JP3894863B2 - Refractive index distribution measurement method of optical crystal wafer - Google Patents

Description

【００２６】
ここでφ₁は位相差の一定成分である。
【００２７】
さらに図3（ｂ）のように試料を９０°回転させ、偏光方向と結晶のｙ軸方向と一致させる。このときの結晶内入射角度をθ_1yとすると観測される位相差分布ΔＹ₁(x、y)は式(11) で与えられる。
【００２８】
【式１１】

【００２９】
ここでn_ey(θ_1y)＞＞Δn_ey(x,y,θ_1y)、 L₀>>ΔL(x,y) であるので
式(11)左辺のΔn_ey(x,y,θ_1y) ・ΔL(x,y)の項は無視することができる。またφ₁＝n_eZ(θ_1Z)・L₀、φ₂＝n_ey(θ_2Z)・ L₀ を仮定すると式(11)より
【００３０】
【式１２】

【００３１】
式(12)を用いて式(11)は式(13)のように変形される。
【００３２】
【式１３】

【００３３】
次に実測される屈折率の空間分布Δn_eZ(x,y,θ_1Z)と結晶のｚ軸偏光の屈折率空間分布Δn_Z(x,y)の関係式を明らかにする。ここで均質な材料を仮定するとP偏光（結晶のｙ軸方向の偏光）異常光屈折率の角度依存性は
【００３４】
【式１４】

