JPS6042901B2 - automatic ellipse meter - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to an ellipsemeter, and in particular to a phase difference between a parallel component Rp and a perpendicular component Rs of a beam that is elliptically polarized by reflection from a sample having a property to be measured. Δ
The present invention relates to an ellipsemeter that uniquely and unambiguously determines the ellipsometer parameter Ψ of an elliptically polarized beam.

Ellipsometers are well known in the prior art. In a classical ellipsemeter, the beam is passed through two manually adjustable polarizing elements. The polarizing element is adjusted to an angle such that the beamed detector produces zero output. By measuring the relative angles of the polarizing elements that produce zero output, the two ellipsometer parameters Δ and ψ are determined.
Here, Δ is the phase difference between the parallel component Rp and the perpendicular component RS of the electric vector of the reflected beam, and TanlP=in. From these parameters, two unknown properties of the optical system that are to be measured are determined. For example, if an elliptically polarized beam is produced by reflection of a linearly polarized beam from a film surface, the thickness and refractive index of the film are determined. If the beam was reflected from a deformed sample, the complex index of refraction of that sample is determined. In other words, the polarization transfer function of the optical system is generally determined. A property of the ellipsometer has been found to be the ability to measure the thickness of a transparent film that reflects a plane-polarized beam to produce an elliptically-polarized beam.

However, a drawback of the classic manual system is that it slows down the processing time and may require a single measurement time due to the manual inspection of the area. Therefore, several methods have been developed to automate the measurement procedure. One such automatic ellipsometer device is disclosed in Japanese Patent Application No. 49-58037.
(Japanese Patent Publication No. 54-10473).

In this application, a second polarizing element (or analyzer) is continuously rotated and the intensity of the transmitted light is monitored as a function of the instantaneous rotation angle of the analyzer. From the resulting data, the polarization state of the light is calculated and thus determined by angle ψ and Δ Fourier analysis. The above method using a rotating analyzer is
It has some desirable features when compared to other automatic ellipsometer techniques.

It has high speed (measurement within 2.0 seconds) and accuracy (polarization azimuth α can be measured with a standard deviation of 0.002 degrees). The high accuracy associated with the rotating analyzer approach results in part from the use of Fourier analysis of the measured light intensity data. The Fourier series is a constant plus a sinusoidal component twice the angular rotation frequency of the analyzer. Random noise in the individual determination of intensity is thus effectively averaged out during one revolution of the analyzer photon, improving measurement accuracy. However, as pointed out earlier,
The rotating analyzer approach suffers from the disadvantage of not being able to distinguish between complementary polarization states of equal orientation and ellipticity but opposite orientation (i.e., left-handed or right-handed polarization states, other things being equal). have

This drawback manifests itself in the ambiguity of the power value of the phase angle Δ. However, the angle ψ is clearly determined. Specifically, the angle ψ clearly varies from 0 degrees to 90 degrees, but Δ varies from 0 degrees to 360 degrees, so the phase angle Δ
This creates ambiguity. Of course, this ambiguity in Δ is due to the fact that when using the rotating analyzer technique, the second measurement is made after changing the polarization by a known amount, or the knowledge of the specimen being measured is obtained in advance. It can be removed by keeping it.

However, the need for a second measurement reduces the speed advantage of the rotating analyzer approach, and knowledge of the required amount is not always available in advance. Although there are basic alternative polarization techniques that do not have the above drawbacks, they cannot be applied to ellipsometers.

For example, D. Clarke and J.F. Grainger classified all the basic combinations of retardation plates and linear detectors and photons as polarimeters (but not as ellipsometers), and one of them It was shown that the two combinations completely determine the polarization state with only one measurement. Regarding this, the authors co-authored 1 Polarized Light and Optical Measurement J (Polarized Light Measurement J) DOpt.
icalMeasurementlPergamOnl
Please refer to NewYOrkll97l). The aim of the invention is to provide a new digital Fourier ellipse meter in which the ellipse parameter Δ is determined unambiguously and uniquely.

