JP2645252B2 - Automatic birefringence meter - Google Patents

Automatic birefringence meter

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Publication number
JP2645252B2
JP2645252B2 JP60052842A JP5284285A JP2645252B2 JP 2645252 B2 JP2645252 B2 JP 2645252B2 JP 60052842 A JP60052842 A JP 60052842A JP 5284285 A JP5284285 A JP 5284285A JP 2645252 B2 JP2645252 B2 JP 2645252B2
Authority
JP
Japan
Prior art keywords
rotating
analyzer
polarization
polarizer
birefringent
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Lifetime
Application number
JP60052842A
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Japanese (ja)
Other versions
JPS61210920A (en
Inventor
正良 山田
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Individual
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Individual
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Priority to JP60052842A priority Critical patent/JP2645252B2/en
Publication of JPS61210920A publication Critical patent/JPS61210920A/en
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Classifications

    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/21Polarisation-affecting properties
    • G01N21/23Bi-refringence

Description

【発明の詳細な説明】 この発明は、平板状にした複屈折物質の主振動方位と
位相遅れを精密に決定する自動複屈折計の測定方法に関
するものであり、複屈折物質の表面状態と入射光源の偏
光特性に影響されずに高い精度で複屈折物質の主振動方
位と位相遅れを決定できる特徴を有している。
Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of measuring an automatic birefringence meter for accurately determining a main vibration direction and a phase delay of a birefringent material formed into a flat plate. It has the feature that the main vibration direction and phase delay of the birefringent substance can be determined with high accuracy without being affected by the polarization characteristics of the light source.

光学的に異方性のある物質、あるいは光学的に等方な
物質に応力などが加わって光学的に異方性を生じている
物質は複屈折を示す。平板にした複屈折物質に振動数が
一定の光の平面波を入射させると、電気ベクトルの直線
的な偏りの方向が互いに直角で位相速度が異なる二つの
平面波に分れて進行し、平板にした複屈折物質を透過し
た二つ平面波に位相遅れを生じる。この二つの平面波の
電気ベクトルの直線的な偏りの方向を主振動方位とい
い、位相遅れとともに物質の屈折率の異方性、すなわち
複屈折に関係する。複屈折は物質の構造や物質に加わっ
ている応力などの外場の影響を敏感に反映するので、複
屈折物質の主振動方位と位相遅れが高い精度で決定でき
れば、物質の構造や性質を調べるのに極めて有用な方法
を与える。また、光学的に等方的な半導体ウェーハ中の
残留歪みや加工歪みにより生じる微少な複屈折が高精度
に測定できれば、半導体結晶製造分野における残留歪み
の定量評価や半導体デバイス製造分野における加工歪み
の評価に有用な検査手段を与える。
A substance which is optically anisotropic or a substance which is optically anisotropic by applying stress to an optically isotropic substance exhibits birefringence. When a plane wave of light with a constant frequency is incident on a birefringent substance made into a flat plate, the direction of the linear deviation of the electric vector is separated into two plane waves with different phase velocities at right angles to each other, and the plate is flattened. A phase lag occurs between the two plane waves transmitted through the birefringent material. The direction of the linear deviation of the electric vector of the two plane waves is called the main vibration direction, and is related to the anisotropy of the refractive index of the substance, that is, the birefringence, together with the phase lag. Since the birefringence sensitively reflects the influence of external fields such as the structure of the material and the stress applied to the material, if the main vibration direction and phase delay of the birefringent material can be determined with high accuracy, investigate the structure and properties of the material To provide a very useful method. In addition, if the microscopic birefringence caused by residual strain and processing strain in an optically isotropic semiconductor wafer can be measured with high accuracy, quantitative evaluation of residual strain in the semiconductor crystal manufacturing field and processing strain in the semiconductor device manufacturing field can be performed. Provides useful inspection tools for evaluation.

