JP2003243309A - Antenna evaluation device and method for plasma generation - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To analytically derive optimum power supply specifications on the basis of an analytically found electric field intensity distribution. <P>SOLUTION: After a target plasma density distribution in an arbitrary specific region in a three-dimensional space where an array antenna is installed and design information of an array antenna are input, an electric field intensity distribution wherein an electric power is individually supplied to each antenna element based on predetermined power supply specifications is calculated by setting a specific dielectric constant in the three-dimensional space considering ion sheaths. Furthermore, under the condition that the plasma density distribution is the target plasma density distribution when the synthesized electric field intensity distribution synthesized from each individual target plasma density distribution, by weighting individual power supply specification based on the principle of superposition of the electric field becomes a distribution state corresponding to the target plasma density distribution, the power supply specifications of a high frequency electric power providing the synthesized electric field intensity distribution of a distribution state corresponding to the target plasma density distribution are solved as the optimum problem. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a plasma generation antenna evaluation apparatus and method, and more particularly to plasma CVD.
The present invention relates to a technique for evaluating the performance of a plasma generation antenna applied to an apparatus.

[0002]

2. Description of the Related Art As is well known, a plasma CVD apparatus is
It is used for various film formations in the manufacture of semiconductor elements, and more specifically, it is used when forming a thin film on a substrate in the manufacturing process of a solar cell or a liquid crystal display panel. In the technical fields of solar cells and liquid crystal display panels, the size of substrates has been increasing in recent years, and it is required to form a film on a large size substrate with uniform characteristics and film thickness. As a conventional technique corresponding to such a large substrate, for example, Japanese Patent Laid-Open No. 2001-1
There is an antenna device and a plasma processing device disclosed in Japanese Patent No. 26899. In this conventional technique, a plurality of microwave antennas (antenna lines) are arranged so as to face the surface of a large substrate, and uniform plasma is generated on the surface of the large substrate.

[0003]

By the way, plasma C
When a uniform property and film thickness are formed on a large substrate using a VD device, the performance of the plasma generation antenna, that is, the electric field intensity distribution in the space near the substrate surface generated by the plasma generation antenna is an important performance item. Becomes This electric field intensity distribution is a requirement that directly defines the plasma density distribution in the space near the substrate surface. However, the electric field intensity distribution by the plasma generation antenna is optimally set experimentally. Therefore, it is necessary to perform many experiments by trial and error until the optimum setting is completed, which requires a lot of time and cost.

The present invention has been made in view of the above problems, and has the following objects. (1) An optimum power supply specification for the plasma generation antenna is analytically derived on the basis of the above-mentioned electric field strength distribution obtained analytically. (2) The electric field strength distribution and the optimum power supply specifications are obtained by a shorter time arithmetic processing.

[0005]

In order to achieve the above object, in the present invention, as a first means relating to a plasma generation antenna evaluation apparatus, a plasma generation targeting an array antenna composed of a plurality of antenna elements is generated. And an input device for inputting a target plasma density distribution in an arbitrary specific area in a three-dimensional space in which the array antenna is installed, and design information of the array antenna, and an antenna evaluation device for the antenna. By setting the relative permittivity of the three-dimensional space in consideration of the ion sheath (region where plasma does not exist), the electric field intensity distribution (individual (Feeding electric field strength distribution) is calculated based on a predetermined electric field analysis algorithm, and the individual feeding electric field strength distributions are superposed on each other. Under the condition that the plasma density distribution of the specific region becomes the target plasma density distribution when the combined electric field strength distribution synthesized by weighting the power supply specifications based on An arithmetic unit that solves as an optimization problem a high-frequency power supply specification that gives a combined electric field strength distribution having a distribution form corresponding to the target plasma density distribution, based on a predetermined problem solving algorithm; and an optimum arithmetic unit obtained by the arithmetic unit. A configuration including an output device that outputs power supply specifications is adopted.

As the second means relating to the plasma generation antenna evaluation apparatus, in the first means, the problem solving algorithm is the conjugate gradient method.

As a third means relating to the plasma generation antenna evaluation apparatus, in the first or second means, the electric field analysis algorithm is FDTD (Finite Deffe
renceTime Domain) method is adopted.

As a fourth means relating to the plasma generation antenna evaluation apparatus, in any one of the first to third means, the specific region is a region near the surface of the substrate on which the film is to be formed.

As a fifth means relating to the plasma generation antenna evaluation apparatus, in any one of the first to fourth means, a configuration is adopted in which the target plasma density distribution is set to a constant value.

As a sixth means relating to the plasma generation antenna evaluation apparatus, in the fifth means, the objective function when solving as an optimization problem is a standard obtained by normalizing the standard deviation of the electric field in a specific region with an average value. The standard deviation is adopted.

