JP7483423B2 - OPTICAL MEASUREMENT METHOD, OPTICAL MEASUREMENT DEVICE, AND OPTICAL MEASUREMENT PROGRAM - Google Patents

OPTICAL MEASUREMENT METHOD, OPTICAL MEASUREMENT DEVICE, AND OPTICAL MEASUREMENT PROGRAM Download PDF

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JP7483423B2
JP7483423B2 JP2020043449A JP2020043449A JP7483423B2 JP 7483423 B2 JP7483423 B2 JP 7483423B2 JP 2020043449 A JP2020043449 A JP 2020043449A JP 2020043449 A JP2020043449 A JP 2020043449A JP 7483423 B2 JP7483423 B2 JP 7483423B2
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大輔 稲野
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    • G—PHYSICS
    • G01—MEASURING; TESTING
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    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/01—Arrangements or apparatus for facilitating the optical investigation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/21—Polarisation-affecting properties
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
    • G01N21/27—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands using photo-electric detection ; circuits for computing concentration

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Description

本発明は、光学測定方法、光学測定装置及び光学測定プログラムに関する。 The present invention relates to an optical measurement method, an optical measurement device, and an optical measurement program.

従来から、試料と、偏光子及び検光子と、の位置関係を試料の平面方向に回転させながら測定を行うことにより、光学次数及びリタデーションを求める光学測定装置が知られている（下記特許文献１及び特許文献２参照）。また、試料の複屈折率または試料の厚さの一方が既知である場合に、リタデーションを測定する方法もある（下記特許文献３参照）。 Conventionally, optical measurement devices are known that determine the optical order and retardation by performing measurements while rotating the positional relationship between the sample, polarizer, and analyzer in the plane direction of the sample (see Patent Documents 1 and 2 below). There is also a method for measuring retardation when either the birefringence of the sample or the thickness of the sample is known (see Patent Document 3 below).

特開平１１－２１１６５６号公報Japanese Patent Application Laid-Open No. 11-211656 特開２００３－１７２６９１号公報JP 2003-172691 A 特開２００３－２４０６７８号公報JP 2003-240678 A

特許文献１及び特許文献２のように、試料と偏光光学系のなす角度を複数通りに変化させて測定する場合、測定装置に試料または偏光光学系を傾斜させる駆動機構が必要となる。また、特に試料のリタデーションが高い場合、次数の特定が困難であり、正確なリタデーションの測定を行うことは困難である。特許文献３の光学測定方法では、試料の複屈折率または試料の厚さの少なくとも一方が既知でなければ、リタデーションの波長分散を測定できない。 When measuring by changing the angle between the sample and the polarizing optical system in multiple ways, as in Patent Documents 1 and 2, the measurement device needs a drive mechanism to tilt the sample or the polarizing optical system. In addition, when the retardation of the sample is particularly high, it is difficult to identify the order, and it is difficult to measure the retardation accurately. In the optical measurement method of Patent Document 3, the wavelength dispersion of retardation cannot be measured unless at least one of the birefringence of the sample or the thickness of the sample is known.

本開示は、上記実情に鑑みてなされたものであり、その目的は、簡易な測定機構を用いて分光スペクトルを測定し、該分光スペクトルに含まれるピーク又はバレイの次数を特定するとともに正確なリタデーションを測定することである。 The present disclosure has been made in consideration of the above-mentioned circumstances, and its purpose is to measure a spectroscopic spectrum using a simple measurement mechanism, identify the order of a peak or valley contained in the spectroscopic spectrum, and measure accurate retardation.

上記課題を解決するために、本開示に係る光学測定方法は、試料に対して、所定の波長域で、複数のピーク及びバレイを含む分光スペクトルを測定するステップと、複数の条件で設定される係数を含む第１波長分散式を用いて、前記試料の厚さを前記ピーク又は前記バレイの表す波長ごとに算出するとともに、前記算出された厚さに基づく評価値が最も大きくなる前記条件において、前記第１波長分散式に含まれる係数を仮決定するステップと、前記複数のピークに含まれる特定のピークの次数を複数通りの条件で設定し、設定された複数の条件のもと、前記複数のピークの各次数と波長に基づいて、第２波長分散式を算出するステップと、仮決定された前記係数を含む第１波長分散式と、前記第２波長分散式と、に基づいて、前記特定のピークの次数を特定するとともに、特定された次数と前記第２波長分散式に基づいて、前記係数を本決定するステップと、前記本決定された前記係数を含む前記第２波長分散式に基づいて、リタデーションを算出するステップと、を含むことを特徴とする。 In order to solve the above problem, the optical measurement method according to the present disclosure includes the steps of: measuring a spectrum including multiple peaks and valleys in a predetermined wavelength range for a sample; calculating the thickness of the sample for each wavelength represented by the peak or the valley using a first wavelength dispersion formula including coefficients set under multiple conditions, and provisionally determining the coefficients included in the first wavelength dispersion formula under the conditions in which the evaluation value based on the calculated thickness is the largest; setting the order of a specific peak included in the multiple peaks under multiple conditions, and calculating a second wavelength dispersion formula based on each order and wavelength of the multiple peaks under the multiple conditions set; identifying the order of the specific peak based on the first wavelength dispersion formula including the provisionally determined coefficients and the second wavelength dispersion formula, and finally determining the coefficient based on the identified order and the second wavelength dispersion formula; and calculating the retardation based on the second wavelength dispersion formula including the finally determined coefficients.

また、本開示に係る光学測定装置は、試料に対して、所定の波長域で、複数のピーク及びバレイを含む分光スペクトルを測定する測定部と、複数の条件で設定される係数を含む第１波長分散式を用いて、前記試料の厚さを前記ピーク又は前記バレイの表す波長ごとに算出するとともに、前記算出された厚さに基づく評価値が最も大きくなる前記条件において、前記第１波長分散式に含まれる係数を仮決定する仮決定部と、前記複数のピークに含まれる特定のピークの次数を複数通りの条件で設定し、設定された複数の条件のもと、前記複数のピークの各次数と波長に基づいて、第２波長分散式を算出する第２波長分散式算出部と、仮決定された前記係数を含む第１波長分散式と、前記第２波長分散式と、に基づいて、前記特定のピークの次数を特定するとともに、特定された次数と前記第２波長分散式に基づいて、前記係数を本決定する本決定部と、前記本決定された前記係数を含む前記第２波長分散式に基づいて、リタデーションを算出するリタデーション算出部と、を含むことを特徴とする。 The optical measuring device according to the present disclosure also includes a measuring unit that measures a spectroscopic spectrum including multiple peaks and valleys in a predetermined wavelength range for a sample; a provisional determination unit that calculates the thickness of the sample for each wavelength represented by the peak or the valley using a first wavelength dispersion formula including coefficients set under multiple conditions, and provisionally determines the coefficients included in the first wavelength dispersion formula under the condition in which the evaluation value based on the calculated thickness is the largest; a second wavelength dispersion formula calculation unit that sets the order of a specific peak included in the multiple peaks under multiple conditions and calculates a second wavelength dispersion formula based on each order and wavelength of the multiple peaks under the multiple conditions that have been set; a final determination unit that identifies the order of the specific peak based on the first wavelength dispersion formula including the provisionally determined coefficients and the second wavelength dispersion formula, and finally determines the coefficient based on the identified order and the second wavelength dispersion formula; and a retardation calculation unit that calculates retardation based on the second wavelength dispersion formula including the finally determined coefficients.