複屈折の測定には、一般的に、単色光源、偏光子、被
測定複屈折物質、検光子および光検出器が用いられ、主
振動方位を決めた後、位相遅れを決定するという二段の
手続きでおこなわれる。しかしながら、これを手動で行
なう場合、調整操作にかなりの熟練を必要とする。さら
に、複屈折の空間的二次元分布を決定するために多点測
定を行なう場合、長い時間を必要とする。複屈折の空間
的二次元分布の自動測定には、第1図に示すように、光
源(1)と分光器または干渉フィルタ(2)からなる単
色光源あるいはレーザから出射する偏りの少ない光を、
レンズ(3)で収束しながら、回転偏光子(4)を通し
て、二軸微動器(6)に取付けた平板状にした複屈折物
質(5)の任意の部分に照射し、その透過光を、回転検
光子(7)とレンズ(8)を通して、光検出器(9)で
測定する偏光透過光測定部と、回転偏光子(4)と回転
検光子(7)の偏光方位と平板状にした複屈折物質
(5)の照射部分を設定する二軸微動器(6)を制御
し、光検出器(9)からの電気出力信号を計測できる表
示・演算処理機能を備えたマイクロプロセッサを用いた
制御・計測・表示・演算処理部(10)あるいは制御・計
算機能を備えた汎用のマイクロコンピュータから構成さ
れる自動複屈折計が広く用いられる。
For the measurement of birefringence, in general, a monochromatic light source, a polarizer, a birefringent substance to be measured, an analyzer and a photodetector are used. It is done in the procedure. However, if this is done manually, the adjusting operation requires considerable skill. Furthermore, when performing multi-point measurements to determine the spatial two-dimensional distribution of birefringence, a long time is required. For automatic measurement of the spatial two-dimensional distribution of birefringence, as shown in FIG. 1, a monochromatic light source composed of a light source (1) and a spectroscope or an interference filter (2) or light with a small bias emitted from a laser is used.
While being converged by the lens (3), an arbitrary portion of the birefringent substance (5) in the form of a flat plate attached to the biaxial tremor (6) is irradiated through the rotating polarizer (4), and the transmitted light is Through a rotating analyzer (7) and a lens (8), the polarization transmitted light measuring unit to be measured by a photodetector (9) and the polarization directions of the rotating polarizer (4) and the rotating analyzer (7) are made flat. A microprocessor having a display / arithmetic processing function capable of controlling a biaxial microtremor (6) for setting an irradiation portion of the birefringent substance (5) and measuring an electric output signal from the photodetector (9) was used. An automatic birefringence meter comprising a general-purpose microcomputer having a control / measurement / display / arithmetic processing unit (10) or a control / calculation function is widely used.

上記のような自動複屈折計において、本発明の複屈折
物質の表面状態と入射光源の偏光特性に影響されずに、
平板状にした複屈折物質の主振動方位と位相遅れを高い
精度で決定する方法について説明する。
In the automatic birefringence meter as described above, without being influenced by the surface state of the birefringent material of the present invention and the polarization characteristics of the incident light source,
A method for determining the main vibration direction and the phase delay of a birefringent material in a flat plate shape with high accuracy will be described.