【００３５】
一軸性結晶を仮定し、Δn_y=Δn_x、 n_x=n_y、とすると n_ey(θ)の空間分布は式(15)であらわされる。
【００３６】
【式１５】

【００３７】
一方、試料を９０°回転させP偏波とｙ軸方向を一致させた場合、結晶ｙ軸方向の偏光異常光屈折率の角度依存性は
【００３８】
【式１６】

【００３９】
n_eZ(θ)の空間分布は式(17)であらわされる。
【００４０】
【式１７】

【００４１】
ここで係数δn_eZ(θ)/δn_Zは式(16)をn_Zで微分することにより次のように求められる。
【００４２】
【式１８】

【００４３】
式(14)から式(18)を用いて、式(13)をΔn_Z(x,y)を用いて書き直すと式(19)が得られる。
【００４４】
【式１９】

【００４５】
式(19)より結晶の複屈折率分布Δn_Z/n_Z−Δn_X/n_X〜（Δn_Z−Δn_X）/n_Zを算出することが可能である。この場合式(19)には試料厚みの空間分布ΔL(x,y)に関する項は含まれていないため厚みむらによらず複屈折率分布のみ抽出できることがわかる。この場合常光屈折率の空間分布が異常光屈折率の空間分布と比べて無視できるほど小さいという仮定は必要無いことがわかる。したがって任意の結晶材料に関しても適用可能である。
【００４６】
またLiNbO3結晶においては図4に示すように異常光屈折率ｎ_e（n_x＝ｎ_y） はLi組成比依存性にほとんど依存しないため空間依存性は極めて小さいためΔn_X(x,y)＝０とすると屈折率分布Δn_Z/n_Zを算出することができる。
【００４７】
以上測定原理について説明したが、実際の測定装置および計算手順を説明する。図6に示すように試料透過位相を測定するためにいわゆる干渉計１を構成する。干渉計はレーザ光源部30と部分反射鏡２0と試料部に配置した試料10を通過して反射鏡３により干渉計に戻った光を干渉させる干渉部から構成されている。参照ミラーまでの光学長を参照ミラーに取り付けたピエゾ素子等でわずかに変化させ干渉リングの動きから試料の位相を算出することができる。
【００４８】
試料部は図3(a)に示すように試料を４５度傾斜させ、P偏光が結晶のｚ軸方向と一致するように配置する。このときに得られる透過波面画像ΔZ₁(x、y)は図7（a）に示すようにｚ軸方向に短縮された楕円の形状となる。
【００４９】
一方、試料を９０°回転させP偏光方向と試料のｙ軸を一致させる（図3（ｂ））。このときに得られた透過波面の画像ΔＹ₁(x、y)図８（a）は結晶のｙ軸方向に短縮された楕円の形状となる。この短軸方向の異なった２つの画像を式(19)を用いて計算するには工夫が必要となる。
【００５０】
両画像とも短軸方向を拡大し、ｙ、ｚ軸方向とも等しい比率の円形の画像に変換する (図7（b）、8（b））。この状態で両画像の軸方向は直交しているのでどちらか一方の画像を（説明ではΔＹ₁(x、y)画像を）９０°逆回転させ両画像の座標軸方向を一致させる（図8（c））。
【００５１】
こうして変換された画像ΔＺ₁(x、y)図７（ｂ）、ΔＹ₁(x、y)図8（ｃ）を用いて式(10)より屈折率分布Δn_Z(x、y)を算出することができる。
【００５２】
以上説明したように、XカットLiNbO３ウエハーの場合、試料を傾けて配置し、P偏光のまま試料を９０°回転させて２つのｚ偏光方向、ｙ偏光方向でのの光路長ΔZ(x、y)、ΔY(x,y)を光学干渉計等により測定することにより、式２０から屈折率分布Δｎ_z(x、y)を計測することが可能であることがわかった。
【００５３】
こうした操作を行うことにより、厚み分布ΔＬ(x、y)による波面歪中に隠れて見えなかった１００００分の１の程度のわずかな屈折率分布を精度よく算出することが可能となった。
またP偏光のみを用いているためウエハー表裏の多重干渉による干渉パターンの影響もなく精度よく測定できる。
【００５４】
さらに精度を向上させるために次の問題を解決する方法が望ましい。まず、試料がない場合の干渉計本体の透過波面に歪もしくは波面に傾きが（バイアス成分）存在する場合、試料を通過させた場合の透過波面にこのバイアス成分が重畳されることになる。従って図７（a）図８（a）に同じバイアス成分が重畳される。図8（c）のように画像を９０度回転させるためこのバイアス成分も９０°回転され、図7（a）,図8（a）の同一量重畳されたバイアス成分でも、式２０で算出する最、キャンセルされずに屈折率の傾斜成分となって観測されることになる。
【００５５】
第二に、試料を９０°回転させて測定するために、同じｙ、ｚ座標上の観測される位相を用いて計算しても、実際には光路は同じでなくｙ、ｚ座標は同じでも90°回転した光路を通過した位相差を用いることになる。このため試料厚みに傾きや大きな厚みむらがある場合は試料厚みむらの差し引き効果が弱く、結果的に計算された屈折率分布にバイアス成分や見かけ上の不均一を生じることになる。
【００５６】
この２点を改良するために、図9に示すように９０°ステップで試料を回転させ、４つの透過波面を計測する（ここではそれぞれ+Z画像(図９（a）)、+Y画像(図９（d）)、-Z画像(図９（b）)、-Y画像(図９（e）)と呼ぶ）。-Z画像は180°画像回転され+Z画像に加えられる。また-Y画像も180°画像回転し+Y画像にくわえ込む。ここでそれぞれ加えられた画像をZ２画像(図９（c）)、Y2画像(図９（f）)とすると、夫々の透過波面画像は直線傾斜などのバイアス成分はキャンセルされることになる。Z2の透過波面分布をΔZ₁(x、y) (図９（c）)、Y2の透過波面分布をΔＹ₁(x、y) (図９（f）)とすると式２０より屈折率分布を計算することができる。このときの試料厚みは2倍となることに注意する必要がある。またZ2,Y2画像を用いることにより、ウエハー厚み方向に光路が９０°回転していることによる効果は空間的に平均化され緩和させることができた。
【００５７】
以上のように９０°ずつ試料を回転させた際の４つの透過波面を用いて計算することにより、その分空間分解能は若干劣化するが、干渉計のバイアス成分の影響を受けることなく精度よく屈折率分布のみを測定することが可能となった。
【００５８】
【発明の実施形態】
第一の実施形態として、ｚカット５インチLiNbO3ウエハーを用い（厚み１０００μｍ）屈折率分布を測定した場合を図10に示す。図10（a）は測定システムの正面図、図10（ｂ）は側面図を示す。透過波面歪（光路長）を測定するために、ZYGO社製の干渉計（GPI-XP）を使用した。反射ミラー３はチルト調整の付属したミラーマウント４に装着され、チルト調整ねじ５，６によりあおりを調整することができる。これらの光学系は防振光学定番上に配置され、全体は温度０．１℃で制御されたクリーンベンチ内に配置されている。
【００５９】
まず干渉計本体１からは６インチ径のHe-Neレーザ光は出射される。出射された光は光軸１２上を伝搬し、反射ミラー３により反射され、同じ光軸１２を通り干渉計本体に戻る。サンプルない状態で反射ミラーのあおりを調整する。
【００６０】
次に図10（a）（ｂ）に示すようにXカットLiNbO3ウエハーの結晶のｘ軸が光軸１２に対して角度４５度となるように回転ステージ７を調整し傾けてセットする。またｚ軸がP偏光方向と一致するように試料台８の上で試料１０をセットする。 この時,図１1（a）に示すように干渉計本体の偏光方向が試料傾斜面内になるP波方向となるようにしまた試料のｚ軸方向がP波偏光と一致する向きに試料をセットし透過波面歪を計測する。この状態で透過波面歪ΔZ(x、y)を測定した結果を図１2に示した。取得したデータは一旦、図示されていないパーソナルコンピュータの記憶装置に記録する。
【００６１】
次に図１1(b)に示すようにウエハー１０を試料台８の上で試料ｘ軸を中心として９０度回転させ、干渉計本体P波偏光方向と結晶ｙ軸が一致するように配置し透過波面歪ΔY(x、y)を計測する。この状態で透過波面歪ΔY(x、y)を測定した結果を図１3に示した。取得したデータは一旦パーソナルコンピュータ（図示せず）上の記憶装置に記録する。
測定が終了後、P波Z軸の透過波面歪ΔZ(x、y)とP波Y軸透過波面歪ΔY(x、y)をパーソナルコンピュータの記憶領域より読み出し、図7、8に示した手順で式(19)に従って屈折率ｎ_zの分布Δｎ_z (x,y)を計算する。計測した結果を図１4に示した。最大.のΔｎ_z (x,y)の量は０．０００３程度であり、小数点４桁めの屈折率分布が抽出できることがわかる。
図１4を見てわかるように図12、13のウエハー厚み分布を反映した形状とはまったく異なった屈折率分布を示しており、ウエハー厚みに依存しない屈折率分布を精度よく計測できることがわかった。
【００６２】
上記実施形態においては、一軸性結晶としてLiNbO3結晶を使用した場合について説明したが、これに限らず他の一軸性結晶であるLiTaO3やKLNであるような他の二軸性結晶の屈折率測定に用いてもよいことは明らかである。
【００６３】
【発明の効果】
以上述べたように、本発明によれば、LiNbO３結晶などのように組成比により屈折率が変化する結晶において、組成比に依存した屈折率分布を迅速に測定する測定法を提供することができる。
【図面の簡単な説明】
【図１】斜め入射での光軸図
【図２】LN反射率の入射角度依存性
【図３】（a）結晶のｚ軸と偏光方向が平行の場合(b)結晶のｙ軸と偏光方向が平行の場合
【図４】LN屈折率のLi組成比依存性
【図５】厚み分布を打ち消して屈折率のみを抽出する方法の説明図
【図６】測定システムを示すブロック図
【図７】測定された画像データの回転変形の仕方を示す図
【図８】測定された画像データの回転変形の仕方を示す図
【図９】透過波面傾斜成分を取り除く測定方法
【図１０】（a）測定装置の正面図（ｂ）測定装置の側面図
【図１１】偏光方向と試料の結晶軸との関係を示す図
【図１２】Z軸偏光の透過波面測定図
【図１３】Y軸方向の透過波面測定図
【図１４】ウエハーの複屈折分布測定図
【符号の説明】
１・・干渉計、 3・・反射鏡、 ４・・ミラーマウント
５、６・・チルト調整ネジ、 ７・・ 回転ステージ、 ８・・ 試料台
１０・・試料、 １２・・光軸[0001]
[Prior art]
With the progress of optical communication and IT, single crystal wafers with electro-optic effect have become an important role to play. In particular, in optical fiber communication, a wavelength division multiplexing WDM system that multiplexes and transmits light of many wavelengths on one optical fiber is used in order to cope with an explosive increase in communication volume. Furthermore, in order to cope with the increase in the amount of information, the modulation speed is increasing from 2.5 GHz to 10 GHz, and further to 40 GHz and 80 GHz in the future. In particular, as a modulator used for a long-distance trunk line system, an optical modulator using an inorganic single crystal lithium neobate (LiNbO3) crystal is used. An optical modulator using lithium neobuate forms a Mach-Zehnder-type waveguide by titanium diffusion and applies an electric field that constitutes an electrode to the Mach-Zender arm part, thereby modulating the refractive index of one arm. Is to modulate.
[0002]
