KR102229335B1 - Distortion Correction and Application Method For Micro Spot Spectroscopic Ellipsometer Including High Magnification Optical System - Google Patents

Abstract

An object of the present invention is to provide a micro-spot spectral ellipse method capable of improving measurement accuracy by correcting a change in polarization state and distortion of an elliptic constant caused by optical devices having a large numerical aperture.
To this end, the distortion correction method of a micro-spot spectroscopic ellipsometer applying a high magnification optical system includes the steps of obtaining a distortion magnitude by a high magnification optical system, calculating an ideal elliptic constant using the distortion magnitude by the high magnification optical system, and the calculated ideal It characterized in that it comprises the step of correcting and applying the spectral ellipse data of the sample by using the elliptic constant.

Description

Distortion Correction and Application Method For Micro Spot Spectroscopic Ellipsometer Including High Magnification Optical System}

The present invention relates to a micro-spot spectroscopic ellipsometer to which a high magnification optical system is applied, and more particularly, to a technology for improving measurement accuracy by correcting a change in polarization state and distortion of an elliptic constant due to optical elements having a large numerical aperture.

Ellipsometry is variously used as a non-destructive measurement method in an industrial field using a variety of thin films, and is particularly useful in non-destructively measuring the thickness of a thin film in the semiconductor field.

Ellipsometry is a method of measuring and analyzing the changed polarization state of reflected light after incident light having a specific polarization state on a sample to obtain density change, optical thickness, complex orange index, etc., which are the factors that changed polarization. As, a device for this is called an elliptic system.

As the recent semiconductor process proceeds with a circuit line width of 1x nm, the process thickness and line width of the thin film are also reduced, and the demand for improving the spatial resolution is increasing even in the spectroscopic ellipsometer field, which is essential for monitoring the thickness of the thin film in the semiconductor field. have.

An ellipsometer including a focusing optical system that makes the area illuminating the surface of the sample very small is called a micro-spot spectroscopic ellipsometer. The micro-spot spectroscopic ellipsometer uses a focusing optical system to focus light on the surface of a sample, and a high magnification optical system is required to realize micro-spots in a very wide wavelength band from the DUV region to the near-infrared region.

In order to implement micro-spots, the applicant arranges the center of a focusing optical system composed of four reflectors to coincide with the optical axis in Korean Patent No. 1922973 to implement an optical system coaxial with the optical axis, and the incident angle of light incident on each reflector A four-reflector optical system was presented so that the reflection coefficients of the p-wave and s-waves according to the reflection are canceled by making this 10 degrees or less. In the above registered patent, a spot size of (10 um) was implemented.

In the above registered patent, a four-reflector focusing optical system is used to implement a small spot, and in order to minimize the change in polarization state that occurs when reflecting from a mirror constituting the focusing optical system, the angle of incidence to each mirror is maintained at 10 degrees or less. . However, as described above, when the angle of incidence to the mirror increases for the purpose of providing high magnification, the distortion of the measured elliptic constant increases when the change in the polarization state due to the reflection of light is at a level that cannot be ignored. There is a drawback that is not applicable.

In addition, Korean Patent Publication No. 2017-0004947 also minimizes the influence on the polarization state of incident light based on the adjustment of angles of incidence to various mirrors and reflection angles therefrom (which can follow a trajectory different from the trajectory of the incident beam). ) Technology to achieve the focusing of the beam of electromagnetic radiation onto the sample has been proposed, but if the angle of incidence to the mirror increases and the change in the polarization state due to reflection becomes insignificant, the distortion of the measured elliptic constant increases. It has the same problem that the elliptic method cannot be applied.

That is, when a high-magnification optical system is applied, the numerical aperture (NA) of elements constituting the optical system, such as a mirror or lens, increases, and accordingly, the incident angle of light incident on the device surface becomes very large. For example, in the case of a 10 magnification optical system, the angle of incidence has a range of approximately 0 to 30°.

가 왜곡된다.When the light enters the reflective surface of the optical system at a large angle and then reflects or refracts, the difference in the reflection or transmission coefficient between the p-wave and the s-wave increases, and the polarization state of the reflected or transmitted light changes.

Is distorted.

의 왜곡은 결정하려는 박막의 두께나 조성비 또는 광학물성 값들을 왜곡시키므로 마이크로 스폿 분광타원계의 활용에 심각한 악영향을 끼친다.Elliptic constant

Since the distortion of the film distorts the thickness, composition ratio, or optical property values of the thin film to be determined, it has a serious adverse effect on the utilization of the micro-spot spectroscopic ellipsometer.

Accordingly, it is an urgent need to develop a technology that can improve measurement accuracy by correcting changes in polarization state and distortion of elliptic constants caused by optical devices with a large numerical aperture.

