JPS6332307A - Optical film thickness measuring instrument - Google Patents
Optical film thickness measuring instrumentInfo
- Publication number
- JPS6332307A JPS6332307A JP17532986A JP17532986A JPS6332307A JP S6332307 A JPS6332307 A JP S6332307A JP 17532986 A JP17532986 A JP 17532986A JP 17532986 A JP17532986 A JP 17532986A JP S6332307 A JPS6332307 A JP S6332307A
- Authority
- JP
- Japan
- Prior art keywords
- reflectance
- film thickness
- value
- film
- layer
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 239000012788 optical film Substances 0.000 title claims 3
- 238000011156 evaluation Methods 0.000 claims abstract description 21
- 230000003595 spectral effect Effects 0.000 claims abstract description 19
- 239000000463 material Substances 0.000 claims abstract description 13
- 239000010408 film Substances 0.000 claims description 57
- 239000010409 thin film Substances 0.000 claims description 11
- 230000003287 optical effect Effects 0.000 claims description 9
- 238000005457 optimization Methods 0.000 claims description 7
- 239000006185 dispersion Substances 0.000 claims description 3
- 239000000470 constituent Substances 0.000 claims description 2
- 238000000034 method Methods 0.000 abstract description 17
- 238000005259 measurement Methods 0.000 abstract description 11
- 238000012545 processing Methods 0.000 abstract description 4
- 239000010410 layer Substances 0.000 description 27
- 238000005070 sampling Methods 0.000 description 8
- 238000010521 absorption reaction Methods 0.000 description 5
- 239000002356 single layer Substances 0.000 description 4
- 238000010586 diagram Methods 0.000 description 3
- 239000010931 gold Substances 0.000 description 3
- 239000000126 substance Substances 0.000 description 3
- 230000000694 effects Effects 0.000 description 2
- PCHJSUWPFVWCPO-UHFFFAOYSA-N gold Chemical group [Au] PCHJSUWPFVWCPO-UHFFFAOYSA-N 0.000 description 2
- 229910052737 gold Inorganic materials 0.000 description 2
- 239000011159 matrix material Substances 0.000 description 2
- 239000000758 substrate Substances 0.000 description 2
- 241000282326 Felis catus Species 0.000 description 1
- 241000257303 Hymenoptera Species 0.000 description 1
- 241001465754 Metazoa Species 0.000 description 1
- XUIMIQQOPSSXEZ-UHFFFAOYSA-N Silicon Chemical compound [Si] XUIMIQQOPSSXEZ-UHFFFAOYSA-N 0.000 description 1
- 230000033228 biological regulation Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 230000036461 convulsion Effects 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 230000001066 destructive effect Effects 0.000 description 1
- 238000009826 distribution Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 230000000737 periodic effect Effects 0.000 description 1
- 230000011514 reflex Effects 0.000 description 1
- 230000001105 regulatory effect Effects 0.000 description 1
- 229910052710 silicon Inorganic materials 0.000 description 1
- 239000010703 silicon Substances 0.000 description 1
Landscapes
- Length Measuring Devices By Optical Means (AREA)
Abstract
Description
【発明の詳細な説明】
〔産業上の利用分野〕
本発明は光学的手段による非接触、非破壊の膜厚測定装
置に関するものである。DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a non-contact, non-destructive film thickness measuring device using optical means.
〔従来技術Ｊ
分光反射率測定装置を用い℃単層の透明薄膜の分光反射
率を測定すると、薄膜の表裏面の反射光の干渉効果によ
り、第５図に示すように反射ＪＥＲＫ測定光の波長λの
変化につれて複数の人
極小または極小が現われ、膜厚に応じた周期的な変化を
示す。そして、１つの極大または極小を与える波長λａ
と他の極大または極小を与える波長λｂとの間に存在す
る極大または極小の数をＮとし、薄膜を構成する物質の
屈折率をｎｆとすると、膜厚ｄは
で与えられることが知られている。[Prior art J] When measuring the spectral reflectance of a single-layer transparent thin film at °C using a spectral reflectance measuring device, the wavelength of the reflected JERK measurement light is changed due to the interference effect of the reflected light from the front and back surfaces of the thin film, as shown in Figure 5. As λ changes, multiple minima or minima appear, showing periodic changes depending on the film thickness. And the wavelength λa giving one maximum or minimum
It is known that the film thickness d is given by , where N is the number of maxima or minima that exist between λb and the wavelength λb that gives the other maximum or minima, and nf is the refractive index of the substance constituting the thin film. There is.
この関係を利用し透−な単層膜の膜厚を測定する装置が
従来から用いられている。Devices that utilize this relationship to measure the thickness of transparent single-layer films have been used in the past.
