JP2910759B1 - Plasma particle analysis method and computer-readable recording medium for recording plasma particle analysis program - Google Patents

Abstract

Abstract: PROBLEM TO BE SOLVED: To reduce the plasma particle analysis processing time without sacrificing analysis accuracy. SOLUTION: The distribution of the particle density of electrons, ions, and neutral particles in the plasma, and the distribution of potential and electron temperature in the plasma are obtained over the entire region of the plasma state using a fluid model, and the distribution in the plasma is obtained from the obtained distribution. The distribution of the electric field intensity and the distribution of the ionization rate are obtained, the ion sheath region and the sub-sheath region are extracted from the entire region in the plasma state from the distribution of the electric field intensity and the distribution of the ionization ratio, and the Monte Carlo method is used in the ion sheath region and the sub-sheath region. In addition to analyzing the motion of electrons, the reaction constant of electrons with electrons, ions, and neutral particles is determined.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a plasma particle analysis method and a computer-readable recording medium for recording a plasma particle analysis program, and more particularly to a fluid model based on a difference equation and a scattering model based on a Monte Carlo method. The present invention relates to a plasma particle analysis method using a so-called hybrid model using a computer and a computer-readable recording medium for recording a plasma particle analysis program.

[0002]

2. Description of the Related Art Conventionally, there is a method using a fluid model as a method for analyzing particles of plasma. In the conventional method using a fluid model, the entire region of the plasma state is divided into a number of meshes, and a continuous equation and Poisson equation are applied to each divided region. Specifically, the continuity equation and Poisson equation are each rewritten as a difference equation, and they are simultaneously applied to each section area for analysis, and the particle density of electrons, ions, and neutral particles in each section area, and the plasma area This is to calculate the distribution of the entire potential. However, in a low-pressure gas plasma, scattering of particles is reduced, and the speed of the particles is largely shifted from the Maxwell distribution centered on the drift speed. For this reason, when applying the plasma particle analysis method to low-pressure gas plasma, there is a major problem that the analysis accuracy is reduced.

On the other hand, a plasma particle analysis method using the Monte Carlo method has been proposed. This method
This is a method of calculating the motion of electrons using random numbers, and a scattering model can be considered. For this reason, there is a great advantage that high-precision analysis including generation and annihilation of each particle by interaction between an electron and each particle can be performed, but there is also a major problem that a calculation time is long. .

On the other hand, recently, an analysis method using a hybrid model combining both a fluid model based on a difference equation of a continuous equation and a Poisson equation and a scattering model based on a Monte Carlo method has been developed. This is described in the literature (J. Sommerer and J. Kushner J. Appl. Phys. 71 (4) 1992
pp.1654-1673). That is, the Monte Carlo method is applied only to the electrons over the entire region between the opposed electrodes for generating the plasma, and the electron energy distribution after a predetermined time and the distribution of the reaction constant between the electrons and each particle are obtained. Further, using these distributions, a fluid model relating to electrons, ions, and neutral particles is analyzed, and each distribution of the particle density and potential at this time is obtained. Using the obtained distributions of the particle density and the potential, the Monte Carlo method is again used to calculate the electron energy distribution and the distribution of the reaction constant between the electrons and each particle after the next predetermined time. By repeating these steps, it is possible to calculate the change over time in the particle density distribution and the potential distribution of each particle. This analysis method using the hybrid model is particularly effective when the energy distribution of electrons deviates from the thermal equilibrium in a low-pressure plasma region which is a problem in the fluid model. Also, there is a great advantage that the calculation time can be greatly reduced as compared with the case where all the analyzes are performed by the Monte Carlo method without using any fluid model.

[0005]

By the way, in the above conventional analysis method using the hybrid model,
In order to increase the calculation accuracy, it is necessary to make the mesh finer. In such a case, the analysis method using the above-described conventional hybrid model still requires a long calculation time. For this reason, development of an analysis method capable of shortening the calculation time without lowering the calculation accuracy is desired.

SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and has a plasma particle analysis method capable of maintaining the accuracy of plasma particle analysis in the entire plasma state and further reducing the calculation time. It is another object of the present invention to provide a computer-readable recording medium for recording a plasma particle analysis program.

[0007]

Means for Solving the Problems To solve the above problems, the invention according to claim 1 relates to a plasma particle analysis method for analyzing a plasma state used for etching or film formation, and the method using a fluid model. Over the entire region of the plasma state, the distribution of the particle density of electrons, ions, and neutral particles in the plasma, and the distribution of the potential and the electron temperature are obtained, and from the obtained distribution, the distribution and the ionization of the electric field intensity in the plasma. Determine the distribution of the rate, extract the ion sheath region and the sub-sheath region from the entire region of the plasma state from the distribution of the electric field intensity and the distribution of the ionization rate, using the Monte Carlo method in the ion sheath region and the sub-sheath region, It is characterized in that the motion of the electrons is analyzed and the reaction constant of the electrons with the electrons, ions and neutral particles is determined.

According to a second aspect of the present invention, when a reaction gas used for etching or film formation is introduced between the opposed electrodes and power is applied to the opposed electrodes to generate plasma between the opposed electrodes. The present invention relates to a plasma particle analysis method for numerically analyzing the plasma state, wherein (1) using a fluid model, at least the distribution of the particle density of electrons, ions and neutral particles existing between the opposed electrodes; The distribution of the potential between the counter electrodes and the distribution of the electron temperature are obtained. (2) The distribution of the electric field intensity and the distribution of the ionization rate are obtained from the distribution of the particle density obtained by the fluid model and the distribution of the electric potential and the electron temperature. (3) From the distribution of the electric field intensity and the distribution of the ionization rate, a plasma region in which the particle density of the electrons is substantially equal to the particle density of the ions; A high ion sheath region than degrees,
Adjacent to the ion sheath region, the electric field intensity and the ionization rate are higher than the plasma region, and extract a sub-sheath region lower than the ion sheath region,
(4) In the ion sheath region and the sub-sheath region, the motion of the electrons is analyzed for a predetermined time by a Monte Carlo method, and the interaction between the electrons and the electrons, ions, and neutral particles is analyzed, and the electrons, It is characterized in that the generation rate and extinction rate of ions and neutral particles are determined.

According to a third aspect of the present invention, when a reaction gas used for etching or film formation is introduced between opposed electrodes and power is applied to the opposed electrodes to generate plasma between the opposed electrodes. A plasma particle analysis method for numerically analyzing the state of the plasma, wherein (1) a particle density distribution of at least electrons, ions, and neutral particles existing between the opposed electrodes using a fluid model; The distribution of the potential between the opposed electrodes and the distribution of the electron temperature are obtained. (2) The distribution of the electric field intensity and the distribution of the ionization rate are obtained from the distribution of the particle density obtained by the fluid model and the distribution of the electric potential and the electron temperature. (3) From the distribution of the electric field intensity and the distribution of the ionization rate, a plasma region where the particle density of the electrons is substantially equal to the particle density of the ions, and the particle density of the ions Extracting an ion sheath region higher than the particle density and a sub-sheath region adjacent to the ion sheath region, the electric field intensity and the ionization rate being higher than the plasma region and lower than the ion sheath region; In the ion sheath region and the sub-sheath region, the motion of the electrons is analyzed for a predetermined time by a Monte Carlo method, and the interaction between the electrons and the electrons, ions, and neutral particles is analyzed, and the electrons, ions, and The generation rate and extinction rate of the neutral particles are obtained, and (5) the electron and ion and the neutral particle generation rate and the extinction rate obtained in the above (4) are used. 1) to obtain the particle density distribution of electrons, ions and neutral particles existing between the opposed electrodes, and the potential and electron temperature distribution between the opposed electrodes. It is a symptom.

