic system is provided, wherein the Mullerian matrix of the incident light is determined by including at least one Stokes vector of the incident light in each group.

In addition, the combination of the azimuth angle of the polarizer and the azimuth angle of the first phase retarder is a combination of (P, C), (P + π, C), (P, C + π), and (P + π, C + π). A Muller matrix elliptic system is provided, characterized in that it is set among ordered pairs corresponding to one combination of.

In addition, the intensity of light passing through the second phase retarder with the azimuth angle C and the analyzer with the azimuth angle A is as, , and the Stokes constants of the incident light S ₀ , S ₁ , S ₂ , S ₃ are As such, a Mueller matrix ellipsometer is provided, which is characterized in that it is determined from the intensity of light measured at the azimuth combination (A, C) of the second phase delay and analyzer.

According to the _present invention, the combination of the azimuth of the polarizer and the azimuth of the phase retarder before the sample, and the azimuth of _the phase retarder and the azimuth of the analyzer after the sample By making it possible to determine the optimal Mueller matrix through the combination, it is possible to provide a free-form driven Mueller matrix ellipsometer that enables easy measurement of the Mueller matrix of a sample even when an imperfect phase retarder is used.

Accordingly, it greatly expands the range of selection of the phase retarder, making it more useful to design, manufacture, and drive the Mueller matrix spectroscopic ellipsometer, which enables operation in a wide wavelength range from DUV to NIR. It can greatly contribute to the measurement and evaluation of nanostructures based on OCD.

1 is a diagram showing a schematic configuration of a Muller matrix elliptic system according to a first embodiment of the present invention;
FIG. 2 is a view for explaining the characteristics of light passing through the polarizer 200 and the first phase retarder 300 shown in FIG. 1;
FIG. 3 is a diagram showing the phase delay angle and electric field transmittance ratio characteristics of the first phase retarder 300 shown in FIG. 1;
FIG. 4 is a diagram for explaining the absolute value characteristics of a Muller matrix made of a combination of azimuth angles of the polarizer 200 and the first phase retarder 300 shown in FIG. 2;

The embodiments described in the present invention and the configurations shown in the drawings are only preferred embodiments of the present invention, and do not represent all the technical ideas of the present invention, so the scope of the present invention is limited to the embodiments and drawings described in the text. should not be construed as being limited by That is, since the embodiment can be changed in various ways and can have various forms, it should be understood that the scope of the present invention includes equivalents capable of realizing the technical idea. In addition, since the object or effect presented in the present invention does not mean that a specific embodiment should include all of them or only such effects, the scope of the present invention should not be construed as being limited thereto.

All terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs, unless defined otherwise. Terms defined in commonly used dictionaries should be interpreted as being consistent with meanings in the context of related art, and cannot be interpreted as having ideal or excessively formal meanings that are not clearly defined in the present invention.

1 is a diagram showing a schematic configuration of a Muller matrix ellipsometer according to a first embodiment of the present invention.

Referring to FIG. 1, the Muller matrix ellipsometer includes a light source 100, a polarizer 200, a first phase retarder 300, a second phase retarder 400, and an analyzer 500 At the rear end of the analyzer 500, an inspection unit 600 for inspecting the state of the sample 10 using the intensity of light received from the analyzer 500 is provided.

That is, the light source 100, the polarizer 200, and the first phase retarder 300 are disposed on one side of the sample 10 to allow light to enter the sample 10, and the second phase retarder 400 and , The analyzer 500 is disposed on the other side of the sample 10 and has a PC ₁ SC ₂ A elliptical structure into which light reflected from the sample 10 is incident.

The light source 100 is a light generating device that irradiates incident light toward the sample 10, and generates light in various wavelength bands ranging from deep ultra violet (DUV) to near infrared, that is, white light.

The polarizer 200 linearly polarizes light output from the light source 100 and outputs the light.

The first phase retarder 300 changes the polarization state of the incident light incident through the polarizer 200 and projects it toward the sample 10 . At this time, the first phase retarder 300 is a quasi-chromatic quarter-wavelength phase retarder, and the phase delay angle δ _c is not 90 degrees, and the electric field transmittance ratio t _c of the fast axis and the slow axis significantly deviate from 1.0.

