JP4005285B2

JP4005285B2 - Followability evaluation method and evaluation apparatus

Info

Publication number: JP4005285B2
Application number: JP31154599A
Authority: JP
Inventors: 竜也宮谷; 克則本間; 邦雄中島
Original assignee: Seiko Instruments Inc
Current assignee: Seiko Instruments Inc
Priority date: 1999-11-01
Filing date: 1999-11-01
Publication date: 2007-11-07
Anticipated expiration: 2019-11-01
Also published as: JP2001133383A

Description

【０００１】
【発明の属する技術分野】
本発明は、追従性評価装置に関する。
【０００２】
【従来の技術】
制御対象物を物体表面の凹凸に追従させる制御装置または制御システムの例として走査型プローブ顕微鏡のひとつである、原子間力顕微鏡をあげ、従来の技術について説明する。
原子間力顕微鏡は、図４に示すように先端にプローブを有するカンチレバー１９、カンチレバーのたわみを検出するたわみ検出器１２、カンチレバーのたわみを一定に保ちながらラスタスキャンを行うためのスキャナ１３、フィードバック制御や、画像表示を行うためのコントローラ１７、コンピュータ２３から構成されている。
【０００３】
走査型プローブ顕微鏡では、プローブ２２がサンプル表面の凹凸に沿うように、プカンチレバー１９または、サンプル２４をサンプル面に垂直な方向へ移動させながらサンプル表面を走査する。したがって、プローブがサンプル表面の凹凸の変化にいかに追従するかが走査型プローブ顕微鏡の測定精度を決める重要な要素である。
【０００４】
これまでは、走査型プローブ顕微鏡システム全体の追従性評価は、実際にサンプルを測定することで行われていた。また、プローブまたはカンチレバー、およびスキャナ個々の追従性の評価はそれぞれの周波数特性を測定することで行われていた。
【０００５】
【発明が解決しようとする課題】
実際のサンプルを測定することで、システム全体の追従性を評価する場合、プローブ形状の影響等があり追従性のみの評価が難しく、また、走査型プローブ顕微鏡の測定対象となるような微小な任意の構造を持つサンプルを作製することが困難なため、追従性評価の対象となる形状は限られてしまう。
【０００６】
プローブまたはカンチレバー、およびスキャナ個々の周波数特性からそれぞれの追従性を評価する場合には、より共振周波数が高いものはより追従性がよい、というように相対的、定性的な評価である。また、共振周波数測定時にカンチレバー等は正弦波的に振動しており、厳密には、正弦波的形状の試料表面の凹凸に対する追従性を評価していることになる。したがって、正弦波的形状以外の試料表面の凹凸に対するカンチレバー等の追従性を、共振周波数によって評価することは間接的であり、定量的な評価を行うことは難しい。
【０００７】
本発明は上記のような従来の問題点を解決することを目的とするもので、走査型プローブ顕微鏡に限らず、制御対象物を任意の形状や軌跡に追従させることを目的とする装置およびシステムの追従性を実際に形状や軌跡に追従させることなく直接的かつ定量的に評価する方法および装置を提供することを目的とする。
【０００８】
【課題を解決するための手段】
走査型プローブ顕微鏡を例に課題を解決するための手段について説明する。
上記のような課題を解決するために、本発明においては、プローブが追従すべきサンプル表面の形状とプローブの走査速度から、サンプル表面の形状に相当する波形の電気信号を生成し、この電気信号または電気信号をアクチュエータで変換した変位に対する、走査型プローブ顕微鏡システム，プローブ，カンチレバー、または、スキャナそれぞれの追従性を評価する方法とした。このようにすることで、実際にサンプル表面を走査することなく、また任意の形状に対する任意の走査速度における追従性を直接定量的に評価することができる。
【０００９】
【発明の実施の形態】
以下に、本発明の実施の形態を図面に基づいて説明する。
［実施の形態１］
図１(a)において、１は制御対象物、２は制御対象物１が追従すべき物体表面の形状である。３および４はそれぞれ第一座標軸，第二座標軸である。図１（ｂ）において、４は第二座標軸、５は時間軸６は形状２の対時間変位、７は制御対象物の対時間変位である。制御対象物１が第一座標軸３の方向へ移動する際に、形状２に沿うように第二座標軸方向の位置を調整して制御対象物１を表面形状に追従させるような制御装置および制御システムにおいて、第一座標軸方向の移動速度ｖが既知であれば、任意の時刻における制御対象物１が追従すべき第二座標軸方向の位置つまり、形状２の対時間変位６を求められる。そこで、制御装置または制御システムによって対時間変位６に追従するように第二座標軸方向の位置を制御された制御対象物１の対時間変位７を測定し、形状の対時間変位６と比較することによって制御装置および制御システムの追従性を直接定量的に評価することができる。
【００１０】
形状の対時間変位６と制御対象物の対時間変位７との比較は、時間領域，周波数領域、またはその双方で行うことができる。
時間領域における比較では、形状の対時間変化６と制御対象物の対時間変化７それぞれの各時刻における傾きを求め比較することで追従性を評価することができる。これは、単純なステップ状の形状等へ対する追従性の評価に有効である。また、形状の対時間変位６をf(t)、制御対象物の対時間変位をh(t)とすると次式で表される
【００１１】
【数１】