A fourth aspect of the present invention is directed to the plasma particle analyzing method according to the third aspect, wherein (1) to (5) according to the third aspect are repeated so that the distance between the opposed electrodes in a steady state is increased. And the distribution of the particle density of electrons, ions, and neutral particles existing in the above, and the distribution of the potential between the opposed electrodes and the electron temperature.

According to a fifth aspect of the present invention, there is provided the method of analyzing particles of plasma according to any one of the first to fourth aspects, wherein a continuous equation, a Poisson equation, and an energy transport are used in the analysis using the fluid model. It is characterized by using an equation.

The invention according to claim 6 relates to a computer-readable recording medium for recording a particle analysis program for causing a computer to execute the plasma particle analysis method according to any one of claims 1 to 5.

[0013]

According to the present inventors, in the actual plasma state, the ionization rate and the electric field intensity are small in the plasma region where the ion density and the electron density occupying about ／ of the entire region are almost equal, and the location is small. We focused on the fact that the change was small, the ionization rate and the electric field intensity were large in the ion sheath region and its peripheral portion, and the change in place was large. Actually, the scattering model by the Monte Carlo method, which calculates the motion of each electron, is applied only to the ion sheath region and its surroundings.In the plasma region, the analysis accuracy is reduced even if the fluid model is applied, not the scattering model. Did not.
According to the configuration of the present invention, a fluid model is applied to electrons, ions, and neutral particles over the entire region of the plasma state, and the motion of electrons is calculated only in the ion sheath region and the periphery using the Monte Carlo method. . Thus, the calculation time can be reduced without lowering the accuracy of the plasma particle analysis method.

Further, by using the energy transfer equation in addition to the continuous equation, Poisson's equation, and the like in the analysis using the fluid model, it is possible to handle electrons and ions that are in a non-equilibrium state in the fluid model. In addition to the improvement, the calculation accuracy of the ionization rate used in determining the ion sheath region and the sub sheath region can be particularly improved. In addition, if the particle analysis method having the above configuration is recorded on a recording medium, technology transfer can be easily performed, and an unspecified number of particles can be used.

[0015]

Embodiments of the present invention will be described below with reference to the drawings. First Embodiment FIG. 1 is a block diagram showing an outline of a plasma particle analysis method according to a first embodiment of the present invention. In the first embodiment, as shown in the figure, the calculation by the fluid model and the calculation by the scattering model are alternately repeated. In other words, one is plasma particle analysis in the whole region of plasma generation using a fluid model, and the other is
9 is a particle analysis of plasma in an ion sheath region and a sub sheath region of a whole plasma generation region using a scattering model by a Monte Carlo method. First, in the fluid model,
Rewrite the continuity equation, Poisson equation and energy transport equation into difference equations.

Hereinafter, a continuous equation, a Poisson equation, and an energy transport equation which are the basis of the difference equation will be described. In this case, the symbols used represent the following physical quantities,
The suffixes j and k attached to the symbols representing the physical quantities represent the types of particles. When j and k = 1, electrons indicate 2, ions 2 indicate neutral particles, and neutral particles 3 indicate neutral particles.

[0017]

(Equation 1)

J _j in the equation (1) indicates the flow velocity, and the equation (2)
Given by Here, the sign of the portion due to the electric field is + for electrons and − for ions, and the term of the portion due to the electric field is deleted for neutral particles.

[0019]

J _j = ± n _j · μ _j · ▽ φ−D _j · ▽ n _j (2)

[0020]

３ ² φ = e / ε ₀ · (n ₂ −n ₁ ) (3)

[0021]

(Equation 4)

[0022]

Q _j = j _j · h _j −K _j (n _j , Te) · ▽ Te (5)

[0023]

H ₁ = 5/2 kb · Te (6)

Here, n _j , n _k : density of electrons, ions and neutral particles (pieces / cm ³ ) S _j : generation rate (pieces / cm ³ · sec) κ _jk : extinction rate (pieces / cm ³⁾ · Sec) φ: potential (V) ε ₀ : dielectric constant of vacuum (F / cm) n ₂ : ion density (pieces / cm ³ ) n ₁ : electron density (pieces / cm ³ ) μ: mobility (Cm ² / V · sec) E: applied electric field (= ▽ φ) (V / cm) D: diffusion constant (cm ² / sec) h ₁ : enthalpy of electrons (erg) q ₁ : heat flux by electrons ( erg / cm ² · sec) j ₁ : flux (pieces / cm ² · sec) K ₁ : thermal conductivity (erg / cm · deg · sec) Te: electron temperature (K) e: electron charge (C) kb: Boltzmann's constant (erg / K).

