JP2009288135A - Defect counting device and defect counting method - Google Patents
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本発明は、結晶等の端面に現れる貫通転位などの欠陥を、カソードルミネッセンス画像に基づいて計数する欠陥計数装置及び欠陥計数方法に関するものである。 The present invention relates to a defect counting apparatus and a defect counting method for counting defects such as threading dislocations appearing on an end face of a crystal or the like based on a cathodoluminescence image.
サファイア基板上にガリウムナイトライドを結晶成長させるときのように、基板上に格子定数の異なる材料を結晶成長させる場合には、その材料に転位が生じ、結晶成長に伴ってその転位が当該成長方向に延びていく現象が生じ得る。このような成長方向に延びる転位を貫通転位と呼ぶ。この貫通転位の存在は、特許文献１に示すように、材料結晶の品質を左右するものであるから、従来、材料結晶における貫通転位の数又は密度を測定することが行われている。 When a material having a different lattice constant is grown on a substrate, such as when gallium nitride is grown on a sapphire substrate, dislocations occur in the material, and the dislocations move along the crystal growth direction. The phenomenon of extending to Such a dislocation extending in the growth direction is called a threading dislocation. The existence of threading dislocations influences the quality of the material crystal, as shown in Patent Document 1, and conventionally, the number or density of threading dislocations in the material crystal has been measured.
その測定には、カソードルミネッセンスが利用される。すなわち、成長中の結晶端面に電子線を照射すると、貫通転位部位ではカソードルミネッセンスが生起されないため、結晶端面のカソードルミネッセンス画像中に貫通転位が暗点（ダークスポット、以下、ＤＳとも言う）として現れる。そこで、このＤＳ数を計数することによって、貫通転位の数又は密度を求めるようにしている。そして、現在のところ、ＤＳ数は目視で数えるのが一般的である。
しかしながら、取得したカソードルミネッセンス画像中に大量のＤＳがある場合、目視で計数するのは容易ではない。また、半導体製造プロセスなどの全自動化を推し進めていく上では、目視計数の工程をマシンプロセスに代替する必要も今後生じ得る。 However, when there is a large amount of DS in the acquired cathodoluminescence image, it is not easy to count visually. In addition, in order to promote full automation of semiconductor manufacturing processes and the like, it may be necessary to replace the visual counting process with a machine process in the future.
そこで、画像解析によって貫通転位数を自動計数することが容易に考えられるが、実際には、複数の貫通転位が所定以上近接していると、画像上では、これら貫通転位が一部重なり合って１つのＤＳとして認識されるため、正確に貫通転位数を計数することが難しい。これに対し、目視の場合は、オペレータの判断によってある程度以上大きなＤＳや形のいびつなＤＳは２つまたはそれ以上の貫通転位として計数されるから、計数誤差は小さい。 Thus, although it is easy to automatically count the number of threading dislocations by image analysis, in reality, when a plurality of threading dislocations are close to each other by a predetermined amount or more, these threading dislocations partially overlap each other on the image. Since it is recognized as one DS, it is difficult to accurately count the number of threading dislocations. On the other hand, in the case of visual observation, since a DS that is larger than a certain degree or an irregularly shaped DS is counted as two or more threading dislocations, the counting error is small.
本発明は、かかる問題点を鑑みてなされたものであって、結晶等の試料端面におけるカソードルミネッセンス画像から、貫通転位などの欠陥数を自動計数する場合に、その誤差を小さくしてより正確に計数できるようにすべく図ったものである。 The present invention has been made in view of such problems, and in the case of automatically counting the number of defects such as threading dislocations from a cathodoluminescence image on a sample end face such as a crystal, the error is reduced and more accurately. This is intended to allow counting.
すなわち、本発明は、結晶等の試料端面のカソードルミネッセンス画像から、当該試料端面に存在する欠陥数を計数する欠陥計数装置に係るものであって、 That is, the present invention relates to a defect counting apparatus that counts the number of defects existing on the sample end face from the cathodoluminescence image of the sample end face such as a crystal,
試料端面のカソードルミネッセンス画像から、当該試料端面に現れる欠陥数を計数する装置であって、
前記画像に現れる欠陥像の数と各欠陥像の面積とを計測して、欠陥像の面積に対する数の分布を算出する欠陥像分布算出部と、前記分布において数が最大となる欠陥像の面積から推測される閾面積よりも小さな面積を有する欠陥像の総数を当該分布から計数することで、近傍の他の欠陥による欠陥像とは欠陥像同士が重合しない欠陥である孤立欠陥の数を算出する孤立欠陥数算出部と、前記閾面積よりも小さな面積を有する欠陥像の総面積である閾下総面積を前記分布結果から算出し、その閾下総面積を前記孤立欠陥の数で除算することで、前記孤立欠陥による欠陥像の面積を算出する孤立欠陥像面積算出部と、前記閾面積よりも大きな面積を有する欠陥像の総面積である閾上総面積を前記分布結果から算出し、前記閾上総面積を前記孤立欠陥像面積で除算することで、近傍の他の欠陥による欠陥像と欠陥像同士が少なくとも一部重合する欠陥である近接欠陥の数を算出する近接欠陥数算出部と、前記孤立欠陥の数と近接欠陥の数とを足し合わせることで、画像に映し出された試料端面に存在する総欠陥数を算出する総欠陥数算出部と、を具備していることを特徴とする。
A device for counting the number of defects appearing on the sample end face from the cathodoluminescence image of the sample end face,
A defect image distribution calculating unit that calculates the number distribution of defect images and the number of defect images appearing in the image and calculating the number distribution with respect to the area of the defect image, and the area of the defect image having the largest number in the distribution By calculating the total number of defect images having an area smaller than the threshold area estimated from the distribution from the distribution, the number of isolated defects that are defects in which defect images do not overlap with each other are calculated. And calculating the total number of sub-thresholds, which is the total area of defect images having an area smaller than the threshold area, from the distribution result, and dividing the total sub-threshold area by the number of isolated defects. An isolated defect image area calculating unit for calculating an area of the defect image due to the isolated defect, and calculating a total area above the threshold which is a total area of the defect image having an area larger than the threshold area from the distribution result, The isolated area By dividing by the image area, a defect image due to other defects in the vicinity and a defect number calculation unit that calculates the number of adjacent defects that are defects in which the defect images overlap at least partially, and the number and proximity of the isolated defects And a total defect number calculating unit for calculating the total number of defects present on the end face of the sample displayed in the image by adding together the number of defects.
