CN102521886B - Three-dimensional simulation method for chemical vapor deposition process - Google Patents
Three-dimensional simulation method for chemical vapor deposition process Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 79
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- 238000005229 chemical vapour deposition Methods 0.000 title claims abstract description 16
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Abstract
The invention relates to a three-dimensional simulation method for a chemical vapor deposition process, belonging to the field of deposition process simulation in micro-electronic processing. The method comprises the steps of: representing material distribution of each position in a simulation region omega by using a cell method (CM) and subdividing the deposition graph surface into a plurality of triangular planes; realizing a transport process of quickly tracking deposition particles by using a Monte Carlo (MC) method in combination with a spatial oct-tree non-uniform subdivision technology, calculating to obtain the triangular planes of the deposition graph surface, and calculating in combination with a deposition model corresponding to current position material and the area of the triangular plane and the like to obtain the deposition velocity of each triangular plane of the deposition graph surface, wherein the blindness of the calculation of the deposition velocity is avoided; and according to the calculation result, obtaining the deposition velocity, and realizing accurate tracking of the deposition surface motion in the chemical vapor deposition (CVD) process by using a level set (LS) method. According to the method, various vapor deposition processes such as low-pressure chemical vapor deposition, plasma enhancement chemical vapor deposition, chemical vapor deposition under atmospheric pressure and the like can be simulated, and deposition simulation of complicated deposition graph composed of a plurality of materials is realized.
Description
Technical field
The invention belongs to Simulation of Sediment Process field in microelectronics processing, provide a kind of and represented simulated domain Ω distribution of material with cell method (CM), realize transporting of deposited particles by Monte Carlo method (MC), realize the analogy method of the chemical vapor deposition (CVD) process of apparent motion by Level Set Method (LS).
Background technology
At present, integrated circuit has been applied to every field, and its industry has become the element of economic development, and global competition is day by day fierce.What these developed to large scale integrated circuit undoubtedly brings new challenge.Along with the characteristic dimension of integrated circuit is constantly dwindled, and its production foundation stone semiconductor wafer constantly increases, and causes the integrated level of integrated circuit more and more higher, and the processing technology of integrated circuit has been proposed to new challenge.In order to improve the integrated level of integrated circuit, etching is proposed to new requirement, one of them is exactly higher depth-width ratio.But the increase of depth-width ratio has brought larger challenge to deposition, affect deposition quality factor and increase, shadow effect impact increases.
In order to improve deposition quality, need the mechanism of profound understanding deposition process processing technology, instruct deposition process parameter designing and equipment design with it.Is at present mainly to realize by trial and error about research in this respect, finds out suitable parameter by a large amount of sedimentation experiments, this method cost that wastes time and energy is on the one hand high, and the proper parameter that experiment draws is on the other hand not optimum.Another kind method is to realize by simulating, and carrys out the deposition morphology on predicted characteristics figure by certain working process parameter, compares with trial and error, can reduce experimentation cost, finds out main Optimal Parameters.Therefore, the simulation of deposition process is understanding and the effective ways of understanding deposition process mechanism.At present, Simulation of Sediment Process method is mainly line algorithm, cell method and Level Set Method etc., and has developed into three-dimensional from two dimension, to realize the more simulation of the deposition process of complex figure.
Line algorithm is mainly applicable to two-dimensional analog, in the time that deposition pattern modification of surface morphology is mild, can realize the accurate tracking at interface, but when time step is large or surface undulation not at ordinary times, be prone to unstable or inaccurate moving interface, be difficult to represent physicochemical property and the surfacing of deposition process impact deposition simultaneously; Level Set Method is accurately steadily and surely to follow the trail of a kind of effective ways at compound movement interface, be applicable to two and three dimensions simulation, can change violent accurately tracking of situation realization by effects on surface, but it can not represent physicochemical property and surfacing in deposition process, the interface that is not suitable for multiple material mimic diagram develops; Cellular method for expressing, by simulated domain Ω is divided into cellular, can represent material and the physicochemical property of optional position, but can not realize the accurate tracking of moving interface.And deposition process is not only subject to processing the impact of condition and technique, be also subject to the impact of deposition position material, simulation tool still can not meet the simulation requirement of complicated many material formation deposition pattern at present.