また、本開示に係る光学測定プログラムは、光学測定装置に用いられるコンピュータで実行される光学測定プログラムであって、試料に対して、所定の波長域で、複数のピーク及びバレイを含む分光スペクトルを測定するステップと、複数の条件で設定される係数を含む第１波長分散式を用いて、前記試料の厚さを前記ピーク又は前記バレイの表す波長ごとに算出するとともに、前記算出された厚さに基づく評価値が最も大きくなる前記条件において、前記第１波長分散式に含まれる係数を仮決定するステップと、前記複数のピークに含まれる特定のピークの次数を複数通りの条件で設定し、設定された複数の条件のもと、前記複数のピークの各次数と波長に基づいて、第２波長分散式を算出するステップと、仮決定された前記係数を含む第１波長分散式と、前記第２波長分散式と、に基づいて、前記特定のピークの次数を特定するとともに、特定された次数と前記第２波長分散式に基づいて、前記係数を本決定するステップと、前記本決定された前記係数を含む前記第２波長分散式に基づいて、リタデーションを算出するステップと、を前記コンピュータに実行させることを特徴とする。 The optical measurement program according to the present disclosure is an optical measurement program executed by a computer used in an optical measurement device, and is characterized in that the computer is caused to execute the following steps: measuring a spectrum including multiple peaks and valleys in a predetermined wavelength range for a sample; calculating the thickness of the sample for each wavelength represented by the peak or the valley using a first wavelength dispersion formula including coefficients set under multiple conditions, and provisionally determining the coefficients included in the first wavelength dispersion formula under the conditions in which the evaluation value based on the calculated thickness is the largest; setting the order of a specific peak included in the multiple peaks under multiple conditions, and calculating a second wavelength dispersion formula based on each order and wavelength of the multiple peaks under the multiple conditions that have been set; identifying the order of the specific peak based on the first wavelength dispersion formula including the provisionally determined coefficient and the second wavelength dispersion formula, and finally determining the coefficient based on the identified order and the second wavelength dispersion formula; and calculating the retardation based on the second wavelength dispersion formula including the finally determined coefficient.

図１は本実施形態に係る光学測定装置の概略構成を示す模式図である。FIG. 1 is a schematic diagram showing a schematic configuration of an optical measuring device according to this embodiment. 図２は本実施形態に係る測定部の概略構成の一例を示す図である。FIG. 2 is a diagram showing an example of a schematic configuration of a measurement unit according to this embodiment. 図３は測定された平行ニコルスペクトルの一例を示す図である。FIG. 3 is a diagram showing an example of a measured parallel Nicol spectrum. 図４は本実施形態にかかるリタデーションを算出する方法を示すフローである。FIG. 4 is a flow chart showing a method for calculating retardation according to this embodiment. 図５は厚さの波長依存性の一例を示す図である。FIG. 5 is a diagram showing an example of the wavelength dependency of thickness. 図６は第１波長分散式及び第２波長分散式をグラフに表した図である。FIG. 6 is a graph showing the first wavelength dispersion equation and the second wavelength dispersion equation. 図７は本発明の効果を検証するための実験結果の一例を示す図である。FIG. 7 is a diagram showing an example of the results of an experiment for verifying the effect of the present invention. 図８は本発明の効果を検証するための実験結果の一例を示す図である。FIG. 8 is a diagram showing an example of the results of an experiment for verifying the effect of the present invention. 図９は本発明の効果を検証するための実験結果の一例を示す図である。FIG. 9 is a diagram showing an example of the results of an experiment for verifying the effect of the present invention. 図１０は本発明の効果を検証するための実験結果の一例を示す図である。FIG. 10 is a diagram showing an example of the results of an experiment for verifying the effect of the present invention. 図１１は、厚さ方向位相差または３次元複屈折率を算出するための方法を示すフローである。FIG. 11 is a flow chart showing a method for calculating the thickness direction retardation or the three-dimensional birefringence. 図１２は、本実施形態に係る測定部の概略構成の他の一例を示す図である。FIG. 12 is a diagram showing another example of the schematic configuration of the measurement unit according to the present embodiment.

本開示における実施形態について、図面を用いて以下に説明する。 Embodiments of this disclosure are described below with reference to the drawings.

図１は、本実施形態の光学測定装置１００の概略構成を示す模式図である。図１に示すように、本実施形態の光学測定装置１００は、情報処理部１０２と測定部１０４とを含む。情報処理部１０２は、制御部１０６と、記憶部１０８と、表示部１１０と、入出力部１１２と、を含む。情報処理部１０２は、例えば、一般的なコンピュータである。制御部１０６、記憶部１０８、表示部１１０及び入出力部１１２は、データバス１１４により相互に電気信号のやり取りができるよう接続されている。 FIG. 1 is a schematic diagram showing the general configuration of an optical measuring device 100 of this embodiment. As shown in FIG. 1, the optical measuring device 100 of this embodiment includes an information processing unit 102 and a measurement unit 104. The information processing unit 102 includes a control unit 106, a storage unit 108, a display unit 110, and an input/output unit 112. The information processing unit 102 is, for example, a general computer. The control unit 106, the storage unit 108, the display unit 110, and the input/output unit 112 are connected to each other via a data bus 114 so that electrical signals can be exchanged between them.

制御部１０６は、プロセッサであるＣＰＵ（Central Processing Unit）である。具体的には、制御部１０６は、機能的に、波長算出部１１６、仮決定部１２０、規格化部１２２、第２波長分散式算出部１２４、本決定部１２６及びリタデーション算出部１２８を含み、各部は、記憶部１０８に記憶されたプログラムに従って後述する演算を行う。 The control unit 106 is a processor, a CPU (Central Processing Unit). Specifically, the control unit 106 functionally includes a wavelength calculation unit 116, a tentative determination unit 120, a normalization unit 122, a second wavelength dispersion equation calculation unit 124, a final determination unit 126, and a retardation calculation unit 128, and each unit performs calculations (described later) according to a program stored in the storage unit 108.

記憶部１０８は、ＲＡＭ（Random Access Memory）などの主記憶装置及びＨＤＤ（Hard Disk Drive）やＳＳＤ（Solid State Drive）等の静的に情報を記録できる補助記憶装置である。記憶部１０８には、光学測定プログラムの他、情報処理部１０２に含まれる各部の動作を制御するプログラムが記憶される。 The storage unit 108 is a main storage device such as a RAM (Random Access Memory) and an auxiliary storage device that can statically record information, such as a HDD (Hard Disk Drive) or SSD (Solid State Drive). In addition to the optical measurement program, the storage unit 108 stores programs that control the operation of each part included in the information processing unit 102.

表示部１１０は、ＣＲＴ（Cathode Ray Tube）やいわゆるフラットパネルディスプレイ等である。表示部１１０は、ユーザに対して視覚的に画像を表示する。 The display unit 110 is a CRT (Cathode Ray Tube) or a so-called flat panel display. The display unit 110 visually displays an image to the user.

入出力部１１２は、キーボードやマウス、タッチパネル等の、ユーザが情報を入力するための一又は複数の機器である。入出力部１１２は、情報処理部１０２が測定部１０４等の外部機器と情報をやり取りするための一又は複数のインタフェースである。例えば、入出力部１１２は、測定部１０４が測定した結果が入力される。入出力部１１２には、有線接続するための各種ポート及び、無線接続のためのコントローラが含まれていてよい。なお、ここで示した情報処理部１０２の構成は一例であり、これ以外の構成のものであってもよい。 The input/output unit 112 is one or more devices, such as a keyboard, mouse, or touch panel, through which the user inputs information. The input/output unit 112 is one or more interfaces through which the information processing unit 102 exchanges information with external devices such as the measurement unit 104. For example, the input/output unit 112 receives the results of measurements made by the measurement unit 104. The input/output unit 112 may include various ports for wired connections and a controller for wireless connections. Note that the configuration of the information processing unit 102 shown here is an example, and other configurations may also be used.