残差二乗和ｇを求めることで追従性を評価することができる。ｇが小さいほどf(t)とh(t)の類似性が高く追従性が良いと言うことになる。
また、時間領域では形状の対時間変位６と制御対象物の対時間変位７との相互相関数を計算することによっても二つの対時間変位の比較をすることができ追従性を評価することができる。
【００１２】
周波数領域では、形状の対時間変位６と制御対象物の対時間変位７それぞれをフーリエ変換し周波数成分を比較することで追従性を評価することができる。また、形状の対時間変位６と制御対象物の対時間変位７とのコヒーレンス関数を計算することで二つの対時間変位を比較することができ追従性を評価することができる。
【００１３】
また、ウエーブレット解析や時間／周波数共同領域解析によって、形状の対時間変位６と制御対象物の対時間変位７との比較を時間領域と、周波数領域双方で行うことができ、より詳細に追従性の評価を行うことができる。
以上のように、形状を対時間変位に変換し、形状の対時間変位に対する制御装置および制御システムの追従性を評価することで、実施に制御対象物を形状へ追従させることなく、任意の形状への制御装置および制御システムの追従性を直接定量的に評価することができる。
【００１４】
［実施の形態２］
図２において、８は疑似形状作成手段、９は制御装置または制御システム、１０は測定手段、１１は追従性評価手段である。
疑似形状作成手段は、図１における第一座標軸方向の速度ｖに基づき、制御装置または制御システム９が制御対象物を追従させる形状を対時間変位に変換する。疑似形状作成手段によって作成された形状の対時間変位に対して、制御対象物が追従するように制御装置または制御システム９は制御対象物の図１における第二座標軸４方向の位置を制御する。このときの制御対象物の対時間変位を測定手段１０で測定する。追従性評価手段は、形状の対時間変位と測定手段１０によって得られた制御対象物の対時間変位とを比較し追従性を直接定量的に評価する。追従性評価手段は、実施の形態１で述べた評価方法で追従性の評価を行う。
【００１５】
このような装置構成とすることで実施に制御対象物を形状へ追従させることなく任意の形状への制御装置および制御システムの追従性を直接定量的に評価することができる。
【００１６】
［実施の形態３］
図３は、走査型プローブ顕微鏡の一つである原子間力顕微鏡の追従性評価装置のブロック図である。おもに、たわみ検出器１２，スキャナ１３，波形発生装置１５，追従性評価用コンピュータ１６，SPM制御装置１７，アクチュエータ１８，カンチレバー１９，スライドガラス２０，試料台２１からなる。
追従性評価用コンピュータ１６は、任意の形状の対時間変位を計算し、波形発生装置１５から電気信号として出力する。また、たわみ検出器によってカンチレバー対時間変位を測定し、形状の対時間変化と比較することによって追従性を評価する。追従性の評価方法はおもに実施の形態１で述べた方法を用いている。
まず、SPMシステム全体の追従性を評価する方法について説明する。
【００１７】
追従性評価用コンピュータ１６で計算した形状の対時間変位を波形発生装置を通して電気信号としてアクチュエータに入力する。このときプローブ２２がスライドガラス２０に常に接触するようにスキャナ１３の位置を調節しておく。アクチュエータは形状の対時間変位に従ってカンチレバーをたわませる。このとき、SPM制御装置１７は、たわみ検出器１２でカンチレバーのたわみを測定し、たわみが一定になるようにスキャナのZ端子にかける電圧を制御する。SPMシステムの追従性が良ければカンチレバーのたわみは一定に保たれ、たわみ検出器の出力は一定になる。追従性評価用コンピュータはたわみ検出器の出力を取り込み形状の対時間変位とカンチレバー先端の対時間変位とを比較する。この場合、二つの対時間変位の類似性が低いほど追従性が良いことになる。さらに、たわみ検出器の出力の時間に対する平坦度の評価も合わせて行う。
【００１８】
カンチレバーの追従性の評価は、波形発生器１６の出力をアクチュエータ１８に入力する。このとき、プローブ２２が常にスライドガラス２０に接触するようにスライドガラス２０の位置を調節し、SPM制御装置１７によってスキャナ１３が伸張しないようにしておく。カンチレバー先端の対時間変位をたわみ検出器によって追従性評価用コンピュータ１６へ取り込み、形状の対時間変位と比較することによってカンチレバーの追従性を評価する。
【００１９】
スキャナの追従性の評価は、波形発生装置１５の出力をスキャナ１３へ入力する。このときカンチレバーの場合と同様に、プローブ２２がスライドガラス２０に接触するようにスキャナ１３の位置を調節しておく。また、カンチレバーはスキャナのＺ方向の共振周波数よりも十分高い共振周波数をもつカンチレバーを用いる。スキャナ１３の対時間変位をカンチレバーとたわみ検出器とで測定し追従性評価用コンピュータ１６へ取り込み、形状の対時間変位と比較し追従性を評価する。
【００２０】
SPM制御装置の追従性は波形発生装置１５の出力をアクチュエータ１８へ入力する。このとき、スキャナの場合と同様にプローブ２２がスライドガラス２０に常に接触するようにスキャナのＺ方向の位置を調節しておく。SPM制御装置のZ出力を追従性評価用コンピュータ１６へ取り込み、対時間変位に変換し形状の対時間変位と比較することでSPM制御装置の追従性を評価する。
【００２１】
以上のようにすることで、SPMシステム全体およびカンチレバー，スキャナ，制御装置等追従性に影響を与える要素の、任意の形状に対する追従性を実際にサンプル表面を走査することなく直接定量的に評価することができる。
【００２２】
【発明の効果】
本発明による追従性評価方法および追従性評価装置は、制御装置または制御システムが制御対象物を追従させるべき形状を対時間変位に変換し、形状の対時間変位と制御装置または制御システムが制御対象物を形状の対時間変位に追従させた際の制御対象物の対時間変位とを比較することによって追従性を評価するため、任意の形状に対する制御装置または、制御システムの追従性を直接定量的に評価することができる。
【図面の簡単な説明】
【図１】本発明の実施の形態１に関わる追従性評価方法を示す説明図である。
【図２】本発明の実施の形態２に関わる追従性評価装置を示す説明図である。
【図３】本発明の実施の形態３に関わる追従性評価装置を示す説明図である。
【図４】従来の原子間力顕微鏡を示す説明図である。
【符号の説明】
１制御対象物
２試料の表面形状
３第一座標軸
４第二座標軸
５時間軸
６形状の対時間変位
７制御対象物の対時間変位
８疑似形状作成手段
９制御装置または制御システム
１０測定手段
１１追従性評価手段
１２たわみ検出器
１３スキャナ
１５波形発生装置
１６追従性評価用コンピュータ
１７ SPM制御装置
１８アクチュエータ
１９カンチレバー
２０スライドガラス
２１試料台
