CN115175430A - Rapid simulation method and system for discharge mode conversion of inductive coupling plasma source - Google Patents
Rapid simulation method and system for discharge mode conversion of inductive coupling plasma source Download PDFInfo
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Abstract
The invention relates to a method and a system for quickly simulating discharge mode conversion of an inductive coupling plasma source, which comprises the following steps: giving initial values to all physical quantities in the plasma source discharge process, and calculating the density of all particles according to the particle number change caused by gas pumping in and out, surface reaction and zone reaction; based on an energy conservation equation, calculating the current electron temperature according to the initial value of the inductive absorption power and the initial value of the capacitive absorption power; determining the electromagnetic field distribution of the plasma source in an inductive mode and a capacitive mode based on a Maxwell equation set; calculating current inductive absorption power and current capacitive absorption power according to the electromagnetic field distribution; iteratively calculating each physical quantity until the difference value between each physical quantity and each physical quantity calculated last time is smaller than a set threshold value, stopping iteration, and outputting the value of each physical quantity; the values of the respective physical quantities are used to characterize the discharge mode conversion process of the inductively coupled plasma source. The plasma characteristic in the discharge mode conversion process can be accurately simulated, and the calculation efficiency is improved.
Description
Technical Field
The invention relates to the technical field of plasma discharge, in particular to a method and a system for quickly simulating discharge mode conversion of an inductively coupled plasma source.
Background
The inductively coupled plasma source has the advantages of low discharge voltage, high plasma density, simple device structure and the like, and is often used in material etching and surface treatment processes. In the inductive coupling discharge process, after the annular current is introduced into the coil, an alternating magnetic field is excited in the whole discharge device. According to Faraday's law of electromagnetic induction, the alternating magnetic field induces an annular electric field. Under the action of the toroidal electric field, electrons inside the discharge chamber are accelerated, and plasma is generated through processes such as ionization and collision, and this discharge mode is called an inductive mode (or H mode). If a lower current is passed through the coil, a higher voltage drop exists across the coil, and the discharge is maintained mainly by the electrostatic field generated by capacitive coupling, this discharge mode is called capacitive mode (or E-mode). Compared with the H mode, when the discharge is in the E mode, the electron density is lower, the sheath layer is thicker, the electron temperature is higher, and the plasma luminous intensity is weaker. In inductively coupled discharges, switching of the discharge mode, and even hysteresis, is observed when the current or power to the coil is regulated back and forth. The abrupt behavior of the discharge mode transition process and the plasma state parameters has important influence on the plasma processing process, and thus needs to be systematically studied.
Disclosure of Invention
The invention aims to provide a method and a system for quickly simulating discharge mode conversion of an inductively coupled plasma source, which can accurately simulate the plasma characteristics in the discharge mode conversion process and can improve the calculation efficiency.
In order to achieve the purpose, the invention provides the following scheme:
the invention provides a rapid simulation method for discharge mode conversion of an inductive coupling plasma source, which comprises the following steps:
s1: giving initial values to all physical quantities of the plasma source in the discharge process to obtain initial values of all the physical quantities; the physical quantities include electron density, electron temperature, ion density, neutral particle density, capacitive absorption power, and inductive absorption power; the ion and neutral particle types are determined by the type of gas used for the plasma source discharge;
s2: based on a particle number conservation equation, calculating the density of each particle in the plasma source discharge process according to the particle number variation caused by pumping gas into and out of the plasma source, the particle number variation caused by surface reaction and the particle number variation caused by bulk reaction; the particle number variation caused by the surface reaction and the particle number variation caused by the bulk reaction are related to the initial value of the electron temperature; the particles include electrons, ions, and neutral particles;
s3: based on an energy conservation equation, calculating the current electron temperature according to the initial value of the inductive absorption power and the initial value of the capacitive absorption power, and taking the current electron temperature as the initial value of the electron temperature of the next cycle iteration;
s4: determining the electromagnetic field distribution of the plasma source in an inductive mode and the electromagnetic field distribution of the plasma source in a capacitive mode based on a Maxwell equation set;
s5: calculating the current inductive absorption power of the plasma source according to the electromagnetic field distribution in the inductive mode; calculating the current capacitive absorption power of the plasma source according to the electromagnetic field distribution in the capacitive mode; taking the current inductive absorption power as an initial value of inductive absorption power of next cycle iteration, and taking the current capacitive absorption power as an initial value of capacitive absorption power of next cycle iteration;
s6: returning to execute the step S2 until the difference value between the value of each physical quantity obtained by calculation and the value of each physical quantity calculated by the last cycle iteration is smaller than the set threshold value, stopping the cycle iteration and outputting the value of each physical quantity; the values of the respective physical quantities are used to characterize a discharge mode conversion process of the inductively coupled plasma source.