When these are actually applied to the particle analysis of plasma, for example, a two-dimensional mesh is generated in a region between the opposing electrodes, and a general difference method is used here as a spatial discretization method. As a method, the three equations (1), (3) and (4) are rewritten into difference equations using an implicit method. Simultaneously calculate them for electrons, ions, and neutrons. In the Monte Carlo method, analysis of a reaction due to collision between an electron and each particle and calculation of electron scattering are performed.

[0026]

[Mathematical formula-see original document] First, the particles that react are j, and the reaction process is m. The collision time interval Δt is the maximum collision frequency ν
_{Using the max} and the general random number r1, the calculation is performed by Δt = −ln (r1) / ν _max (7). Here, Δt is set to be sufficiently smaller than the time interval δt. Next, generate a general random number r2

[0027]

In the case of Equation 8] _{r2> ν l, null / ν} max (8), the actual collision occurs.

[0028]

Where ν _{l, null} is Is the ineffective collision reaction frequency at which no reaction occurs.

[0029]

The type m of the reaction is determined by P1 _{, m-1} <r2 <P1 _{, m} (10). Here, P _{l, m} is the sum of the reaction probabilities. l indicates the energy range.

In determining the type m of the reaction according to the equation (10) _, a table of the energy ranges of a plurality of electrons and the probabilities P1 _{, m} of all reactions occurring in this energy range is prepared. After doing so, a random number r2 is generated. Then, as shown in the equation (10), the reaction corresponding to the random number r2 is determined from the reaction probabilities P1 _{, m} corresponding to the energies of these electrons. The types of reactions include elementary reaction processes that occur in plasma, such as ionization, electron attachment, and electron collision. Based on this reaction, the formulas (11) and (1)
According to 2), the particle generation rate S _j for the reaction process m
And the extinction rate κ _jk .

[0031]

S _j = S _j + Δ _1j (11)

[0032]

Κ _jk = κ _jk + Δ _2j (12)

Here, Δ _1j and Δ _2j are the generation rate and the extinction rate per corresponding particle. Next, analysis of electron scattering will be described. The random numbers r3, r4 are generated, and the trajectory of the scattered electrons is calculated by equations (13) to (15). θ and ψ indicate the polar angle and azimuth after scattering, respectively.

[0034]

Cos θ = 1-2r3 (13)

[0035]

Sin θ = √ (1−cos 2 θ) (14)

[0036]

１５ = 2π · r4 (15)

The energy of the scattered electrons is expressed by equation (16). Eei and Eef indicate the energy of the electrons before and after scattering, respectively.

[0038]

Eef = Eei · (1 + cosθ) / 2 (16)

Further, in order to analyze the motion of the electrons after the scattering, the equation of motion shown by the equation (17) is used.

[0040]

[Equation 17]

[0041]

V _x = dx / dt (18)

[0042]

V _y = dy / dt (19)

Here, m: mass of electron (g) υ (vec): velocity of particle expressed by vector (cm / sec) υx: x component of velocity of particle (cm / sec) υy: velocity of particle y component (cm / sec) E (vec): electric field intensity (V / cm) expressed by a vector B (vec): magnetic field (Wb / cm) expressed by an externally applied vector