２２プローブ
２３コンピュータ
２４サンプル[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a follow-up evaluation device.
[0002]
[Prior art]
As an example of a control device or control system for causing a control object to follow the unevenness of an object surface, an atomic force microscope, which is one of scanning probe microscopes, will be described and the conventional technology will be described.
As shown in FIG. 4, the atomic force microscope includes a cantilever 19 having a probe at its tip, a deflection detector 12 for detecting the deflection of the cantilever, a scanner 13 for performing a raster scan while keeping the deflection of the cantilever constant, and feedback control. And a controller 17 and a computer 23 for displaying images.
[0003]
In the scanning probe microscope, the sample surface is scanned while moving the cantilever 19 or the sample 24 in a direction perpendicular to the sample surface so that the probe 22 follows the unevenness of the sample surface. Therefore, how the probe follows the change in the unevenness of the sample surface is an important factor that determines the measurement accuracy of the scanning probe microscope.
[0004]
Until now, follow-up evaluation of the entire scanning probe microscope system has been performed by actually measuring a sample. Further, the followability of each probe or cantilever and scanner has been evaluated by measuring the respective frequency characteristics.
[0005]
[Problems to be solved by the invention]
When evaluating the followability of the entire system by measuring an actual sample, it is difficult to evaluate only the followability due to the influence of the probe shape, etc. Since it is difficult to produce a sample having the structure, the shape to be subjected to follow-up evaluation is limited.
[0006]
When evaluating the followability of each of the probe or cantilever and the individual frequency characteristics of the scanner, the higher the resonance frequency, the better the followability, and the relative and qualitative evaluation. Further, the cantilever or the like vibrates sinusoidally at the time of measuring the resonance frequency, and strictly speaking, the followability to the unevenness of the sample surface having a sinusoidal shape is evaluated. Therefore, it is indirect to evaluate the followability of the cantilever or the like with respect to the unevenness of the sample surface other than the sinusoidal shape by the resonance frequency, and it is difficult to perform quantitative evaluation.
[0007]
An object of the present invention is to solve the above-described conventional problems, and is not limited to a scanning probe microscope, and an apparatus and system for causing a controlled object to follow an arbitrary shape or locus. It is an object of the present invention to provide a method and an apparatus for directly and quantitatively evaluating the followability of an object without actually following the shape or trajectory.