Optionally, the density of each particle is calculated using the formula:
R s,j ＝k s n s ；
wherein j represents the particle type, R in,j Is indicated by qiVariation of the number of particles, R, caused by pumping of the body into the plasma source out,j Representing the amount of change in the number of particles due to pumping of gas out of the plasma source,
represents the amount of change in the number of particles, R, due to bulk reactions s,j Represents the amount of change in the number of particles, k, due to surface reaction l Coefficient of response, k, of the l-th individual area s Coefficient of surface reaction, n l1 、n l2 And n s Which represents the density of each particle in the discharge gas.
Optionally, the formula for calculating the electron temperature is as follows:
wherein, T e Is the electron temperature, P ind To inductively absorb power, P cap For capacitively absorbing power, V is the volume of the plasma discharge chamber, e is the elementary charge, n e Is the electron density, n i Is the ion density, n l Is the density of the first seed particles, ε l Is the energy threshold of the first reaction, k l Is the coefficient of response of the l-th individual area, k s,i Is the surface reaction coefficient, V, of the i-th ion s Is a plasma levitation potential.
Optionally, the electromagnetic field distribution of the plasma source in the inductive mode is expressed by:
wherein E is θ1 (r, z) denotes the angular component of the electric field, B r1 (r, z) denotes the radial component of the magnetic field, B z1 (r, z) represents the axial component of the magnetic field; h is 1 Is the plasma region height in the plasma source, J 1 (λ m r) is a first order bessel function,
is the m-th zero of the first order Bessel function, R is the plasma source chamber radius, J 0 (λ m r) is a zero order Bessel function;
A m is a coefficient, z represents the axial position, ω is the angular frequency of the external power supply, ε p C is the speed of light in vacuum.
Optionally, the electromagnetic field distribution of the plasma source in the capacitive mode is expressed as:
wherein, B θ1 (r, z) denotes the angular component of the magnetic field, E r1 Denotes the radial component of the electric field, E z1 Represents the axial component of the electric field, J 0 (α m r) is a zero order Bessel function, J 1 (α m r) is a first order Bessel function;
Optionally, the formula for calculating the current inductive absorption power of the plasma source and the current capacitive absorption power of the plasma source is specifically:
wherein, the first and the second end of the pipe are connected with each other,
representing the current inductive or capacitive absorbed power, mu 0 Is the magnetic permeability of the vacuum and is,
which represents the vector of the magnetic field distribution,
represents the electric field distribution vector, and Re represents the real part.
To achieve the above object, the present invention further provides a system for fast simulation of discharge mode switching of an inductively coupled plasma source, the system comprising:
the assignment unit is used for assigning initial values to all physical quantities of the plasma source in the discharge process to obtain initial values of all the physical quantities; the physical quantities include electron density, electron temperature, ion density, neutral particle density, capacitive absorption power, and inductive absorption power; the ion and neutral particle types are determined by the type of gas used for the plasma source discharge;
the particle density calculating unit is used for calculating the density of each particle in the plasma source discharge process according to the particle number variation caused by pumping the gas into and out of the plasma source, the particle number variation caused by surface reaction and the particle number variation caused by body region reaction based on a particle number conservation equation; the particle number variation caused by the surface reaction and the particle number variation caused by the bulk reaction are related to the initial value of the electron temperature; the particles include electrons, ions, and neutral particles;
the current electronic temperature calculation unit is used for calculating the current electronic temperature according to the initial value of the inductive absorption power and the initial value of the capacitive absorption power based on an energy conservation equation and taking the current electronic temperature as the initial value of the electronic temperature of the next cycle iteration;
the electromagnetic field distribution determining unit is used for determining the electromagnetic field distribution of the plasma source in an inductive mode and the electromagnetic field distribution in a capacitive mode based on Maxwell equations;
the current power calculation unit is used for calculating the current inductive absorption power of the plasma source according to the electromagnetic field distribution in the inductive mode; calculating the current capacitive absorption power of the plasma source according to the electromagnetic field distribution in the capacitive mode; taking the current inductive absorption power as an initial value of inductive absorption power of next cycle iteration, and taking the current capacitive absorption power as an initial value of capacitive absorption power of next cycle iteration;
the circulating iteration and result output unit is connected with the particle density calculation unit and is used for returning and calculating the density of each particle, the current electronic temperature, the electromagnetic field distribution, the current inductive absorption power and the current capacitive absorption power until the difference value between the calculated value of each physical quantity and the value of each physical quantity calculated in the last circulating iteration is smaller than a set threshold value, stopping the circulating iteration and outputting the value of each physical quantity; the values of the respective physical quantities are used to characterize a discharge mode conversion process of the inductively coupled plasma source.
