JP2000012527A - Method and apparatus for determining etching end point - Google Patents

Abstract

PROBLEM TO BE SOLVED: To satisfactory determine the etching end point by the mode decomposition of an input pattern, using an orthogonal function system, in which the time change of the spectrum intensity of a plasma light is set, and determining the etching end point, based on the coefficient values of specified decomposed mode. SOLUTION: An extracted plasma light is converted into a voltage signal through a monochromator and a photomultipier tube and sent to an input part 21 via an A/D converter, an output signal from the input part 21 is sent to a pattern decomposing step 24 via a noise filter 22 and signal pattern forming step 23, a sent pattern function is decomposed for each degree component, using orthonormal functions, only specified determining elements are sent to an end point determining logic 25 which sends the determined result to an output part 26, and the output part 26 gives a detection signal to an etcher controller when the determined result indicates the etching end point, whereby even when the exposed area ratio is low, the etching end point can be satisfactorily determined.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] The present invention relates to a process for dry-etching a semiconductor material using plasma,
The present invention relates to an etching end point determining method and an etching end point determining apparatus for determining the end point.

[0002]

2. Description of the Related Art FIG. 5 is an explanatory view for explaining a plasma etching step in a semiconductor manufacturing process. In the figure, reference numeral 6 denotes a substrate, on which a film 31 as a processing material is formed. Further, a mask 32 is applied on the upper portion thereof, and the mask 32 is subjected to patterning removal only by etching or the like only at an etched portion. Such a substrate 6 is fixed in a reaction chamber of a plasma etching apparatus (not shown), and the etched portion of the film 31 from which the mask 32 has been removed is etched.

[0003] Plasma generated when electrons collide with a reaction gas is used for plasma etching. Specifically, electrons supplied by a high-frequency discharge or a microwave discharge collide with reaction gas molecules introduced into the reaction chamber, causing decomposition, ionization, and activation (neutral radical generation) of the gas molecules, resulting in plasma. Generate. Various ion species and excited species (radicals) exist in the plasma. The radicals generated in this manner change the processed portion of the film 31 formed on the substrate 6 into a volatile reaction product, thereby performing etching.

At this time, if the etching of the film 31 is not completed or the substrate 6 is over-etched, a wiring failure such as a disconnection or a short circuit occurs, which affects the characteristics of a semiconductor to be manufactured. Therefore, it is an important issue in the etching process to detect the end point so that the etching ends at the boundary between the film 31 and the substrate 6.

As a conventional method for detecting the end point of the etching, for example, there is a "method for detecting the end point of the dry etching reaction" disclosed in Japanese Patent Application Laid-Open No. 56-115536. This involves extracting a specific wavelength component of plasma light during an etching reaction in a dry etching process, detecting a decreasing tendency of the light amount immediately before the end of the etching reaction based on a differential value of a function representing the light amount per time, and then detecting the light amount. This is a method in which the point when the value falls below a certain value is set as the end point of the etching. Another conventional method is disclosed in, for example,
There is an "etching end point detection method" disclosed in JP-A-62127. This is because a part of the plasma light during the etching reaction is selectively extracted, the amount of change in the amount of light is obtained based on the second derivative of the function representing the amount of light per time, and the amount of change immediately before the end of the etching reaction is equal to the set value. Is determined as the end point of the etching.

[0006]

Generally, a high frequency is superimposed on a light quantity of a plasma light, that is, a spectrum intensity due to noise. Further, depending on the type of gas used for etching, a waveform representing a spectrum intensity may have low-frequency fluctuation. Such fluctuations are peculiar to the plasma depending on the gas type and cannot be avoided. These events cause erroneous detection in a situation where the end point of etching is detected based on the amount of change in spectral intensity.

[0007] All of the above-mentioned prior arts utilize the amount of change in spectral intensity for end point detection. Therefore, for example, the ratio of the area of the portion to be etched (unmasked portion) to the area to be etched (substrate area) as in a hole etching process for a contact hole and a via hole of a silicon oxide film (hereinafter referred to as an etching aperture ratio) ) Is small, specifically, about 4% or less, the detection accuracy is poor because the difference between the amount of change in the spectrum intensity to be used and the noise component superimposed on it is small, and further 1% In the following cases, it is extremely difficult to determine the end point by distinguishing between the spectral intensity and its noise component.