[0008]
[Means for Solving the Problems]
Means for solving the problem will be described taking a scanning probe microscope as an example.
In order to solve the above problems, in the present invention, an electric signal having a waveform corresponding to the shape of the sample surface is generated from the shape of the sample surface to be followed by the probe and the scanning speed of the probe. Alternatively, the followability of each of the scanning probe microscope system, the probe, the cantilever, and the scanner with respect to the displacement obtained by converting the electric signal by the actuator is evaluated. In this way, it is possible to directly and quantitatively evaluate the followability at an arbitrary scanning speed for an arbitrary shape without actually scanning the sample surface.
[0009]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of the present invention will be described below with reference to the drawings.
[Embodiment 1]
In FIG. 1A, 1 is a control object, and 2 is a shape of an object surface that the control object 1 should follow. 3 and 4 are a first coordinate axis and a second coordinate axis, respectively. In FIG. 1B, 4 is the second coordinate axis, 5 is the time axis 6 is the displacement of the shape 2 with respect to time, and 7 is the displacement of the controlled object with respect to time. When the control object 1 moves in the direction of the first coordinate axis 3, a control device and a control system that adjust the position in the second coordinate axis direction along the shape 2 to cause the control object 1 to follow the surface shape. If the moving speed v in the first coordinate axis direction is known, the position in the second coordinate axis direction that the controlled object 1 should follow at an arbitrary time, that is, the displacement 6 of the shape 2 with respect to time can be obtained. Therefore, the time displacement 7 of the controlled object 1 whose position in the second coordinate axis direction is controlled so as to follow the time displacement 6 by the control device or the control system is measured and compared with the shape displacement 6 over time. Thus, the followability of the control device and the control system can be directly and quantitatively evaluated.
[0010]
The comparison of the shape displacement with time 6 and the control object displacement with time 7 can be performed in the time domain, the frequency domain, or both.
In the comparison in the time domain, the followability can be evaluated by obtaining and comparing the slopes of the shape change with time 6 and the change with time 7 of the control object at each time. This is effective for evaluating the followability to a simple step-like shape or the like. Further, when the displacement of the shape 6 with respect to time is f (t) and the displacement of the controlled object with respect to time is h (t), it is expressed by the following equation.
[Expression 1]