Optionally, the electromagnetic field distribution of the plasma source in inductive mode is expressed by:
wherein, E θ1 (r, z) denotes the angular component of the electric field, B r1 (r, z) denotes the radial component of the magnetic field, B z1 (r, z) represents the axial component of the magnetic field; h is 1 Is the plasma region height in the plasma source, J 1 (λ m r) is a first order bessel function,
is the m-th zero of the first order Bessel function, R is the plasma source chamber radius, J 0 (λ m r) is a zero order Bessel function;
A m is a coefficient, z represents the axial position, ω is the angular frequency of the external power supply, ε p C is the speed of light in vacuum.
Optionally, the electromagnetic field distribution of the plasma source in the capacitive mode is expressed as:
wherein, B θ1 (r, z) denotes the angular component of the magnetic field, E r1 Denotes the radial component of the electric field, E z1 Represents the axial component of the electric field, J 0 (α m r) is a zero order Bessel function, J 1 (α m r) is a first order Bessel function;
is the mth zero point of the zero-order Bessel function, R is the radius of the plasma source chamber,
T m is a coefficient, z represents the axial position, ω is the angular frequency of the external power supply, ε p C is the speed of light in vacuum.
Optionally, the formula for calculating the current inductive absorption power of the plasma source and the current capacitive absorption power of the plasma source is specifically:
wherein the content of the first and second substances,
representing the current inductive or capacitive absorbed power, mu 0 Is the magnetic permeability of the vacuum, and is,
which represents the vector of the magnetic field distribution,
represents the electric field distribution vector, and Re represents the real part.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a rapid simulation method and a rapid simulation system for discharge mode conversion of an inductive coupling plasma source, wherein the method comprises the following steps: giving initial values to each physical quantity of the plasma source in the discharge process, and calculating the density of each particle according to the particle number variation caused by pumping the gas into and out of the plasma source and the particle number variation caused by surface reaction and body area reaction on the basis of a particle number conservation equation; based on an energy conservation equation, calculating the current electron temperature according to the initial value of the inductive absorption power and the initial value of the capacitive absorption power, and taking the current electron temperature as the initial value of the electron temperature of the next cycle iteration; determining the electromagnetic field distribution of the plasma source in an inductive mode and a capacitive mode based on a Maxwell equation set; calculating the current inductive absorption power according to the electromagnetic field distribution in the inductive mode; calculating the current capacitive absorption power according to the electromagnetic field distribution in the capacitive mode; taking the current inductive absorption power as an initial value of inductive absorption power of next cycle iteration, and taking the current capacitive absorption power as an initial value of capacitive absorption power of next cycle iteration; returning to recalculate each physical quantity until the difference value between the value of each physical quantity and the value of each physical quantity calculated in the last cycle iteration is smaller than a set threshold value, stopping the cycle iteration and outputting the value of each physical quantity; the values of the respective physical quantities are used to characterize a discharge mode conversion process of the inductively coupled plasma source. The invention can accurately simulate the plasma characteristics in the discharge mode conversion process and simultaneously improve the calculation efficiency.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic diagram of an inductively coupled plasma source according to the present invention;
FIG. 2 is a flow chart of a method for rapid simulation of discharge mode switching of an inductively coupled plasma source according to the present invention;
FIG. 3 is a schematic block diagram of a fast simulation system for discharging mode conversion of an inductively coupled plasma source according to the present invention;
FIG. 4 is a diagram of the electric field distribution results calculated by the simulation method (left column) and finite difference time domain (right column) of the present invention;
FIG. 5 is a graph of conversion efficiency with power at different pressures;
FIG. 6 is a graph of conversion efficiency versus power for different pressures obtained by the simulation method of the present invention.
