JP3898329B2 - Method of measuring LSAW propagation characteristics using an acoustic microscope - Google Patents

Description

次に、音速変化の差分ΔV(Δf, h₀)と周波数変化Δｆの関係を求めるために、図５Ａの曲線から次式(11)により図５Ｂに示す換算曲線を求める。
ΔV(Δf, h₀)＝ΔV_LSAW(f₁+Δf, h₀)−ΔV_LSAW(f₂+Δf, h₀) (11)
ただし、0 ≦Δf ≦Δf₁₂ (12)
ここで、図５Ｂの曲線は単調増加関数となっており、ΔV(Δf, h₀)とΔｆの間に１対１の対応関係が成立する。厚さｈでのV_LSAW(f, h) は図４Ｂに示した厚さｈ₀ でのV_LSAW(f, h₀)の周波数特性波形をそのまま周波数軸方向及び速度軸方向にずらした波形となるので、式(10)と式(11)を比較すると、図５Ｂの換算曲線からΔV(Δf, h)=ΔV(Δf, h₀)となるΔf=Δf_cを求めることにより、厚さがΔｈ異なることと等価な周波数変化Δf_cが求められることがわかる。即ち、測定点Ｐa で周波数f₁とf₂でそれぞれ音速V_LSAW(f₁, h)及びV_LSAW(f₂, h)を測定して式(10)よりΔV(Δf, h) を求め、図５Ｂから対応するΔf_cが決定される。これより図５Ａを利用して、任意の測定点Ｐa におけるΔV_LSAW(f₁, h)及びΔV_LSAW(f₂, h)に対応する測定点Ｐ₀ におけるΔV_LSAW(f₁+Δf_c, h₀)及びΔV_LSAW(f₂+Δf_c, h₀)が求まるので、式(８)，(９)から任意の測定点Ｐa での真値V_LSAWaが次式(13)のように求められる。
【００１６】

以上、本発明の測定手順を示した。ここでは、簡単のために２つの周波数f₁、f₂を図５Ａにおいてそれぞれ最小、最大となるように選択したが、換算曲線における１対１の対応がつく範囲ならばどの周波数を選択してもよい。例えば図５Ａの音速変化ΔV_LSAW(f, h₀)の曲線において、周波数f₁とf₂を互いに逆勾配の単調変化領域内、例えば極小値から周波数ｆと共に増加して極大値までの周波数領域と、その極大値から減少して次の極小値までの周波数領域とからそれぞれ任意に選択すれば、図５Ｂの換算曲線は必ず単調関数となる。実際に例えばf₂をΔV_LSAW(f, h₀)の極大値を与える周波数近傍（ただし、極大値を与える周波数より大）に選べば、極小値近傍でのΔV_LSAW(f, h₀)の変化率が極大値近傍でのそれより小さいため、例えばf₁を図５Ａに示す速度変化曲線の極小値を与える周波数より多少低く選択しても換算曲線は単調関数となる。
【００１７】
換算曲線の単調増加の関係を保ちつつ、式(12)に示すΔｆの範囲が最大になるようにf₁、f₂(f₁<f₂) を選択したとき、本手法において測定可能な試料の厚さ分布の最大値Δh_maxは、試料中のバルク縦波音速をV_Lとして次式(14)で与えられる。厚さ分布がΔh_maxを越える場合は、Δh_maxを越えない範囲に測定領域を分割し、それぞれの領域内で測定基準点を決め分割領域毎に測定を行えばよい。
【００１８】
Δh_max＝(V_L/2f₂)(Δf₁₂/ΔF) (14)
実施例
以上、この発明による測定方法の原理を基準測定点Ｐ₀ に対し任意の測定点Ｐa での真値V_LSAWaを求める場合について説明したが、実際の測定においては試料面上の所望の直線（例えば直径）に沿って一定間隔でV_LSAW を測定する場合の手順を具体例で以下に説明する。
【００１９】
ステップＳ１： 試料は３インチの両面光学研磨されたＺカットのLiNbO₃ウェハで、中央部の厚さが約 377μｍ、周辺部の厚さが約381〜382μｍと厚さに分布があり、ちょうど図４Ａのような形状をしている。試料面上で最も薄いと予想される中央の点（原点Ｐ₀ とし、厚さをｈ₀ とする）において、結晶Ｙ軸方向伝搬のLSAW速度の周波数特性を、200〜240MHz の範囲で0.2MHzごとに測定した。結果を図６Ａに実線で示す。この曲線は図４Ｂにおける太実線の曲線に対応する。図中の点線は、実線の測定値に対してΔＦ＝9.6MHzの周期で２回の移動平均を行なった結果であり、裏面反射波の影響による測定誤差を除去したものである。周波数によって得られる値が異なっているが、これは超音波デバイスの周波数特性と考えられる。
【００２０】
ステップＳ２： 図６Ａの実線から点線を差し引くことにより、裏面反射波の影響による音速変化ΔV_LSAW(f, h₀)を求めた結果を図６Ｂに示す。この曲線は図５Ａの曲線に対応する。ここで、図６Ｂにおいて周波数f₁、f₂を、予想される厚さの最大変化約５μｍの変化による誤差を補正できることと、測定点Ｐ₀ が必ずしも試料の最も薄い場所ではないということを考慮して、f₁=220.4MHz、f₂=224.6MHzとした。
【００２１】
ステップＳ３： ウェハ直径上において、周波数f₁、f₂でのＹ軸伝搬のLSAW速度V_LSAW(f₁, h)，V_LSAW(f₂, h)の分布を、測定点Ｐ₀ を通る直線に沿って１mmごとに±30mmの範囲で測定した。結果を図７Ａに示す。LSAW速度のプロファイルはf₁、f₂で異なるが、この原因は主に裏面反射波の影響によるものである。また、それぞれの測定値には図６Ａの点線に示されるように、超音波デバイスの周波数特性による音速変化が含まれている。
【００２２】
ステップＳ４： f₁、f₂における裏面反射波の影響による音速変化分の差ΔV(Δf, h)を求めるために、図７Ａの実線から点線を差し引き、更に図６Ａに示す音速シフト分ΔV_f12を差し引く。結果を図７Ｂに示す。
ステップＳ５： 次に、図６ＢからΔV(Δf, h₀)と周波数変化Δｆの関係を示す換算曲線を式(11)により求める。ただし、Δｆの範囲は次式(15)を満たすものとする。
【００２３】
-(f₂-f_m) ≦Δf ≦ (f_m-f₁) (15)
図８Ａに求めた換算曲線を示す。ここで、図６ＢのΔV_LSAW(Δf, h₀)が最大となる周波数がf_m＝224.2MHzであるので、-0.4MHz≦Δf≦3.8MHzである。
ステップＳ６： 図７Ｂの音速変化の差分ΔV(Δf, h) と、図８Ａの換算曲線からΔV(Δf, h)＝ΔV(Δf, h₀) となるΔf=Δf_cを各測定点に対して求めることにより、厚さがΔh 異なることと等価な周波数の変化Δf を見積もることができる。結果を図８Ｂに示す。なお、換算曲線においてデータのない部分は前後のデータを用いて直線補間した。
