CN112464588B - Argon plasma electron density calculation method based on simplified collision radiation model - Google Patents
Argon plasma electron density calculation method based on simplified collision radiation model Download PDFInfo
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Abstract
The application provides an argon plasma electron density calculation method based on a simplified collision radiation model, which comprises the steps of determining dominant particle reaction types in argon plasma; according to the reaction type, a rate balance equation of the excited argon atoms with the energy level of 2p is written in a column; simplifying the rate balance equation; determining a spectral line intensity formula according to the simplified rate balance equation; determining a spectral line intensity ratio calculation formula according to the spectral line intensity formula; determining an argon plasma electron density calculation formula; and (3) fitting and calculating parameters of the electron density calculation formula. By simplifying the argon plasma collision radiation model and integrating microscopic parameters with low precision and lacking microscopic parameters, the more accurate and reliable high-pressure, low-ionization-degree and large-area plasma electron density can be obtained.
Description
Technical Field
The invention belongs to the technical field of plasmas, and particularly relates to an argon plasma electron density calculation method based on a simplified collision radiation model.
Background
Dielectric barrier discharge (Dielectric Barrier Discharge, DBD) is a non-equilibrium gas discharge with insulating medium inserted into the discharge space, also called dielectric barrier corona discharge or silent discharge, and has been widely used in various chemical reactors, and in modification, grafting, surface tension improvement, cleaning and hydrophilic modification of polymer and metal films and plates in industry.
The electron density is an important characteristic parameter of the plasma, and is closely related to a plurality of factors such as plasma reaction conditions, reaction types, reaction coefficients, gas components, gas temperature and the like, and particularly under medium-high pressure, the determination process of the electron density is a highly coupled, nonlinear and complex process. The existing electron density diagnosis method is mostly aimed at plasmas with low air pressure, high electron density and small dimension, and the determination of the electron density of plasmas with higher air pressure, low ionization degree and large area is mostly based on a current method or an empirical formula, so that the problems of low precision, poor applicability and the like exist. Therefore, it is necessary to obtain a better and more accurate electron density calculation method, and a necessary method foundation is provided for plasma electron density parameter regulation and control and related research.
The collision radiation model establishes the relation between the light intensity ratio of the radiation spectrum line and the electron density, and the key point is the determination and simplification of the reaction particles and the reaction types. The linear ratio method based on the relative light intensity can be applied to plasma diagnosis of a wide range of electron density under various reaction conditions, and is also the core of the electron density determination method based on the collision radiation model. In recent years, studies on electron density determination methods based on collision radiation models have been focused on discharge reactions at low gas pressures and short gaps, and there have been few studies on higher gas pressures and longer gaps.
Disclosure of Invention
The invention provides an argon plasma electron density calculation method based on a simplified collision radiation model, so as to obtain more accurate and reliable high-pressure, low-ionization-degree and large-area plasma electron density.
There is provided an argon plasma electron density calculation method based on a simplified collision radiation model, the method comprising the steps of:
s1, determining the dominant particle reaction type in argon plasma;
s2, according to the reaction type, writing a rate balance equation of the excited argon atoms with the energy level of 2 p;
s3, simplifying the rate balance equation;
s4, determining a spectral line intensity formula according to the simplified rate balance equation;
s5, determining a spectral line intensity ratio calculation formula according to the spectral line intensity formula;
s6, determining an argon plasma electron density calculation formula;
and S7, parameter fitting and calculation of the electron density calculation formula.
Preferably, at higher gas pressures or at atmospheric pressure, the dominant particle reaction types are:
(1) Electron collision excitation and de-excitation reactions of ground state atoms
Wherein e represents an electron, ar g Represents a ground state argon atom, ar s Ar represents an argon atom at 1s energy level x An argon atom representing an energy level of 2p or higher, wherein the energy levels are paschen energy levels, as described below;
(2) Electron collision excitation and de-excitation reactions of 1s energy level atoms
(3) Collision transition reaction of ground state atoms and high level atoms
Wherein Ar is g Is not Ar x An argon atom of 2p or higher energy level;
(4) Spontaneous emission reaction of high energy level atoms
Ar hl →Ar i +hν (5)
Ar i →Ar s +hν (6)
Wherein Ar is hl An Ar atom having an energy level of 2p or more, ar i Is an argon atom with 2p energy level, h is a Planck constant, and v is the photon frequency emitted by the spontaneous emission reaction of the high-energy-level atom.