また、本発明は同欠陥計数装置に係るものであって、
前記画像に現れる欠陥像の数と各欠陥像の面積とを計測して、欠陥像の面積に対する数の分布を算出する欠陥像分布算出部と、横軸を欠陥像の面積、縦軸を欠陥像の数とした分布グラフにおける最大ピークから左側のグラフ線に、ガウシアン曲線の左側部分をフィッティングさせ、そのガウシアン曲線で囲まれる範囲内に存在する欠陥像の総数を前記分布から計数することで、近傍の他の欠陥による欠陥像とは欠陥像同士が重合しない欠陥である孤立欠陥の数とする孤立欠陥数算出部と、前記ガウシアン曲線のピーク座標における欠陥像の面積を、孤立欠陥による孤立欠陥像の面積として算出する孤立欠陥像面積算出部と、欠陥像の総面積から孤立欠陥像の総面積を減算し、その値を前記孤立欠陥像面積で除算することで、近傍の他の欠陥による欠陥像と欠陥像同士が少なくとも一部重合する欠陥である近接欠陥の数を算出する近接欠陥数算出部と、前記孤立欠陥の数と近接欠陥の数とを足し合わせることで、画像に映し出された試料端面に存在する総欠陥数を算出する総欠陥数算出部と、を具備していることを特徴とする。
Further, the present invention relates to the defect counting apparatus,
A defect image distribution calculation unit that measures the number of defect images appearing in the image and the area of each defect image, and calculates a distribution of the number of the defect images with respect to the area of the defect image; By fitting the left part of the Gaussian curve to the left graph line from the maximum peak in the distribution graph as the number of images, and counting the total number of defect images existing within the range surrounded by the Gaussian curve from the distribution, The defect image due to other defects in the vicinity is the number of isolated defects that are the number of isolated defects that do not overlap with each other, and the area of the defect image at the peak coordinate of the Gaussian curve is determined by the isolated defect due to the isolated defect. An isolated defect image area calculation unit that calculates the area of the image, and subtracts the total area of the isolated defect image from the total area of the defect image, and divides the value by the area of the isolated defect image to thereby determine other defects in the vicinity. By adding the number of adjacent defects and the number of adjacent defects, the number of adjacent defects and the number of adjacent defects that calculate the number of adjacent defects that are defects in which the defect images are at least partially overlapped with each other are displayed in the image. And a total defect number calculating section for calculating the total number of defects existing on the end face of the sample.
また、本発明は、試料端面のカソードルミネッセンス画像から、当該試料端面に現れる欠陥数を計数する欠陥計数方法に係るものであって、
前記画像に現れる欠陥像の数と各欠陥像の面積とを計測して、欠陥像の面積に対する数の分布を算出する欠陥像分布算出ステップと、数が最大となる欠陥像の面積よりも、分布態様から定まる量だけ大きな面積である閾面積を推測する閾面積推測ステップと、前記閾面積よりも小さな面積を有する欠陥像の総数を前記分布結果から算出し、その総数をもって、近傍の他の欠陥による欠陥像とは欠陥像同士が重合しない欠陥である孤立欠陥の数とする孤立欠陥数算出ステップと、前記閾面積よりも小さな面積を有する欠陥像の総面積である閾下総面積を前記分布結果から算出し、その閾下総面積を前記孤立欠陥の数で除算した値をもって、前記孤立欠陥による欠陥像の面積とする孤立欠陥像面積算出ステップと、前記閾面積よりも大きな面積を有する欠陥像の総面積である閾上総面積を前記分布結果から算出し、前記閾上総面積を前記孤立欠陥像面積で除算した値をもって、近傍の他の欠陥による欠陥像と欠陥像同士が少なくとも一部重合する欠陥である近接欠陥の数とする近接欠陥数算出ステップと、前記孤立欠陥の数と近接欠陥の数との和を算出し、その値をもって、画像に映し出された試料端面に存在する総欠陥数とする総欠陥数算出ステップと、を行うことを特徴とする。
Further, the present invention relates to a defect counting method for counting the number of defects appearing on the sample end face from the cathodoluminescence image of the sample end face,
The defect image distribution calculating step for measuring the number of defect images appearing in the image and the area of each defect image, and calculating the distribution of the number with respect to the area of the defect image, than the area of the defect image having the maximum number, A threshold area estimation step for estimating a threshold area which is an area larger than an amount determined from the distribution mode, and the total number of defect images having an area smaller than the threshold area is calculated from the distribution result. The defect image by the defect is the number of isolated defects that is the number of isolated defects that do not overlap with each other, and the distribution of the sub-threshold total area that is the total area of the defect image having an area smaller than the threshold area. An isolated defect image area calculating step for calculating the area of the defect image by the isolated defect with a value obtained by dividing the total sub-threshold area by the number of isolated defects, and an area larger than the threshold area. The total area above the threshold, which is the total area of the defect image to be calculated, is calculated from the distribution result, and a value obtained by dividing the total area above the threshold by the area of the isolated defect image has at least one defect image and other defect images in the vicinity. The proximity defect number calculating step, which is the number of adjacent defects that are partially overlapping defects, and the sum of the number of isolated defects and the number of adjacent defects are calculated, and the value is present on the end face of the sample displayed in the image. And performing a total defect number calculating step as a total defect number.