At this time, the polarization state of the light incident on the sample 10 is reflected and output in a deformed form according to optical and structural characteristics such as the complex refractive index and thickness of the sample 10 .

The second phase retarder 400 changes the polarization state of the reflected light incident from the sample 10 side and outputs it to the analyzer 500. At this time, the second phase retarder 400 is a quaternary colorimetric quarter-wavelength phase retarder, and like the first phase retarder 300, the phase delay angle δ _c is not 90 degrees, and the electric field transmittance ratio between the fast axis and the slow axis It has the characteristic that t _c deviates significantly from 1.0.

The analyzer 500 outputs only specific polarized light among reflected light incident from the second phase retarder 400 to the inspection unit 600 .

The inspection unit 600 analyzes the measurement light input from the analyzer 500 to determine the Stokes vector of the incident light according to the azimuthal combination of the polarizer 200 and the first phase retarder 300 and the second phase retarder 400. The state of the sample is inspected by determining the Mueller matrix of the sample using the Stokes vector of the emitted light corresponding to the azimuthal combination between the analyzers 500.

At this time, the Stokes vector of the incident light and the Stokes vector of the outgoing light are respectively , the Mueller matrix of the sample If expressed as Incident light Muller matrix made of the elements of the Stokes vector corresponding to and the outgoing light Muller matrix Satisfies the relationship shown in Equation 1 below.

here, , , ego,

, am.

And, the Mueller matrix of the sample from Equation 1 can be expressed as in Equation 2.

That is, the inspection unit 600 determines the Stokes vectors of four different incident lights. Stokes vectors of the emitted light corresponding to each By securing them, the incident Mueller matrix from them and the outgoing Muller matrix are configured as in Equation 1, respectively, and the Mueller matrix of the sample according to Equation 2 decide

At this time, in Equation 2, the inverse matrix in order to save should be If two incident lights with the same polarization state are included when constructing becomes

and, As the polarization states of the incident lights constituting are mutually independent, deviates from 0 more Since the error of decision is small to have the largest possible value should configure them.

Accordingly, in the present invention, the azimuth angle of the polarizer 200 and the first phase retarder 300 is calculated as the incident light Muller matrix absolute value of Incident light Stokes vector so that has a maximum value of 0.2 or more set as a combination to construct them.

Hereinafter, the process of determining the azimuth of the polarizer 200 and the first phase retarder 300 will be described in detail.

First, the Stokes vector As shown in FIG. 2, the azimuth angle is The polarizer 200 and the azimuth angle of the fast axis are When the first phase retarder 300 continuously passes through the first phase retarder 300, the Stokes vector of the light passing through the first phase retarder 300 Is expressed as in Equation 3 below.

here, and are each azimuth The Mueller matrix and azimuth of the phase retarder with is the Muller matrix of the polarizer, which is the Muller matrix of the phase retarder with an azimuth angle of 0 degrees. and the Muller matrix of the polarizer with an azimuth angle of 0 degrees , and the rotation angle is is the Muller matrix of the optical rotor, , expressed as in Equation 4.

here, and , and the rotation angle is Mullerian matrix of phosphorus optical rotor Is equal to Equation 5.

here, , and In the case of an ideal phase retarder with the absorption constants and phase delay angle of the optical absorption phase retarder becomes, is the rotation angle is the Mullerian matrix of the optical rotor.

And, the absorption constant is the electric field transmission ratio of the fast axis and the slow axis and has the same relationship as Equation 6.

And, when unpolarized light having no polarization dependence is incident, the Stokes vector of Equation 3 above Is expressed as in Equation 7.

In addition, in the case of an ideal quarter-wavelength phase delay ( , , ), Equation 7 becomes as simple as Equation 8.