Preferably, the specific steps of step S2 are:
let the energy level be i, the rate balance equation for the excited argon atom of column-written 2p energy level is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,n e is the electron density in the plasma, n g Is the density of the ground state argon atoms, other subscripts of n, s, x, i respectively represent Ar s 、Ar x 、Ar i The number density, k of particles ex 、k et 、k gt 、k de The reaction coefficients respectively representing electron collision excitation of the ground state atoms, electron collision excitation of the 1s energy level atoms, collision transition between the ground state atoms and the high energy level atoms and collision de-excitation of the 2p energy level atoms and electrons, A is an Einstein coefficient, and subscripts of the reaction coefficients indicate conversion conditions of the particles in the reaction to show distinction.
Preferably, the specific steps of step S3 are:
neglecting electron collision de-excitation reaction, simplifying the rate balance equation, wherein the simplified rate balance equation is as follows:
according to equation (8), four coefficients are redefined as follows:
wherein k is i1 Is the global excitation reaction coefficient, k, of the ith energy level i2 And k i3 Is equivalent collision reaction coefficient, namely collision excitation reaction of electrons and 1s energy level argon atoms and ground state sourceCollision transition reaction of son with high-level argon atom, A i Is the equivalent Einstein coefficient, bringing formulae (9), (10), (11) and (12) into formula (8) yields:
n e n g k i1 ＝n e n i k i2 +n g n i k i3 +A i n i (13)
when the gas pressure is low, the collision transition reaction with the high-level argon atom is ignored, and the formula (13) becomes:
n e n g k i1 ＝n e n i k i2 +A i n i (14)
when the electron density is low, the collision excitation reaction of electrons with 1 s-level argon atoms is ignored, and formula (13) becomes:
n e n g k i1 ＝A i n i (15)。
preferably, the line intensity formula is determined as:
preferably, the ratio of line intensities of the i and j th energy levels is:
preferably, the calculation formula of the electron density of the argon plasma is as follows:
preferably, the specific steps of step S7 are:
estimating electron density by using a current method for fitting to obtain corresponding equivalent reaction coefficient k i 2、k i 3、k j 2、k j 3 ratio of global excitation reaction coefficients k i 1/k j 1 by theoretical calculation。
Preferably k i1 And k is equal to j1 As a global excitation reaction coefficient, which is a function of electron temperature, the arrhenius form of the reaction has the following calculation formula:
wherein K is 0 、C 0 And E is 0 Is a constant related to the ith and jth energy levels, k i1 /k j1 With electron temperature T only e Related to the following.
Preferably, the electron density is estimated by a current method for fitting to obtain the corresponding equivalent reaction coefficient k i 2、k i 3、k j 2、k j 3 comprises:
determination of the voltage u of the air gap during discharge by simulation of a one-dimensional fluid model g D is the distance between two parallel dielectric plates, resulting in the average field strength in the air gap:
the relationship between current density and electron density is as follows:
j d ＝n e eμ e E g (21)
the current density is calculated as follows:
wherein:
j d discharge current density/A/m 2 ，
e-the amount of charge carried by the electrons/C,
μ e -electron mobility/m 2 /V/s，
E g Air gap average field intensity/V/m, wherein the air gap field intensity is obtained by air gap voltage calculation, u g Is the effective value of the air gap voltage, d is the distance between two parallel dielectric plates, and the air gap voltage u g Given by the one-dimensional fluid simulation,
the estimated electron density is combined with the formula (18) to obtain the corresponding equivalent reaction coefficient k by fitting i2 、k i3 、k j2 、k j3 。
Based on the above embodiments, the method for calculating the electron density of the argon plasma based on the simplified collision radiation model according to the embodiments of the present invention includes the steps of determining the dominant particle reaction type in the argon plasma; according to the reaction type, a rate balance equation of the excited argon atoms with the energy level of 2p is written in a column; simplifying the rate balance equation; determining a spectral line intensity formula according to the simplified rate balance equation; determining a spectral line intensity ratio calculation formula according to the spectral line intensity formula; determining an argon plasma electron density calculation formula; and (3) fitting and calculating parameters of the electron density calculation formula. By simplifying the argon plasma collision radiation model and integrating microscopic parameters with low precision and lacking microscopic parameters, the more accurate and reliable high-pressure, low-ionization-degree and large-area plasma electron density can be obtained.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.