On the other hand, in the present invention, as a first means relating to the plasma generation antenna evaluation method, there is provided a plasma generation antenna evaluation method for evaluating an array antenna composed of a plurality of antenna elements. And the step of inputting the target plasma density distribution in an arbitrary specific area in the three-dimensional space in which the plasma generation antenna is installed into the arithmetic unit, and forming on the surface of the plasma generation antenna. Considering the ion sheath (region where plasma does not exist), the above 3
By setting the relative permittivity of the three-dimensional space, the electric field strength distribution (individual power supply electric field strength distribution) in the three-dimensional space when individual antenna elements are individually fed with the specified feeding specifications is based on a predetermined electric field analysis algorithm. The composite electric field strength distribution obtained by combining the step of calculating by the arithmetic unit and the individual electric power supply electric field strength distributions with the electric power supply specification weighted based on the principle of superposition of electric fields has a distribution form corresponding to the target plasma density distribution. In the case where the plasma density distribution of the specific region becomes the target plasma density distribution, the power supply specification of the high frequency power that gives the combined electric field strength distribution of the distribution form corresponding to the target plasma density distribution is given to the predetermined problem solving algorithm. Based on this, a configuration having a step of solving as an optimization problem using an arithmetic unit is adopted.

As a second means related to the plasma generation antenna evaluation method, in the first means, the problem solving algorithm is a conjugate gradient method.

As a third means relating to the plasma generation antenna evaluation method, in the first or second means, the electric field analysis algorithm is FDTD (Finite Deffe
renceTime Domain) method is adopted.

As a fourth means relating to the plasma generation antenna evaluation method, in any one of the first to third means, the specific region is a region near the surface of the substrate on which the film is to be formed. To do.

As a fifth means relating to the plasma generation antenna evaluation method, in any one of the first to fourth means, the target plasma density distribution is set to a constant value.

As a sixth means relating to the plasma generation antenna evaluation method, the objective function in solving the optimization problem in the fifth means is a standard obtained by normalizing the standard deviation of the electric field in a specific region with an average value. The standard deviation is adopted.

[0017]

The present invention is a performance evaluation technique for a plasma generation antenna (particularly an array antenna composed of a plurality of antenna elements) used in a plasma CVD apparatus or the like. As a more comprehensive technical idea, the plasma generation antenna is installed. This is for setting the feeding specification of the plasma generation antenna that satisfies the target plasma density distribution in an arbitrary specific area in the three-dimensional space. That is, the feed amplitude and the feed phase of the high frequency power to the plasma generation antenna (each antenna element) required to realize the electric field intensity distribution in the specific region corresponding to the target plasma density distribution in the specific region are analytically obtained. By doing so, the feeding specification of the plasma generation antenna that satisfies the target plasma density distribution is evaluated.

In the present invention, when the relative permittivity of the three-dimensional space required for analytically obtaining the electric field intensity distribution is set, it is formed on the surface of the plasma generating antenna (each antenna element). The electric field formed in the plasma is more accurately estimated by considering the ion sheath (region where plasma does not exist). Considering the ion sheath, the analytically obtained impedance of the plasma generation antenna was very close to the experimental result, and its effectiveness was confirmed.

Further, according to the present invention, the electric field strength distribution (individual power supply electric field strength distribution) in the three-dimensional space when the individual antenna elements are individually fed under the specified feeding specifications is calculated based on a predetermined electric field analysis algorithm. , It is specified when the combined electric field strength distribution obtained by combining the individual electric field strength distributions obtained in this way with the feeding specifications as the weighting based on the theory of superposition of electric fields has a distribution form corresponding to the target plasma density distribution. Under the condition that the plasma density distribution of the region becomes the target plasma density distribution, the high-frequency power feeding specifications that give the combined electric field strength distribution of the distribution form corresponding to the target plasma density distribution are optimized based on a predetermined problem solving algorithm. By adopting the means of solving as a problem, it is possible to realize a composite electric field strength distribution equivalent to an arbitrary target plasma density distribution. Analytically determining the feeding specifications of the high-frequency power.

Such means is, for example, plasma CVD.
It can be considered to be applied to a plasma generation antenna whose performance requirement is to form a film with a uniform film thickness on a relatively large substrate, such as an array antenna provided for the apparatus. In this case, it is possible to design an array antenna for achieving the required film forming performance with almost no experiment.

[0021]

BEST MODE FOR CARRYING OUT THE INVENTION An embodiment of a plasma generation antenna evaluation apparatus and method according to the present invention will be described below with reference to the drawings. The present embodiment relates to the design of an array antenna (plasma generation antenna) used in a plasma CVD apparatus, and the three-dimensional space in which the plasma generation antenna is installed is a vacuum chamber internal space, and the three-dimensional space described above. The specific region in the space is a space near the surface of the substrate (a space near the surface of the substrate) that is arranged to face the array antenna so as to face it.

FIG. 1 is a functional block diagram of a plasma generation antenna evaluation apparatus according to this embodiment. This Figure 1
In FIG. 1, reference numeral 1 is an input device, 2 is a calculation device, 3 is an output device, and 4 is a storage device. The plasma generation antenna evaluation device configured by such various functional elements is realized by installing an application program such as an FDTD analysis program and a conjugate gradient method program in a general-purpose computer, for example.

