Evaluation methods for insulating films

Abstract

The evaluation method for the insulating film includes: binarizing m SEM images obtained using an insulating film containing multiple pores to generate m binarized images; using the m binarized images, extracting the largest pore from each of the multiple pores in the m binarized images to obtain m of the aforementioned largest pores; calculating the pore diameter for each of the m largest pores to obtain m pore diameters; calculating the double logarithm of the cumulative probability F(x) for the m pore diameters and plotting the double logarithm of the cumulative probability F(x) relative to the n pore diameters; defining the double logarithm of the cumulative probability F(x) as y, defining the pore diameter as x, and defining a mathematical formula; and calculating the predicted value of the largest pore diameter, which is the maximum value among the pore diameters of the multiple pores contained in the insulating film, based on the relationship between the volume ratio T of the volume Vs and the volume Va of the insulating film and y, wherein the volume Vs is the product of the sum of the areas of the m SEM images and the average value of the largest pore diameters extracted from the m SEM images.

Description

[Technical Field]

[0001] One embodiment of the present invention relates to a method for evaluating insulating films. [Previous Technology]

[0002] Semiconductor devices are devices that utilize the semiconductor properties of silicon and the like. In recent years, semiconductor devices have been incorporated into almost all electronic devices, making it possible to control the functions of various electronic devices. Semiconductor devices are constructed by stacking insulating and conductive films on a substrate such as a silicon wafer (Si-wafer) and patterning these films or substrates. For example, these films are stacked on the substrate using semiconductor manufacturing equipment capable of performing methods such as vapor deposition, sputtering, chemical vapor deposition (CVD), or chemical reactions of the substrate, and these films or substrates are patterned using semiconductor manufacturing equipment capable of performing photolithography processes.

[0003] A semiconductor manufacturing apparatus includes a stage (hereinafter referred to as a stage) for setting a substrate. For example, the components included in the stage include: a substrate, an insulating film formed on the substrate, a cooling plate, an electrostatic chuck, etc. Furthermore, methods such as sputtering and anodizing are known for forming an insulating film on the surface of the substrate included in the stage. Patent Documents 1 and 2 disclose a stage that, as one of the purposes of suppressing the decrease in the insulation of the stage, includes using ceramic sputtering to form an insulating film on the surface of a substrate.

[0004] 『Patent Documents』 《Patent Document 1》: Japanese Patent Publication No. 2014-013874 《Patent Document 2》: Japanese Registered Utility Model Patent No. 2600558 [Summary of the Invention]

[0005] [The problem that the invention is intended to solve]

[0006] The properties of the insulating and conductive films used in semiconductor devices, as described above, are significantly affected by the conditions under which these films are formed and etched. For example, these conditions include the gas (reactant gas) supplied to the semiconductor manufacturing apparatus and the voltage applied to the stage. Accordingly, for example, the insulating film formed on the surface of the substrate of the stage must be able to suppress degradation caused by the applied voltage, i.e., have high withstand voltage (high insulation characteristics). For example, in order to obtain an insulating film with high withstand voltage, it is known that the area ratio of the pores contained in the insulating film is defined as the porosity, and the withstand voltage (insulation characteristics) of the insulating film is evaluated through the porosity. Therefore, in order to obtain an insulating film with high withstand voltage, it is important to establish an evaluation method for evaluating the withstand voltage (insulation characteristics) of the insulating film.

[0007] One of the objectives of the embodiments of the present invention is to provide a novel evaluation method for insulating films.

[0008] 〔Technical means to solve the problem〕

[0009] An evaluation method for an insulating film according to one embodiment of the present invention includes: using an insulating film containing multiple pores to obtain m (m is a positive integer) SEM images for n (n is a positive integer) SEM samples; binarizing the aforementioned m SEM images to generate m binarized images; using the aforementioned m binarized images, extracting the largest pore from each of the aforementioned multiple pores to obtain m of the aforementioned largest pores; calculating the pore diameter for each of the aforementioned m of the aforementioned largest pores to obtain m of the aforementioned pore diameters; calculating the double logarithm of the cumulative probability F(x) for the aforementioned m of the aforementioned pore diameters, and plotting the double logarithm of the aforementioned cumulative probability F(x) relative to the aforementioned m of the aforementioned pore diameters. A diagram of pore size; define the double logarithm of the aforementioned cumulative probability F(x) as y, define the pore size as x, define mathematical formula (1), where the value α (value α is greater than 0) is the scale parameter, and the value λ (value λ is greater than 0) is the pore size when the double logarithm of the cumulative probability F(x) becomes 0; calculate the volume Vs of the sum of the areas of the aforementioned m SEM images and the average value of the aforementioned maximum pore size extracted from the aforementioned m SEM images, and the volume Va of the aforementioned insulating film, calculate the volume ratio T of volume Vs and volume Va; based on the relationship between the aforementioned volume ratio T and the aforementioned y shown by mathematical formula (5), calculate the predicted value of the maximum pore size, which is the maximum value among the aforementioned multiple pore sizes contained in the aforementioned insulating film.