As the modulation speed increases from 10 GHz to 40 GHz, the required element length increases, and a more uniform lithium neobate wafer is desired. Also, if the Li concentration is different, the titanium diffusion speed at the time of waveguide creation is different, so the optical waveguide size changes and the mode diameter of the light changes. It is considered that the manufacturing margin decreases as the design is performed at a higher speed, and even a slight change in waveguide characteristics causes a change in the operating voltage, resulting in a deterioration in yield. For this reason, a LiNbO3 substrate for a high-speed modulator of 40 GHz or more is desired to have a uniform composition distribution with a Li concentration fluctuation of 0.01 mol% or less.
[0003]
On the other hand, it is known that the Li / Nb composition ratio changes during crystal growth when the Li / Nb composition ratio deviates from the congruent composition (Li = 48.5 mol%). Therefore, the composition ratio is usually different between the upper part and the lower part of the grown ingot. Variations in composition are also observed within the wafer. Therefore, it is important to measure the Li / Nb composition ratio distribution with high accuracy in order to evaluate wafers for optical applications.
[0004]
Conventionally, as a method of measuring such a Li / Nb composition ratio, a method of cutting a wafer and measuring a Curie temperature by thermal analysis such as DTA (Differential Thermal Analysis) or DSC (Differential Scanning Calorimetory) is known. This is based on the fact that the Curie temperature Tc changes linearly with respect to the Li concentration (ΔTc / ΔLi to 1 ° C / mol%), but the measurement accuracy itself is limited (0.6 ° C) The spatial resolution is also poor (3 mm) and cannot be used practically. In addition, it is a destructive inspection and takes a long time to measure (3 hours for one point measurement).
[0005]
Conventionally, it is known that the refractive index for extraordinary light decreases linearly with respect to the Li concentration. (U.Schlarb and K.Betzler Physical Review B Vol.50, No2, 751 (1994))
If this is utilized, if the refractive index distribution with respect to extraordinary light is measured, the Li concentration distribution can be measured.
[0006]
It can be easily imagined that by measuring the change of the transmitted wavefront of the wafer, the refractive index concentration distribution in the wafer can be measured and calculated. As a device for measuring such a transmitted wavefront, for example, an interferometer such as a Twiman Green interferometer or a Michelson interferometer has been put into practical use, which has characteristics of non-contact, non-destructive, and non-contaminating. However, this method has problems in the following two points.
[0007]
The first problem is the multiple interference effect. Since the wafer is usually polished in parallel, when light is allowed to pass, some of the light undergoes multiple reflections, and so-called interference patterns also occur at the same time. For this reason, there is a problem that necessary information is buried because the interference pattern is superimposed on the image of the transmitted wavefront itself. In order to avoid such an interference effect, it is necessary to polish the wafer to a substrate having a wedge of about 3 ° instead of a parallel plate. Wedge polishing is technically difficult, especially for large wafers, and requires a lot of labor. Further, since the wafer as a product is a parallel plate, there is a problem that it cannot be used for product inspection. Although non-reflective coating can be performed on both sides, there is a problem that a coating process is required and it cannot be used particularly in product inspection or in-line rapid measurement.
[0008]
The second problem is that only the refractive index distribution cannot be detected. When the thickness of the measurement sample is ideally parallel and the thickness distribution is so small that it can be ignored, the refractive index distribution can be calculated by measuring the transmitted wavefront distortion with the sample thickness being constant. However, in general, this assumption does not hold. In particular, since a large thickness unevenness exists for a wafer-shaped large sample, normal thickness measurement of transmitted wavefronts cannot distinguish the refractive index distribution from the wafer thickness unevenness and the refractive index distribution. This will be specifically described as follows.
[0009]
If the spatial change in refractive index is Δn (x, y), the spatial change in wafer thickness is ΔL (x, y), and the constant values are n ₀ and L ₀ , the refractive index is n (x, y) and the wafer The thickness L (x, y) is expressed as in equations (1) and (2).
n (x, y) = n ₀ + Δn (x, y) (1)
L (x, y) = L ₀ + ΔL (x, y) (2)
Accordingly, the optical length OL (Optical Length) is expressed by equation (3).
OL (x, y) = n (x, y) · L (x, y) = (n ₀ + Δn (x, y)) · (L ₀ + ΔL (x, y))
= n ₀ L ₀ + L ₀ · Δn (x, y) + n ₀ · ΔL (x, y) + Δn (x, y) · ΔL (x, y) (3)
If the second minute amount (third term on the right side) of the equation (3) is ignored, the equation (3) is approximated as shown in (4).
L (x, y) to n ₀ L ₀ + L ₀ · Δn (x, y) + n ₀ · ΔL (x, y) (4)