図２は、測定部１０４の概略構成を示す模式図である。図２に示すように、測定部１０４は、光源２０２と、光ファイバ２０４と、集光レンズ２０６と、偏光子２０８と、回転試料ステージ２１０と、検光子２１４と、マルチチャンネル分光器２１６と、を含む。なお、図２に示す測定部１０４は、平行ニコルスペクトルを測定する場合を示す一例である。 Figure 2 is a schematic diagram showing the general configuration of the measurement unit 104. As shown in Figure 2, the measurement unit 104 includes a light source 202, an optical fiber 204, a focusing lens 206, a polarizer 208, a rotating sample stage 210, an analyzer 214, and a multichannel spectrometer 216. Note that the measurement unit 104 shown in Figure 2 is an example showing the case where a parallel Nicol spectrum is measured.

光源２０２は、例えば白色の光を発するハロゲンランプである。光源２０２は、測定の対象である波長域の光を発する光源２０２であれば、他の種類の光源２０２であってもよい。光源２０２が発した光は、光ファイバ２０４を経由し、集光レンズ２０６によって平行光に変換される。 The light source 202 is, for example, a halogen lamp that emits white light. The light source 202 may be of another type, so long as it emits light in the wavelength range that is the subject of measurement. The light emitted by the light source 202 passes through an optical fiber 204 and is converted into parallel light by a condenser lens 206.

偏光子２０８は、直線偏光子である。偏光子２０８は、集光レンズ２０６によって変換された平行光のうち、透過軸方向の成分のみを透過させる。 The polarizer 208 is a linear polarizer. The polarizer 208 transmits only the component in the transmission axis direction of the parallel light converted by the focusing lens 206.

回転試料ステージ２１０は、試料２１２が配置される。偏光子２０８を経由した光の進行方向をZ軸方向とした場合に、回転試料ステージ２１０は、回転試料ステージ２１０に配置された試料２１２の表面とZ軸とのなす角度が変更できるように構成される。図２では、試料２１２の表面をXY平面とした場合、X軸とZ軸とのなす角度及びY軸とZ軸とのなす角度がいずれも９０度である場合を示している。また、回転試料ステージ２１０は、偏光子２０８を透過した光のうち、測定対象となる波長域の成分を透過する材料で形成される。なお、測定部１０４は、回転試料ステージ２１０を有しない構成であってもよい。 The rotating sample stage 210 has a sample 212 placed on it. When the light passing through the polarizer 208 travels in the Z-axis direction, the rotating sample stage 210 is configured to change the angle between the surface of the sample 212 placed on the rotating sample stage 210 and the Z-axis. In FIG. 2, when the surface of the sample 212 is the XY plane, the angle between the X-axis and the Z-axis and the angle between the Y-axis and the Z-axis are both 90 degrees. The rotating sample stage 210 is made of a material that transmits the components of the wavelength range to be measured out of the light that has passed through the polarizer 208. The measurement unit 104 may be configured without the rotating sample stage 210.

検光子２１４は、直線偏光子であって、偏光子２０８と透過軸が平行になるように配置される。試料２１２を透過した光は、波長に応じて、X軸成分とY軸成分に位相差が生じる。検光子２１４は、当該位相差の生じた光の透過軸方向の成分のみを透過させる。透過した光は集光レンズ２０６によって集光され、光ファイバ２０４を経由してマルチチャンネル分光器２１６に入力される。 The analyzer 214 is a linear polarizer and is arranged so that its transmission axis is parallel to the polarizer 208. The light transmitted through the sample 212 has a phase difference between the X-axis component and the Y-axis component depending on the wavelength. The analyzer 214 transmits only the component of the light in the transmission axis direction that has the phase difference. The transmitted light is focused by the focusing lens 206 and input to the multichannel spectrometer 216 via the optical fiber 204.

マルチチャンネル分光器２１６は、入力された光の強度を、波長ごとに弁別して測定する。具体的には、例えば、マルチチャンネルアナライザは、図３に示すような平行ニコルスペクトルを測定する。図３の縦軸は、マルチチャンネルアナライザが測定した強度から換算した透過率であって、横軸は波長である。試料２１２を透過した後の光は、波長によってX軸成分とY軸成分の位相が異なるため、透過率の波長依存性は、図３に示すように、波形状である。 The multichannel spectrometer 216 measures the intensity of the input light by distinguishing it according to wavelength. Specifically, for example, the multichannel analyzer measures a parallel Nicol spectrum as shown in FIG. 3. The vertical axis of FIG. 3 is the transmittance converted from the intensity measured by the multichannel analyzer, and the horizontal axis is the wavelength. After passing through the sample 212, the phase of the X-axis component and the Y-axis component differ depending on the wavelength, so the wavelength dependence of the transmittance is wavy, as shown in FIG. 3.

次に、図４に示すフローを用いて、本実施形態にかかるリタデーションの測定方法及び制御部１０６に含まれる各部の機能について説明する。まず、測定部１０４は、試料２１２に対して、所定の波長域で、複数のピーク及びバレイを含む分光スペクトルを測定する（S402）。具体的には、例えば、測定部１０４は、図３に示すような、４００ｎｍ乃至８００ｎｍの波長域で複数のピーク及びバレイを含む平行ニコルスペクトルを測定する。 Next, the retardation measurement method according to this embodiment and the functions of each unit included in the control unit 106 will be described using the flow shown in FIG. 4. First, the measurement unit 104 measures an optical spectrum including multiple peaks and valleys in a predetermined wavelength range for the sample 212 (S402). Specifically, for example, the measurement unit 104 measures a parallel Nicol spectrum including multiple peaks and valleys in a wavelength range of 400 nm to 800 nm as shown in FIG. 3.

次に、波長算出部１１６は、演算波長域に含まれる各ピーク及びバレイの表す波長を算出する（S404）。具体的には、例えば、波長算出部１１６は、演算波長域として、５００ｎｍから７５０ｎｍの範囲を設定する。図３の例では、波長算出部１１６は、当該演算波長域に含まれる７個のピーク及び７個のバレイのそれぞれ表す波長を算出する。なお、当該演算波長域は、ユーザが入出力部１１２に入力することにより設定されてよい。 Next, the wavelength calculation unit 116 calculates the wavelengths represented by each peak and valley included in the calculation wavelength range (S404). Specifically, for example, the wavelength calculation unit 116 sets the range from 500 nm to 750 nm as the calculation wavelength range. In the example of FIG. 3, the wavelength calculation unit 116 calculates the wavelengths represented by each of the seven peaks and seven valleys included in the calculation wavelength range. The calculation wavelength range may be set by a user inputting it into the input/output unit 112.

次に、仮決定部１２０は、複数の条件で設定される係数を含む第１波長分散式を用いて、試料の厚さをピーク又はバレイの表す波長ごとに算出するとともに、算出された厚さに基づく評価値が最も大きくなる条件において、第１波長分散式に含まれる係数を仮決定する（S406）。具体的には、例えば、仮決定部１２０は、数１乃至数４を用いて波長分散係数A,B及びCを仮決定する。数１は、λCの関数である厚さを算出する数式である。

Figure 0007483423000001
Next, the tentative determination unit 120 calculates the thickness of the sample for each wavelength represented by the peak or valley using a first wavelength dispersion equation including coefficients set under multiple conditions, and tentatively determines the coefficients included in the first wavelength dispersion equation under the condition that maximizes the evaluation value based on the calculated thickness (S406). Specifically, for example, the tentative determination unit 120 tentatively determines the wavelength dispersion coefficients A, B, and C using Equations 1 to 4. Equation 1 is an equation for calculating the thickness, which is a function of λC .
Figure 0007483423000001

数１において、iは、ピーク及びバレイの指数である。例えば、iは、S404で算出された１４個のピークの表す波長及びバレイの表す波長のうち、最も長い波長740nmのピークの指数は０であり、最も短い波長500nmのバレイの指数は１３である。λは波長である。λCは、隣接するピークの中間波長または隣接するバレイの中間波長であって、数２で表される。