The present invention has been made in view of the above-mentioned circumstances, and a signal change of plasma light during an etching reaction is taken as a pattern, and the signal change pattern is analyzed by using an orthogonal function system. It is an object of the present invention to provide an etching end point determination method capable of clarifying a change tendency and appropriately determining an etching end point even when an etching aperture ratio is small.

[0009]

According to a first aspect of the present invention, there is provided a method for determining an etching end point, comprising extracting one or more specific wavelength components of plasma light during an etching reaction when a film formed on a substrate is etched by plasma. An etching end point determination method for determining an etching end point based on a change in the spectrum intensity, wherein a temporal change in the spectrum intensity of the extracted plasma light within a predetermined period is set as an input pattern, and the set input pattern is defined as an orthogonal function. A mode is decomposed using a system, and an etching end point is determined based on a value of a coefficient of a predetermined mode among coefficients of the decomposed mode.

[0010] A method of determining an etching end point according to a second aspect of the present invention is to obtain a plurality of wavelength components of the extracted plasma light by modal decomposition of a temporal change in the spectrum intensity within a predetermined period using an orthogonal function system. The etching end point is estimated based on the value of the coefficient of the given mode, and the etching end point is determined by summing up the etching end points estimated for each wavelength component.

According to a third aspect of the present invention, in the method of determining an end point of etching, a value of a coefficient in a predetermined mode crosses a predetermined first threshold value a predetermined number of times and then crosses a second threshold value a predetermined number of times. It is characterized by estimating or determining that the etching end point has been reached.

[0012] A method of determining an etching end point according to a fourth aspect of the present invention performs a noise removal process on a set input pattern.
It is characterized in that the input pattern after processing is subjected to mode decomposition using an orthogonal function system.

According to a fifth aspect of the present invention, there is provided an etching end point judging apparatus which extracts one or more specific wavelength components of plasma light during an etching reaction when etching a film formed on a substrate by plasma, and changes a spectrum intensity thereof. An etching end point determining apparatus that determines an etching end point by using an input function, a setting unit that sets a temporal change in the spectral intensity of the extracted plasma light within a predetermined period as an input pattern, and using the set input pattern by an orthogonal function system. And a determination unit for determining an etching end point based on a value of a coefficient of a predetermined mode among the coefficients of the decomposed mode.

The outline of pattern analysis using an orthonormal function system as the orthogonal function system will be described below. The sampling period of the A / D converter for A / D converting the signal after photoelectric conversion is ΔT, and the output signal at time t = kΔT is y
(K). Since y (k) has a noise component, the noise component is simply removed by calculating, for example, N moving averages. Assuming that the signal after removing the noise component is y _m (k), y _m (k) is expressed as follows.

[0015]

(Equation 1)

FIG. 6 shows C ₄ F ₈ and O as reactive gases.
_{In the} silicon oxide film etching process using ₂ ,
It is a graph which shows the change of the output signal y (k) when an etching aperture ratio is 4%. In the figure, the horizontal axis represents time, and the vertical axis represents spectrum intensity, and the output signal y
(K), from which the output signal y (k) generally shows a gradual increase while vibrating violently with a substantially constant amplitude, and a gradual decrease once around 43 seconds from the start of measurement. After turning to, it can be seen that the trend is gradually increasing again around 48 seconds. Similarly, FIG. 7 is a graph showing a change in the output signal y (k) when the etching aperture ratio is 1%. It can be seen that the output signal y (k) has a uniform and gradually increasing tendency while vibrating violently with a substantially constant amplitude.

FIG. 8 is a graph showing a change in a signal y _m (k) obtained by removing a noise component from the output signal y (k) shown in FIG. In the figure, the horizontal axis represents time, and the vertical axis represents spectrum intensity, and represents the signal y _m (k).
From the waveform, the substantially constant amplitude vibration seen in the output signal y (k) is filtered, and the increasing and decreasing tendency of the output signal y (k) appears more clearly. Similarly, FIG. 9 is a graph showing a change in the signal y _m (k) obtained by removing the noise component from the output signal y (k) shown in FIG. Oscillations of approximately constant amplitude seen in the output signal y (k) are filtered, and the increasing tendency of the output signal y (k) appears more clearly. Although the moving average method has been exemplified as a method for removing the noise component, a Butterworth filter (or Wagner filter) that is general in the field of signal processing technology may be used.

