A bias inductively coupled plasma source optimization method, system and electronic equipment

Abstract

The present invention provides a bias inductively coupled plasma source optimization method, system and electronic equipment, which relates to the field of bias inductively coupled plasma technology, including: determining the electric field and inductive deposition power density of the bias inductively coupled plasma source, thereby obtaining body fluid parameters and sheath parameters of each sheath; determining and using the random heating flux of the sheath to the body as the boundary condition of the body electron energy equation in the two-dimensional fluid model of the body during the next iteration, determining the electric field of the bias inductively coupled plasma source until both the body fluid parameters and the sheath parameters converge, and obtaining a time-space varying electric field; and then determining the ion Monte Carlo collision model to obtain the ion energy distribution and ion angle distribution at different positions of the plate. The ion energy distribution and ion angle distribution in the bias inductively coupled plasma source can be determined simultaneously and quickly, thereby improving the efficiency of optimizing the discharge characteristics of the bias inductively coupled plasma source.

Description

Technical Field

[0001] The present invention relates to the technical field of bias inductively coupled plasma sources, and in particular to a bias inductively coupled plasma source optimization method, system and electronic equipment. Background Art

[0002] As we all know, inductively coupled plasma sources are widely used in semiconductor processes, such as etching and deposition processes. With the improvement of process requirements, the requirements for etching performance are becoming more and more stringent. As important parameters in the process, ion energy distribution and ion angle distribution are directly related to the etching performance. By applying a bias power supply to the plate of the inductively coupled plasma source, the ion energy distribution and ion angle distribution can be regulated, thereby better modulating the etching process.

[0003] Numerical simulation methods are often used to study the ion energy distribution and ion angle distribution in biased inductively coupled plasma. At present, the commonly used models are the overall model coupled sheath model and the ion Monte Carlo collision model. In this hybrid simulation method, the overall model provides parameters such as plasma density and electron temperature, the sheath model calculates the electric field in the sheath, and the ion Monte Carlo collision model calculates the energy and angle distribution of the ions based on the electric field in the sheath. The advantage of this simulation method is the fast calculation speed, but the disadvantage is also obvious, that is, this method cannot give the spatial distribution of plasma parameters, and cannot obtain the ion energy distribution and ion angle distribution at different positions of the plate. The full-area fluid model coupled ion Monte Carlo collision model is also a commonly used method. In this method, the body and sheath of the plasma are solved simultaneously, and the sheath can be calculated self-consistently. Then, the ion Monte Carlo collision model is used to calculate the ion energy distribution and ion angle distribution at different positions of the plate. The advantage of this method is that it is relatively self-consistent, and the disadvantage is that due to the large difference in the spatial scale between the sheath and the body, the numerical solution is difficult and the calculation efficiency is low. Therefore, it is important to propose a simulation method that meets the requirements and is efficient in order to optimize the discharge characteristics of the biased inductively coupled plasma source and thus optimize the etching process. Summary of the invention

[0004] The object of the present invention is to provide a bias inductively coupled plasma source optimization method, system and electronic equipment, which can simultaneously and quickly determine the ion energy distribution and ion angle distribution in the bias inductively coupled plasma source, thereby improving the efficiency of optimizing the discharge characteristics of the bias inductively coupled plasma source.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A bias inductively coupled plasma source optimization method, comprising:

[0007] Obtaining parameters of a biased inductively coupled plasma source; the parameters include discharge gas pressure, power and chamber size;

[0008] Determining the electric field and inductive deposition power density of the biased inductively coupled plasma source according to the parameters;

[0009] Determine the two-dimensional fluid model of the body region according to the induced deposition power density, obtain the body region fluid parameters, and simultaneously obtain the plasma density and electron temperature at the sheath boundary; the body region fluid parameters include the electron density, ion density, electron temperature and bipolar electrostatic field of the body region;

[0010] Determine multiple one-dimensional sheath models according to the plasma density and electron temperature at the sheath boundary, and obtain sheath parameters of each sheath; the sheath parameters include sheath electron density, sheath ion density, sheath potential and sheath electric field in the sheath; the one-dimensional sheath model corresponds to the sheath in the biased inductively coupled plasma source one by one;