Here Δ is the phase angle, ie the difference between the parallel and perpendicular components of the light beam that is elliptically polarized by reflection. Another object is to provide an improved automatic method capable of unambiguously determining the elliptical polarization phase angle Δ in a single measurement, while having all of the desirable features of the rotating analyzer ellipsemeter described in the aforementioned application. To provide an ellipse meter.

In the apparatus and method for achieving these objects, rather than providing a continuously rotating analyzer as disclosed in said application, the analyzer is fixed and a quarter-wavelength analyzer is placed in the path of the light beam. The delay element is rotated continuously.

As in that application, the intensity of the light passing through the analyzer is measured by a photodetector, which generates a signal proportional to the intensity of the light striking it. However, because of the provision of a rotating quarter-wavelength delay element in the present invention, the photodetector signal contains information that allows the phase angle Δ to be unambiguously and uniquely determined when it is numerically Fourier analyzed. Specifically, the Fourie coefficient for determining Δ is SinΔ
and COsΔ, thus uniquely determining the sign of the phase angle Δ (ie, the direction of the elliptical polarization). In contrast, in a rotating analyzer type ellipsemeter, only the COsΔ term is available, and since Δ varies from 0 degrees to 360 degrees, the phase angle Δ cannot be uniquely determined without a second measurement. I couldn't do it. Furthermore, the presence of the term Sin Δ in the present invention allows accurate measurement of Δ. Especially this thing is 1
This is the case when c0sΔl is close to 1. Another object of the invention is to provide a method for adjusting an ellipsemeter to compensate for imperfections in a rotating quarter-wave retardation element. Figures 1 through 3 are excerpted from said application and provide background for understanding the improvements provided by the present invention.

In FIG. 1, a monochromatic light source 10, for example a 1 mw HeNe laser, generates a light beam fixed at a known angle (typically about 451) to the plane of incidence of a light beam 21 impinging on the surface of a sample 20. The light then passes through a polarizing prism 12.

This beam further passes through a fixed quarter wave plate 14 at a known angle (this may not be optional) and a spot defining hole 18. The reflected beam 22 is elliptically polarized and passes through a beam-defining aperture 24 and a continuously driven (eg, 5 revolutions per second) rotating polarizing prism (analyzer) 26. Light from analyzer 26 is detected by a linear light sensing device 28, such as a photomultiplier tube. FIG. 2 shows the electrical parts of the ellipsemeter of FIG. 1 in detail. In addition to the elements shown in FIG. 1, FIG. 2 shows an angle encoder 30 associated with the rotary analyzer 26 and its two output terminals 31 and 33. In the actual configuration, the encoder 30 is connected to the analyzer 2
6 is placed on a hollow shaft that rotates. The output from terminal 31 provides one trigger pulse per revolution of analyzer 26, and terminal 33 provides a pulse for each equal division of one revolution of analyzer. The pulse appearing at terminal 33 is
It is applied to an analog-to-digital (AD) converter 32 as a trigger. The output terminal 35 of the photomultiplier tube 28 is
Connected as an analog input of converter 32. The output signal of the photomultiplier tube 28 generally takes a waveform such as 34. Converter 32 converts the analog input from the photomultiplier tube to a discrete digital output. Its output takes a waveform such as 36. The digital output of converter 32 is applied to data analyzer 38. The data analyzer may be a small computer such as an IBMll3O. Data analyzer 38
In , the data are numerically Fourier analyzed to determine the Fourier coefficients (it is these coefficients that are needed for the ellipsoidal analysis of the reflected light, not the total Fourier transform). Once the normalized second harmonic coefficients of the Fourier transform are ascertained, standard elliptic equations are evaluated to find the computable parameters characterizing the optical properties of the sample. These parameter values may be typewritten or visually displayed on a storage cathode tube, numeric display tube, or the like. More specifically, data analyzer 38 of FIG. 3 is shown performing numerical Fourier analysis of digital input waveform 36.