Drawings
In order to more clearly illustrate the technical solutions of the present application, the drawings that are needed in the embodiments will be briefly described below, and it will be obvious to those skilled in the art that other drawings can be obtained from these drawings without inventive effort.
FIG. 1 is a block diagram of a simplified impinging radiation model-based plasma electron density calculation method according to an embodiment of the present invention;
FIG. 2 is a graph showing the calculated relationship between the electron drift rate and the reduced field strength of argon gas according to an embodiment of the present invention;
FIG. 3 is a graph showing the measured values of waveforms of applied voltage and current density at 0.6atm and 3kV according to an embodiment of the present invention;
FIG. 4 shows the electron density distribution of the air gap in the axial direction of the electrode at 0.6atm,3kV of the embodiment of the present invention;
FIG. 5 ratio of global excitation coefficients k for an embodiment of the invention 51 /k 11 And electron temperature T e Is a relationship of (2);
FIG. 6 shows spectral lines of an argon dielectric barrier discharge plasma in the wavelength range of 737.7nm to 752nm in an embodiment of the invention;
FIG. 7 is a graph showing the intensity ratio I of the discharge gas pressure to the voltage amplitude 5 /I 1 A test value of the change;
FIG. 8 shows electron density results (using 751.5nm to 750.4nm spectral line ratio) at different discharge conditions, electron temperatures for an embodiment of the invention;
FIG. 9 is a graph showing the intensity ratio I of the discharge gas pressure to the voltage amplitude 1 /I 3 Is a variation of (2);
FIG. 10 shows the ratio of the global excitation coefficients k 'for an embodiment of the invention' 11 /k′ 31 And electron temperature T e Is a relationship of (2);
FIG. 11 shows electron density results (using 750.4nm to 738.4nm spectral line ratios) at different discharge conditions and electron temperatures for an embodiment of the present invention.
Detailed Description
In order to enable those skilled in the art to better understand the technical solutions in the present application, the following description will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the accompanying drawings in the embodiments of the present application. It will be apparent that the described embodiments are only some, but not all, of the embodiments of the present application. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments herein without making any inventive effort, shall fall within the scope of the present application.
Referring to fig. 1, the argon plasma electron density calculation method based on the simplified collision radiation model is performed as follows:
s1: the type of particle reaction dominant in the argon plasma was determined.
The dominant particle reaction type in argon plasma is determined, and at higher or atmospheric pressure, the dominant particle reaction type is:
(1) Electron collision excitation and de-excitation reactions of ground state atoms
Wherein e represents an electron, ar g Represents a ground state argon atom, ar s Ar represents an argon atom at 1s energy level x An argon atom representing an energy level of 2p or higher, wherein the energy levels are paschen energy levels, as described below;
(2) Electron collision excitation and de-excitation reactions of 1s energy level atoms
(3) Collision transition reaction of ground state atoms and high level atoms
Wherein Ar is g Is not Ar x An argon atom of 2p or higher energy level;
(4) Spontaneous emission reaction of high energy level atoms
Ar hl →Ar i +hν (5)
Ar i →Ar s +hν (6)
Wherein Ar is hl An Ar atom having an energy level of 2p or more, ar i Is an argon atom with 2p energy level, h is a Planck constant, and v is the photon frequency emitted by the spontaneous emission reaction of the high-energy-level atom.
S2: the rate balance equation for the excited argon atoms at the 2p level is written according to the reaction type.