Figure 0007483423000002
In the formula 1, i is the index of the peak and the valley. For example, among the wavelengths represented by the 14 peaks and the wavelengths represented by the valleys calculated in S404, the index of the peak with the longest wavelength of 740 nm is 0, and the index of the valley with the shortest wavelength of 500 nm is 13. λ is the wavelength. λ C is the mid-wavelength of the adjacent peaks or the mid-wavelength of the adjacent valleys, and is expressed by the formula 2.
Figure 0007483423000002

Δｎ(λ)は、波長λにおける複屈折率であって、例えば数３に示すようにコーシーの波長分散式と未知の波長分散係数A,B及びCを用いて算出される。

Figure 0007483423000003
Δn(λ) is the birefringence at wavelength λ, and is calculated using Cauchy's wavelength dispersion formula and unknown wavelength dispersion coefficients A, B, and C, for example, as shown in Equation 3.
Figure 0007483423000003

仮決定部１２０は、数１で算出される厚さに基づく評価値が最大となるように、第１波長分散式に含まれる波長分散係数A,B及びCを仮決定する。例えば、仮決定部１２０は、数１を用いて各ピークまたはバレイ波長で算出された厚さと、数４とを用いて、標準偏差σを算出し、標準偏差σの逆数を評価値とする。

Figure 0007483423000004
The tentative determination unit 120 tentatively determines the wavelength dispersion coefficients A, B, and C included in the first wavelength dispersion formula so as to maximize the evaluation value based on the thickness calculated by Equation 1. For example, the tentative determination unit 120 calculates the standard deviation σ using the thickness calculated at each peak or valley wavelength using Equation 1 and Equation 4, and sets the reciprocal of the standard deviation σ as the evaluation value.
Figure 0007483423000004

数４において、dλC,iは、各指数iについて、隣接するピークの中間波長または隣接するバレイの中間波長ごとに算出された試料２１２の厚さである。maxは、演算波長域における指数の最大値である。上記例では、演算波長域にピーク及びバレイが合わせて１４個含まれることから、maxの値は１３である。 In Equation 4, d λC,i is the thickness of the sample 212 calculated for each index i at the mid-wavelength of the adjacent peak or the mid-wavelength of the adjacent valley. max is the maximum value of the index in the calculation wavelength range. In the above example, the calculation wavelength range includes a total of 14 peaks and valleys, so the value of max is 13.

具体的には、仮決定部１２０は、標準偏差σの逆数を評価値とし、非線形最小二乗法を用いて波長分散係数A,B及びCを算出する。なお、当該アルゴリズムは一例であって、標準偏差σの逆数である評価値が最大となる条件における波長分散係数A,B及びCが特定できれば他のアルゴリズムを用いて波長分散係数A,B及びCが仮決定されてもよい。 Specifically, the tentative determination unit 120 uses the reciprocal of the standard deviation σ as the evaluation value and calculates the chromatic dispersion coefficients A, B, and C using the nonlinear least squares method. Note that this algorithm is only an example, and the chromatic dispersion coefficients A, B, and C may be tentatively determined using other algorithms as long as the chromatic dispersion coefficients A, B, and C under the conditions where the evaluation value, which is the reciprocal of the standard deviation σ, is maximized, can be identified.

図５は、仮決定部１２０が波長分散係数A,B及びCを仮決定するまでに、繰り返し変更された波長分散係数A,B及びCのうち３通りの条件において算出された厚さdと波長との関係を表す図である。図５に示す例では、波長分散係数Bが13723である条件が、厚さｄの標準偏差が最も小さい。従って、仮決定部１２０は、当該条件で算出されたA,B及びCを波長分散係数として仮決定する。 Figure 5 shows the relationship between thickness d and wavelength calculated under three conditions for the wavelength dispersion coefficients A, B, and C that are repeatedly changed before the tentative determination unit 120 tentatively determines the wavelength dispersion coefficients A, B, and C. In the example shown in Figure 5, the condition where the wavelength dispersion coefficient B is 13723 has the smallest standard deviation of thickness d. Therefore, the tentative determination unit 120 tentatively determines A, B, and C calculated under this condition as the wavelength dispersion coefficients.

なお、評価値は、他の方法で算出されてもよい。具体的には、評価値は、算出された厚さの波長依存性が小さいほど大きい値となるように設定されてもよい。例えば、仮決定部１２０は、S406において各条件下で算出された厚さの波長依存性に対して、1次式の近似直線を算出してもよい。そして、仮決定部１２０は、当該近似式に含まれる傾きが最も小さくなる条件におけるA,B及びCを波長分散係数として仮決定してもよい。すなわち、仮決定部１２０は、厚さの波長依存性が最も平坦となる条件におけるA,B及びCを波長分散係数として仮決定してもよい。 The evaluation value may be calculated by other methods. Specifically, the evaluation value may be set to a larger value as the calculated wavelength dependency of the thickness is smaller. For example, the tentative determination unit 120 may calculate an approximation line of a linear expression for the wavelength dependency of the thickness calculated under each condition in S406. Then, the tentative determination unit 120 may tentatively determine A, B, and C under the condition in which the slope included in the approximation formula is smallest as the wavelength dispersion coefficients. In other words, the tentative determination unit 120 may tentatively determine A, B, and C under the condition in which the wavelength dependency of the thickness is flattest as the wavelength dispersion coefficients.

次に、規格化部１２２は、仮決定された波長分散係数A,B及びCを含む第１波長分散式を規格化する（S410）。具体的には、規格化部１２２は、数５を用いて、所定の波長λnにおけるリタデーションを基準として、第１波長分散係数を規格化する。所定の波長λnは、適宜設定されてよいが、ここでは、６００ｎｍであるとする。なお、数５に含まれるA’,B’及びC’は、規格化された後の波長分散係数である。

Figure 0007483423000005
Next, the normalization unit 122 normalizes the first wavelength dispersion formula including the provisionally determined wavelength dispersion coefficients A, B, and C (S410). Specifically, the normalization unit 122 normalizes the first wavelength dispersion coefficient using Equation 5 with the retardation at a predetermined wavelength λn as a reference. The predetermined wavelength λn may be set appropriately, but is assumed to be 600 nm here. Note that A', B', and C' included in Equation 5 are the wavelength dispersion coefficients after normalization.
Figure 0007483423000005

次に、第２波長分散式算出部１２４は、次数が複数通りに設定された条件のもと、各ピークまたはバレイの次数と第１波長分散式に基づいて、第２波長分散式を算出する（S412）。具体的には、第２波長分散式算出部１２４は、複数のピークに含まれる特定のピークの次数を複数通りの条件で設定し、設定された複数の条件のもと、複数のピークの各次数と波長に基づいて、第２波長分散式を算出する。例えば、演算波長域に含まれるピークまたはバレイのうち、最も波長の長いピークまたはバレイが表す波長をλ0と設定し、該ピークの次数をm0とする。第２波長分散式算出部１２４は、図３に表す測定結果に含まれる波長７４０ｎｍにおけるピークの次数m0が１０である条件と、次数m0が１１である条件と、次数m0が１２である条件を設定する。各ピーク及び各バレイが表す波長におけるリタデーションRe.(λi)は、数６及び数７で表される。

Figure 0007483423000006
Figure 0007483423000007
 Next, the second wavelength dispersion formula calculation unit 124 calculates the second wavelength dispersion formula based on the order of each peak or valley and the first wavelength dispersion formula under the condition where the order is set in a plurality of ways (S412). Specifically, the second wavelength dispersion formula calculation unit 124 sets the order of a specific peak included in the plurality of peaks under a plurality of conditions, and calculates the second wavelength dispersion formula based on each order and wavelength of the plurality of peaks under the plurality of conditions. For example, the wavelength represented by the peak or valley with the longest wavelength among the peaks or valleys included in the calculation wavelength range is set as λ 0 , and the order of the peak is set as m 0. The second wavelength dispersion formula calculation unit 124 sets the condition that the order m 0 of the peak at the wavelength of 740 nm included in the measurement result shown in FIG. 3 is 10, the condition that the order m 0 is 11, and the condition that the order m 0 is 12. The retardation Re.(λ i ) at the wavelength represented by each peak and each valley is expressed by Equation 6 and Equation 7.
Figure 0007483423000006
Figure 0007483423000007