また、本発明は、同欠陥計数方法に係るものであって、
前記画像に現れる欠陥像の数と各欠陥像の面積とを計測して、欠陥像の面積に対する数の分布を算出する欠陥像分布算出ステップと、横軸を欠陥像の面積、縦軸を欠陥像の数とした分布グラフにおける最大ピークから左側のグラフ線に、ガウシアン曲線の左側部分をフィッティングさせ、そのガウシアン曲線で囲まれる範囲内に存在する欠陥像の総数を前記分布結果から算出し、その総数をもって、近傍の他の欠陥による欠陥像とは欠陥像同士が重合しない欠陥である孤立欠陥の数とする孤立欠陥数算出ステップと、前記ガウシアン曲線のピーク座標における欠陥像の面積をもって、孤立欠陥による孤立欠陥像の面積とする孤立欠陥像面積算出ステップと、欠陥像の総面積から孤立欠陥像の総面積を減算し、その値を前記孤立欠陥像面積で除算した値をもって、近傍の他の欠陥による欠陥像と欠陥像同士が少なくとも一部重合する欠陥である近接欠陥の数とする近接欠陥数算出ステップと、前記孤立欠陥の数と近接欠陥の数との和を算出し、その値をもって、画像に映し出された試料端面に存在する総欠陥数とする総欠陥数算出ステップと、を行うことを特徴とする。
Further, the present invention relates to the defect counting method,
A defect image distribution calculating step for measuring the number of defect images appearing in the image and the area of each defect image, and calculating a distribution of the number with respect to the area of the defect image, the horizontal axis is the defect image area, and the vertical axis is the defect. The left part of the Gaussian curve is fitted to the left graph line from the maximum peak in the distribution graph as the number of images, and the total number of defect images existing within the range surrounded by the Gaussian curve is calculated from the distribution result. With the total number, the defect image by the other defects in the vicinity and the number of isolated defects that are defects in which the defect images do not overlap with each other, and the area of the defect image at the peak coordinates of the Gaussian curve, the isolated defect The step of calculating the area of the isolated defect image by the step of calculating the area of the isolated defect image, subtracting the total area of the isolated defect image from the total area of the defect image, and dividing the value by the area of the isolated defect image. And the number of adjacent defects and the number of adjacent defects and the number of adjacent defects, and the number of adjacent defects and the number of adjacent defects that are defects in which defect images due to other defects in the vicinity and the defect images at least partially overlap with each other. The sum defect is calculated, and the total defect number calculating step is performed by using the value as the total defect number present on the sample end face projected in the image.
貫通転位は、試料端面全体でみて同じ数（又は同じ密度）であっても、試料端面全体に平均的に散らばっているよりは、１箇所乃至複数箇所に集中的に存在する方が、例えば半導体デバイスとして用いやすい。その指標を提示するには、前記孤立欠陥数と近接欠陥数との比、又はその比を示す値、例えば前記孤立欠陥数と総欠陥数との比など、を算出する比率算出部をさらに具備しているものが好ましい。 Even though the number of threading dislocations is the same (or the same density) as viewed from the entire sample end face, it is more intensively present in one place or a plurality of places, for example, than in the case where they are scattered on the entire sample end face. Easy to use as a device. In order to present the index, the apparatus further includes a ratio calculation unit that calculates a ratio between the number of isolated defects and the number of adjacent defects, or a value indicating the ratio, for example, a ratio between the number of isolated defects and the total number of defects. What is doing is preferable.
上述した本発明によれば、試料端面のカソードルミネッセンス画像における欠陥像の面積に対する欠陥像数の分布に基づいて、孤立欠陥による欠陥像と近接欠陥による欠陥像とを推定的に分離したうえで、まずは、孤立欠陥の数と孤立欠陥像の面積を算出しておき、その後、前記孤立欠陥数と孤立欠陥像面積を用いた補正演算によって近接欠陥数を算出するようにしているため、自動的でありながらより正確に欠陥数を計数することができる。 According to the present invention described above, based on the distribution of the number of defect images with respect to the area of the defect image in the cathode luminescence image of the sample end face, the defect image due to the isolated defect and the defect image due to the proximity defect are presumably separated, First, the number of isolated defects and the area of the isolated defect image are calculated, and then the number of adjacent defects is calculated by a correction operation using the number of isolated defects and the area of the isolated defect image. It is possible to count the number of defects more accurately.
次に、本発明の一実施形態を図面を参照して説明する。なお、本発明はこの実施形態のみに限定されるものではないのは言うまでもない。 Next, an embodiment of the present invention will be described with reference to the drawings. Needless to say, the present invention is not limited to this embodiment.
本実施形態に係る欠陥計数装置１００は、例えば半導体デバイス用の材料を結晶成長させる結晶成長装置に付帯して設けられるものであって、試料である前記結晶の成長端面に電子線を照射し、そのカソードルミネッセンス画像から、当該結晶に存在する欠陥（ここでは例えば貫通転位）の数を計数し、あるいは欠陥の密度を測定するものである。 The defect counting apparatus 100 according to the present embodiment is provided, for example, attached to a crystal growth apparatus for crystal growth of a material for a semiconductor device, and irradiates an electron beam onto a growth end face of the crystal as a sample, From the cathodoluminescence image, the number of defects (here, threading dislocations) present in the crystal is counted, or the density of the defects is measured.