In the case of the rotating analyzer type ellipse meter of the patent application, the normalization coefficient A2,■ of the Fourier series is determined. The standard elliptical type is
The sample is evaluated to obtain the desired sample parameters such as film thickness and refractive index. Also shown in FIG. 3 is a printing press 40 and a visual indicator 42. The information printed or displayed includes the azimuth angle α, ellipticity X1, elliptic meter parameters ψ and Δ,
These include film thickness and refractive index. In order to perform Fourier analysis using the data analyzer 38, I●B●
IBM INSTALLATION NEWS published by IBM
A program called System/7 Fast Fourier Transform Program RPQP82OOO, described in LETl'ER) can be used.

Further, as shown in the said application and described herein, a means for mounting the polarizing element 12 is used such that the angle of the polarizing element relative to the incident surface is at a selected angle, such as 0, 17, 45, 900, etc. Set.

FIG. 4 is a schematic diagram illustrating the improved ellipsometer of the present invention. For ease of understanding, the elements in FIG.
They have the same numbers as the elements shown in FIGS. Thus, monochromatic light source 10 sends a light beam through fixed polarizer 12 and the beam is projected onto the surface of sample 20 at an angle of incidence φ. Of course, like the rotating analyzer ellipsemeter of the above-mentioned application, the polarizer 12 is adjustably mounted so that its azimuth angle is set at different discrete predetermined angles with respect to the plane of incidence. The reflected beam is then passed through a rotating quarter-wave optical retarder (or compensator) 50, such as a quarter-wave plate. The compensator is rotated at a constant angular velocity by a suitable drive shaft. The rotation angle of the compensator at that time is 0c
It is indicated by. The light passing through the compensator is directed to a fixed analyzer 52 and the light passing through the analyzer impinges on a photodetector 28 which sends an electrical analog signal to terminal 35 that is a function of the intensity of the light passing through the analyzer 52. occurs in To facilitate understanding of the present invention, the following combinations of optical element azimuth angles appear to yield the simplest form of intensity data obtained.

The polarizer 12 is set at an angle of 45 degrees to the plane of incidence, and the fixed analyzer 52 is set at an angle of 0 degrees. Furthermore,
The fast axis of the compensator 50 assumes an instantaneous angle θc with respect to the plane of incidence, and assuming the compensator is ideal (i.e., has exactly a quarter wavelength delay), the photodetector The intensity 1 (θc) of the light in the vessel 28 is expressed by the following equation. Here, the Fourier coefficients in (1) are as follows.

It is only the ratio of the Fourier coefficients that contains the desired information about the sample parameters ψ and Δ. Therefore, the average intensity level A. It is convenient to divide each coefficient by . Therefore, by solving equations (4) and (5), ψ and Δ are as follows.

From the above equations, it can be seen how measuring the intensity of light transmitted by the combination of rotating compensator 50 and fixed analyzer 52 as a function of compensator azimuth 0c completely determines the polarization state of the incident light. We explain what results in a clear determination and therefore a clear determination of the sample ● parameters ψ and Δ for the ellipse meter.

Additional information to remove ambiguity is that the intensity 1 (0c) in equation (1) is a constant value, the COS2Oc term, and Sin2θ
It arises from the fact that it consists of the C term, the COS4Oc term, and the Sin4θC term). This means that the intensity obtained from a rotating analyzer type ellipse meter as shown in Figure 3 is a constant and COS2
This is in contrast to the case where it consists only of the O term and the Sin2θ term.
Referring to equation (1), one of the sinusoidal components, B4s
in4θc contains four times the compensator angular frequency and thus yields essentially the same information as data obtained from a rotating analyzer ellipsemeter, while the sinusoidal terms A2COS2θc and 8Sin2Oc contain twice the angular frequency. Note that the phase of the latter term changes by 180 degrees by changing the polarization direction of the incident light. Thus, it is clear that the numerical Fourier analysis method employed in the rotational compensator type ellipsemeter can be applied to the analysis of the intensity data I(θc) obtained with the rotational compensator type ellipsemeter in FIG. The advantages of the ellipse meter according to the invention are also clear from equations (2) to (7).