【００２４】
ステップＳ７： 図８Ｂより、f₁、f₂における各測定点の裏面反射波の影響による音速変化は、それぞれ図６ＢからΔV_LSAW(f₁+Δf_c, h₀)及びΔV_LSAW(f₂+Δf_c, h₀)として求められる。f₁、f₂に対して求めた裏面反射波の影響による音速変化曲線をそれぞれ図９Ａに実線、点線で示す。図９Ａより、裏面反射波による音速変化ΔV_LSAW(f+Δf_c, h₀) は最大で4.82m/s であることがわかる。
【００２５】
ステップＳ８： 図７Ａに示したLSAW速度の測定値から、図９Ａの音速変化をそれぞれ差し引くことにより、裏面反射波により生じた誤差を補正する。f₁、f₂に対する補正後の結果をそれぞれ図９Ｂに実線、点線で示す。図９Ｂの補正結果はf₁とf₂で絶対値が異なっているが、これは前述した超音波デバイスの周波数特性によるものであり、相対的な音速分布を調べる上では問題にならない。絶対値が必要な場合は、標準試料を用いた絶対校正法（文献３参照）により絶対値を得ることができる。
【００２６】
ここで絶対校正法について簡単に説明する。まず、標準試料（例えばＧＧＧ単結晶）に対し実際に測定した弾性定数より計算したLSAW速度の理論値を求める。このときのV(z)曲線の干渉周期Δｚ（図２参照）に相当する値をΔｚ_ST(calc.) とする。次に、同じ標準試料に対してＬＦＢ超音波顕微鏡システムでLSAW速度を測定し、その時のΔｚに相当する値をΔｚ_ST(meas.) とする。この両者の比をとることで次式(16)に示す校正係数が決定する。
【００２７】
K(V)＝Δｚ_ST(calc.)/Δｚ_ST(meas.) (16)
後は、実際の試料に対して測定されたLSAW速度（図９Ｂの実線及び点線）のΔｚに相当する値、Δｚ(measured)に対し、それぞれ次式(17)に示すように校正係数K(V)を掛けて、得られたΔｚ(calibrated)を式(１)に代入することでLSAW速度の絶対値が得られる。
【００２８】
Δｚ(calibrated)＝K(V)Δｚ(measured) (17)
図９Ｂの測定結果が正しく測定されているか確認するため、試料の測定ライン上の０、±15、±30mmの位置でそれぞれLSAW速度の周波数特性を測定し、その移動平均を行なった結果を、f₁、f₂に対して図９Ｂにそれぞれ○、□で表す。この結果と先に得られた測定結果とは、±0.5m/s以内でよく一致している。このことから、本手法による補正によって裏面反射波の影響による測定誤差を十分除去できていることがわかる。
【００２９】
以上、この発明によるLSAW伝搬特性の測定方法を説明した。上記では簡便な例として、測定対象である薄い試料に対するLSAW速度の周波数特性の移動平均値を用いて、超音波デバイスの周波数特性を除去する手順を示したが、その他の方法として次のようなことが考えられる。測定試料と同種で、裏面反射波の影響がない厚い試料を準備し、その試料に対してLSAW速度の周波数特性を測定すれば、それがそのまま超音波デバイスの周波数特性として得られ、移動平均を使った上記測定方法と同様に測定が行える。この場合、移動平均値を用いるよりも正確な超音波デバイスの周波数特性が得られ、測定精度が向上すると考えられる。あるいは、準備する厚い試料を標準試料（例えばＧＧＧ単結晶）としても同様な超音波デバイスの周波数特性が得られると考えられる。ただし、絶対値に関しては前述した絶対値校正法により校正されるものである。
【００３０】
【発明の効果】
以上述べたようにこの発明によれば、試料の厚さ分布を直接測定することを必要とせず、試料上のある１点についてのみLSAW速度の周波数特性の測定を行ない、他の測定点は２つの周波数で測定を行なうだけ、すなわち各点で２回の測定を行なうだけで各測定点の真値を得ることができ、測定点が多ければ多いほど、測定時間の大幅な短縮が実現できる。また、ＰＦＢ超音波顕微鏡を用いた場合も同様な手順で、同様な効果が得られる。
【００３１】
なお、この発明では上述したように薄い試料におけるLSAW伝搬特性の分布を効率よく測定できるが、もし、試料のLASW伝搬特性の分布が均一であると仮定できる場合は、逆に試料の厚さの分布が測定できる。例えば式(５)から任意の測定点Ｐa での試料の厚さはh=h₀+Δh=h₀(1+Δf/f)と表せるので、Δf として図８Ｂに示した各測定点Ｐa に対応するΔf_cを与え、ｆとしてf₁又はf₂を与えることにより測定点Ｐa での試料の厚さｈを基準位置Ｐ₀ での厚さh₀に対する割合として計算できる。基準位置Ｐ₀ での厚さh₀は、例えば測定した周波数特性ΔＦ及び試料中の縦波音速V_Lの測定値又は理論値を用いて式(２)から計算することができる。
【図面の簡単な説明】
【図１】ＬＦＢ超音波顕微鏡の測定原理を説明する図。
【図２】 V(z)曲線を示す図。
【図３】試料の表面及び裏面からの反射波のタイムチャートを示しており、Ａが厚い試料の場合の図、Ｂが薄い試料の場合の図である。
【図４】Ａは厚さ分布のある試料形状の例を示した図、Ｂは薄い試料に対するLSAW速度の周波数特性を示す図である。
【図５】Ａは裏面反射波の影響による見掛け上の音速変化を示す図、Ｂは換算曲線を示す図である。
【図６】Ａは試料上の最も薄い点におけるLSAW速度の周波数特性を示す図、Ｂは裏面反射波の影響による見掛け上の音速変化を示す図である。
【図７】Ａは試料の径方向のLSAW速度分布の測定結果を示す図、ＢはＡに示す測定結果の差分を示す図である。
【図８】Ａは換算曲線を示す図、Ｂは試料厚さの変化をそれと等価な周波数の変化に見積った結果を示す図である。
【図９】Ａは見積った補正すべき値の結果を示す図、Ｂは補正結果を示す図である。
（参考文献）
（文献１）J. Kushibiki and N. Chubachi, "Material Characterization by Line-Focus-Beam Acoustic Microscope," IEEE Trans. Sonics and Ultrason., vol.SU-32, pp. 189-212 (1985).
（文献２）櫛引、荒川、大橋、"直線集束ビーム超音波顕微鏡による材料評価法における試料裏面反射波の影響--試料厚さに関する検討--"、日本音響学会春季講演論文集、pp.1035-1036、平成９年３月.