Next, a numerical analysis of a plasma state was performed using a parallel plate type etching apparatus shown in FIG. As shown in FIG. 2A, the etching apparatus has parallel plate electrodes 1 and 2, and the lower electrode 1 on the cathode side also serves as a mounting table on which an object to be etched is mounted. High frequency power supplied from a high frequency (RF: Radio Frequency) power supply 3 is applied to the upper electrode 2 on the anode side, and the lower electrode 1 on the cathode side is set to the ground potential. The plasma of argon (Ar) introduced between the opposed electrodes 1 and 2 is generated. From the anode side to the cathode side, a plasma region, a sub-sheath region and an ion sheath region are formed between the opposed electrodes 1 and 2 in which the electron density and the ion density are substantially equal. Using this etching apparatus, a hybrid model was applied in a plasma region, a sub-sheath region, and an ion sheath region, and plasma particle analysis was performed.

FIGS. 4 to 7 show the processing procedure of the numerical analysis.
FIG. First, in step P1,
The width w of the electrodes 1 and 2 and the distance d are set. Next,
In the step P2, the area between the counter electrodes 1 and 2 is finely divided,
Generate a two-dimensional mesh. Then, Step P3
Then, based on this mesh,
Here, the general difference method is used, and the time
From the equations (1), (3) and (4) using the solution method,
Create an expression. In this case, the mobility μ and the diffusion constant D
Type, location, and time, depending on
μ^h _ji, D^h _jiReplace with

Next, in step P4, high-frequency power (voltage Va) as shown in FIG.
(T)) is applied to the upper electrode 2. As a boundary condition, the cathode is grounded, and the potential of the anode at a specific time is defined as Va. Next, in step P5, a time step δt is set in order to create a continuous difference equation. Step P
At 6, the time parameter h = 1 is set to initialize the time. In Step P7, time t = h × δt is set.

In step P8, the density of each particle is set as a variable.
n^h _ji, Potential φ^h _ji, Electron temperature Te^h _i,
Particle generation rate S^h _jiAnd extinction rate κ^h _jkiInitial value of
And set the particle generation rate S as a constant^h _ji, Extinction rate κ^h
_jki, Μ^h _ji, And D^h _jiSet the initial value of.
In steps P9 to P10, these boundary conditions
Is considered, and the simultaneous equations obtained from the above difference equations are
From the matrix calculation, each time (t = h × δt: h = 1,.
n), the nodes of each mesh (the mesh position is represented by i)
And the distance between adjacent meshes is represented by δi. )
And potential φ ^h _i , The density n of each particle^h _ji(J =
1, 2, 3) and electron temperature Te^h _iAsk for.

In step P11, it is determined whether or not the variables have converged. If not converged, step P12
And the density n ^h _{ji of} each particle and the potential φ ^h
_i, performs a modification of the electron temperature Te ^h _i, returns to the step P9. If it is determined that the convergence has occurred, step P13
Proceeds _{^{to, (φ h i + 1 -φ}} h) / with obtaining the electric field strength by .delta.i, the electron temperature Te ^h obtained in fluid model
The distribution of the ionization rate r ^h _ji is calculated from _{i using} Expression (20).

[0049]

Equation 20] _{^{r h ji = n h 1i ·}} n h 3i · exp (-Eac / (kb · Te h i)) (2 0) Here, Eac is the activation energy of the neutral particles (eV) is there.

FIG. 3A shows the distribution of the particle density between the counter electrodes.
FIG. 3B shows the calculation results of the distribution of the electric field intensity (solid line) and the distribution of the ionization rate (dotted line). Next, step P
At 14, the ion sheath region, as shown in FIGS.
And a sub-sheath region. As shown in FIG. 3B, the ionization rate and the electric field intensity are small in the plasma region and large in the ion sheath region, but relatively large in the region adjacent to the ion sheath region. And an ion sheath region. This region is defined as a sub-sheath region. Specifically, for example, it is defined as a region where the ionization rate is 100 times or more of the plasma region.