Korean Patent Registration No. 1922973 "Micro-spot spectroscopic ellipsometer applied with 4-reflector" Korean Patent Publication No. 2017-0004947 "Beam focusing and beam focusing optical device"

The object of the present invention for solving the disadvantages of the background technology is to present a technique for correcting the change of polarization state and distortion of the elliptic constant by optical elements with a large numerical aperture, and through this, micro-spot spectroscopy using a high-magnification optical system. We are trying to develop the elliptic method.

According to a preferred aspect of the present invention for solving the problem, the steps of obtaining a distortion magnitude by the high magnification optical system, calculating an ideal elliptic constant using the distortion magnitude by the high magnification optical system, and calculating the calculated ideal elliptic constant There is provided a method for correcting distortion of a micro-spot spectroscopic ellipsometer to which a high magnification optical system is applied, comprising the step of correcting the spectral ellipse data of the sample by using.

And, the amount of distortion due to the high magnification optical system is defined by simulation using at least one of refractive index, thin film thickness information, and incident angle for the high magnification optical system, or by arranging the system at an incidence angle of 90° and using an elliptic constant measured without a sample. Can be defined by

According to the present invention, it is possible to provide a micro-spot spectroscopy elliptical method capable of improving measurement accuracy by correcting a change in polarization state and distortion of an elliptic constant caused by optical devices having a large numerical aperture.

Applicant actually implemented a micro-spot smaller than 5 um using a high magnification (10X) optical system, maintaining this spot size, and applying the distortion correction technology developed in this proposal to the measured distorted spectral elliptic constant. Was derived.

_{1 and 2 are spectral ellipse data of SiO 2} (d=100 nm)/c-Si samples measured or calculated using a spectroscopic ellipsometer.

Hereinafter, a preferred embodiment of the present invention will be described in detail with reference to the accompanying drawings.

The electric field of light passing through each element and reaching the photodetector in the PCSA (P: polarizer, C: compensator, S: sample, A: analyzer) arrangement applied in a general elliptical system uses Jones matrix and Jones vector. Then it is expressed as follows.

는 시료의 작용을 나타내는 존스행렬로서, 분광 타원계로 측정하고자 하는 시료의 타원상수(ψ, Δ)에 대한 이상적인 측정값을 나타낸다.In Equation 1, te is a transmission axis, fs is a fast axis, T is a matrix representing an action of each element, and R is a rotation matrix. double

Is the Jones matrix representing the action of the sample, and represents the ideal measurement value for the elliptic constant (ψ, Δ) of the sample to be measured with a spectroscopic ellipsometer.

,

,

,

인 4개의 광학소자가 있을 경우 시료면에 입사하는 빛의 전기장은 수학식 2와 같다. In the micro-spot spectroscopic ellipsometer, a high-magnification optical system is symmetrically located between the polarizer/top box and the sample, and between the sample and the analyzer, and the polarization action by the optical elements constituting the high-magnification optical system is reflected as follows. For example, each Jones matrix between the polarizer/top box and the sample

,

,

,

When there are four optical devices, the electric field of light incident on the sample surface is equal to Equation 2.

In addition, the electric field after the light reflected from the sample passes through the same four high-magnification optical elements and the analyzer positioned symmetrically between the sample and the analyzer is shown in Equation 3 below.

을 수학식 4와 같이 정의한다.In order to find out the effect of polarization by high magnification optical devices on the elliptic constant, the pseudo Jones matrix of the sample is as follows.

Is defined as in Equation 4.

을 다음과 같이 정의하면 수학식 5와 같다.Here, the effective Jones matrix of the high-magnification optical element

Equation 5 is defined as follows.

는 수학식 6과 같이 간단한 표현으로 나타낼 수 있다.Pseudo-Jones Matrix

Can be expressed as a simple expression as shown in Equation 6.

Substituting Equation 2 into Equation 3 and using Equation 6, the electric field of light passing through each element and reaching the photodetector in the PCSA ellipsometer having a high magnification optical system is expressed as Equation 7.

에 포함되어 있으며 일반적인 타원계를 사용하여 구한 타원상수와는 수학식 6와 같이 관계지어짐을 확인할 수 있다. 따라서 수학식 5로 표현되는 고배율 광학소자들의 유효존스행렬

을 먼저 구한 다음 수확식 6을 역방계산한 아래 수학식 8에 시료의 유사존스행렬

을 대입하여 시료의 존스행렬

을 구하고 이로부터 타원상수를 얻는다. Comparing Equation 1 and Equation 7, the elliptic constant measured in an ellipsometer with a high magnification optical system is the pseudo-Jones matrix of the sample.

It can be seen that it is included in and is related to the elliptic constant obtained using a general elliptic system as shown in Equation 6. Therefore, the effective Jones matrix of high-magnification optical devices represented by Equation 5

The pseudo-Jones matrix of the sample is obtained in Equation 8 below, which is calculated in reverse direction of the harvesting equation 6.

By substituting

And get the elliptic constant from it.