[0010] [Effects of the Invention]

[0011] According to one embodiment of the present invention, a novel evaluation method for insulating films is provided.

Implementation Method

[0020] The following describes an evaluation method for an insulating film according to one embodiment of the present invention with reference to the drawings. However, the present invention can be implemented in various forms without departing from its spirit and is not limited to the description of the embodiments exemplified below.

[0021] The drawings are intended to make the explanation clearer, and show the width, thickness, shape, etc. of each part compared to the actual appearance. However, they are only examples and are not intended to limit the interpretation of the present invention. Furthermore, in this specification and the drawings, sometimes the same symbols are used to mark elements that have the same function as those already described in the existing drawings, and repeated descriptions are omitted.

[0022] In this specification and drawings, when multiple identical or similar structures are described in general, the same symbols are used, and when such structures are described individually, a hyphen and a number are added after the symbol.

[0023] In this specification, the words "first", "second" or "third" etc., used to indicate the advantages of each component are used to distinguish the advantages of each component and have no additional meaning unless otherwise specified.

[0024] In the following description, for ease of explanation, terms indicating directions such as "up" and "down" will sometimes be used. The direction of gravity relative to the platform is "down", and the opposite is "up".

[0025] [1. Background of the Invention]

[0026] For example, studies have been conducted on the withstand voltage (insulation performance) of the insulating film contained in the stage for mounting semiconductor devices.

[0027] Generally speaking, insulating films with high withstand voltage have low porosity. As described in "Problem to be Solved by the Invention," in order to find insulating films with high withstand voltage, it is known that the area ratio of the pores contained in the insulating film is defined as porosity, and the withstand voltage (insulation characteristic) of the insulating film is evaluated through porosity. However, when evaluating insulating films through porosity, there are cases where even a low porosity results in a low withstand voltage, and there are also cases where even a high porosity results in a high withstand voltage. That is, when evaluating insulating films, a low porosity does not necessarily guarantee a high withstand voltage (good insulation performance). Therefore, in order to improve the withstand voltage (insulation performance) of insulating films, it is important to find a new evaluation method for insulating films.

[0028] In one embodiment of the present invention, with the aim of improving the withstand voltage (insulation performance), an attempt was made to use extreme value statistics in the evaluation method of the insulating film. As a result, it was found that by using extreme value statistics in the evaluation method of the insulating film, the withstand voltage (insulation performance) of the insulating film can be represented by the maximum pore size predicted by extreme value statistics. In addition, the method of using extreme value statistics is generally a known method, and detailed description is omitted here. For example, the estimation method using extreme value statistics is disclosed in "Method for estimating the maximum local corrosion depth using extreme value statistics" (Boshoku Gijutsu 37, 768-773 (1988)) of the 60-1 Subcommittee of the Japan Corrosion Prevention Association.

[0029] Details are described with reference to Figures 1 to 8 in the various embodiments described below; one embodiment of the present invention is a method for evaluating insulating films.

[0030] For example, the evaluation method of the insulating film according to one embodiment of the present invention includes: obtaining m (m is a positive integer) SEM images for n (n is a positive integer) SEM samples obtained using an insulating film 120 containing a plurality of pores 126, 127; binarizing the aforementioned m SEM images to generate m binarized images; using the aforementioned m binarized images, extracting the largest pore 127 among the plurality of pores 126, 127 from each of the aforementioned m binarized images to obtain m of the aforementioned largest pores 127; calculating the pore diameter for each of the aforementioned n of the aforementioned largest pores 127 to obtain m of the aforementioned pore diameters; calculating the double logarithm of the cumulative probability F(x) for the aforementioned m of the aforementioned pore diameters, and plotting the double logarithm of the aforementioned cumulative probability F(x). Relative to the aforementioned m images of the aforementioned pore diameters, the double logarithm of the aforementioned cumulative probability F(x) is defined as y, and the pore diameter is defined as x, as defined in the mathematical formula (1) described below; at this time, the numerical value α is the same as the aforementioned scale parameter, and the numerical value λ is the pore diameter when the double logarithm of the cumulative probability F(x) becomes 0. The volume Vs is calculated as the product of the sum of the areas of the aforementioned m SEM images and the average of the maximum pore diameters extracted from the aforementioned m SEM images, and the volume Va of the aforementioned insulating film is calculated. The volume ratio T of the volume Vs and the volume Va is calculated. Based on the relationship between the aforementioned volume ratio T and the aforementioned y as shown in the mathematical formula (5) described below, the predicted value of the maximum pore diameter (predicted maximum pore diameter) is calculated as the maximum value among the pore diameters of the aforementioned multiple pores 126 and 127 contained in the aforementioned insulating film 120.

[0031] As a result, the evaluation method for insulating films according to one embodiment of the present invention can calculate the predicted maximum pore size. Furthermore, as shown in Figure 7, the predicted maximum pore size and the withstand voltage of the insulating film for which the predicted maximum pore size is used as the evaluation result have a good negative correlation. Therefore, by using the evaluation method for insulating films according to one embodiment of the present invention, the predicted maximum pore size of the insulating film relative to the required withstand voltage can be calculated, and the withstand voltage corresponding to the predicted maximum pore size of the insulating film can be calculated.