例えば、波長７４０ｎｍにおけるピークの次数が１０である条件下では、λ0、λ1、λ2のリタデーションは数８乃至数１０で表される。

Figure 0007483423000008
Figure 0007483423000009
Figure 0007483423000010
 For example, under the condition that the order of the peak at a wavelength of 740 nm is 10, the retardations λ 0 , λ 1 and λ 2 are expressed by the following equations (8) to (10).
Figure 0007483423000008
Figure 0007483423000009
Figure 0007483423000010

同様に、演算波長域に含まれる全てのピーク及びバレイが表す波長のリタデーションは、上記数６または数７を用いて算出される。また、波長７４０ｎｍにおけるピークの次数が１１である条件と、１２である条件と、において、第２波長分散式算出部１２４は、同様の演算を行う。 Similarly, the retardation of the wavelengths represented by all peaks and valleys included in the calculation wavelength range is calculated using the above formula 6 or formula 7. In addition, the second wavelength dispersion equation calculation unit 124 performs a similar calculation under the condition that the order of the peak at a wavelength of 740 nm is 11 and the condition that it is 12.

次に、第２波長分散式算出部１２４は、波長分散係数αm0,βm0及びγm0を含み、数１１で表される第２波長分散式を算出する。数１１で表されるように、第２波長分散式は、第１波長分散式と同様に、コーシーの波長分散式である。

Figure 0007483423000011
Next, the second wavelength dispersion equation calculation unit 124 calculates a second wavelength dispersion equation including the wavelength dispersion coefficients α m0 , β m0 , and γ m0 and expressed by Equation 11. As expressed by Equation 11, the second wavelength dispersion equation is the Cauchy wavelength dispersion equation, similar to the first wavelength dispersion equation.
Figure 0007483423000011

第２波長分散式算出部１２４は、各条件下で、数６及び数７を用いて算出した各リタデーションの値と、数１１を用いて算出した各リタデーションの値と、の残差が最も小さくなるように、波長分散係数αm0,βm0及びγm0を算出する。 The second wavelength dispersion equation calculation unit 124 calculates the wavelength dispersion coefficients α m0, β m0 , and γ m0 so that the residual between each retardation value calculated using equations 6 and 7 and each retardation value calculated using equation 11 under each condition is minimized.

さらに、規格化部１２２は、所定の波長λnのリタデーションを基準として、各条件下で算出された波長分散係数αm0,βm0及びγm0を含む第２波長分散式を規格化する。なお、所定の波長λnは、S410で用いられた６００ｎｍである。規格化された第２波長分散式は、数１２で表される。

Figure 0007483423000012
Furthermore, the normalization unit 122 normalizes the second wavelength dispersion equation including the wavelength dispersion coefficients α m0 , β m0 , and γ m0 calculated under each condition, based on the retardation of a predetermined wavelength λn. The predetermined wavelength λn is 600 nm, which is used in S410. The normalized second wavelength dispersion equation is expressed by Equation 12.
Figure 0007483423000012

ここで、αm0’,βm0’及びγm0’は、規格化後の第２波長分散式に含まれる波長分散係数である。図６は、波長７４０ｎｍにおけるピークの次数m0が１０である条件と、１１である条件と、１２である条件において算出された規格化後の第２波長分散式を表す図である。 Here, αm0 ', βm0 ', and γm0 ' are chromatic dispersion coefficients included in the second chromatic dispersion formula after normalization. Fig. 6 is a diagram showing the second chromatic dispersion formula after normalization calculated under the condition that the order m0 of the peak at the wavelength of 740 nm is 10, 11, and 12.

次に、本決定部１２６は、仮決定された係数を含む第１波長分散式と、第２波長分散式と、に基づいて、特定のピークの次数を特定するとともに、特定された次数と第２波長分散式に基づいて、係数を本決定する（S414）。具体的には、本決定部１２６は、S412において算出され、規格化された各第２波長分散式と、S410において算出された第１波長分散式と、を比較する。そして、本決定部１２６は、第１波長分散式と最も一致する第２波長分散式が算出された条件に基づいて、次数を特定する。 Next, the main determination unit 126 identifies the order of a specific peak based on the first wavelength dispersion equation including the provisionally determined coefficient and the second wavelength dispersion equation, and finally determines the coefficient based on the identified order and the second wavelength dispersion equation (S414). Specifically, the main determination unit 126 compares each of the second wavelength dispersion equations calculated and normalized in S412 with the first wavelength dispersion equation calculated in S410. The main determination unit 126 then identifies the order based on the conditions under which the second wavelength dispersion equation that most closely matches the first wavelength dispersion equation was calculated.

図６は、各条件で算出された規格化後の第２波長分散式とともに、S410において算出された規格化後の第１波長分散式を表す。図６に示すように、S410において算出された第１波長分散式は、波長７４０ｎｍにおけるピークの次数m0が１１である条件下で算出された第２波長分散式と最も一致度が高い。従って、本決定部１２６は、波長７４０ｎｍにおけるピークの次数m0が１１であると特定する。さらに、本決定部１２６は、次数m0が１１である条件下で算出された規格化前の第２波長分散式に含まれるαm0,βm0及びγm0を波長分散係数として本決定する。 6 shows the first wavelength dispersion equation after normalization calculated in S410 together with the second wavelength dispersion equation after normalization calculated under each condition. As shown in FIG. 6, the first wavelength dispersion equation calculated in S410 has the highest degree of agreement with the second wavelength dispersion equation calculated under the condition that the order m0 of the peak at a wavelength of 740 nm is 11. Therefore, the main determination unit 126 specifies that the order m0 of the peak at a wavelength of 740 nm is 11. Furthermore, the main determination unit 126 finally determines α m0 , β m0 , and γ m0 included in the second wavelength dispersion equation before normalization calculated under the condition that the order m0 is 11 as the wavelength dispersion coefficient.

次に、リタデーション算出部１２８は、本決定された係数を含む第２波長分散式に基づいて、リタデーションを算出する（S416）。具体的には、リタデーション算出部１２８は、S414で本決定されたαm0,βm0及びγm0を含む数１１と、ユーザにより入力部に入力された波長と、に基づいて、ユーザが所望する波長におけるリタデーションを算出する。 Next, the retardation calculation unit 128 calculates the retardation based on the second wavelength dispersion equation including the determined coefficients (S416). Specifically, the retardation calculation unit 128 calculates the retardation at the wavelength desired by the user based on Equation 11 including α m0 , β m0 , and γ m0 determined in S414 and the wavelength input to the input unit by the user.

以上のように本発明によれば、簡易な測定機構を用いて分光スペクトルを測定し、該分光スペクトルに含まれるピーク又はバレイの次数を特定するとともに正確なリタデーションを測定することができる。本発明の効果について、実測のデータを用いて説明する。 As described above, according to the present invention, it is possible to measure a spectrum using a simple measurement mechanism, identify the order of the peak or valley contained in the spectrum, and measure accurate retardation. The effects of the present invention will be explained using actual measurement data.

図７は、リタデーションの異なる２枚の単層の水晶板である試料２１２（単層試料１及び単層試料２）について、S402のステップでそれぞれ測定された分光スペクトル（本例では平行ニコルスペクトル）を示す図である。 Figure 7 shows the optical spectra (parallel Nicol spectra in this example) measured in step S402 for sample 212 (single-layer sample 1 and single-layer sample 2), which are two single-layer quartz plates with different retardations.

図８は、図７で示した２枚の単層の水晶板を重ね合わせて作成された試料２１２（重ね合わせ試料）について、S402のステップで測定された分光スペクトル（本例では平行ニコルスペクトル）を示す図である。 Figure 8 shows the optical spectrum (parallel Nicol spectrum in this example) measured in step S402 for sample 212 (superimposed sample) created by superimposing two single-layer quartz plates shown in Figure 7.