Also, as shown in FIG. 3A, from the relationship between the electron density and the ion density, the ion sheath region has almost no electrons and the ion sheath region has a very high ion density compared to the electron density. I can say. The sub-sheath region can be said to be a region where the electron density has an intermediate value between the plasma region and the ion sheath region, and the ion density is higher than the electron density. Next, steps P15 to P24
In the ion sheath region and the sub-sheath region extracted by the above method, the analysis of the reaction due to the collision and the movement of the electrons are calculated using the Monte Carlo method. The particle density distribution, electric field strength, and the like obtained by the fluid model are used for calculating the motion of the particles. Here, the PIC (Particle In Cell) method is not used. In addition, the collision of particles is calculated using a collisionless model.

Although the mesh used in the fluid model is used as it is, all the particle densities in the mesh are not calculated, and the motion of a number of electrons proportional to the particle density in the mesh is typically represented. To analyze. In some cases, when applying the Monte Carlo method in the ion sheath region and the sub sheath region, a mesh different from the mesh used in the fluid model may be newly generated.

First, steps P15 to P22
Then, random numbers r1 and r2 are generated, and equations (7) to (10) are generated.
Is used to analyze the reaction due to collision. In this case, it is determined in step P20 whether the collision involves a reaction or an invalid collision. If the collision is invalid, the process proceeds to step P17, where the collision time is incremented and the reaction is analyzed. Steps P18 to P20
Then, we analyze the motion of the electron until the next collision. When an actual collision accompanied by a reaction occurs, the process proceeds to Step P21. For example, when the reaction particles are electrons having an energy range of 1.0 to 1.2 eV, the reaction process is ionization, and the reaction equation is represented by the following equation. (21).

[0054]

Ar + e ⁻ → Ar ⁺ + 2e ⁻ (21)

Next, in step P22, based on this reaction, the reaction process m is calculated according to equations (11) and (12).
Request generation rate ^S _{h ji} and extinction ratio kappa ^h _JKI particles against. Equations (22) and (23) show rewrites of the generation rate S _j and the extinction rate κ _jk of the equation (11) by _adding the position parameter (i) and the time parameter (h).

[0056]

[Number 22] ^{_{S h ji = S h ji +}} Δ1j (22)

[0057]

Κ ^h _jki = κ ^h _jki + Δ2j (23)

Specifically, when applied to the case of the ionization reaction of the formula (21), the following is obtained.

[0059]

S ^h _1i = S ^h _1i + Δ11 (24)

[0060]

S ^h _3i = S ^h _3i + Δ13 (25)

[0061]

Κ ^h _31i = κ ^h _31i + Δ23 (26)

Next, in step P23, equations (13) to (13)
Calculate the scattering angle using random numbers r3 and r4 according to (15)
And the equation of motion (17) to (19)
Calculate your movement. This calculation is performed only for electrons
It is. Next, at step P24, the energy equation (1)
According to 6), the energy of the electrons after scattering is calculated. time
This calculation is repeated until the step becomes δt, and step P
At 25, the accumulated reaction process m
Generation rate S of falling particles^h _ji And extinction rate κ ^h _jkiSeeking
Confuse. Next, in step P26, analysis using a scattering model
Resulting particle generation rate S^h _jiAnd extinction rate κ^h _jkiThe value of the
And increase by the time step δt.
After that, use the fluid model again in all regions to
Perform child analysis. This allows high-frequency power to be applied to the counter electrode.
If added, analyze the plasma state at each time interval δt
be able to.

In some cases, it is possible to repeat these calculations until a steady solution with respect to time is obtained by repeating these calculations. In general, a state in which a constant voltage is applied, and the same physical quantity obtained even after a lapse of time hardly changes, but a steady solution in this case means that the applied voltage repeated is equal. However, it refers to a state in which the difference between the same physical quantities that has been obtained has almost disappeared (for example, a point where repeated applied voltages as indicated by t1 and t2 in FIG. 2B are equal). As a result of actually simulating the energy of ions at the time of the etching reaction using the above-described analysis method, it was possible to shorten the calculation time and to maintain the calculation accuracy at the same level as in the past.