[0032] Furthermore, the stage for mounting a substrate, which includes an insulating film evaluated by the evaluation method of the insulating film according to one embodiment of the present invention, has good voltage withstand capability and insulation characteristics. Accordingly, the stage according to one embodiment of the present invention can suppress the decline in long-term reliability.

[0033] In the following embodiments, the evaluation method of the insulating film according to one embodiment of the present invention will be described in detail.

[0034] [2. First Embodiment]

[0035] The platform 100 related to the first embodiment of the present invention will now be described with reference to Figures 1 to 7.

[0036] [2-1. Overview of Platform 100]

[0037] The general outline of the platform 100 will now be described with reference to Figures 1 to 3. Figure 1 is a perspective view showing the structure of the platform 100. Figure 2 is a top view showing the structure of the platform 100. Figure 3 is a cross-sectional view showing the platform 100 along section A1-A2.

[0038] The stage 100 has a disk-shaped form. For example, the stage 100 has a diameter capable of holding a 12-inch silicon wafer. Furthermore, the stage 100 includes a substrate 110, an insulating film 120, an upper surface (first surface 122), a bottom surface (second surface 114), holes 102, and trenches 104 capable of holding a substrate (e.g., a silicon wafer). The arrangement, number, and shape of the holes 102 and trenches 104 can be appropriately varied according to the specifications and applications of the semiconductor manufacturing apparatus. Furthermore, the stage 100 may include a cooling plate, an electrostatic chuck, etc.

[0039] The substrate 110 includes a first surface 112 and a second surface 114 opposite to the first surface 112. In addition, the substrate 110 may also be bonded with multiple substrates.

[0040] The insulating film 120 includes a first surface 122 and a second surface 124 opposite to the first surface 122. The insulating film 120 is provided in such a way that it covers the substrate 110 and is in contact with the substrate 110. The second surface 124 of the insulating film 120 contacts the first surface 112 of the substrate 110. Furthermore, the insulating film 120 is provided in such a way that it covers the inner wall of the hole 102 and the inner wall of the groove 104 and is in contact with the inner wall of the hole 102 and the inner wall of the groove 104. Although not shown, the insulating film 120 is provided in such a way that it covers the side surface of the substrate 110 and is in contact with the side surface of the substrate 110. Furthermore, although the insulating film 120 in the stage 100 shown in FIG3 is provided on the first surface 112 of the substrate 110 as an example, the insulating film 120 may also be provided in such a way that it covers the second surface 114 and is in contact with the second surface 114.

[0041] The groove 104 can be a flow channel for the circulation of a medium, or it can be a groove equipped with a heat source. For example, the medium and the heat source can be used to control the temperature of a substrate placed on the stage 100. For example, the medium is a liquid such as water, isopropanol, ethylene glycol, or silicone oil. The medium can be used to cool the stage 100 or to heat the stage 100. For example, the heat source is a sheath heater. The sheath heater has the function of generating heat by energizing it.

[0042] For example, hole 102 is a hole for lifting pins used to lift a substrate placed on stage 100.

[0043] For example, the groove 104 and the hole 102 may be contained within the interior of a bonding substrate where multiple substrates are joined, and may be a space contained within the interior of a bonding substrate where multiple substrates are joined (not shown). Furthermore, the groove 104 and the hole 102 may be formed of a porous body. For example, by constructing the groove 104 and the hole 102 in a manner that includes a porous body, a medium such as gas can flow from one of the groove 104 and the hole 102 to the other (circulation). More specifically, a plurality of through holes are formed in the porous body, and the porous body allows one of the groove 104 and the hole 102 to communicate with the other, enabling the flow of a medium (circulation). For example, a porous ceramic system.

[0044] The material used in the substrate 110 is a metal, ceramic, etc. Furthermore, the material used in the substrate 110 can also be glass. For example, metals include alloys of aluminum (Al), titanium (Ti), and stainless steel. Aluminum is used as an example of the material used in the substrate 110.

[0045] The material used in the insulating film 120 may be a material that satisfies the desired insulation properties and the desired withstand voltage characteristics. For example, the material used in the insulating film 120 is an inorganic insulating material. For example, the inorganic insulating material is a metal oxide, specifically, an oxide or composite oxide of at least one element selected from alkaline earth metals, rare earth metals, aluminum, tantalum (Ta), titanium, chromium (Cr), zirconium (Zr), yttrium (Y), and silicon (Si). For example, the material used in the insulating film 120 is aluminum oxide (Al2O3).

[0046] [2-2. An example of a cross-section of stage 100]

[0047] The construction of the cross-section of the platform 100 will now be described with reference to Figure 3. The construction may be the same as or similar to that in Figures 1 and 2, depending on the requirements.

[0048] As explained in "2-1", the insulating film 120 contains aluminum oxide and is disposed in such a way that it covers the substrate 110 and contacts the substrate 110.