Next, the time series signal of y _m (k) is stored in the storage device for a fixed time U = 2MΔT, and the pattern function z of the signal change at time t = kΔT is stored.
_k (τ) is defined as follows.

[0019]

(Equation 2)

Next, the pattern function z _k (τ) of the signal change at time t = kΔT is decomposed into a plurality of order components using an orthonormal function system. An example of the orthonormal function system is shown below. _{ψ 0 (τ) = A ψ} 1 (τ) = Bτ ψ 2 (τ) = Cτ 2 + D ψ 3 (τ) = Eτ 3 + Fτ ψ 4 (τ) = Gτ 4 + Hτ 2 + K ... coefficients A, B, C, D, E, F, G, H, K,... Are coefficients determined so as to satisfy the following normalized orthogonal condition. Note that δ _ij is 1 when i = j, and i ≠ j
Is a function that is 0 when. Symbols <and> represent inner products.

[0021]

(Equation 3)

By calculating the inner product of the signal change pattern function z _k (τ) and the orthonormal function system, the time t = kΔ
The component w _i (k) of order i in T is obtained. Below w
_i (k).

[0023]

(Equation 4)

The pattern function z _k (τ) decomposed into a plurality of order components based on the above function is expressed as follows using an orthonormal function system. _{z k (τ) = w 0} (k) ψ 0 (τ) + w 1 (k) ψ
_{1 (τ) + w 2 (} k) ψ 2 (τ) + w 3 (k) ψ
₃ (τ) +…

FIG. 10 is an explanatory diagram for explaining a pattern function z _k (τ) _obtained by pattern analysis using an orthonormal function system. That is, low order components represent components of simple changes in the pattern function, and high order components represent components of complex changes. Among these, the component value of the lower dimension of the pattern function is used for the determination of the etching end point according to the present invention. If the etching aperture ratio is small, w _i
Since the absolute value of (k) is also small, W _i (k) obtained by multiplying the above-described w _i (k) by a gain Q of an appropriate magnitude may be used as the i-th component. The following shows W _i (k). _{W i (k) = Q ×} w i (k)

FIG. 11 shows the primary components when the measurement conditions are an etching aperture ratio of 4%, a sampling period ΔT = 10 msec, and the number of moving averages N = 100, M = 300, and a gain Q = 100,000. W is a graph showing changes in ₁ (k). The figure shows the waveform pattern of the primary component W ₁ (k) by assigning time to the horizontal axis and component values to the vertical axis. According to the waveform, the increase and decrease of the component values from the start of measurement are shown. The level is gradually lowered while repeating alternately, crossing the time axis around 46 seconds, recording a value below this, that is, a negative value, then turning to an increasing trend and crossing the time axis again around 53 seconds It can be seen that. FIG.
Is also 1 when the etching aperture ratio is 1%.
Is a graph showing changes in the next component W ₁ (k). According to the waveform, the level is gradually lowered while alternately increasing and decreasing the component value from the start of measurement, and the value crosses the time axis below 52 seconds after 52 seconds, that is, a negative value It turned to an increasing trend, and it can be seen that it crossed the time axis again at around 55 seconds.

As the orthogonal function system, there are a Legendre function, a Hermitian function, a Chebyshev function and the like in addition to the above-mentioned orthonormal function system. The orthogonal function system described above has a feature that a prescribed function is simple and easy to understand. Another characteristic of orthogonal function expansion is that it is suitable for real-time processing because calculating the coefficient of the orthogonal function in advance allows the calculation result to be obtained simply by calculating the inner product of the coefficients in the actual calculation processing. No. Furthermore, it is possible to easily increase the expansion order as needed.

The determination of the etching end point will be described.
The determination of the end point is performed in a value range defined by threshold values Vp and Vn (Vn ≦ Vp) appropriately set according to the etching process, that is, a value range Rp and a value range Rp representing a region in which the value is larger than the threshold value Vp. Is greater than or equal to the threshold Vn and the threshold V
The value range Rz representing the region that is equal to or less than p and the threshold value Vn
The determination is performed based on which of the value ranges Rn representing the smaller regions is included.