More specifically, the input device 1 is, for example, a keyboard, various pointing devices, and / or a removable storage device, a communication device, or the like, and design information such as a physical shape of an array antenna to be evaluated, It is for inputting into the arithmetic unit 2 various information necessary for evaluating the target plasma density distribution in the space near the substrate surface and the array antenna. The input device 1
In the case of a keyboard or various pointing devices, the above-mentioned various information is calculated by the evaluator's manual work.
On the other hand, when the input device 1 is a removable storage device or a communication device, the above-mentioned various types of pre-built information are collectively input to the arithmetic device 2.

Here, the design information is, for example, CAD.
It is CAD data regarding the shape and various electrical setting conditions of an array antenna separately designed by using a (Computer Aded Design) device. The CAD data is input to the arithmetic unit 2 via a removable storage device as the input device 1 or a communication device. It is also conceivable that the arithmetic unit 2 is provided with a CAD function to design the shape of the array antenna using the present plasma generation antenna evaluation apparatus and generate CAD data by setting electrical setting conditions. In this case, the evaluator (designer) operates the keyboard and various pointing devices to carry out the design work of the array antenna.

FIG. 2 is a front view and a side view showing the shape of the array antenna in this embodiment. As shown in this figure, the array antenna A is composed of a total of 25 U-shaped antenna elements # 1 to # 25 arranged at regular intervals in one surface (installation surface) parallel to the glass substrate S. There is.
The configuration of such an array antenna A is the same as the prior application (Japanese Patent Application No. 2001-296332) by the present inventors.
Each of these U-shaped antenna elements # 1 to # 25 has two parallel elements.
It is composed of one straight line portion and a bent portion connecting the straight line portions, and each straight line portion is arranged to face the rectangular glass substrate S at regular intervals. The glass substrate S is arranged so as to face the array antenna A by having its edge supported by the support frame B.

As shown in FIG. 2, the length of the straight line portion of each U-shaped antenna element # 1 to # 25 is 1.6 m, and each U-shaped antenna element # 1 to # 25 and the glass substrate S are Distance is 4
4 mm, and although not shown, each U-shaped antenna element # 1
The cross section of # 25 is a square with a side of 4 mm, and the distance between them is 72 m.
It is set to m (that is, the mutual interval of the linear portions is 36 mm).

Further, each U-shaped antenna element # 1 to # 25.
Is set at one end to a feeding point to which high-frequency power is supplied and at the other end to a grounding point electrically grounded. Output impedance 5 is provided to the feeding points of the U-shaped antenna elements # 1 to # 25 via a coaxial cable having a characteristic impedance of 50Ω.
High frequency power is supplied from a high frequency power source of 0Ω, and the ground point is grounded by being connected to the inner wall of the vacuum chamber C. Furthermore, each U-shaped antenna element # 1 to #
In 25, the feeding point and the grounding point are arranged alternately. That is, in the front view of FIG. 2, in all the U-shaped antenna elements # 1 to # 25, the end portion (one end) located on the left side is the feeding point, and the end portion (the other end) located on the right side is the grounding point. It is set.

The array antenna A, the support frame B and the glass substrate S for which the shape and power feeding conditions are set in this way are housed in a rectangular vacuum chamber C, and are composed of x-axis, y-axis and z-axis. A three-dimensional Cartesian coordinate system is set. x
The axis is in the arrangement direction of each U-shaped antenna element # 1 to # 25,
The z-axis is the extending direction of the straight line portion of each U-shaped antenna element # 1 to # 25, and the y-axis is orthogonal to the plane formed by the x-axis and the z-axis (that is, the above-mentioned installation surface). The direction is set to. The glass substrate S has a short side of 1
This is a large-sized substrate having a length of 200 mm and a long side set to 1672 mm, and corresponds to an amorphous silicon substrate used for a solar cell, a liquid crystal display panel or the like.

Returning to the explanation of FIG. 1, the target plasma density distribution is the target of the density distribution (plasma density distribution) of the plasma generated in the vacuum chamber C by the electric field of the array antenna A. It is a target function (target plasma density distribution function) in which each position in the space near the surface is a variable. The target plasma density distribution is arbitrarily set by the evaluator, and may be a uniform distribution at each position, or the plasma density becomes higher as it approaches the center of the space near the surface. It may be set as follows. However, in this embodiment, since the array antenna A used in the plasma CVD apparatus for the purpose of forming a uniform film thickness on the substrate is evaluated, the target plasma density distribution function is It is a constant value regardless of the position.

The computing device 2 stores the various information input from the input device 1 in the storage device 4 and computes the various information based on the FDTD analysis program or the conjugate gradient method program stored in the storage device 4 in advance. By processing, the power supply specification to the array antenna A as the final product is calculated, and the power supply specification is output to the output device 3. In addition, the above-mentioned power supply specification is applied to each U constituting the array antenna A.
It is defined by the feed amplitude and the feed phase of the high frequency power that feeds the V-shaped antenna elements # 1 to # 25.

The FDTD analysis program is an analysis program based on a general three-dimensional FDTD analysis method as an electric field simulation method for a communication antenna. In the three-dimensional FDTD analysis method, the relative permittivity of the space around the antenna to be analyzed, and the cell size and the number of cells for partitioning the space around the antenna into an orthogonal lattice (hereinafter, referred to as a cell) having a predetermined size are set as analysis conditions. By doing so, the electric field strength distribution in the space around the antenna to be analyzed is calculated for each cell.