[0049] Furthermore, as shown in the enlarged view of region 125 in the upper part of FIG3, the insulating film 120 includes a plurality of pores 126. The pore diameter of the pore 126 is the pore diameter X. For example, among the plurality of pores 126, the pore diameter of the largest pore 127 is the largest pore diameter Xm. In addition, although the shape of the pores shown in FIG3 is circular, the actual shape of the pores can be various. For example, the pore 126 can be a tiny void contained in the insulating film 120, can be a bubble, can be a pore, can be an open pore connected to the outside air, or can be a closed pore inside the insulating film 120. The pore 126 can also be referred to as a pore, void, etc.

[0050] For example, the thickness H1 of the insulating film 120 is 150 μm or more and 600 μm or less.

[0051] [2-3. Construction of Platform 100]

[0052] The manufacturing method of the stage 100 will now be described with reference to Figure 3. The same or similar structure as that in Figures 1 and 2 may be described as needed.

[0053] When the fabrication of the stage 100 begins, an insulating film 120 is formed on the prepared substrate 110 using a laminator 180. At this time, the angle between the first surface 112 and the laminator 180 is set as the lamination angle θ, and the velocity (e.g., particle velocity) of the laminated material 182 ejected from the laminator 180 is set as the particle velocity Vx. Furthermore, the distance between the nozzle 181 and the first surface 112 is set as distance D, and the nozzle 181 of the laminator 180 can move on a semicircle or circle with distance D as its radius to adjust the lamination angle θ.

[0054] Various spraying methods can be used in the method of manufacturing the stage 100. For example, the spraying method used in the method of manufacturing the stage 100 is atmospheric (piezo) plasma spraying. By using atmospheric (piezo) plasma spraying as the method of manufacturing the stage 100, the adhesion between the insulating film 120 and the substrate 110 is improved.

[0055] For example, the laminator 180 moves along the first surface 112 from one end of the substrate 110 to the other end in the first direction D11, while spraying particulate laminate 182 onto the first surface 112 (first lamination). Furthermore, the laminator 180 can move along the first surface 112 from the other end of the substrate 110 to one end in the second direction D12, while spraying particulate laminate 182 onto the first surface 112 (second lamination), and the laminator 180 can also repeat the first lamination and the second lamination. Next, the laminator 180 moves along the first surface 112 from one end of the substrate 110 to one end along the first direction D11, simultaneously spraying granular laminar material 182 onto the first surface 112. The laminator 180 can also move a specified distance along the first surface 112 in a direction intersecting the first direction D11, moving from the other end of the substrate 110 to one end along the second direction D12, simultaneously spraying granular laminar material 182 onto the first surface 112. Furthermore, the laminator 180 can also spray granular laminar material 182 onto the first surface 112 of the rotating substrate 110.

[0056] Furthermore, although not shown in the illustration, the molten material 182 formed on the substrate 110 is flat, and the insulating film 120 includes a plurality of flat molten materials 182. The molten material 182 contains aluminum oxide, and the insulating film 120 contains aluminum oxide. For example, the insulating film 120 containing the flat molten material 182 is formed by overlapping it onto the substrate 110. As a result, the insulating film 120 becomes dense.

[0057] At this time, the spray angle θ is 45 degrees or more and 90 degrees or less. And the velocity Vx is 250 m / sec or more and 600 m / sec or less.

[0058] For example, if the spraying machine 180 forms the insulating film 120 on the substrate 110 when the spraying angle θ is less than 45 degrees, the sprayed material 182 on the substrate 110 will deform, and the formed insulating film 120 will contain many defects such as cracks. Furthermore, if the spraying machine 180 forms the insulating film 120 on the substrate 110 when the particle velocity Vx is less than 250 m / sec, the sprayed material 182 on the substrate 110 will not be sufficiently flattened, and the formed insulating film 120 will contain many defects such as cracks. Moreover, if the spraying machine 180 forms the insulating film 120 on the substrate 110 when the particle velocity Vx is higher than 600 m / sec, the sprayed material 182 will scatter on the substrate 110, and the formed insulating film 120 will contain many defects such as cracks.

[0059] On the other hand, by using the manufacturing method of the stage 100, an insulating film 120 with a maximum pore diameter Xm of 40 μm or less (see Figure 7) can be formed on the substrate 110. Furthermore, by using the manufacturing method of the stage 100, an insulating film 120 containing pores 126 with a dimensional parameter α of 2.5 or less can be formed on the substrate 110.

[0060] Although details will be described later, the insulating film 120 with a dimensional parameter α of 2.5 or less has a high withstand voltage (see Figure 6) and good insulation characteristics. As a result, the stage 100 containing the insulating film 120 has a high withstand voltage and good insulation characteristics. Accordingly, the stage 100 can suppress the decline in long-term reliability.