図９は、図７の測定結果と、S404乃至S416のステップで算出した第２波長分散式と、を用いて算出されたリタデーションの波長依存性を表す図である。図１０は、図８の測定結果と、S404乃至S416のステップで算出した第２波長分散式と、を用いて算出されたリタデーションの波長依存性を表す図である。また、図１０は、図９に示す２枚の単層の水晶板におけるリタデーションの波長依存性を足し合わせた計算値を併せて示している。 Figure 9 shows the wavelength dependence of retardation calculated using the measurement results of Figure 7 and the second wavelength dispersion formula calculated in steps S404 to S416. Figure 10 shows the wavelength dependence of retardation calculated using the measurement results of Figure 8 and the second wavelength dispersion formula calculated in steps S404 to S416. Figure 10 also shows the calculated value obtained by adding up the wavelength dependence of retardation for the two single-layer quartz plates shown in Figure 9.

２枚の単層の水晶板のリタデーションの合計値と、重ね合わせ試料のリタデーションは、理論上一致するはずである。しかしながら、S404乃至S416のステップにおいて、第２波長分散式に含まれる波長分散係数が正確に算出されなかった場合、２枚の単層の水晶板のリタデーションの合計値と、重ね合わせ試料のリタデーションは異なるおそれがある。本発明によれば、図１０に示すように、計算値と実測値との一致度は高い。従って、本発明によれば、正確なリタデーションを測定できることが確認された。 Theoretically, the sum of the retardation of the two single-layer quartz plates and the retardation of the stacked sample should match. However, if the wavelength dispersion coefficient included in the second wavelength dispersion formula is not calculated accurately in steps S404 to S416, the sum of the retardation of the two single-layer quartz plates and the retardation of the stacked sample may differ. According to the present invention, as shown in FIG. 10, there is a high degree of agreement between the calculated value and the measured value. Therefore, it has been confirmed that the present invention can measure accurate retardation.

なお、本発明は、上記実施形態に限られず種々の変形が可能である。例えば、本発明は、図４に示すフローで算出されたリタデーションを用いて、試料の厚さ方向位相差または３次元屈折率を算出してもよい。図１１は、試料の厚さ方向位相差または３次元屈折率を算出するために方法を示すフローである。 The present invention is not limited to the above embodiment, and various modifications are possible. For example, the present invention may calculate the thickness direction phase difference or the three-dimensional refractive index of a sample using the retardation calculated by the flow shown in FIG. 4. FIG. 11 is a flow diagram showing a method for calculating the thickness direction phase difference or the three-dimensional refractive index of a sample.

まず、変数としてiが０に設定される（S1102）。次に、回転試料ステージ２１０の傾斜角度は、変数iの各値と予め対応して設定されたθi度に設定される（S1104）。変数iの値が０である場合、回転試料ステージ２１０の傾斜角度は、θ0度に設定される。 First, a variable i is set to 0 (S1102). Next, the tilt angle of the rotating sample stage 210 is set to θ i degrees, which is set in advance in correspondence with each value of the variable i (S1104). When the value of the variable i is 0, the tilt angle of the rotating sample stage 210 is set to θ 0 degrees.

そして、回転試料ステージ２１０の傾斜角度が維持された状態で、リタデーションが測定される（S1106）。具体的には、S402のステップと同様に、測定部１０４は、光の進行方向と試料２１２の表面のなす角度がθ0度である場合に、平行ニコルスペクトルを測定する。そして、S404乃至S416のステップで算出された本係数に基づいてリタデーションを算出する。 Then, while the tilt angle of the rotating sample stage 210 is maintained, the retardation is measured (S1106). Specifically, similar to step S402, the measurement unit 104 measures the parallel Nicol spectrum when the angle between the light traveling direction and the surface of the sample 212 is θ 0 degrees. Then, the retardation is calculated based on the main coefficient calculated in steps S404 to S416.

次に変数iが所定の定数nと一致するか判定される（S1108）。変数iが所定の定数nと一致する場合はS1112へ進み、一致しない場合S1110へ進む。なお、厚さ方向位相差または３次元屈折率を算出するために十分な回数のS1106ステップが実行されるように、所定の定数nは、適宜設定される。 Next, it is determined whether the variable i matches a predetermined constant n (S1108). If the variable i matches the predetermined constant n, proceed to S1112, and if not, proceed to S1110. Note that the predetermined constant n is appropriately set so that step S1106 is executed a sufficient number of times to calculate the thickness direction retardation or the three-dimensional refractive index.

変数iが所定の定数nと一致しない場合、変数iはインクリメントされる（S1110）。そして、回転試料ステージ２１０の傾斜角度は、変数iの各値と予め対応して設定されたθi度に変更される（S1104）。そして、S402のステップと同様に、測定部１０４は、光の進行方向と試料２１２の表面のなす角度がθi度である場合に、平行ニコルスペクトルを測定する。さらに、S404乃至S416のステップで算出された本係数に基づいてリタデーションが算出される。 If the variable i does not match the predetermined constant n, the variable i is incremented (S1110). Then, the tilt angle of the rotating sample stage 210 is changed to θ i degrees that is set in advance corresponding to each value of the variable i (S1104). Then, similar to step S402, the measurement unit 104 measures the parallel Nicol spectrum when the angle between the light traveling direction and the surface of the sample 212 is θ i degrees. Furthermore, the retardation is calculated based on the main coefficient calculated in steps S404 to S416.

以上のように、角度を変更するステップと、リタデーションを測定するステップと、を所定の回数繰り返し実行することにより複数のリタデーションが算出される。そして、算出された複数のリタデーションに基づいて、試料の厚さ方向位相差または３次元屈折率が算出される（S1112）。なお、回転試料ステージ２１０の傾斜角度は、偏光子２０８を透過した光の進行方向と試料表面のなす角度であるため、当該角度を変更しながら測定したリタデーションにより、試料の厚さ方向位相差または３次元屈折率を算出することができる。当該計算方法は、既知のものであるため、詳細な説明は省略する。 As described above, the step of changing the angle and the step of measuring the retardation are repeated a predetermined number of times to calculate multiple retardations. Then, based on the multiple calculated retardations, the thickness direction phase difference or the three-dimensional refractive index of the sample is calculated (S1112). Note that since the tilt angle of the rotating sample stage 210 is the angle between the traveling direction of the light transmitted through the polarizer 208 and the sample surface, the thickness direction phase difference or the three-dimensional refractive index of the sample can be calculated from the retardation measured while changing this angle. This calculation method is known, so a detailed description will be omitted.

また、本発明にかかる測定部１０４は、顕微光学系を含んでいてもよい。具体的には、例えば、測定部１０４は、図１２に示す構成であってもよい。図２と同様の構成については説明を省略する。具体的には、測定部１０４は、図２の構成に加えて、対物レンズ１２０２と、ハーフミラー１２０４と、観察用カメラ１２０６と、を含む。対物レンズ１２０２は、試料２１２の測定対象となる微細な領域を透過した光を検光子２１４に導く。ハーフミラー１２０４は、集光レンズ２０６を経由した光を分離する。分離された光の一部は、マルチチャンネル分光器２１６に入力され、他の一部は観察用カメラ１２０６に入力される。これにより、試料２１２の測定対象となる微細な領域のリタデーションを測定できるとともに、当該微細な領域を観察用カメラ１２０６で観察することができる。 The measurement unit 104 according to the present invention may also include a microscopic optical system. Specifically, for example, the measurement unit 104 may have the configuration shown in FIG. 12. The same configuration as that in FIG. 2 will not be described. Specifically, the measurement unit 104 includes an objective lens 1202, a half mirror 1204, and an observation camera 1206 in addition to the configuration in FIG. 2. The objective lens 1202 guides light that has passed through a minute region of the sample 212 to be measured to the analyzer 214. The half mirror 1204 separates the light that has passed through the condenser lens 206. A part of the separated light is input to the multichannel spectrometer 216, and the other part is input to the observation camera 1206. This makes it possible to measure the retardation of the minute region of the sample 212 to be measured, and to observe the minute region with the observation camera 1206.