In order to simulate the electric field generated by the array antenna A using the FDTD analysis program, the electric field of the array antenna A causes the electric field in the vacuum chamber C, that is, each of the U-shaped antenna elements # 1 to #.
It is necessary to set the relative permittivity of plasma generated in the vicinity of 25. In this embodiment, in this formulation,
As shown in FIG. 3, an ion sheath of a predetermined thickness formed in the vicinity of the periphery of each U-shaped antenna element, that is, a plasma nonexistence region is considered.

Since the present array antenna A converts the source gas into plasma by high-frequency power, the ions do not respond to the frequency of the high-frequency power, and the ions in the vicinity of the periphery of each U-shaped antenna element # 1 to # 25. Ions can be considered to be stationary. That is, as shown in the drawing, in the vicinity of the peripheries of the U-shaped antenna elements # 1 to # 25, the ion sheaths over a certain thickness from the surface of the U-shaped antenna elements # 1 to # 25, that is, the relative permittivity It can be considered that a vacuum region (where plasma does not exist) in which is 1 is formed.

The conjugate gradient method program is used as a solution for a general optimization problem, and solves the optimal problem based on the conjugate gradient method which is one of various optimization algorithms.

The details of the arithmetic processing executed by the arithmetic unit 2 will be described later, but as an outline of the processing, the arithmetic unit 2
Under the assumption that the plasma density distribution in the space near the substrate surface becomes the target plasma density distribution when the electric field intensity distribution in the space near the substrate surface has a distribution form corresponding to the target plasma density distribution, By setting the relative permittivity of the space near the array antenna A in consideration of the ion sheath formed on the surface of the array antenna A, the relative dielectric constant with respect to the array antenna A necessary for forming the electric field intensity distribution corresponding to the target plasma density distribution is set. Analytical determination of high-frequency power supply specifications.

The output device 3 is, for example, an external storage device, a monitor, a printer, or a communication device, and outputs the power supply specifications obtained as a result of the arithmetic processing of the arithmetic device 2. That is, if the output device 3 is an external storage device, the power supply specifications are stored and saved, if the output device 3 is a monitor, the power supply specifications are displayed, and if the output device 3 is a printer, the power supply specifications are printed on paper, while the output device 3 is a communication device. In this case, the power supply specifications are sent to the outside.

The storage device 4 stores various information necessary for the arithmetic unit 2 to calculate the power supply specifications. Specifically, the storage device 4 stores the electric field strength distribution (individual power supply electric field strength distribution) in the vacuum chamber C when the U-shaped antenna elements # 1 to # 25 are individually supplied with power according to the specified power supply specifications. An individual power feeding electric field distribution storage area 4a for storing in advance, a target plasma density distribution storage area 4b for storing the target plasma density distribution input from the input device 1, and an F for storing an FDTD analysis program.
A DTD analysis program storage area 4c, a conjugate gradient method program storage area 4d for storing a conjugate gradient method program, and the like are provided.

Next, a method for evaluating the array antenna A using the plasma generation antenna evaluation apparatus having the above structure will be described in detail with reference to the flow chart shown in FIG.

In this evaluation method, first, the design information of the array antenna A and the analysis conditions regarding the FDTD method are input from the input device 1 to the arithmetic device 2 (step S1).
The design information includes the shape of the array antenna A including the positional relationship with the glass substrate S as described above (see FIG. 2) and electrical setting conditions such as designation of a feeding point and a ground point.
The data is input to the arithmetic unit 2. The analysis conditions are the cell size, the number of cells in the x-axis, y-axis, and z-axis directions and the plasma parameter, and the input device 1 is selected by the evaluator.
It is manually input from. The plasma parameters are plasma frequency, collision frequency and sheath thickness (thickness of ion sheath).

In this embodiment, the cell size Δx =
4 mm, number of cells in x-axis direction = 583, number of cells in y-axis direction = 75, number of cells in z-axis direction = 487, plasma frequency ω
p = 300 MHz, collision frequency ν = 200 Ms ⁻¹ , and sheath thickness = 4 mm. The shape of the array antenna A is as described in FIG. 2 and the above description.

When the input process of the design information and the analysis condition is completed, the arithmetic unit 2 causes the target plasma density distribution to have the three-dimensional coordinates in the three-dimensional orthogonal coordinate system of the x-axis, the y-axis, and the z-axis. It is input from the input device 1 as a function of (x, y, z) (step S2). Since the array antenna A of the present embodiment is intended to form a thin film having a uniform film thickness on the glass substrate S, the target plasma density distribution is input as a constant having a constant value on the surface of the glass substrate S. To be done.

Subsequently, the arithmetic unit 2 selects each of the U-shaped antenna elements # 1 to # 25 based on the FDTD analysis program stored in the FDTD analysis program storage area 4c and the analysis conditions input in step S1. The individual power supply electric field strength distribution is calculated (step S3).