Although it is desirable to make the wafer thickness uniform, in reality, the deviation ΔL (x, y) from the parallel wafer thickness distribution is about 1 μm with a 5-inch diameter. Since n ₀ is about 2.2, the size of the third term is a value of 2.2 μm. Further, the refractive index fluctuation Δn (x, y) corresponding to the Li concentration deviation of 0.01 mol% is about 0.0001, and the wafer thickness L ₀ is about 800 μm, so the second term size is about 0.08 μm. is there. Therefore, the size of the second term of the equation (4) to be measured is 2 to 3 orders of magnitude smaller than the size of the third term due to the uneven thickness. For this reason, it is impossible to measure the Li concentration distribution through refractive index distribution measurement by wavefront observation. Because of these two problems, it is difficult to measure the refractive index distribution using an interferometer and calculate the composition ratio distribution.
[0010]
[Problems to be solved by the invention]
In view of the problems of the prior art, the object of the present invention is not affected by the interference between the front and back of the wafer, and is not affected by the wafer thickness distribution. It is to be able to measure.
[0011]
[Means for Solving the Problems]
According to the present invention, in a refractive index or birefringence distribution measurement method by transmission wavefront measurement, in a sample having two opposing main surfaces on which light can enter, the vertical direction of the main surface is a constant inclination angle with respect to the optical axis. Yo sample is inclined, the first transmitted wavefront in a case where to match the polarization direction of the P polarized light to the first principal axis of the sample, the second main spindle in which the polarization direction of the P polarized light orthogonal to the first spindle In this method, the refractive index or the birefringence distribution is measured from the second transmitted wavefront in the case of matching.
[0012]
Further, according to the present invention, in a refractive index or birefringence distribution measurement method by transmission wavefront measurement, in a sample having two main surfaces facing each other on which light can be incident, the vertical direction of the main surface is a constant inclination angle with respect to the optical axis. sample is inclined so that, a second transmitted wavefront of the case of rotating a first transmitted wavefront of when to match the first principal axis of the sample the polarization direction of the P polarized light, the more 180 ° sample The refractive index from the third transmitted wavefront when the polarization direction of the P-polarized light coincides with the second principal axis direction orthogonal to the first principal axis and the fourth transmitted wavefront when the sample is further rotated by 180 degrees a method of measuring the birefringence distribution.
[0013]
Here, the constant inclination angle is preferably a Brewster angle at which no reflection occurs. This is because setting the sample at the Brewster angle can reduce errors in measurement values due to multiple interference on both surfaces of the sample.
[0014]
The birefringent crystal is preferably LiNbO3 whose principal surface perpendicular direction coincides with the x or y axis, and the birefringent crystal is preferably LiNbO3 whose principal surface perpendicular direction coincides with the z axis. By doing in this way, even when the sample is rotated, elliptical polarization or the like does not occur when passing through the sample, so that more accurate measurement can be performed.
[0015]
The present invention separates the light generated from the light source unit into measurement light and reference light, and means for passing a measurement light to the subject sample, to interfere with the reference light measuring light that has passed through the test object, interference wherein an image acquisition unit for capturing an image, the apparatus comprising a computing unit for analyzing the acquired image to calculate the refractive index or birefringence distribution of the test sample using any method of measuring the And a refractive index or birefringence distribution measuring device.
[0016]
FIG. 4 shows the Li / Nb composition ratio dependence of the ordinary and extraordinary refractive indexes of LiNbO3 crystals calculated based on the data shown in Document 1. It can be seen that the ordinary light component n _o (n _x , n _y ) of the refractive index is constant regardless of the composition ratio, whereas the extraordinary light component ne (nz) of the refractive index has a strong correlation with the composition ratio. . If there is a Li / Nb composition ratio distribution in the LiNbO3 wafer, the refractive index for polarized light in the ordinary light direction is constant, but the refractive index for polarized light in the extraordinary light changes in proportion to the Li / Nb composition ratio. Means that
[0017]
On the other hand, the distribution of the wafer thickness ΔL (x, y) is the same for both extraordinary light and ordinary light if the location is the same. Therefore, the thickness distribution ΔL (x, y) is calculated from the transmitted wavefront measurement of ordinary light polarization, and the thickness distribution ΔT (x, y) is used to cancel the effect of the thickness distribution in the transmitted wavefront measurement of abnormal light polarization. Only the refractive index distribution can be extracted.