第2図に示すように、自動複屈折計の基準方位(OX)
に対して、互いに直交する複屈折物質の主振動方位(O
D′)と(OD″)のうちの1つ、例えば、(OD′)が角
度(ψ)を、また、回転偏光子(4)の偏光方位(OP)
が角度(φ)をなしており、その回転偏光子(4)の偏
光方位(OP)に対して回転検光子(7)の偏光方位(O
A)が角度(χ)をなしている系に、強度(I0)の光が
入射する場合、その透過光の強度(I)は、複屈折物質
の表面における反射(反射率:R)を考慮に入れ、文献
(M.Born and E.Wolf:Principles of Optics,4th ed.,P
ermgamon Press,p.695,1970)に従うと、 (A)I=I0(1−R)[cos2χ−sin2(φ−ψ) ×sin2(φ−ψ+χ)sin2δ/2] と表わされる。ここに、(ψ)と(δ)は、それぞれ、
測定しようとする平板状の複屈折物質の主振動方位と位
相遅れである。今、この系で次の2つの場合を考える。
As shown in Fig. 2, the reference direction (OX) of the automatic birefringence meter
With respect to the principal vibration direction (O
D ′) and one of (OD ″), for example, (OD ′) is the angle (ψ), and the polarization orientation (OP) of the rotating polarizer (4).
Is at an angle (φ), and the polarization direction (O) of the rotating analyzer (7) is relative to the polarization direction (OP) of the rotating polarizer (4).
When light of intensity (I 0 ) is incident on a system in which A) forms an angle (χ), the intensity (I) of the transmitted light is determined by the reflection (reflectance: R) on the surface of the birefringent material. Take into account the literature (M. Born and E. Wolf: Principles of Optics, 4th ed., P.
According to Ermgamon Press, p.695, 1970), (A) I = I 0 (1-R) 2 [cos 2 χ−sin2 (φ−ψ) × sin2 (φ−ψ + χ) sin 2 δ / 2] Is represented. Where (ψ) and (δ) are
The main vibration direction and the phase lag of the flat birefringent material to be measured. Now consider the following two cases in this system.

(a)回転偏光子(4)の偏光方位と回転検光子(7)
の検出方位が平行の場合(χ=0)、 式(A)は、 (B)I=I0(1−R)[1−sin22(φ−ψ) ×sin2δ/2] となる。
(A) Polarization direction of rotating polarizer (4) and rotating analyzer (7)
Detecting when the orientation is parallel (χ = 0), formula (A), (B) I || = I 0 (1-R) 2 [1-sin 2 2 (φ-ψ) × sin 2 δ / 2 ].

(b)回転偏光子(4)の偏光方位と回転検光子(7)
の検出方位が垂直の場合(χ=π/2)、 式(A)は (C)I=I0(1−R)2sin22(φ−ψ) ×sin2δ/2 となる。
(B) Polarization direction of rotating polarizer (4) and rotating analyzer (7)
If the detected orientation of the vertical (χ = π / 2), wherein (A) is the (C) I ⊥ = I 0 (1-R) 2 sin 2 2 (φ-ψ) × sin 2 δ / 2 .

これら2つの場合(a)と(b)、すなわち、式
(B)と(C)から、本発明の基本となる方程式 (D)I/(I+I)=sin22(φ−ψ)sin2δ/
2 が基まる。
If these two (a) and (b), i.e., the formula (B) (C), and the underlying equation (D) I ⊥ / (I ⊥ + I ||) of the present invention = sin 2 2 (.phi.- ψ) sin 2 δ /
2 based.

方程式(D)は入射光強度(I0)と複屈折物質表面の
反射率(R)に関係していないのが特徴である。(I
/(I+I))の最大値は(sin2δ/2)であり、最
小値を与える(φ)が主振動方位(ψ)である。したが
って、この方程式(D)を用いれば、複屈折物質の表面
状態と入射光源の偏光特性に影響されずに、複屈折物質
の主振動方位(ψ)と位相遅れ(δ)が決定できる。さ
らに高い精度で主振動方位(ψ)と位相遅れ(δ)を決
定するには、回転偏光子の偏光方位(φ)の関数として
測定した(I)と(I)から求める(I/(I
+I))のすべての値に対して、最小二乗法を用いた
最適パラメータ推定法を適用するば良い。
Equation (D) is characterized in that it does not relate to the incident light intensity (I 0 ) and the reflectivity (R) of the birefringent material surface. (I
/ ( I⊥ + I‖ )) is the maximum value of (sin 2 δ / 2), and (φ) giving the minimum value is the main vibration direction (ψ). Therefore, by using this equation (D), the main vibration direction (ψ) and the phase delay (δ) of the birefringent material can be determined without being affected by the surface state of the birefringent material and the polarization characteristics of the incident light source. To determine the main vibration direction ([psi) and the phase lag ([delta]) with higher accuracy, determined from measured as a function of the polarization orientation (phi) of the rotating polarizer (I ‖) and (I ⊥) (I / (I
+ I ||) for all values of), we apply the optimum parameter estimation method using the minimum square method.

