JP3036981B2 - Method and apparatus for quantifying surface irregularities - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for evaluating a very fine uneven shape on the surface of an object to be evaluated, and more particularly, to a method and an apparatus for quantifying a three-dimensional shape of the surface unevenness. It is.

[0002]

2. Description of the Related Art Conventionally, as a means for measuring a state having irregularities in a surface shape, a stylus, a laser, an electron beam, or the like is scanned over the surface, and the state is measured according to a JIS standard (surface roughness standard). Evaluation is made using numerical values such as height (Rmax), ten-point average roughness (Rz), and center line average roughness (Ra).

[0003] Regarding the surface irregularities of a transparent material such as glass or a metal thin film, the ratio of the scattered transmitted light to the total transmitted light (scattered transmitted light + straight transmitted light) when light passes through the material, that is, the so-called haze ratio, is defined as the surface roughness. It has been used as a means of evaluating the condition.

[0004]

However, both of the conventional means are not means for quantitatively expressing the three-dimensional shape of the surface. For example, even when Ra, Rmax, and the like have the same value, three-dimensional surface irregularities may differ when observed with a scanning electron microscope (SEM). Further, even when the haze ratio is the same, the three-dimensional surface state may be different. The reason is that the three-dimensional surface shape, Ra, Rmax, etc., and the haze ratio are independent parameters.

More specifically, the inventors of the present application, when evaluating the surface irregularities of a transparent electrode of an amorphous Si solar cell, discriminate Ra, Rmax, etc., and haze ratio between pyramid type, dome type, etc. grain shapes. Was aware of the problem of not getting enough. Therefore, it is necessary to develop a method and an apparatus for quantifying the surface unevenness, which can distinguish three-dimensional surface unevenness such as a pyramid type and a dome type.

An object of the present invention is to provide a method and an apparatus for quantifying the surface unevenness which can satisfy the above-mentioned demands.

[0007]

According to the method for quantifying the surface irregularities of the present invention, the height of the irregularities on the surface of the object to be evaluated is measured at measurement points arranged in a matrix, and the height of the matrix is measured. Data for each measurement point, and for each measurement point, a first derivative representing the inclination of the concavo-convex shape in eight directions is calculated from each measurement point based on the height data, and the value of the first derivative in the eight directions is calculated. The direction having the maximum value is defined as the inclination direction, and first-order differential data in the form of a matrix based on the maximum value is generated. For each measurement point, the uneven shape in the inclination direction is determined based on the first-order differential data. The second derivative indicating the degree of R is calculated to generate second derivative data in the form of a matrix, and the height data, the first derivative data, and the second derivative data are respectively processed to obtain a third order of surface irregularities. And generating statistical data to quantify the shape.

The surface unevenness quantification apparatus of the present invention measures the height of the unevenness of the surface of the object to be evaluated at measurement points arranged in a matrix, and generates a matrix-like height data. And for each measurement point, for each measurement point, calculate the first derivative representing the inclination of the concavo-convex shape in eight directions from each measurement point based on the height data, and calculate the value of the first derivative in the eight directions. In the above, a direction having a maximum value is defined as a tilt direction, primary differential data generating means for generating a matrix-like primary differential data based on the maximum value, and for each measurement point, based on the primary differential data. A second derivative data generating means for calculating a second derivative representing the degree of R of the concavo-convex shape in the inclination direction to generate a second derivative data in a matrix, the height data and the first derivative And statistical data generating means for processing the second derivative data to generate statistical data for quantifying the three-dimensional shape of the surface irregularities, and means for displaying and outputting the statistical data. I do.

[0009]

According to the present invention, the shape of the unevenness on the surface of the evaluation object is expressed numerically by the inclination and the R degree at each point, and quantified using the average value, the maximum value, the minimum value, the standard deviation and the like. Plan.