[0018]
The x-cut LiNbO3 will be specifically described below. The LiNbO 3 crystal is a uniaxial crystal, and the extraordinary refractive index ne is in the z-axis direction, and the x and y axes have the same refractive index and the ordinary refractive index no. As shown in FIG. 5, the X-cut is another name for the wafer shape in which the X-axis is oriented in the direction perpendicular to the wafer surface, and the z-axis direction in which the refractive index changes in proportion to the Li / Nb composition ratio exists in the main surface of the wafer. . A y-axis equivalent to the x-axis also exists in the main surface.
ne (x, y) = ne ₀ + Δne (x, y) (5)
no (x, y) = no ₀ (6)
L (x, y) = L ₀ + ΔL (x, y) (2)
Therefore, the optical path length is expressed by equation (3).
The optical path length OLo for ordinary light is
OLo (x, y) = no0 · L (x, y) = no ₀ · (L ₀ + ΔL (x, y))) (7)
The optical path length OLe for extraordinary light is
OLe (x, y) = ne (x, y) · L (x, y) = (ne ₀ + Δn (x, y)) · (L ₀ + ΔL (x, y))
~ Ne0 (L ₀ + ΔL (x, y)) + L ₀ · Δn (x, y) (8)
Therefore, rewriting equation (8) using equation (7)
OLe (x, y) = ne ₀ OLo (x, y) / no ₀ + L ₀ · Δne (x, y) (9)
The optical path length OL can be measured by an interferometer or the like. Therefore, OLe (x, y) and OLo (x, y) are values that can be actually measured. Assuming that the extraordinary refractive index ne ₀ , the ordinary refractive index no ₀ , and the wafer thickness L ₀ are known, the refractive index distribution Δne (x, y) can be calculated from the equation (9). From the refractive index distribution of the extraordinary light, it is possible to derive the Li / Nb composition ratio distribution using the configuration curve of FIG.
[0019]
However, when measuring at normal incidence, multiple interference occurs between the front and back of the wafer, and the phase distribution observed due to this influence slightly overlaps the multiple interference pattern, affecting the festival that extracts a slight refractive index distribution. Will receive.
[0020]
In order to solve these problems, the present invention focuses on the fact that the interference effect between the front and back sides can be reduced if only P-polarized light is used, and the present invention focuses on the difference in the composition ratio dependence of the refractive index due to the difference in polarization. It was. As shown in FIG. 1, let us consider a case where the principal surface normal direction of the LiNbO3 wafer is inclined with respect to the optical axis so that the incident angle is θ. If the plane including the normal direction of the main surface of the wafer and the optical axis is defined as the incident plane, the polarized light in the incident plane is referred to as P-polarized light, and the polarized light in the direction perpendicular to the incident plane is referred to as S-polarized light. FIG. 2 shows the calculated reflectance per one wafer surface when the incident angle θ is changed.
[0021]
In the case of vertical incidence of θ = 0 degree, reflection of about 15% occurs for both S wave and P polarization. When tilted, the reflectivity decreases with respect to P-polarized light, and there is a point at which no reflection occurs at about θ = 65 degrees. This is known to exist only in P-polarized light at an angle called the Brewster angle. (Optical and electromagnetic theory, Miyoshi Tanroku, Bafukan 1987) On the other hand, for S waves, the reflectance increases monotonically with the angle, and there is no angle at which no reflection occurs.
[0022]
The present invention pays attention to this point, and comes up with the idea of measuring only the refractive index distribution by tilting the normal direction of the main surface of the wafer with respect to the optical axis and using only P-polarized light to reduce or eliminate the effect of interference. It's just a matter of things. Ideally, the reflectivity can be completely reduced to 0 by inclining it so as to coincide with the Brewster angle. However, since the tilt angle is large and the image of the transmitted wavefront is flattened, the spatial resolution is deteriorated.
[0023]
Further, the refractive index distribution cannot be calculated from Equation 9 as long as the wafer is tilted. Since the wafer main surface normal direction is used obliquely, further detailed analysis is required.
[0024]
The operation principle will be described below using an X-cut LiNbO3 wafer as an example. Consider a case where the wafer is tilted so that the incident angle with respect to the normal direction of the main wafer surface is θ. First, as shown in FIG. 3A, the wafer is set in a direction in which the polarization axis of the P wave coincides with the z axis of the crystal. The angle of incidence within the crystal at this time is θ _1z . Assuming that the wafer thickness has a distribution in the plane (x, y), it is the sum of the constant thickness regardless of the position and the component ΔL (x, y) depending on the two-dimensional position of the wafer. Appears. If the constant refractive index component n _ez (θ _1z ) and the spatially dependent component are Δn _ez (x, y, θ _1z ), and the observed phase difference distribution is ΔZ ₁ (x, y), then the phase difference The distribution is expressed as in Equation (10).
[0025]
[Formula 10]