Description of the symbols:
the device comprises a plasma area-1, a dielectric window-2, a vacuum shielding area-3, a planar coil-4, an external power supply-5, an assignment unit-6, a particle density calculation unit-7, a current electronic temperature calculation unit-8, an electromagnetic field distribution determination unit-9, a current power calculation unit-10 and a loop iteration and result output unit-11.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for quickly simulating discharge mode conversion of an inductively coupled plasma source, which can accurately simulate the plasma characteristics in the discharge mode conversion process and can improve the calculation efficiency.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a schematic diagram of an inductively coupled plasma source according to the present invention, in which the chamber has an axisymmetric structure (the left dotted line is the axis of symmetry), and therefore only a section of the discharge device is shown. The whole plasma source discharge device is divided into three regions, namely a plasma region 1, a dielectric window 2 (oblique lines) and a vacuum shielding region 3. A planar coil 4 is placed above the dielectric window and, by connection to an external power supply 5, an electromagnetic field is excited throughout the interior of the discharge chamber, thereby generating a plasma.
As shown in fig. 2, the present invention provides a method for fast simulation of discharge mode switching of an inductively coupled plasma source, the method comprising:
s1: giving initial values to all physical quantities of the plasma source in the discharge process to obtain initial values of all the physical quantities; the physical quantities include electron density, electron temperature, ion density, neutral particle density, capacitive absorption power, and inductive absorption power; the type of ions and neutral particles being determined by the type of gas used for the plasma source discharge, e.g. Ar discharge, where the ions are Ar only + ；H 2 Discharge, then the ion has H + 、H 2 + Or H 3 + 。
S2: based on a particle number conservation equation, calculating the density of each particle in the plasma source discharge process according to the particle number variation caused by pumping gas into and out of the plasma source, the particle number variation caused by surface reaction and the particle number variation caused by bulk reaction; the particle number variation caused by the surface reaction and the particle number variation caused by the bulk reaction are related to the initial value of the electron temperature; the particles include electrons, ions, and neutral particles. The body region reaction refers to the reaction in the plasma cavity, and two or three kinds of particles collide to generate new particles; surface reactions refer to the movement of certain particles to the surface of the chamber, colliding with the surface of the chamber, and then generating new particles. The density of each particle is obtained by solving the particle number conservation equation for such particles.
S3: based on an energy conservation equation, calculating the current electron temperature according to the initial value of the inductive absorption power and the initial value of the capacitive absorption power, and taking the current electron temperature as the initial value of the electron temperature of the next cycle iteration.
S4: and determining the electromagnetic field distribution of the plasma source in an inductive mode and the electromagnetic field distribution of the plasma source in a capacitive mode based on the Maxwell equation set.
S5: calculating the current inductive absorption power of the plasma source according to the electromagnetic field distribution in the inductive mode; calculating the current capacitive absorption power of the plasma source according to the electromagnetic field distribution in the capacitive mode; and taking the current inductive absorption power as an initial value of inductive absorption power of next cycle iteration, and taking the current capacitive absorption power as an initial value of capacitive absorption power of next cycle iteration.
S6: returning to execute the step S2 until the difference value between the value of each physical quantity obtained by calculation and the value of each physical quantity calculated by the last loop iteration is smaller than the set threshold value, stopping the loop iteration, and outputting the value of each physical quantity; the values of the respective physical quantities are used to characterize a discharge mode conversion process of the inductively coupled plasma source.
Further, in step S2, the density of each particle is calculated by the formula:
R s,j ＝k s n s ； (2)
wherein j represents the particle type, R in,j Representing the amount of change in the number of particles, R, due to pumping of gas into the plasma source out,j Representing the amount of change in the number of particles due to pumping of gas out of the plasma source,
represents the amount of change in the number of particles, R, due to bulk reaction s,j Indicating a surface reactionAmount of change in the number of particles, k l Coefficient of response, k, of the l-th individual area s Coefficient of surface reaction, n l1 、n l2 And n s The density of each particle in the discharge gas is shown.