The rate balance equation for the excited argon atom (let level be i) for column-written 2p energy level is as follows:
wherein n is e Is the electron density in the plasma, n g Is the density of the ground state argon atoms, other subscripts of n, s, x, i respectively represent Ar s 、Ar x 、Ar i The number density, k of particles ex 、k et 、k gt 、k de The reaction coefficients respectively representing electron collision excitation of the ground state atoms, electron collision excitation of the 1s energy level atoms, collision transition between the ground state atoms and the high energy level atoms and collision de-excitation of the 2p energy level atoms and electrons, A is an Einstein coefficient, and subscripts of the reaction coefficients indicate conversion conditions of the particles in the reaction to show distinction.
S3: simplifying the rate balance equation.
The rate balance equation is simplified, and since the electron collision de-excitation reaction is the reverse reaction of the electron collision excitation reaction of the atomic atoms in the ground state, which is weaker than other reaction processes, the reverse reaction can be ignored in the model without causing larger errors, so that the formula (7) can be rewritten as follows:
according to equation (8), four coefficients are redefined as follows:
wherein k is i1 Is the global excitation reaction coefficient, k, of the ith energy level i2 And k i3 Is equivalent collision reaction coefficient, namely collision excitation reaction of electrons and 1s energy level argon atoms and collision transition reaction of ground state atoms and high energy level argon atoms, A i Is the equivalent einstein coefficient. Bringing formulae (9), (10), (11) and (12) into formula (8) yields:
n e n g k i1 ＝n e n i k i2 +n g n i k i3 +A i n i (13)
when the gas pressure is low, the density of the ground state atoms is low, and the collision transition reaction with the high-level argon atoms is negligible, and thus, the formula (13) may become:
n e n g k i1 ＝n e n i k i2 +A i n i (14)
considering theoretical compatibility with the Corona model, when the electron density is low, the collision excitation reaction of electrons with 1 s-level argon atoms can be ignored, so that formula (13) becomes:
n e n g k 1i ＝A i (15)
this is consistent with the Corona model which considers only the collision excitation of electrons with atoms in the ground state and the spontaneous emission of atoms in high energy levels.
S4: and determining a spectral line intensity formula according to the simplified rate balance equation.
Determining a line intensity formula, which can be derived from formula (13):
s5: and determining a spectral line intensity ratio calculation formula according to the spectral line intensity formula.
Determining a spectral line intensity ratio calculation formula, considering the jth energy level in the 2p energy levels, and obtaining the ratio of the spectral line intensities of the ith energy level and the jth energy level according to a line ratio method, wherein the ratio is as follows:
s6: and determining an argon plasma electron density calculation formula.
The calculation formula for determining the electron density of the argon plasma is as follows:
s7: and (5) performing parameter fitting and calculation on an electron density calculation formula.
Estimating electron density by using a current method for fitting to obtain corresponding equivalent reaction coefficient k i2 、k i3 、k j2 、k j3 Ratio k of global excitation reaction coefficients i1 /k j1 Is obtained by theoretical calculation.
k i1 And k is equal to j1 As a global excitation reaction coefficient, which is a function of electron temperature, the arrhenius form of the reaction has the following calculation formula:
wherein K is 0 、C 0 And E is 0 Is a constant related to the ith, j energy level, see k i1 /k j1 With electron temperature T only e Related to the following.
Determination of the voltage u of the air gap during discharge by simulation of a one-dimensional fluid model g D is the distance between two parallel dielectric plates, thus finding the average field strength in the air gap:
the relationship between current density and electron density is as follows:
j d ＝n e eμ e E g (21)
the calculation formula for the current density can be obtained as follows:
wherein:
j d discharge current density/A/m 2 ；
e-the amount of charge carried by the electron/C;
μ e -electron mobility/m 2 /V/s；
E g Air gap average field strength/V/m.
Wherein the air gap field intensity can be calculated by air gap voltage, u g Is the effective value of the air gap voltage and d is the distance between two parallel dielectric plates. Air gap voltage u g Given by one-dimensional fluid simulation.