[0026]
Here, φ ₁ is a constant component of the phase difference.
[0027]
Further, as shown in FIG. 3B, the sample is rotated by 90 ° so that the polarization direction coincides with the y-axis direction of the crystal. The phase difference distribution ΔY ₁ (x, y) observed when the intra-crystal incident angle at this time is θ _1y is given by equation (11).
[0028]
[Formula 11]

[0029]
Here, n _ey (θ _1y ) >> Δn _ey (x, y, θ _1y ), L ₀ >> ΔL (x, y), so Δn _ey (x, y, θ _1y ) on the left side of equation (11) • The term ΔL (x, y) can be ignored. Assuming φ ₁ = n _eZ (θ _1Z ) · L ₀ and φ ₂ = n _ey (θ _2Z ) · L ₀
[Formula 12]

[0031]
Using equation (12), equation (11) is transformed into equation (13).
[0032]
[Formula 13]

[0033]
Next, the relational expression between the refractive index spatial distribution Δn _eZ (x, y, θ _1Z ) actually measured and the refractive index spatial distribution Δn _Z (x, y) of the z-axis polarization of the crystal will be clarified. Assuming a homogeneous material, the angular dependence of the P-polarized light (polarized light in the y-axis direction of the crystal) extraordinary light refractive index is
[Formula 14]

[0035]
Assuming a uniaxial crystal, Δn _y = Δn _x , If n _x = n _y , then the spatial distribution of n _ey (θ) is expressed by equation (15).
[0036]
[Formula 15]

[0037]
On the other hand, when the sample is rotated 90 ° so that the P polarization and the y-axis direction coincide with each other, the angular dependence of the polarization anomalous refractive index in the crystal y-axis direction is
[Formula 16]

[0039]
The spatial distribution of n _eZ (θ) is expressed by equation (17).
[0040]
[Formula 17]

[0041]
Here, the coefficient Δn _eZ (θ) / Δn _Z is obtained as follows by differentiating the equation (16) by n _Z.
[0042]
[Formula 18]

[0043]
Using equation (14) to equation (18) and rewriting equation (13) using Δn _Z (x, y), equation (19) is obtained.
[0044]
[Formula 19]