（文献３）J. Kushibiki and M. Arakawa, "A Method for Calibrating theLine-Focus-Beam Acoustic Microscopy System.", IEEE Trans. UFFC., vol. 45, no. 2,March(1998), in press.[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for measuring the acoustic characteristics of a thin sample, that is, the LSAW propagation velocity, using an ultrasonic microscope.
[0002]
[Prior art]
An ultrasonic microscope has been developed as a technique for analyzing and evaluating new substances and material properties. Measurement methods using an ultrasonic microscope include an image measurement method and a quantitative measurement method. In the quantitative measurement method, the V (z) curve analysis method is used, and the propagation characteristics (sound speed, propagation attenuation) of LSAW excited on the sample surface are measured. For this measurement, a point focused ultrasonic beam (PFB) and a linearly focused ultrasonic beam (LFB) can be used. Here, an LFB ultrasonic microscope dedicated to quantitative measurement (see Reference 1) will be taken up and described. FIG. 1 shows a cross-sectional view of an LFB ultrasonic device (referring to a rod 2 on which an ultrasonic transducer 1 and an acoustic lens 3 are formed) and a sample system as the basic principle. The coordinate axes are taken as shown in the figure with the focal point 6 as the origin.
[0003]
The plane ultrasonic wave excited by the ultrasonic transducer 1 is focused in a wedge shape by the opening surface of the acoustic lens 3 formed in a semi-cylindrical shape, and is irradiated onto the surface of the sample 5 through the water 4 which is a liquid sound field medium. Is done. At this time, the ultrasonic wave incident at the critical angle θ _LSAW excites the LSAW on the sample surface. LSAW propagates while re-radiating longitudinal waves into water at an angle of θ _LSAW . The reflected ultrasonic wave from the sample 5 returns to the transducer 1 again through the water 4 and the acoustic lens 3, but when the LFB ultrasonic device is moved closer to the sample side from the state where the sample is at the focal point 6 (this operation is called defocusing). ) The components that effectively contribute to the transducer output are only two components that approximately take the paths of # 0 and # 1 shown in FIG. 1 from the conventional measurement model. The component taking the # 0 path is a direct reflection component from the sample surface, while the component taking the # 1 path is a component including the LSAW propagation characteristics. By performing defocusing, an interference waveform of the above two components called a V (z) curve is obtained as a transducer output (see FIG. 2). By obtaining the dip period Δz of the V (z) curve based on the V (z) curve analysis method, the phase velocity V _LSAW of the _LSAW is obtained from the equation (1).
[0004]
V _LSAW = V _W / √ {1- (1-V _W / 2fΔz) ² } (1)
Here, V _W is the longitudinal sound velocity in water, and f is the ultrasonic frequency.