Further, in step S3, the formula for calculating the electron temperature is as follows:
wherein, T e Is the electron temperature, P ind To inductively absorb power, P cap For capacitively absorbing power, V is the volume of the plasma discharge chamber, e is the elementary charge, n e Is the electron density, n i Is the ion density, n l The density of the first type of particles, each type of particle density, is obtained through the step S2, and an initial value is adopted when the first time is called; when the subsequent calling is carried out, the density obtained by the calculation of the step S2 in the last iteration is adopted; epsilon l Is the energy threshold of the first reaction, k l Is the coefficient of response of the first individual area, k s,i Is the surface reaction coefficient, k, of the i-th ion l And k s,i Both of which are generally functions of electron temperature, V s Is a plasma levitation potential.
Further, in step S4, in the H mode, the electromagnetic field is solved as follows:
the distribution of the electromagnetic field can be obtained by solving Maxwell equations
Wherein E is an electric field, B is a magnetic field, μ 0 Is the vacuum permeability; ε is the dielectric constant, and ε = ε in the vacuum and plasma regions 0 In the dielectric window region, there is epsilon = epsilon 0 ε t ，ε 0 Is the vacuum dielectric constant ε t Is the relative permittivity of the medium; j is current, J =0 in the vacuum and dielectric window region, and J = J in the plasma region p Plasma current J p Satisfy the requirements of
Wherein e is a meta charge, n e Is the electron density (given by step S2), m e Is the electron mass, v eff Is the effective collision frequency.
Taking the rotation degree of two sides of the formula (4), then substituting the formula (5) and utilizing
Can obtain
The change in electric field and current over time is considered to be simple harmonic, i.e.
And substituting equation (6) into equation (7) yields:
where ω is the angular frequency of the external power supply and c is the speed of light in vacuum; kappa is the relative dielectric constant, and has a value of kappa =1 in the vacuum region and kappa = ε in the dielectric window region t In the plasma region, there are
Wherein the electron plasma frequency is ω pe ＝(e 2 n e /ε 0 m e ) 1/2 。
In the H-mode, the electromagnetic field component is
Then in the case of axial symmetry, equation (8) can be written as:
considering the proper boundary, through mathematical derivation, the expression of the electromagnetic field distribution of the plasma source in the inductive mode can be obtained as follows:
wherein, E θ1 (r, z) denotes the angular component of the electric field, B r1 (r, z) denotes the radial component of the magnetic field, B z1 (r, z) represents the axial component of the magnetic field; h is 1 Is the plasma region height in the plasma source, J 1 (λ m r) is a first order bessel function,
is the m-th zero of the first order Bessel function, R is the plasma source chamber radius, J 0 (λ m r) is a zero order Bessel function;
A m is a coefficient, z represents the axial position, ω is the angular frequency of the external power supply, ε p C is the speed of light in vacuum.
Further, in the E mode, the solving process of the electromagnetic field is as follows:
in the E mode, the electromagnetic field component is
Taking the rotation degree of two sides of the formula (5), then substituting the formula (4) and utilizing
And equation (6), one can obtain:
by taking the proper boundary into consideration, through mathematical derivation, the electromagnetic field distribution expression of the plasma source in the capacitive mode in the plasma region can be obtained:
wherein, B θ1 (r, z) denotes the azimuthal component of the magnetic field, E r1 Denotes the radial component of the electric field, E z1 Represents the axial component of the electric field, J 0 (α m r) is a zero order Bessel function, J 1 (α m r) is a first order Bessel function;
is the mth zero point of the zero-order Bessel function, R is the radius of the plasma source chamber,
T m is a coefficient, z represents the axial position, ω is the angular frequency of the external power supply, ε p C is the speed of light in vacuum.
The solving method of the electromagnetic field in the step S4 is basically the same as the electromagnetic field result directly calculated by adopting finite difference of time domain, but the calculation mode of the invention has high calculation efficiency.
Further, in step S5, the inductive absorption power P can be obtained by substituting the electromagnetic field distributions in the H mode and the E mode into the formula (15) ind And a capacitive absorbed power P cap . The formula adopted for calculating the current inductive absorption power of the plasma source and the current capacitive absorption power of the plasma source is specifically as follows:
wherein the content of the first and second substances,
representing the current inductive or capacitive absorbed power, mu 0 Is the magnetic permeability of the vacuum and is,
which represents the vector of the magnetic field distribution,
represents the electric field distribution vector, and Re represents the real part.
To achieve the above object, the present invention further provides a system for fast simulation of discharge mode switching of an inductively coupled plasma source, as shown in fig. 3, the system comprising: an assignment unit 6, a particle density calculation unit 7, a current electron temperature calculation unit 8, an electromagnetic field distribution determination unit 9, a current power calculation unit 10, and a loop iteration and result output unit 11.
