JPH01143127A - Surface shape measuring method by scanning electron microscope - Google Patents

Abstract

PURPOSE:To shorten the process time and correctly calculate the normal line direction or inclination by using the relationship between the signals obtained from four detectors or their integral times detectors and differential coefficients of two directions crossing at right angles. CONSTITUTION:A sample is scanned by a focused electron beam, and secondary electrons emitted from the surface of the sample are detected by four detectors 401-404. The secondary electrons emitted from the secondary electron emission point 302 on the sample 301 are emitted in four directions according to the cosine rule. Since the four detectors are applied with the electric field between them and the sample to collect secondary electrons respectively, the secondary electrons emitted toward the first - fourth quadrants are gradually bent by the electric field on their orbits and detected when they reach the first-fourth detectors 401-404. In this case, the relational expression between the signals obtained by the detectors and the differential coefficients of two directions crossing at right angles in the normal line direction of the surface or on the horizontal plane is used to determine the differential coefficients of positions on the sample, the differential coefficients are added or integrated in sequence, and the surface shape of the sample is measured. The process time is thereby shortened, and the normal line direction or inclination can be correctly calculated.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a method for measuring the surface shape of a microfabricated object using a scanning electron microscope (hereinafter referred to as SEM), and particularly relates to a method for measuring the surface shape of a microfabricated object, etc. using a scanning electron microscope (hereinafter referred to as SEM). Concerning a shape measurement method.

[Conventional technology]

Recently, there have been many attempts to reconstruct the surface shape based on image shading information. Collect the relationship between the backscattered electron detection output and the normal line obtained using A method is disclosed. Also, JP-A-56-150
Publication No. 303.

Patent Registration No. 462147 (Application published in 1979-1799)
9), Journal of Electron Microscopy Vol. 34, No. 4, pp. 328-337 (1985
(2013)
croscopy vol, 34. &4pp, 32g
-337 (1985)), two backscattered electron or secondary electron detectors facing each other are attached to the SEM, and the difference in their detection outputs or the square difference is approximately proportional to the slope in the direction connecting the two detectors. Using the empirical fact that
Find the slope of each point on the cross section in the direction connecting the two detectors,
The cross-sectional shape was determined based on this information.

[Problem that the invention seeks to solve]

However, in the above-mentioned Japanese Patent Application Laid-open No. 62-6112, it takes time to determine the normal direction by comparing it with the value of the standard sample, and local scratches on the reference sample directly affect the results. There were some inconveniences, such as:

In addition, in the method using the other two detectors, the formula for calculating the slope is empirical and is not necessarily accurate.
If there is a tilt component in a direction perpendicular to the direction in which the detectors are connected, there is a problem that the tilt becomes inaccurate.

The present invention has been made in view of the above circumstances, and its purpose is to solve the above-mentioned problems in the conventional SEM surface shape measurement method, shorten the processing time, and accurately measure the normal direction or inclination. An object of the present invention is to provide a method for measuring surface shape using SEM that allows calculation.

[Means for solving problems]

The above-mentioned object of the present invention is an SEM that scans a sample with a focused electron beam, detects secondary electrons emitted according to the surface shape of the sample, and creates an image by correlating the detected signal amount with the image density. , four detectors or an integer multiple thereof are installed surrounding the sample, and the relational expression between the signal obtained from the detectors and the differential coefficient in the normal direction of the surface or in two orthogonal directions in the horizontal plane is calculated. The method is characterized in that the surface shape of the sample is measured by determining the differential coefficients of each point on the sample using , and sequentially adding or integrating the differential coefficients. This is accomplished by a surface profile measurement method using SEM.

[Effect]

In SEM, a focused electron beam scans the sample, and secondary electrons are emitted from the sample surface in response.

Reflected electrons and the like are detected and their intensity is displayed as image density on a synchronously scanning CRT.

As with conventional methods, it is not sufficient to empirically determine the image density and the normal direction or the inclination of the surface, but an accurate normal or inclination can be obtained by adding theoretical analysis.

For example, in FIG. 3, the secondary electrons are
From the secondary electron emission point 302 above, the normal line 30 indicated by
It is emitted with an intensity according to the "cosine law" centered on 3.

Regarding this, see 1. For example, C. W. Oatley, translated by Shizuo Kimoto, "Scanning Electron Microscope Equipment Edition" (published by Corona Publishing), Volume 4.
You can refer to the chapter.

Specifically, the number of secondary electrons emitted from the normal to a solid angle dΩ in the direction α is given by the following equation, where N is the total number of secondary electrons.