図１は、このような欠陥計数装置１００の基本的な構成例を示している。この図１において、符号１は、結晶端面Ｓｃ上に電子線を走査しながら照射する電子線照射装置であり、符号２は、前記電子線の走査によって結晶端面Ｓｃで生じるカソードルミネッセンスを検出し、当該結晶端面Ｓｃのエリア画像（以下、カソードルミネッセンス画像と言う）を取得する撮像装置である。 FIG. 1 shows a basic configuration example of such a defect counting apparatus 100. In FIG. 1, reference numeral 1 denotes an electron beam irradiation apparatus that irradiates an electron beam while scanning the crystal end face Sc, and reference numeral 2 detects cathodoluminescence generated on the crystal end face Sc by scanning the electron beam. This is an imaging device that acquires an area image of the crystal end face Sc (hereinafter referred to as a cathodoluminescence image).
また、符号３は、前記カソードルミネッセンス画像を処理して結晶端面Ｓｃに存在する欠陥数を計数する機能を有した情報処理装置である。 Reference numeral 3 denotes an information processing apparatus having a function of processing the cathodoluminescence image and counting the number of defects existing on the crystal end face Sc.
しかして、この情報処理装置３は、ＣＰＵやメモリ、ＡＤコンバータ、バッファなどのデジタル乃至アナログ電子回路で構成されるものであり、メモリに記憶させた所定のプログラムにしたがってＣＰＵやその周辺機器が作動することにより、欠陥数を計数するための機能、すなわち、欠陥像分布算出部３１、孤立欠陥数算出部３２、孤立欠陥像面積算出部３３、近接欠陥数算出部３４、総欠陥数算出部３５、閾面積算出部３６、散らばり度算出部３７等としての機能を発揮する（図２参照）。 The information processing apparatus 3 is composed of digital or analog electronic circuits such as a CPU, memory, AD converter, and buffer. The CPU and its peripheral devices operate according to a predetermined program stored in the memory. Thus, the function for counting the number of defects, that is, the defect image distribution calculating unit 31, the isolated defect number calculating unit 32, the isolated defect image area calculating unit 33, the adjacent defect number calculating unit 34, and the total defect number calculating unit 35 are obtained. The threshold area calculation unit 36, the dispersion degree calculation unit 37, and the like are exhibited (see FIG. 2).
次に、これら各部の詳細説明を兼ねて、本欠陥計数装置１００の動作（欠陥計数方法）を説明する。 Next, the operation (defect counting method) of the defect counting apparatus 100 will be described together with a detailed description of these parts.
結晶端面Ｓｃの電子線走査領域におけるカソードルミネッセンス画像が、撮像装置２によって取得されると、その画像データは情報処理装置３に送信され、前記欠陥像分布算出部３１で処理される。 When a cathode luminescence image in the electron beam scanning region of the crystal end face Sc is acquired by the imaging device 2, the image data is transmitted to the information processing device 3 and processed by the defect image distribution calculation unit 31.
すなわち、欠陥像分布算出部３１は、前記画像データにノイズ処理を施す。このノイズ処理としては、例えば、画像における明るさ０のドット（暗点）を周囲から一定数減少させ、その後、残った明るさ０のドットを周囲に向かって前記一定数増加させるようにしている。このことによって、１ドットのみの暗点のようなノイズと思われる小さな暗点は、最初のドット減少動作によって消失し、次のドット増加動作によって復活することは無いから、ノイズを消去することができる。
次にこの欠陥像分布算出部３１は、ノイズ処理を施した前記画像データに基づいて、欠陥像数と、各欠陥像の画像上における面積とをそれぞれ計測するとともに、一定範囲で区成された面積範囲毎の欠陥像数（頻度）を算出し、欠陥像の面積に対する数の分布を算出する（欠陥像分布算出ステップ）。そして、その分布を示す分布データを、メモリの所定領域に設定した分布データ格納部Ｄ１に格納する。
That is, the defect image distribution calculation unit 31 performs noise processing on the image data. As this noise processing, for example, dots with 0 brightness (dark spots) in the image are decreased by a certain number from the surroundings, and then the remaining dots with brightness 0 are increased by a certain number toward the surroundings. . As a result, a small dark spot that seems to be noise, such as a dark spot of only one dot, disappears by the first dot reduction operation, and is not restored by the next dot increase operation. it can.
Next, the defect image distribution calculation unit 31 measures the number of defect images and the area of each defect image on the image based on the image data subjected to noise processing, and is defined within a certain range. The number of defect images (frequency) for each area range is calculated, and the number distribution with respect to the area of the defect image is calculated (defect image distribution calculating step). Then, the distribution data indicating the distribution is stored in the distribution data storage unit D1 set in a predetermined area of the memory.
さらにこの実施形態では、当該欠陥像分布算出部３１が、前記分布データの内容を、図３に示すように、横軸を面積（一定範囲で区成された面積範囲のうちの中心面積）、縦軸を欠陥像数（頻度）とした分布グラフにしてディスプレイに表示する。 Furthermore, in this embodiment, the defect image distribution calculation unit 31 shows the content of the distribution data, as shown in FIG. 3, the horizontal axis is the area (the central area of the area range defined by a certain range), The vertical axis is a distribution graph with the number of defect images (frequency) displayed on the display.
ここで、理解のためにこの分布グラフについての説明をしておく。 Here, this distribution graph will be described for the sake of understanding.