The assignment unit is 7 units and is used for assigning initial values to all physical quantities of the plasma source in the discharge process to obtain initial values of all the physical quantities; the physical quantities include electron density, electron temperature, ion density, neutral particle density, capacitive absorption power, and inductive absorption power; the ion and neutral particle types are determined by the type of gas used for the plasma source discharge.
The particle density calculating unit 7 is used for calculating the density of each particle in the plasma source discharge process according to the particle number variation caused by pumping the gas into and out of the plasma source, the particle number variation caused by surface reaction and the particle number variation caused by body region reaction based on a particle number conservation equation; the particle number variation caused by the surface reaction and the particle number variation caused by the bulk reaction are related to the initial value of the electron temperature; the particles include electrons, ions, and neutral particles.
And the current electronic temperature calculating unit 8 is used for calculating the current electronic temperature according to the initial value of the inductive absorption power and the initial value of the capacitive absorption power based on an energy conservation equation, and taking the current electronic temperature as the initial value of the electronic temperature of the next cycle iteration.
And the electromagnetic field distribution determining unit 9 is used for determining the electromagnetic field distribution of the plasma source in an inductive mode and the electromagnetic field distribution of the plasma source in a capacitive mode based on Maxwell equations.
A current power calculating unit 10, configured to calculate a current inductive absorption power of the plasma source according to the electromagnetic field distribution in the inductive mode; calculating the current capacitive absorption power of the plasma source according to the electromagnetic field distribution in the capacitive mode; and taking the current inductive absorption power as an initial value of inductive absorption power of next cycle iteration, and taking the current capacitive absorption power as an initial value of capacitive absorption power of next cycle iteration.
A circulating iteration and result output unit 11, connected to the particle density calculation unit 7, for calculating the particle density, the current electronic temperature, the electromagnetic field distribution, the current inductive absorption power, and the current capacitive absorption power in return, stopping the circulating iteration until the difference between the calculated values of the physical quantities and the values of the physical quantities calculated in the last circulating iteration is smaller than a set threshold, and outputting the values of the physical quantities; the values of the respective physical quantities are used to characterize a discharge mode conversion process of the inductively coupled plasma source.
Further, the electromagnetic field distribution of the plasma source in the inductive mode is expressed as:
wherein E is θ1 (r, z) denotes the angular component of the electric field, B r1 (r, z) denotes the radial component of the magnetic field, B z1 (r, z) represents the axial component of the magnetic field; h is a total of 1 Is the plasma region height in the plasma source, J 1 (λ m r) is a first order bessel function,
is the m-th zero of the first order Bessel function, R is the plasma source chamber radius, J 0 (λ m r) is a zero order Bessel function;
A m is a coefficient, z represents the axial position, ω is the angular frequency of the external power supply, ε p C is the speed of light in vacuum.
Further, the electromagnetic field distribution expression of the plasma source in the capacitive mode is as follows:
wherein, B θ1 (r, z) denotes the angular component of the magnetic field, E r1 Denotes the radial component of the electric field, E z1 Represents the axial component of the electric field, J 0 (α m r) is a zero order Bessel function, J 1 (α m r) is a first order Bessel function;
is the mth zero point of the zero-order Bessel function, R is the radius of the plasma source chamber,
T m is a coefficient, z represents the axial position, ω is the angular frequency of the external power supply, ε p C is the speed of light in vacuum.
Further, the formula adopted for calculating the current inductive absorption power of the plasma source and the current capacitive absorption power of the plasma source is specifically as follows:
wherein the content of the first and second substances,
representing the current inductive or capacitive absorbed power, mu 0 Is the magnetic permeability of the vacuum and is,
which represents the vector of the magnetic field distribution,
represents the electric field distribution vector, and Re represents the real part.
The electromagnetic field calculated by the simulation method of the invention has high precision, and better accords with the electric field distribution obtained by directly solving Maxwell equation sets by adopting time domain finite difference, as shown in figure 4, the left column in the figure is the electric field distribution calculated by the simulation method of the invention, and the right column is the electric field distribution calculated by the time domain finite difference.