For this purpose, first, the height information of the surface is digitized and the inclination direction at an arbitrary point is read. next,
First-order differentiation is performed at an arbitrary point, and the inclination at that point is calculated. Subsequently, the primary differentiation result is further secondary differentiated, and the R degree at that point is quantified. As a result, the shape of the surface irregularities can be quantified. That is, the shape can be quantified three-dimensionally.

To digitize surface height information, means for digitally digitizing two-dimensional surface height information, such as a scanning tunneling microscope (STM), an atomic force microscope (AFM), and a stylus The height at each point arranged in a matrix is measured by the equation surface roughness calculation. Thus, height information is obtained as surface information.

The inclination direction at each point is determined as follows. That is, the height data of each point is compared with the other points in the eight directions around, that is, the difference is obtained, and the direction in which the difference is the maximum value is defined as the inclination direction of the point. At this time, there is a possibility that an erroneous inclination value may be obtained in comparison with an adjacent point, so that the inclination direction is determined by comparing with a further point as necessary.

At each point, the differential (1
Take the second derivative) to calculate the slope. Further, the gradient is differentiated (second-order differentiation) to determine the R degree at each point. If the surface shows a linear shape, the result of the second derivative is “0”. It can be seen that the point is convex upward or downward depending on the difference between the + value and the − value of the secondary differentiation result. The magnitude of the R degree can be recognized based on the magnitude of the absolute value of the second derivative result.

Consider the results of the first and second derivatives of the pyramid and dome shapes. Under the assumption that the pyramid type has many straight slopes and the dome type has many convex slopes, the following equation is obtained. Pyramid type: Z = aS + b or Z = −aS + b (1) Dome type: Z = −aS ² + b (2) These equations are shown in FIGS. 1 (a) and 1 (b). Equation (1),
Differentiating (2), Z '= a or Z' =-a (3) Z '=-2aS (4) This indicates the slope, and equation (3) indicates that the pyramid type has high peaks of a and −a, and equation (4) indicates that the dome type does not generate high peaks. When the equations (3) and (4) are differentiated, Z ″ = 0 (5) Z ″ = − 2a (6) This represents the R degree, and equation (5) indicates that the R degree is 0 in the pyramid type, and equation (6)
Indicates that the dome shape is upwardly convex. In the dome type, the absolute value of the second differential result increases as the degree of R increases.

The above results are summarized in the following table.

[Table 1] First-order differential results for pyramid and dome shapes,
Since the second derivative has the above properties,
When the shape is quantified (quantified) by calculating the height information of the surface, the average value, the maximum value, the minimum value, and the standard deviation of the primary differentiation result and the secondary differentiation result, the surface fine irregularities Evaluation becomes possible.

[0016]

FIG. 2 is a basic flow chart for explaining a method for quantifying the surface unevenness according to the present invention. FIG. 3 is a basic functional block diagram of a quantification device that performs this method.

A basic example of the present invention is an amorphous Si
A case where the surface irregularities of the transparent electrode (SnO ₂ ) of the solar cell are quantified will be described.

First, the surface of the transparent electrode of the solar cell was STM1
The surface height information (hereinafter, referred to as STM data) measured and numerically converted to 0 is taken into the central processing unit 20 (step S1). STM data is, for example, 10 μm
Height data of points (measurement points) of a 256 × 256 matrix is included in an area of × 10μ. FIG. 4 (a)
Shows a part of the STM data in which height data corresponding to each point of the 256 × 256 matrix is entered and displayed. For convenience of explanation, the X direction and the Y direction are determined as shown in the figure.

Next, as shown in FIG. 4 (b), an eight-direction first derivative calculator 21 calculates a first derivative of each point with an adjacent point in eight directions by the following equation (step S1). S2).

F ′ (S) = {f (S + ΔS) −f (S)} / ΔS (7) where ΔS is a distance between adjacent points. ΔS between adjacent points in a direction forming an angle of 45 ° with respect to the X-axis or Y-axis direction (hereinafter, referred to as an oblique direction) is √2 times between adjacent points in the X-axis or Y-axis direction.