The estimated electron density is combined with the formula (18) to obtain the corresponding equivalent reaction coefficient k by fitting i2 、k i3 、k j2 、k j3 。
The control equation of the one-dimensional fluid model of the plasma mainly comprises a particle conservation continuity equation, an electron energy conservation equation and a poisson equation:
wherein n is i 、Γ i 、S i 、q i 、μ i 、D i Respectively representing density, drift-diffusion flux, net generation rate, electric quantity, drift coefficient and diffusion coefficient; e is the electric field strength; epsilon is the average electron energy; e (E) j 、K j Respectively energy loss and reaction coefficient; m is m e 、m He The mass of electrons and He molecules, respectively; k (K) el The momentum transfer is fast recording; k (k) b 、T e 、T He The boltzmann is well-known, the electron temperature and the He gas temperature are respectively; epsilon 0 Is vacuum magnetic permeability. The product of electron mobility and air gap field strength is the electron drift rate, expressed as:
v d ＝μ e E g (26)
the definition formula is as follows:
wherein:
e-electric field strength/V/m, here equal to E g ；
N-neutral particle number density/m -3 Here, the ground state argon atomic number density n g ；
E/N-reduced field strength/V.m 2 ；
m e -electronic mass/kg;
epsilon-electron energy/eV;
σ m total collision cross section/eV;
f-electron energy distribution function.
The electron energy distribution function is obtained by approximately solving the Boltzmann equation by two terms, and the distribution function f (r, v, t) of electrons in a 6-dimensional phase space satisfies the Boltzmann equation:
wherein: v is the electron velocity; e is the electron charge amount; m is m e Is electron quality; e is an electric field;
is a velocity gradient operator; c is a collision term related to f.
Simplifying the above method to obtain f 0 Convection-diffusion continuous equation of (2)
Wherein the method comprises the steps of
Wherein: sigma (sigma) ε Is the total elastic collision section; epsilon 0 Is vacuum dielectric constant; k (k) b Is the boltzmann constant; n is the gas number density; m is the mass of the particles.
Wherein S represents energy loss due to inelastic collision:
C k is the energy loss caused by the k-type inelastic collision of electrons with other particles, and the probability of collision between electrons is very small and can be ignored. C (C) exc 、C att 、C ion Energy losses due to excitation collisions, adsorption collisions and ionization collisions, respectively.
C exc ＝-γx k [εσ k (ε)f 0 (ε)-(ε+Δε k )σ k (ε+Δε k )f 0 (ε+Δε k )] (31)
C att ＝-γx k εσ k (ε)f 0 (ε) (32)
C ion ＝-γx k [εσ k (ε)f 0 (ε)-2(2ε+Δε k )σ k (2ε+Δε k )f 0 (2ε+Δε k )] (33)
Wherein: delta epsilon k Valve energy for a k-th type collision; lambda is a guarantee f 0 Factors meeting normalization conditions, f 0 The requirements are satisfied:
as shown in FIG. 2, the dielectric plate is Polytetrafluoroethylene (PTFE) with a thickness of 0.5mm, the air pressure is 0.6atm, the voltage amplitude is 3kV, and when the frequency is 10kHz, the voltage and current density curves are applied in two periods after the discharge is stabilized, and the maximum value of the current density in the discharge is 12.5A/m 2 . The gas discharge gap is small, and although each discharge period has a plurality of current pulses, the duration is about 1 mu s, the gas discharge gap belongs to glow discharge, and diffusion type plasma distribution is still formed in the space.
FIG. 3 shows the relationship between electron drift rate and reduced field strength, and FIG. 4 shows the electron density calculated by amperometric calculation under different discharge conditions.
Ar (2 p) 5 →1s 4 ) (λ= 751.5 nm) spectral line and Ar (2 p) 1 →1s 2 ) (λ=750.4 nm) as two lines required for the line ratio method. k (k) i1 And k is equal to j1 As global excitation reaction coefficient, is a function of electron temperature, and is calculated by adopting an Arrhenius form calculation formula shown in a formula (19), 2p 5 Energy level and 2p 1 Ratio k of energy level global excitation reaction coefficients 51 /k 11 The relationship with electron temperature is shown in fig. 5.