[0011] Determine whether the body fluid parameters and sheath parameters are converged, and obtain a determination result;

[0012] If the judgment result is no, the random heating flux of the sheath to the body region is determined according to the sheath parameters, and the random heating flux is used as the boundary condition of the body region electron energy equation in the body region two-dimensional fluid model in the next iteration to return to the step of "determining the electric field and inductive deposition power density of the biased inductively coupled plasma source";

[0013] If the judgment result is yes, determining that the sheath electric field at the last iteration is a spatiotemporally varying electric field;

[0014] The ion Monte Carlo collision model is determined based on the spatiotemporally varying sheath electric field to obtain ion energy distribution and ion angle distribution at different positions of the electrode plate.

[0015] Optionally, after determining the ion Monte Carlo collision model based on the spatiotemporal varying sheath electric field to obtain the ion energy distribution and ion angle distribution at different positions of the electrode plate, the method further includes:

[0016] The discharge characteristics of the biased inductively coupled plasma source are optimized according to the ion energy distribution and ion angle distribution at different positions of the electrode plate.

[0017] Optionally, determining the electric field and inductive deposition power density of the biased inductively coupled plasma source according to the parameters includes:

[0018] Constructing a Helmholtz equation; the Helmholtz equation is constructed based on the parameters when the electromagnetic field and current in the biased inductively coupled plasma source satisfy the harmonic approximation principle;

[0019] Solving the Helmholtz equation to obtain the electric field of the biased inductively coupled plasma source;

[0020] determining an inductive deposition power density based on an electric field of a biased inductively coupled plasma source;

[0021] Wherein, the Helmholtz equation is:

[0022] The induction deposition power density is:

[0023] in, is the gradient operator; E is the induced electric field, ε is the dielectric constant, σ is the plasma conductivity, j is the imaginary unit; ω is the power angular frequency; μ0 is the vacuum permeability; J coil is the coil current density, P ind is the induced deposition power density; Re(.) is the operation of taking the real part of the complex number; J p is the plasma current density, E * is the complex conjugate of the induced electric field.

[0024] Optionally, the two-dimensional fluid model of the body region includes a body region ion continuity equation, a body region ion momentum equation, a body region electron energy equation, an electron flux migration and diffusion equation, an electron density equation and a body region bipolar electrostatic field equation; the electron density equation is constructed based on a quasi-neutral condition; the body region bipolar electrostatic field equation is constructed based on the principle that the ion current density in the body region bipolar electrostatic field is equal to the electron current density;

[0025] The body ion continuity equation is:

[0026] Among them, n i is the density of the ions, is the gradient operator; Γ i is the ion flux, S i is the ion source term, t is the time;

[0027] The bulk ion momentum equation is:

[0028] Among them, m i is the ion mass, u i is the ion orientation velocity, q i is the charge of the ion, E s is the body bipolar electrostatic field, k B is the Boltzmann constant, T i is the ion temperature, M i is the ion collision term;

[0029] The electron energy equation is:

[0030] Among them, n e is the electron density, T e is the electron temperature, Q e is the electron energy flux, S energy is the energy source term of the electron, S energy =-eΓ e ·E s +P ind -E e , E e is the collision energy loss term, P ind is the induction deposition power density;

[0031] The electron flux migration diffusion equation is:

[0032] Among them, Γ e is the electron flux; μ e is the electron mobility, D e is the diffusion coefficient of electrons;

[0033] Electron density equation; en e =q i n i ;

[0034] Among them, n i is the ion density; e is the unit charge;

[0035] The bipolar electrostatic field equation in the body region is:

[0036] Optionally, the method further includes:

[0037] The sheath ion density is determined by the sheath ion continuity equation and the sheath ion momentum equation;

[0038] The sheath electron density is determined by the Boltzmann relation;

[0039] The sheath potential is determined by Poisson's equation;

[0040] The sheath electric field is determined by the sheath electric field equation.

[0041] Optionally, the sheath ion continuity equation is: x is the spatial coordinate of the sheath;

[0042] The sheath ion momentum equation is:

[0043] The Boltzmann relation: n e (x) is the sheath electron density,

[0044] n0 is the electron density at the edge of the sheath calculation region, is the potential at the edge of the sheath calculation region,

[0045] The Poisson equation is: ε0 is the dielectric constant of vacuum, is the electric potential in the sheath.