しかしながら、多層膜では各層の分光反射率の周期性が
重なり合った総和として反射率が測定されるため、単純
に前述の関係式を適用して各層の膜厚を求めろことがで
きない。このため、従来は多層膜を付着させるべき基材
と同じ材質から取る参照用小片を用意して、各層を形成
する度毎に新しい参照用小片に基材と同時に層を、１、
形成させ、各層毎に参照用小片上に形成された単層膜
の厚さを測定して、多層膜の各層の厚さとしていた。し
かし、これでは全体の膜厚の測定に非常に時間がかかる
ばかりでな（、多層に重ねた個々の膜厚が単層状態でＩ
ｔ定した値と常に同じであるという保証もないので、必
ずしも正確に多層膜の各層の膜厚を表わしているとは言
えない、という問題があった。However, in a multilayer film, the reflectance is measured as the sum of the periodicities of the spectral reflectances of each layer, so it is not possible to simply apply the above-mentioned relational expression to determine the film thickness of each layer. For this reason, conventionally, a reference piece made of the same material as the substrate to which the multilayer film is to be attached is prepared, and each time a layer is formed, a layer is applied to the new reference piece at the same time as the substrate.
The thickness of the single layer film formed on the reference piece was measured for each layer, and the thickness was determined as the thickness of each layer of the multilayer film. However, this method not only takes a very long time to measure the overall film thickness (but also the thickness of each individual film in a multi-layered state is
Since there is no guarantee that t is always the same as the determined value, there is a problem in that it cannot necessarily be said to accurately represent the thickness of each layer of the multilayer film.
また、単層膜であっても］ Ｏｎｍ以下のようジに
な必需に薄いものや測定波長域内に光学的吸収がある膜
などのように分光反射率の周期性がはっきりしないもの
では、膜厚の測定が困難であった。In addition, even if it is a single layer film] If the periodicity of the spectral reflectance is not clear, such as a film that is extremely thin (onm or less) or a film that has optical absorption within the measurement wavelength range, the film thickness was difficult to measure.
上記に鑑み、本発明は２層膜においては各層の膜厚を同
時に測定することかでき、しかも測定波長域内に光学的
吸収がある場合等におい℃も膜厚測定が可能な元学式膜
士測定装置を提供することを目的とするものである。In view of the above, the present invention is a former academic film specialist that can simultaneously measure the film thickness of each layer in a two-layer film, and can also measure film thickness at °C in cases where there is optical absorption within the measurement wavelength range. The purpose is to provide a measuring device.
〔問題点を解決するための手段Ｊ
基材上に設けた光学薄膜の反射率は、薄膜の入射側媒質
および基材および薄膜の各層の構成物質の屈折率、各層
の膜厚、測定光の入射角および波長が与えられると一義
的に定まる。したがって、これらのうちの］つのパパラ
メタの値は、反射早お工び他のパラメータの値が与えら
れれば、逆算に工り求めることができる。[Means for solving the problem J The reflectance of an optical thin film provided on a base material is determined by the refractive index of the thin film's incident side medium and the constituent materials of the base material and each layer of the thin film, the film thickness of each layer, and the measurement light. It is uniquely determined when the incident angle and wavelength are given. Therefore, the value of one of these parameters can be obtained by backward calculation if the values of the reflex speed and other parameters are given.
本発明はこの点に着目し℃成されたものである。本発明
に係る膜厚測定装置は第１図に示すようＫ、分光反射率
測定手段】と、反射率演算手段２と、膜厚決定手段３と
を具えている。膜厚を求める場合には、まず分光反射率
測定手段】により各層を構成する物質が既知である薄膜
について、所定の波長域において一定の入射角の測定光
で分光反射率を測定する。そして、この中からい（つか
の波長を適宜選択し、この波長に対する反射早の値を以
後の処理のために選定しておく。一方、反射率演算手段
２においては既知の各屈折率、測定光の入射角、および
上で選択した波長を反射率を求める公式に代入し、膜厚
のみを変数とする関数として各波長における反射率を計
算により求める。次いで、膜厚決定手段３において、上
記の測定値と計算値の各波長における差の総体の大小を
判定するために定めた評価関数値を評価関数演算手段４
により求め、この評価関数値が最も小さくなるような礪
膜厚の値の組を大域最適化手段５により大禁最適化の手
法を用いて決定する。The present invention has been developed by paying attention to this point. As shown in FIG. 1, the film thickness measuring device according to the present invention comprises a spectral reflectance measuring means K, a reflectance calculating means 2, and a film thickness determining means 3. When determining the film thickness, first, the spectral reflectance of a thin film whose materials constituting each layer are known is measured using measurement light at a constant angle of incidence in a predetermined wavelength range using a spectral reflectance measuring means. Then, a certain wavelength is selected as appropriate from among these, and the value of the reflection speed for this wavelength is selected for subsequent processing.Meanwhile, in the reflectance calculating means 2, each known refractive index, the measured The incident angle of light and the wavelength selected above are substituted into the formula for calculating the reflectance, and the reflectance at each wavelength is calculated as a function with only the film thickness as a variable.Next, in the film thickness determining means 3, the above-mentioned The evaluation function calculation means 4 calculates the evaluation function value determined in order to determine the total magnitude of the difference between the measured value and the calculated value at each wavelength.
