JP5368507B2 - Surface characteristic analysis system with self-calibration function - Google Patents

Abstract

Two phase modulators or polarizing elements are employed to modulate the polarization of an interrogating radiation beam before and after the beam has been modified by a sample to be measured. Radiation so modulated and modified by the sample is detected and up to 25 harmonics may be derived from the detected signal. The up to 25 harmonics may be used to derive ellipsometric and system parameters, such as parameters related to the angles of fixed polarizing elements, circular deattenuation, depolarization of the polarizing elements and retardances of phase modulators. A portion of the radiation may be diverted for detecting sample tilt or a change in sample height. A cylindrical objective may be used for focusing the beam onto the sample to illuminate a circular spot on the sample. The above-described self-calibrating ellipsometer may be combined with another optical measurement instrument such as a polarimeter, a spectroreflectometer or another ellipsometer to improve the accuracy of measurement and/or to provide calibration standards for the optical measurement instrument. The self-calibrating ellipsometer as well as the combined system may be used for measuring sample characteristics such as film thickness and depolarization of radiation caused by the sample.

Description

  The present invention relates generally to a system for measuring surface properties of a sample, such as a semiconductor, and more particularly to such a system with a self-calibration function.

  This application is a continuation-in-part of US patent application Ser. No. 09 / 246,922 filed on Feb. 9, 1999.

  Spectrophotometers and ellipsometers have been used to measure surface properties such as film thickness and refractive index of single or multiple layers on a substrate such as a semiconductor. Commonly found materials on semiconductors include oxides, nitrides, polysilicon, titanium and titanium nitride. The ellipsometer can utilize a single wavelength or broadband light source, a polarizer, a modulator, an analyzer and at least one intensity detector. In this type of conventional ellipsometer, light from a light source is modulated and detected by a detector. The detector signal is analyzed to calculate ellipsometric parameters. This type of ellipsometer is described, for example, in US Pat. No. 5,608,526.

  Ellipsometric measurements are sensitive to environments such as temperature changes and mechanical vibrations. For this purpose, ellipsometers are periodically calibrated to account for such environmental effects. Standard samples of known thickness and optical properties have been used during calibration. However, with the continuous downsizing of semiconductor devices, an ultrasensitive ellipsometer that can measure a coating layer with a thickness on the order of several angstroms has been developed. These systems require a standard sample with a thin film for accurate calibration. When such thin film standards are used, even minor oxidation or contamination can affect and result in significant calibration errors. Accordingly, it would be desirable to provide an improved surface optical measurement system such as an ellipsometer with better calibration characteristics. In International Application No. PCT / US98 / 11562, a stable wavelength calibration ellipsometer is used to accurately determine the film thickness on a standard sample. The measurement results from the calibration ellipsometer are used to calibrate other optical measurement devices in the thin film optical measurement system. However, to do this, it is necessary to calibrate the standard sample with a calibration ellipsometer each time the thin film optical measurement system is used for measurement, which can be cumbersome. In addition, the properties of one or more coatings on the standard sample may change between calibration and measurement times, especially if not all measurements are made immediately after the calibration procedure. .

  US Pat. No. 5,416,588 presents another approach where sufficiently small phase modulation (typically on the order of 3-4 °) is applied by a photoelastic modulator (PEM). Yes. By limiting the phase modulation to a few degrees, the detectable signal is reduced proportionally, so that the signal-to-noise ratio of the schema in US Pat. No. 5,416,588 is for many applications. May be below desired level. By using only small phase modulation, the amount of information obtained about the parameters of the measurement system itself is limited, which may make it impossible to characterize all the important system parameters in some systems.

  None of the above systems are completely satisfactory. Accordingly, it would be desirable to provide an ellipsometer with improved calibration characteristics that do not have the above difficulties. It is particularly desirable to provide an ellipsometer with a self-calibration function.

US patent application Ser. No. 09 / 246,922 US Pat. No. 5,608,526 International Application No. PCT / US98 / 11562 US Pat. No. 5,416,588 US Pat. No. 4,306,809 US Pat. No. 5,747,813

"ANALYSIS OF SEMICONDUCTOR SURFACES WITH VERY THIN NATIVE OXIDE LAYERS BY COMBINED IMMERSION AND MULTIPLE ANGLE OF INCIDENCE ELLIPSOMETRY", Ivan OHLIDAL and Frantisek LUKES, "Applied Surface Science 35 (1988-89) 259-273, North Holland, Amsterdam "Rotating-compensator multichannel ellipsometry for characterization of the evolution of nonuniformities in diamond thin-film growth," Joungchel Lee et al., Applied Physics Letters, Vol. 72, No. 8, February 23, 1998, pp. 900-902

  An ellipsometer with a self-calibration function is proposed. Instead of calibrating ellipsometer system parameters that may change over time or due to environmental factors, they can be derived from data measured with the ellipsometer along with ellipsometric parameters. Therefore, there is no need for a standard sample or calibration ellipsometer. All the user needs to do is derive the system parameters along with the ellipsometric parameters so that any changes in the system parameters that can affect the measurement accuracy of the ellipsometric parameters can be taken into account. Since the system parameters can be derived from the same data from which the ellipsometric parameters are derived, there is no need to assume that the system parameters remained the same between the calibration process and the measurement process. Changes can also be explained accurately. The present invention is also not limited to small phase modulation. Thus, the signal-to-noise ratio of the instrument is sufficient for self-calibration in a wide range of systems and applications.

  In a preferred embodiment, a beam of radiation having a linearly polarized component is provided to the sample. Radiation from the beam modified by the sample is detected. The polarization of the beam of radiation is modulated prior to its detection, and one or more ellipsometric parameters of the sample and one or more parameters of the system used in the above process are derived without limitation on the magnitude of the modulation. The

  In conventional ellipsometers, substantially unpolarized radiation is supplied to the polarizer by the light source, polarizing the radiation before the radiation is applied to the sample, and the radiation from the polarized beam is changed after modification by the sample. The radiation is passed to the analyzer before it is applied to the detector. In the conventional schema, either the polarizer or the analyzer is rotated, but not both. As one improved design in aspects related to the present invention, the beam of radiation is passed through a first rotating polarizer prior to application to the sample. Radiation from the modified beam by the sample is also modulated by the second rotating polarizer to provide a modulated beam. Radiation from the modulated beam is detected by a detector. From the detector output, one or more ellipsometric parameters of the sample are obtained. Preferably, system parameters as well as one or more ellipsometric parameters are derived from the detected radiation in order to self-calibrate the system and increase measurement accuracy. Also preferably, the beam of radiation is passed through a fixed polarizer between the radiation source and the detector.

  As yet another improved design, radiation from a beam having a polarization component is provided to the sample. Radiation from the beam modulated by the sample is detected. The radiation from the beam is modulated before or after modification by the sample, but before its detection by the rotating polarization element. The detected modulated radiation is also passed through a fixed linear polarizer prior to its detection. Next, one or more ellipsometric parameters of the sample can be derived from the detected radiation.

  Another factor that affects the measurement accuracy of the ellipsometer is the change in focus due to sample tilt or sample height variation. In conventional ellipsometry, the optical path used to detect focusing accuracy and sample tilt is separate from the path used for ellipsometry measurements. This results in errors due to drift or upset between the two subsystems. The present invention diverts a portion of the radiation directed at the detector to a sensitive detector for detecting inaccuracies in focusing due to factors such as sample tilt or changes in sample height. Intended. This feature can be used in other surface optical measurement systems such as ellipsometry as well as spectrophotometry.

  In semiconductor manufacturing, it is often done to keep small electrical contact pads on the wafer that can be used for ellipsometric measurements, in which case the area is often square. The illumination beam in ellipsometry is typically directed at the sample at an oblique angle. Therefore, if the illumination beam has a circular cross section, the resulting illumination spot on the sample will be elliptical. Since the size of a square pad reserved for ellipsometry on a semiconductor may be small, it may be difficult to fit an elliptical spot within such a pad. If a cylindrical objective lens is used to focus the illumination beam on the sample, this has the effect of flattening the elliptical spot and well within the pad boundary. Preferably, the cylindrical objective lens focuses the illumination beam into a spot that is substantially circular in shape.

  The ellipsometer described above is advantageously used with another optical instrument for measuring the sample. Preferably, ellipsometer and other optical instrument outputs can be used to derive sample information and ellipsometer parameters to enhance measurement accuracy. In one application, the combination system may be used to measure sample film thickness information and the depolarization of radiation caused by the sample. Derived depolarization can exhibit sample properties such as surface roughness.

  Alternatively, the various configurations of the ellipsometer can be used alone to measure the film thickness and the depolarization caused by the sample, with or without deriving the ellipsometer system parameters from the same measurement output.

  For simplicity of description, identical components are identified by the same numbers in this application.