In actual measurement, a high frequency burst pulse is input to the transducer as an electrical signal, the input signal is converted into ultrasonic waves by the transducer, and the sample is irradiated through water. A cylindrical lens with a radius of curvature of 1 mm is used for the 200 MHz band, and the pulse width is usually about 500 nsec and the pulse repetition frequency is about 20 kHz. Of the reflected signals from the electrical end, the lens opening surface, the sample, etc., only the reflected signal from the sample is extracted by the high frequency gate circuit to perform signal processing. Considering reflected wave component from the back propagating a path # 0 'in FIG. 1, the use of the pulse signal, when the sample is sufficiently thick, the gate period P _G by a gate circuit as shown in FIG. 3A for example By extracting the signal only in the interval, the reflected wave 32 from the back surface of the sample can be completely separated from the reflected wave 31 from the sample surface, but cannot be separated as shown in FIG. 3B when the sample is thin.
[0005]
When the LSAW velocity is measured by changing the ultrasonic frequency for a thin sample in which a reflected wave from the back surface of the sample (hereinafter referred to as a back surface reflected wave) is included in the detection signal, it is shown by a thick solid line in FIG. 4B. Periodic changes appear. This period ΔF depends on the sample thickness h and the bulk longitudinal wave sound velocity V _L in the sample, and is expressed by the equation (2).
ΔF = V _L / 2h (2)
As can be seen from this, there is a problem that an error is included in the measured value depending on the ultrasonic frequency and the sample thickness due to the influence of the back surface reflected wave. However, the measurement error due to the influence of this back surface reflected wave, that is, the speed change, is such that V _LSAW (f, h) has a periodicity as shown by the thick solid line in FIG. It is known that it can be removed by performing a moving average with a period of (see reference 2).
[0006]
[Problems to be solved by the invention]
The LFB ultrasonic microscope apparatus has a feature that the acoustic characteristics of the microscopic region can be measured over a wide range on the sample surface. However, for example, when performing in-plane evaluation of acoustic characteristics on a thin, large-diameter sample such as a wafer, the frequency characteristics of the LSAW speed are measured at each measurement point as described above, and the moving average is calculated. The method of obtaining the true value of each point by performing the measurement requires a very long time, and there is a drawback that a quick and accurate measurement cannot be performed. In general, the thickness of the sample has a distribution, and therefore the magnitude of the measurement error due to the influence of the back-surface reflected wave differs at each measurement point, and it is difficult to obtain a true value by a method other than the above.
[0007]
An object of the present invention is to provide a method that can shorten the measurement time and efficiently measure the LSAW propagation velocity.
[0008]
[Means for Solving the Problems]
From the correspondence between the conversion curve created based on the frequency characteristics of the LSAW velocity at one point on the sample surface and the difference between the measured values at the two frequencies at the other measurement points, the back surface at each measurement point. Estimate changes in measured LSAW speed due to the effect of reflected waves, and correct the measured values.
[0009]
DETAILED DESCRIPTION OF THE INVENTION
A case where the measured value of the LSAW speed for a sample having a concave thickness distribution as shown in FIG. 4A is corrected will be described. First, it is assumed that the acoustic characteristics of the sample are uniform. A measurement point P ₀ on the sample surface having a thickness h ₀ is selected, and the frequency characteristic of the LSAW speed is measured at that point. At this time, it is assumed that the frequency characteristic V _LSAW (f, h ₀ ) as shown by the thick solid line in FIG. 4B is obtained due to the influence of the back surface reflected wave. The actual measurement further includes a change in the measurement value due to the frequency characteristics of the ultrasonic device, but will be omitted here for simplicity. When a moving average is taken with a period ΔF with respect to the thick solid line in FIG. 4B, a true value V _LSAW (dotted line) of the LSAW speed at the measurement point P ₀ is obtained. Here, if any other measurement point on the sample surface is Pa, and the thickness of the measurement point Pa is thicker than the measurement point P ₀ by a minute amount Δh (Δh << h ₀ ), the frequency characteristic at the measurement point Pa is obtained. V _LSAW (f, h ₀ + Δh) is obtained by shifting the frequency characteristic (thick solid line) at thickness h ₀ by Δf as shown by the thin solid line in FIG. is there.
[0010]
V _LSAW (f, h ₀ + Δh) = V _LSAW (f + Δf, h ₀ ) (3)
In FIG. 4B, when attention is paid to the measured values of the LSAW speeds of the thick solid line and the thin solid line at the frequency f, ΔV ′ _LSAW = V _LSAW (f + Δf, h ₀ ) −V _LSAW (f, It can be seen that a difference of h ₀ ) occurs. Therefore, the frequency difference Δf equivalent to the difference in thickness Δh can be obtained by obtaining a frequency satisfying the following expression (4) on the thick solid line in FIG. 4B.
[0011]
V _LSAW (f + Δf, h ₀ ) = V _LSAW (f, h ₀ ) + ΔV ' _LSAW (4)
That is, this corresponds to obtaining a frequency change Δf that satisfies the relationship of the following equation (5), where the product of the frequency f and the thickness h of the sample is constant.
(h ₀ + Δh) f = h ₀ (f + Δf) (5)
Therefore, the difference in sound speed between the measured value of the sound speed at the frequency f + Δf and the true value V _LSAW for the sample of thickness h ₀ is expressed as ΔV _LSAW (f + Δf, h ₀ ) = V _LSAW (f + Δf, h ₀ ) − V _LSAW (6)
Then, the true value at the measurement point Pa can be obtained by the following equation (7) obtained by substituting equation (3) into equation (6).