Summary of the invention
The object of the invention is the weak point for overcoming prior art, a kind of three-dimensional simulation method of chemical vapor deposition processes is proposed, the method has multiple vapor deposition processes such as can simulating under low-pressure chemical vapor deposition, plasma enhanced chemical vapor deposition, atmospheric pressure chemical vapor deposition, realizes the deposition simulation of the deposition pattern that complicated multiple material forms.
The three-dimensional simulation method of a kind of chemical vapor deposition processes that the present invention proposes, is characterized in that, comprises the following steps:
1) obtain initial parameter: according to actual process equipment and deposition gases, estimate to calculate electric field boundary parameter, participate in type, quantity and the velocity distribution of deposited particles; Input simulated domain and deposition pattern; Set the cellular length of side; Set simulated time T; Set maximum forward travel distance;
2) simulated domain is carried out to cellular division, be divided into multiple cellulars, each cellular is to material that should cellular position, and obtains corresponding deposition of material model; Triangulation is carried out in deposition pattern surface, be divided into multiple planar deltas, to calculate the sedimentation velocity of each planar delta, obtain the motion of whole deposition pattern;
3) represent the bee-line to deposition pattern of each point in simulated domain with level set function, and initialization level set function
make it to meet formula (1)
In formula (1)
0 level set while representing t=0 moment, i.e. deposition pattern, Ω represents simulated domain, Ω
1(t) represent gas, Ω
2(t) represent material; Ω=Ω
1(t) ∪ Ω
2(t) ∪ Γ (t);
represent the point in simulated domain, under cartesian coordinate system
represent the point in simulated domain Ω
to the distance of deposition pattern Γ (t);
4) utilize Octree non-homogeneous subdivision technology in space to carry out mesh generation to simulated domain, each grid is made up of multiple cellulars, to realize quick tracking deposited particles movement locus, obtains the contact position on deposited particles and deposition pattern surface; According to deposited particles type, quantity and velocity distribution, by Monte Carlo MC method, deposited particles is carried out to stochastic sampling and obtain the deposited particles that will simulate; According to the deposited particles type that will simulate, utilize space Octree technology to realize the transport process of the deposited particles that quick tracking will simulate, calculate the deposited particles parameter that arrives deposition position; According to the deposited particles parameter of the material of deposition position and arrival deposition position, select corresponding sedimentation model, calculate and upgrade the deposition of the planar delta of deposition position; The deposited particles number that reaches regulation goes to step 5);
5) calculate each planar delta sedimentation velocity according to the deposition of each planar delta, area and surface unit normal vector; According to planar delta sedimentation velocity and maximum forward travel distance calculated step time interval Δ T; According to each planar delta sedimentation velocity, utilize numerical computation method to solve level set governing equation and realize the motion on deposition pattern surface; Reinitialize level set function; Again triangulation is carried out in current deposition pattern surface, and according to current deposition pattern, upgrade information in cellular, the cellular that state is changed replaces with new deposition materials;
6) upgrade after simulated time T=T-Δ T, if T=0 goes to step 7), otherwise go to step 4);
7) output analog result, generates and shows final three-dimensional deposition pattern according to all planar deltas of deposition pattern.
Feature of the present invention and beneficial effect:
The invention provides one cell method (CM) and represent simulated domain Ω distribution of material, realize transporting of particle by Monte Carlo (MC) method, in conjunction with the sedimentation model of different materials, calculate the deposition of each position, deposition pattern surface, the blindness of having avoided sedimentation velocity to calculate; According to obtaining sedimentation velocity, realize chemical vapor deposition (CVD) process surface evolution by Level Set Method (LS).The present invention can simulate the multiple vapor deposition processes such as chemical vapor deposition under low-pressure chemical vapor deposition, plasma enhanced chemical vapor deposition, atmospheric pressure, realize the deposition simulation of the deposition pattern that complicated multiple material forms, solved in simulation in the past, exist constituent material single, simulate the problems such as inaccurate.