[0045]
From the formula (19), it is possible to calculate the birefringence distributions Δn _Z / n _Z −Δn _X / n _X to (Δn _Z −Δn _X ) / n _{Z of the} crystal. In this case, since the expression (19) does not include a term relating to the spatial distribution ΔL (x, y) of the sample thickness, it can be seen that only the birefringence distribution can be extracted regardless of the thickness unevenness. In this case, it is understood that it is not necessary to assume that the spatial distribution of the ordinary light refractive index is negligibly small compared to the spatial distribution of the extraordinary light refractive index. Therefore, it can be applied to any crystal material.
[0046]
Further, in the LiNbO3 crystal, as shown in FIG. 4, the extraordinary refractive index _ne (n _x = _ny ) hardly depends on the Li composition ratio dependence, and therefore the spatial dependence is very small. Therefore, Δn _X (x, y) = If 0, the refractive index distribution Δn _Z / n _Z can be calculated.
[0047]
Although the measurement principle has been described above, an actual measurement apparatus and calculation procedure will be described. As shown in FIG. 6, a so-called interferometer 1 is configured to measure the sample transmission phase. The interferometer includes a laser light source unit 30, a partial reflection mirror 20 and an interference unit that causes light reflected by the reflection mirror 3 to return to the interferometer through the sample 10 disposed in the sample unit. The phase of the sample can be calculated from the movement of the interference ring by slightly changing the optical length to the reference mirror with a piezo element or the like attached to the reference mirror.
[0048]
As shown in FIG. 3 (a), the sample portion is inclined by 45 degrees and arranged so that the P-polarized light coincides with the z-axis direction of the crystal. The transmitted wavefront image ΔZ ₁ (x, y) obtained at this time has an elliptical shape shortened in the z-axis direction as shown in FIG.
[0049]
On the other hand, the sample is rotated by 90 ° so that the P-polarized light direction coincides with the y-axis of the sample (FIG. 3B). The transmitted wavefront image ΔY ₁ (x, y) obtained at this time has an elliptical shape shortened in the y-axis direction of the crystal. It is necessary to devise to calculate two images with different short axis directions using the equation (19).
[0050]
Both images are enlarged in the minor axis direction and converted into circular images with the same ratio in both the y and z axis directions (FIGS. 7B and 8B). In this state, since the axial directions of both images are orthogonal, either one of the images (in the explanation, the ΔY ₁ (x, y) image) is reversely rotated by 90 ° so that the coordinate axis directions of both images coincide with each other (FIG. 8 ( c)).
[0051]
Image ΔZ ₁ (x, y) converted in this way FIG. 7B, ΔY ₁ (x, y) Refractive index distribution Δn _Z (x, y) is calculated from equation (10) using FIG. 8C. can do.
[0052]
As described above, in the case of an X-cut LiNbO3 wafer, the sample is placed at an angle, and the sample is rotated 90 ° with the P-polarized light, and the optical path length ΔZ (x, y in the two z-polarized and y-polarized directions is obtained. ), by measuring the [Delta] y (x, y) of the optical interferometer and the like, it was found that it is possible to measure the refractive index distribution Δn _z (x, y) from equation 20.
[0053]
By performing such an operation, it was possible to accurately calculate a slight refractive index distribution of about 1/10000 that was hidden behind the wavefront distortion due to the thickness distribution ΔL (x, y) and was not visible.
In addition, since only P-polarized light is used, it is possible to measure accurately without the influence of interference patterns due to multiple interference on the front and back of the wafer.
[0054]
In order to further improve accuracy, a method for solving the following problem is desirable. First, when there is distortion or inclination (bias component) in the transmitted wavefront of the interferometer body when there is no sample, this bias component is superimposed on the transmitted wavefront when the sample is passed. Accordingly, the same bias component is superimposed on FIG. 7 (a) and FIG. 8 (a). As shown in FIG. 8C, this bias component is also rotated by 90 ° in order to rotate the image by 90 degrees, and the bias component with the same amount superimposed in FIG. 7A and FIG. However, it is observed as a gradient component of the refractive index without being canceled.
[0055]
Second, in order to measure by rotating the sample by 90 °, even if calculation is performed using the observed phase on the same y and z coordinates, the optical path is not the same and the y and z coordinates are the same. The phase difference passing through the optical path rotated by 90 ° is used. For this reason, if the sample thickness is inclined or has large thickness unevenness, the effect of subtracting the sample thickness unevenness is weak, and as a result, a bias component or apparent nonuniformity is generated in the calculated refractive index distribution.
[0056]
In order to improve these two points, the sample is rotated in 90 ° steps as shown in FIG. 9 and four transmitted wavefronts are measured (here, + Z image (FIG. 9 (a)), + Y image ( 9D), -Z image (FIG. 9B), -Y image (referred to as FIG. 9E)). -Z image is rotated 180 ° and added to + Z image. The -Y image is also rotated 180 ° and added to the + Y image. If the added images are Z2 image (FIG. 9C) and Y2 image (FIG. 9F), bias components such as linear inclination are canceled in each transmitted wavefront image. If the transmitted wavefront distribution of Z2 is ΔZ ₁ (x, y) (Fig. 9 (c)) and the transmitted wavefront distribution of Y2 is ΔY ₁ (x, y) (Fig. 9 (f)), the refractive index distribution is obtained from Equation 20. Can be calculated. It should be noted that the sample thickness at this time is doubled. Also, by using the Z2 and Y2 images, the effect of rotating the optical path by 90 ° in the wafer thickness direction was spatially averaged and alleviated.
[0057]
As described above, calculation is performed using the four transmitted wavefronts when the sample is rotated by 90 °, so that the spatial resolution is slightly degraded. However, the refraction is performed accurately without being affected by the bias component of the interferometer. It became possible to measure only the rate distribution.
[0058]
DETAILED DESCRIPTION OF THE INVENTION
As a first embodiment, FIG. 10 shows a case where a refractive index profile is measured using a z-cut 5 inch LiNbO 3 wafer (thickness: 1000 μm). FIG. 10 (a) is a front view of the measurement system, and FIG. 10 (b) is a side view. In order to measure the transmitted wavefront distortion (optical path length), an interferometer (GPI-XP) manufactured by ZYGO was used. The reflection mirror 3 is mounted on a mirror mount 4 with tilt adjustment, and tilt can be adjusted by tilt adjustment screws 5 and 6. These optical systems are arranged on a classic anti-vibration optical system, and the whole is arranged in a clean bench controlled at a temperature of 0.1 ° C.
[0059]
First, a 6-inch diameter He—Ne laser beam is emitted from the interferometer body 1. The emitted light propagates on the optical axis 12, is reflected by the reflecting mirror 3, and returns to the interferometer body through the same optical axis 12. Adjust the tilt of the reflecting mirror without a sample.
[0060]
Next, as shown in FIGS. 10A and 10B, the rotary stage 7 is adjusted and tilted so that the x-axis of the crystal of the X-cut LiNbO 3 wafer is at an angle of 45 degrees with respect to the optical axis 12. Further, the sample 10 is set on the sample stage 8 so that the z-axis coincides with the P polarization direction. At this time, set the sample so that the polarization direction of the interferometer body is the P-wave direction in the sample tilt plane and the z-axis direction of the sample coincides with the P-wave polarization as shown in FIG. 11 (a). The transmitted wavefront distortion is measured. The measurement result of the transmitted wavefront distortion ΔZ (x, y) in this state is shown in FIG. The acquired data is once recorded in a storage device of a personal computer (not shown).
[0061]
Next, as shown in FIG. 11 (b), the wafer 10 is rotated 90 degrees on the sample stage 8 around the sample x axis, and the interferometer body P wave polarization direction is aligned with the crystal y axis and transmitted. The wavefront distortion ΔY (x, y) is measured. The result of measuring the transmitted wavefront distortion ΔY (x, y) in this state is shown in FIG. The acquired data is once recorded in a storage device on a personal computer (not shown).
After the measurement is completed, the P wave Z-axis transmitted wavefront distortion ΔZ (x, y) and the P-wave Y-axis transmitted wavefront distortion ΔY (x, y) are read from the storage area of the personal computer, and the procedure shown in FIGS. in calculating the distribution [Delta] n _z refractive index n _z (x, y) according to equation (19). The measured results are shown in FIG. The maximum Δn _z (x, y) amount is about 0.0003, and it can be seen that the refractive index distribution of the fourth decimal place can be extracted.
As can be seen from FIG. 14, the refractive index distribution is completely different from the shape reflecting the wafer thickness distribution of FIGS. 12 and 13, indicating that the refractive index distribution independent of the wafer thickness can be accurately measured.
[0062]
In the above embodiment, the case where a LiNbO3 crystal is used as a uniaxial crystal has been described. However, the present invention is not limited to this, and the refractive index of other biaxial crystals such as LiTaO3 and KLN which are other uniaxial crystals can be measured. Obviously, it may be used.
[0063]
【The invention's effect】
As described above, according to the present invention, it is possible to provide a measurement method for quickly measuring a refractive index distribution depending on a composition ratio in a crystal such as a LiNbO 3 crystal whose refractive index changes depending on the composition ratio. .
[Brief description of the drawings]
[Fig. 1] Optical axis diagram at oblique incidence [Fig. 2] Incident angle dependence of LN reflectivity [Fig. 3] (a) When crystal z-axis and polarization direction are parallel (b) Crystal y-axis and polarization When the directions are parallel [FIG. 4] Dependence of the LN refractive index on the Li composition ratio [FIG. 5] An explanatory diagram of a method of extracting only the refractive index by canceling the thickness distribution [FIG. 6] A block diagram showing the measurement system [FIG. FIG. 8 is a diagram showing how to rotate and measure the measured image data. FIG. 8 is a diagram showing how to rotate and measure the measured image data. FIG. 9 is a measuring method for removing the transmitted wavefront slope component. Front view of the measuring device (b) Side view of the measuring device [FIG. 11] A diagram showing the relationship between the polarization direction and the crystal axis of the sample [FIG. 12] A transmitted wavefront measurement diagram of the Z-axis polarized light [FIG. Transmission wavefront measurement diagram [Fig. 14] Wafer birefringence distribution measurement diagram [Explanation of symbols]
1 ... Interferometer 3 ... Reflector 4 ... Mirror mount 5 6 ... Tilt adjustment screw 7 ... Rotary stage 8 ... Sample stage 10 ... Sample 12 ... Optical axis