The primary differential data generation unit 22 determines the maximum value of the primary differential in eight directions at each point and obtains a maximum value of 256 ×
Generate the first derivative data of the 256 matrix. Note that, at each point, the direction in which the maximum value of the first derivative is obtained is defined as the inclination direction.

256 × 256 obtained in this way
From the primary differential data of the matrix, the secondary differential calculation unit 2
In step 3, the second derivative f ″ (S) in eight directions is calculated in the same manner as the first derivative is obtained (step S4).

Next, the secondary differential data generator selects the secondary differential in the inclination direction at which the maximum value of the primary differential is obtained from the secondary differentials in the eight directions, and selects the secondary differential of the 256 × 256 matrix. Differential data is generated (step S5).

In the description of the operation section, it has been described that, when generating the second derivative data, the derivative is performed only in the inclination direction determined by the calculation of the first derivative. However, in actuality, steps S4 and S5 are performed in preparing the program. In the second differentiation as in the above, the processing of differentiating in each of the eight directions and selecting a differential value in the tilt direction is performed.

The STM data fetched from the STM, the primary differential data obtained by calculation, and the secondary differential data obtained by calculation are statistically processed by the statistical processing section 25 (steps S6, S7, S8), and the height is calculated. The average value, the maximum value, the minimum value, the median value, the standard deviation, the degree of distortion, and the degree of sharpness of the data (STM data), primary differential data, and secondary differential data are obtained. For the second derivative data, a + part average value and a -part average value are further calculated.

The calculated statistical data is output and displayed on the printer or display 30 (step S9).

From the numerical values thus quantified, it becomes possible to evaluate the fine irregularities on the transparent electrode surface of the solar cell.

Although the basic example of the present invention has been described above,
Due to small changes in STM data or noise, ΔS
If is small, there is a possibility that only micro-change points may be measured, and such measurement may not obtain statistical data for proper evaluation. Therefore, the present invention uses the following processing method.

To remove noise from STM data, the STM data is smoothed using a spatial filter in computer image processing technology. The spatial filter processing will be described with reference to FIG. FIG. 5A shows STM data of a 256 × 256 matrix displaying height data. FIG. 5B shows a 3 × 3 spatial filter as an example. The coefficients of the spatial filter are all “1”.

The 3 × 3 measurement point area 40 shown in FIG. 5A is subjected to spatial filter processing to obtain (3 × 1 + 5 × 1 + 6 × 1).
+ 1 × 1 + 9 × 1 + 1 × 1 + 2 × 1 + 2 × 1 + 1 × 1)
The average value 3.3 of the height data is calculated according to / 9, and this average value is replaced with the height data of the measurement point at the center of the area 40 as shown in FIG. In this manner, noise can be removed by performing spatial filtering and smoothing the data at all measurement points. In this example, the spatial filter coefficients are all “1”, but it is also possible to weight the coefficients. Although the 3 × 3 spatial filter has been described above, a 5 × 5, 7 × 7 spatial filter can also be used.

The above spatial filter processing is a well-known technique in image processing, and will not be described further.

In the basic description of the present invention, 1
Both the second derivative and the second derivative are calculated based on the data between adjacent points. However, if ΔS is small as described above, there is a possibility that only a micro change point is measured. Therefore, it is sufficient to increase ΔS. However, if ΔS is increased, noise may be introduced. Therefore, in order to reduce the influence of noise, the concept of averaging and weighting in the spatial filter is adopted to eliminate the disadvantage caused by increasing ΔS.

FIG. 6A shows a 3 × 3 differential filter for weighted differentiation in the X direction, and FIG. 6B shows a 3 × 3 differential filter for weighted differentiation in the oblique direction. For example, the region 40 in FIG.
When the differential filter is applied, the following calculation is performed.