Brief description of the drawings
Fig. 1 is the program flow diagram of the inventive method;
Fig. 2 is the vertical cross-section of two-dimensional representation simulated domain Ω;
Fig. 3 is system cartesian coordinate system of living in.
Embodiment
The present invention proposes a kind of three-dimensional simulation method of chemical vapor deposition processes, by reference to the accompanying drawings and implement be described in detail as follows:
As shown in Figure 1, embodiment comprises the following steps method overall procedure of the present invention:
1) obtain initial parameter: according to actual process equipment and deposition gases, estimate to calculate electric field boundary parameter E
c, type S, the quantity N of participation deposited particles
sand velocity distribution P
v; Input simulated domain Ω and deposition pattern Γ (t); Set cellular length of side l; Set simulated time T; Set maximum forward travel distance dist;
2) simulated domain Ω is carried out to cellular division, be divided into multiple cellulars, each cellular is to material that should cellular position, and obtains corresponding deposition of material model; Triangulation is carried out in deposition pattern Γ (t) surface, be divided into multiple planar deltas, to calculate the sedimentation velocity of each planar delta, obtain the motion of whole deposition pattern Γ; Specifically comprise:
2.1) simulated domain Ω is carried out to cellular division: simulated domain Ω is divided into the cellular that some length of sides are l (square), for storing the material of each cellular position of simulated domain Ω; As certain cellular current state is: state=0, represents that this cellular position is vapor phase areas; State=1 represents that this cellular position is the first material; State=2 represents that this cellular position is that (every kind of material all has different separately physicochemical property to the second material in deposition process, shows as the difference of sedimentation model; Sedimentation model difference just because of reacting gas to different materials, while calculating deposition, select the corresponding deposition of material model of material having with deposition position (contact position on deposited particles and deposition pattern surface));
2.2) triangulation is carried out in deposition pattern Γ (t) surface: require (this is the minimum feature in semiconducter process process) according to the characteristic dimension of deposition pattern Γ to be simulated (t), utilize surface triangulation algorithm, deposition pattern Γ to be simulated (t) surface is divided into multiple planar deltas, by calculating the sedimentation velocity of each planar delta, obtain the motion of deposition pattern Γ whole to be simulated (t);
3) represent in simulated domain Ω that with level set function each point is to the bee-line of deposition pattern Γ (t), initialization level set function
make it to meet formula (1)
In formula (1)
0 level set (border of two materials, namely deposition pattern) while representing t=0 moment, as shown in Figure 2, in figure, white portion 1 represents gas Ω to the vertical cross-section of simulated domain Ω
1(t), hatched example areas 2 represents material Ω
2(t), dotted line represents section; Ω=Ω
1(t) ∪ Ω
2(t) ∪ Γ (t);
represent the point in simulated domain, under cartesian coordinate system
represent the point in simulated domain Ω
to the distance of deposition pattern Γ (t);
4) utilize Octree non-homogeneous subdivision technology in space to carry out mesh generation to simulated domain Ω, each grid is made up of multiple cellulars, to realize quick tracking deposited particles movement locus, obtain the contact position on deposited particles and deposition pattern surface, if while there is plasma in simulated domain Ω, according to simulated domain Ω electric field boundary condition, utilize existing finite difference method, calculating plasma forms electromotive force in simulated domain Ω; According to deposited particles type S, quantity Ns and velocity distribution Pv, by Monte Carlo MC method, deposited particles is carried out to stochastic sampling and obtain the deposited particles that will simulate
according to the deposited particles that will simulate
type, utilize space Octree technology to realize the transport process of the deposited particles that quick tracking will simulate, calculate the deposited particles parameter that arrives deposition position
according to the deposited particles parameter of the material of deposition position and arrival deposition position