The global optimization means 5 determines a set of values for the diastasis thickness such that the evaluation function value is the smallest using a large-scale optimization method.
この工うＫ、本発明においては分光反射率の周期性を利
用するのではな（、所定の波長域内の複数点において測
定により求めた分光反射率の値を良（表わすように各層
の膜厚を決定する、という手法を利用することにより、
多層膜の各層の膜厚を同時に求めることができろもので
ある。そして、膜厚の決定に大域最適化法を応用するこ
とにより、より正確に膜厚を決定することができるもの
である。However, in the present invention, the periodicity of the spectral reflectance is not utilized (the value of the spectral reflectance obtained by measurement at multiple points within a predetermined wavelength range is By using the method of determining
It is possible to simultaneously determine the thickness of each layer of a multilayer film. By applying the global optimization method to determining the film thickness, the film thickness can be determined more accurately.
第２図は本発明の一実施例を示す１２７７図、第３図は
膜厚決定手段におけるデータ処理の７０−チャートであ
る。FIG. 2 is a 1277 diagram showing an embodiment of the present invention, and FIG. 3 is a 70-chart of data processing in the film thickness determining means.
第２図におい℃、目工分光器７−および光電変換手段８
を具えた分光反射率もり定装置、６は被測定多層膜、９
はデータ選足手段、１０は屈折率計算手段、２は反射率
演算手段、３は膜厚決定手段、４は評価関数演算−＋一
段、５は膜厚区間規制手段】】、平均値計算手段】２お
よび判定手段】３を具えた大域最適化手段である。In FIG.
6 is a multilayer film to be measured, 9 is a spectral reflectance measurement device equipped with
10 is a data selection means, 10 is a refractive index calculation means, 2 is a reflectance calculation means, 3 is a film thickness determination means, 4 is an evaluation function calculation -+1 stage, 5 is a film thickness interval regulation means]], an average value calculation means ]2 and determination means]3.
分光反射率測定装置】においては、屈折率ｎｓの碁打上
に設けられた屈折率ｎｌ、 ｎ２・・・・・・ｎＨの物
質から底るＮ層多層膜６が屈！７？″４ｎｏの媒質中に
置かれ℃いる。この多層膜６に図示しない光源から所定
の波長域に及ぶスペクトル分布を有する測定光を、所定
の入射角ψ０で入射させ、反射光を分光器７を介して元
ＩＥ変換手段８で受けて、所定の波長範囲における分光
反射率を連続的に測定する。この測定値から、データ選
定手段９においてＭヶの波長λ１．λ２．−・・・・λ
ＭＫ対応する反射率データＢ１ｍ、 Ｈ，ｍ、・・聞、
ＲＭ”が選定される。ここで、Ｍを太き（すると膜
厚決定の精度が高まるがデータ処理に時間がかかるので
、精度と時間の関係で適当な値を選べば′良い。尚、予
め定めたＭヶの波長につい℃のみ反射率測定を行なう場
合には、データ選定手段９は不要である。In the spectral reflectance measuring device, an N-layer multilayer film 6 formed from materials with refractive indexes nl, n2...nH provided on a board with refractive index ns is refracted! 7? Measurement light having a spectral distribution covering a predetermined wavelength range is made incident on this multilayer film 6 from a light source (not shown) at a predetermined incident angle ψ0, and the reflected light is passed through a spectrometer 7. The spectral reflectance in a predetermined wavelength range is continuously measured by the source IE conversion means 8.From this measured value, the data selection means 9 selects M wavelengths λ1.λ2.-...λ
Reflectance data corresponding to MK B1m, H, m,...
RM'' is selected.Here, make M thicker (this will increase the accuracy of determining the film thickness, but it will take time to process the data, so it is better to choose an appropriate value in terms of accuracy and time. In the case where the reflectance measurement is performed only in degrees Celsius for M wavelengths, the data selection means 9 is not necessary.
一方、反射率演算手段２においては、反射率？求める公
式にしたがい既知の屈折率ｎ。、 ｎｌ。On the other hand, in the reflectance calculation means 2, the reflectance? Known refractive index n according to the desired formula. , nl.