[0046] The sheath electric field equation is:

[0047] Among them, E sheath is the sheath electric field.

[0048] Optionally, the ion energy distribution is:

[0049] Among them, f(ε j ) represents the ion energy distribution function; N(ε j ) is the energy located at The number of ions between them; Δε is the ion energy interval;

[0050] The ion angle distribution is:

[0051] Among them, f(θ j ) is the ion angle distribution function, N(θ j ) is the angle located at is the number of ions between them, and Δθ is the ion angular separation.

[0052] A bias inductively coupled plasma source optimization system, comprising:

[0053] A parameter acquisition module, used to acquire parameters of a bias inductively coupled plasma source; the parameters include discharge gas pressure, power and chamber size;

[0054] An electric field and inductive deposition power density determination module, used to determine the electric field and inductive deposition power density of the biased inductively coupled plasma source according to the parameters;

[0055] A two-dimensional fluid model determination module is used to determine the two-dimensional fluid model of the body region according to the induced deposition power density, obtain body region fluid parameters, and simultaneously obtain the plasma density and electron temperature at the sheath boundary; the body region fluid parameters include the electron density, ion density, electron temperature and bipolar electrostatic field of the body region;

[0056] A sheath parameter determination module is used to determine multiple one-dimensional sheath models according to the plasma density and electron temperature at the sheath boundary to obtain sheath parameters of each sheath; the sheath parameters include sheath electron density, sheath ion density, sheath potential and sheath electric field in the sheath; the one-dimensional sheath model corresponds to the sheath in the biased inductively coupled plasma source one by one;

[0057] A judgment module, used to judge whether the body fluid parameters and sheath parameters are converged, and obtain a judgment result; if the judgment result is no, the random heating flux of the sheath to the body is determined according to the sheath parameters, and the random heating flux is used as the boundary condition of the body electron energy equation in the two-dimensional fluid model of the body in the next iteration and the electric field and induced deposition power density solving module is called; if the judgment result is yes, the spatiotemporal variation sheath electric field determination module is called;

[0058] A time-space varying sheath electric field determination module is used to determine that the sheath electric field at the last iteration is a time-space varying electric field;

[0059] The ion energy distribution and ion angle distribution determination module is used to determine the ion Monte Carlo collision model based on the spatiotemporal variation sheath electric field to obtain the ion energy distribution and ion angle distribution at different positions of the electrode plate.

[0060] An electronic device comprises a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the above-mentioned bias inductively coupled plasma source optimization method.

[0061] The memory is a readable storage medium.

[0062] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0063] The present invention provides a bias inductively coupled plasma source optimization method, system and electronic equipment. The method comprises: obtaining parameters of the bias inductively coupled plasma source; the parameters include discharge gas pressure, power and chamber size; determining the electric field and inductive deposition power density of the bias inductively coupled plasma source according to the parameters; determining a two-dimensional fluid model of a body region according to the inductive deposition power density to obtain body region fluid parameters, and simultaneously obtaining plasma density and electron temperature at a sheath boundary; the body region fluid parameters include electron density, ion density, electron temperature and bipolar electrostatic field of the body region; determining multiple one-dimensional sheath models according to the plasma density and electron temperature at the sheath boundary to obtain sheath parameters of each sheath; the sheath parameters include sheath electron density, sheath temperature and sheath density in the sheath. Ion density, sheath potential and sheath electric field; the one-dimensional sheath model corresponds to the sheath in the bias inductively coupled plasma source one by one; determine whether the body fluid parameters and sheath parameters are converged to obtain a judgment result; if the judgment result is no, determine the random heating flux of the sheath to the body according to the sheath parameters, and use the random heating flux as the boundary condition of the body electron energy equation in the two-dimensional fluid model of the body in the next iteration to return to the step "determine the electric field and inductive deposition power density of the bias inductively coupled plasma source"; if the judgment result is yes, determine that the sheath electric field at the last iteration is a spatiotemporal electric field; determine the ion Monte Carlo collision model based on the spatiotemporal sheath electric field, and obtain the ion energy distribution and ion angle distribution at different positions of the plate. The ion energy distribution and ion angle distribution in the bias inductively coupled plasma source can be determined simultaneously and quickly, thereby improving the efficiency of optimizing the discharge characteristics of the bias inductively coupled plasma source. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0065] Figure 1 This is a flow chart of the bias inductively coupled plasma source optimization method in Example 1 of the present invention;