欠陥である貫通転位が生じている箇所ではカソードルミネッセンスが生じないため、画像上での欠陥像は、図４に示すように、ＤＳとして黒く現れる。そして本来は、１つの欠陥について１つの欠陥像が独立して現れるべきであるが、検出系の解像度や精度などの要因で、実際には、ある一定距離以上、欠陥同士が近接していると、画像上では欠陥像の一部同士が重なり合い、面積の大きな１つの欠陥像として認識される。そこで、以下、近傍の他の欠陥による欠陥像とは欠陥像同士が重合しない欠陥、つまり欠陥像同士が重合するような範囲には、他の欠陥が存在しない欠陥のことを孤立欠陥といい、近傍の他の欠陥による欠陥像と欠陥像同士が少なくとも一部重合する欠陥、つまり欠陥像同士が重合する範囲に１以上の他の欠陥が存在する欠陥のことを近接欠陥ということとすれば、この分布グラフは、図５に示すように、孤立欠陥による欠陥像の分布、２つの近接欠陥による欠陥像の分布、３つの近接欠陥による欠陥像の分布といったように、孤立欠陥と近接欠陥による分布が重なり合い、全体としてみれば、分布グラフは対称形にならず、ピークから右側の傾斜が左側の傾斜に比べてなだらかな非対称形状となると考えられる。 Since the cathodoluminescence does not occur at the position where the threading dislocation which is a defect occurs, the defect image on the image appears black as DS as shown in FIG. Originally, one defect image should appear independently for one defect, but due to factors such as the resolution and accuracy of the detection system, if the defects are actually close to each other over a certain distance. On the image, part of the defect images overlap each other and are recognized as one defect image having a large area. Therefore, hereinafter, the defect image due to other defects in the vicinity is a defect in which the defect images do not overlap each other, that is, in the range where the defect images overlap each other, a defect in which no other defect exists is called an isolated defect, If the defect image and the defect image due to other defects in the vicinity are at least partially polymerized, that is, a defect having one or more other defects in the range where the defect images are polymerized, is referred to as a proximity defect, As shown in FIG. 5, this distribution graph shows a distribution of defect images due to isolated defects and a distribution of defect images due to two adjacent defects. When viewed as a whole, the distribution graph does not have a symmetrical shape, and the slope on the right side from the peak is considered to be a gentle asymmetrical shape compared to the slope on the left side.
次に、閾面積算出部３６が、分布データ格納部Ｄ１から前記分布データを取得し、その分布データが示す分布結果に基づいて孤立欠陥の数を算出する。ここでは、まず、前記分布グラフにおけるピークでの欠陥像の面積よりも若干大きい面積を閾面積と推定する。より具体的には、図３に示すように、例えば分布グラフ上での最大ピーク点より右側であって、最大ピーク点での欠陥像数（頻度）よりもやや小さい（約６０％〜９５％の範囲内における予め定められた値）欠陥像数となるポイントでの欠陥像面積を、閾面積と推定算出する（閾面積推測ステップ）。 Next, the threshold area calculation unit 36 acquires the distribution data from the distribution data storage unit D1, and calculates the number of isolated defects based on the distribution result indicated by the distribution data. Here, first, an area slightly larger than the area of the defect image at the peak in the distribution graph is estimated as a threshold area. More specifically, as shown in FIG. 3, for example, it is on the right side of the maximum peak point on the distribution graph and is slightly smaller than the number of defects (frequency) at the maximum peak point (about 60% to 95%). The defect image area at a point that is the number of defect images) (predetermined value within the range) is estimated and calculated as a threshold area (threshold area estimation step).
そして、孤立欠陥数算出部３２が、その閾面積よりも小さな面積を有する欠陥像の総数を前記分布データから算出し、その総数をもって、孤立欠陥数とする（孤立欠陥数算出ステップ）。その理由は、前述した孤立欠陥の分布曲線は、図５に示すように分布グラフの最大ピークよりも左側の曲線にフィッティングさせたガウシアン曲線に近似すると考えられ、閾面積を前述のように設定すれば、その閾面積よりも小さな面積を有する欠陥像の総数は、ほぼ孤立欠陥数と推定できるからである。なお、この閾面積を、オペレータの入力より受け付けるようにしても構わない。分布グラフによる分布態様を見れば、オペレータが閾面積を推測できるからである。 Then, the isolated defect number calculation unit 32 calculates the total number of defect images having an area smaller than the threshold area from the distribution data, and sets the total number as the number of isolated defects (isolated defect number calculation step). The reason is that the above-mentioned isolated defect distribution curve approximates to a Gaussian curve fitted to the curve on the left side of the maximum peak of the distribution graph as shown in FIG. 5, and the threshold area is set as described above. For example, the total number of defect images having an area smaller than the threshold area can be estimated as the number of isolated defects. Note that this threshold area may be received from an operator input. This is because the operator can estimate the threshold area by looking at the distribution mode based on the distribution graph.
次に、前記孤立欠陥像面積算出部３３が、前記閾面積よりも小さな面積を有する欠陥像の総面積である閾下総面積を前記分布結果から算出し、その閾下総面積を前記孤立欠陥の数で除算して、単一の孤立欠陥による欠陥像の最も確からしい面積を算出する（孤立欠陥像面積算出ステップ）。この面積は、単一の孤立欠陥による欠陥像の代表面積又は平均面積と考えられ、以下、孤立欠陥像面積とも言う。これを式で表現すると以下のようになる。
次に、近接欠陥数算出部３４が、前記閾面積よりも大きな面積を有する欠陥像の総面積である閾上総面積を前記分布結果から算出し、当該閾上総面積を前記孤立欠陥像面積で除算して近接欠陥の数を算出する（近接欠陥数算出ステップ）。これを式で表現すると以下のようになる。
そして、総欠陥数算出部３５が、前記孤立欠陥の数と近接欠陥の数との和を算出し、その値をもって、画像に映し出された結晶端面Ｓｃに存在する総欠陥数とするとともに、その総欠陥数で結晶端面Ｓｃの走査面積を割ることにより、欠陥密度をも算出する。総欠陥数の算出式は以下のようである。
なお、この総欠陥数あるいは欠陥密度は、半導体デバイスとしてこの結晶材料を評価する場合、小さい方がよい。
Then, the total defect number calculation unit 35 calculates the sum of the number of isolated defects and the number of adjacent defects, and sets the value as the total number of defects existing on the crystal end face Sc displayed in the image, and The defect density is also calculated by dividing the scanning area of the crystal end face Sc by the total number of defects. The formula for calculating the total number of defects is as follows.