・・・・−・ｎＱ＋ｎＳ および入射角ψＵおよび上
で選定した波長λ凰、・・・・・・、λＭ を用いて、
膜厚を変数とするＭヶの反射率Ｒ１，叩・・、ＲＭ
を計算する。Using ......-nQ+nS and the incident angle ψU and the wavelength λ凰 selected above, ......, λM,
Reflectance R1 of M pieces with film thickness as a variable, Hit..., RM
Calculate.
ここで反射率の公式とし℃は公知の
を用いることができる。但し、ηｉは各層の英効屈折皐
で、ｔｉ層の入射角をψｉ 、屈折率をｎｉ とする
とＰ成分については ηｉ ” ｎ ｉ ／ ｅ０８９
’ ｉ ＋Ｓ成分についてはη１＝−ｎｉｅ０８何で与
えられるもの、ｍ、２．・・・・−・、ｒｎ２２は薄膜
の特性行列の要素で波長をλ、第１層における膜厚をｄ
Ｉ、位相を２π
ｄｉ ” ７ ｎｉ ｄｉ ｅｏ！ψｉとし、特性行列
なＴｉ とするとき、ｊを虚数単位とし℃
で与えられるものである。、各層に光学的吸収がある場
合には、当然屈折率は複素数となる。また、各層や基材
の屈折率の波長による分散を考慮する必要がある場合に
データ選定手段９で選定した波長に対応する屈折率の値
が既知でないときは、屈折率計算手段１０においてその
物質の固有の分散式を用いるか、あるいはその前後の波
長における既知の屈折１４ｇＫを用いて適当な補間法に
より屈折率を求め、これを用い℃反射率を計算すれば良
い。Here, a known formula for reflectance can be used for °C. However, ηi is the effective refraction ratio of each layer, and if the incident angle of the ti layer is ψi and the refractive index is ni, then for the P component, ηi ” ni / e089
' For the i + S component, η1=-nie08 is given by m, 2. ......, rn22 is an element of the characteristic matrix of the thin film, where the wavelength is λ and the film thickness in the first layer is d.
I, the phase is 2π di ” 7 ni di eo!ψi, and the characteristic matrix Ti is given in degrees Celsius, where j is the imaginary unit.If each layer has optical absorption, naturally, the refraction The index is a complex number.In addition, when it is necessary to consider dispersion of the refractive index of each layer or base material due to wavelength, and the value of the refractive index corresponding to the wavelength selected by the data selection means 9 is not known, the refractive index The calculation means 10 may use a dispersion formula specific to the substance or use known refraction 14gK at wavelengths before and after the refractive index to obtain the refractive index by an appropriate interpolation method, and use this to calculate the reflectance in degrees Celsius.
以上の測定された反射率データと計算された反射率関数
とに基いて、膜厚の決定が行なわれる。The film thickness is determined based on the measured reflectance data and the calculated reflectance function.
まず、評価関数演算手段４において、測定データと計算
データの総体的な差の大きさを評価するための評価関数
ＫＲＩｒｎ、・・、−、Ｒ／ｌ、 Ｒｓｃ＊・・・・・
・。First, in the evaluation function calculating means 4, evaluation functions KRIrn, . . . , −, R/l, Rsc*, .
・.
ＲＭ を代入して、評価間数頭を求める。これは膜厚ｄ
Ｉ、・・・・・・ｄＮの関数となる。評＃関数としては
、例えば
のようなものが考えられる。ここで、ｋは適当な整数、
ｔｉは誤差の許容度を表わす係数で精度を上げる（ Ｒ
ｒ”と朗０の差を拡大してみる）必ｐがあるときはｔ８
を小さくし、逆の場合は大きくする。Substitute RM to find the number of animals to be evaluated. This is the film thickness d
I, ... is a function of dN. As the evaluation function, the following can be considered, for example. Here, k is an appropriate integer,
ti is a coefficient that represents the error tolerance and increases accuracy (R
Try expanding the difference between "r" and ro0) If necessary, use t8
Make it smaller, and vice versa make it larger.
この関数が最小値をとる点ではＲｌｍとＨ、ｅ との
差が全体的にみて最も小さくなっているから、この点に
おけるｄｔ、・・・・＝ｍ ｄＮ’）ｉを被測定多層膜
の各１の膜厚と考えてよい、最小値を求める方法として
は、変数ｄ１．・・・・−・ｄＮに適当な初期値を与え
℃評価関数値を求め１次いでこの値が減少するようＫｆ
ｆｉ数の値を少しずつ変化させて評価関数の最小値を求
める近似方法もあるが、評価関数が複数の極小値を持つ
場合には局所的な極値に収束してしまい、最小値を与え
るｄｌ、−・・−・。At the point where this function takes the minimum value, the difference between Rlm and H,e is the smallest overall, so dt,...=m dN')i at this point is the value of the multilayer film to be measured. The method for finding the minimum value, which can be considered as the film thickness of each variable d1.・・・Give an appropriate initial value to dN, calculate the °C evaluation function value, and then set Kf so that this value decreases.