1 shows an ellipsometer using two phase retarders illustrating a first embodiment of the present invention. 2 is a graph plot illustrating an example of a detector signal as a function of time at the detector output of the system of FIG. Fig. 4 shows a self-calibrating ellipsometer using two rotating polarization elements illustrating a second embodiment of the invention. 4 is a graph plot of detector signal over time illustrating the detector output of the system of FIG. FIG. 6 is a schematic diagram illustrating the angular definition of various elements that change the polarization of radiation directed at a sample. 4 is a flow chart illustrating a method for deriving ellipsometric parameters and system parameters in the systems of FIGS. 1 and 3 for illustrating the present invention. Illustrating eight self-calibrating ellipsometers illustrating additional embodiments of the present invention, each using two or more polarization elements or a combination of phase retarders and polarization elements. Illustrating eight self-calibrating ellipsometers illustrating additional embodiments of the present invention, each using two or more polarization elements or a combination of phase retarders and polarization elements. Illustrating eight self-calibrating ellipsometers illustrating additional embodiments of the present invention, each using two or more polarization elements or a combination of phase retarders and polarization elements. Illustrating eight self-calibrating ellipsometers illustrating additional embodiments of the present invention, each using two or more polarization elements or a combination of phase retarders and polarization elements. Illustrating eight self-calibrating ellipsometers illustrating additional embodiments of the present invention, each using two or more polarization elements or a combination of phase retarders and polarization elements. Illustrating eight self-calibrating ellipsometers illustrating additional embodiments of the present invention, each using two or more polarization elements or a combination of phase retarders and polarization elements. Illustrating eight self-calibrating ellipsometers illustrating additional embodiments of the present invention, each using two or more polarization elements or a combination of phase retarders and polarization elements. Illustrating eight self-calibrating ellipsometers illustrating additional embodiments of the present invention, each using two or more polarization elements or a combination of phase retarders and polarization elements. FIG. 2 is a schematic diagram of a sample tilt and focus detection subsystem illustrating a portion of the system of FIG. 1 and another aspect of the present invention. FIG. 4 is a schematic diagram of a sample tilt and focus detection subsystem illustrating part of the system of FIG. 3 and another aspect of the present invention. 1 is a schematic diagram of a combined measuring instrument including a spectroscopic ellipsometer and an ellipsometry system, illustrating a preferred embodiment of the parent application invention. FIG. FIG. 10 is a perspective view of the ellipsometry system of FIG. 9. FIG. 10 is a simplified schematic diagram of a portion of the system of FIG. 9 for ellipsometric parameter measurement. 11B illustrates the illumination aperture of FIG. 11A. FIG. 2 is a simplified schematic diagram of a portion of a system for measuring ellipsometric parameters, illustrating another embodiment of the parent application invention. FIG. 10 is a simplified schematic diagram of a system for measuring the ellipsometric parameters of FIG. 9 in which an illumination beam or reflected beam is passed through an aperture, illustrating a preferred embodiment of the parent application invention. FIG. 13B is a schematic diagram of the aperture of FIG. 13A associated with the sample birefringence axis, illustrating the invention of the parent application.

  FIG. 1 shows an ellipsometer using two phase retarders, illustrating a first embodiment of the present invention. As shown in FIG. 1, the ellipsometer 10 includes a radiation source 12, which can provide substantially single wavelength radiation. An ultrastable helium neon laser may be used to provide substantially single wavelength radiation. Radiation from the source 12 is passed through a fixed polarizer 14. The fixed polarizer 14 is such that the radiation passing through it has a linearly polarized component. The fixed polarizer 14 is preferably a linear polarizer that is fixed in that orientation for the remaining optical components of the system 10. Alternatively, the fixed polarizer 14 may have elliptical polarization that includes a linearly polarized component in the radiation that passes through it. As explained, radiation with a linearly polarized component is preferably supplied to the modulator 16, but this is not required and that radiation with the polarized component supplied to the modulator 16 is sufficient. It will be understood that it is within the scope of the present invention.

  Radiation 11 having a polarization component, preferably a linear polarization component, exiting the polarizer 14 is focused by a lens 16 and passed through a phase retarder 18 and applied to a sample surface, such as a semiconductor wafer 20, which is The polarization of the radiation including the polarization state of the polarization component is changed by reflection or the like. For samples other than semiconductor wafers, the radiation can be altered by transmission, scattering, diffraction or further processes, but such and other variations are within the scope of the invention. After being modified by the sample 20, the modified radiation 13 is passed through a second phase retarder 22, collected by a lens 24, passed through a second fixed polarizer 26, and applied to a low noise photodetector 28. Is done.

  The retarders 18, 22 are rotated at different speeds to modulate the polarization of the radiation before and after the polarization by the sample 20. The radiation detected by the detector 28 is supplied to the data acquisition unit 30 in order to derive the ellipsometric parameters of the wafer 20.

  The system 10 differs from the polarimeter proposed by Azzam in US Pat. No. 4,306,809, which is fully incorporated herein by reference. Azzam derives the Mueller matrix of the sample. The system 10 can be used to derive not only the ellipsometric parameters using the radiation detected from the detector 28, but also the parameters of the components in the system 10 itself. These system parameters include, for example, the overall magnification of fixed polarizer 14 and analyzer 26, angle (polarization axis orientation) and circular attenuation compensation, and retarder 18, 24 angle, phase, linear attenuation and polarization modulation (retarder). Dance) amplitude and any polarization in the radiation supplied by the radiation source 12 is included. The overall magnification may include source intensity and detector responsiveness. The angles of the polarizer 14 and the analyzer 26 can be changed by the sample tilt in the direction across the plane of incidence of the radiation.

  As will be shown more clearly below, using the system 10 of FIG. 1, 25 harmonics are generated, which is more than enough to determine both ellipsometric and system parameters. Since the system parameters are derived from the output of the detector 28 along with the ellipsometric parameters, the system 10 is self-calibrating so that there is no need to calibrate the system parameters beforehand. Thus, there is no need to use a standard sample or calibration instrument for calibration. Each time a measurement is made, system parameters are derived at the same time as the ellipsometric parameters, so that the ellipsometric parameters are accurately derived without being adversely affected by fluctuations in the system parameters, where these system parameters are equally accurate. Can be calculated. In addition, system parameters such as attenuation compensation, depolarization and aperture integral effects can be difficult to calibrate in conventional systems. In contrast, these factors are automatically taken into account in the system 10 of FIG.

  FIG. 2 is a plot of a graph showing an example of detector signal as a function of time at the output of detector 28. Instead of a phase retarder or other phase modulator, the elements 18, 22 can also be polarizers.

  FIG. 3 shows a self-calibrating broadband ellipsometer 100 using two rotating polarization elements or phase retarders to illustrate a second embodiment of the present invention. Initially, it is assumed that two rotating polarizer elements are used in system 100. As shown in FIG. 3, system 100 includes a broadband source 102. In order to provide broadband radiation, it may be desirable to use xenon lamps as well as deuterium lamps to cover a broad spectrum, including the deep ultraviolet region, so that the radiation supplied by source 12 is in the range of 190 to about 1 micron. It reaches. Obviously, light sources providing multiple wavelength radiation (eg, from multiple lasers) or other wavelengths can also be used and are within the scope of the present invention.

  The fixed polarizer 14 causes the radiation passing therethrough to have a polarization component, preferably linearly polarized light. Radiation having such a component is fed to a rotating polarization element or phase modulator 106 and focused on the sample 20 by a mirror 108. Radiation modified by the sample 20, such as by reflection or transmission (or any of the processes listed above for FIG. 1), is collected by the collection mirror 110 and passes through the rotating polarization element 112 to the fixed analyzer 26. Relayed. The radiation exiting the analyzer 26 is then fed to a spectrometer 120 for separating the broadband radiation into various wavelength components so that the intensity of the various wavelengths can be detected individually. Such intensity is then provided to the data acquisition system 30 for analysis.

  In order to avoid chromatic aberration, focusing and focusing mirrors are used instead of lenses, and spectrometers are used to separate the various wavelengths in the detected broadband radiation into measuring wavelength components. The radiation source 102 is a broadband source instead of a laser. FIG. 4 is a graph plotting the intensity signal in one of the wavelength components detected by the spectrometer 20. Unlike systems in which a phase retarder is used, a rotating linear polarizer passes substantially no radiation when its polarization axis is perpendicular to that of the fixed polarizer 14. For this reason, the intensity periodically becomes substantially zero.

式中、初期角度Ｐ₀ およびＡ₀ は、ｔが０のときの偏光子および解析器要素１０６、１１２の初期角度に相当する。 FIG. 5 is a schematic diagram illustrating the relative orientation of the entrance plane, the axis of the fixed polarizer 14 and the axis of the rotating polarizing element 106 to illustrate the embodiment of FIG. FIG. 5 is a view taken along a direction opposite to the direction of the illumination beam 122 (ie, looking inside). As shown in FIG. 5, the reference x-axis is along the entrance surface of the beam 122 directed to the sample 20 and its reflection 124. The axis of the fixed polarizer 14 is along the arrow x ′ at the angle P1, and the axis of the rotating polarizing element 106 is along the arrow x ″ at the angle P ₀ + P (t) from the x axis. The element 106 is rotated. Therefore, its axis changes as a function of time t. Therefore, if P ₀ is the angle of that axis at time 0, the angle of that axis at time t is P ₀ + P (t). ₀ + A (t) is the angle of the rotation analyzer 112 with respect to the entrance plane when viewed along the direction opposite to the direction of the beam 124 changed (reflected in the case of FIG. 3) in FIG. Therefore, if the polarizing element 106 rotates at the frequency f _P and the polarizing element 112 rotates at the frequency f _A , the polarization angle of the axis of the rotating polarizing elements 106 and 112 is expressed by the following equation (1): P _R t) given by a a _R (t) a (wherein t is time It is).