It should be noted that the total number of defects or the defect density is preferably small when this crystal material is evaluated as a semiconductor device.
また、この実施形態では、情報処理装置３に、結晶端面Ｓｃにおける欠陥の散らばり度を算出する散らばり度算出部３７をさらに設けている。この散らばり度算出部３７は、以下の式によって散らばり度を算出する（散らばり度算出ステップ）。
この散らばり度は、全体の欠陥総数に対する孤立欠陥数の比率を示している。孤立欠陥数の比率が大きいと、それだけ散らばって欠陥が点在していることとなるから、半導体デバイスとしてこの結晶材料を評価する場合は、この散らばり度は小さいほど良い。 The degree of dispersion indicates the ratio of the number of isolated defects to the total number of defects. If the ratio of the number of isolated defects is large, the number of the scattered defects is scattered and the defects are scattered. Therefore, when this crystal material is evaluated as a semiconductor device, the smaller the degree of scattering, the better.
しかして、このようにして算出された欠陥数（総欠陥数、近接欠陥数、孤立欠陥数）や欠陥密度、散らばり度などは、全部又はオペレータの選択等によりその一部がディスプレイに表示される。 Thus, the number of defects (total number of defects, the number of adjacent defects, the number of isolated defects), the defect density, the degree of dispersion, etc. calculated in this way are displayed on the display in whole or in part by the operator's selection. .
したがって、このような構成の欠陥計数装置１００又は欠陥計数方法であれば、結晶端面Ｓｃのカソードルミネッセンス画像から取得した欠陥像の面積−頻度分布に基づいて、孤立欠陥による欠陥像と近接欠陥による欠陥像とを推定的に分離したうえで、まずは、孤立欠陥の数と孤立欠陥像の面積を算出しておき、その後、前記孤立欠陥数と孤立欠陥像面積を用いた補正演算によって近接欠陥数を算出するようにしているため、自動的でありながらより正確に総欠陥数あるいは欠陥密度を計数することができる。 Therefore, with the defect counting apparatus 100 or the defect counting method having such a configuration, based on the area-frequency distribution of the defect image acquired from the cathode luminescence image of the crystal end face Sc, the defect image due to the isolated defect and the defect due to the proximity defect First, the number of isolated defects and the area of the isolated defect image are calculated, and then the number of adjacent defects is calculated by a correction operation using the number of isolated defects and the area of the isolated defect image. Since the calculation is performed, the total number of defects or the defect density can be counted more accurately while being automatic.
さらに、孤立欠陥数と近接欠陥数を別々に算出して、前記散らばり度をも算出し、表示できるようにしているため、結晶を、欠陥数だけでなく散らばり度からも評価できるようになる。 Furthermore, since the number of isolated defects and the number of adjacent defects are calculated separately so that the degree of scattering can be calculated and displayed, the crystal can be evaluated not only from the number of defects but also from the degree of scattering.
なお、本発明は前記実施形態に限られるものではない。
例えば、孤立欠陥数の算出方法として、図６に示すように、前記分布グラフにおける最大ピークから左側のグラフ線に、単一のガウシアン曲線の左側部分をフィッティングさせ、そのガウシアン曲線で囲まれる範囲内に存在する欠陥像の総数を前記分布から算出し、その総数をもって、孤立欠陥数としてもよい。このガウシアン曲線は、前記実施形態でも述べたように、孤立欠陥による欠陥像の分布を示していると考えられるからである。
The present invention is not limited to the above embodiment.
For example, as a method for calculating the number of isolated defects, as shown in FIG. 6, the left portion of a single Gaussian curve is fitted to the graph line on the left side from the maximum peak in the distribution graph, and within the range surrounded by the Gaussian curve. The total number of defect images existing in the image may be calculated from the distribution, and the total number may be used as the number of isolated defects. This is because the Gaussian curve is considered to indicate the distribution of defect images due to isolated defects as described in the above embodiment.
したがってこの場合、孤立欠陥像面積は、前記ガウシアン曲線のピーク座標における欠陥像の面積とすればよい。 Therefore, in this case, the area of the isolated defect image may be the area of the defect image at the peak coordinates of the Gaussian curve.
また、近接欠陥数は、欠陥像の総面積（すなわち分布グラフ全体で囲まれる面積）から孤立欠陥像の総面積（すなわち前記ガウシアン曲線で囲まれる面積）を減算し、その値を前記孤立欠陥像面積で除算すれば求められる。 Also, the number of adjacent defects is obtained by subtracting the total area of isolated defect images (that is, the area surrounded by the Gaussian curve) from the total area of defect images (that is, the area surrounded by the entire distribution graph), and obtaining the value as the isolated defect image. Calculated by dividing by area.
さらに、精度は落ちる可能性はあるが、場合によっては、前記分布グラフにおける最大ピークでの欠陥像面積を、孤立欠陥像面積ｓｐ１としてもよい。 Furthermore, although there is a possibility that the accuracy is lowered, in some cases, the defect image area at the maximum peak in the distribution graph may be the isolated defect image area sp1 .
また、閾面積の設定良否をオペレータが把握しやすくするために、図４に示すような画像上における欠陥像ＤＳを、設定された閾面積より大きいものとそれ以下のものとに、色分けする（例えば、大きいものを黒、それ以下のものを赤にする）などして、オペレータに視覚的に識別可能に表示するようにしても構わない。このことにより、直感的な把握を行いやすくなる。 In addition, in order to make it easy for the operator to grasp whether or not the threshold area is set, the defect image DS on the image as shown in FIG. 4 is color-coded into those larger than the set threshold area and those smaller than the threshold area ( For example, the larger one may be displayed in black and the lower one may be displayed in red. This facilitates intuitive grasping.