Since ψ is always between 0 degrees and 90 degrees, it is uniquely determined, but Δ is between 0 degrees and 360 degrees, so Δ is determined based on equation (5) or equation (7). Also, two values are obtained and it is not possible to determine which of them it is. However, in the ellipsemeter of the present invention, the correct value of Δ can be determined by using the additional information contained in the term (■) as shown in equation (3). That is,
The Fourier coefficients that determine Δ are B4 in equation (5) and B2 in equation (3), and these equations include SinΔ and COs
Since Δ is included, Δ can be uniquely determined by solving both equations. The axial encoder 30 of FIG. 4 provides the same functionality as in the rotating analyzer ellipse meter 30 shown in FIG.

However, the axial encoder 30 of FIG. 4 is driven by the same axis that rotates the compensator 50, and the axial encoder 30 of FIG.
The timing pulses generated above correspond to the rotation of compensator 50. This point differs from the case of the rotating analyzer 26 shown in FIGS. 1 and 2. The intensity signal from the output of the photodetector 28 is digitized in an AD converter 32 and then numerically Fourier analyzed in a data analyzer 38 to determine the values of Δ and Ψ as described in the aforementioned application. Ru. The embodiment of the invention of FIG. 5 is similar to the embodiment of FIG. 4, except that a rotational compensator 50 is placed in the path of the incident beam 21 between the polarizer 12 and the sample 20.

The same result is obtained from the configuration of FIG. 5, but in the mathematical calculations the azimuthal angles of polarizer 12 and analyzer
The opposite is true for analysis of diagram composition. For the above calculations, an ideal compensator was assumed.

In practice, the compensator only provides approximately a quarter-wave delay for all wavelengths of interest and exhibits negligible differences in propagation along its two principal axes. In classical ellipsometers, these imperfections required two manual zero measurements to compensate for the non-ideal compensator. As explained below, the rotational compensator type ellipsemeter of the present invention has the following features:
It is calibrated to compensate for these imperfections. These imperfections in the compensator affect the measured data as follows.

Express the complex propagation ratio in the slow direction of the compensator in terms of two compensator parameters Ψc and Δc (assuming Ψ and Δ are sample parameters): Here, ideally Ψc=45 degrees and Δc=9
It is 0 degrees. The coefficients of equation (1) are as follows. The effects of compensator imperfections are removed by characterizing the compensator prior to determining corresponding values of Ψc and Δc. This is done, for example, by taking measurements such that the light from the polarizer 12 of FIG. 4 is directed directly to the rotation compensator 50 without being reflected from the sample. Such a configuration optically corresponds to Ψ=4 in the above
5 degrees, equivalent to setting Δ=0 degrees. The resulting coefficients for the calibration measurements are therefore of the form: Solving the compensator parameters gives the following:

Furthermore, there is an experimental test for this measurement. That is, A. is equal to h and A. must be zero. By characterizing (i.e., calibrating) the compensator in this manner, the sample parameters can be determined for the imperfect compensator by solving the equation: Here, therefore, the correctly compensated value for the two values of Δ allowed by equation (16) is determined from the value of B2 as before.

Equation (16) is equivalent to equation (7), indicating that compensator imperfections only affect the value of the sample parameter Ψ. As is clear from these descriptions, Fourier analysis of the intensity versus compensator azimuth data allows for a fast and unique determination of the sample parameters Ψ and Δ.