In addition, by adopting the scheme of the invention, the plasma characteristics in the discharge mode conversion process can be accurately described, and the plasma characteristics are well consistent with experimental measurement results, as shown in fig. 5 and 6. In the E mode, the density of particles is low, and the density of particles in the H mode is high, and the transition process of the discharge mode can be observed by observing a graph of the density changing with the power. Therefore, the technical scheme of the invention can be used for qualitatively researching the mode conversion process in the discharge process of the inductive coupling plasma source.
Moreover, by adopting the simulation method of the invention, the space part of the electromagnetic field can be directly obtained, and the electromagnetic field can be iteratively solved by adopting a finite difference time domain method without each lattice point in space. The plasma characteristics are described by adopting an integral model, so that a large number of nonlinear equation systems are prevented from being solved at each lattice point in space, and the simulation efficiency of the simulation method is higher than that of the traditional fluid mechanics method.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A method for rapid simulation of discharge mode switching for an inductively coupled plasma source, the method comprising:
s1: giving initial values to all physical quantities of the plasma source in the discharge process to obtain initial values of all the physical quantities; the physical quantities include electron density, electron temperature, ion density, neutral particle density, capacitive absorption power, and inductive absorption power; the ion and neutral particle types are determined by the type of gas used for the plasma source discharge;
s2: based on a particle number conservation equation, calculating the density of each particle in the plasma source discharge process according to the particle number variation caused by pumping gas into and out of the plasma source, the particle number variation caused by surface reaction and the particle number variation caused by bulk reaction; the particle number variation caused by the surface reaction and the particle number variation caused by the bulk reaction are related to the initial value of the electron temperature; the particles include electrons, ions, and neutral particles;
s3: based on an energy conservation equation, calculating the current electron temperature according to the initial value of the inductive absorption power and the initial value of the capacitive absorption power, and taking the current electron temperature as the initial value of the electron temperature of the next cycle iteration;
s4: determining the electromagnetic field distribution of the plasma source in an inductive mode and the electromagnetic field distribution of the plasma source in a capacitive mode based on a Maxwell equation set;
s5: calculating the current inductive absorption power of the plasma source according to the electromagnetic field distribution in the inductive mode; calculating the current capacitive absorption power of the plasma source according to the electromagnetic field distribution in the capacitive mode; taking the current inductive absorption power as an initial value of inductive absorption power of next cycle iteration, and taking the current capacitive absorption power as an initial value of capacitive absorption power of next cycle iteration;
s6: returning to execute the step S2 until the difference value between the value of each physical quantity obtained by calculation and the value of each physical quantity calculated by the last cycle iteration is smaller than the set threshold value, stopping the cycle iteration and outputting the value of each physical quantity; the values of the respective physical quantities are used to characterize a discharge mode conversion process of the inductively coupled plasma source.
2. The method of claim 1, wherein the density of each particle is calculated using the formula:
R s,j ＝k s n s ；
wherein j represents the particle type, R in,j Representing the amount of change in the number of particles, R, due to pumping of gas into the plasma source out,j Representing the amount of change in the number of particles due to pumping of gas out of the plasma source,
represents the amount of change in the number of particles, R, due to bulk reaction s,j Represents the amount of change in the number of particles, k, due to surface reaction l Coefficient of response, k, of the l-th individual area s Coefficient of surface reaction, n l1 、n l2 And n s Which represents the density of each particle in the discharge gas.
3. The method of claim 2, wherein the electron temperature is calculated by the formula:
wherein, T e Is the electron temperature, P ind To inductively absorb power, P cap For capacitive absorption of power, V is the volume of the discharge chamber of the plasma source, e is the elementary charge, n e Is the electron density, n i Is the ion density, n l Is the first seed particleOf density of ∈ of l Is the energy threshold of the first reaction, k l Is the coefficient of response of the l-th individual area, k s,i Is the surface reaction coefficient, V, of the i-th ion s Is a plasma levitation potential.
4. The method of claim 1, wherein the electromagnetic field distribution of the plasma source in the inductive mode is expressed as:
wherein, E θ1 (r, z) denotes the angular component of the electric field, B r1 (r, z) denotes the radial component of the magnetic field, B z1 (r, z) represents the axial component of the magnetic field; h is a total of 1 Is the plasma region height in the plasma source, J 1 (λ m r) is a first order bessel function,
is the m-th zero of the first order Bessel function, R is the plasma source chamber radius, J 0 (λ m r) is a zero order Bessel function;
A m is a coefficient, z represents the axial position, ω is the angular frequency of the external power supply, ε p C is the speed of light in vacuum.