[0066] Figure 2 Graph showing the variation of the ion energy distribution function at the center of the lower plate with the bias voltage amplitude in Example 1 of the present invention;

[0067] Figure 3 The ion angle distribution function at the center of the lower plate changes with the bias amplitude in Example 1 of the present invention;

[0068] Figure 4Schematic diagram of the biased inductively coupled plasma source in Example 1 of the present invention. DETAILED DESCRIPTION

[0069] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0070] The object of the present invention is to provide a bias inductively coupled plasma source optimization method, system and electronic equipment, which can simultaneously and quickly determine the ion energy distribution and ion angle distribution in the bias inductively coupled plasma source, thereby improving the efficiency of optimizing the discharge characteristics of the bias inductively coupled plasma source.

[0071] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0072] Example 1

[0073] like Figure 1 and Figure 4 As shown, the present invention provides a bias inductively coupled plasma source optimization method, comprising:

[0074] Step 101: Obtaining parameters of a biased inductively coupled plasma source; the parameters include discharge gas pressure, power, and chamber size.

[0075] Step 102: Determine the electric field and inductive deposition power density of the biased inductively coupled plasma source according to the parameters.

[0076] Step 102 includes:

[0077] Step 1021: constructing the Helmholtz equation; the Helmholtz equation is constructed based on parameters when the electromagnetic field and current in the biased inductively coupled plasma source satisfy the harmonic approximation principle.

[0078] Step 1022: Solve the Helmholtz equation to obtain the electric field of the biased inductively coupled plasma source.

[0079] Step 1023: Determine the inductive deposition power density according to the electric field of the biased inductively coupled plasma source.

[0080] The Helmholtz equation is:

[0081] The induction deposition power density is:

[0082] in, is the gradient operator; E is the induced electric field, ε is the dielectric constant, σ is the plasma conductivity, j is the imaginary unit; ω is the power angular frequency; μ0 is the vacuum permeability; J coil is the coil current density, P ind is the induced deposition power density; Re(.) is the operation of taking the real part of the complex number; J p is the plasma current density, E * is the complex conjugate of the induced electric field.

[0083] Specifically, the induced electromagnetic field generated by the radio frequency coil is solved by the frequency domain method:

[0084] The induced electromagnetic field satisfies Maxwell's equations:

[0085]

[0086]

[0087] Where E is the induced electric field, B is the induced magnetic field, and J p is the plasma current density, J coil is the coil current density, μ0 is the vacuum magnetic permeability, and ε is the dielectric constant.

[0088] The plasma density satisfies the following equation:

[0089]

[0090] Where e is the unit charge, n e is the electron density, m e is the mass of the electron, v en is the elastic collision frequency of electrons with the background gas. Assume that the electromagnetic field and current satisfy the harmonic approximation, that is, The following Helmholtz equation can be obtained:

[0091]

[0092] Where σ is the plasma conductivity and ω is the power angular frequency. By solving the above Helmholtz equation, the induced electric field can be obtained. Based on the induced electric field, the induced deposition power density can be further calculated.

[0093] Step 103: determining a two-dimensional fluid model of the body region according to the induced deposition power density, obtaining body region fluid parameters, and simultaneously obtaining plasma density and electron temperature at the sheath boundary; body region fluid parameters include electron density, ion density, electron temperature and bipolar electrostatic field of the body region;

[0094] According to the induced deposition power density, the two-dimensional fluid model of the body region is solved to obtain the body fluid parameters; the body fluid parameters include the electron density, ion density, electron temperature and bipolar electrostatic field of the body region; at the same time, the plasma density and electron temperature at the sheath boundary are obtained.

[0095] The two-dimensional fluid model of the body region includes the body ion continuity equation, the body ion momentum equation, the body electron energy equation, the electron flux migration and diffusion equation, the electron density equation and the body bipolar electrostatic field equation; the electron density equation is constructed based on the quasi-neutral condition; the body bipolar electrostatic field equation is constructed based on the principle that the ion current density is equal to the electron current density in the body bipolar electrostatic field.