In the equation, the initial angles P ₀ and A ₀ correspond to the initial angles of the polarizer and analyzer elements 106, 112 when t is zero.

The detector signal S ^(m) _{D at the} spectrometer 120 is then modulated by these rotating polarization elements and recorded as a function of time t. Here, “m” in the equation for the detector signal indicates that this is a measured detector signal rather than a theoretical one from the model. This same note applies to other quantities below.

  One example of a detector signal is shown in FIG. As shown below, 25 harmonics can be derived from the measured detector signal, in which case the model harmonics and 25 harmonics to derive ellipsometric and system parameters are derived. You can compare. However, before discussing such a comparison, the model of the system must first be considered, as explained below.

として表すことができる。
式中、
Ｓ_P （Ｐ）：試料に入射するビームの４×１ストークスベクトル、
Ｍ_s ：試料の４×４ミュラー行列、
Ｓ’_A （Ａ）：解析器中の要素を表すミュラー行列の第１行の投射。 System modeling <br/> Mueller matrix representation of the detector signal Analytically, the detector signal is

Can be expressed as
Where
S _P (P): 4 × 1 Stokes vector of the beam incident on the sample,
M _s : 4 × 4 Mueller matrix of the sample,
S ′ _A (A): projection of the first row of the Mueller matrix representing the elements in the analyzer.

  In the last part of Equation 2, for simplicity, P (t) and A (t) are simply written as P and A, and it is understood that these are functions of time. The same simplification is made in the description below.

式中、
Ｒ：ミュラー回転行列、
Ｍ_P1：固定偏光子１４のミュラー行列
Ｍ_P ：生成側の回転偏光要素１０６のミュラー行列。 The generation side of the element modeling system 100 on the polarization generation side includes a fixed polarizer 14, a rotating polarizer 106 and a mirror 108. All system parameters and rotation angle P on the generator side are encoded into the Stokes vector S _P (P). The Mueller formulation is then used to describe the light behavior in each element on the production side and the propagation from one element to the next. Assuming that the light source 102 is completely unpolarized, the following equation is obtained:

Where
R: Mueller rotation matrix,
M _P1 : Mueller matrix of the fixed polarizer 14 M _P : Mueller matrix of the rotating polarization element 106 on the generation side.

式中、
Ｍ_A1：固定解析器２６のミュラー行列
Ｍ_A ：解析側の回転偏光要素１１２のミュラー行列。 Modeling Elements on the Analysis Side The analysis side has a mirror 110, a rotating polarizer 112, and a fixed polarizer 26. All analysis-side system parameters and the rotation angle A of the polarizer 112 with respect to the x-axis are encoded in the projection of the first row of the Mueller matrix representing the analysis-side element S ′ _A (A).
Similarly,

Where
M _A1 : Mueller matrix of the fixed analyzer 26 M _A : Mueller matrix of the rotating polarization element 112 on the analysis side.

式中、ａ₀₀，ａ₀₁，，，は、システム１００の生成側を特徴付ける係数である。 From the harmonics related to the rotation angle on the polarization generation side of the Fourier analysis mathematical expression (3), each element in the Stokes vector S _P (P) has five harmonics, that is, DC of the rotation frequency f _P , 2 It is found to consist of heavy and quadruple harmonics.

In the equation, a ₀₀ , a ₀₁ , and are coefficients that characterize the generation side of the system 100.

式中、ｂ₀₀，ｂ₀₁，，，は、システム１００の解析側を特徴付ける係数である。 Similar to the harmonics related to the rotation angle on the analysis side, the first row of the analysis-side Mueller matrix consists of five harmonics.

In the equation, b ₀₀ , b ₀₁ , and are coefficients that characterize the analysis side of the system 100.

The harmonics of the detector signal Obviously, the detector signal consists of 25 harmonics.

の最小化により、高調波係数Ｆ_c0 ^(m) 、Ｆ_cn ^(m) 、およびＦ_sn ^(m) 、ｎ＝１，２，，，１２が決定される。回帰において、ベクトルｘは次式として定義される。

Regression
Regression of harmonic coefficient F Preferably 100 to several thousand data points in the time domain are obtained by measurement. Sample structure (film index and thickness) and system parameters (incident angles, angles P ₀ , P ₁ , A ₀ , A ₁ , depolarization, etc. for fixed polarizers and analyzers) are directly derived from detector signal data Can be regressed. However, this regression is non-linear. Non-linear regression of 1000 data points is not very efficient. On the other hand, the regression of the F coefficient is linear, thus improving the regression efficiency. The following formula,

, Harmonic coefficients F _c0 ^(m) , F _cn ^(m) , and F _sn ^(m) , n = 1, 2,. In regression, the vector x is defined as

Sample Structure and System Parameter Regression In the above linear regression, sample structure and system parameters are not used. On the other hand, harmonic coefficients are related to sample structure and system parameters. In fact, they are nonlinear functions associated with sample structure and system parameters. These nonlinear relationships are obtained by the system model and the membrane model.

式中、「ｍ」が付された量は、上記で説明したように分光計１２０からの測定された検出器信号から得られ、モデルからのものではない。 Methods for constructing such systems and membrane models are known to those skilled in the art and will not be described in detail here. As a result, the sample structure and system parameters can be returned to the following equation (11).

Where the quantity labeled “m” is obtained from the measured detector signal from the spectrometer 120 as described above and not from the model.

  The process for deriving ellipsometric parameters and system parameters is described with reference to FIG. Initially, raw data is obtained as described above, which appears at the output of spectrometer 120 (block 150). A Fourier analysis is performed on the data to obtain 25 measured biharmonic coefficients (blocks 152, 154). The membrane model and system model are configured as shown in equation 10 (block 156). System parameters considered may include one, some or all of those discussed above (block 156). The regression algorithm of Equation 11 above is then executed to solve for the harmonic coefficient F (block 158). From these F-factors, ellipsometric parameters n, k and system parameters may then be derived (block 160). System parameters that can be derived from the spectrometer output include, for example, the overall magnification, angle (polarization axis orientation) and circular attenuation compensation of the fixed polarizer 14 and analyzer 26, and the angle of polarizer 106 and analyzer 112, depolarization. , And any polarization of radiation provided by source 102 is included. The same model and process as described above can be used when the sources 102, 12 are replaced with radiation sources having several unpolarized components.

  Referring to FIG. 3, the rotation elements 106 and 112 are phase modulators such as phase retarders instead of polarization elements, and constitute substantially the same expression as the above expression, that is, the expressions (1) to (11). A process similar to that described above with respect to FIG. 6 can be performed to derive ellipsometric and system parameters. When elements 106, 112 are phase modulators, each of these elements has a fast axis and a slow axis. One of these two axes is treated as the element axis, and the same analysis above can be applied to measure and derive ellipsometric parameters n, k and system parameters. The same applies if one or more of the elements 106, 112 are a combination of one or more phase modulators and one or more polarizers.

  The method described above is also applicable to the system 10 of FIG. Thus, the output of detector 28 is then used to derive ellipsometric and system parameters as listed above for elements 12, 14, 16, 18, 22, 24 and 26 above.

  From the above analysis, 25 harmonics are sufficient to solve or derive ellipsometric and system parameters. In some applications, not all 25 harmonics are required to derive such parameters. In such a case, a simpler system than that shown in FIGS. 1 and 3 may be used instead. Such a configuration is shown in FIGS. 7A-7H. To simplify the drawing, the light source, detector, data acquisition and analysis device are omitted. 7A-7B illustrate a conventional ellipsometer that uses two polarizers. In FIG. 7A, unpolarized light passes through the rotating polarizer 206 and is supplied to the sample 20. The radiation reflected by the sample is passed through a fixed polarizer 226 and sent to a detector to derive ellipsometric parameters. In FIG. 7B, unpolarized radiation is passed through the fixed linear polarizer 214 and applied to the sample 20. The reflected radiation is then passed through the rotating polarizer 212 before it is applied to the detector to derive ellipsometric parameters.

  The configurations illustrated in FIGS. 7C-7H are possible and are advantageously used in accordance with the present invention. Thus, in FIG. 7C, unpolarized radiation is passed through the rotating polarizer 206 and applied to the sample 20, and the radiation modified by the sample is then passed through the rotation analyzer 212, whether the radiation is single wavelength or broadband. To a detector such as detector 28 or spectrometer 120. In FIG. 7D, unpolarized radiation is applied to the sample 20 first through the fixed polarizer 214 and then through the rotating polarizer 206. The modified radiation is passed to the fixed analyzer 226 and sent to the detector. In FIG. 7E, unpolarized radiation is passed through the fixed polarizer 214, modified by the sample 20, and passed through the rotation analyzer 212 and fixed analyzer 226 and applied to the detector. In FIG. 7F, unpolarized radiation is applied to the sample 20 through the fixed polarizer 214, the rotating polarizer 206, and the radiation modified by the sample is passed through the rotational analyzer 212 to the detector. In FIG. 7G, unpolarized radiation is applied to the sample 20 through the rotating polarizer 206, and the radiation modified by the sample is sent to the detector through the rotational analyzer 212 and the fixed analyzer 226. The configuration of FIG. 7H is the same as the configuration of FIG. 3 except that no focusing mirror is used.