−cos a dΩ −−−−(1
)π These secondary electrons are detected by four first to fourth detectors 401 to 404, as shown in FIG. The secondary electrons emitted from the secondary electron emission point 302 on the sample 301 are
It is emitted most in the direction 03, but it is emitted in all directions according to the above-mentioned cosine law. For each of the four detectors,
An electric field is applied between the sample and the sample to collect secondary electrons. Therefore, the secondary electrons emitted in the direction of the first quadrant in FIG.
1 and is detected. Similarly, secondary electrons emitted in the direction of the second quadrant are sent to the second detector 402, secondary electrons emitted in the direction of the third quadrant are sent to the third detector 403, and secondary electrons emitted in the direction of the fourth quadrant are sent to the second detector 402. The emitted secondary electrons are detected by the fourth detector 404.

Regarding the above-mentioned physical model, please refer to the 33rd Applied Physics Association Lecture Materials, pp. 356 (2a-ZA-
7) “Theoretical analysis of secondary electron contrast of minute shapes” (
1986) is helpful.

Also, from the above physical model, i = 1.2, 3.4, and the signal strength of the i-th detector is 1. Then, ■, can be obtained by the following solid angle integral in each quadrant regarding the solid angle area on the tangential plane 304 shown in FIG.

I 4 nee f cosad Ω, i = 1.2, 3.4 ■ This equation includes the total amount of secondary electron emission N, but in the end it is summarized into an equation that is unrelated to N, so the inclination angle of the surface Knowledge regarding N, which changes due to etc., is not required.

Here, we will prove the following three lemmas on the hemisphere. Since all normal directions are aligned on a hemispherical surface, the relationship between the surface normal and image density on a hemispherical surface can be used as is to determine the normal to the surface of a general sample.

[Lemma 1] When IR=I4+I, tIt, = L+ L, I
R/N and IL/N are X on the hemisphere 501 in FIG. 5(a).
It takes a constant value on a constant cross section 502.

(Proof of Lemma 1) 8 is the total sum of secondary electrons emitted in the X positive direction.

■ is the total sum of secondary electrons emitted in the negative direction of X (
N=IR+IL), on the cross section 502, the positional relationship between the normal line, the tangent plane, and the yz plane (or the cross section 502) is
It remains unchanged simply by rotating around the axis. From now on, I
The solid angle region of the integral of equation (2) above for Ry I L remains unchanged simply by rotating around the X axis, and I R/
N, IL/N remains unchanged.

[Lemma 2] On the cross section of y=Q on the hemisphere, the following equation f corresponds to the X differential of the surface.

(Proof of Lemma 2) A normal polar coordinate display as shown in FIG. 6 is taken.

■. The integral of the above equation (2) for
nθ. , O, cos θo), then it becomes as follows.

However, the direction vector of (θ, φ) is expressed as e = (sinθcosψ, sinθsinψ, c
os O), π・za=sinθ, sinθcosψ+cosθ, co
sθ Also, O□8 is the upper limit of the integral range of θ and is determined by the tangent plane. Specifically, it is sufficient to find θ of the intersection line between the plane f''1J=o and the plane y=tanψ·X.

0≦θ. Considering π/2, it is given by the following formula.

This integral can be evaluated analytically and is given by the following equation.

■□=-(1+sinθ.) Similarly, IL: -(1-sinθ,) From this, the X differential, that is, -tanθ. [Lemma 3] In Figure 5(b), the X differential P at point A on the hemisphere
Given a and the y differential q0 at point B, the normal at point C is determined as follows.

As T=(-pl-q+1), (Proof of Lemma 3) The equation of the sphere is x 2+ y ” + z ” = R”
Then, the X differential of point A and the X differential of point B are given by the following equations.

aZ Therefore, it is expressed using pl, , qo, and the equation for the hood is obtained.

Using the above three lemmas, the normal at point C in FIG. 5(b) can be calculated as follows: 11. I2. It can be determined from the values of I, , I4.

First, from Lemma 1, we can find the values of IR/N and IL/N at point A. Since Equation (3) of Lemma 2 is homogeneous in the denominator and numerator with respect to , I, we can find the X differential of point A from this. Similarly, I1 and I2. By combining I and I4 (considered as I, , I) and repeating the same operation, the X differential of point B can be found.

If Lemma 3 is used here, the purpose can be achieved.

As a result, the X differential p and y differential q of point C are given as follows.

...(6) 73(I□+L"Ia"L)-2((Iz"IJ"(I
z''I□)2+(I□+L)2+(1,+I□)2) This relational expression is an accurate theoretical expression, unlike the conventional method that uses an empirical expression.

Once the normal line is obtained, the surface shape can be obtained by sequentially adding and integrating this information.

X ” 1 r '/ = altitude of point J, X differential, X
Letting the differentials be Z iJy piJ+ qiJ, respectively, 2. . With Z as a reference value, ZiJ is obtained, for example, as follows.

〔Example〕

Embodiments of the present invention will be described in detail below with reference to the drawings.