On the other hand, the first phase retarder 400 is a broadband phase retarder that can be used in a wide wavelength band ranging from deep ultra violet (DUV) to near infrared (NIR), and as shown in FIG. delay angle decreases monotonically from about 150° to about 25° depending on the wavelength, and the electric field transmittance ratio has a characteristic showing fast oscillation around 1.0.

The Stokes vector of the light passing through the linear polarizer 200 and the first phase retarder 300 having the characteristics of FIG. 2 can be calculated using Equation 7, and the azimuth P of the polarizer 200 and the first Table 1 shows Stokes vectors corresponding to a representative (P, C) combination of the azimuth angle C of the phase retarder 400.

In Table 1, the polarization states are divided into three groups, the first group (xy) consists of linear polarization with the transmission axis parallel to the x-axis and linear polarization with the transmission axis parallel to the y-axis, and the second group (±45) consists of linearly polarized light with its transmission axis at +45 degrees with the x-axis and linearly polarized light with its transmission axis at -45 degrees with the x-axis. When a delayer is used), each is composed of

At this time, the six polarization states form mutually independent Stokes vectors, and four Stokes vectors can be selected by randomly selecting one Stokes vector from each group and one Stokes vector from among the remaining three Stokes vectors.

,

)조합에 대응되는 제1 그룹의 입사광 스톡스벡터와, (±

, ±

) 조합에 대응되는 제2 그룹의 입사광 스톡스벡터 및, (O,±

) 조합에 대응되는 제3 그룹의 입사광 스톡스벡터들을 이용하여 생성되며, 이때 제1 그룹의 입사광 스톡스벡터는 , 상기 제2 그룹의 입사광 스톡스벡터는 , 상기 제3 그룹의 입사광 스톡스벡터는 이고, 상기 입사광 뮬러행렬은 각 그룹에서 적어도 하나의 입사광 스톡스벡터를 포함하여 생성된다.That is, the incident light Muller matrix is (0,0), (

,

) the incident light Stokes vector of the first group corresponding to the combination, (±

, ±

) the Stokes vector of incident light of the second group corresponding to the combination, and (O,±

) is generated using the incident light Stokes vectors of the third group corresponding to the combination, wherein the incident light Stokes vectors of the first group are , the incident light Stokes vector of the second group is , the Stokes vector of the incident light of the third group is , and the incident light Muller matrix is generated by including at least one incident light Stokes vector in each group.

In addition, P + π is used instead of the azimuth angle P of the polarizer 200, which is a combination (P, C) of the azimuth angle P of the polarizer 200 and the azimuth angle C of the first phase retarder 300, which are optically equivalent combinations, or Among the combinations using C+π instead of the azimuth angle C of the first phase retarder 300, that is, combinations of (P+π,C), (P, C+π), and (P+π, C+π) It is also possible to set among ordered pairs corresponding to one combination.

, π+

)조합에 대응되는 제1 그룹의 입사광 스톡스벡터와, (π±

, π±

) 조합에 대응되는 제2 그룹의 입사광 스톡스벡터 및, (π,π±

) 조합에 대응되는 제3 그룹의 입사광 스톡스벡터들을 이용하여 생성될 수 있다.For example, the incident light Muller matrix is (π, π), (π +

, π+

) Stokes vector of incident light of the first group corresponding to the combination, (π±

, π±

) the Stokes vector of the incident light of the second group corresponding to the combination, and (π, π ±

) can be generated using the third group of incident light Stokes vectors corresponding to the combination.

The incident Muller matrix with the four Stokes vectors selected in this way Forming the determinant represents the wavelength dependence characteristic as shown in FIG.

According to Figure 4, the determinant has a maximum value of 2.0 near 270 nm (see FIG. 3) where the first phase retarder 400 exhibits an ideal quarter-wavelength phase delay characteristic, and is greater than 2.0 in a wavelength range that deviate from the ideal quarter-wavelength phase delay characteristic. It can be seen that it gradually decreases.

At this time, the magnitude and wavelength dependence of the determinant is the Stokes vector constituting the incident Muller matrix It varies greatly depending on the contents of, for example, one Stokes vector is selected from each group in Table 1, , It can be seen that the determinant of the incident Mueller matrix constructed by adding the Stokes vector corresponding to shows a very small size and irregular wavelength dependence as shown in FIG. 4 (b).