Here, the plasma parameters constituting the above analysis conditions will be described in more detail. The relative permittivity εp (plasma relative permittivity) of the high frequency discharge plasma is generally expressed by the following equation (1). In this equation (1), ωp is the plasma frequency, ν is the collision frequency (collision frequency between electrons and neutral particles), and ω is the angular frequency of high-frequency power (excitation angular frequency). As shown in this equation (1), the plasma relative permittivity εp is a complex number, and the real part is a negative value less than 1 in many cases.

[0044]

[Equation 1]

In this embodiment, since the target plasma density distribution is a constant value (constant), that is, the plasma density is uniform, the plasma relative permittivity εp is a constant value. Further, since it can be assumed that the plasma parameter has a constant value regardless of the position in the vacuum chamber C, the sheath thickness at each portion of each U-shaped antenna element # 1 to # 25 has a constant value. Based on these conditions, in the present embodiment, the plasma parameters that define the plasma relative permittivity εp, that is, the plasma frequency ωp is 300 MHz, the collision frequency ν is 200 Ms ⁻¹ , and the sheath thickness is 4 mm.

That is, the arithmetic unit 2 has an ion sheath (relative dielectric constant) of 4 mm in the vertical direction from the surface in the vicinity of the periphery of each U-shaped antenna element # 1 to # 25 having a rectangular cross section (see FIG. 3). The analysis model of the array antenna A in which the material plasma having the above-mentioned plasma relative permittivity εp exists outside the ion sheath is set as the analysis target by the FDTD analysis program.

FIG. 5 is a diagram showing the effectiveness of such an analytical model, showing the impedance characteristics of the U-shaped antenna elements # 1 to # 25 based on the presence or absence of an ion sheath. In FIG. 5, (a) shows the resistance change characteristic according to the power supply frequency, and (b) shows the reactance change characteristic. For both resistance and reactance, the change characteristics (solid line) when the plasma parameters are set as described above are in line with the measured values (marked with ○), and it is effective to consider the ion sheath. I can confirm.

The arithmetic unit 2 performs the FDTD on the above analytical model.
By processing the method based on the FDTD analysis program, the individual feeding electric field strength distributions for the respective U-shaped antenna elements # 1 to # 25 are calculated, and the individual feeding electric field strength distributions are stored in the individual feeding electric field strength distribution storage area 4a. Store.

That is, the arithmetic unit 2 calculates the electric field value in the space near the surface of the substrate over all the cells when power is individually fed from the 25 U-shaped antenna elements # 1 to # 25 according to the specified feeding specifications. Then, the electric field value of each cell is stored in the electric field distribution storage area 4a as an individual power supply electric field strength distribution. Each individual feed electric field strength distribution is naturally calculated in consideration of the ion sheath. As a result, in the electric field distribution storage area 4a in the storage device 4, for each cell set in step S3, 25 electric field values when the U-shaped antenna elements # 1 to # 25 are individually fed with power are stored. Stored / saved.
In the present embodiment, in calculating each individual power supply electric field strength distribution based on such an FDTD method, in order to reduce the memory capacity necessary for the arithmetic processing, the RC method (Recursive Convergence) is used.
volution scheme).

When the calculation of the individual power supply electric field strength distribution is completed, the arithmetic unit 2 determines each U-shaped antenna element # 1 to # based on the conjugate gradient method program stored in the conjugate gradient method program storage area 4d. The power supply specifications for 25 are solved as an optimization problem (step S4).

That is, the arithmetic unit 2 synthesizes the individual power supply electric field intensity distributions obtained in advance in step S3 on the basis of the "superposition principle" regarding the electric fields to obtain the resultant electric field intensity distribution as the target plasma density distribution. Based on the assumption that the plasma density distribution in the space near the substrate surface is equal to the target plasma density distribution when the distribution pattern is equivalent to (constant value), the optimum value of the power supply specifications that gives the above composite electric field strength distribution is determined. Derive. It should be noted that "superposition theory"
As is well known, is a basic principle in the electric field that an electric field generated by power feeding from a plurality of power sources is obtained by combining individual electric fields obtained when a single power is fed to each power source.

Here, as a general theory, when the cell number of each cell is expressed as a discrete variable indicated by (k, l, m), the individual number when individual power is fed to the nth U-shaped antenna element #n The power supply electric field strength distribution En is expressed by the following equation (2).

[0053]

[Equation 2]

When the feeding voltage represented by the equation (3) by the feeding amplitude Cn and the feeding phase θn is used as a weighting function for such an individual feeding electric field intensity distribution En, the combined electric field strength distribution E is obtained. Is expressed as in equation (4).

[0055]

[Equation 3]

[0056]

[Equation 4]

When the combined electric field intensity distribution E has a distribution form corresponding to the target plasma density distribution (constant value) in this way, the weighting variables, that is, the feed amplitude Cn and the feed phase θn are the combined electric field intensity distribution E and the target. It can be obtained by solving an optimization problem under the condition that the objective function D showing the difference from the plasma density distribution is minimized. In the present embodiment, the standardized standard deviation of the electric field shown in the following equation (5) is used as the objective function D. This standardized standard deviation is a value obtained by standardizing the standard deviation of the electric field in the space near the substrate surface by the average value, as shown in equation (5),
Ns is the number of cells on the substrate surface.