[0012]
V _LSAW = V _LSAW (f, h ₀ + Δh) −ΔV _LSAW (f + Δf, h ₀ ) (7)
That is, by using the frequency characteristic of the LSAW velocity at the measurement point P ₀ and the true value obtained by the moving average, the influence of the back surface reflected wave can be obtained without measuring the frequency characteristic of the LSAW velocity at any other measurement point. It can be corrected.
Next, consider the general case where the acoustic properties of the sample are non-uniform. At this time, since the true value V _LSAWa of the LSAW speed at an arbitrary measurement point Pa is different from the true value V _{LSAW at the} measurement point P ₀ , the thin solid line V _LSAW (f, h ₀ + Δh) in FIG. Will do. Therefore, a procedure of a measurement method that can be applied even when there is a distribution in the LSAW speed by using the difference in sound speed change at the two frequencies is shown below.
[0013]
First, as described above, from the frequency characteristic of the LSAW velocity (thick solid line in FIG. 4B) measured at the reference measurement point P ₀ (assumed to be the thinnest point here) on the sample surface with respect to the sample of FIG. The value V _LSAW (dotted line in FIG. 4B) is subtracted to obtain the sound velocity change ΔV _LSAW (f, h ₀ ) due to the influence of the back surface reflected wave when the frequency f is changed at the measurement point P ₀ . The result is shown in FIG. 5A. Here, as shown in FIG. 5A, for example, the frequencies f ₁ and f _{2 at} which the speed change ΔV _LSAW (f, h ₀ ) is minimum and maximum are selected, and Δf ₁₂ = f ₂ −f ₁ . When the LSAW speed is measured at the frequencies f ₁ and f ₂ at an arbitrary measurement point Pa with the thickness h = h ₀ + Δh, the measured values are expressed by the following equations (8) and (9), respectively.
[0014]
V _LSAW (f ₁ , h) = V _LSAWa + ΔV _LSAW (f ₁ , h) (8)
V _LSAW (f ₂ , h) = V _LSAWa + ΔV _LSAW (f ₂ , h) (9)
Here, V _LSAWa represents the true value at the measurement point Pa, and ΔV _LSAW (f ₁ , h) and ΔV _LSAW (f ₂ , h) represent the LSAW velocity change from the true value due to the influence of the back surface reflected wave. By subtracting equation (9) from equation (8), the difference ΔV (Δf, h) of the change in sound velocity due to the influence of the back surface reflected wave at f ₁ and f ₂ is obtained as in the following equation (10).
[0015]

Next, in order to obtain the relationship between the difference in sound speed change ΔV (Δf, h ₀ ) and the frequency change Δf, a conversion curve shown in FIG. 5B is obtained from the curve in FIG. 5A by the following equation (11).
ΔV (Δf, h ₀ ) = ΔV _LSAW (f ₁ + Δf, h ₀ ) −ΔV _LSAW (f ₂ + Δf, h ₀ ) (11)
However, 0 ≤ Δf ≤ Δf ₁₂ (12)
Here, the curve in FIG. 5B is a monotonically increasing function, and a one-to-one correspondence relationship is established between ΔV (Δf, h ₀ ) and Δf. V _LSAW (f, h) at the thickness h is a waveform obtained by shifting the frequency characteristic waveform of V _LSAW (f, h ₀ ) at the thickness h ₀ shown in FIG. 4B in the frequency axis direction and the velocity axis direction as it is. since, when compared to formula (10) wherein the (11), [Delta] V (Delta] f, h) from the calibration curve of FIG. _{5B = ΔV (Δf, h 0} ) by obtaining the become Delta] f = Delta] f _c, the thickness it can be seen that Δh different equivalent frequency change Delta] f _c is determined. That is, the sound speeds V _LSAW (f ₁ , h) and V _LSAW (f ₂ , h) are measured at the measurement points Pa at the frequencies f ₁ and f ₂ , respectively, and ΔV (Δf, h) is obtained from the equation (10), corresponding Delta] f _c is determined from FIG. 5B. Thus, using FIG. 5A, ΔV _LSAW (f ₁ + Δf _c , h at a measurement point P ₀ corresponding to ΔV _LSAW (f ₁ , h) and ΔV _LSAW (f ₂ , h) at an arbitrary measurement point Pa ₀ ) and ΔV _LSAW (f ₂ + Δf _c , h ₀ ) are obtained, the true value V _LSAWa at an arbitrary measurement point Pa is obtained from the equations (8) and (9) as in the following equation (13). .
[0016]

The measurement procedure of the present invention has been described above. Here, for the sake of simplicity, the two frequencies f ₁ and f ₂ are selected to be the minimum and maximum in FIG. 5A, respectively. However, any frequency can be selected as long as it has a one-to-one correspondence in the conversion curve. Also good. For example, in the curve of the sound speed change ΔV _LSAW (f, h ₀ ) in FIG. 5A, the frequencies f ₁ and f ₂ are in a monotonic change region with opposite slopes, for example, the frequency region from the minimum value to the maximum value by increasing with the frequency f. If the frequency range from the maximum value to the next minimum value is arbitrarily selected, the conversion curve in FIG. 5B always becomes a monotone function. For example, if f ₂ is selected near the frequency that gives the maximum value of ΔV _LSAW (f, h ₀ ) (but larger than the frequency that gives the maximum value), ΔV _LSAW (f, h ₀ ) near the minimum value Since the rate of change is smaller than that in the vicinity of the maximum value, for example, even if f ₁ is selected somewhat lower than the frequency that gives the minimum value of the speed change curve shown in FIG. 5A, the conversion curve becomes a monotone function.