[0096] The ion continuity equation in the bulk region is:

[0097] Among them, n i is the density of ions, is the gradient operator; Γ i is the ion flux, S i is the ion source term, t is the time;

[0098] The momentum equation of the bulk ions is:

[0099] Among them, m i is the ion mass, u i is the ion orientation velocity, q i is the charge of the ion, E s is the body bipolar electrostatic field, k B is the Boltzmann constant, T i is the ion temperature, M i is the ion collision term;

[0100] The electron energy equation is:

[0101] Among them, n e is the electron density, T e is the electron temperature, Q e is the electron energy flux, S energy is the energy source term of the electron, S energy =-eΓ e ·E s +P ind -E e , E e is the collision energy loss term, P ind is the induction deposition power density;

[0102] The electron flux migration diffusion equation is:

[0103] Among them, Γe is the electron flux; μ e is the electron mobility, D e is the diffusion coefficient of electrons;

[0104] Electron density equation; en e =q i n i ;

[0105] Among them, n i is the ion density; e is the unit charge;

[0106] The bipolar electrostatic field equation in the body region is:

[0107] Step 104: Determine multiple one-dimensional sheath models according to the plasma density and electron temperature at the sheath boundary to obtain sheath parameters of each sheath; the sheath parameters include sheath electron density, sheath ion density, sheath potential and sheath electric field in the sheath; the one-dimensional sheath model corresponds to the sheath in the biased inductively coupled plasma source one by one.

[0108] Among them, the sheath ion density is determined by the sheath ion continuity equation and the sheath ion momentum equation; the sheath electron density is determined by the Boltzmann relationship; the sheath potential is determined by the Poisson equation; and the sheath electric field is determined by the sheath electric field equation.

[0109] Specifically, the sheath ion continuity equation is: x is the spatial coordinate of the sheath.

[0110] The momentum equation of sheath ions is:

[0111] The Boltzmann relation is: n e (x) is the sheath electron density.

[0112] n0 is the electron density at the edge of the sheath calculation region, is the potential at the edge of the sheath calculation region,

[0113] Poisson's equation is: ε0 is the dielectric constant of vacuum, is the electric potential in the sheath.

[0114] The electric field equation of the sheath is:

[0115] Among them, E sheath is the sheath electric field.

[0116] The specific steps are as follows:

[0117] The plasma density n at the sheath boundary calculated using the body region e and the electron temperature T e , calculate multiple one-dimensional sheath models at different radial positions. The sheath model can obtain the electron density n in the sheath e (x), ion density n i (x), potential, electric field and other parameters. In the sheath model, the continuity equation and momentum equation of the ions are solved.

[0118] Continuity equation for ions:

[0119]

[0120] The momentum equation for the ion is:

[0121]

[0122] Assuming that the electron density satisfies the Boltzmann relation, we have:

[0123]

[0124] where n0 is the electron density at the edge of the sheath calculation region, determined by the fluid model in step 2. is the potential at the edge of the sheath calculation region and is set to 0. is the electric potential in the sheath, determined by Poisson’s equation:

[0125]

[0126] Where ε0 is the dielectric constant of vacuum. So the electric field in the sheath is:

[0127]

[0128] When solving the Poisson equation, the potential at the lower plate is needed. Assume that the potential at the lower plate is V bias Meet V bias =V dc +V RF . Where V dc is the self-bias voltage, V RF is the RF voltage.

[0129] The self-bias voltage in the dual-frequency case is calculated by the following formula:

[0130]

[0131] in T is the RF period, ω1 and ω2 are two angular frequencies, V1 and V2 are the corresponding amplitudes, and φ is the relative phase. In the case of single frequency, the self-bias voltage is:

[0132]

[0133] Where I0(x) is the zero-order modified Bessel function.