Electron density estimated by amperometric method and experimentally obtained intensity ratio, at k 51 /k 11 In the known case, four equivalent collision reaction coefficients k are solved by a fitting method 52 、k 53 、k 12 And k 13 . FIG. 6 shows the relative light intensity of the spectral line of argon DBD in the wavelength range of 737.7nm to 752nm at a voltage amplitude of 3.5kV and a frequency of 10kHz under a pressure of 0.6atm, and Ar (2 p) 3 →1s 4 )(λ＝738.4nm)、Ar(2p 5 →1s 4 ) (λ= 751.5 nm) and Ar (2 p) 1 →1s 2 ) (λ=750.4 nm). Meanwhile, the three spectral lines are optically thin as can be seen from the half-width, and can be used for solving the electron density by a line ratio method.
According to the measured relative light intensity of spectral lines under different discharge conditions, the ratio I of the light intensity of 751.5nm and 750.4nm spectral lines is obtained 5 /I 1 As shown in fig. 7. It can be seen that the ratio of the light intensities of the two spectral lines increases with increasing air pressure, however, when the air pressure is the same, the trend of the change in the ratio of the light intensities is not obvious with increasing voltage amplitude, the voltage amplitude increases at 0.4atm, the ratio of the light intensities increases, and the ratio of the light intensities slightly decreases with increasing voltage amplitude at 0.6atm and 0.8 atm.
Equivalent collision reaction coefficient k 52 、k 53 、k 12 And k 13 The electron density and the light intensity ratio measured by the Levenberg-Marquardt method (Levenberg-Marquardt method) and the general global optimization method (Universal Global Optimization method) fit. Considering that the electron temperature was not measured in the experiment, several sets of equivalent collision reaction coefficients at different electron temperatures were fitted with reference to the electron temperature range (0.6-1.2 eV) obtained in the simulation, and the results are shown in table 1. It can be seen from the table that the equivalent collision reaction coefficient obtained by fitting changes in a small range within the same order of magnitude along with the change of the electron temperature, and the stability of the data fitting result is stronger. Wherein k is 51 /k 11 According to different electron temperatures, the electron temperature is obtained through theoretical calculation.
TABLE 1
Fig. 8 shows the electron density results calculated by fitting coefficients at different electron temperatures at different gas pressures and voltage amplitudes using a 751.5nm to 750.4nm spectral line ratio, and by comparison, the simulated electron density and the electron density estimated by the amperometric method under the corresponding discharge conditions are shown in fig. 8. As can be seen from FIG. 8, the electron density ranges from about 1X 10 under different discharge conditions 16 -3×10 16 m -3 Between them. As can be seen by comparison, in the medium-high pressure range, the electron density obtained by using the fitting coefficients under different electron temperatures has little difference, and the electron density obtained by simulation has better conformity with the electron density obtained by simulation. In a certain error range, the fitting result and the electron density estimated by the current density have better consistency. Therefore, the electron density calculation formula obtained through simplified CRM has good universality in the middle-high pressure range and certain precision.
As a check for calculating electron density by the line ratio method, another group of spectral line ratios of argon DBD are taken to calculate electron density, ar (2 p) 1 →1s 2 ) (λ=750.4 nm) and Ar (2 p) 3 →1s 4 ) (λ= 738.4 nm). According to the measured relative light intensity of spectral lines under different discharge conditions, the ratio I of light intensity of 750.4nm and 738.4nm spectral lines is obtained 1 /I 3 As shown in fig. 9. It can be seen that the ratio of the light intensity of the two spectral lines is greatly reduced along with the increase of the air pressure, and the ratio of the light intensity is slightly reduced along with the increase of the voltage amplitude when the air pressure is the same.
Ratio of global excitation reaction coefficients k' 11 /k′ 31 The relationship between the electron temperature and the electron temperature was obtained by the same calculation method as described above and is shown in FIG. 10. Equivalent collision reaction coefficient k' 12 、k′ 13 、k′ 32 And k' 33 The same is true from fitting the electron density measured by amperometric methods to the experimentally measured light intensity ratio. The fitted reaction coefficients are shown in the table for the electron temperature range of 0.6-1.2eV2.