This, in turn, eliminates the ambiguity associated with the value of Δ determined by a rotating analyzer ellipse without sacrificing speed. Further, the rotational compensator type ellipsemeter of the present invention has Sln
Generating a Δ term results in a more accurate determination of the value of Δ, especially when the value of IcOsΔI approaches 1. Furthermore, the effects of non-ideal compensators are accurately compensated for by the rotating compensator ellipsemeter of the present invention without making any rough assumptions that the compensators are ideal. In the above description,
The symbols Rp and Rs were applied to the parallel and perpendicular components of the electric vector of the elliptically polarized reflected light beam, respectively. Additionally, sample ellipse parameters (Ψ and Δ) were defined for RpRs above. This Rp and R
Although the use of s may be taken to assume plane-polarized incident light with an orientation of 45 degrees from the plane of incidence, the present application is also relevant to the general case of elliptically polarized incident and reflected light. . In this case, it is defined as follows. Kokoreichi'
Pi? EL are the parallel and perpendicular components of the elliptically polarized incident light beam, respectively, and E♂ and E are the parallel and perpendicular components, respectively, of the elliptically polarized reflected light beam.

Rp and Rs are thus the sample reflection coefficients for parallel and perpendicularly polarized light, respectively. Ellipsometer sample parameters ψ and Δ are related to Rp and Rs by the following relationships: Thus, in general, Δ is the phase difference between the parallel reflection coefficient Rp and the perpendicular reflection coefficient Rs of the sample, and ψ is defined as follows.

Here, the vertical line indicates the absolute value of the complex ratio Rp/Rs.

The invention allows a complete and unambiguous determination of ψ and Δ for the general case of elliptically polarized incident and reflected light.

[Brief explanation of drawings]

FIG. 1 is a schematic diagram of the mechanical part of the rotating analyzer type ellipse meter disclosed in the prior application, FIG. 2 is a schematic diagram of the electrical part of the ellipse meter of FIG. FIG. 4 is a schematic diagram showing the data analysis and display functions of the ellipse meter shown in FIG.
The figure is a partial schematic diagram of another embodiment of the improved ellipsemeter. 10... Light source, 12... Polarizer, 20
...Sample, 22 ...Reflected beam, 2
8...Photodetector, 30...Axis encoder, 31, 33...Terminal, 32...AD
Converter, 38... Data analyzer, 50...
Compensator, 52...analyzer.

Claims (1)

[Claims] 1 A monochromatic light source arranged to direct a light beam of a known wavelength onto the sample at a known angle of incidence, and a monochromatic light source placed in the path of the incident light beam to plane-polarize the incident light beam and at a given angle relative to the plane of incidence of the beam. a polarizing element fixed at an angle, an analyzer placed in the path of the elliptically polarized light beam reflected from said sample, and said analyzer for generating an electrical signal that is a function of the intensity of the reflected light beam. in the path of the light beam for periodically changing the polarization of the light beam in an automatic ellipse comprising a photoresponsive device responsive to the beam passing through the ellipsoid, an angular encoder, an analog-to-digital converter, and data analysis means. a rotating optical compensator is provided, the analyzer is fixed at a known angle with respect to the plane of incidence, and a first pulse is generated for each revolution of the optical compensator to determine the selected rotation angle during one revolution; the angular encoder is associated with the optical compensator to generate a second pulse every time, the analog-to-digital converter is responsive to the pulses from the angular encoder and an electrical signal from the optically responsive device to is digitized based on the second pulse, and when the electrical signal is subjected to Fourier numerical analysis, it has a sin Δ term and a cos
The signal is such as to produce a Fourier coefficient including a Δ term (where Δ is the phase difference between the parallel component Rp and the perpendicular component Rs of the electric vector of the beam reflected from the sample), and the data analysis means calculates the phase difference Δ and Angle Ψ (tanΨ=R
An automatic ellipsemeter, characterized in that, in response to the digital signals of the transducers and the first pulse, Fourier analysis is performed on the digital signals to determine p/Rs).