In addition, the inspection unit 600 does not satisfy the 4-minute-wavelength phase delay condition, and the outgoing light Stokes vector for the light passing through the second phase retarder 400 having light absorption and the analyzer 500 Determine the Stokes constant of

That is, the inspection unit 600 determines that the Stokes vector is After continuously passing the second phase retarder 400 having an azimuth angle C and the analyzer 500 having an azimuth angle A using the incident light as an incident wave, the intensity of the emitted light is measured as a function of (A, C), and then Analyze to determine the Stokes constant.

Stokes vector If the light passes through the second phase retarder 400 and the analyzer 500 continuously, the Stokes vector of the transmitted light Is equal to Equation 9.

here, and are each azimuth If the Mueller matrix and azimuth of the analyzer of is the Mueller matrix of the phase retarder, expressed as Equation 10.

That is, after substituting Equation 5 into Equation 10 and substituting it into Equation 9, the intensity of light passing through the second phase delayer 400 and the analyzer 500 is A as in Equation 11 ( It can be expressed as a function of analyzer azimuth) and C (second phase retarder azimuth).

here,

is,

S ₀ ,S ₁ ,S ₂ ,S ₃ are Stokes constants of incident light, which can be determined from a combination of light intensities represented by I(A,C), preferably a combination that satisfies Equation 12. there is.

That is, according to the above embodiment, in the Muller matrix ellipsoid of the PC ₁ SC ₂ A arrangement structure, without rotating the phase retarders, the combination of the azimuth angle of the polarizer and the azimuth angle of the phase retarder before the sample, and the azimuth angle of the phase retarder after the sample The optimal Mueller matrix can be determined through the azimuthal combination of analyzers.

100: light source, 200: polarizer,
300: first phase delayer, 400: second phase delayer,
500: analyzer, 600: inspection unit,
10: sample.

Claims (6)

In a Mullerian matrix elliptic system having a structure of arrangement of light source-polarizer-first phase retarder-sample-second phase retarder-analyzer,
The first phase retarder and the second phase retarder are phase retarders that deviate from the quarter-wavelength phase delay characteristics,
The azimuth angle of the polarizer and the first phase retardant is the incident light Muller matrix absolute value of Incident light Stokes vector such that is greater than 0.2 Muller matrix elliptic system, characterized in that set to a combination that satisfies.
According to claim 1,
The combination (P, C) of the azimuth angle P of the polarizer and the azimuth angle C of the first phase retarder,
(0,0),(

,

), (±

, ±

), (O, ±

) Muller matrix elliptic system, characterized in that set in.
According to claim 2,
The incident light Muller matrix is (0,0), (

,

) the incident light Stokes vector of the first group corresponding to the combination, (±

, ±

) the Stokes vector of incident light of the second group corresponding to the combination, and (O, ±

) Mullerian matrix ellipsoid, characterized in that determined using the third group of incident light Stokes vectors corresponding to the combination.
According to claim 3,
The incident light Stokes vector of the first group is ,
The incident light Stokes vector of the second group is ,
The incident light Stokes vector of the third group is ego,
The Muller matrix ellipsometer, characterized in that the incident light Muller matrix is determined by including at least one incident light Stokes vector in each group.
According to claims 2 and 3,
In addition, the combination of the azimuth angle of the polarizer and the azimuth angle of the first phase retarder is a combination of (P, C), (P + π, C), (P, C + π), and (P + π, C + π). A Muller matrix elliptic system, characterized in that set among ordered pairs corresponding to one combination of.
According to claim 1,
The intensity of the light passing through the second phase retarder with the azimuth angle C and the analyzer with the azimuth angle A is
as,
is set to
The Stokes constants of the incident light S ₀ , S ₁ , S ₂ , S ₃ are
Mueller matrix elliptic system, characterized in that it is determined from the intensity of light measured at the azimuth combination (A, C) of the second phase retarder and the analyzer.