また、結晶のみならず、アモルファスなどの試料における欠陥数計数をしてもよいし、その他、本発明は前記実施形態に限られず、その趣旨を逸脱しない限りにおいて種々変更が可能である。 Further, the number of defects may be counted not only in crystals but also in samples such as amorphous. In addition, the present invention is not limited to the above embodiment, and various modifications can be made without departing from the spirit of the present invention.
１００・・・欠陥計数装置
Ｓｃ・・・結晶端面
３１・・・欠陥像分布算出部
３２・・・孤立欠陥数算出部
３３・・・孤立欠陥像面積算出部
３４・・・近接欠陥数算出部
３５・・・総欠陥数算出部
３７・・・比率算出部
DESCRIPTION OF SYMBOLS 100 ... Defect counter Sc ... Crystal end surface 31 ... Defect image distribution calculation part 32 ... Isolated defect number calculation part 33 ... Isolated defect image area calculation part 34 ... Proximity defect number calculation part 35 ... Total defect number calculation unit 37 ... Ratio calculation unit
Claims (5)
前記画像に現れる欠陥像の数と各欠陥像の面積とを計測して、欠陥像の面積に対する数の分布を算出する欠陥像分布算出部と、
前記分布において数が最大となる欠陥像の面積から推測される閾面積よりも小さな面積を有する欠陥像の総数を当該分布から計数することで、近傍の他の欠陥による欠陥像とは欠陥像同士が重合しない欠陥である孤立欠陥の数を算出する孤立欠陥数算出部と、
前記閾面積よりも小さな面積を有する欠陥像の総面積である閾下総面積を前記分布結果から算出し、その閾下総面積を前記孤立欠陥の数で除算することで、前記孤立欠陥による欠陥像の面積を算出する孤立欠陥像面積算出部と、
前記閾面積よりも大きな面積を有する欠陥像の総面積である閾上総面積を前記分布結果から算出し、前記閾上総面積を前記孤立欠陥像面積で除算することで、近傍の他の欠陥による欠陥像と欠陥像同士が少なくとも一部重合する欠陥である近接欠陥の数を算出する近接欠陥数算出部と、
前記孤立欠陥の数と近接欠陥の数とを足し合わせることで、画像に映し出された試料端面に存在する総欠陥数を算出する総欠陥数算出部と、を具備していることを特徴とする欠陥計数装置。 A device for counting the number of defects appearing on the sample end face from the cathodoluminescence image of the sample end face,
A defect image distribution calculating unit that measures the number of defect images appearing in the image and the area of each defect image, and calculates the distribution of the number with respect to the area of the defect image;
By counting the total number of defect images having an area smaller than the threshold area estimated from the area of the defect image having the largest number in the distribution from the distribution, the defect images due to other defects in the vicinity are defect images. Isolated defect number calculation unit for calculating the number of isolated defects that are defects that do not overlap,
By calculating the total sub-threshold area, which is the total area of defect images having an area smaller than the threshold area, from the distribution result, and dividing the total sub-threshold area by the number of isolated defects, the defect image of the isolated defect An isolated defect image area calculation unit for calculating an area;
By calculating the total area above the threshold, which is the total area of the defect image having an area larger than the threshold area, from the distribution result, and dividing the total area above the threshold by the area of the isolated defect image, defects due to other defects in the vicinity Proximity defect number calculation unit for calculating the number of adjacent defects that are defects in which the image and the defect image are at least partially overlapped,
A total defect number calculating unit that calculates the total number of defects present on the sample end face projected on the image by adding the number of isolated defects and the number of adjacent defects. Defect counting device.
前記画像に現れる欠陥像の数と各欠陥像の面積とを計測して、欠陥像の面積に対する数の分布を算出する欠陥像分布算出部と、
横軸を欠陥像の面積、縦軸を欠陥像の数とした分布グラフにおける最大ピークから左側のグラフ線に、ガウシアン曲線の左側部分をフィッティングさせ、そのガウシアン曲線で囲まれる範囲内に存在する欠陥像の総数を前記分布から計数することで、近傍の他の欠陥による欠陥像とは欠陥像同士が重合しない欠陥である孤立欠陥の数を算出する孤立欠陥数算出部と、
前記ガウシアン曲線のピーク座標における欠陥像の面積を、孤立欠陥による孤立欠陥像の面積として算出する孤立欠陥像面積算出部と、
欠陥像の総面積から孤立欠陥像の総面積を減算し、その値を前記孤立欠陥像面積で除算することで、近傍の他の欠陥による欠陥像と欠陥像同士が少なくとも一部重合する欠陥である近接欠陥の数を算出する近接欠陥数算出部と、
前記孤立欠陥の数と近接欠陥の数とを足し合わせることで、画像に映し出された試料端面に存在する総欠陥数を算出する総欠陥数算出部と、を具備していることを特徴とする欠陥計数装置。 A device for counting the number of defects appearing on the sample end face from the cathodoluminescence image of the sample end face,
A defect image distribution calculating unit that measures the number of defect images appearing in the image and the area of each defect image, and calculates the distribution of the number with respect to the area of the defect image;
Fitting the left part of the Gaussian curve from the maximum peak in the distribution graph with the horizontal axis representing the area of the defect image and the vertical axis representing the number of defect images to the left graph line, and the defects existing within the range surrounded by the Gaussian curve By counting the total number of images from the distribution, the defect image due to other defects in the vicinity and the number of isolated defects that calculate the number of isolated defects that are defects that do not overlap the defect images,
An isolated defect image area calculating unit that calculates the area of the defect image at the peak coordinates of the Gaussian curve as the area of the isolated defect image due to the isolated defect;
By subtracting the total area of the isolated defect image from the total area of the defect image and dividing the value by the area of the isolated defect image, the defect image due to other defects in the vicinity and the defect image at least partially overlap each other. A proximity defect number calculating unit for calculating the number of certain adjacent defects;
A total defect number calculating unit that calculates the total number of defects present on the sample end face projected on the image by adding the number of isolated defects and the number of adjacent defects. Defect counting device.