具体的な手順としては、例えば、 i.まず、回転偏光子(4)と回転検光子(7)の偏光方
位を平行(χ=0)にして、基準方位(OX)から10度毎
に1回転(φ=0゜、10゜、20゜、…、350゜)の透過
光の強度(I)を測定する。測定結果例を第3(a)
図に示す。
As a specific procedure, for example, i. First, the polarization directions of the rotating polarizer (4) and the rotating analyzer (7) are set to be parallel (χ = 0), and 1 for every 10 degrees from the reference direction (OX). The intensity (I ) of the transmitted light at the rotation (φ = 0 °, 10 °, 20 °,..., 350 °) is measured. An example of the measurement result is shown in FIG.
Shown in the figure.

ii.同様に、回転検光子(4)と回転検光子(7)の偏
光方位を垂直(χ=π/2)にして、基準方位(OX)から
10度毎に1回転(φ=0゜、10゜、20゜、…、350゜)
の透過光の強度(I)を測定する。測定結果例を第3
(b)図に示す。
ii. Similarly, the polarization directions of the rotating analyzer (4) and the rotating analyzer (7) are set to be vertical (χ = π / 2), and the reference direction (OX) is set.
One rotation every 10 degrees (φ = 0 °, 10 °, 20 °, ..., 350 °)
Of the transmitted light (I ) is measured. Third example of measurement results
(B) Shown in the figure.

iii.測定した透過光の強度(I)と(I)から10度
毎に1回転分の(I/(I+I))の大きさを計
算する。計算結果例を第3(c)図に示す。
iii. Calculate the magnitude of ( I⊥ / ( I⊥ + I‖ )) for one rotation every 10 degrees from the measured transmitted light intensity ( I‖ ) and ( I⊥ ). FIG. 3 (c) shows an example of the calculation result.

iv.10度毎に1回転分の計算結果(I/(I
))の36点が方程式(D)を満たすように、主振動
方位(ψ)と位相遅れ(δ)をパラメータとする最小二
乗法を用いた最適パラメータ推定法を適用する。この
時、主振動方式(ψ)は(I/(I+I))の最
小値を与える(φ)と一致し、また、位相遅れ(δ)
は、(I/(I+I))の最大値、すなわち(si
n2δ/2)によって与えられる。最適パラメータ推定結果
例を第3(c)図に示す。
one rotation of the calculated results for each iv.10 degrees (I / (I +
An optimal parameter estimation method using the least squares method using the main vibration direction (ψ) and the phase delay (δ) as parameters so that the 36 points of I‖ )) satisfies the equation (D) is applied. At this time, the main vibration method (ψ) matches (φ) giving the minimum value of ( I⊥ / ( I⊥ + I‖ )), and also has a phase delay (δ).
Is the maximum value of ( I⊥ / ( I⊥ + I‖ )), that is, (si
n 2 δ / 2). FIG. 3 (c) shows an example of the optimum parameter estimation result.