[0017]
When f ₁ and f ₂ (f ₁ <f ₂ ) are selected so that the range of Δf shown in Equation (12) is maximized while maintaining the relationship of monotonic increase of the conversion curve, the sample that can be measured in this method The maximum value Δh _max of the thickness distribution is given by the following equation (14), where the bulk longitudinal wave velocity in the sample is V _L. When the thickness distribution exceeds Delta] h _max is to divide the measurement area in the range not exceeding Delta] h _max, may be performed measured every determined divided regions reference point within each region.
[0018]
Δh _max = (V _L / 2f ₂ ) (Δf ₁₂ / ΔF) (14)
The principle of the measurement method according to the present invention has been described above for the case where the true value V _LSAWa is _obtained at an arbitrary measurement point Pa with respect to the reference measurement point P _{0. In} actual measurement, a desired straight line on the sample surface is obtained. The procedure for measuring V _LSAW at regular intervals along (for example, the diameter) will be described below as a specific example.
[0019]
Step S1: The sample is a 3 inch double-sided optically polished Z-cut LiNbO ₃ wafer, with a central thickness of about 377 μm and a peripheral thickness of about 381 to 382 μm. It has a shape like 4A. The frequency characteristic of the LSAW velocity of propagation in the crystal Y-axis direction is 0.2 MHz in the range of 200 to 240 MHz at the center point (the origin is P ₀ and the thickness is h ₀ ) that is expected to be the thinnest on the sample surface. Measured every time. The result is shown by a solid line in FIG. 6A. This curve corresponds to the thick solid curve in FIG. 4B. The dotted line in the figure is the result of performing a moving average twice with a period of ΔF = 9.6 MHz on the measurement value of the solid line, and is obtained by removing the measurement error due to the influence of the back surface reflected wave. Although the value obtained differs depending on the frequency, this is considered to be the frequency characteristic of the ultrasonic device.
[0020]
Step S2: FIG. 6B shows the result of _{obtaining the} sound velocity change ΔV _LSAW (f, h ₀ ) due to the influence of the back surface reflected wave by subtracting the dotted line from the solid line in FIG. 6A. This curve corresponds to the curve of FIG. 5A. Here, in FIG. 6B, it is considered that the frequencies f ₁ and f ₂ can correct errors due to the expected maximum change in thickness of about 5 μm, and that the measurement point P ₀ is not necessarily the thinnest place of the sample. F ₁ = 220.4 MHz and f ₂ = 224.6 MHz.
[0021]
Step S3: A straight line passing through the measurement point P ₀ on the distribution of the LSAW velocities V _LSAW (f ₁ , h) and V _LSAW (f ₂ , h) of Y-axis propagation at the frequencies f ₁ and f ₂ on the wafer diameter And measured within a range of ± 30 mm every 1 mm. The results are shown in FIG. 7A. The LSAW velocity profile differs between f ₁ and f ₂ , but this is mainly due to the influence of the back reflected wave. Each measurement value includes a change in sound speed due to the frequency characteristics of the ultrasonic device, as indicated by the dotted line in FIG. 6A.
[0022]
Step S4: In order to obtain the difference ΔV (Δf, h) of the sound speed change due to the influence of the back surface reflected wave at f ₁ and f _2, the dotted line is subtracted from the solid line in FIG. 7A, and further the sound speed shift amount ΔV _f12 shown in FIG. Is deducted. The result is shown in FIG. 7B.
Step S5: Next, a conversion curve indicating the relationship between ΔV (Δf, h ₀ ) and the frequency change Δf is obtained from the equation (11) from FIG. 6B. However, the range of Δf satisfies the following formula (15).
[0023]
-(f ₂ -f _m ) ≤ Δf ≤ (f _m -f ₁ ) (15)
FIG. 8A shows the calculated conversion curve. Here, since the frequency at which ΔV _LSAW (Δf, h ₀ ) in FIG. 6B is maximum is f _m = 224.2 MHz, −0.4 MHz ≦ Δf ≦ 3.8 MHz.
Step S6: sound velocity change of the difference ΔV (Δf, h) of FIG. 7B and, ΔV (Δf, h) from the calibration curve of FIG. _{8A = ΔV (Δf, h 0} ) and the respective measurement points Delta] f = Delta] f _c made to Thus, it is possible to estimate a frequency change Δf equivalent to a difference in thickness Δh. The result is shown in FIG. 8B. In the conversion curve, the portion without data was linearly interpolated using the preceding and following data.
[0024]
Step S7: From FIG. 8B, the change in sound velocity due to the influence of the back surface reflected wave at each measurement point at f ₁ and f ₂ is ΔV _LSAW (f ₁ + Δf _c , h ₀ ) and ΔV _LSAW (f ₂ + Δf _c , h ₀ ). The sound velocity change curves due to the influence of the back surface reflection wave obtained for f ₁ and f ₂ are shown by solid lines and dotted lines in FIG. 9A, respectively. FIG. 9A shows that the maximum change in sound speed ΔV _LSAW (f + Δf _c , h ₀ ) due to the back-surface reflected wave is 4.82 m / s.