｛6 × (+1) + 1 × (+1) + 1 × (+1) + 3 ×
(−1) + 1 × (−1) +2 (−1)｝ / 3 × ΔS _{1 When} the differential filter of FIG. 6B is applied to the area 40 of FIG. Such calculations are performed.

｛1 × (+1) + 1 × (+1) + 2 × (+1) + 1 ×
(−1) + 3 × (−1) +5 (−1)｝ / 3 × ΔS ₂ ΔS ₁ and ΔS ₂ are distances between the centers of gravity. If the distance between adjacent points is “1”, ΔS ₁ = 2 ΔS ₂ = 1.88
It is.

In the differential filter as shown in FIGS. 6A and 6B, since XS ₁ and ΔS ₂ are different, X, Y
An error occurred between the differential value in the direction and the differential value in the oblique direction.

Therefore, 3 × so that ΔS ₁ = ΔS _2.
The weight coefficient of the weighted differential filter of No. 3 is selected as shown in FIG. FIG. 7A shows a 3 × 3 differential filter for weighted differentiation in the X direction, and FIG. 7B shows a 3 × 3 differential filter for weighted differentiation in the oblique direction.

The distance ΔS ₁ between the centers of gravity in the case of FIG.
It is calculated as follows:

ΔS ₁ = {(− 2 + 2) ² + (− 2−3−2) ² } ^1/2
× 2 / (2 + 3 + 2) = 2 Further, the distance ΔS ₂ between the centers of gravity in the case of FIG. 7B is calculated as follows.

ΔS ₂ = {(2 + 3) ² + (3 + 2) ² } ^1/2 × 2 /
(2 + 3 + 2) ≒ 2.02 By calculating the differentiation using the weighted differential filters of FIGS. 7A and 7B, a differential value having a small error between the X direction, the Y direction and the oblique direction can be obtained. You can ask.

FIGS. 7 (a) and 7 (b) show the differential filters for calculating the differential in the direction indicated by the dotted arrow. It will be readily apparent that a derivative filter is obtained.

It is assumed that such a weighted differential filter is used for both the first derivative and the second derivative.

The first and second differential data are obtained from the STM data, which is the height information of the transparent electrode (SnO ₂ ) of the amorphous Si solar cell, using the differential filter shown in FIG. A specific example of statistical data obtained by statistically processing the first, second and third derivative data will be described.

When obtaining the height data by measuring the transparent electrode (SnO ₂ ) used in such a solar cell by STM, about 25 to 40 electrodes per grain (0.1 to 1 micron in size) Measurement points were taken.

FIG. 8 shows a cross-sectional view of an amorphous Si solar cell to facilitate understanding. The light enters from the glass plate, is scattered by the display fine irregularities (texture structure) of the transparent electrode, and enters the amorphous Si. The light is scattered and enters the amorphous Si, so that the conversion efficiency is improved.