TABLE 2
FIG. 11 shows the results of electron density calculated using the coefficients of fit at different electron temperatures at different gas pressures and voltage amplitudes for a spectral line ratio of 750.4nm to 738.4nm, for comparison, and for a corresponding discharge condition, the electron density estimated by amperometric method, and the spectral line ratio of 751.5nm to 750.4nm (I 5 /I 1 ) And electron density calculation results at an electron temperature of 0.8 eV. As can be seen by comparison, when the same spectral line ratio is adopted in the middle-high air pressure range, the electron density difference obtained by using the fitting coefficients under different electron temperatures is not large, and in a certain error range, the fitting result has better consistency with the electron density estimated by the current density, and the fitting result also has better consistency with the electron density obtained by simulation. When different spectral line ratios are adopted, the electron density obtained by calculation by using the fitting coefficient under the same electron temperature is generally close, and the method can be considered to have better consistency in a certain error range.
Since the foregoing embodiments are all described in other modes by reference to the above, the same parts are provided between different embodiments, and the same and similar parts are provided between the embodiments in the present specification. And will not be described in detail herein.
Other embodiments of the present application will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the application and including such departures from the present disclosure as come within known or customary practice within the art to which the application pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the application being indicated by the following claims.
It is to be understood that the invention is not limited to the precise arrangements and instrumentalities shown in the drawings, which have been described above, and that various modifications and changes may be effected without departing from the scope thereof. The scope of the invention is limited only by the appended claims.
Claims (7)
1. An argon plasma electron density calculating method based on a simplified collision radiation model, which is characterized by comprising the following steps of:
s1, determining the dominant particle reaction type in argon plasma;
at higher gas pressures or at atmospheric pressure, the dominant types of particle reactions are:
(1) Electron collision excitation and de-excitation reactions of ground state atoms
Wherein e represents an electron, ar g Represents a ground state argon atom, ar s Ar represents an argon atom at 1s energy level x An argon atom representing an energy level of 2p or higher, wherein the energy levels are paschen energy levels, as described below;
(2) Electron collision excitation and de-excitation reactions of 1s energy level atoms
(3) Collision transition reaction of ground state atoms and high level atoms
Wherein Ar is y Is not Ar x An argon atom of 2p or higher energy level;
(4) Spontaneous emission reaction of high energy level atoms
Ar hl →Ar i +hv (5)
Ar i →Ar s +hν (6)
Wherein Ar is hl Is an argon atom with an energy level greater than 2p, ar i An argon atom with 2p energy level, h is Planck constant, and v is the photon frequency radiated by the spontaneous radiation reaction of the high-energy-level atom;
s2, according to the reaction type, writing a rate balance equation of the excited argon atoms with the energy level of 2 p;
let the energy level be i, the rate balance equation for the excited argon atom of column-written 2p energy level is as follows:
wherein n is e Is the electron density in the plasma, n g Is the density of the ground state argon atoms, n s Represents Ar s Number density of particles, n x Represents Ar x Number density of particles, n i Represents Ar i The number density, k of particles ex 、k et 、k gt 、k de Respectively representing the reaction coefficients of electron collision excitation of the basic state atoms, electron collision excitation of the 1s energy level atoms, collision transition between the basic state atoms and the high energy level atoms and collision de-excitation of the 2p energy level atoms and electrons, wherein A is Einstein coefficient, k ex，g→i Represents the ground state atom Ar g Conversion to Ar by electron-impact excitation reaction i Transformation conditions, k et，s→i Represents 1s energy level atom Ar s Conversion to Ar by electron-impact excitation reaction i Transformation conditions, k gt，x→i Representing a high-level atom Ar x Conversion to Ar by collision transition reaction with ground state atoms i Transformation conditions, k de，i→g Represents a 2p energy level atom Ar i Conversion to Ar by electron collision de-excitation reaction g Transformation conditions, k et，i→s Represents a 2p energy level atom Ar i Through electron collisionExcitation reaction to Ar s Transformation conditions, k gt，i→x Represents a 2p energy level atom Ar i Conversion to Ar by collision transition reaction with ground state atoms x Transformation conditions of A x→i Is Ar x To Ar i Einstein coefficient of transformation, A i→s Is Ar i To Ar s Transformed einstein coefficients;