以上のように、本発明の自動複屈折計における複屈折
物質の主振動方位(ψ)と位相遅れ(δ)を決定する方
法は、入射光強度(I0)と複屈折物質表面の反射率
(R)に依存しない方程式(D)に基づいて、複屈折物
質の主振動方位(ψ)と位相遅れ(δ)を最小二乗法を
用いた最適パラメータ推定法を適用して決定する方法を
取るので、高い精度で複屈折を評価することができる。
本発明は、光学的に等方的な半導体ウェーハ中の残留歪
みや加工歪みにより生じる微少な複屈折を高精度で評価
できるので、半導体結晶製造分野における残留歪みの定
量評価や半導体デバイス製造分野における加工歪みの評
価に用いることができる。したがって、各種製造分野に
おける評価あるいは検査手段としての複屈折計の用途が
大いに拡大するとともに、研究手段としての複屈折計の
用途も拡大する。
As described above, the method for determining the main vibration direction (ψ) and the phase delay (δ) of the birefringent substance in the automatic birefringence meter according to the present invention is based on the incident light intensity (I 0 ) and the reflectance of the birefringent substance surface. Based on the equation (D) that does not depend on (R), a method of determining the principal vibration direction (ψ) and the phase delay (δ) of the birefringent material by applying the optimal parameter estimation method using the least square method is adopted. Therefore, birefringence can be evaluated with high accuracy.
The present invention is capable of evaluating, with high accuracy, minute birefringence caused by residual strain and processing strain in an optically isotropic semiconductor wafer, so that quantitative evaluation of residual strain in the semiconductor crystal manufacturing field and semiconductor device manufacturing field can be performed. It can be used for evaluation of processing strain. Therefore, the use of the birefringence meter as an evaluation or inspection means in various manufacturing fields is greatly expanded, and the use of the birefringence meter as a research means is also expanded.

【図面の簡単な説明】[Brief description of the drawings]

第1図は一般的な自動複屈折計の構成を示すブロック図
である。(1)は光源、(2)は分光器または干渉フィ
ルタ、(3)はレンズ、(4)は回転偏光子、(5)は
平板状にした複屈折物質、(6)は二軸微動器、(7)
は回転検光子、(8)はレンズ、(9)は光検出器、
(10)はマイクロプロセッサを用いた制御・計測・表示
・演算処理部である。 第2図は、偏光透過光測定における基準方位(OX)、複
屈折物質の主振動方位(OD′)と(OD″)、偏光子の偏
光方位(OP)及び検光子の偏光方位(OA)の関係を示す
図である。 第3図は本発明の測定方法に基づいて得られる測定結果
と最適パラメータ推定結果を示す図である。
FIG. 1 is a block diagram showing a configuration of a general automatic birefringence meter. (1) is a light source, (2) is a spectroscope or an interference filter, (3) is a lens, (4) is a rotating polarizer, (5) is a birefringent substance in a plate shape, and (6) is a biaxial microtremor. , (7)
Is a rotating analyzer, (8) is a lens, (9) is a photodetector,
(10) is a control / measurement / display / arithmetic processing unit using a microprocessor. FIG. 2 shows the reference azimuth (OX), the main vibration azimuths (OD ′) and (OD ″) of the birefringent substance, the polarization azimuth (OP) of the polarizer, and the polarization azimuth (OA) of the analyzer in the polarization transmission light measurement. Fig. 3 is a diagram showing a measurement result obtained based on the measurement method of the present invention and an optimum parameter estimation result.

Claims (1)