[0058]

[Equation 5]

When deriving the feed specification based on the conjugate gradient method program, the arithmetic unit 2 sets the condition that the above objective function D, that is, the standardized standard deviation is minimized, and each U-shaped antenna that satisfies this condition. A power supply specification for the elements # 1 to # 25 is obtained. In the present embodiment, in order to reduce the calculation time required to solve the optimization problem, of the power supply amplitude and the power supply phase constituting the power supply specification, the power supply amplitude is set to a specific constant value, and the power supply phase is optimized. I tried to find only the solution.

Then, the arithmetic unit 2 obtains the optimum solution of the feeding phase that minimizes the objective function D (step S).
5) Output the optimal solution to the output device 3. FIG. 6 is a table showing the optimum solution (optimal phase) of the feeding phase output to the output device 3. Of the U-shaped antenna elements # 1 to # 25, the U-shaped antenna elements # 1, # 2, and # 2 located at the ends.
It can be seen that the U-shaped antenna elements # 3 to # 23 except for # 4 and # 25 have a phase difference of approximately 170 degrees between the U-shaped antenna elements adjacent to each other.

FIG. 7 is a diagram showing the electric field intensity distribution on the substrate surface and the film thickness distribution on the glass substrate S corresponding to the optimum phase, which shows the effectiveness of this embodiment. In FIG. 7, (a) shows the optimum phase for each U-shaped antenna element # 1.
Is a result (calculated value) of the electric field intensity distribution on the substrate surface obtained by the FDTD method when power is supplied to
The intensity of the electric field on the surface of the substrate is shown by the density. Further, (b) is a result (experimental value) of measuring the film thickness of the thin film actually formed on the glass substrate S when each U-shaped antenna element # 1 to # 25 is fed with the optimum phase. , The magnitude of the film thickness of each part on the surface of the substrate is shown by shading. In these (a) and (b), the lower side is U
The straight line side of each of the U-shaped antenna elements # 1 to # 25, and the upper side is the bent side of each of the U-shaped antenna elements # 1 to # 25.

In an experiment for forming a thin film, a sufficient amount of monosilane gas as a raw material gas was introduced into the actually manufactured vacuum chamber C to cause discharge, and the film thickness of the amorphous silicon film formed on the glass substrate S was changed. It was measured. Amorphous silicon precursors are said to be produced by a single collision of monosilane gas and electrons. Further, by supplying a sufficiently large amount of raw material gas into the vacuum chamber C, consideration was given to obtain more appropriate experimental results by avoiding a state in which the raw material is depleted.

Looking at the calculated value of the electric field strength distribution, there is a region where the electric field strength is slightly lower in the lower left corner of the substrate surface, and there is a region where the electric field strength is slightly lower than the center of the right side. Foreseen. As a result of the experiment, it was confirmed that the growth rate of the film was slightly slowed in these parts. Thus, it was found that the electric field strength distribution corresponding to the optimum phase and the film thickness distribution show a fairly good agreement.

In the calculation result of the electric field strength distribution, each U
A striped pattern reflecting the arrangement of the character-shaped antenna elements # 1 to # 25 is seen, but in the experimental value of the film thickness distribution, the film thickness change corresponding to such striped pattern does not occur. In such a difference, in the calculation of the electric field strength distribution, only the electric field strength distribution that controls the generation of plasma is calculated, but in the experiment of the film thickness distribution, the effects of diffusion and extinction are observed at the same time. It is considered that the observation results are blurred compared to when only the occurrence is examined.

FIG. 8 is to be compared with FIG.
The calculation result of the electric field strength distribution and the experimental value of the film thickness distribution in the case of feeding in-phase to all the U-shaped antenna elements # 1 to # 25 are shown. (A) is the calculation result of the electric field strength distribution, and (b) is the experimental value of the film thickness distribution. According to (a), the calculation result of the electric field strength distribution in the in-phase power feeding shows the result of the electric field synthesis by the "superposition principle", and a strong electric field strength portion is generated near the power feeding portion.
In such a region where the electric field is strong, a large plasma density (electron density) can be obtained, so that it is estimated that the growth rate of the film becomes high. Therefore, as an experimental value of the film thickness distribution, a film thickness distribution similar to the above calculation result of the electric field intensity distribution should be obtained.

When (a) and (b) in FIG. 8 are compared, the tendency that the electric field strength becomes strong in the vicinity of the power feeding portion and the film thickness at this portion becomes thicker coincides. Further, it is shown that a region where the electric field is slightly strong is generated also in the bent portions of the U-shaped antenna elements # 1 to # 25, and it can be seen that the film thickness of this portion is considerably thick. As described above, the calculation result of the electric field intensity distribution and the experimental value of the film thickness distribution substantially qualitatively match, but do not always completely match. It is considered that this difference is related to the calculation of the electric field strength under the assumption of uniform plasma in the calculation of the electric field strength distribution.

The standardized standard deviation described above was "1.01" in the case of in-phase power feeding, but decreased to "0.469" in the case of power feeding in accordance with the optimum phase. In the above-mentioned prior application (Japanese Patent Application No. 2001-296332), it is disclosed that the phase difference between adjacent antennas is set to 180 degrees. However, as a result of the present embodiment, a phase difference of about 170 degrees is an electric field intensity distribution. It has been found to result in good homogeneity of It is virtually impossible to experimentally derive such a detailed optimization of the feeding phase.