[0134] At the same time, the sheath will produce a random heating effect on the body. The sheath model calculates the random heating flux S at the boundary. stoc The size of (t) is as follows:

[0135]

[0136] in n es is the electron density at the sheath boundary, u es is the velocity at the edge of the sheath. At the boundary between the sheath and the body, the boundary condition of the electron temperature equation is

[0137] Step 105: determine whether the body fluid parameters and sheath parameters are converged, and obtain a determination result; if the determination result is no, determine the random heating flux of the sheath to the body according to the sheath parameters, and use the random heating flux as the boundary condition of the body electron energy equation in the body two-dimensional fluid model in the next iteration and return to step 102; if the determination result is yes, execute step 106;

[0138] Step 106: Determine that the sheath electric field at the last iteration is a spatiotemporally varying electric field;

[0139] Step 107: Determine the ion Monte Carlo collision model based on the spatiotemporally varying sheath electric field to obtain the ion energy distribution and ion angle distribution at different positions of the electrode.

[0140] When the iteration converges, the time-space varying sheath electric field E calculated by the sheath model is sheath (x, t), passed to the ion Monte Carlo collision model. The ion Monte Carlo collision model can obtain the ion energy and angular distribution at different radial positions of the electrode. The specific calculation process is as follows: first initialize the ion position and velocity (1D3V, that is, one-dimensional space and three-dimensional velocity). In the present invention, the initial position of the ion is selected at the edge of the sheath calculation area, and the initial velocity is selected as the Maxwell distribution. Under the action of the electric field, the ions move in a manner that satisfies Newton's laws. During the movement, the ions will collide with background neutral particles. The collision process is processed as follows: first, the probability of each collision process occurring is calculated based on the collision cross section, and then the collision type is determined based on the pseudo-collision technology. The ion Monte Carlo collision model runs until all ions reach the electrode, and then begins to count the ion energy distribution function and angular distribution function.

[0141] The ion energy distribution is:

[0142] Where f(εj) represents the ion energy distribution function; N(εj) is the energy in The number of ions between them; Δε is the ion energy interval; is the total number of ions. The ion energy is v x ,v y ,v z are the three components of the ion velocity.

[0143] The ion angular distribution is:

[0144] Among them, f(θ j ) is the ion angle distribution function, N(θ j ) is the angle located at is the number of ions between them, and Δθ is the ion angular separation. is the total number of ions. The ion angle is calculated as

[0145] Step 108: Optimizing the discharge characteristics of the biased inductively coupled plasma source according to the ion energy distribution and ion angle distribution at different positions of the electrode plate.

[0146] like Figure 2 and Figure 3 As shown in the figure, when the discharge pressure is 1Pa and the discharge power of the bias inductively coupled plasma source is 50W, the ion energy distribution function (IEDF) and the ion angle distribution function (IADF) are at the center of the lower plate. As the bias amplitude changes, the frequency of the bias is 13.56MHz. It can be seen that under single-frequency discharge, the ion energy distribution function is a typical bimodal distribution, and moves to the high energy region as the bias increases. The ion angle distribution function moves to the small angle region as the bias increases.

[0147] Example 2

[0148] In order to execute the method corresponding to the above embodiment 1 to achieve the corresponding functions and technical effects, a bias inductively coupled plasma source optimization system is provided below, including:

[0149] A parameter acquisition module, used to acquire parameters of a bias inductively coupled plasma source; the parameters include discharge gas pressure, power and chamber size;

[0150] An electric field and inductive deposition power density determination module, used to determine the electric field and inductive deposition power density of the biased inductively coupled plasma source according to the parameters;

[0151] A two-dimensional fluid model determination module is used to determine the two-dimensional fluid model of the body region according to the induced deposition power density, obtain body region fluid parameters, and simultaneously obtain the plasma density and electron temperature at the sheath boundary; the body region fluid parameters include the electron density, ion density, electron temperature and bipolar electrostatic field of the body region;

[0152] A sheath parameter determination module is used to determine multiple one-dimensional sheath models according to the plasma density and electron temperature at the sheath boundary to obtain sheath parameters of each sheath; the sheath parameters include sheath electron density, sheath ion density, sheath potential and sheath electric field in the sheath; the one-dimensional sheath model corresponds to the sheath in the biased inductively coupled plasma source one by one;

[0153] A judgment module, used to judge whether the body fluid parameters and sheath parameters are converged, and obtain a judgment result; if the judgment result is no, the random heating flux of the sheath to the body is determined according to the sheath parameters, and the random heating flux is used as the boundary condition of the body electron energy equation in the two-dimensional fluid model of the body in the next iteration and the electric field and induced deposition power density solving module is called; if the judgment result is yes, the spatiotemporal variation sheath electric field determination module is called;

[0154] A time-space varying sheath electric field determination module is used to determine that the sheath electric field at the last iteration is a time-space varying electric field;

[0155] The ion energy distribution and ion angle distribution determination module is used to determine the ion Monte Carlo collision model based on the spatiotemporal variation sheath electric field to obtain the ion energy distribution and ion angle distribution at different positions of the electrode plate.