[0061] [2-4. Evaluation method for insulating film 120]

[0062] The evaluation method for the insulating film 120 will now be described with reference to Figures 4 to 6. Figure 4 is a flowchart illustrating the evaluation method for the insulating film 120. Figure 5 is a schematic diagram illustrating the relationship between the pore size X, the double logarithm of the cumulative probability of the insulating film 120, and the melt-blown film volume T. Figure 6 is a plot illustrating the relationship between the dimensional parameter α and the withstand voltage. Figure 7 is a plot illustrating the relationship between the predicted maximum pore size and the withstand voltage. Constructions identical or similar to those in Figures 1 to 3 may be described as required.

[0063] For example, the evaluation method of the insulating film 120 includes steps 110 (S110) to 180 (S180).

[0064] At the start of the evaluation of the insulating film 120, an SEM image of the cross-section of the insulating film 120 containing multiple pores is obtained using a photographic device such as a digital camera (illustrated but not shown) (S110). For example, using the insulating film 120 containing multiple pores, n (where n is a positive integer) SEM samples are made, including the cross-section of the insulating film 120 for SEM observation. Images are taken for the n SEM samples, resulting in m (where m is a positive integer) SEM images. For example, when n is multiple, images can be taken for each of the n SEM samples to obtain m SEM images, or images can be taken for the n SEM samples in a manner that the total number of images is m. Furthermore, when n is 1, images are taken for 1 SEM sample, resulting in m SEM images. For example, when observing the cross-section of the insulating film 120 (SEM sample), the magnification of the microscope is 500x to 700x. For example, the SEM specimen is a specimen with different cross sections within the same insulating film 120. Furthermore, multiple SEM specimens can also be SEM specimens obtained from the cross sections of each of multiple different insulating films 120, such as insulating film 120-1, insulating film 120-2, etc., with the sum of the points being n.

[0065] Next, the SEM image obtained in S110 is binarized (step 120 (S120)). For example, the obtained SEM image is converted into an image consisting only of black and white (binarized image) according to a set specified threshold. That is, a binarized image is generated using the obtained SEM image. For example, binarizing the obtained SEM image includes: using an image processing device including a CPU and other computing processing circuits to convert the SEM image data of the obtained SEM image into binarized image data. For example, in S120, multiple SEM samples (with a value of n of 2 or more) are used to capture images in a manner that sums to 60 images (m=60), and 60 binarized images are obtained based on the 60 SEM images.

[0066] Next, using the binarized image converted in S120, the largest aperture (maximum aperture) is extracted from the multiple apertures in the binarized image (step 130 (S130)). For example, extracting the maximum aperture includes: using an image processing device, detecting the boundary (boundary line) between the white and black areas of the image data in the binarized image, and extracting the largest aperture among the multiple apertures. S130 can be performed on each of all acquired binarized images. For example, if 60 binarized images are acquired in S120, then S130 can be performed on each of the 60 binarized images. As a result, 60 maximum apertures can be extracted.

[0067] Next, the pore diameter of the largest pore captured in S130 is calculated (step 140 (S140)). For example, calculating the pore diameter of the largest pore includes: using an image processing device, calculating the diameter (pore diameter) of the circumference defined by the boundary line detected in S130. As explained with reference to FIG3, the pores of the mechanism shown in FIG3 are circular, but the actual shape of the pores can vary. Therefore, the pore diameter of the largest pore is calculated through the processing in S140. For example, if 60 largest pores are captured in S130, the pore diameter of each of the 60 largest pores can be calculated.

[0068] Next, a graph is plotted on the logarithm of the cumulative probability F(x) of the largest pore diameter captured in S140 relative to the pore diameter of the largest pore (step 150 (S150)). For example, using the arithmetic processing circuit in the image processing device or the arithmetic processing circuit including the CPU of the control circuit for controlling the image processing device and the photographic device, the logarithm of the cumulative probability F(x) of the largest pore diameter of each is calculated, the pore diameter of the largest pore (μm) is defined as the x-axis, and the logarithm of the cumulative probability F(x) is defined as the y-axis, and a graph is plotted (for example, Figure 5).

[0069] Next, using the drawing made in S150, the slope of the graph 152 and the diameter of the largest pore when the logarithm of the cumulative probability F(x) becomes 0 are calculated (step 160 (S160)). Furthermore, the graph interpolated from the graph 152 is graph 154. For example, using the arithmetic processing circuit within the image processing device or the arithmetic processing circuit of the CPU included in the control circuit for controlling the image processing device and the photographic device, the mathematical formula (1) is defined by the least squares method. Here, F(x) is called the cumulative probability (-), x is called the diameter of the largest pore (μm), the value α is called the scale parameter, and the value λ is called the position parameter (diameter of the largest pore) (μm). The slope of the graph is the slope 1 / α, and the value λ is the diameter of the largest pore λ when the logarithm of the cumulative probability F(x) becomes 0. Furthermore, the values ​​α and λ are greater than 0. In addition, when the number of images acquired is small, the Minimum Variance Linear Unbiased Estimator Method (MVLUE) can be used to calculate the scale parameter α and the location parameter λ.