  Thus, in the configurations of FIGS. 7C, 7F, 7G and 7H, before and after modification by the sample, it can be changed by a rotating polarizer or analyzer, in which case the radiation can pass through one or more fixed polarizing elements. You can not pass. In the configurations of FIGS. 7D and 7E, the radiation is passed through a fixed polarization element before and after modification by the sample, but only one rotating polarizer or analyzer is used either before or after modification by the sample. Not both before and after the change.

  When the instrument or configuration of FIGS. 7C-7E is used, five harmonics may be generated from the detected signal. The five harmonics may be sufficient to derive ellipsometric and system parameters for some applications. In certain applications, more harmonics may be necessary or desirable, and for these applications, FIGS. 7F, 7G, 7H and 3 would be desirable.

  The above analysis can be modified slightly for any one of the configurations of FIGS. 7C-7H described above. Obviously, if no mirrors are used as in FIG. 3, the system parameters that require these mirrors may be omitted in the analysis. If no rotating polarizer is used to change the radiation before it is applied to the sample, the variable P representing the rotational axis angle of the rotating polarizer can be set to a constant or zero. If no rotation analyzer is used to modify the radiation after it has been reflected or otherwise changed by the sample, the amount A representing the angle of the rotation analyzer can also be set to a constant or zero. . Apart from such differences, the above analysis can be applied to derive ellipsometric parameters in the configurations of FIGS. 7C-7H.

  For reasons discussed above, it may be advantageous to derive system parameters along with ellipsometric parameters for some applications, but also do not derive system parameters as in the configurations of FIGS. 3 and 7C-7H. It may be sufficient to simply derive the ellipsometric parameters. Such and other modifications are within the scope of the present invention.

  In order to generate 25 harmonics, the two polarizers, modulators (18, 22 and 106, 112) should be rotated at different speeds. If the rotation speed of one polarizer or modulator is an integer multiple of the rotation speed of the other pair, there may not be enough information for 25 harmonics to be derived from the detector signal. . Therefore, in order to derive 25 harmonics, it is desirable that the rotational speed of each of the two polarizers or modulators is an integer that cannot be divided by the rotational speed of the other polarizer or modulator. In other words, it is desirable that the maximum and minimum common denominators of two integer velocities be 1. Further, in order to obtain sufficient detector information, at least one of the two modulators or polarizers is more than 13 times while the detector signal is detecting radiation modulated by the sample and by the modulator or polarizer. It is desirable to rotate with full rotation.

  These two polarizers or phase modulators can be rotated continuously or intermittently. If the rotation is intermittent, the detector can be used to detect while the phase modulator or polarizer is stationary. Instead of using a rotating polarizer or a rotating retarder, a photoelastic modulator or a Pockels cell can be used instead. The rotary retarder can be a Fresnel ROM. The configuration of FIGS. 7A-7G can be accomplished by removing one or more elements 14, 106, 112, 26 from the system 100 of FIG. 3, which can be accomplished by the motor 250 of FIG. The algorithm described above with respect to FIG. 6 and the equations can be performed by data acquisition 30, which can simply be a computer.

  FIG. 8A is a schematic diagram of a portion of the system of FIG. 1 and an apparatus for sensing sample tilt or sample height. As mentioned above, in conventional measurement systems, the tilt or height of the sample is measured via a separate optical path that is different from the measurement path. This can make the system unwieldy and inaccurate. Despite a properly calibrated system, measurement of sample tilt and height is important because such inaccuracies can lead to measurement errors. Thus, as shown in FIG. 8A, after being modified by the sample, the radiation passes through a modulator, such as phase modulator 22 or rotating polarizer 112, through lens 24 and stationary analyzer 26, and to grating 302. It is done. Most of the energy of the beam appears as a zero order beam that passes through the aperture 304 to the detector 28. The radiation in beam 13 is substantially monochromatic, so that diffraction grating 302 diffracts the diffracted + 1st order beam toward detector 306. Detector 306 is positioned such that the total optical path from lens 24 to grating 302 and from grating 302 to detector 306 is substantially equal to the focal length of lens 24. Thus, instead, even if the surface 20a of the sample 20 is at a lower level 20a ′, the + 1st order rays from the surface 20a ′ and the grating 302 are still directed to the detector 306 in the same direction, thereby detecting The detection of the vessel 306 is not affected by the sample height. However, detector 306 detects the tilt of the sample from position 20a to position 20a ", which can cause a change in the direction of the + first order ray from grating 320. Thus, surface 20a has the proper tilt. If the detector 306 has been calibrated, the detector 306 can be used to detect sample tilt, in which case such detection is not affected by changes in sample height. .

  Detector 308 is installed to detect −1st order diffraction from grating 302. The detector 308 is calibrated to detect the sample surface 20a at an appropriate height. Thus, if the sample surface 20a is lowered (or raised) to the position 20a ′ shown in dotted line in FIG. 8A, this causes a change in direction of −1 diffraction and is sensed by the detector 308. It will be.

  FIG. 8B is a schematic diagram of a portion of the system 100 of FIG. 3 and an apparatus for sensing changes in sample tilt and sample height. Instead of using a grating that is wavelength dependent, two elements that are essentially transparent but slightly reflective, such as the two pellicles shown in FIG. 8B, can be used. Thus, the pellicles 312, 314 can be placed in the optical path between the fixed analyzer 26 and the spectrometer 120. Both pellicles are positioned almost perpendicular to the optical path and most of the radiation passes through the two pellicles, but a small amount of radiation is reflected in a direction slightly off the optical path by the pellicle to detector 316, Directed to 318 respectively. Detector 316 is placed so that the total optical path length between mirror 110 and pellicle 312 and between pellicle 312 and detector 316 is substantially equal to the focal length of mirror 110. For reasons similar to those described for detector 306 in FIG. 8A, detector 316 can be used to detect sample tilt without being affected by changes in sample height. Also, like detector 308 in FIG. 8A, detector 318 is calibrated to detect sample surface 20a at an appropriate height so that changes in sample height are detected by detector 318. .

  In semiconductor manufacturing, it is often done to ensure a small electrical contact pad area on the wafer that can be used for ellipsometric measurements, where the area is often square. The illumination beam in ellipsometry is typically directed at the sample at an oblique angle. Thus, if the illumination beam has a circular cross section, the resulting illumination spot on the sample will be elliptical. Since a square pad secured on a semiconductor for ellipsometry can be small in size, it can be difficult to fit an elliptical spot in such a pad.

  Using or adding a cylindrical objective lens to focus the illumination beam on the sample has the effect that the elliptical spot can be flattened to fit well within the pad limits. Preferably, the cylindrical objective lens focuses the illumination beam into a spot that is substantially circular in shape. Therefore, in order to flatten the illumination spot on the sample 20, the lens 16 of FIG. 1 can be a cylindrical lens, or a cylindrical lens can be added to FIG. Similarly, in order to make the illumination spot on the sample 20 flat, the mirror 108 in FIG. 3 can also be a cylindrical mirror, or a cylindrical mirror can be added. Preferably, the focusing force at the entrance surface of the lens 16 or mirror 108 or lens and mirror combination is such that the illumination spot is circular.

  The following description with respect to FIGS. 9 to 13B is taken essentially from Patent Application No. 09 / 246,922 filed on Feb. 9, 1999.

  FIG. 9 is a schematic diagram of a combined instrument including a spectroscopic ellipsometer and an ellipsometric system for illustrating a preferred embodiment of the parent application invention. Before discussing the combined instrument spectroscopic ellipsometer, the ellipsometric system 1008 will first be described in some detail with reference to FIGS. As will be shown below, preferably the system 1008 is advantageously used with a spectroscopic (or single wavelength) ellipsometer, as in the combination instrument of FIG. 9, while the system itself is used for sample measurements. Is also advantageous.

  The overall optical arrangement of the ellipsometric system 1008 is similar to the spectral reflectometer described in US Pat. No. 5,747,813 and retains its simplicity. However, unlike such a spectral reflectometer, the system 1008 of the parent application invention is more than a polarization insensitive reflectance spectrum as in the system of US Pat. No. 5,747,813. The ellipsometric reflectance spectrum is measured. Thus, the system 1008 is more sensitive to surface properties than the system of US Pat. No. 5,747,813. In a preferred embodiment, the parent application invention is illustrated as detecting radiation reflected by the sample, whereas the parent application invention was essentially conveyed by the sample, as described in this application. It will be understood that it will work if radiation is detected instead, and such and other variations are within the scope of the invention of the parent application and the present application. For simplicity, the preferred embodiment is described below as a measurement of emitted radiation, but it is understood that such an explanation can be easily extended to the measurement of transmitted radiation.