select corresponding sedimentation model, calculate and upgrade the deposition of the planar delta of deposition position; The deposited particles number that reaches regulation goes to step 5); Specifically comprise:
4.1) utilize Octree non-homogeneous subdivision technology in space to carry out mesh generation to simulated domain Ω, to realize quick tracking Particles Moving track, obtain the contact position on particle and deposition pattern surface.Grid cutting algorithm be by containing the space rectangular parallelepiped of simulated domain Ω by being divided into 8 identical sub-rectangular parallelepiped grids as 3 change in coordinate axis direction of Fig. 3 cartesian coordinate system (z direction of principal axis is downward), be organized into an Octree.If the quantity of contained planar delta is greater than given threshold values ε in a certain sub-rectangular parallelepiped grid
Δ(general ε
Δ=4), again by the further subdivision of this sub-rectangular parallelepiped grid, until the quantity of the contained planar delta of each grid is less than or equal to given threshold values ε
Δ; If while there is plasma in simulated domain Ω, according to simulated domain Ω electric field boundary condition E
c, utilizing existing finite difference method, calculating plasma forms electromotive force in simulated domain Ω, and obtaining the satisfied Poisson equation of electric field by the Maxwell equation of Theory of Electromagnetic Field is ▽
2Φ=-ρ/ε
0, this ▽
2represent Laplace operator, Φ represents electromotive force (unit for volt), and ρ is electric charge volume density (unit for coulomb per cubic meter), and ε
0permittivity of vacuum (unit is farad/rice); According to positive charge and electron charge in partial simulation region ψ under stable state and approach 0 condition, electric field can be reduced to Laplace's equation ▽
2Φ=0 solves, and can utilize so existing finite difference method, asks and obtains each point electromotive force in simulated domain Ω in conjunction with boundary condition; In each rectangular parallelepiped grid, except having planar delta, also preserve the electric field that plasma forms, for simulating the motion of charged ion;
4.2) according to deposited particles type S, number of particles N
swith deposited particles velocity distribution P
v, by Monte Carlo MC method, deposited particles is carried out to stochastic sampling and obtains the deposited particles that will simulate
wherein, i represents deposited particles sequence number;
represent deposited particles
position, under cartesian coordinate system,
initial z=0, represents simulated domain Ω gas phase coboundary, x, and y produces at random according to simulated domain Ω size; s
ithe type that represents deposited particles, is arranged by deposited particles component;
representative
initial velocity, by isotropic Distribution and Maxwell's Velocity
Produce,
Respectively cartesian coordinate system x, y, the component velocity of tri-directions of z, and-∞ < v
ix, v
iy<+∞, v
iz> 0, M
ifor deposited particles quality, k is Boltzmann constant, T
iit is deposited particles temperature; Deposited particles type comprises that all neutral bioactive molecule, atom and the ionization ion of participation role are (as used H
2, N
2and CH
4plasma enhanced chemical vapor deposition Si
3n
4time, in deposition gases, contain a large amount of N
2 +ion, N atom and CN particle);
4.3) according to deposited particles
type, utilize space Octree technology to realize the transport process of following the tracks of fast deposited particles, calculate the deposited particles parameter that arrives deposition position
If s
i∈ ion, deposited particles
motion be to be subject to the impact of electric field E that plasma forms, accelerate caused motion (because electric field density is inhomogeneous,
not uniformly accelrated rectilinear motion, in order simplifying, this motion can be regarded as and be formed as uniformly accelrated rectilinear motion by the Δ t time interval, therefore,
movement locus be broken line instead of straight line); Specifically be calculated as follows:
According to the electric field E of simulated domain Ω, Newton's laws of motion and deposited particles current location
and speed
calculate the reposition after the Δ t time interval
with new speed
then by
with
determine line segment AB, utilize space Octree technology to determine whether this line segment intersects with deposition pattern surface, if non-intersect and this line segment does not leave simulated domain Ω, by reposition
with new speed
as current location
and speed
constantly repeat this process until intersect with deposition pattern surface, find the planar delta Δ crossing with deposition pattern
i; Calculate again deposited particles