More specifically, if the change tendency of the output signal y (k) of the A / D converter is a down slope, W ₁
After (k) belongs to the range Rn S times or more, first the range Rz
Alternatively, at time t = k _d ΔT at which Rp is reached, the time of the etching end point is determined to be (k _d -αM) ΔT. α is
This value is appropriately set when 0 ≦ α ≦ 1. Also,
When the change trend of the output signal y (k) is upslope, W ₁ (k) is at time t = k _u ΔT that led to the first range Rz or Rn after belonged least S times range Rp,
Determining the time of etching end point and (k _u -αM) ΔT.

The etching end point judging method of the first to fourth inventions and the etching end point judging apparatus of the fifth invention analyze the waveform pattern of a given input signal using an orthogonal function system. Thus, it is hardly affected by the noise superimposed on the input signal, specifically, the spectrum intensity of the plasma light. Therefore, even when the etching aperture ratio is small, the end point of the etching can be determined well.

When the emission spectrum of the reaction product produced by the etching reaction and the emission spectrum of the reaction gas used for the etching reaction are extracted from the plasma light during the etching reaction, the former is obtained near the etching end point. Shows the behavior of a down slope, and the latter shows the behavior of an up slope. For example, in the etching process of the silicon oxide film by fluorocarbon gas such as C ₄ F _8, SiF
439.7 nm of F shows a down slope, and 687.5 nm of F shows an up slope.

FIG. 13 is an explanatory diagram showing such emission spectrum intensities at two specific wavelengths. In the figure, the time axis is assigned to the horizontal axis and the spectrum intensity is assigned to the vertical axis, and the change over time in the emission spectrum intensity at two specific wavelengths, namely, the specific wavelength of the reaction product and the specific wavelength of the reaction gas is shown. Immediately after the start of the etching reaction, a period in which the spectrum intensities of the reaction product and the reaction gas are both unstable is observed. Thereafter, as the etching reaction proceeds, the spectrum intensity A of the reaction product is higher and the spectrum intensity B of the reaction gas is higher.
Is stable at a low level (reaction phase). Then, as the etching end point is approached, the spectrum intensity A of the reaction product shows a decreasing tendency, and the spectrum intensity B of the reaction gas shows an increasing tendency (end period). After the etching end point,
The spectral intensity A of the reaction product is stable at a low level, and the spectral intensity B of the reaction gas is stable at a high level.

Based on such two temporal characteristics of the spectrum intensities, the waveform pattern of the emission spectrum related to the reaction product and the waveform pattern of the emission spectrum related to the reaction gas are combined, and the etching is performed based on the respective waveform patterns. Is estimated, and the estimated end points of the plurality of etchings are integrated to determine the etching end point based on, for example, an AND condition or an OR condition, thereby improving the reliability of the determination result.

In the etching end point judging method according to the third aspect of the present invention, a plurality of wavelength components are extracted from the plasma light, the etching end point is estimated on the basis of the change over time of each waveform pattern, and the estimated etching end points are integrated. Since the etching end point is determined, the etching end point can be determined with higher reliability.

[0035]

FIG. 1 is a block diagram showing the configuration of a plasma etching apparatus according to an embodiment of the present invention. The plasma etching system uses Electron Cyclotron Res
Onance (hereinafter, referred to as ECR) is to generate plasma by excitation to etch a processed portion of a film formed on a substrate, that is, a portion not masked by a mask.

In FIG. 1, reference numeral 1 denotes a cylindrical plasma generation chamber, and at the center of the upper side wall of the plasma generation chamber 1, a microwave inlet 1b sealed with a quartz glass plate 1a is provided, and the microwave inlet 1b faces the microwave inlet 1b. A plasma outlet 1c is formed at the center of the lower side wall. Furthermore, a flow passage 2 for flowing cooling water is formed in the other side wall of the plasma generation chamber 1, and the water flow pipe 2 a
And drain pipe 2b.

The microwave introduction port 1b is connected to one end of a microwave waveguide 3 emitted from a microwave oscillator (not shown), and a reaction chamber 4 is provided on the plasma outlet 1c side of the plasma generation chamber 1. It is installed continuously. An exciting coil 5 for forming a magnetic field having a required strength in the plasma generation chamber 1 is provided around the plasma generation chamber 1 and concentrically therewith.