  The conventions showing the sample path, the reference path, the field illumination path, the measurement illumination path and the ellipsometer path are shown in the upper right corner of FIG. As noted above, the overall optical arrangement in a system for measuring ellipsometric parameters is described below with reference to FIGS.

  9 and 10 each show the same embodiment of the optical system according to the parent application invention for measuring ellipsometric parameters. The focusing portion and other optical elements of the system 1008 of FIG. 9 and the spectroscopic ellipsometer are omitted in FIG. 10 to simplify the illustration. These elements are described below with the diagram most clearly showing their arrangement with respect to other elements. Referring to FIG. 9, the optical system 1008 for measuring the relative reflectance spectrum of the wafer 1003 includes an illumination subsystem, a reflectometer subsystem, an observation subsystem, and an autofocus subsystem, and any particular An optical element can also be part of one or more subsystems. The illumination subsystem includes a lamp 1010 such as a xenon arc lamp that emits a light beam 1012 of visible and / or ultraviolet (UV) light, a lamp housing window 1014, an off-axis parabolic mirror 1016, a flip-in UV cutoff filter 1018, a color. It includes a filter wheel 1020, a plane mirror 1022, a concave mirror 1024, an aperture mirror 1028 with a flip-in 40 μm fine focus aperture 1030, a large achromatic lens 1032, a field illumination shutter 1031, a folding mirror 1036, and a small achromatic lens 1038. In FIG. 10, the objective lens 1040 includes mirrors 1040a and 1040b and a housing 1040 ′ for housing the mirrors, but oblique illumination from a spectroscopic ellipsometer (not shown in FIG. 10) between the housing and the wafer. There is enough space left for the beam.

  The illumination system provides a combined beam 1042 consisting of a measurement beam 25 and a field illumination beam 1034. The lamp 1010 emits a light beam 1012 through the lamp housing window 1014. The lamp housing window is not necessary for optical reasons, but is provided in case the lamp 1010 should crack or rupture. Xenon lamps are preferred over other lamps such as tungsten or deuterium lamps. This is because a xenon lamp gives a flatter output covering the spectrum from UV to near infrared. An additional deuterium lamp 1088 is used with the xenon lamp 1010 to cover a broader spectrum, including deep UV, to provide a sample beam having a wavelength component in the range of 190-220 nm. By using the two lamps together, the resulting combined spectrum of radiation supplied for sample detection can be extended to a range of about 190-800 to 830 nm. Extending the spectrum to the deep UV range is useful for photolithography. The radiation from lamp 1088 is focused by lens 1093, reflected by mirror 1095 to filter 1018, and combined with the radiation from lamp 1010 to form a combined beam 1012 '. Radiation from deuterium lamp 1088 can be included in or excluded from measurement beam 1025 by moving mirror 1095 along or out of the path of beam 1012 along arrow 1099.

  An off-axis parabolic mirror 1016 collimates the light beam 1012, which is combined with radiation from the lamp 1088 to form a beam 1012 ′, and then optionally with a flip-in UV cutoff filter 1018 and a color filter wheel 1020. Can be filtered. The flip-in UV cut-off filter 1018 partially limits the spectrum of the light beam 1012 ′ so that the first and second order diffracted beams do not overlap when the light beam 1012 ′ is diffused by the diffraction grating. Used for. A portion of the light beam 1012 ′ is reflected by the plane mirror 1022 to the concave mirror 1024 to form a measurement beam 1025. Concave mirror 1024 focuses measurement beam 1025 onto aperture mirror 1028.

  Another portion of the light beam 1012, the field illumination beam 1034, is focused near the folding mirror 1036 by the large achromatic lens 1032, which reflects the image of the lamps 1010, 1088 towards the small achromatic lens 1038. . A small achromatic lens 1038 collects the light in the field illumination beam 1034 before the light reflects from the aperture mirror 1028. The aperture mirror 1028 is a fused silica plate having a reflective coating on one side, and an aperture for the measurement beam 1025 provided by etching 150 μm square on the reflective coating. The aperture is placed on one of the conjugate diameters of the objective lens 1040. Field illumination can be blocked by placing a field illumination shutter 1031 in the optical path of the field illumination beam 1034.

  The narrow measurement beam 1025 and the wide field illumination beam 1034 are recombined at the aperture mirror 1028, the field illumination beam 1034 reflects off the front surface of the aperture mirror 1028, the measurement beam 1025 passes through the aperture and polarizer 1102, and the polarizer Can be moved into or out of the path of beam 1025 by motor 1101.

  FIG. 9 shows the reflectometer, observation and autofocus subsystem of optical system 1008, objective lens 1040, beam splitter mirror 1045, sample beam 1046, optional reference beam 1048, concave mirror 1050, plane mirror 1043, reference spectroscopic. Reference plate 1052 with meter pinhole 1056, Sample plate 1054 with sample spectrometer pinhole 1058, second folding mirror 1068, diffraction grating 1070, sample linear photodiode array 1072, reference linear photodiode array 1074, short Focal length achromatic lens 1080, mirror 1082, beam splitter cube 1084, pentaprism 1086, long focal length achromatic lens 1090, neutral density filter wheel 1097, third folding mirror 1091 and video camera 1 Including 96. Some of these components are not shown in FIG. 10 for simplicity.

  Several magnifications are possible for the objective lens 1040. In one embodiment, a Schwarzschild-type totally reflective objective lens can be attached to a rotatable turret that allows several different objective lenses (not shown) during the optical path of the sample beam 1046. You can put one of them. A low power refractive element can be included in the optical path of the sample beam 1046 without significantly affecting the measurements in the parent application invention.

  The measurement of the relative reflectance spectrum of the wafer 1003 will be described next. When the field illumination shutter 1031 is placed in the path of the field illumination beam 1034, the combined beam 1042 consists only of the measurement beam 1025. The combined beam 1042 is split by a beam splitting mirror 1045, which is a fully reflecting mirror placed to deflect half of the combined beam 1042 towards the objective lens 1040, thus forming a sample beam 1046, which is the combined beam. The other undeflected half of 1042 forms a reference beam 1048. Since the sample beam 1046 and the optional reference beam 1048 are derived from the same source, lamps 1010, 1088, and the combined beam 1042 is radially uniform, the reference beam 1048 and the sample beam 1046 have proportionally dependent spectral intensities. Furthermore, since the beam splitting mirror 1045 is a perfect reflector in half of the optical path rather than a partial reflector in the entire optical path, the continuous broadband spectrum is reflected with good brightness.

  Reference beam 1048 initially does not interact with beam splitting mirror 1045 but illuminates concave mirror 1050 instead. The concave mirror 1050 is slightly off axis so that the reference beam 1048 is reflected on the back of the beam splitting mirror 1045, in which case the plane mirror 1043 re-reflects the reference beam 1048 in line with the reference spectrometer pinhole 1056. To do. A plane mirror 1043 is provided to realign the reference beam 1048 with the sample beam 1046 so that both beams pass through respective spectrometer pinholes that are substantially parallel. This makes it easier to align the spectrometer elements for both channels. This is because the reference beam enters the spectrometer parallel to the sample beam.

  Since the reference beam 1048 does not interact with the surface of the beam splitting mirror 1045 that reflects the beam 1046, there is no loss of reference intensity as the reference beam 1048 passes through the beam splitting mirror 1045. Since the reference beam 1048 interacts with the mirror 1043 at the back of the beam splitting mirror 1045, no light has passed through the beam splitting mirror 1045, so these two mirrors are independent. Indeed, in another embodiment where it is not easy to place the two reflecting surfaces of the beam splitting mirror 1045 together on one optical element, the reflecting surfaces are on separate mirror elements.

  The focal length of the concave mirror 1050 is such that the reference beam 1048 is focused on the reference spectrometer pinhole 1056. Light that passes through the reference spectrometer pinhole 1056 and is reflected by the bending mirror 1068 is diffused by the diffraction grating 1070. The resulting first order diffracted beam is collected by a reference linear photodiode array 1074, thereby measuring the relative reference spectrum.

  The polarized sample beam 1046 is reflected from the beam splitting mirror 1045 toward the objective lens 1040, in which case the sample beam 1046 is focused on the wafer 1003 and the reflected sample beam 1046 ′ is reflected by the objective lens 1040 to the sample spectrometer. Focused on the pinhole 1058. The reflected sample beam 1046 ′ does not interact with the beam splitter 1045 on the reflected path. This is because the reflected sample beam 1046 ′ passes through the space behind the beam splitting mirror 1045, and the reference beam 1048 also passes there. Radiation from the reflected sample beam 1046 ′ from the sample 1003 passes through the analyzer 1104 before it reaches the pinhole 1058. The light that passes through the sample spectrometer pinhole 1058 and is reflected by the bending mirror 1068 is diffused by the diffraction grating 1070 according to the wavelength of the light. Similar to the reference beam, the resulting first order diffracted beam of the sample beam is collected by the sample linear photodiode array 1072, thereby measuring the sample ellipsometry spectrum. Since the two beams intersect at the diffraction grating 1070, the photodiode array that is apparently aligned with the sample beam 1046 in FIG. 10 is actually a photodiode array for the reference beam 1048, and vice versa. Polarizer 1102 and analyzer 1104 do not rotate and are preferably stationary. Accordingly, the analyzer 1104 analyzes the radiation that is changed by the sample and collected by the objective lens 1040 according to a fixed polarization plane.