FIG. 2 is a hardware configuration diagram of a surface profile measuring apparatus in which four secondary electron detectors are attached to a SEM, which is an embodiment of the present invention. In FIG. 2, the electron gun 1 of the mirror body 101
The electron beam 103 emitted from the electron lens system 10
4, the sample 10 on the sample stage 105
6. Correspondingly, secondary electrons 107 are emitted from the sample 106, and the first detector 108. Second detector 109. Third detector 110. It is detected by the fourth detector 111.

The signal is processed by a computer 113 that operates based on instructions from the keyboard 112, and the detector signal itself or the processed result is displayed on a display 114.

FIG. 1 is a flowchart of processing in an embodiment of the present invention. In step 201, the scanning signals of each detector are input. In step 202, the slope component of the surface element in the X-axis direction and the slope component of the surface element in the X-axis direction are determined from the signals of the four detectors as described in the section of the function. In this embodiment, the following equation is used.

However, the signals of the detectors 108 to 111, respectively, are
I,,I,,I,,I4.

ν'3(■, +I, +I, +L)-2((I,"I2)
"÷L+L)"+(D+t)2+a,+rt)") Here, the constants 1 and 2 are determined in advance by calibration. In other words, when using a sample whose surface shape is known in advance, The above constants are set to values of 1 and 2 that most faithfully represent the shape.

In step 203, the slope components obtained in step 202 are one-dimensionally added and integrated from the reference point.

This addition and integration is performed, for example, according to equation (7) shown above.

In step 204, this result is displayed.

According to this embodiment, since a theoretical formula based on the SEM imaging principle is used, there is an effect that a surface shape with little distortion can be obtained at high speed.

The above-mentioned embodiment is shown as an example, and the present invention should not be limited thereto.

〔Effect of the invention〕

As described above, according to the present invention, a sample is scanned with a focused electron beam, secondary electrons emitted according to the surface shape of the sample are detected, and the detected signal amount and image density are made to correspond. In the SEM for imaging, four or an integral multiple of four detectors are installed to surround the sample, and the differential coefficients of the signal obtained from the detector and the normal direction of the surface or two orthogonal directions in the horizontal plane are The differential coefficient of each point on the sample is determined using the relational expression, and the surface shape of the sample is measured by sequentially adding or integrating the differential coefficients, so the processing time is short. This has the remarkable effect of realizing a surface profile measurement method using SEM that can accurately calculate the normal direction or inclination.

[Brief explanation of the drawing]

Fig. 1 is a flowchart of processing in an embodiment of the present invention, Fig. 2 is a hardware configuration diagram of a surface profile measuring device in which four secondary electron detectors are attached to an SEM, and Fig. 3 is a diagram of a SEM.
A diagram showing the formation process of M, Figure 4 is a plan view around the sample,
FIG. 5 and FIG. 6 are diagrams showing the coordinate system. 101: mirror body, 102: electron gun, 103: electron beam, 10
4: Electron lens system, 105: Sample stage, 106: Sample, 1
07: Secondary electron, 108: First detector, 109: Second
Detector, 110: Third detector, 111: Fourth detector, 1
12: Keyboard, 113: Computer, 114: Display. \I - Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 (a) (b) y

Claims (1)

[Claims] 1. Scan the sample with a focused electron beam, detect secondary electrons emitted according to the surface shape of the sample, and create an image by correlating the detected signal amount with the image density. In a scanning electron microscope, four detectors or an integral multiple of four detectors are installed to surround the sample, and the signals obtained from the detectors and the differential coefficients in the normal direction of the surface or in two orthogonal directions in the horizontal plane are A surface using a scanning electron microscope, characterized in that the surface shape of the sample is measured by determining the differential coefficient of each point on the sample using the relational expression, and sequentially adding or integrating the differential coefficients. Shape measurement method. 2. The above relational expression is the signal value of the four detectors surrounding the sample,
Alternatively, if the number of detectors is an integral multiple of 4 is divided into four groups each consisting of the same number of detectors, the sum of the signal values of each group is calculated as follows.
I_A, I_ every 90 degrees clockwise or counterclockwise
B, I_C, and I_D, the direction that bisects the direction of I_A and I_D is the x axis, the direction that bisects the direction of I_B and I_C is the y axis, the height direction is the z axis, and the surface equation is z= h(
The surface shape measuring method using a scanning electron microscope according to claim 1, characterized in that when x, y), the following equation is satisfied. ▲There are mathematical formulas, chemical formulas, tables, etc.▼ 3. The signal values I_A, I_B, I_C, I_d and ∂h/∂x, ∂h/∂y are constant additions and constants that take into account the characteristics of the scanning electron microscope. 3. The surface shape measuring method using a scanning electron microscope according to claim 2, wherein correction such as multiplication or a combination thereof is performed.