There is an approximation method that finds the minimum value of the evaluation function by changing the value of the fi number little by little, but if the evaluation function has multiple local minimum values, it converges to a local maximum value and gives the minimum value. dl, --・・−・.
ｄＮ が正しく求まらない場合がある。dN may not be found correctly.
そこで１６本発明においＣは入城最適化法を用いて評価
関数Ｅの最小値を与えるｄｌ、・・・・・・、 ｄＮを
求めるよ５Ｋしているが、ここでまず、本笑抱例に用い
℃いる入城最適化法の概念を第４図を用い℃説明する。Therefore, in the present invention, C uses the entrance optimization method to find dl, ..., dN that gives the minimum value of the evaluation function E, but first, let us consider the present example. The concept of the entry optimization method used will be explained using FIG.
−変数ｘ（Ｆ）関数ｙ＝ｆ（幻の最小値を求める場合、
まず最小値を含む変数の変動区間Ｈａを指定する。この
区間における−の景大榎をＦｏ とする。そして、区
間ＨａＰＪＫおいて適当な数のサンプリング点ｘ ｒ
＋・・・・・・、ｘＬを決め、これらに対応するｆ（ｘ
）の籠の平均値り小さい。そこでｙ＝ｆ（ｘ）と’！＝
Ｆｌの交点で決まる新たな変数Ｘの区間Ｈ１を求め、こ
の区間内で再び適当な数のサンプリング点をとり、式−
の平均値を求める。この手順を繰返すと、その度毎に平
均値は小さくなって行き局所的な極小値の有無に拘らず
Ｆ！、 １（１で示すようにｆ（勾の最小値およびそれ
を与えるＸの値に向って収束して行く。２つの平均値の
差Ｆｌ＋１−Ｆｌ あるいは２つの変動区間の幅の差
Ｈ１＋□〜Ｈ，がある程度以上小さくなれば、実質的に
最小値に到達したとみなして良い。- Variable x (F) function y = f (when finding the phantom minimum value,
First, a variable range Ha of the variable including the minimum value is specified. Let Fo be the negative Kei Oen in this section. Then, an appropriate number of sampling points x r in the interval HaPJK
+..., xL is determined, and the corresponding f(x
) is smaller than the average value of the basket. So y=f(x) and '! =
Find the interval H1 of the new variable X determined by the intersection of Fl, take an appropriate number of sampling points again within this interval, and use the formula -
Find the average value. If this procedure is repeated, the average value will become smaller each time, and regardless of the presence or absence of local minimum values, F! , 1(1) converges toward the minimum value of f(gradient and the value of If H, becomes smaller than a certain level, it can be considered that the minimum value has been substantially reached.
この方法を適用するため、まず膜厚区間規制手段１］に
膜厚を変動させるべき区間の初期値（ｄＩ ３ｏ’＋
（ｄ２）＋＋ 、 ・−＝ｒ （ｄＮ）ｏを与える。In order to apply this method, first, the initial value (dI 3o'+
(d2)++ , ・−=r (dN)o is given.
これは、被測定多層ｙ４６の設計厘および製作時の条件
等を考慮して決定するが、それらがわからない場合は求
めるべき膜厚値を含むと推定される区間を与える。ここ
で、この区間の端における評価関数の最大値Ｅ。を求め
て粘（。次に、評価関数の平均値を計算するため、平均
値計算手段］２では、まず上記の区間内に、おいて適当
な数の（ｄ五、・・・・・・、 ｄＮ）の壇の組Ｄ１＝
（ｄｒ １＋・・・・・・、 ｄＮｌ）＊Ｄ！”（ｄｌ
？＋ ”””＋ ｄＮｚ ）ｔ Ｄｓ＝（ｄ１５＋
”””ｔ ｄＮＳ）をサンプリング点として指定する。This is determined by considering the design and manufacturing conditions of the multilayer y46 to be measured, but if these are not known, an interval estimated to include the film thickness value to be determined is provided. Here, the maximum value E of the evaluation function at the end of this interval. Then, in order to calculate the average value of the evaluation function, the average value calculation means] 2 first calculates an appropriate number of (d5,...) within the above interval. , dN) platform set D1=
(dr 1+..., dNl)*D! ”(dl
? + “””+ dNz )t Ds=(d15+
"""t dNS) is designated as the sampling point.