On the other hand, when the optimum solution is not obtained in step S4, the judgment in step S5 is "N".
o ", the design is changed (step S
7). This design change is a correction process of the design information of the array antenna A input in step S1, and is a process in which the evaluator inputs the correction information from the input device 1 to the arithmetic unit 2. If such a design change is made, steps S3 to
The process of S6 is repeated.

According to this embodiment, the following effects can be obtained. (1) Since the electric field strength distribution of the array antenna A is analytically obtained in consideration of the ion sheath, the time required for designing the array antenna A can be significantly shortened without relying on experiments for feeding specifications. Is.

(2) Since the optimum value of the feeding specification of the array antenna A is obtained by using the "superposition principle", it is possible to greatly reduce the calculation time of the arithmetic unit 2 for deriving the optimum value. is there. If you want to find the optimum value of the power supply specifications without using "superposition theory", you need to use a super computer for all arithmetic processing.
Although the calculation time is 9 hours and the memory capacity is required to be about 2.4 Gbyte, according to the present embodiment, the individual power supply electric field intensity distribution of each U-shaped antenna element # 1 to # 25 is obtained in advance by using a spar computer. The process of deriving the optimum value of the power supply specification can be obtained in about 1 minute by inputting the individual power supply electric field intensity distribution as data to a general engineering workstation. The memory capacity required for deriving an optimum value using this engineering workstation is about 250 Mbytes.

(3) Further, in the present embodiment, among the power supply specifications, the power supply amplitude is fixed to a constant value, and the optimum solution of only the power supply phase is obtained by the arithmetic unit 2. It is possible to reduce the calculation time required to solve (4) Since the impedance characteristic of the array antenna A can be obtained more accurately by considering the ion sheath, the output impedance of the antenna drive circuit can be easily set.

[0072]

As described above, according to the present invention,
A plasma generation antenna evaluation device for evaluating an array antenna composed of a plurality of antenna elements, wherein a target plasma density distribution in an arbitrary specific area in a three-dimensional space in which the array antenna is installed, and design information of the array antenna 3D when individual antenna elements are individually fed with specified feeding specifications by setting the relative permittivity of the 3D space in consideration of the input device for inputting and the ion sheath formed on the surface of the antenna element. The electric field strength distribution in the space is calculated based on a predetermined electric field analysis algorithm, and the individual electric field strength distributions are combined by weighting the electric power supply specifications based on the theory of superposition of electric fields. When the plasma density distribution in a specific region becomes the target plasma density distribution when the distribution form is equivalent to the density distribution Under such conditions, a calculation device that solves the power supply specification of the high-frequency power that gives a combined electric field strength distribution in a distribution form corresponding to the target plasma density distribution as an optimization problem based on a predetermined problem solving algorithm, and the calculation device Since it is provided with an output device that outputs the optimum feeding specification, the composite electric field strength distribution by the array antenna and the feeding specification to the array antenna can be analytically and accurately obtained. Therefore, also for the array antenna, it is possible to reduce the development period and the development cost.

Further, since the individual feeding electric field strength distributions are combined based on the principle of superposition of electric fields, the feeding specification giving the combined electric field strength distribution of the distribution form corresponding to the target plasma density distribution is obtained. Can be calculated in a shorter time and with a smaller required memory capacity. If such a calculation method is not adopted, it is necessary to use a calculation device having the calculation capacity of a supercomputer, and it is virtually impossible to analytically determine the power supply specifications at the development site of the plasma generation antenna. However, according to the present invention, since the power supply specification can be calculated using the engineering workstation, the contribution to the development of the plasma generation antenna is great.

[Brief description of drawings]

FIG. 1 is a functional block diagram showing a functional configuration of a plasma generation antenna evaluation apparatus according to an embodiment of the present invention.

FIG. 2 is a front view and a side view showing a shape of an array antenna A according to an embodiment of the present invention.

FIG. 3 is a schematic diagram of an ion sheath formed near the periphery of each U-shaped antenna element # 1 to # 25 in one embodiment of the present invention.

FIG. 4 is a flowchart showing an evaluation method of the array antenna A according to the embodiment of the present invention.

FIG. 5 is an impedance characteristic of each U-shaped antenna element # 1 to # 25 based on the presence or absence of an ion sheath in one embodiment of the present invention.

FIG. 6 is a table showing an optimum solution (optimal phase) of a feeding phase in the embodiment of the present invention.

FIG. 7 is a diagram showing an electric field intensity distribution (calculated value) on the substrate surface and a film thickness distribution (experimental value) on the glass substrate S corresponding to the optimum phase in one embodiment of the present invention.

FIG. 8 is a diagram showing an electric field intensity distribution (calculated value) on a substrate surface and a film thickness distribution (experimental value) on a glass substrate S corresponding to in-phase power feeding in one embodiment of the present invention.