[0156] Example 3

[0157] This embodiment provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute a bias inductively coupled plasma source optimization method according to Embodiment 1.

[0158] Among them, the memory is a readable storage medium.

[0159] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0160] This article uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the method and core ideas of the present invention. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A bias inductively coupled plasma source optimization method, characterized in that: include: Obtaining parameters of a biased inductively coupled plasma source; the parameters include discharge gas pressure, power and chamber size; Determining the electric field and inductive deposition power density of the biased inductively coupled plasma source according to the parameters; Determine the two-dimensional fluid model of the body region according to the induced deposition power density, obtain the body region fluid parameters, and simultaneously obtain the plasma density and electron temperature at the sheath boundary; the body region fluid parameters include the electron density, ion density, electron temperature and bipolar electrostatic field of the body region; Determine multiple one-dimensional sheath models according to the plasma density and electron temperature at the sheath boundary, and obtain sheath parameters of each sheath; the sheath parameters include sheath electron density, sheath ion density, sheath potential and sheath electric field in the sheath; The one-dimensional sheath model corresponds one-to-one to the sheath in the biased inductively coupled plasma source; Determine whether the body fluid parameters and sheath parameters are converged, and obtain a determination result; If the judgment result is no, the random heating flux of the sheath to the body region is determined according to the sheath parameters, and the random heating flux is used as the boundary condition of the body region electron energy equation in the body region two-dimensional fluid model in the next iteration to return to the step of "determining the electric field and inductive deposition power density of the biased inductively coupled plasma source"; If the judgment result is yes, determining that the sheath electric field at the last iteration is a spatiotemporally varying electric field; The ion Monte Carlo collision model is determined based on the spatiotemporally varying sheath electric field to obtain ion energy distribution and ion angle distribution at different positions of the electrode plate.

2. The bias inductively coupled plasma source optimization method according to claim 1, characterized in that: After determining the ion Monte Carlo collision model based on the spatiotemporal variation sheath electric field to obtain the ion energy distribution and ion angle distribution at different positions of the electrode plate, the method further includes: The discharge characteristics of the biased inductively coupled plasma source are optimized according to the ion energy distribution and ion angle distribution at different positions of the electrode plate.

3. The method for optimizing a biased inductively coupled plasma source according to claim 1, characterized in that: Determining the electric field and inductive deposition power density of the biased inductively coupled plasma source according to the parameters comprises: Constructing a Helmholtz equation; the Helmholtz equation is constructed based on the parameters when the electromagnetic field and current in the biased inductively coupled plasma source satisfy the harmonic approximation principle; Solving the Helmholtz equation to obtain the electric field of the biased inductively coupled plasma source; determining an inductive deposition power density based on an electric field of a biased inductively coupled plasma source; Wherein, the Helmholtz equation is: The induction deposition power density is: in, is the gradient operator; E is the induced electric field, ε is the dielectric constant, σ is the plasma conductivity, j is the imaginary unit; ω is the power angular frequency; μ0 is the vacuum permeability; J coil is the coil current density, P ind is the induced deposition power density; Re(.) is the operation of taking the real part of the complex number; J p is the plasma current density, E * is the complex conjugate of the induced electric field.