そして、各組の値を評価関数に代入し１１（Ｄ□）、・
・・・・・Ｅｌ： （Ｄｓ）を計算し、それらの平均値
を求めろ。サンプリング点の数、サンプリング点同士の
間隔は任意でよい。Then, substitute the values of each set into the evaluation function and get 11(D□),
...El: Calculate (Ds) and find their average value. The number of sampling points and the interval between sampling points may be arbitrary.
次に、判定手段】３においては、上記のサンプリング点
におけるＥ（ＤＩ）、・・・・・・、Ｅ（Ｄｓ）のうち
小さい方からｔａ＆、・・・・・・、Ｅｔ を選び、
これらの平均値からの分散
を求める。そして、最小値への収束度を判定するために
予め定めた数εとＧｌ とを比較する。Next, in determination means [3], select ta&, ..., Et from the smaller of E(DI), ..., E(Ds) at the above sampling points,
Find the variance from these average values. Then, in order to determine the degree of convergence to the minimum value, a predetermined number ε is compared with Gl.
］＋＋εであれば平均値Ｅ１ がまだ評価関数の最小［
Ｋ充分収束し℃いない状態である。この場（ｄＮ）１．
を求め、膜厚区間規制手段１１の（ｄＩ３＊。]++ε, the average value E1 is still the minimum of the evaluation function [
K has not converged sufficiently yet. This field (dN)1.
(dI3*) of the film thickness section regulating means 11.
・・・・・・ＩｃｄＮ）Ｑを新たな膜厚変動区間で置替
えるとともＫ ＥｏをＥｌで置替え（、再び平均値計算
手段］１のサンプリング点を選択するステップへ戻り、
以後これを繰返す。Ｕ回繰返してＧｕ＜ξとなったとす
れば、平均［Ｅｕと各サンプリング点における評価関数
僅とがきわめて近いからこの状態で実質的に最小［Ｋ収
束したものとし℃、このとき得られ℃いる（ｄＩ３ｕ、
・・・・・・＋ （ｄＮ）ｕの中から適当に定めた（ｄ
Ｉ、・・・・・・ｅ ａＮ）の組を各層の膜厚とし℃出
力する。εを充分小さくしておけば各区間（ｄＩ ｈ＋
ｒ −−＊ （ｄＮ）ｕ は非常に狭くなるのでそ
の中のどの値を膜厚として採用し又も実用上置わりはな
い。. . . IcdN) Q is replaced with a new film thickness variation interval, and K Eo is replaced with El (again, average value calculation means). Return to the step of selecting the sampling point in 1.
Repeat this from now on. If it is repeated U times and Gu < ξ, then the average [Eu and the evaluation function at each sampling point are very close, so in this state it is assumed that the minimum [K has converged, ℃, and the value obtained at this time is ℃. (dI3u,
・・・・・・+ (dN) Appropriately determined from u (d
The film thickness of each layer is set as the set of I, . . . If ε is made small enough, each interval (dI h+
Since r--*(dN)u is very narrow, there is no practical difference in which value is adopted as the film thickness.
（実験例）
ごこでは、入射媒質は空気（ｒＬＱ＝１）、Ｋ１層はＭ
ｇＦｔ （（ｌｌ＝１．３８） −Ｋ ２層は金Ａｕ（
ｎｚ ＝ ｎ鵞’ −Ｌｋ、 ｌ、第３層は８％（ｈ
（＋１３ ＝ １．４５ ）、基材はシリコン５ｉ（ｎ
ε＝ ｎ３’ ｔｋ３ ）とし、各層の膜厚がｄｌ＝
７０ａｍ 、 ｄｚ＝２０ｎｍ 、 ｄｚ＝１５０ａｍ
と予めわかつ℃いるものにつき、上で述べた方法を用
い℃改めて膜厚を求め℃みた。(Experiment example) Here, the incident medium is air (rLQ=1), and the K1 layer is M
gFt ((ll=1.38) -K The second layer is gold Au (
nz = n鵞' -Lk, l, the third layer is 8% (h
(+13 = 1.45), the base material is silicon 5i(n
ε=n3' tk3), and the film thickness of each layer is dl=
70am, dz=20nm, dz=150am
The film thickness was determined again using the method described above and measured at ℃.