[Explanation of symbols]

1 ... Input device 2 ... Computing device 3 ... Output device 4 ... Storage device 4a ... storage area for individual electric field distribution 4b ... Target plasma density distribution storage area 4c ... FDTD analysis program storage area 4d: conjugate gradient method program storage area # 1 to # 25 ... U-shaped antenna element A: Array antenna (plasma generation antenna) B: Support frame C ... vacuum chamber S: Glass substrate

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Hitoshi Ueda             3-13-1, Minami-cho, Fuchu-shi, Tokyo Corp.             Tomi Room 201 (72) Tomoko Takagi             2-9-10 Ichinomiya, Tama-shi, Tokyo Funada             Room 203 (72) Inventor Norikazu Ito             2947-1 Jobancho, Machida City, Tokyo Maison Pa             Luthere II Room 204 (72) Inventor Masao Yamadera             2-2-1 Otemachi, Chiyoda-ku, Tokyo Stone             Kawashima Harima Heavy Industries Co., Ltd. F term (reference) 4G075 AA24 AA30 BB10 BC04 CA47                 4K030 KA30 KA39                 5F045 AA08 BB10 EH19

Claims (12)

[Claims] 1. A plasma generation antenna evaluation apparatus for evaluating an array antenna including a plurality of antenna elements, wherein a target plasma density distribution in an arbitrary specific area in a three-dimensional space in which the array antenna is installed, It is defined by setting the relative permittivity of the three-dimensional space in consideration of the input device (1) for inputting the design information of the array antenna and the ion sheath (region where plasma does not exist) formed on the surface of the antenna element. The electric field strength distribution (individual power supply electric field strength distribution) in the three-dimensional space when the individual electric power is individually fed to each antenna element according to the power supply specification is calculated based on a predetermined electric field analysis algorithm, and the individual electric power supply field strength distributions are calculated. Based on the theory of superposition of electric fields, the composite electric field strength distribution synthesized by weighting the power supply specifications corresponds to the target plasma density distribution. Under the condition that the plasma density distribution in the specific region becomes the target plasma density distribution when it becomes a form, the power supply specification of the high frequency power that gives the combined electric field strength distribution of the distribution form corresponding to the target plasma density distribution is set to a predetermined value. Plasma comprising an arithmetic unit (2) for solving an optimization problem based on a problem solving algorithm, and an output unit (3) for outputting an optimum power supply specification obtained by the arithmetic unit (2) Generation antenna evaluation device. 2. The plasma generation antenna evaluation apparatus according to claim 1, wherein the problem solving algorithm is a conjugate gradient method. 3. The electric field analysis algorithm is FDTD (F
3. The plasma generation antenna evaluation apparatus according to claim 1, wherein the plasma generation antenna evaluation method is an inite Defference Time Domain method. 4. The plasma generation antenna evaluation apparatus according to claim 1, wherein in the case of a plasma generation antenna in a plasma CVD apparatus or the like, the specific region is a region near the surface of the substrate. 5. The plasma generation antenna evaluation apparatus according to claim 1, wherein the target plasma density distribution has a constant value. 6. The plasma generation antenna according to claim 5, wherein the objective function when solving as an optimization problem is a standardized standard deviation obtained by normalizing the standard deviation of the electric field in a specific region with an average value. Evaluation device. 7. A plasma generation antenna evaluation method for evaluating an array antenna including a plurality of antenna elements, wherein design information of the plasma generation antenna is input,
A step of inputting a target plasma density distribution in an arbitrary specific area in a three-dimensional space in which the plasma generation antenna is installed into an arithmetic device, and an ion sheath (presence of plasma is not present) formed on the surface of the plasma generation antenna. By setting the relative permittivity of the three-dimensional space in consideration of the area), the electric field strength distribution in the three-dimensional space (individual electric power supply field strength distribution) when individual antenna elements are individually fed with the specified feeding specifications Is calculated by a calculation device based on a predetermined electric field analysis algorithm, and the combined electric field intensity distribution obtained by synthesizing the individual electric power supply electric field intensity distributions by weighting the electric power supply specifications based on the principle of superposition of electric fields is the target plasma density. Under the condition that the plasma density distribution of the specific area becomes the target plasma density distribution when the distribution form is equivalent to the distribution And a step of solving a power supply specification of high-frequency power that gives a combined electric field strength distribution having a distribution form corresponding to the target plasma density distribution as an optimization problem using an arithmetic device based on a predetermined problem solving algorithm. Evaluation method for plasma generation antenna. 8. The method for evaluating an antenna for plasma generation according to claim 7, wherein the problem solving algorithm is a conjugate gradient method. 9. The electric field analysis algorithm is FDTD (F
The method for evaluating an antenna for plasma generation according to claim 7 or 8, which is an inite Defference Time Domain) method. 10. The plasma generation antenna evaluation method according to claim 7, wherein in the case of a plasma generation antenna in a plasma CVD apparatus or the like, the specific region is a region near the surface of the substrate. 11. The method for evaluating an antenna for plasma generation according to claim 7, wherein the target plasma density distribution is set to a constant value. 12. The plasma generation antenna according to claim 11, wherein the objective function when solving as an optimization problem is a standardized standard deviation obtained by normalizing the standard deviation of the electric field in a specific region with an average value. Evaluation methods.