At the center of the reaction chamber 4, a substrate 6 as an object to be processed is provided.
Is provided, and the mounting table 7 is provided with a suction mechanism 8 using an electrostatic chuck or the like, and is configured to apply high frequency power. A gas supply pipe 4a for supplying a reaction gas, for example, a chlorofluorocarbon gas such as C ₄ F _8, is provided on a side wall of the reaction chamber 4, and an exhaust port 4b is provided at the center of a lower side wall of the reaction chamber 4. . Further, on the side wall of the reaction chamber 4, there is provided a window 9 for taking out plasma light made of quartz glass.

The plasma light taken out by the take-out window 9 of the reaction chamber 4 is provided to a monochromator 11 where the required spectral portion, for example, when the reactive gas is fluorocarbon gas such as C ₄ F ₈ is silicon fluoride Specific wavelength of (SiF)
Only the 439.7 nm plasma light is split and the photomultiplier tube 12
Given to. The spectral intensity of the spectrum applied to the photomultiplier tube 12 is converted into a voltage signal, and is converted into an A / D converter.
13 where it is converted to a digital signal.

The digital signal is an end point detection computer.
14 where the data is processed to determine the etch end point. The end point detection computer 14 outputs a detection signal when an etching end point is detected.
Give to 15. Etching apparatus controller 15, when receiving the detection signal, to terminate the etching reaction,
The supply of microwaves by the microwave oscillator (not shown) and the supply of high-frequency power to the mounting table 7 are stopped.

Next, an outline of the operation of the above-described plasma etching apparatus will be described. The plasma etching apparatus adsorbs and fixes the substrate 6 mounted on the mounting table 7 by the suction mechanism 8, and exhausts the gas through the exhaust port 4 b to reach the required pressure in the plasma generation chamber 1 and the reaction chamber 4. After that, the reaction gas is supplied at a predetermined flow rate from the gas supply pipe 4a. A predetermined current is supplied to the exciting coil 5 to form a magnetic field in the plasma generation chamber 1, and a microwave is introduced into the plasma generation chamber 1 to excite the reaction gas by ECR to generate plasma. Further, high-frequency power is applied to the mounting table 7.

The generated plasma is guided from the plasma outlet 1c to the reaction chamber 4 by the diverging magnetic field formed by the exciting coil 5, and is irradiated on the substrate 6 fixed on the mounting table 7. The high-frequency power applied to the mounting table 7 accelerates ions in the plasma. The irradiated plasma reacts with a film (not shown) formed on the substrate 6 by etching, so that the film is etched. The plasma light during this etching reaction is extracted from the extraction window 9,
Only the required spectrum portion is used for determining the etching end point.

FIG. 2 is a data flow diagram showing the processing steps of the end point detection computer 14. The output signal y (k) of the A / D converter 13 is received by the input unit 21 and sent to the noise filter 22. The output signal y (k) sent to the noise filter 22 has its noise component removed therefrom by a moving average method or the like, and the processed signal y _m (k) is sent to a signal pattern creation step 23. The signal y _m (k) sent to the signal pattern creation step 23 is processed into a pattern function z _k (τ), which is time-series data, and sent to the pattern decomposition step 24.

The pattern function z _k (τ) sent to the pattern decomposition step 24 is decomposed there for each order component using an orthonormal function system, and a predetermined judgment element, for example, a primary component w
Only ₁ (k) is sent to the end point determination logic 25. The judgment element sent to the end point judgment logic 25 receives the end point judgment there, and the judgment result is sent to the output unit 26. The output unit 26 provides a detection signal to the etching apparatus controller 15 when the given determination result indicates that the etching end point has been detected.

FIG. 3 shows the primary component W ₁ (k) shown in FIG.
Iterative threshold S = 200 for the signal change pattern of
It is a graph showing the determination result when Vp = Vn = 0 and α = 0. In the figure, the horizontal axis represents time, and the vertical axis is assigned a judgment value to represent the value of a judgment flag (a flag that becomes an excited state at the end point of etching), and the judgment flag is excited around 53 seconds from the start of measurement. Thus, it can be seen that the etching end point is well determined. Also, FIG.
FIG. 13 is a graph illustrating a determination result regarding a signal change pattern of the primary component W ₁ (k) illustrated in FIG. 12. 55 from the start of measurement
It can be seen that the determination flag is excited around second, and that the etching end point is well determined even when the etching aperture ratio is 1%.