測定光を垂直入射（（ｐｏ＝ｏ ）とし、波長４００ｎ
ｒｎから８００ ｎｍ の範囲内で９ケの波長を選択
し、各波長につい℃ｎ２とｎ３は文献ｊ
（Ｈａｎｄｂｏｏｋ ｏｌｏｐｔｔｅａｌ Ｃｏｎａｔ
ａｎｔｓ ｏｆ ５ｏｌｉｃｈ−Ａｅａｄｅｍｉ ｅ
Ｐｒｅｓｓ ） ＷＴ ｉａ ｆ）金とシリーンのデー
タに（ｎ、にとも２０コ）基ぎ補間して求めたものを用
いてＲ１＋・・・・・・、ＲＡＴｔ計算により求めた。The measurement light is perpendicularly incident ((po=o), and the wavelength is 400n.
Nine wavelengths were selected within the range of 800 nm from rn, and for each wavelength, ℃n2 and n3 were determined from the literature.
ants of 5olich-Aeademie
Press) WT ia f) R1+..., RATt calculation using data obtained by interpolating gold and sireen data (n, both 20 pieces).
欠に、ｄＩ、ｄｘ、ｒｌｓＹ：未知数として電□・・・
・・・、Ｒ４を求め、これらを用い℃各層の膜厚を求め
たところ、ε＝１０ としてｄ、＝７０．００ｎｍ 、
ｄ＊＝２０．００ｎｍ 、 ｄｘ＝３５０．０１ ｎ
ｍを得た。In short, dI, dx, rlsY: electric □...
..., R4 was determined, and the film thickness of each layer was determined using these values. Assuming ε=10, d=70.00 nm,
d*=20.00nm, dx=350.01n
I got m.
この例からも明らかなよ５に、多層でしかも光学的吸収
を有するものにおいて、高ｎ１度で膜厚を求めることが
できる。As is clear from this example, it is possible to determine the film thickness at a high n1 degree in a multilayer structure with optical absorption.
尚、本例においては反射率の測定データと計喝
算データの差を肝価する関数として第（１）を用いてい
るが、例えば各波長における差の単なる和。In this example, the function (1) is used as a function that evaluates the difference between the measured reflectance data and the calculated data, but for example, it is simply the sum of the differences at each wavelength.
のように誤差が相殺してしまうような関数を除けば、種
々のものが利用できることは言うまでもない。また、こ
の例では大域最適化法としてＪ、Ｏｐｔ、 Ｓｏｃ、Ａ
ｍ、 ｖｏｌ、 ７２．１９８２ ＰＰ１５２２〜】
５２８に開示された方法を説明したが、他にも例えばＡ
ｐｐｌｉｅｄ ｏｐｔ台ｖｏｌ ４ 、 ］ ９６５
ｐｐ９３７〜９４６ に開示された如き方法を初めとし
ていくつかの例が知られており、適宜これらを用いても
良いことはもちろんである。It goes without saying that a variety of functions can be used, except for functions whose errors cancel each other out, such as . In addition, in this example, J, Opt, Soc, A are used as global optimization methods.
m, vol, 72.1982 PP1522~]
Although the method disclosed in A.
pplied opt machine vol 4, ] 965
Several examples are known, including the method disclosed in pp. 937-946, and it goes without saying that these may be used as appropriate.
また、本例では膜厚のみを変数としたが、変数が更に増
加しても本質的に変わるところはないので、本例は例え
ば屈折率も未知の薄膜の膜厚、屈折率を同時に求めよう
とする場合にも容易に拡張できる。即ち、この場合には
各層の膜厚に加え屈折率も未知数とし’ｃ ａｔ 、・
・・・・・＋ ＲＭを求め、以後のデータ処理を行なえ
ば良い。In addition, in this example, only the film thickness was used as a variable, but there is essentially no change even if the variable increases further, so in this example, for example, let's simultaneously calculate the film thickness and refractive index of a thin film whose refractive index is unknown. It can be easily extended to other cases. That is, in this case, in addition to the film thickness of each layer, the refractive index is also assumed to be unknown, 'cat,
...+ RM can be obtained and the subsequent data processing can be performed.
〔発明の効果）
本発明は分光反射率の同期性を利用するものと異なり、
多層膜の各層の膜厚を同時に求めることができ、しかも
光学的吸収を有する物質を用いたものにおいても、入射
光が基材外画まで透過できるようなものであればその膜
厚を求めることができる。[Effects of the Invention] The present invention differs from those that utilize synchronization of spectral reflectance;
The thickness of each layer of a multilayer film can be determined at the same time, and even if a substance with optical absorption is used, the thickness can be determined if the incident light can pass through to the outside of the base material. Can be done.