incident direction and planar delta normal angle θ
i; And utilize surface reflection model (according to θ
ivalue and reflection threshold values θ
0relatively, if θ > is θ
0, according to mirror-reflection rule, deposited particles is reflected, otherwise deposited particles is deposited on this cellular position) calculate reflection or deposit even θ
i> θ
0(θ
0> π/3) time, calculate according to principle of reflection
reposition
new speed
as current location
and speed
go to step 4.3) continue to carry out; Otherwise go to step 4.4);
If s
ithe neutral active particle of ∈,
motion be constant speed
the rectilinear motion that direction is constant, utilizes space Octree technology to calculate fast this straight line and the crossing planar delta Δ of deposition pattern Γ (t)
i; According to absorption probability model, (incident particle is with adsorption probability S again
c(0 < S
c< 1) determine that this particle is absorption or scattering, 1-S
cprobability particle scattering, reflection angle and incident angle are irrelevant, meet diffuse reflecting distribution) determine that scattering still adsorbs, produce random number p(0≤p≤1), if p > S
cfor scattering, generate at random scattering angle and speed and calculate current location
and speed
go to step 4.3) continue to carry out; Otherwise go to step 4.4);
4.4) according to the deposited particles parameter of the material of deposition position and arrival deposition position
select concrete sedimentation model, calculate and upgrade the deposition of the planar delta of deposition position:
Strengthen vapor deposition processes as example taking plasma, select corresponding sedimentation model can be expressed as formula (2):
Wherein:
represent plasma-enhanced deposition coefficient, generally obtain by experiment, it and particle rapidity
θ is relevant with deposition materials state for Particles Moving direction plane normal angle; K
d(state) sedimentation coefficient of expression neutral particle, state is relevant with material, is also to obtain by experiment; F
ionand F
drepresentative moves to the upper ion-flow rate of the upper planar delta ds of deposition pattern Γ (t) and neutral particle flow respectively; θ represents the angle of deposited particles and planar delta normal direction;
If s
i∈ ion,
If s
ithe neutral active particle of ∈,
Wherein:
represent planar delta Δ
ion deposition,
represent
plasma-enhanced deposition coefficient; K
d(state) represent neutral particle
sedimentation coefficient;
with
represent respectively current particle
ion-flow rate and the neutral particle flow of representative;
4.5) repeating step 4.2)-4.4), the population that reaches regulation goes to step 5);
5) according to the deposition of each planar delta
area
and unit normal vector
calculate each planar delta sedimentation velocity
according to planar delta sedimentation velocity and maximum forward travel distance dist (dist > 0) calculated step time interval Δ T; According to each planar delta sedimentation velocity
utilize numerical computation method to solve level set governing equation and realize the motion on deposition pattern surface; Reinitialize level set function; Again triangulation is carried out in current deposition pattern surface, and according to current deposition pattern Γ (t), upgrade information in cellular, the cellular that state is changed replaces with new deposition materials; Specifically comprise:
5.1) according to the deposition of each planar delta
area
and unit normal vector
calculate each planar delta sedimentation velocity
5.2) according to planar delta sedimentation velocity and maximum forward travel distance dist (dist > 0) calculated step time interval Δ T;
Wherein: dist represents maximum forward travel distance, ls represents to form deposition pattern Γ (t) planar delta collection;
5.3) according to each planar delta sedimentation velocity
utilize numerical computation method to solve level set governing equation (formula (5)) and realize surperficial motion;
φ
t+V·▽φ=0 (5)
Wherein: φ
tbe the local derviation of level set function φ to time t, ▽ φ is the gradient that φ locates at (x, y, z), and V represents the speed that field of definition each point (x, y, z) is located, and is approximately its place planar delta sedimentation velocity
while utilizing numerical computation method to solve, level set function field of definition (simulated domain Ω) be carried out to discretize and process; Owing to will use whole each position and speed of simulated domain Ω (velocity field) in the time solving level set governing equation, and we can only calculate the speed of deposition pattern Γ (t) each point in deposition process, therefore, the velocity field of whole simulated domain Ω will be calculated by superficial velocity.In order to raise the efficiency; here adopt narrow-band level set method, only calculate near near the speed (deposition pattern Γ (t), the speed of position equals the sedimentation velocity apart from the upper planar delta of its nearest deposition pattern Γ (t)) of the position of deposition pattern Γ (t);