[0070]

[0071] Next, the volume ratio of the insulating film 120 to the volume of the target insulating film 120 (target insulating film) is calculated (step 170 (S170)). For example, the volume ratio is calculated using the arithmetic processing circuit in the image processing device or the arithmetic processing circuit containing the CPU included in the control circuit for controlling the image processing device and the photographic device. For example, the drawing made in S150 is a drawing relative to the pore diameter of the 60 largest pores. Here, the SEM observation is obtained by taking the original 60 SEM images with the pore diameter of the 60 largest pores. The average thickness (μm) of the 60 SEM samples used in the aforementioned SEM observation is defined as the average thickness h, the sum of the areas (μm2) of the 60 SEM images is defined as the total area s of the SEM images, and the volume (μm3) of the insulating film 120 (volume Vs), that is, the total volume Vs of the 60 SEM samples, can be expressed by mathematical formula (2). Furthermore, the thickness (μm) of the insulating film 120 is defined as thickness H1, the area (μm2) that needs to withstand voltage (insulation performance) in the stage 100 is defined as area Sa, and the volume (μm3) (volume Va) of the insulating film 120 (target insulating film) can be expressed by mathematical formula (3). As a result, the volume ratio T can be expressed by mathematical formula (4). For example, the area of ​​the SEM image can be the surface area of ​​the photographed insulating film 120, the average thickness h can be the average pore diameter of the largest pore, and the area Sa that needs to withstand voltage (insulation performance) in the stage 100 can be the area of ​​the first surface 122 of the insulating film 120, or it can be the surface area of ​​the substrate placed on the stage 100. In addition, for example, the surface area of ​​the substrate placed on the stage 100 corresponds to the surface area of ​​a 12-inch (approximately 300 mm) silicon wafer.

[0072]

[0073]

[0074]

[0075] Next, the predicted maximum pore size (S180) is calculated. The natural logarithm of the volume ratio T is proportional to the double logarithm of the cumulative probability F(x), and can therefore be expressed by mathematical formula (5). That is, the natural logarithm of the volume ratio T is equivalent to mathematical formula (1). For example, the predicted maximum pore size corresponding to the volume ratio T is calculated using the arithmetic processing circuit in the image processing device or the arithmetic processing circuit containing the CPU included in the control circuit for controlling the image processing device and the photographic device. At this time, the maximum pore size is the maximum value among all the pore sizes of the plurality of pores contained in the insulating film 120, and the calculated predicted maximum pore size is the predicted value of the aforementioned maximum pore size.

[0076]

[0077] For example, as shown in Figure 5, the first axis (y1 axis) is defined as the double logarithm of the cumulative probability F(x), and the second axis (y2) is defined as the natural logarithm (lnT) of the volume ratio T. The predicted maximum pore size X1 at volume ratio T1 can then be calculated. Furthermore, the pore size on the x-axis shown in Figure 5 is relative to the maximum pore size of the y1 axis system, and relative to the predicted maximum pore size of the y2 axis system.

[0078] For example, when the scale parameter α increases, the slope of the graph decreases, so the graph is plotted in region 170 as shown in Figure 5. At this time, the predicted maximum pore size calculated using the volume ratio T becomes larger than the maximum pore size or the predicted maximum pore size shown by mathematical formulas (1) and (5). Furthermore, when the scale parameter α decreases, the slope of the graph increases, so the graph is plotted in region 160 as shown in Figure 5. At this time, the predicted maximum pore size calculated using the volume ratio T becomes smaller than the maximum pore size or the predicted maximum pore size shown by mathematical formulas (1) and (5).

[0079] The evaluation of the insulating film 120 ends when the predicted maximum pore size X1 is calculated. For example, if the predicted maximum pore size X1 is below the maximum pore size set in a manner that satisfies the specified withstand voltage of the insulating film 120, the evaluated characteristics of the insulating film 120 can be determined to be good. On the other hand, if the predicted maximum pore size X1 is greater than the maximum pore size set in a manner that satisfies the specified withstand voltage of the insulating film 120, the evaluated characteristics of the insulating film 120 can be determined to be poor.

[0080] For example, if a graph is plotted showing the relationship between the dimensional parameter α in the insulating film 120 evaluated using the insulating film evaluation method related to one embodiment of the present invention and the measured result of the withstand voltage (kV / mm) of the insulating film 120, it will become the graph shown in FIG6. Furthermore, if a graph is plotted showing the relationship between the predicted maximum pore size of the insulating film 120 evaluated using the insulating film evaluation method related to one embodiment of the present invention and the measured result of the withstand voltage (kV / mm) of the insulating film 120, it will become the graph shown in FIG7. FIG7 uses dashed lines 156 to represent first approximation lines and lines interpolated from these lines, based on multiple plots. In addition, the thickness H1 of the insulating film 120 in the plots shown in FIG6 and FIG7 is 200 μm or more and 250 μm or less, as an example.

[0081] As shown in Figure 6, the withstand voltage of the insulating film 120 has a good negative correlation with the scale parameter α. That is, it can be understood that if the scale parameter α decreases (the slope 1 / α of mathematical formula (1) increases), the withstand voltage will increase. Accordingly, by using the evaluation method of the insulating film 120, the scale parameter α relative to the required withstand voltage can be calculated, and the required withstand voltage corresponding to the scale parameter α of the pores 126 and 127 of the insulating film 120 can be calculated.