As described above, in the first embodiment, the fluid model is applied to electrons, ions, and neutral particles over the entire region, and the Monte Carlo method is used only in the ion sheath region and the sub-sheath region around the ion sheath region. To calculate the motion of electrons. Thus, the calculation time can be reduced without lowering the accuracy of the plasma particle analysis method. In addition, by using a continuous equation, a Poisson equation, and an energy transport equation in the analysis using the fluid model, electrons that are in non-equilibrium in the fluid model,
Ions can be handled, and not only can the calculation accuracy be improved, but also the calculation accuracy of the ionization rate used in determining the ion sheath region and the sub-sheath region can be particularly improved.

{Second Embodiment} Next, a second embodiment of the present invention will be described.
The second embodiment of the present invention relates to a computer-readable recording medium storing a program of the method for analyzing plasma particles according to the first embodiment. The plasma particle analysis method according to the first embodiment is programmed into a program according to the flowcharts shown in FIGS. 4 to 7 described in the first embodiment, and is used for recording on a magnetic disk or a semiconductor memory of a computer. The information is recorded on a recording medium such as a portable magnetic tape, a magnetic disk, and a semiconductor memory. Thereby, the method for analyzing plasma particles according to the first embodiment can be stored, and can be used repeatedly. In addition, technology transfer can be easily performed, and unspecified large numbers can be easily used.

Although the embodiment of the present invention has been described in detail with reference to the drawings, the specific configuration is not limited to this embodiment, and there are design changes and the like without departing from the gist of the present invention. Is also included in the present invention. For example, in the above-described first embodiment, a general difference method, for example, a control volume method is used as a method of spatially discretizing a differential equation in numerical calculation by a fluid model.
Other difference methods may be used. Although the implicit method is used as the method of time discretization, other discretization methods can be used.

[0067]

As described above, according to the structure of the present invention, the fluid model is applied to the electrons, ions, and neutral particles over the entire region, and the Monte Carlo method is applied only to the ion sheath region and the periphery thereof. Since the motion of electrons is calculated by using the method, the calculation time can be reduced without impairing the accuracy of the method for analyzing plasma particles. In addition, by using the energy transfer equation in addition to the continuous equation, Poisson's equation, and the like for the analysis using the fluid model, it is possible to handle electrons and ions that are in non-equilibrium in the fluid model. In particular, the calculation accuracy of the ionization rate used when determining the ion sheath region and the sub sheath region can be improved.
According to the recording medium of the sixth aspect, the technology transfer of a particle analysis program for causing a computer to execute the plasma particle analysis method according to any one of the first to fifth aspects can be easily performed, and an unspecified large number of the programs can be transferred. Things are readily available.

[Brief description of the drawings]

FIG. 1 is a schematic explanatory diagram for describing an outline of a plasma particle analysis method according to an embodiment of the present invention.

FIG. 2A is a diagram illustrating a plasma device used in the particle analysis method, and FIG. 2B is a diagram illustrating a high-frequency power waveform applied to a counter electrode to generate plasma.

FIG. 3A is a graph showing a distribution of particle density obtained by a fluid model in the plasma particle analysis method according to the embodiment of the present invention, and FIG. 3B is a graph showing an electric field intensity obtained by the fluid model; It is a graph which shows distribution and distribution of an ionization rate.

FIG. 4 is a flowchart (part 1) showing a procedure of a plasma particle analysis method according to the embodiment.

FIG. 5 is a flowchart (part 2) showing the procedure of the plasma particle analysis method according to the embodiment.

FIG. 6 is a flowchart (part 3) showing a procedure of the plasma particle analysis method according to the embodiment;

FIG. 7 is a flowchart (part 4) showing the procedure of the plasma particle analysis method according to the embodiment.