The followability can be evaluated by obtaining the residual sum of squares g. The smaller g is, the higher the similarity between f (t) and h (t) is, and the better the followability is.
In the time domain, it is possible to compare two displacements with respect to time by calculating the number of cross-correlations between the shape displacement 6 with respect to time and the displacement 7 with respect to the controlled object. it can.
[0012]
In the frequency domain, the followability can be evaluated by Fourier transforming the shape displacement with respect to time 6 and the displacement with respect to time 7 of the object to be controlled, and comparing the frequency components. Further, by calculating the coherence function of the shape displacement with respect to time 6 and the displacement object with respect to time 7, the two displacements with respect to time can be compared, and the followability can be evaluated.
[0013]
In addition, the comparison between the shape displacement with time 6 and the control object displacement with time 7 can be performed both in the time domain and in the frequency domain by wavelet analysis and time / frequency joint domain analysis. Sexuality can be evaluated.
As described above, by converting the shape into the displacement with respect to time and evaluating the followability of the control device and the control system with respect to the displacement with respect to the shape, any shape can be obtained without causing the controlled object to follow the shape. The followability of the control device and the control system can be directly and quantitatively evaluated.
[0014]
[Embodiment 2]
In FIG. 2, 8 is a pseudo-shape creating means, 9 is a control device or control system, 10 is a measuring means, and 11 is a follow-up evaluation means.
Based on the velocity v in the first coordinate axis direction in FIG. 1, the pseudo shape creating means converts the shape that the control device or the control system 9 follows the control object into a displacement with respect to time. The control device or the control system 9 controls the position of the control object in the direction of the second coordinate axis 4 in FIG. 1 so that the control object follows the time displacement of the shape created by the pseudo shape creation means. The displacement with respect to time of the controlled object at this time is measured by the measuring means 10. The followability evaluation unit compares the shape displacement with respect to time with the displacement of the control object with respect to time obtained by the measurement unit 10 to directly and quantitatively evaluate the followability. The followability evaluation means evaluates the followability by the evaluation method described in the first embodiment.
[0015]
By adopting such a device configuration, it is possible to directly and quantitatively evaluate the followability of the control device and the control system to an arbitrary shape without causing the control object to follow the shape in practice.
[0016]
[Embodiment 3]
FIG. 3 is a block diagram of a follow-up evaluation device for an atomic force microscope, which is one of scanning probe microscopes. It mainly comprises a deflection detector 12, a scanner 13, a waveform generator 15, a follow-up evaluation computer 16, an SPM controller 17, an actuator 18, a cantilever 19, a slide glass 20, and a sample stage 21.
The follow-up evaluation computer 16 calculates an arbitrary shape displacement with respect to time, and outputs it from the waveform generator 15 as an electrical signal. In addition, the cantilever versus time displacement is measured by a deflection detector, and the followability is evaluated by comparing with the change in shape with respect to time. The follow-up evaluation method mainly uses the method described in the first embodiment.
First, a method for evaluating the followability of the entire SPM system will be described.
[0017]