5. The method of claim 1, wherein the electromagnetic field distribution of the plasma source in the capacitive mode is expressed as:
wherein, B θ1 (r, z) denotes the angular component of the magnetic field, E r1 Denotes the radial component of the electric field, E z1 Represents the axial component of the electric field, J 0 (α m r) is a zero order Bessel function, J 1 (α m r) is a first order Bessel function;
6. The method of claim 1, wherein the formula for calculating the current inductively absorbed power of the plasma source and the current capacitively absorbed power of the plasma source is specifically:
wherein the content of the first and second substances,
representing the current inductive or capacitive absorbed power, mu 0 Is the magnetic permeability of the vacuum and is,
which represents the vector of the magnetic field distribution,
represents the electric field distribution vector, and Re represents the real part.
7. A system for rapid simulation of discharge mode switching in an inductively coupled plasma source, the system comprising:
the assignment unit is used for assigning initial values to all physical quantities of the plasma source in the discharge process to obtain initial values of all the physical quantities; the physical quantities include electron density, electron temperature, ion density, neutral particle density, capacitive absorption power and inductive absorption power; the ion and neutral particle types are determined by the type of gas used for the plasma source discharge;
the particle density calculating unit is used for calculating the density of each particle in the plasma source discharge process according to the particle number variation caused by pumping the gas into and out of the plasma source, the particle number variation caused by surface reaction and the particle number variation caused by body region reaction based on a particle number conservation equation; the particle number variation caused by the surface reaction and the particle number variation caused by the bulk reaction are related to the initial value of the electron temperature; the particles include electrons, ions, and neutral particles;
the current electronic temperature calculation unit is used for calculating the current electronic temperature according to the initial value of the inductive absorption power and the initial value of the capacitive absorption power based on an energy conservation equation and taking the current electronic temperature as the initial value of the electronic temperature of the next cycle iteration;
the electromagnetic field distribution determining unit is used for determining the electromagnetic field distribution of the plasma source in an inductive mode and the electromagnetic field distribution in a capacitive mode based on Maxwell equations;
the current power calculation unit is used for calculating the current inductive absorption power of the plasma source according to the electromagnetic field distribution in the inductive mode; calculating the current capacitive absorption power of the plasma source according to the electromagnetic field distribution in the capacitive mode; taking the current inductive absorption power as an initial value of inductive absorption power of next cycle iteration, and taking the current capacitive absorption power as an initial value of capacitive absorption power of next cycle iteration;
the circulating iteration and result output unit is connected with the particle density calculation unit and is used for returning and calculating the density of each particle, the current electronic temperature, the electromagnetic field distribution, the current inductive absorption power and the current capacitive absorption power until the difference value between the calculated value of each physical quantity and the value of each physical quantity calculated in the last circulating iteration is smaller than a set threshold value, stopping the circulating iteration and outputting the value of each physical quantity; the values of the respective physical quantities are used to characterize a discharge mode conversion process of the inductively coupled plasma source.
8. The system of claim 7, wherein the electromagnetic field distribution of the plasma source in the inductive mode is expressed as:
wherein E is θ1 (r, z) denotes the angular component of the electric field, B r1 (r, z) denotes the radial component of the magnetic field, B z1 (r, z) represents the axial component of the magnetic field; h is 1 Is the plasma region height in the plasma source, J 1 (λ m r) is a first order bessel function,
is the mth zero of the first order Bessel function, R is the plasma source chamber radius, J 0 (λ m r) is a zero order Bessel function;
A m is a coefficient, z represents the axial position, ω is the angular frequency of the external power supply, ε p C is the speed of light in vacuum.
9. The system of claim 7, wherein the electromagnetic field distribution of the plasma source in the capacitive mode is expressed as:
wherein, B θ1 (r, z) denotes the angular component of the magnetic field, E r1 Denotes the radial component of the electric field, E z1 Represents the axial component of the electric field, J 0 (α m r) is a zero order Bessel function, J 1 (α m r) is a first order Bessel function;
10. The system of claim 7, wherein the formula for calculating the current inductively absorbed power of the plasma source and the current capacitively absorbed power of the plasma source is specifically:
wherein the content of the first and second substances,
representing the current inductive or capacitive absorbed power, mu 0 Is the magnetic permeability of the vacuum and is,
which represents the vector of the magnetic field distribution,
represents the electric field distribution vector, and Re represents the real part.
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