  The relative reflectance spectrum is then obtained by simply dividing the sample light intensity at each wavelength by the relative reference intensity at each wavelength. This typically requires 512 division calculations, in which case a 512 diode linear photodiode array may be used to record the sample and reference spectra. In a preferred embodiment, the spectrum ranges from about 190 nm to 800 to 830 nm.

  In one embodiment of the parent application, the diffraction grating 1070 is a concave holographic grating and the spectrometer pinholes are 15 mm apart. Since neither beam can be centered on the grating at 15 mm intervals, the diffraction grating is holographically corrected to image multiple spectra. One such grating is Instruments S.M. A. Multiple spectral imaging grating made by Also, depending on the detector angle, the grating is designed so that the reflection from the detector falls away from the grating.

  The combined beam 1042, which may include field illumination, is reflected from the beam splitter mirror 1045 toward the wafer 1003. When reflectance spectrum measurement and autofocus are being performed, field illumination is off to minimize scattered light.

  The ellipsometry system 1008 in FIGS. 9 and 10 differs from that described in US Pat. No. 5,747,813 in that the sample beam 1046 is polarized in the system of the present application. Thus, when the sample beam 1046 is reflected toward the sample 1003 by the objective lens 1040, the beam focused on the wafer has multiple or multiple different polarization states. This will be explained more clearly with reference to FIGS. 11A and 11B. Sample beam 1046 is focused by mirror 1040a toward mirror 1040b, which then focuses the beam toward sample 1003 as shown in FIG. 11A. FIG. 11B is a schematic diagram of the illumination aperture of the sample beam 1046 when focused on the wafer 1003. The various quantities in FIGS. 11A and 11B are defined by referring to the cylindrical coordinates ρ, φ and θ, where ρ is the radius of the point in the coordinate system (distance to the origin) and φ is the point Is the angle from the surface perpendicular to the sample surface to the reference surface perpendicular to the sample surface, and θ is the angle from the normal line to the sample surface (incident angle to the normal line) connecting the point and the origin is there.

With respect to FIG. 11A, assume that the polarizer 1102 has a polarization plane defined by the plane of φ _P , so that the sample beam 1046 exiting the polarizer and reflected by the beam splitting 1045 also has this polarization. Yes. If the beam 1046 is reflected first by the mirror 1040a and then by the mirror 1040b that focuses the beam on the sample 1003, the beam focused on the sample 1003 can be various as shown in FIGS. 11A and 11b. Arrives at the entrance surface of In FIG. 11B, the polarization plane φ _{P of the} beam 1046 is indicated by 1103.

  From the above description, the beam splitting mirror 1045 bends approximately half of the polarized beam into the sample beam 1046 and passes the other half of the beam as the reference beam 1048. For this reason, the illumination aperture (shaded area 1106) in FIG. 11B appears in a substantially semicircular shape. Therefore, the radiation focused on the sample 1003 by the objective lens 1040 is incident on the sample with an incident surface extending in a semicircular region. Radiation incident on the wafer at one incidence surface at one value of angle φ in the region has s- and p-polarizations different from radiation of an incidence surface having another angle φ in the region. The s- and p-polarizations of radiation at different entrance planes, by definition, have different orientations, so that the polarization state of incident radiation at one entrance plane is different from that of radiation at another entrance plane. Accordingly, the radiation incident on the sample 1003 has multiple or multiple polarization states as a function of φ.

  The beam focused on the sample 1003 decreases in intensity according to the combined reflection coefficient of the objective lenses 1040a and 1040b as compared with the sample beam 1046, as will be described below. Radiation emanating from the sample beam 1046 and focused onto the sample by the objective lens 1040 is reflected by the sample, thereby again reducing its intensity and changing the phase of each polarization component as a function of the sample's reflection coefficient. Such radiation is reflected by objective lens 1040 and passes through beam splitting 1045 and analyzer 1104 to the spectrometer. In a preferred embodiment, the same objective lens that is used to focus the radiation onto the sample can also be used to collect the reflected radiation towards the analyzer and spectrometer, while this is necessary It will be appreciated that additional focusing objectives can be used in addition to the focusing objective, and that such and other variations are within the scope of the parent application and the present application.

式中、Ｅ_inは偏光子１１０２による偏光後のビーム１０４６中の放射の電場、Ｅ₀ はその振幅、Ｅ_s ⁱⁿ、Ｅ_p ⁱⁿはｓ−およびｐ−偏光に沿った放射の成分である。放射が対物レンズを出た後は、以下のようになる。

式中、Ｅ_out は試料１００３による反射後のビーム１０４６中の放射の電場、Ｅ_s ^out 、Ｅ_p ^out ｓ−およびｐ−偏光に沿った成分、さらにｒ^s _s （ｒ^o _s ）およびｒ^s _p （ｒ^o _p ）は試料（対物レンズ）についてのｓ−およびｐ−偏光についての反射係数である。対物レンズについての反射係数は、図１１Ａに示されるような２つの鏡の反射係数の積、すなわちｒ^o _s ＝ｒ^o1 _s ｒ^o2 _s およびｒ^o _p ＝ｒ^o1 _p ｒ^o2 _p である。φ_a の偏光面を有する解析器通過後、分光計における電界は、ｐ_a に沿って以下のように得られるであろう。

検出器電流は以下のように表現できる。

もし偏光子１１０２が省略されれば、半円形アパーチャについての検出器電流は以下のようになる。

式（１６）において、Ｒ^o _s 、Ｒ^s _s 、Ｒ^o _p 、Ｒ^s _p はそれぞれ｜ｒ^o _s ｜² 、｜ｒ^s _s ｜² 、｜ｒ^o _p ｜² 、｜ｒ^s _p ｜² として定義される。ｒ^o _s 、ｒ^s _s 、ｒ^o _p およびｒ^s _p が入射角の関数、すなわちρの関数であることは銘記しておかなければならない。図９〜図１１Ｂに示されるように偏光子１１０２が所定位置にある場合には、分光器における強度が試料および対物レンズのｓ−およびｐ−反射率の関数ならびにΔ^o 、Δ^s の関数である場合に一般式を導くことができ、Δ^o 、Δ^s は式、

（式中、ｒ^s _p 、ｒ^s _s はｐ−およびｓ−偏光における放射の試料表面の複合反射係数であり、ｒ^o _p 、ｒ^o _s はｐ−およびｓ−偏光における放射の対物レンズの複合反射係数である）で定義され、式中、Ψ^o 、Ψ^s 、Δ^o およびΔ^s もエリプソメトリックパラメータである。従って、システム１００８は偏光感受性である。 Consider radiation incident from a point 1105 having the coordinates (ρ, φ) of FIG. 11B into the semicircular illumination aperture, polarized and directed along the direction φ _P toward the origin on the sample surface. The electric field at this point can be decomposed into s- and p-polarized light shown in FIGS. 11A and 11B as follows.

Where E _in is the electric field of radiation in the beam 1046 after polarization by the polarizer 1102, E ₀ is its amplitude, E _s ⁱⁿ , E _p ⁱⁿ are the components of the radiation along the s- and p-polarizations. After the radiation exits the objective lens:

Where E _out is the electric field of radiation in the beam 1046 after reflection by the sample 1003, E _s ^out , E _p ^out s− and components along the p-polarization, and r ^s _s (r ^o _s ) and r ^s. _p (r ^o _p ) is the reflection coefficient for s- and p-polarized light for the sample (objective lens). The reflection coefficient for the objective lens is the product of the reflection coefficients of the two mirrors as shown in FIG. 11A, ie, r ^o _s = r ^o1 _s r ^o2 _s and r ^o _p = r ^o1 _p r ^o2 _p . After passing through an analyzer with a polarization plane of φ _a, the electric field in the spectrometer will be obtained along p _a as follows:

The detector current can be expressed as:

If the polarizer 1102 is omitted, the detector current for the semicircular aperture is:

In the formula _{^{(16), R o s,}} R s s, R o p, R s p are each ^{_{| r o s | 2, |}} r s s | 2, | r o p | 2, | r s p | 2 Is defined as It should be noted that r ^o _s , r ^s _s , r ^o _p and r ^s _p are functions of the incident angle, i.e. ρ. As shown in FIGS. 9-11B, when the polarizer 1102 is in place, the intensity at the spectroscope is a function of the s- and p-reflectances of the sample and objective lens as well as a function of Δ ^o , Δ ^s . In some cases, a general formula can be derived, where Δ ^o and Δ ^s are

(Where r ^s _p , r ^s _s are the combined reflection coefficients of the sample surface of radiation in p- and s-polarized light, and r ^o _p , r ^o _s are the objective lens of radiation in p- and s-polarized light. Where Ψ ^o , Ψ ^s , Δ ^o and Δ ^s are also ellipsometric parameters. Thus, system 1008 is polarization sensitive.