Example 1 Transparent electrode (SnO ₂ film) Film thickness: 6150 angstroms Grain shape: pyramid type Haze ratio: 5.0% SEM photograph: FIG. 9 Statistical data STM data Primary differential data Secondary differential data Average value 80. 7589 (nm) 26.6484 0.001576 Maximum value 174.532 (nm) 72.9935 0.932572 Minimum value 0 0 -0.92528 Median value 78.6428 (nm) 25.2556 -0.00728 Standard deviation 29 0.0841 (nm) 13.923 0.215649 Distortion -0.30279 -0.55730 -0.27607 Sharpness 2.83009 2.98879 7.83088 + Partial average 0.174389 -Partial average -0. 12828 example 2 transparent electrode (SnO ₂ film) film thickness: 6150 Ningstrom Grain shape: Pyramid haze ratio: 7.0% SEM photograph: Fig. 10 Statistical data STM data Primary differential data Secondary differential data Average value 85.8242 (nm) 28.2704 0.001880 Maximum value 187.792 (Nm) 74.527 1.03619 Minimum value 00 -1.0281 Median value 84.3149 (nm) 27.6621 -0.00809 Standard deviation 30.2138 (nm) 13.8612 0.220702 Strain degree -0 .25499 -0.38947 -0.14049 Sharpness 2.77171 2.86697 9.0705 + average value of 0.177596-average value of -0.12855 Example 3 Transparent electrode (SnO ₂ film) Film thickness: 5700 angstroms Grain shape: Dome shape Haze rate: 7.2% SEM photograph: Fig. 11 Statistical data STM data Primary differential data Secondary differential data Average value 105.247 (nm) 26.8368 -0.00085 Maximum value 203.621 (nm) 75.2309 1.088 Minimum value 0 0 −1.0795 Median value 104.627 (nm) 25.4545 −0.017 Standard deviation 33.0929 (nm) 13.978 0.210183 Strain degree −0.19893 −0.44292 −0.09932 Sharpness 2 0.98318 2.84706 10.3231 + average value of part 0.166137-average value of part -0.12122 Example 4 Transparent electrode (SnO ₂ film) Film thickness: 5450 Å Grain shape: Dome type Photo: Fig. 12 Statistical data STM data First derivative data Second derivative data Data Average 100.709 (nm) 26.4187 -0.00053 Maximum 207.415 (nm) 75.8747 1.13981 Minimum 00 -1.13091 Median 99.4916 (nm) 24.619- 0.00890 standard deviation 31.1651 (nm) 14.3043 0.225364 distortion degree -0.14591 -0.54721 0.25075 sharpness 2.64208 2.944404 9.90896 + part average value 0.167901-part Average value -0.13692 It is possible to evaluate the uneven shape of the transparent electrode surface from the statistical data.

FIG. 13 is a graph plotting the change in the short-circuit current of the solar cell with respect to the haze ratio of the transparent electrode for an amorphous Si solar cell using a transparent electrode having a pyramid-shaped or dome-shaped fine irregular surface.
However, the short-circuit current is represented by a ratio to a standard transparent electrode having a small surface unevenness (closer to flatness) and a haze ratio of 2 to 3%. According to FIG. 13, there is a difference in short-circuit current between the pyramid type and the dome type, and a larger short-circuit current can be obtained with the pyramid type. As described above, it is understood that the short-circuit current depends not only on the haze ratio but also on the uneven shape of the surface of the transparent electrode.

In the above embodiments, particularly, the quantification of the surface irregularities of the transparent electrode of the solar cell has been described. However, it is clear that the present invention can be widely applied to the quantification of the surface irregularities.

[0049]

According to the present invention, the surface irregularities (height,
(Degree of inclination, R degree) can be quantified. Therefore,
Conventionally, it was not possible to evaluate the three-dimensional surface unevenness state by the surface roughness and the haze ratio, but the present invention has made it possible.

The method and apparatus for quantifying the surface unevenness of the present invention can be used in various fields and are extremely useful.

[Brief description of the drawings]

FIG. 1 is a diagram showing equations representing pyramid and dome shapes.

FIG. 2 is a basic flowchart for explaining the method for quantifying the surface unevenness of the present invention.

FIG. 3 is a basic functional block diagram of a quantification device for implementing the method of the present invention.

FIG. 4 is a diagram showing a part of STM data and eight directions at the time of first-order differentiation.

FIG. 5 is a diagram for explaining spatial filter processing.

FIG. 6 is a diagram for explaining differential filter processing.

FIG. 7 is a diagram for explaining weighted differential filter processing.

FIG. 8 is a sectional view of an amorphous Si solar cell.

FIG. 9 is an SEM photograph of the surface of a transparent electrode (SnO ₂ ).

FIG. 10 is an SEM photograph of a surface of a transparent electrode (SnO ₂ ).

FIG. 11 is an SEM photograph of a surface of a transparent electrode (SnO ₂ ).