5.4) reinitialize level set function by formula (6), make it to meet formula (1):
Wherein: φ
0represent present level set function,
be the level set function that will calculate, its steady state solution is the symbolic distance function that meets formula (1), sign (φ
0) sign function, in order to solve conveniently, by its smooth be formula (7), ε > 0 is very little positive number;
5.5) again triangulation is carried out in current deposition pattern surface, and according to current deposition pattern Γ (t), upgrade information in cellular, the cellular that state is changed replaces with new deposition materials;
6) upgrade after simulated time T=T-Δ T, if T=0 goes to step 7), otherwise go to step 4);
7) output analog result, generates and shows final three-dimensional deposition pattern according to all planar deltas of deposition pattern.
Claims (4)
1. a three-dimensional simulation method for chemical vapor deposition processes, is characterized in that, comprises the following steps:
1) obtain initial parameter: according to actual process equipment and deposition gases, estimate type, quantity and the velocity distribution of electric field boundary parameter, participation deposited particles; Input simulated domain and deposition pattern; Set the cellular length of side; Set simulated time T; Set maximum forward travel distance;
2) simulated domain is carried out to cellular division, be divided into multiple cellulars, each cellular is to material that should cellular position, and obtains corresponding deposition of material model; Triangulation is carried out in deposition pattern surface, be divided into multiple planar deltas, to calculate the sedimentation velocity of each planar delta, obtain the motion of whole deposition pattern;
3) represent the bee-line to deposition pattern of each point in simulated domain with level set function, and initialization level set function
make it to meet formula (1)
In formula (1)
0 level set while representing t=0 moment, i.e. deposition pattern, Ω represents simulated domain, Ω
1(t) represent gas, Ω
2(t) represent material; Ω=Ω
1(t) ∪ Ω
2(t) ∪ Γ (t);
represent the point in simulated domain, under cartesian coordinate system
represent the point in simulated domain Ω
to the distance of deposition pattern Γ (t);
4) utilize Octree non-homogeneous subdivision technology in space to carry out mesh generation to simulated domain, each grid is made up of multiple cellulars, to realize quick tracking deposited particles movement locus, obtains the contact position on deposited particles and deposition pattern surface; According to deposited particles type, quantity and velocity distribution, by Monte Carlo MC method, deposited particles is carried out to stochastic sampling and obtain the deposited particles that will simulate; According to the deposited particles type that will simulate, utilize space Octree technology to realize the transport process of the deposited particles that quick tracking will simulate, calculate the deposited particles parameter that arrives deposition position; According to the deposited particles parameter of the material of deposition position and arrival deposition position, select corresponding sedimentation model, calculate and upgrade the deposition of the planar delta of deposition position; The deposited particles number that reaches regulation goes to step 5);
5) calculate each planar delta sedimentation velocity according to the deposition of each planar delta, area and surface unit normal vector; According to planar delta sedimentation velocity and maximum forward travel distance calculated step time interval Δ T; According to each planar delta sedimentation velocity, utilize numerical computation method to solve level set governing equation and realize the motion on deposition pattern surface; Reinitialize level set function; Again triangulation is carried out in current deposition pattern surface, and according to current deposition pattern, upgrade information in cellular, the cellular that state is changed replaces with new deposition materials;
6) upgrade after simulated time T=T-Δ T, if T=0 goes to step 7), otherwise go to step 4);
7) output analog result, generates and shows final three-dimensional deposition pattern according to all planar deltas of deposition pattern.