[0025]
Step S8: The error caused by the back-surface reflected wave is corrected by subtracting the sound speed change in FIG. 9A from the measured value of the LSAW speed shown in FIG. 7A. The results after correction for f ₁ and f ₂ are shown by solid lines and dotted lines in FIG. 9B, respectively. Although the absolute value of the correction result in FIG. 9B is different between f ₁ and f ₂ , this is due to the frequency characteristics of the ultrasonic device described above, and this is not a problem in examining the relative sound velocity distribution. When an absolute value is required, the absolute value can be obtained by an absolute calibration method using a standard sample (see Document 3).
[0026]
Here, the absolute calibration method will be briefly described. First, the theoretical value of the LSAW velocity calculated from the elastic constant actually measured for a standard sample (for example, GGG single crystal) is obtained. A value corresponding to the interference period Δz (see FIG. 2) of the V (z) curve at this time is defined as Δz _ST (calc.). Next, the LSAW velocity is measured with the LFB ultrasonic microscope system for the same standard sample, and a value corresponding to Δz at that time is set to Δz _ST (meas.). By taking the ratio of the two, the calibration coefficient shown in the following equation (16) is determined.
[0027]
K (V) = Δz _ST (calc.) / Δz _ST (meas.) (16)
Thereafter, with respect to the value corresponding to Δz of the LSAW velocity (solid line and dotted line in FIG. 9B) measured for the actual sample, Δz (measured), as shown in the following equation (17), the calibration coefficient K ( The absolute value of the LSAW velocity can be obtained by multiplying V) and substituting the obtained Δz (calibrated) into equation (1).
[0028]
Δz (calibrated) ＝ K (V) Δz (measured) (17)
In order to confirm whether the measurement result of FIG. 9B is measured correctly, the frequency characteristics of the LSAW velocity were measured at 0, ± 15, and ± 30 mm positions on the measurement line of the sample, respectively, and the result of moving average was obtained. For f ₁ and f ₂ , in FIG. This result and the previously obtained measurement result agree well within ± 0.5 m / s. From this, it can be seen that the measurement error due to the influence of the back surface reflected wave can be sufficiently removed by the correction by this method.
[0029]
The LSAW propagation characteristic measuring method according to the present invention has been described above. In the above, as a simple example, the procedure for removing the frequency characteristic of the ultrasonic device using the moving average value of the frequency characteristic of the LSAW velocity for the thin sample to be measured has been shown. It is possible. If you prepare a thick sample that is the same type as the measurement sample and is not affected by the reflected wave from the back surface, and measure the frequency characteristic of the LSAW velocity for that sample, it can be obtained as it is as the frequency characteristic of the ultrasonic device, and the moving average is calculated. Measurement can be performed in the same manner as the above-described measurement method. In this case, it is considered that the frequency characteristic of the ultrasonic device is more accurate than using the moving average value, and the measurement accuracy is improved. Alternatively, it is considered that the same frequency characteristic of the ultrasonic device can be obtained even if a thick sample to be prepared is used as a standard sample (eg, GGG single crystal). However, the absolute value is calibrated by the absolute value calibration method described above.
[0030]
【The invention's effect】
As described above, according to the present invention, it is not necessary to directly measure the thickness distribution of the sample, the frequency characteristic of the LSAW speed is measured only at one point on the sample, and the other measurement points are 2 The true value of each measurement point can be obtained only by performing measurement at one frequency, that is, by performing measurement twice at each point. The more measurement points, the greater the reduction in measurement time can be realized. In addition, when a PFB ultrasonic microscope is used, the same effect can be obtained by the same procedure.
[0031]
In the present invention, as described above, the distribution of LSAW propagation characteristics in a thin sample can be measured efficiently. However, if the distribution of LASW propagation characteristics of the sample can be assumed to be uniform, the thickness of the sample is reversed. Distribution can be measured. For example, the thickness of the sample at an arbitrary measurement point Pa can be expressed as h = h ₀ + Δh = h ₀ (1 + Δf / f) from the equation (5), so that Δf is shown at each measurement point Pa shown in FIG. 8B. to give the corresponding Delta] f _c, it can be calculated a thickness h of the sample at the measurement point Pa as a percentage of the thickness h ₀ of the reference position P ₀ by providing f ₁ or f ₂ as f. Thickness h at the reference position P _{0 0} can be calculated from equation (2) using, for example, measurements or theoretical value of the longitudinal wave acoustic velocity V _L of the frequency characteristic ΔF and samples were measured.
[Brief description of the drawings]
FIG. 1 is a diagram for explaining the measurement principle of an LFB acoustic microscope.
FIG. 2 is a diagram showing a V (z) curve.
FIGS. 3A and 3B are time charts of reflected waves from the front surface and the back surface of a sample. FIG. 3A is a diagram in the case of a thick sample, and FIG.
FIG. 4A is a diagram showing an example of a sample shape having a thickness distribution, and FIG. 4B is a diagram showing frequency characteristics of LSAW speed for a thin sample.
FIG. 5A is a diagram showing an apparent change in sound speed due to the influence of a back-surface reflected wave, and B is a diagram showing a conversion curve.
FIG. 6A is a diagram showing the frequency characteristics of the LSAW velocity at the thinnest point on the sample, and B is a diagram showing an apparent change in sound velocity due to the influence of the back surface reflected wave.
7A is a diagram showing the measurement result of the LSAW velocity distribution in the radial direction of the sample, and B is a diagram showing the difference between the measurement results shown in A. FIG.
FIG. 8A is a diagram showing a conversion curve, and FIG. 8B is a diagram showing a result of estimating a change in sample thickness to a change in frequency equivalent to that.