의 비대각선 성분들은 0이므로 고배율 광학소자들의 유효존스행렬은 수학식 9와 같이 쓸 수 있다.On the other hand, if the high magnification optical elements have rotational symmetry and the light incident on the optical element is on the incident surface relative to the sample surface, the effective Jones matrix of the high magnification optical element

Since the non-diagonal components of are 0, the effective Jones matrix of high-magnification optical devices can be written as in Equation 9.

도 대각성분만을 가지므로 수학식 10과 같이 쓸 수 있다.At this time, the pseudo-Jones matrix

Since also has only diagonal components, it can be written as in Equation 10.

In Equation 10, the pseudo value means an elliptic constant measured when distortion occurs by a high magnification optical system.

The final goal of the present invention is to obtain the elliptic constants (ψ, Δ) in a state where there is no distortion as shown in Equation 2. The elliptic constants of Equation 2 have a simple and specific expression as shown in Equations 11 and 12 below.

As shown in Equation 8 above, if the distortion magnitude (eff) due to the high magnification optical system is known, the ideal elliptic constant can be obtained from the measured pseudo elliptic constant.

The amount of distortion caused by the high-magnification optical system (Equation 9) is defined by simulation using the refractive index, thin film thickness information, and incident angle for the high-magnification optical system, or the system is arranged with an incidence angle of 90° and the elliptic constant measured without a sample is used. Can be defined by

Equations 11 and 12 can be obtained by substituting the Jones matrices and Equations 9 and 10 representing the action of the Equation Sample into Equation 8 and arranging them.

The ideal elliptic constant (tanψ) can be obtained by _{measuring tanψ pseudo} distorted by a high magnification optical system and then calculating the distortion amount tan ² ψ _eff by the high magnification optical system as a correction value as shown in Equation 11.

In addition, the ideal elliptic constant (Δ) can be obtained by _{measuring Δ pseudo} distorted by the high magnification optical system and then calculating the distortion amount Δ _eff by the high magnification optical system as a correction value as shown in Equation 12.

_{1 and 2 are spectral ellipse data of SiO 2} (d=100 nm)/c-Si samples measured or calculated using a spectroscopic ellipsometer.

과 같이 표현될 수 있으며, 여기서, α 및 β는 푸리에 계수를 의미한다. 도 1과 도 2는 시료의 분광타원 데이터 성분 중 포톤 에너지에 대한 α 및 β값의 변화를 나타낸 것이다.The intensity of light received from the analyzer is

It can be expressed as, where α and β mean Fourier coefficients. 1 and 2 show changes in α and β values for photon energy among spectral ellipse data components of a sample.

In the graphs of Figs. 1 and 2, three curves are shown. Among them, _{the line consisting of "□ " represents the spectral ellipse data of the SiO 2} (d=100 nm)/c-Si sample measured using a spectroscopic ellipsometer to which a high-magnification reflective micro-spot (spot size 5 um) was applied. . In addition, _{the ideal spectral elliptic graph of the sample having the SiO 2} (d=100 nm)/c-Si structure is shown as a solid line, and the distortion of the elliptic constant due to the high magnification optical device is The applied and calculated spectral ellipse graph is indicated by a dotted line.

1 and 2, the ideal spectral ellipse graph (solid line) is very different from the measured value of a spectroscopic ellipsometer to which a high magnification optical system with elliptic constant distortion by a high magnification optical element is applied, but a subdivision ellipse graph calculated by applying the distortion It can be confirmed that the (dotted line) matches well with the measured value.

Therefore, through the above-described method, an ideal measurement result can be obtained even in a state in which the elliptic constant is distorted by the high magnification optical element.

Although the present invention has been described in connection with the above-mentioned preferred embodiments, it is possible to make various modifications or variations without departing from the spirit and scope of the invention. Accordingly, the scope of the appended claims will include such modifications or variations that fall within the gist of the present invention.

Claims (4)

In the distortion correction method of a micro spot spectroscopic ellipsometer to which a high magnification optical system is applied,
Obtaining a distortion level due to the high magnification optical system;
Calculating an ideal elliptic constant by using the distortion magnitude by the high magnification optical system;
Compensating the distortion correction and application method of the micro-spot spectroscopic ellipsometer using a high magnification optical system, comprising the step of correcting the spectral ellipse data of the sample using the calculated ideal elliptic constant.
The method of claim 1,
The amount of distortion due to the high magnification optical system is defined by simulation using at least one of refractive index, thin film thickness information, and incident angle for the high magnification optical system, or by arranging the system with an incidence angle of 90° and using an elliptic constant measured without a sample. Distortion correction and application method of a micro-spot spectroscopic ellipsometer applying a high-magnification optical system, characterized in that.
The method of claim 1,
The distortion amount due to the high magnification optical system is expressed by the following equation, and tanψ _eff and Δ _eff represent the amount of distortion of the elliptic constant.

The method of claim 3,
The ideal elliptic constants tanψ and Δ are calculated through the following equations, and distortion correction and application method of a micro-spot spectroscopic ellipsometer employing a high magnification optical system, characterized in that:

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