2. method as claimed in claim 1, is characterized in that described step 2) specifically comprise:
2.1) simulated domain is carried out to cellular division: simulated domain Ω is divided into the cellular that some length of sides are l, for storing the material of each cellular position of simulated domain Ω; While calculating deposition, the corresponding deposition of material model of material that selection has with deposition position, deposition position is the contact position on deposited particles and deposition pattern surface;
2.2) triangulation is carried out in deposition pattern surface: according to the characteristic dimension requirement of deposition pattern Γ (t), utilize surface triangulation algorithm, deposition pattern Γ (t) surface is divided into multiple planar deltas, by calculating the sedimentation velocity of each planar delta, obtain the motion of whole deposition pattern Γ (t).
3. method as claimed in claim 1, is characterized in that described step 4) specifically comprise:
4.1) utilize Octree non-homogeneous subdivision technology in space to carry out mesh generation to simulated domain, to realize quick tracking Particles Moving track, obtain the contact position on particle and deposition pattern surface; Grid cutting algorithm is that the space rectangular parallelepiped containing simulated domain Ω is divided into 8 identical sub-rectangular parallelepiped grids by 3 change in coordinate axis direction of cartesian coordinate system, is organized into an Octree; If the quantity of contained planar delta is greater than given threshold epsilon in a certain sub-rectangular parallelepiped grid
Δ, again by the further subdivision of this sub-rectangular parallelepiped grid, until the quantity of the contained planar delta of each grid is less than or equal to given threshold epsilon
Δ; If while there is plasma in simulated domain Ω, according to simulated domain Ω electric field boundary condition E
c, utilizing existing finite difference method, calculating plasma forms electromotive force in simulated domain Ω, and obtaining the satisfied Poisson equation of electric field by the Maxwell equation of Theory of Electromagnetic Field is ▽
2Φ=-ρ/ε
0, this ▽
2represent Laplace operator, Φ represents electromotive force, and ρ is electric charge volume density, and ε
0it is permittivity of vacuum; According to positive charge and electron charge in partial simulation region ψ under stable state and approach 0 condition, electric field is reduced to Laplace's equation ▽
2Φ=0 solves, and utilizes existing finite difference method, asks and obtains each point electromotive force in simulated domain Ω in conjunction with boundary condition; In each rectangular parallelepiped grid, except having planar delta, also preserve the electric field that plasma forms, for simulating the motion of charged ion;
4.2) according to deposited particles type S, number of particles N
swith deposited particles velocity distribution P
v, by Monte Carlo MC method, deposited particles is carried out to stochastic sampling and obtains the deposited particles that will simulate
wherein, i represents deposited particles sequence number;
represent deposited particles
position, under cartesian coordinate system,
initial z=0, represents simulated domain Ω gas phase coboundary, x, and y produces at random according to simulated domain Ω size; s
ithe type that represents deposited particles, is arranged by deposited particles component;
representative
initial velocity, by isotropic Distribution and Maxwell's Velocity
produce,
v
ix, v
iy, v
izrespectively cartesian coordinate system x, y, the component velocity of tri-directions of z, and-∞ < v
ix, v
iy<+∞, v
iz> 0, M
ifor deposited particles quality, k is Boltzmann constant, T
iit is deposited particles temperature;
4.3) according to deposited particles
type, utilize space Octree technology to realize the transport process of following the tracks of fast deposited particles, calculate the deposited particles parameter s that arrives deposition position
i, θ
i,
If s
i∈ ion, deposited particles
motion be to be subject to the impact of electric field E that plasma forms, accelerate caused motion; Specifically be calculated as follows:
According to the electric field E of simulated domain Ω, Newton's laws of motion and deposited particles current location
and speed
calculate the reposition after the Δ t time interval
with new speed