FIG. 12 is an SEM photograph of a surface of a transparent electrode (SnO ₂ ).

FIG. 13 is a graph plotting a change in short-circuit current with respect to a haze ratio.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 10 STM 20 Central processing unit 21 8-direction primary differential calculation part 22 Primary differential data generation part 23 8-direction secondary differential calculation part 24 Secondary differential data generation part 25 Statistical processing part 30 Printer or display

────────────────────────────────────────────────── ─── Continuing on the front page (72) Inventor Goichi Ishihara 3-11 Kandanishikicho, Chiyoda-ku, Tokyo Bond Building 4F Inside Nexus Co., Ltd. (56) References JP-A-57-120193 (JP, A) (58) Field surveyed (Int.Cl. ⁷ , DB name) G01B 21/00-21/32

Claims (10)

(57) [Claims] 1. A method for measuring the height of unevenness on the surface of an object to be evaluated at measurement points arranged in a matrix to generate matrix-like height data. Based on each of the measurement points, a first derivative representing the inclination of the concavo-convex shape in eight directions is calculated, and the direction having the largest value among the values of the first derivative in the eight directions is determined as the inclination direction. First derivative data in the form of a matrix based on the values is generated. For each measurement point, the second derivative indicating the degree of R of the concavo-convex shape in the inclination direction is calculated based on the first derivative data, and the second derivative of the matrix is calculated. Generating secondary differential data, processing the height data, the primary differential data, and the secondary differential data to generate statistical data for quantifying a three-dimensional shape of surface irregularities. Method for quantifying the surface irregularities that occur. 2. The surface unevenness according to claim 1, wherein said statistical data is at least one of an average value, a maximum value, a minimum value, a median value, a standard deviation, a degree of distortion, and a degree of sharpness. Shape quantification method. 3. The calculation of the first derivative and the second derivative is performed by
2. The method according to claim 1, wherein the difference between the values of the two measurement points is divided by the distance between the two measurement points. 4. The quantification of surface irregularities according to claim 2, wherein in calculating said first and second derivatives, a value of the first and second derivatives is obtained by a weighting filter process. Method. 5. The method according to claim 4, wherein the weighting coefficients in said weighting filter processing are selected such that the distance between the centers of gravity in eight directions is substantially equal. 6. A height data generating means for measuring heights of irregularities on the surface of an evaluation object at measurement points arranged in a matrix and generating matrix-like height data; , Based on the height data, calculate the first derivative representing the inclination of the concavo-convex shape in eight directions from each measurement point, and among the values of the first derivative in the eight directions,
Primary differential data generating means for defining a direction having a maximum value as a tilt direction and generating a matrix of primary differential data based on the maximum value; and for each measurement point, the tilt based on the primary differential data. Secondary differential data generating means for calculating a secondary differential representing the degree of R of the concavo-convex shape in the direction to generate a secondary differential data in a matrix, the height data, the primary differential data, and the secondary differential data Statistical data generating means for processing data and generating statistical data for quantifying the three-dimensional shape of the surface unevenness, and means for displaying and outputting the statistical data, quantification of the surface unevenness shape apparatus. 7. The surface unevenness according to claim 6, wherein the statistical data is one or more of an average value, a maximum value, a minimum value, a median value, a standard deviation, a degree of distortion, and a degree of sharpness. Shape quantification device. 8. The calculation of the first derivative and the second derivative is performed by
The apparatus according to claim 6, wherein the difference between the values of the two measurement points is divided by the distance between the two measurement points. 9. The quantitative determination of surface irregularities according to claim 6, wherein in calculating the first and second derivatives, a value of the first derivative and a value of the second derivative are obtained by weighting filter processing. Device. 10. The apparatus according to claim 9, wherein the weighting coefficients in the weighting filter processing are selected such that the distance between the centers of gravity in eight directions is substantially equal.