[Explanation of symbols]

 1 lower electrode 2 upper electrode 3 high frequency power supply

Claims (6)

(57) [Claims] 1. A plasma particle analysis method for analyzing a plasma state used for etching or film formation, wherein electrons, ions, and neutral particles in the plasma are analyzed over a whole region of the plasma state using a fluid model. Find the distribution of particle density, distribution of potential and distribution of electron temperature,
The distribution of the electric field intensity and the distribution of the ionization rate in the plasma are obtained from the obtained distribution, and the ion sheath region and the sub-sheath region are extracted from the entire region in the plasma state based on the distribution of the electric field intensity and the distribution of the ionization ratio. In the ion sheath region and the sub-sheath region, the motion of the electrons is analyzed using a Monte Carlo method, and the reaction constant of the electrons and the electrons, ions, and neutral particles is determined. Particle analysis method. 2. The method according to claim 1, wherein a reaction gas used for etching or film formation is introduced between the opposed electrodes, and power is applied to the opposed electrodes to generate plasma between the opposed electrodes. A particle analysis method for a plasma to be analyzed, wherein (1) a distribution of a particle density of at least electrons, ions, and neutral particles existing between the counter electrodes, and a distribution of a potential between the counter electrodes using a fluid model. And (2) obtaining the distribution of the electric field intensity and the distribution of the ionization rate from the distribution of the particle density obtained by the fluid model, the distribution of the electric potential and the distribution of the electron temperature, and (3) From the distribution of the electric field intensity and the distribution of the ionization rate, a plasma region in which the particle density of the electrons is substantially equal to the particle density of the ions, and the particle density of the ions is higher than the particle density of the electrons A high ion sheath region and a sub-sheath region adjacent to the ion sheath region, wherein the electric field intensity and the ionization rate are higher than the plasma region and lower than the ion sheath region. In the sheath region and the sub-sheath region, the motion of the electrons is analyzed for a predetermined time by a Monte Carlo method, and the interaction between the electrons and the electrons, ions, and neutral particles is analyzed, and the electrons, ions, and neutral particles are analyzed. A method for analyzing particles of plasma, comprising determining a generation rate and an extinction rate of a plasma. 3. The method according to claim 1, wherein a reaction gas used for etching or film formation is introduced between the opposing electrodes, and power is applied to the opposing electrodes to generate plasma between the opposing electrodes. A particle analysis method for a plasma to be analyzed, wherein (1) a distribution of a particle density of at least electrons, ions, and neutral particles existing between the counter electrodes, and a distribution of a potential between the counter electrodes using a fluid model. And (2) obtaining the distribution of the electric field intensity and the distribution of the ionization rate from the distribution of the particle density obtained by the fluid model, the distribution of the electric potential and the distribution of the electron temperature, and (3) From the distribution of the electric field intensity and the distribution of the ionization rate, a plasma region in which the particle density of the electrons is substantially equal to the particle density of the ions, and the particle density of the ions is higher than the particle density of the electrons A high ion sheath region and a sub-sheath region adjacent to the ion sheath region, the electric field intensity and the ionization rate being higher than the plasma region and lower than the ion sheath region. (4) The ion sheath In the region and the sub-sheath region, the motion of the electrons is analyzed for a predetermined time by the Monte Carlo method, and the interaction between the electrons and the electrons, ions and neutral particles is analyzed, and the electrons, ions and neutral particles are analyzed. (5) Using the generation rate and the extinction rate of the electrons, ions, and neutral particles obtained in the above (4), and performing the above (1) while the predetermined time has elapsed. Determining the distribution of the particle density of electrons, ions, and neutral particles existing between the counter electrodes, and the distribution of the potential and the distribution of the electron temperature between the counter electrodes. Plasma particle analysis method to be. 4. The method according to claim 3, wherein (1) to (5) are repeated, wherein electrons present between the counter electrodes in a steady state are provided.
A method for analyzing plasma particles, wherein a distribution of particle densities of ions and neutral particles and a distribution of potential and electron temperature between the counter electrodes are obtained. 5. The method according to claim 1, wherein a continuity equation, a Poisson equation, and an energy transport equation are used in the analysis using the fluid model. 6. A computer-readable recording medium for recording a particle analysis program for causing a computer to execute the plasma particle analysis method according to claim 1.