[0082] As shown in Figure 7, the withstand voltage of the insulating film 120 has a strong negative correlation with the predicted maximum pore size of the insulating film 120. That is, it can be understood that if the predicted maximum pore size becomes smaller, the withstand voltage will become higher. Accordingly, by using the evaluation method of the insulating film 120, the predicted maximum pore size of the insulating film 120 relative to the required withstand voltage can be calculated, and the required withstand voltage corresponding to the predicted maximum pore size of the insulating film 120 can be calculated.

[0083] For example, the withstand voltage of the stage including the cooling plate of the semiconductor device can generally be set to 10 kV / mm or higher. For example, the condition for the insulating film 120 to meet the withstand voltage of 10 kV / mm or higher can be that the dimensional parameter α is greater than 0 and less than 2.5, greater than 0 and less than 1.5, or greater than 0 and less than 1.0. Furthermore, the condition for the insulating film 120 to meet the withstand voltage of 10 kV / mm or higher can be that the position parameter (pore diameter) λ is 5 or higher and less than 8. That is, when the dimensional parameter α is greater than 0 and less than 2.5 and the position parameter λ is 5 or higher and less than 8, the withstand voltage of the insulating film 120 will be 10 kV / mm or higher, and the insulation characteristics of the insulating film 120 will become good.

[0084] Generally speaking, the thickness of the insulating film can be expected to vary from product to product, and it is conceivable that if the thickness of the insulating film 120 increases, the pore size will increase. However, the mathematical formulas (1) to (5) calculated using the insulating film evaluation method related to the embodiments of the present invention can be used to calculate the predicted maximum pore size regardless of the thickness of the insulating film 120, and the specified withstand voltage of the insulating film can be defined.

[0085] [3. Second Embodiment]

[0086] The structure of a semiconductor manufacturing apparatus related to the second embodiment of the present invention will now be described with reference to FIG8. The semiconductor manufacturing apparatus includes a stage 100. For example, the semiconductor manufacturing apparatus is a film processing apparatus 200. The film processing apparatus 200 is a so-called CVD apparatus. Furthermore, the structure of the film processing apparatus 200 described with reference to FIG8 is an example, and the structure of the film processing apparatus 200 is not limited to the structure shown in FIG8. Moreover, the film processing apparatus 200 is not limited to a CVD apparatus. In the description of the film processing apparatus 200, structures that are the same as or similar to those described with reference to FIGS. 1 to 7 will be described as needed.

[0087] Figure 8 is a schematic cross-sectional view of the film processing apparatus 200. The film processing apparatus 200 performs a chemical reaction with the reactive gases, thereby chemically forming various films on a substrate. The film processing apparatus 200 includes a cavity 202. The cavity 202 performs a chemical reaction with the reactive gases and provides space for chemically forming various films on the substrate.

[0088] An exhaust device 204 is connected to the cavity 202. For example, the exhaust device 204 can reduce the pressure inside the cavity 202. An inlet pipe 206 is provided in the cavity 202. The inlet pipe 206 can introduce the reaction gas into the cavity 202 via a valve 208. Various gases can be used as the reaction gas depending on the membrane to be formed. Furthermore, the reaction gas can also be liquid at room temperature. For example, the reaction gas system includes silane, dichlorosilane, tetraethoxysilane, tungsten fluoride, trimethylaluminum, etc. By using silane, dichlorosilane, tetraethoxysilane, etc., thin films such as silicon, silicon oxide, or silicon nitride can be formed on the substrate. Furthermore, by using tungsten fluoride or trimethylaluminum, thin films or metal oxide films such as tungsten, aluminum, or aluminum oxide can be formed on the substrate.

[0089] A microwave source 212 is disposed on the upper part of the cavity 202 via a waveguide 210. The microwave source 212 includes an antenna for supplying microwaves. Microwaves generated by the microwave source 212 are introduced into the cavity 202 through the waveguide 210. The reactive gas is plasma-plated by microwaves, and the chemical reaction of the gas is promoted by various active species contained in the plasma. The products obtained through the chemical reaction are deposited on the substrate, and a thin film is formed on the substrate.

[0090] Magnet 244 can also be disposed within cavity 202 as any configuration. Magnet 244 can increase plasma density. Magnet 216 and magnet 218 can also be further disposed on the side of cavity 202. Magnet 216 and magnet 218 can be permanent magnets or electromagnets with electromagnetic coils.

[0091] A stage 100 for mounting a substrate is disposed below the cavity 202. With the substrate disposed on the stage 100, a thin film can be formed on the substrate. A power supply 224 can also be connected to the stage 100 as an arbitrary configuration. The power supply 224 can apply a voltage equivalent to high-frequency power to the stage 100.