また、上記では、実験結果の一例として試料２１２が水晶板である場合について説明したが、試料２１２は、液晶パネルであってもよい。本発明によれば、S406にステップで試料２１２の厚さを算出することができるため、液晶パネルのセルギャップを測定することができる。 In addition, in the above, an example of the experimental results was described in which the sample 212 was a quartz plate, but the sample 212 may also be a liquid crystal panel. According to the present invention, the thickness of the sample 212 can be calculated in step S406, and therefore the cell gap of the liquid crystal panel can be measured.

また、上記において、測定部１０４が測定する分光スペクトルが平行ニコルスペクトルである場合について説明したが、分光スペクトルは平行ニコルスペクトルに限られない。分光スペクトルは、偏光光学系で得られる分光情報を含むスペクトルであればよく、例えば直交ニコルスペクトルであってもよい。 In the above description, the optical spectrum measured by the measuring unit 104 is a parallel Nicol spectrum, but the optical spectrum is not limited to a parallel Nicol spectrum. The optical spectrum may be any spectrum including spectral information obtained by a polarization optical system, and may be, for example, a crossed Nicol spectrum.

また、上記において、第１波長分散式及び第２波長分散式がコーシーの波長分散式である場合について説明したが、第１波長分散式及び第２波長分散式はコーシーの波長分散式に限られない。第１波長分散式は及び第２波長分散式は、複屈折率と波長との関係を表す多項式であればよく、例えば、数１３で表されるセルマイヤーの波長分散式であってもよい。

Figure 0007483423000013
In the above description, the first and second wavelength dispersion formulas are Cauchy's wavelength dispersion formulas, but the first and second wavelength dispersion formulas are not limited to the Cauchy's wavelength dispersion formula. The first and second wavelength dispersion formulas may be polynomials expressing the relationship between birefringence and wavelength, and may be, for example, the Sellmeyer's wavelength dispersion formula expressed by Equation 13.
Figure 0007483423000013

また、リタデーションを算出する方法は、図４に示すフローで示される方法に限られない。具体的には、まず、演算波長域に含まれる最も波長の長いピークの次数をm0（所定の整数）と設定する。次に、当該ピークの次数がm0である条件下において、演算波長域に含まれる各ピーク及び各バレイの表す波長について、リタデーションを算出する。そして、算出された各ピーク及び各バレイの表す波長におけるリタデーションを用いて、数３で表されるコーシーの波長分散式に対してフィッティングを行う。フィッティングで算出された次数と、設定された次数m0の残差δm0を算出する。次に、演算波長域に含まれる最も波長の長いピークの次数をm0+1と設定し、同様に次数m0+1の残差δm0を算出する。演算波長域に含まれる最も波長の長いピークの次数がm0から所定の値まで変化させながら、各次数について次数の残差を算出する。以上のステップで算出された残差のうち最も残差が小さく条件における次数を、演算波長域に含まれる最も波長の長いピークの次数として特定する。さらに、特定された次数に基づいて、演算波長域に含まれる各ピーク及び各バレイの表す波長について、リタデーションを算出する。算出されたリタデーションと、数３で表されるコーシーの波長分散式に対してフィッティングを行うことで、波長分散式に含まれる各係数を決定する。そして、係数が決定された波長分散式を用いて、任意の波長におけるリタデーションが算出されてもよい。 In addition, the method of calculating the retardation is not limited to the method shown in the flow shown in FIG. 4. Specifically, first, the order of the peak with the longest wavelength included in the calculation wavelength range is set to m 0 (a predetermined integer). Next, under the condition that the order of the peak is m 0 , the retardation is calculated for the wavelength represented by each peak and each valley included in the calculation wavelength range. Then, fitting is performed on the Cauchy wavelength dispersion formula represented by Equation 3 using the retardation at the wavelength represented by each peak and each valley calculated. The residual δm 0 between the order calculated by fitting and the set order m 0 is calculated. Next, the order of the peak with the longest wavelength included in the calculation wavelength range is set to m 0 +1, and the residual δm 0 of the order m 0 +1 is similarly calculated. The residual of the order is calculated for each order while changing the order of the peak with the longest wavelength included in the calculation wavelength range from m 0 to a predetermined value. The order under the condition where the residual calculated in the above steps is the smallest is identified as the order of the peak with the longest wavelength included in the calculation wavelength range. Furthermore, based on the identified order, the retardation is calculated for the wavelengths represented by each peak and each valley included in the calculation wavelength range. Each coefficient included in the wavelength dispersion formula is determined by fitting the calculated retardation to the Cauchy wavelength dispersion formula represented by Equation 3. Then, the retardation at any wavelength may be calculated using the wavelength dispersion formula with the determined coefficient.

１００ 光学測定装置、１０２ 情報処理部、１０４ 測定部、１０６ 制御部、１０８ 記憶部、１１０ 表示部、１１２ 入出力部、１１４ データバス、１１６ 波長算出部、１２０ 仮決定部、１２２ 規格化部、１２４ 第２波長分散式算出部、１２６ 本決定部、１２８ リタデーション算出部、２０２ 光源、２０４ 光ファイバ、２０６ 集光レンズ、２０８ 偏光子、２１０ 回転試料ステージ、２１２ 試料、２１４ 検光子、２１６ マルチチャンネル分光器、１２０２ 対物レンズ、１２０４ ハーフミラー、１２０６ 観察用カメラ。

 100 Optical measuring device, 102 Information processing unit, 104 Measurement unit, 106 Control unit, 108 Memory unit, 110 Display unit, 112 Input/output unit, 114 Data bus, 116 Wavelength calculation unit, 120 Provisional determination unit, 122 Standardization unit, 124 Second wavelength dispersion formula calculation unit, 126 Final determination unit, 128 Retardation calculation unit, 202 Light source, 204 Optical fiber, 206 Condenser lens, 208 Polarizer, 210 Rotating sample stage, 212 Sample, 214 Analyzer, 216 Multichannel spectrometer, 1202 Objective lens, 1204 Half mirror, 1206 Observation camera.

Claims (6)