s3, simplifying the rate balance equation;
neglecting electron collision de-excitation reaction, simplifying the rate balance equation, wherein the simplified rate balance equation is as follows:
according to equation (8), four coefficients are redefined as follows:
wherein k is i1 Is the global excitation reaction coefficient, k, of the ith energy level i2 And k i3 Is equivalent collision reaction coefficient, namely collision excitation reaction of electrons and 1s energy level argon atoms and collision transition reaction of ground state atoms and high energy level argon atoms, A i Is the equivalent Einstein coefficient, bringing formulae (9), (10), (11) and (12) into formula (8) yields:
n e n g k i1 ＝n e n i k i2 +n g n i k i3 +A i n i (13)
when the gas pressure is low, the collision transition reaction with the high-level argon atom is ignored, and the formula (13) becomes:
n e n g k i1 ＝n e n i k i2 +A i n i (14)
when the electron density is low, the collision excitation reaction of electrons with 1 s-level argon atoms is ignored, and formula (13) becomes:
n e n g k i1 ＝A i n i (15)
s4, determining a spectral line intensity formula according to the simplified rate balance equation;
s5, determining a spectral line intensity ratio calculation formula according to the spectral line intensity formula;
s6, determining an argon plasma electron density calculation formula;
and S7, parameter fitting and calculation of the electron density calculation formula.
2. The simplified collision radiation model based argon plasma electron density calculation method as claimed in claim 1, wherein the line intensity formula is determined as:
3. the simplified collision radiation model based argon plasma electron density calculation method as claimed in claim 2, wherein the ratio of spectral line intensities of the ith and jth energy levels is:
4. the method for calculating the electron density of the argon gas plasma based on the simplified collision radiation model according to claim 3, wherein a calculation formula of the electron density of the argon gas plasma is:
5. the method for calculating electron density of argon gas plasma based on simplified collision radiation model as claimed in claim 4, wherein step S7 comprises the specific steps of:
estimating electron density by using a current method for fitting to obtain corresponding equivalent reaction coefficient k i2 、k i3 、k j2 、k j3 Ratio k of global excitation reaction coefficients i1 /k j1 Is obtained by theoretical calculation.
6. The method for calculating electron density of argon gas plasma based on simplified collision radiation model as claimed in claim 5, wherein k is i1 And k is equal to j1 As a global excitation reaction coefficient, which is a function of electron temperature, the arrhenius form of the reaction has the following calculation formula:
wherein K is 0 、C 0 And E is 0 Is a constant related to the ith and jth energy levels, k i1 /k j1 With electron temperature T only e Related to the following.
7. The method for calculating electron density of argon gas plasma based on simplified collision radiation model as claimed in claim 6, wherein electron density is estimated by amperometric estimation for fitting to obtain corresponding equivalent reaction coefficient k i2 、k i3 、k j2 、k j3 Comprising the following steps:
determination of the voltage u of the air gap during discharge by simulation of a one-dimensional fluid model g D is the distance between two parallel dielectric plates, resulting in the average field strength in the air gap:
the relationship between current density and electron density is as follows:
j d ＝n e eμ e E g (21)
the electron density is calculated as follows:
wherein:
j d discharge current density/A/m 2 ，
e-the amount of charge carried by the electrons/C,
μ e -electron mobility/m 2 /V/s，
E g Air gap average field strength/V/m,
wherein the air gap field intensity is obtained by air gap voltage calculation, u g Is the effective value of the air gap voltage, d is the distance between two parallel dielectric plates, and the air gap voltage u g Given by the one-dimensional fluid simulation,
the estimated electron density is combined with the formula (18) to obtain the corresponding equivalent reaction coefficient k by fitting i2 、k i3 、k j2 、k j3 。
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| CN104121991A (en) * | 2014-07-03 | 2014-10-29 | 清华大学 | Plasma emission spectroscopy two-dimensional space distribution measuring system |
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