[0092] For example, when the stage 100 is equipped with a sheath heater (not shown), the heater power supply 230 for controlling the sheath heater can be connected to the stage 100. The power supply 226 for the electrostatic chuck used to fix the substrate to the stage 100, the temperature controller 228 for controlling the temperature of the medium circulating inside the stage 100 (groove 104), and the rotation control device (not shown) for rotating the stage 100 around the rotation axis 106 can also be connected to the stage 100 as arbitrary configurations. For example, by using the sheath heater, the heater power supply 230, and the temperature controller 228, the temperature of the stage 100 can be controlled simultaneously with the temperature of the substrate placed on the stage 100.

[0093] The film processing apparatus 200 according to the second embodiment includes a stage 100. As a result, the film processing apparatus 200 can uniformly heat the substrate and precisely control the heating temperature. The stage 100 has excellent insulation properties, so the withstand voltage of the film processing apparatus 200 increases in response to the voltage applied to the substrate. Furthermore, the film processing apparatus 200 with its increased withstand voltage has excellent long-term reliability, so users can reduce the number of maintenance cycles required for the film processing apparatus 200.

[0094] Although the example of the insulating film 120 being disposed on the substrate 110 included in the stage 100 of the semiconductor manufacturing apparatus has been described as an embodiment of the present invention, the embodiments of the present invention are not limited to semiconductor manufacturing apparatuses. For example, the substrate 110 on which the insulating film 120 is disposed may be a component used in the aerospace field, a component used in the automotive field, or a component including the insulating film 120 disposed on an aluminum-containing substrate 110.

[0095] As embodiments of the present invention, the structures of the insulating film, the stage, the method for manufacturing the stage, the method for evaluating the insulating film, and the semiconductor manufacturing apparatus described above can be appropriately combined and implemented as long as they do not contradict each other. Furthermore, as embodiments of the present invention, the structures of the insulating film, the stage, the method for manufacturing the stage, the method for evaluating the insulating film, and the semiconductor manufacturing apparatus described above can be appropriately interchanged as long as they do not contradict each other. Moreover, based on each embodiment, any addition, deletion, or design modification of appropriate constituent elements by those skilled in the art to which this invention pertains is included within the scope of this invention, provided it captures the essence of the invention.

[0096] Furthermore, even if there are other effects that are different from those achieved by the various embodiments described above, those that are obvious from the description in this specification or that can be easily predicted by those skilled in the art to which this invention pertains should be understood as being achieved by this invention. [Simplified Explanation of the Diagram]

[0012] Figure 1 is a perspective view illustrating the structure of the platform related to the first embodiment of the present invention.

[0013] Figure 2 is a top view illustrating the structure of the platform related to the first embodiment of the present invention.

[0014] Figure 3 is a schematic diagram illustrating the manufacturing method of the platform related to the first embodiment of the present invention, with the cross section of the platform shown in Figure 2 along line A1-A2 as an example.

[0015] Figure 4 is a flowchart illustrating the evaluation method of the insulating film related to the first embodiment of the present invention.

[0016] Figure 5 is a schematic diagram illustrating the relationship between the double logarithm of the cumulative probability of the pore size and the insulating film and the melt-sprayed volume film in relation to the first embodiment of the present invention.

[0017] Figure 6 is a diagram illustrating the relationship between the dimensional parameter α and the withstand voltage in relation to the first embodiment of the present invention.

[0018] Figure 7 is a diagram illustrating the relationship between the predicted maximum pore size and the withstand voltage in relation to the first embodiment of the present invention.

[0019] Figure 8 is a schematic diagram showing a cross-section of a semiconductor manufacturing apparatus including a stage related to the second embodiment of the present invention.

Claims

1. A method for evaluating an insulating film, comprising: binarizing m (where m is a positive integer) SEM images obtained using an insulating film containing multiple pores to generate m binarized images; using the m binarized images, extracting the largest pore from each of the multiple pores in the m binarized images to obtain m largest pores; calculating the pore diameter for each of the m largest pores to obtain m pore diameters; calculating the logarithm of the cumulative probability F(x) for the m pore diameters, and plotting the logarithm of the cumulative probability F(x) relative to the m pore diameters; and plotting the logarithm of the cumulative probability F(x). Let y be the pore diameter and x be the pore diameter. Define mathematical formula (1). At this time, the numerical value α (value α is greater than 0) is the scale parameter, and the numerical value λ (value λ is greater than 0) is the pore diameter when the double logarithm of the cumulative probability F(x) becomes 0. Calculate the volume Vs of the sum of the areas of the aforementioned m SEM images and the average value of the aforementioned maximum pore diameter extracted from the aforementioned m SEM images, and the volume Va of the aforementioned insulating film. Calculate the volume ratio T of volume Vs and volume Va. Based on the relationship between the aforementioned volume ratio T and the aforementioned y shown in mathematical formula (5), calculate the predicted value of the maximum pore diameter, which is the maximum value among the aforementioned multiple pore diameters contained in the aforementioned insulating film.

2. The evaluation method for the insulating film as described in claim 1, wherein the aforementioned volume Vs is given by mathematical formula (2), the average value of the pore diameter of the aforementioned m largest pores is defined as the average thickness h, and the area of ​​the aforementioned m SEM images is defined as s.

Images