4. The method for optimizing a biased inductively coupled plasma source according to claim 1, characterized in that: The two-dimensional fluid model of the body region includes the body region ion continuity equation, the body region ion momentum equation, the body region electron energy equation, the electron flux migration and diffusion equation, the electron density equation and the body region bipolar electrostatic field equation; the electron density equation is constructed based on the quasi-neutral condition; the body region bipolar electrostatic field equation is constructed based on the principle that the ion current density in the body region bipolar electrostatic field is equal to the electron current density; The body ion continuity equation is: Among them, n i is the density of ions, is the gradient operator; Γ i is the ion flux, S i is the ion source term, t is the time; The bulk ion momentum equation is: Among them, m i is the ion mass, u i is the ion orientation velocity, q i is the charge of the ion, E s is the electrostatic field, k B is the Boltzmann constant, T i is the ion temperature, M i is the ion collision term; The electron energy equation is: Among them, n e is the electron density, T e is the electron temperature, Q e is the electron energy flux, S energy is the energy source term of the electron, S energy =-eΓ e ·E s +P ind -E e , E e is the collision energy loss term, P ind is the induction deposition power density; The electron flux migration diffusion equation is: Among them, Γ e is the electron flux; μ e is the electron mobility, D e is the diffusion coefficient of electrons; Electron density equation; en e =q i n i ; Among them, n i is the ion density; e is the unit charge; The bipolar electrostatic field equation in the body region is:

5. The method for optimizing a biased inductively coupled plasma source according to claim 4, characterized in that: The method further comprises: The sheath ion density is determined by the sheath ion continuity equation and the sheath ion momentum equation; The sheath electron density is determined by the Boltzmann relation; The sheath potential is determined by Poisson's equation; The sheath electric field is determined by the sheath electric field equation.

6. The method for optimizing a biased inductively coupled plasma source according to claim 5, characterized in that: The sheath ion continuity equation is: x is the spatial coordinate of the sheath; The sheath ion momentum equation is: The Boltzmann relation: n e (x) is the sheath electron density; n0 is the electron density at the edge of the sheath calculation region, is the potential at the edge of the sheath calculation region, The Poisson equation is: ε0 is the dielectric constant of vacuum, is the electric potential in the sheath; The sheath electric field equation is: Among them, E sheath is the sheath electric field.

7. The method for optimizing a biased inductively coupled plasma source according to claim 5, characterized in that: The ion energy distribution is: Among them, f(ε j ) represents the ion energy distribution function; N(ε j ) is the energy located at The number of ions between them; Δε is the ion energy interval; The ion angle distribution is: Among them, f(θ j ) is the ion angle distribution function, N(θ j ) is the angle located at is the number of ions between them, and Δθ is the ion angular separation.

8. A bias inductively coupled plasma source optimization system, characterized in that: include: A parameter acquisition module, used to acquire parameters of a bias inductively coupled plasma source; the parameters include discharge gas pressure, power and chamber size; An electric field and inductive deposition power density determination module, used to determine the electric field and inductive deposition power density of the biased inductively coupled plasma source according to the parameters; A two-dimensional fluid model determination module is used to determine the two-dimensional fluid model of the body region according to the induced deposition power density, obtain body region fluid parameters, and simultaneously obtain the plasma density and electron temperature at the sheath boundary; the body region fluid parameters include the electron density, ion density, electron temperature and bipolar electrostatic field of the body region; A sheath parameter determination module is used to determine multiple one-dimensional sheath models according to the plasma density and electron temperature at the sheath boundary to obtain sheath parameters of each sheath; the sheath parameters include sheath electron density, sheath ion density, sheath potential and sheath electric field in the sheath; the one-dimensional sheath model corresponds to the sheath in the biased inductively coupled plasma source one by one; A judgment module, used to judge whether the body fluid parameters and sheath parameters are converged, and obtain a judgment result; if the judgment result is no, the random heating flux of the sheath to the body is determined according to the sheath parameters, and the random heating flux is used as the boundary condition of the body electron energy equation in the two-dimensional fluid model of the body in the next iteration and the electric field and induced deposition power density solving module is called; if the judgment result is yes, the spatiotemporal variation sheath electric field determination module is called; A time-space varying sheath electric field determination module is used to determine that the sheath electric field at the last iteration is a time-space varying electric field; The ion energy distribution and ion angle distribution determination module is used to determine the ion Monte Carlo collision model based on the spatiotemporal variation sheath electric field to obtain the ion energy distribution and ion angle distribution at different positions of the electrode plate.

9. An electronic device, characterized in that: The invention comprises a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform a bias inductively coupled plasma source optimization method according to any one of claims 1 to 7.

10. An electronic device according to claim 9, characterized in that: The memory is a readable storage medium.

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