前記画像に現れる欠陥像の数と各欠陥像の面積とを計測して、欠陥像の面積に対する数の分布を算出する欠陥像分布算出ステップと、
数が最大となる欠陥像の面積よりも、分布態様から定まる量だけ大きな面積である閾面積を推測する閾面積推測ステップと、
前記閾面積よりも小さな面積を有する欠陥像の総数を前記分布結果から算出し、その総数をもって、近傍の他の欠陥による欠陥像とは欠陥像同士が重合しない欠陥である孤立欠陥の数とする孤立欠陥数算出ステップと、
前記閾面積よりも小さな面積を有する欠陥像の総面積である閾下総面積を前記分布結果から算出し、その閾下総面積を前記孤立欠陥の数で除算した値をもって、前記孤立欠陥による欠陥像の面積とする孤立欠陥像面積算出ステップと、
前記閾面積よりも大きな面積を有する欠陥像の総面積である閾上総面積を前記分布結果から算出し、前記閾上総面積を前記孤立欠陥像面積で除算した値をもって、近傍の他の欠陥による欠陥像と欠陥像同士が少なくとも一部重合する欠陥である近接欠陥の数とする近接欠陥数算出ステップと、
前記孤立欠陥の数と近接欠陥の数との和を算出し、その値をもって、画像に映し出された試料端面に存在する総欠陥数とする総欠陥数算出ステップと、を行うことを特徴とする欠陥計数方法。 A method for counting the number of defects appearing on the sample end face from the cathodoluminescence image of the sample end face,
A defect image distribution calculating step of measuring the number of defect images appearing in the image and the area of each defect image, and calculating a distribution of the number with respect to the area of the defect image;
A threshold area estimation step for estimating a threshold area which is an area larger than the area of the defect image having the maximum number by an amount determined from the distribution mode;
The total number of defect images having an area smaller than the threshold area is calculated from the distribution result, and the total number of defects is the number of isolated defects that are defects in which defect images do not overlap with each other. A step of calculating the number of isolated defects;
A total sub-threshold area, which is a total area of defect images having an area smaller than the threshold area, is calculated from the distribution result, and a value obtained by dividing the total sub-threshold area by the number of isolated defects is used to calculate the defect image of the isolated defect. An isolated defect image area calculating step as an area;
The total area above the threshold, which is the total area of the defect image having an area larger than the threshold area, is calculated from the distribution result, and a value obtained by dividing the total area above the threshold by the area of the isolated defect image has a defect due to other nearby defects. A proximity defect number calculating step that is the number of adjacent defects that are defects in which the image and the defect image are at least partially polymerized, and
Calculating the sum of the number of isolated defects and the number of adjacent defects, and performing the total defect number calculation step using the value as the total number of defects present on the sample end face projected on the image. Defect counting method.
前記画像に現れる欠陥像の数と各欠陥像の面積とを計測して、欠陥像の面積に対する数の分布を算出する欠陥像分布算出ステップと、
横軸を欠陥像の面積、縦軸を欠陥像の数とした分布グラフにおける最大ピークから左側のグラフ線に、ガウシアン曲線の左側部分をフィッティングさせ、そのガウシアン曲線で囲まれる範囲内に存在する欠陥像の総数を前記分布結果から算出し、その総数をもって、近傍の他の欠陥による欠陥像とは欠陥像同士が重合しない欠陥である孤立欠陥の数とする孤立欠陥数算出ステップと、
前記ガウシアン曲線のピーク座標における欠陥像の面積をもって、孤立欠陥による孤立欠陥像の面積とする孤立欠陥像面積算出ステップと、
欠陥像の総面積から孤立欠陥像の総面積を減算し、その値を前記孤立欠陥像面積で除算した値をもって、近傍の他の欠陥による欠陥像と欠陥像同士が少なくとも一部重合する欠陥である近接欠陥の数とする近接欠陥数算出ステップと、
前記孤立欠陥の数と近接欠陥の数との和を算出し、その値をもって、画像に映し出された試料端面に存在する総欠陥数とする総欠陥数算出ステップと、を行うことを特徴とする欠陥計数方法。 A method for counting the number of defects appearing on the sample end face from the cathodoluminescence image of the sample end face,
A defect image distribution calculating step of measuring the number of defect images appearing in the image and the area of each defect image, and calculating a distribution of the number with respect to the area of the defect image;
Fitting the left part of the Gaussian curve from the maximum peak in the distribution graph with the horizontal axis representing the area of the defect image and the vertical axis representing the number of defect images to the left graph line, and the defects existing within the range surrounded by the Gaussian curve Calculating the total number of images from the distribution result, and calculating the number of isolated defects as the number of isolated defects that are defects in which defect images do not overlap with the defect images due to other defects in the vicinity;
An isolated defect image area calculating step in which the area of the defect image at the peak coordinates of the Gaussian curve is the area of the isolated defect image due to the isolated defect;
Subtract the total area of the isolated defect image from the total area of the defect image and divide the value by the area of the isolated defect image to obtain a defect in which the defect image and the defect image due to other defects in the vicinity overlap at least partially. A proximity defect count calculating step for determining the number of proximity defects;
Calculating the sum of the number of isolated defects and the number of adjacent defects, and performing the total defect number calculation step using the value as the total number of defects present on the sample end face projected on the image. Defect counting method.
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| JPS63253242A (en) * | 1987-04-10 | 1988-10-20 | Daicel Chem Ind Ltd | Inspecting device for flaw |
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