Claims (6)

In the refractive index or birefringence distribution measurement method by transmitted wavefront measurement, the sample is tilted so that the vertical direction of the main surface is at a constant tilt angle with respect to the optical axis in a sample having two main surfaces facing each other where light can enter. is allowed, if fitted to the second spindle which is perpendicular to the first transmitted wavefront in a case where to match the polarization direction of the P polarized light to the first principal axis of the measurement sample, a first main axis the polarization direction of the P polarized light A method of measuring a refractive index or a birefringence distribution from the second transmitted wavefront. In the refractive index or birefringence distribution measurement method by transmitted wavefront measurement, the sample is tilted so that the vertical direction of the main surface is at a constant tilt angle with respect to the optical axis in a sample having two main surfaces facing each other where light can enter. The first transmitted wavefront when the polarization direction of the P- polarized light coincides with the first principal axis of the measurement sample, the second transmitted wavefront when the sample is further rotated 180 degrees, and the polarization of the P-polarized light The refractive index or birefringence distribution is calculated from the third transmitted wavefront when the direction is coincident with the second principal axis direction orthogonal to the first principal axis and the fourth transmitted wavefront when the sample is further rotated 180 degrees. a method of measuring. Wherein, Method person according to claim 1 or claim 2, wherein the predetermined tilt angle is Brewster angle at which no reflection. The birefringent crystals, methods better according to any one of claims 1 to 3, characterized in that the LiNbO3 main surface perpendicular direction coincides with the x or y axis. The birefringent crystals, methods better according to any one of claims 1 to 3, characterized in that the LiNbO3 main surface perpendicular direction is coincident with the z-axis. The light generated from the light source unit is separated into reference light and measurement light, the measurement light and means for passing the test sample to interfere with the reference light measuring light that has passed through the test object, image acquisition to capture interference image and parts, the apparatus comprising a computing unit for analyzing the acquired image to calculate the refractive index or birefringence distribution of the test sample with how one of claims 1 to 3 Characteristic refractive index or birefringence distribution measuring device.

Images