システムがΔにおける変化に対し感受性を有するには、２（φ_p −φ_a ）＝ｍπである。もしφ_p ＝φ_a'であれば下記のようになる。

Ｂ．φ₀ ＝π／２

もしφ_p ＝φ_a ＝π／２であれば下記のようになる。

Below are some special cases.
A. φ ₀ = π

For the system to be sensitive to changes in Δ, 2 (φ _p −φ _a ) = mπ. If φ _p = φ _{a ′} , then

B. φ ₀ = π / 2

If φ _p = φ _a = π / 2, then:

From the above analysis, the cosine coefficient cos (Δ ^o + Δ ^s ) of the third term of equations (18) and (20) is the same when the polarizer and analyzer angles are the same, ie polarizer 1102 and analyzer 1104. Is maximized when they have substantially the same plane of polarization. In other words, a single polarizer can be used to operate as both a polarizer and an analyzer, as shown in FIG. As shown in FIG. 12, a polarizer 1116 can be used to replace the polarizer 1102 and the analyzer 1104. The sample channel of the photodiode array is proportional to equation (19). In this configuration, only one polarizer is required and the polarizer and analyzer are self-aligned. As yet another option, if the splitter 1045 is a polarizing beam splitter, the polarizer 1102 and analyzer 1104 can all be omitted. In order to increase the film thickness detection sensitivity, a wave plate or other retarder element 1190 indicated by a dotted line is inserted between the beam splitter 1045 and the analyzer 1104 in FIG. 9 to obtain the equations (18) and (20). A phase shift can be introduced into the independent variable of the cosine coefficient cos (Δ ^o + Δ ^s ) of the third term. Preferably, the phase shift in the collected radiation caused by element 190 prior to analysis and diffusion is about π / 4. The mirror coating thickness of mirrors 1040a, 1040b can also be selected to improve sensitivity in thin film thickness detection, so that the total change in phase in the radiation focused and collected by mirrors 1040a, 1040b is approximately π / 2. This then causes Δ ^{o to} be π / 2 in the independent variable of the cosine coefficient cos (Δ ^o + Δ ^s ) in the third term of equations (18), (20), thereby causing the cosines in these equations to The term is converted to a sine term.

  The ellipsometric spectrum measured for the detector current in array 1072 can be used to derive useful information about sample 1003. For example, if the material types of many different layers on the sample 1003 are known so that their refractive index can be estimated, such a detector current derives the layer thickness and the exact refractive index. Can be sufficient. Methods for such derivation are known to those skilled in the art and need not be discussed at length here. Alternatively, the detector signal can be combined with ellipsometric measurements to derive film thickness and refractive index. It is advantageous to use broadband radiation for detection in ellipsometry systems. This is because data points can be obtained at many different wavelengths. Such an abundance of data points is very useful for determining the thickness and refractive index of multiple layers on a sample, allowing more accurate curve fitting algorithms to be applied or to verify measurement accuracy. Can be.

  System 1008 can also be used to detect other parameters of the sample surface. From the above equations and explanations relating to the figures, in particular FIG. 11A and FIG. 11B, the reflection spectrum detected by the spectrometer of the photodiode array 1072 uses information about Δ, which is an ellipsometric parameter in ellipsometry. It is commonly used and is related to the film thickness and refractive index at the sample surface. Thus, if certain aspects of the sample surface are known, such known aspects can be combined with ellipsometric parameter related information measured by system 1008 to provide useful information about the sample such as film thickness and refractive index. Can be derived.

  In a preferred embodiment, the spectrum obtained from the photodiode array 1072 is compared to a reference spectrum from the photodiode array 1074 to derive ellipsometric parameters, thereby improving the signal to noise ratio. However, for some applications, such ellipsometric parameters can be derived from the reflection spectrum alone without using the reference spectrum. For such applications, the reference beam 1048 is not required, and all components and reference spectra associated with the generation of the beam 1048 may be omitted in FIGS. Such and other variations are within the scope of the invention of the parent application and the present application.

  The spectroscopic ellipsometer 1300 of the combination measuring instrument in FIG. 9 will be described. As shown in FIG. 9, a portion of the radiation exiting the xenon arc lamp 1010 and through the focus 1018, 1020 is redirected by the beam splitter 1302 to the fiber optic cable 1304, which provides the radiation to the collimator 1306. To do. After being collimated, the beam is polarized by a polarizer 1310 and focused on a wafer 1003 by a focusing mirror 1312. Such beam reflections are collected by collection mirror 1314, reflected by folding mirror 1316, and passed through analyzer 1320 before being supplied to spectrometer 1322 and detector 1324 for detection. Polarizer 1310 and analyzer 1320 are rotated relative to each other so that the amplitude and phase of changes in the polarization state of beam 1308 caused by reflection at wafer 1003 can be measured. For a more detailed description of the operation of the spectroscopic ellipsometer 1300, see US Pat. No. 5,608,526.

  To measure a sample having a thin film layer, it may be desirable to use a combination instrument including an ellipsometric parameter measurement system 1008 and a spectroscopic ellipsometer 1300 as shown in FIG. System 1008 and spectroscopic ellipsometer 1300 are positioned such that sample beam 1046 and sample beam 1308 are focused on substantially the same spot on wafer 1003. The ellipsometric parameters measured by the system 1008 can then be combined with the ellipsometric parameters measured by the system 1300 to derive useful information such as film thickness and film refractive index. Ellipsometric parameters obtained with system 1008 and ellipsometric parameters obtained with system 1300 are "" ANALYSIS OF SEMICONDUCTOR SURFACES WITH VERY THIN NATIVE OXIDE LAYERS BY COMBINED IMMERSION AND MULTIPLE ANGLE OF INCIDENCE ELLIPSOMETRY ", Ivan OHLIDAL and Frantisek. LUKES, “Applied Surface Science 35 (1988-89) 259-273, North Holland, Amsterdam” (Non-Patent Document 1) can be used in combination.

  Even if the spectral range of some spectroscopic ellipsometers does not extend to deep UV, such as about 157 nm, it is possible to accurately measure the refractive index at such wavelengths by using a combination instrument. is there. Thus, the combination meter can be used to measure the refractive index across the combined spectrum of the spectroscopic ellipsometer and polarimeter system 1008. By using data from both the combination instrument and the system 1008 and the spectroscopic ellipsometer, the thickness and refractive index of the various films of the sample can be found at wavelengths in the spectroscopic ellipsometer spectrum. This thickness information can be used in conjunction with data from the combination instrument to find the refractive index of the film in the deep ultraviolet region. The number of detectors in arrays 1072, 1074 and detector 1324 in spectrometer 1322 can be selected to obtain data with optimal results at the desired wavelength.

  In an alternative embodiment, the sample beams 1046, 1308 need not be focused on the same spot on the wafer 1003. Wafer 1003 can be moved in a conventional manner by rotation or linear translation, or a combination of the two movements, so that spots measured by system 1008 are subsequently measured by system 1300 and vice versa. Similarly, the data obtained by these two systems measuring the same spot can be combined in the same way as described above. Since the rotational and translational movements are controlled, the relative positions of the spots being measured by the two systems 1008, 1300 can be correlated.

  Preferably, the spectroscopic ellipsometer is combined with the ellipsometric system 1008 as described, while the system 1008 can be combined with a single wavelength ellipsometer. For this purpose, the arrangement of FIG. 9 needs to be slightly modified by removing the diffraction grating in the optical path of spectrometer 1322 between mirror 1321 and detector 1324. A laser having a wavelength in the ellipsometric spectrum can be used as a radiation source for a single wavelength ellipsometer. By making measurements with a single wavelength ellipsometer and system 1008, it is still possible to derive film thickness and refractive index at wavelengths across the ellipsometric spectrum.

  The above description with reference to FIGS. 9-13B is taken essentially from the parent application.

  In order for the ellipsometer 1300 of FIG. 9 to self-calibrate, the ellipsometer is modified according to any one of the schemas of FIGS. 1, 3, and 7C-7H to determine ellipsometer parameters and sample characteristics. In order to provide sufficient information, it is necessary to provide more than 5 harmonics. In other words, the polarizer 1310 can be replaced with any one of a combination including one or both of the rotating polarizer 206 and the fixed polarizer 214, and the analyzer 1320 can also be fixed as shown in FIGS. 7C-7H. One or a combination of analyzer 226 and rotation analyzer 212 can be replaced. Alternatively, the ellipsometer 1300 can be modified by inserting a phase modulator (such as a phase retarder) in the path of radiation between the polarizer 1310 and the sample and / or the path between the sample and the analyzer 1320.

  In the same manner as described above for deriving the various system parameters of the ellipsometer 1300 as well as the ellipsometric parameters of the sample 1003, the output of the spectrometer 1322 is similar to the processor 30 in function (not shown but functionally). ) So that the ellipsometer 1300 has a self-calibration function with all the attendant advantages described above. The self-calibration feature of the ellipsometer 1300 can be advantageously applied to any other optical instrument used with it, such as the polarimeter 1008 of FIG. In one embodiment, both instruments 1008, 1300 can be used to measure the same sample 1003, and the output of both instruments can be used to measure the sample characteristics as well as the ellipsometer 1300 to make the measurement of the sample 1003 more accurate. Can be used to derive parameters. In another embodiment, the self-calibrating ellipsometer 1300 can be used to calibrate the polarimeter 1008 as described below.