9A is a diagram showing a result of an estimated value to be corrected, and B is a diagram showing a correction result. FIG.
(References)
(Reference 1) J. Kushibiki and N. Chubachi, "Material Characterization by Line-Focus-Beam Acoustic Microscope," IEEE Trans. Sonics and Ultrason., Vol.SU-32, pp. 189-212 (1985).
(Reference 2) Kushibiki, Arakawa, Ohashi, "Effects of reflected waves on the back of a sample in a material evaluation method using a linearly focused beam ultrasonic microscope--Examination of the thickness of a sample-", Spring Meeting of the Acoustical Society of Japan, pp.1035 -1036, March 1997.
(Reference 3) J. Kushibiki and M. Arakawa, "A Method for Calibrating the Line-Focus-Beam Acoustic Microscopy System.", IEEE Trans. UFFC., Vol. 45, no. 2, March (1998), in press.

Claims (6)

In the method of measuring the propagation characteristics of leaky surface acoustic waves (LSAW) propagating on the surface of a thin sample with an ultrasonic microscope,
(a) Measure the frequency characteristics of the LSAW speed at the reference point on the sample surface, obtain the frequency characteristics of the LSAW speed change due to the reflection from the back surface of the sample from the frequency characteristics,
(b) A difference between the two LSAW speed changes at two constant frequencies at the reference point is obtained as a conversion curve with respect to the two frequency changes.
(c) Measure the LSAW speeds at the two constant frequencies at each of a plurality of arbitrary points on the sample surface, and obtain the difference between them.
(d) The speed change corresponding to the difference value at each point is estimated from the conversion curve, thereby correcting the LSAW speed measured at each point. In the LSAW propagation characteristic measuring method according to claim 1 , when the thicknesses of the sample at the reference point and an arbitrary point are represented as h ₀ and h, respectively.
Step (a) above is
(a-1) Measure the LSAW velocity V _LSAW (f, h ₀ ) for each frequency f at the reference point on the sample,
(a-2) Obtain LSAW speed change ΔV _LSAW (f, h ₀ ) due to back reflection of the sample at each frequency at the reference point as frequency characteristics of the speed change,
Step (b) above is
(b-1) Two frequencies f ₁ and f ₂ are selected within a substantially monotonic change region of opposite slopes of the LSAW speed change, respectively.
(b-2) above LSAW velocity change obtained in step _{(a-2) ΔV LSAW (} f, h 0) speed change when the above two frequencies f ₁ and f ₂ shifted Δf respectively [Delta] V _LSAW (f ₁ + Δ f, h ₀ ) and Δ V _LSAW (f ₂ + Δ f, h ₀ ) , the difference ΔV (Δf, h ₀ ) is obtained as a conversion curve,
Step (c) above is
(c-1) Measure the LSAW velocities V _LSAW (f ₁ , h) and V _LSAW (f ₂ , h) at the two frequencies f ₁ and f ₂ at each arbitrary point on the sample,
(c-2) The difference ΔV (Δf, h) between the two LSAW velocities V _LSAW (f ₁ , h) and V _LSAW (f ₂ , h) at each of the above points as the speed change difference at that point determined, determine the frequency change Delta] f _c at the reference point corresponding to the speed change difference from the calibration curve,
Step (d) above is
(d-1) A change in velocity due to the back reflection at the _two frequencies f ₁ and f ₂ at each arbitrary point is converted into a converted velocity change ΔV _LSAW (f ₁ + Δf _c , h ₀ ) and ΔV _LSAW (f ₂ + Δf _c, h ₀₎ as determined from the frequency characteristics of the speed change [Delta] V _LSAW in the frequency change Delta] f _c and the reference point (f, h _0),
(d-2) The LSAW velocities V _LSAW (f ₁ , h) and V _LSAW (f ₂ , f ₂ at the _two frequencies f ₁ and f ₂ at each arbitrary point obtained in step (c-1) Subtract the corresponding change in the converted speed change ΔV _LSAW (f ₁ + Δf _c , h ₀ ) and ΔV _LSAW (f ₂ + Δf _c , h ₀ ) obtained in step (d-1) from at least one of h) To obtain the true value V _LSAWa of the speed at that point. 3. The method of measuring LSAW propagation characteristics according to claim 2 , wherein the step (a-2) includes moving average the frequency characteristics of the measured LSAW velocity V _LSAW (f, h ₀ ), and using the obtained moving average value as the LSAW. This is a step of obtaining the frequency characteristic of the change in the measured speed by subtracting from the frequency characteristic of the speed. In LSAW propagation characteristics measuring method according to claim 2 or 3, the two frequencies f ₁ and f ₂ is the frequency at which the curve of the LSAW velocity change is almost minimum, selecting each frequency becomes substantially maximum. 5. The LSAW propagation characteristic measurement method according to claim 1, wherein the LSAW velocity is measured by dividing the sample thickness distribution into regions within a predetermined value. 6. The method of measuring LSAW propagation characteristics according to claim 1, wherein the interference period Δz (calc. Of the V (z) curve obtained based on the theoretical value of the LSAW velocity calculated from the elastic constant of the standard sample in advance. ) And the calibration coefficient determined from the interference period Δz (meas.) Of the V (z) curve obtained by measuring the LSAW speed of the standard sample with the ultrasonic microscope, the above steps (a) and (c) Calibrating the measured LSAW speed at, using the calibrated value as the LSAW speed.

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