In the above embodiment, the etching is performed.
Component w for determining the end point of ₁Use only (k)
Has been described, but another component, namely, 2
Next and third order components may be added and used for the determination.

[0047]

According to the etching end point judging methods of the first to fourth inventions and the etching end point judging apparatus of the fifth invention, a given input signal is taken as a pattern, and this waveform pattern is used in an orthogonal function system. It is less susceptible to noise superimposed on the spectral intensity of the spectrum selectively extracted for pattern analysis, and therefore, it is possible to determine the end point of etching well even when the etching aperture ratio is small.

According to the etching end point judging method of the third invention, a plurality of wavelength components of the plasma light during the etching are extracted and the etching end point is judged based on the temporal change of each waveform pattern, so that a more accurate judgment result can be obtained. Can be obtained.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration of a plasma etching apparatus according to an embodiment of a method for determining an etching end point according to the present invention.

FIG. 2 is a data flow diagram showing a process of an end point detection computer.

FIG. 3 is a graph showing a determination result for a signal change pattern of a primary component.

FIG. 4 is a graph showing a determination result for a signal change pattern of a primary component.

FIG. 5 is an explanatory diagram illustrating a plasma etching step in a semiconductor manufacturing process.

FIG. 6 is a graph showing a change in an output signal when an etching aperture ratio is 4%.

FIG. 7 is a graph showing a change in an output signal when an etching aperture ratio is 1%.

FIG. 8 is a graph showing a change in a signal obtained by removing a noise component from an output signal.

FIG. 9 is a graph showing a change in a signal obtained by removing a noise component from an output signal.

FIG. 10 is an explanatory diagram illustrating a pattern function that has been subjected to pattern analysis using an orthonormal function system.

FIG. 11 shows a case where the etching aperture ratio is 4%.
It is a graph which shows the change of the next component.

FIG. 12 shows a case where the etching aperture ratio is 1%.
It is a graph which shows the change of the next component.

FIG. 13 is an explanatory diagram showing emission spectrum intensities at two specific wavelengths.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Plasma generation room 3 Waveguide 4 Reaction room 6 Substrate 13 A / D converter 14 End point detection computer 22 Noise filter 23 Signal pattern creation process 24 Pattern disassembly process 25 End point judgment logic

Continued on the front page F term (reference) 2G043 AA03 CA02 CA07 EA08 FA03 FA06 GA06 GB01 JA04 LA02 MA01 MA04 NA01 NA05 5F004 BA14 CB02 CB16 DA00 DA03

Claims (5)

[Claims] When etching a film formed on a substrate by plasma, one or more specific wavelength components of plasma light during an etching reaction are extracted, and an etching end point is determined based on a change in spectrum intensity thereof. A method of setting a temporal change in the spectral intensity of the extracted plasma light within a predetermined period as an input pattern, mode-decomposing the set input pattern using an orthogonal function system, and calculating a coefficient of the decomposed mode. Wherein the etching end point is determined based on a value of a coefficient of a predetermined mode. 2. A method according to claim 1, wherein each of the plurality of wavelength components of the extracted plasma light is etched based on a mode coefficient obtained by modulating the change over time of the spectral intensity within a predetermined period using an orthogonal function system. 2. The method according to claim 1, wherein an end point is estimated, and the etching end point is determined by summing up the etching end points estimated for each wavelength component. 3. After the coefficient value of the predetermined mode crosses the predetermined first threshold value a predetermined number of times, and crosses the second threshold value a predetermined number of times, it is estimated that the etching end point has been reached. The method according to claim 1 or 2, wherein the determination is made. 4. The etching end point according to claim 1, wherein the set input pattern is subjected to noise removal processing, and the processed input pattern is subjected to mode decomposition using an orthogonal function system. Judgment method. 5. When etching a film formed on a substrate by plasma, one or more specific wavelength components of plasma light during an etching reaction are extracted, and an etching end point is determined based on a change in spectrum intensity thereof. An apparatus, comprising: setting means for setting, as an input pattern, a temporal change in the spectrum intensity of the extracted plasma light within a predetermined period; decomposition means for modulating the set input pattern using an orthogonal function system; Determining means for determining an etching end point based on a value of a coefficient of a predetermined mode among the coefficients of the performed mode.