  Ellipsometers typically include an internal standard sample held in a relatively stable environment within the ellipsometer housing. In another embodiment, such an internal standard sample of an ellipsometer, such as ellipsometer 1300, can be used to provide a standard for calibration of other optical instruments. Therefore, if the sample 1003 is an internal standard sample of the ellipsometer 1300, sample characteristics such as film thickness and refractive index can be accurately measured by the self-calibration ellipsometer 1300 as described above. Can be provided to other optical instruments such as a polarimeter 1008. Since the ellipsometer 1300 is self-calibrating, no external calibration standards are required for its calibration so that the user can accurately characterize the internal standard 1003 to provide calibration standards for other optical instruments. You can be sure that it was measured.

  Instead of combining the self-calibrating ellipsometer 1300 with the polarimeter 1008, the ellipsometer can be combined with the spectral reflectometer by simply removing the polarizer 1002 and analyzer 1004 from the polarimeter 1008. Obviously, a narrowband reflectometer can be combined with the ellipsometer 1300 if a narrowband radiation source is used instead of a broadband source. Alternatively, the self-calibrating ellipsometer 1300 can be used in combination with another ellipsometer (single wavelength or broadband) or any other type of optical sample meter. The outputs of both instruments can be used in essentially the same manner as described above to derive sample characteristics as well as characteristics of ellipsometer 1300 or other instruments in combination with ellipsometer 1300. All such combinations are within the scope of the present invention.

  In International Application No. PCT / US98 / 11562, a stable wavelength calibration ellipsometer is used to accurately determine the film thickness on a standard sample. Measurement results from this calibration ellipsometer are used to calibrate other optical instruments. However, in order for a stable wavelength calibration ellipsometer to provide a calibration standard by accurately determining the film thickness on a standard sample, the stable wavelength calibration of the ellipsometer itself must be accurately calibrated. Therefore, the calibration of the stable wavelength calibration ellipsometer itself must rely on other calibration standards that are readily available or not. The self-calibrating ellipsometer of the present invention has no such disadvantages. Since the various parameters of this ellipsometer can be derived without any pre-calibration or relying on any other calibration standard, the above problems are avoided.

  Certain sample properties, such as surface roughness, can cause depolarization of radiation applied to the sample. Therefore, by measuring the depolarization of the radiation caused by the sample, the sample surface properties such as surface roughness can be confirmed. For examples of depolarization measurements to determine surface roughness, see "" Rotating-compensator multichannel ellipsometry for characterization of the evolution of nonuniformities in diamond thin-film growth, "Joungchel Lee et al., See Applied Physics Letters, Vol. 72, No. 8, February 23, 1998, pp. 900-902 (Non-Patent Document 2). This can be done with an ellipsometer (whether self-calibrating or not) that measures film thickness information and depolarization of the radiation caused by the sample. Since an ellipsometer can be used to measure changes in the polarization state of the radiation caused by the sample, the film thickness information as well as the depolarization caused by the sample provides sufficient information about such changes in the polarization state. If it is, it can obtain | require from ellipsometry measurement. This is usually due to the polarization induced by the sample when the polarization state of the radiation is modulated at a certain frequency and when the ellipsometer output provides signal components at five or more harmonics of such modulation frequency. It means that enough information is provided to seek resolution. Preferably, a self-calibrating ellipsometer of any one of the configurations of FIGS. 1, 3 and 7C-7H can be used to perform the measurement. Preferably, the ellipsometer 1300 is such that sufficient information is provided in the same measurement output to derive ellipsometer parameter characteristics and sample film thickness and depolarization caused by the sample, For application, the ellipsometer configuration is preferably such that the ellipsometer detector output includes five or more harmonics of the modulation frequency. In order to provide more information, it may be preferable for the ellipsometer 1300 to measure over a spectrum of wavelengths and provide output at various wavelengths across that spectrum. It is also possible to first perform a self-calibration procedure with the ellipsometer's internal standard sample before using the ellipsometer to measure film thickness information and depolarization of the radiation caused by the sample.

  The combined instrument 1300, 1008 shown in FIG. 9 can be used to measure the depolarization of the radiation caused by the sample, in which case the output of both systems 1008, 1300 is the sample membrane in a single measurement. It is used to derive thickness information, depolarization of the radiation caused by the sample, and ellipsometer 1300 parameters. This process is a simple extension of the technique described in the Ivan Ohlidal and Frantisek Lukes paper cited above by including various system parameters of the ellipsometer 1300 in the process. Such processes are known to those skilled in the art in view of their current application and will not be described in detail here. Preferably, the ellipsometer 1300 measures over a spectrum of wavelengths and provides sufficient information to derive sample properties and ellipsometer system parameters.

  Although the present invention has been described above with reference to various embodiments, it will be understood that changes and modifications can be made without departing from the scope of the present invention, the scope of which is It should be defined only by the claims and the equivalents thereof. Thus, a processor is used to perform the various calculations and algorithms described above, but other circuits such as dedicated circuits, programmable logic controllers for such calculations or integrated circuits implemented in the form of discrete components. It will be understood that they can be used and that they are within the scope of the present invention.

Claims (22)

A method for measuring a sample comprising:
Providing a beam of radiation; and
Passing the beam through a first fixed or rotating polarizing element such that polarized radiation from the beam is delivered to the sample;
After modification by the sample, the steps of using a second circular polarization element that provides a modulated beam, modulating the radiation from the beam,
Detecting radiation from the modulated beam;
Using a fixed linear polarizer to polarize the modulated beam prior to detecting radiation from the modulated beam;
Deriving one or more ellipsometric parameters of the sample from the detected radiation;
Including methods. The method of claim 1, wherein
The method further includes rotating the first and second elements at different speeds, and one of the two elements is fully rotated 13 or more times while the detecting step detects radiation from the beam. Method. The method of claim 1, wherein
A method in which two elements are rotated at two speeds substantially forming a ratio of two integers while each detecting step detects radiation from the beam, and each of the two integers is not divisible by the other . The method of claim 1, wherein
A method in which the two elements are rotated continuously or intermittently. The method of claim 4, wherein
The detecting step detects the radiation when the element is substantially stationary while the element is continuously rotated, or when the element is intermittently rotated. The method of claim 1, wherein
Said providing comprises passing unpolarized radiation through a fixed linear polarizer. The method of claim 1, wherein
The providing step provides a beam of broadband radiation. The method of claim 1, wherein
The method wherein the radiation in the beam has a wavelength ranging from about 190 to 830 nm. The method of claim 1, wherein
The deriving step comprises deriving two elements or one or more parameters of a system used in the providing step, the detecting step or the modulating step. The method of claim 9, wherein
The deriving step derives the parameters of the system such that the ellipsometric parameters are accurately derived without calibration of the parameters of the system or two elements. The method of claim 1, wherein
The deriving step derives one or more parameters including the overall magnification of the system, the orientation or attenuation compensation of the polarization axis of the polarizer, and the polarization of any radiation in the beam. An instrument for measuring a sample,
A source providing a beam of radiation;
A first fixed or rotating polarizing element that passes the beam such that polarized radiation from the beam is delivered to the sample;
A second rotating polarization element that modulates radiation from the beam to provide a modulated beam after modification by the sample;
A fixed linear polarizer that polarizes the modulated beam to provide a polarized and modulated beam;
A detector for detecting radiation from the polarized and modulated beam;
Means for deriving one or more ellipsometric parameters of the sample from the detected radiation;
Instrument comprising a. The instrument of claim 12,
An instrument in which one of the two elements is fully rotated more than 13 times while the detector detects radiation from the beam. The instrument of claim 12,
An instrument in which two elements are rotated at two speeds substantially forming a ratio of two integers while each of the two integers is not divisible by the other while the detector detects radiation from the beam. The instrument of claim 12,
An instrument in which the two elements are rotated continuously or intermittently. The instrument of claim 15, wherein
The detector is an instrument that detects the radiation when the element is substantially stationary while the element is continuously rotated, or when the element is intermittently rotated. The instrument of claim 12,
The source includes an apparatus that provides unpolarized radiation and a fixed linear polarizer that transmits the unpolarized radiation. The instrument of claim 17,
The device is an instrument that provides a beam of broadband radiation. The instrument of claim 12,
The instrument wherein the radiation in the beam has a wavelength ranging from about 190 to 830 nm. The instrument of claim 12,
The means for deriving comprises deriving one or more parameters of two elements or other elements of the instrument. The instrument of claim 20,
The means for deriving the instrument derives parameters of the instrument such that the ellipsometric parameters are accurately derived without calibration of the parameters of the system or two elements. The instrument of claim 12,
The means for deriving one or more parameters including the overall magnification of the instrument, the orientation or attenuation compensation of the polarization axis of the polarizer, and the polarization of any radiation in the beam.

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