The displacement with respect to time of the shape calculated by the follow-up evaluation computer 16 is input to the actuator as an electric signal through the waveform generator. At this time, the position of the scanner 13 is adjusted so that the probe 22 always contacts the slide glass 20. The actuator deflects the cantilever according to the displacement of the shape with respect to time. At this time, the SPM controller 17 measures the deflection of the cantilever with the deflection detector 12 and controls the voltage applied to the Z terminal of the scanner so that the deflection is constant. If the tracking performance of the SPM system is good, the deflection of the cantilever will be kept constant and the output of the deflection detector will be constant. The computer for evaluating follow-up takes the output of the deflection detector and compares the displacement with respect to time of the shape and the displacement with respect to time of the tip of the cantilever. In this case, the lower the similarity between the two displacements with respect to time, the better the followability. Furthermore, the flatness of the output of the deflection detector with respect to time is also evaluated.
[0018]
To evaluate the followability of the cantilever, the output of the waveform generator 16 is input to the actuator 18. At this time, the position of the slide glass 20 is adjusted so that the probe 22 is always in contact with the slide glass 20, and the scanner 13 is prevented from expanding by the SPM control device 17. The follower displacement of the cantilever tip with respect to time is taken into the followability evaluation computer 16 by a deflection detector, and the followability of the cantilever is evaluated by comparing with the shape displacement with respect to time.
[0019]
Evaluation of the followability of the scanner is performed by inputting the output of the waveform generator 15 to the scanner 13. At this time, as in the case of the cantilever, the position of the scanner 13 is adjusted so that the probe 22 contacts the slide glass 20. The cantilever is a cantilever having a resonance frequency sufficiently higher than the resonance frequency in the Z direction of the scanner. The displacement with respect to time of the scanner 13 is measured by a cantilever and a deflection detector, taken into the computer 16 for evaluating followability, and the followability is evaluated by comparing with the displacement with respect to time of the shape.
[0020]
The followability of the SPM control device inputs the output of the waveform generator 15 to the actuator 18. At this time, as in the case of the scanner, the position of the scanner in the Z direction is adjusted so that the probe 22 always contacts the slide glass 20. The Z output of the SPM controller is taken into the follow-up evaluation computer 16 and converted into a displacement with respect to time, and the followability of the SPM controller is evaluated by comparing it with the displacement with respect to time of the shape.
[0021]
By doing as described above, the follow-up ability of the SPM system as a whole and cantilever, scanner, control device and other elements that affect follow-up ability to any shape can be directly and quantitatively evaluated without actually scanning the sample surface. be able to.
[0022]
【The invention's effect】
The followability evaluation method and the followability evaluation apparatus according to the present invention convert a shape that the control device or the control system should follow the object to be controlled into a time displacement, and the shape displacement with respect to time and the control device or the control system are controlled objects. In order to evaluate the followability by comparing the displacement of the object to be controlled with time when the object is made to follow the displacement of the object with respect to time, the followability of the control device or control system for any shape is directly quantitative. Can be evaluated.
[Brief description of the drawings]
FIG. 1 is an explanatory diagram showing a follow-up evaluation method according to Embodiment 1 of the present invention.
FIG. 2 is an explanatory diagram showing a follow-up evaluation device according to Embodiment 2 of the present invention.
FIG. 3 is an explanatory diagram showing a follow-up evaluation device according to Embodiment 3 of the present invention.
FIG. 4 is an explanatory view showing a conventional atomic force microscope.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Control object 2 Sample surface shape 3 1st coordinate axis 4 2nd coordinate axis 5 Time axis 6 Shape displacement with respect to time 7 Control object with respect to time displacement 8 Pseudo-shape creation means 9 Controller or control system 10 Measurement means 11 Tracking Evaluation means 12 Deflection detector 13 Scanner 15 Waveform generator 16 Follow-up evaluation computer 17 SPM controller 18 Actuator 19 Cantilever 20 Slide glass 21 Sample stand 22 Probe 23 Computer 24 Sample