then by
with
determine line segment AB, utilize space Octree technology to determine whether this line segment intersects with deposition pattern surface, if non-intersect and this line segment does not leave simulated domain Ω, by reposition
with new speed
as current location
and speed
constantly repeat this process until intersect with deposition pattern surface, find the planar delta Δ crossing with deposition pattern
i; Calculate again deposited particles
incident direction and planar delta normal angle θ
i; And utilize surface reflection model to calculate reflection or deposition, even θ
i> θ
0time, θ
0be reflection threshold value, calculate deposited particles according to principle of reflection
reposition
new speed
as current location
and speed
go to step 4.3) continue to carry out, otherwise go to step 4.4);
If s
i∈ neutral active particle, deposited particles
motion be constant speed
the rectilinear motion that direction is constant, utilizes space Octree technology to calculate fast this straight line and the crossing planar delta Δ of deposition pattern Γ (t)
i; Still adsorb according to absorption probability model decision scattering again, produce random number p, if p > is S
cfor scattering, S
cfor absorption probability, generate at random scattering angle and speed and calculate current location
and speed
go to step 4.3) continue to carry out; Otherwise go to step 4.4);
4.4) according to the deposited particles parameter s of the material of deposition position and arrival deposition position
i, θ
i,
select concrete sedimentation model, calculate and upgrade the deposition of the planar delta of deposition position:
If plasma strengthens vapor deposition processes, select corresponding sedimentation model can be expressed as formula (2):
Wherein:
represent plasma-enhanced deposition coefficient, K
d(state) sedimentation coefficient of expression neutral particle, state represents material; F
ionand F
drepresentative moves to the upper ion-flow rate of the upper planar delta ds of deposition pattern Γ (t) and neutral particle flow respectively; θ represents the angle of deposited particles and planar delta normal direction;
If s
i∈ ion,
If s
ithe neutral active particle of ∈,
Wherein:
represent planar delta Δ
ion deposition,
represent
plasma-enhanced deposition coefficient; K
d(state) represent neutral particle
sedimentation coefficient;
with
represent respectively current particle
ion-flow rate and the neutral particle flow of representative;
4.5) repeating step 4.2)-4.4), the population that reaches regulation goes to step 5).
4. method as claimed in claim 1, is characterized in that described step 5) specifically comprise:
5.1) according to the deposition of each planar delta
area
and unit normal vector
calculate each planar delta sedimentation velocity
5.2) according to planar delta sedimentation velocity and maximum forward travel distance dist calculated step time interval Δ T;
Wherein: dist represents maximum forward travel distance, ls represents to form deposition pattern Γ (t) planar delta collection;
5.3) according to each planar delta sedimentation velocity
utilize numerical computation method to solve level set governing equation (5) and realize surperficial motion;
φ
t+V·▽φ=0 (5)
Wherein: φ
tbe the local derviation of level set function φ to time t, ▽ φ is the gradient that φ locates at (x, y, z), and V represents the speed that field of definition each point (x, y, z) is located, and is approximately its place planar delta sedimentation velocity
; While utilizing numerical computation method to solve, level set function field of definition is carried out to discretize and adopted narrow-band level set method, calculate the speed of deposition pattern Γ (t) near surface position;
5.4) reinitialize level set function by formula (6), make it to meet formula (1):
Wherein: φ
0represent present level set function,
be the level set function that will calculate, its steady state solution is the symbolic distance function that meets formula (1), sign (φ
0) sign function, in order to solve conveniently, by its smooth be formula (7), ε > 0 is very little positive number;
5.5) again triangulation is carried out in current deposition pattern surface, and according to current deposition pattern Γ (t), upgrade information in cellular, the cellular that state is changed replaces with new deposition materials.
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