第１図は本発明の詳細な説明するための図、第２図は本
発明の一実施例を示すグルツク図、考許出願人
第 ５図
第３図Fig. 1 is a diagram for explaining the present invention in detail, Fig. 2 is a diagram showing one embodiment of the present invention, Fig. 5, Fig. 3 of the applicant
Claims (2)
光学薄膜の分光反射率を測定するための分光反射率測定
手段と、該分光反射率測定手段により得られる複数の反
射率データを測定した波長において既知の屈折率に基づ
き膜層のみを変数とする関数として上記光学薄膜の反射
率を算出する反射率演算手段と、該反射率演算手段より
得られる反射率値と上記反射率データとの各波長におけ
る差の総体的な大きさを示す評価関数を上記反射率値お
よび反射率データに基いて膜厚の関数として算出するた
めの評価関数演算手段と、該評価関数が最小値となるよ
うな膜厚の値を大域最適化法により求めるための大域最
適化手段と、を具備して成る光学式膜厚測定装置。(1) A spectral reflectance measuring means for measuring the spectral reflectance of an optical thin film whose refractive index of each layer, base material, and incident medium is known, and a plurality of reflectance data obtained by the spectral reflectance measuring means. reflectance calculation means for calculating the reflectance of the optical thin film as a function with only the film layer as a variable based on the known refractive index at the measured wavelength; a reflectance value obtained from the reflectance calculation means and the reflectance data; an evaluation function calculation means for calculating an evaluation function indicating the overall size of the difference at each wavelength between the An optical film thickness measuring device comprising: global optimization means for determining a film thickness value such that
の各波長における値の一部を、該層の構成物質の固有の
分散式を用いるか、または該物質の既知の屈折率値から
補間することにより求めるための屈折率計算手段を具え
た特許請求の範囲第１項の光学式膜厚測定装置。(2) To calculate the reflectance value, a part of the value of the refractive index of each layer at each wavelength may be calculated by using a dispersion equation specific to the constituent material of the layer, or by using a known refractive index of the material. An optical film thickness measuring device according to claim 1, comprising means for calculating a refractive index by interpolation from a value.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP17532986A JPH0731049B2 (en) | 1986-07-25 | 1986-07-25 | Optical film thickness measuring device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP17532986A JPH0731049B2 (en) | 1986-07-25 | 1986-07-25 | Optical film thickness measuring device |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPS6332307A true JPS6332307A (en) | 1988-02-12 |
| JPH0731049B2 JPH0731049B2 (en) | 1995-04-10 |
Family
ID=15994171
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP17532986A Expired - Fee Related JPH0731049B2 (en) | 1986-07-25 | 1986-07-25 | Optical film thickness measuring device |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH0731049B2 (en) |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4999508A (en) * | 1988-12-29 | 1991-03-12 | Olympus Optical Co., Ltd. | Optical film thickness measuring device for measuring two-layer film thicknesses using spectral reflectance |
| JPH0666524A (en) * | 1992-06-29 | 1994-03-08 | Hughes Aircraft Co | Device and method for metrologically processing thickness of thin film layer on thin film layer having deformed shaped and prtially deformed inclination |
| JPH07260437A (en) * | 1993-12-22 | 1995-10-13 | Hughes Aircraft Co | Method and device for measuring film thickness in multilayered thin-film laminated layer |
| JPH10253324A (en) * | 1997-03-06 | 1998-09-25 | Matsushita Electric Ind Co Ltd | Method for measuring film thickness of multi-layer thin film, and method and device for manufacturing optical information recording medium |
| JP2007533977A (en) * | 2004-03-11 | 2007-11-22 | アイコス・ビジョン・システムズ・ナムローゼ・フェンノートシャップ | Wavefront manipulation and improved 3D measurement method and apparatus |
-
1986
- 1986-07-25 JP JP17532986A patent/JPH0731049B2/en not_active Expired - Fee Related
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4999508A (en) * | 1988-12-29 | 1991-03-12 | Olympus Optical Co., Ltd. | Optical film thickness measuring device for measuring two-layer film thicknesses using spectral reflectance |
| JPH0666524A (en) * | 1992-06-29 | 1994-03-08 | Hughes Aircraft Co | Device and method for metrologically processing thickness of thin film layer on thin film layer having deformed shaped and prtially deformed inclination |
| JPH07260437A (en) * | 1993-12-22 | 1995-10-13 | Hughes Aircraft Co | Method and device for measuring film thickness in multilayered thin-film laminated layer |
| JPH10253324A (en) * | 1997-03-06 | 1998-09-25 | Matsushita Electric Ind Co Ltd | Method for measuring film thickness of multi-layer thin film, and method and device for manufacturing optical information recording medium |
| JP2007533977A (en) * | 2004-03-11 | 2007-11-22 | アイコス・ビジョン・システムズ・ナムローゼ・フェンノートシャップ | Wavefront manipulation and improved 3D measurement method and apparatus |
Also Published As
| Publication number | Publication date |
|---|---|
| JPH0731049B2 (en) | 1995-04-10 |
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