Claims

A control device that relatively moves the control object in a second coordinate axis direction substantially perpendicular to the object surface along the unevenness of the object surface while relatively moving the control object in a first coordinate axis direction substantially parallel to the object surface. In a method for evaluating the followability of each element that can affect the control system or followability,
Based on the moving speed of the object in the first coordinate axis direction, the uneven surface shape of the object surface is represented as a change in the second coordinate axis direction with respect to time by replacing the first coordinate axis with a time axis, and the shape versus time Obtaining a displacement;
Obtaining the displacement with respect to time of the controlled object by causing the controlled object to follow the displacement with respect to time of the shape;
A followability evaluation method comprising: a followability evaluation stage that compares the displacement of the shape with respect to time and the displacement of the control object with respect to time.

2. The tracking according to claim 1, wherein a comparison between the displacement of the shape with respect to time and the displacement of the control object with respect to time is performed in the time domain, the frequency domain, or both. Sex assessment method.

A comparison between the displacement of the shape with respect to time and the displacement of the control object with respect to time in the follow-up evaluation stage is a change in unit time of the displacement with respect to time of the shape and displacement of the control object with respect to time in the time domain. 3. The followability evaluation method according to claim 2, wherein the rates are compared.

The comparison between the displacement of the shape with respect to time and the displacement of the control object with respect to time in the follow-up evaluation stage is a residual square of the displacement of the shape with respect to time and the displacement of the control object with respect to time in the time domain. 3. The followability evaluation method according to claim 2, wherein the followability evaluation method is performed by calculating a sum.

The comparison between the displacement of the shape with respect to time and the displacement of the control object with respect to time in the follow-up evaluation stage is a cross-correlation function between the displacement of the shape with respect to time and the displacement of the control object with respect to time in the time domain. The followability evaluation method according to claim 2, wherein calculation is performed.

Comparing the displacement of the shape with respect to time and the displacement of the control object with respect to time in the follow-up evaluation step calculates a coherence function between the displacement of the shape with respect to time and the displacement of the control object with respect to time. The followability evaluation method according to claim 2, wherein the followability is evaluated.

The comparison of the displacement of the shape with respect to time and the displacement of the control object with respect to time in the follow-up evaluation stage is based on the wavelet analysis or the time / frequency joint area of the displacement of the shape with respect to time and the displacement of the control object with respect to time 3. The followability evaluation method according to claim 2, wherein the followability evaluation method is performed by analysis.

A control device for moving the control object in a second coordinate axis direction substantially perpendicular to the object surface along the unevenness of the object surface while moving the control object in a first coordinate axis direction substantially parallel to the object surface; In the follow-up evaluation device for each element that can affect the control system or follow-up,
Based on the moving speed of the control object in the first coordinate axis direction, the uneven surface shape of the object surface is represented as a change in the second coordinate axis direction with respect to time by replacing the first coordinate axis with a time axis, Pseudo-shape creating means for obtaining displacement with respect to time;
Measurement means for causing the control object to follow the displacement of the shape with respect to time and obtaining the displacement of the control object with respect to time;
A follow-up evaluation device having follow-up evaluation means for comparing the displacement of the shape with respect to time and the displacement of the control object with respect to time.

The follow-up according to claim 8, wherein the follow-up evaluation means compares the displacement of the shape with respect to time and the displacement of the control object with respect to time in the time domain, the frequency domain, or both. Sex evaluation device.

A comparison between the displacement of the shape with respect to time and the displacement of the control object with respect to time in the follow-up evaluation means is a change per unit time of the displacement with respect to time of the shape and displacement of the control object with respect to time in the time domain. 9. The followability evaluation apparatus according to claim 8, wherein the rates are compared.

A comparison of the displacement of the shape with respect to time and the displacement of the control object with respect to time in the follow-up evaluation means is a residual square of the displacement of the shape with respect to time and the displacement of the control object with respect to time in the time domain. The followability evaluation apparatus according to claim 8, wherein the followability evaluation apparatus is performed by calculating a sum.

The comparison of the displacement with respect to time of the shape and the displacement with respect to time of the control object in the follow-up evaluation means is a cross-correlation function between the displacement with respect to time of the shape in the time domain and the displacement with respect to time of the control object. The followability evaluation apparatus according to claim 8, wherein the followability evaluation apparatus calculates the followability.

Comparing the displacement of the shape with respect to time and the displacement of the control object with respect to time in the follow-up evaluation step calculates a coherence function between the displacement of the shape with respect to time and the displacement of the control object with respect to time. The followability evaluation apparatus according to claim 8, wherein the followability evaluation apparatus is characterized.

A comparison of the displacement of the shape with respect to time and the displacement of the control object with respect to time in the follow-up evaluation means is based on a wavelet analysis or a time / frequency joint area with respect to the displacement of the shape with respect to time and the displacement of the control object with respect to time. 9. The followability evaluation apparatus according to claim 8, wherein the followability evaluation apparatus is performed by analyzing.

9. The followability according to claim 8, wherein the pseudo shape creating means includes means for generating an electric signal having a waveform corresponding to the displacement of the shape with respect to time, and means for converting the electric signal into displacement. Evaluation device.

The follow-up evaluation device according to claim 8, wherein the control device or the control system is a scanning probe microscope.

9. The follow-up evaluation apparatus according to claim 8, wherein each element that can influence the follow-up performance is a scanner, a cantilever, a probe, or a feedback control system in a scanning probe microscope.