試料に対して、所定の波長域で、複数のピーク及びバレイを含む分光スペクトルを測定するステップと、
複数の波長分散係数を含む第１波長分散式を用いて、前記試料の厚さを前記ピーク又は前記バレイの表す波長ごとに算出するとともに、前記算出された厚さに基づく評価値が最も大きくなるように算出された波長分散係数を、前記複数のピークの各光学次数を特定するために用いる波長分散係数として仮決定するステップと、
前記複数のピークに含まれる特定のピークの光学次数として複数通りの値を想定し、当該特定のピークの光学次数が想定した各値である条件のもと、前記複数のピークの各光学次数と波長に基づいて、第２波長分散式を算出するステップと、
仮決定された前記波長分散係数を含む第１波長分散式と、前記第２波長分散式と、に基づいて、前記特定のピークの光学次数を特定するとともに、特定された光学次数と前記第２波長分散式に基づいて、前記波長分散係数を本決定するステップと、
前記本決定された前記波長分散係数を含む前記第２波長分散式に基づいて、リタデーションを算出するステップと、
を含み、
前記評価値は、前記算出された厚さの波長依存性または標準偏差が小さいほど大きい値であることを特徴とする光学測定方法。 measuring a spectroscopic spectrum including a plurality of peaks and valleys in a predetermined wavelength range for a sample;
A step of calculating the thickness of the sample for each wavelength represented by the peak or the valley using a first wavelength dispersion formula including a plurality of wavelength dispersion coefficients, and provisionally determining the wavelength dispersion coefficient calculated so that the evaluation value based on the calculated thickness is the largest as the wavelength dispersion coefficient used to identify each optical order of the plurality of peaks ;
A step of assuming a plurality of values as the optical order of a specific peak included in the plurality of peaks, and calculating a second wavelength dispersion formula based on each optical order and wavelength of the plurality of peaks under a condition that the optical order of the specific peak is each of the assumed values ;
specifying an optical order of the specific peak based on a first wavelength dispersion equation including the provisionally determined wavelength dispersion coefficient and the second wavelength dispersion equation, and finally determining the wavelength dispersion coefficient based on the specified optical order and the second wavelength dispersion equation;
Calculating the retardation based on the second wavelength dispersion equation including the determined wavelength dispersion coefficient;
Including,
An optical measurement method , characterized in that the evaluation value is larger as the wavelength dependency or standard deviation of the calculated thickness is smaller . 前記第１波長分散式及び前記第２波長分散式は、コーシーの波長分散式であることを特徴とする請求項１に記載の光学測定方法。 The optical measurement method according to claim 1, characterized in that the first wavelength dispersion formula and the second wavelength dispersion formula are Cauchy's wavelength dispersion formula. 前記分光スペクトルは、平行ニコルスペクトルであることを特徴とする請求項１または２に記載の光学測定方法。 The optical measurement method according to claim 1 or 2, characterized in that the optical spectrum is a parallel Nicol spectrum. 光の進行方向と前記試料の表面のなす角度を変更するステップと、
前記角度が維持された状態で前記分光スペクトルを測定し、前記本決定された前記波長分散係数を含む前記第２波長分散式に基づいて、リタデーションを測定するステップと、
前記角度を変更するステップと、前記リタデーションを測定するステップと、を所定の回数繰り返し実行することにより算出された複数のリタデーションに基づいて、前記試料の厚さ方向位相差または３次元屈折率を算出するステップと、
をさらに含むことを特徴とする請求項１乃至３のいずれかに記載の光学測定方法。 changing an angle between a direction of light travel and a surface of the sample;
measuring the spectrum while the angle is maintained, and measuring retardation based on the second wavelength dispersion equation including the determined wavelength dispersion coefficient;
A step of calculating a phase difference in a thickness direction or a three-dimensional refractive index of the sample based on a plurality of retardations calculated by repeatedly executing the step of changing the angle and the step of measuring the retardation a predetermined number of times;
The optical measurement method according to any one of claims 1 to 3 , further comprising: 試料に対して、所定の波長域で、複数のピーク及びバレイを含む分光スペクトルを測定する測定部と、
複数の波長分散係数を含む第１波長分散式を用いて、前記試料の厚さを前記ピーク又は前記バレイの表す波長ごとに算出するとともに、前記算出された厚さに基づく評価値が最も大きくなるように算出された波長分散係数を、前記複数のピークの各光学次数を特定するために用いる波長分散係数として仮決定する仮決定部と、
前記複数のピークに含まれる特定のピークの光学次数として複数通りの値を想定し、当該特定のピークの光学次数が想定した各値である条件のもと、前記複数のピークの各光学次数と波長に基づいて、第２波長分散式を算出する第２波長分散式算出部と、
仮決定された前記波長分散係数を含む第１波長分散式と、前記第２波長分散式と、に基づいて、前記特定のピークの光学次数を特定するとともに、特定された光学次数と前記第２波長分散式に基づいて、前記波長分散係数を本決定する本決定部と、
前記本決定された前記波長分散係数を含む前記第２波長分散式に基づいて、リタデーションを算出するリタデーション算出部と、
を含み、
前記評価値は、前記算出された厚さの波長依存性または標準偏差が小さいほど大きい値であることを特徴とする光学測定装置。 A measurement unit that measures a spectroscopic spectrum including a plurality of peaks and valleys in a predetermined wavelength range for a sample;
A provisional determination unit that calculates the thickness of the sample for each wavelength represented by the peak or the valley using a first wavelength dispersion formula including a plurality of wavelength dispersion coefficients, and provisionally determines the wavelength dispersion coefficient calculated so that the evaluation value based on the calculated thickness is the largest as the wavelength dispersion coefficient used to identify each optical order of the plurality of peaks ;
a second wavelength dispersion formula calculation unit that assumes a plurality of values as the optical order of a specific peak included in the plurality of peaks, and calculates a second wavelength dispersion formula based on each optical order and wavelength of the plurality of peaks under a condition that the optical order of the specific peak is each of the assumed values ;
a final determination unit that specifies an optical order of the specific peak based on a first wavelength dispersion equation including the provisionally determined wavelength dispersion coefficient and the second wavelength dispersion equation, and that finally determines the wavelength dispersion coefficient based on the specified optical order and the second wavelength dispersion equation;
A retardation calculation unit that calculates a retardation based on the second wavelength dispersion equation including the determined wavelength dispersion coefficient;
Including,
An optical measuring device according to claim 1, wherein the evaluation value is larger as the wavelength dependency or standard deviation of the calculated thickness is smaller. 光学測定装置に用いられるコンピュータで実行される光学測定プログラムであって、
試料に対して、所定の波長域で、複数のピーク及びバレイを含む分光スペクトルを測定するステップと、
複数の波長分散係数を含む第１波長分散式を用いて、前記試料の厚さを前記ピーク又は前記バレイの表す波長ごとに算出するとともに、前記算出された厚さに基づく評価値が最も大きくなるように算出された波長分散係数を、前記複数のピークの各光学次数を特定するために用いる波長分散係数として仮決定するステップと、
前記複数のピークに含まれる特定のピークの光学次数として複数通りの値を想定し、当該特定のピークの光学次数が想定した各値である条件のもと、前記複数のピークの各光学次数と波長に基づいて、第２波長分散式を算出するステップと、
仮決定された前記波長分散係数を含む第１波長分散式と、前記第２波長分散式と、に基づいて、前記特定のピークの光学次数を特定するとともに、特定された光学次数と前記第２波長分散式に基づいて、前記波長分散係数を本決定するステップと、
前記本決定された前記波長分散係数を含む前記第２波長分散式に基づいて、リタデーションを算出するステップと、
を前記コンピュータに実行させ、
前記評価値は、前記算出された厚さの波長依存性または標準偏差が小さいほど大きい値であることを特徴とする光学測定プログラム。

 An optical measurement program executed by a computer used in an optical measurement device,
measuring a spectroscopic spectrum including a plurality of peaks and valleys in a predetermined wavelength range for a sample;
A step of calculating the thickness of the sample for each wavelength represented by the peak or the valley using a first wavelength dispersion formula including a plurality of wavelength dispersion coefficients, and provisionally determining the wavelength dispersion coefficient calculated so that the evaluation value based on the calculated thickness is the largest as the wavelength dispersion coefficient used to identify each optical order of the plurality of peaks ;
A step of assuming a plurality of values as the optical order of a specific peak included in the plurality of peaks, and calculating a second wavelength dispersion formula based on each optical order and wavelength of the plurality of peaks under a condition that the optical order of the specific peak is each of the assumed values ;
specifying an optical order of the specific peak based on a first wavelength dispersion equation including the provisionally determined wavelength dispersion coefficient and the second wavelength dispersion equation, and finally determining the wavelength dispersion coefficient based on the specified optical order and the second wavelength dispersion equation;
Calculating the retardation based on the second wavelength dispersion equation including the determined wavelength dispersion coefficient;
causing the computer to execute
The optical measurement program according to claim 1, wherein the evaluation value is larger as the wavelength dependency or standard deviation of the calculated thickness is smaller.

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JP2003042722A (en) 2001-08-01 2003-02-13 Toppan Printing Co Ltd Film-thickness measuring method
JP2003172691A (en) 2001-12-06 2003-06-20 Unie Opt:Kk Instrument and method for measuring birefringence taking wavelength dependency into account
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