(57)【特許請求の範囲】(57) [Claims] 【請求項1】外部制御信号にて任意の偏光方位に設定で
きる回転偏光子(4)と任意の方位の偏光成分を検出で
きる回転検光子(7)を用いる自動複屈折計であって、
光源(1)と分光器または干渉フィルタ(2)からなる
単色光源あるいはレーザから出射する偏りの少ない光
を、回転偏光子(4)を通して、二軸微動器(6)に取
付けた平板状にした複屈折物質(5)の任意の部分に照
射し、その透過光を、回転検光子(7)を通して、光検
出器(9)で測定する偏光透過光測定部と、回転偏光子
(4)と回転検光子(7)の偏光方位と平板状にした複
屈折物質(5)の照射部分を設定する二軸微動器(6)
を制御し、光検出器(9)からの電気出力信号を計測で
きる表示・演算処理機能を備えたマイクロプロセッサを
用いた制御・計測・表示・演算処理部(10)あるいは制
御・計算機能を備えた汎用のマイクロコンピュータから
構成される自動複屈折計を用いて、複屈折物質の主振動
方位と位相遅れを決定する方法において、回転偏光子
(4)と回転検光子(7)の偏光方位を平行にして回転
した場合と垂直にして回転した場合の回転偏光子(4)
の回転角度(φ)の関数としての透過光強度(I及び
)を測定し、下記の式(D)に最小二乗法を用いた
最適パラメータ推定法を適用して、複屈折物質の主振動
方位(ψ)及び位相遅れ(δ)を決定する方法。 記 (D)I/(I+I)=sin22(φ−ψ)sin2δ/
2 但し、(D)式において φ:回転偏光子の回転角度 I:回転偏光子と回転検光子の偏光方位を平行にして
回転した場合の透過光強度 I:回転偏光子と回転検光子の偏光方位を垂直にして
回転した場合の透過光強度 ψ:複屈折物質の主振動方位 δ:複屈折物質の位相遅れ
1. An automatic birefringence meter using a rotating polarizer (4) that can be set to an arbitrary polarization direction by an external control signal and a rotation analyzer (7) that can detect a polarization component in an arbitrary direction.
A monochromatic light source composed of a light source (1) and a spectroscope or an interference filter (2) or a light having a small bias emitted from a laser is formed into a flat plate attached to a biaxial microtremor (6) through a rotating polarizer (4). An arbitrary part of the birefringent material (5) is irradiated, and the transmitted light is passed through a rotary analyzer (7) to be measured by a photodetector (9). A two-axis microtremor (6) for setting the direction of polarization of the rotating analyzer (7) and the irradiation part of the birefringent substance (5) in the form of a plate.
Control / measurement / display / arithmetic processing unit (10) using a microprocessor with a display / arithmetic processing function capable of controlling the electric output signal from the photodetector (9) or a control / calculation function In the method of determining the main vibration direction and the phase delay of the birefringent material using an automatic birefringence meter composed of a general-purpose microcomputer, the polarization directions of the rotating polarizer (4) and the rotating analyzer (7) are determined. Rotating polarizer when rotated parallel and vertically (4)
The transmitted light intensity (I 回 転 and I と し て ) as a function of the rotation angle (φ) of is measured, and the optimal parameter estimation method using the least squares method is applied to the following equation (D) to obtain the birefringent substance. A method for determining the main vibration direction (ψ) and the phase delay (δ). Serial (D) I ⊥ / (I ⊥ + I ||) = sin 2 2 (φ- ψ) sin 2 δ /
2 However, phi in (D) equation: Rotation angle I of the rotating polarizer ‖: rotation when rotated in the parallel polarization direction of the polarizer and rotating analyzer transmitted light intensity I ⊥: rotating polarizer and rotating analyzer Transmitted light intensity when the polarization direction of is rotated vertically ψ: Principal vibration direction of birefringent material δ: Phase lag of birefringent material
JP60052842A 1985-03-15 1985-03-15 Automatic birefringence meter Expired - Lifetime JP2645252B2 (en)

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Application Number Priority Date Filing Date Title
JP60052842A JP2645252B2 (en) 1985-03-15 1985-03-15 Automatic birefringence meter

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Application Number Priority Date Filing Date Title
JP60052842A JP2645252B2 (en) 1985-03-15 1985-03-15 Automatic birefringence meter

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JPS61210920A JPS61210920A (en) 1986-09-19
JP2645252B2 true JP2645252B2 (en) 1997-08-25

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Publication number Priority date Publication date Assignee Title
JP2792315B2 (en) * 1992-03-10 1998-09-03 松下電器産業株式会社 Birefringence measurement device
JP2923884B2 (en) 1997-05-13 1999-07-26 日本電気株式会社 Optical transceiver
CN100378445C (en) * 2004-12-28 2008-04-02 中国科学院上海光学精密机械研究所 Intelligent synthesized measuring apparatus for half wave voltage of extinction ratio in crystal, and phase delay of wave plate

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JPH0676965B2 (en) * 1983-07-25 1994-09-28 小林 ▼じん▲三 A method for determining the optical constant of a crystal having optical activity

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