CN103020384B - Aluminum gate CMP chemical reaction kinetics simulation and layout design optimization method - Google Patents

Abstract

The invention provides an aluminum gate CMP chemical reaction kinetics simulation method and a layout design optimization method. The aluminum gate CMP chemical reaction dynamics simulation method comprises the following steps: optimizing the concentration of each component in the grinding fluid of the aluminum gate CMP based on the chemical reaction kinetic model of the aluminum gate CMP; simulating the aluminum gate in a preset time period based on the chemical reaction kinetic model of the aluminum gate CMP and the optimized concentration of each component in the grinding liquid of the aluminum gate CMP, and predicting the variation of the surface height of the aluminum gate; and acquiring a simulated metal disc value and a simulated medium erosion value of the surface of the aluminum gate based on the predicted variation of the surface height of the aluminum gate. The basic model of the simulation method reasonably explains and simulates the surface height in real time on the basis of a chemical reaction mechanism for the aluminum gate CMP in the HKMG process, and essentially reveals the working principle of the aluminum gate CMP.

Description

The emulation of alum gate CMP Chemical Kinetics and layout design optimization method

Technical field

The present invention relates to integrated circuit fabrication process and CMP modeling technique field, be specifically related to the emulation of a kind of alum gate CMP Chemical Kinetics and layout design optimization method.

Background technology

Cmp (CMP), as a kind of ultra-precision surface process technology, has now been widely used in the field such as IC manufacturing, micromachine, is also a key process technique of manufacturability design flow process simultaneously.

At present, high-k gate dielectric and metal gate technique (HKMG) make semicon industry obtain sustainable development as the prevailing technology technology of 32/28 nanometer nodes.In HKMG " first grid " and " post tensioned unbonded prestressed concrete " two kinds of process programs, because " post tensioned unbonded prestressed concrete " can more freely arrange and allocate work function value and the threshold voltage of gate material, thus make the circuit performance of chip more stable and reliable.Therefore, " post tensioned unbonded prestressed concrete " technique is widely applied in semicon industry.But, the nanoscale polishing on " post tensioned unbonded prestressed concrete " process metal surface becomes the important factor in order of restriction chip performance lifting, the stability of CMP and reliability will determine the success or failure of whole technique to a great extent, therefore, understand HKMG CMP in depth, and its effect produced when acting on different crystal tubular construction all has great importance to the optimization of technique, the design of domain, particularly reliable CMP emulation mode can alum gate surface topography after accurate simulation CMP and the data such as butterfly, erosion.

How chemically in alum gate surface removal process, because the metal film of deposit is thinner, chemical action is very outstanding, reaction mechanism carries out real-time simulation to the surface elevation of alum gate CMP in HKMG technique particularly important.

Summary of the invention

In view of this, the invention provides the Chemical Kinetics emulation mode of a kind of alum gate CMP, with the angle of chemically reaction mechanism, real-time simulation is carried out to the surface elevation of alum gate CMP in HKMG technique.

Present invention also offers a kind of layout design optimization method, with fast and effeciently for manufacturability design provides optimisation strategy.

For achieving the above object, technical scheme of the present invention is as follows:

An emulation mode for alum gate CMP Chemical Kinetics, comprises step:

Based on alum gate CMP chemical reaction kinetic model, optimize each concentration of component in the lapping liquid of alum gate CMP;

Based on each concentration of component in the lapping liquid of the described alum gate CMP after described alum gate CMP chemical reaction kinetic model and optimization, alum gate is carried out to the emulation of predetermined amount of time, the variable quantity of prediction alum gate surface elevation;

Based on the variable quantity predicting the described alum gate surface elevation obtained, obtain Simulated metal dish value and the emulated media erosion value on alum gate surface;

Described alum gate CMP chemical reaction kinetic model is:

$\mathrm{MRR}(x,y,t)=\frac{M}{{\mathrm{\ρ}}_0}\frac{(k_6{k}_2+k_2{k}_3[\mathrm{Oxi}\left](x,y,t)\right)\left(k_4\right[\mathrm{CA}](x,y,t)+k_5)}{k_2{k}_3\left[\mathrm{Oxi}\right](x,y,t)+(k_2+k_1[\mathrm{In}\left](x,y,t)\right)\left(k_4\right[\mathrm{CA}](x,y,t)+k_5)};$

Wherein, MRR (x, y, t) is alum gate grinding clearance, and M is the atomic mass of aluminium, ρ ₀for the density of aluminium, the concentration that [Oxi] (x, y, t) is oxygenant in lapping liquid, the concentration that [In] (x, y, t) is inhibitor in lapping liquid, the concentration that [CA] (x, y, t) is sequestrant in lapping liquid, k _i(i=1 ..., 6) be chemical reaction rate constant, x is selected coordinate system coordinate figure along the x-axis direction, and y is selected coordinate system coordinate figure along the y-axis direction, and t is the simulation time of alum gate CMP.

Further, in the lapping liquid of described optimization alum gate CMP, each concentration of component is specially:

The initial value of each concentration of component in A, acquisition lapping liquid;

B, based on described alum gate CMP chemical reaction kinetic model, adopt each concentration of component in described lapping liquid initial value obtain alum gate grinding clearance;

C, judge described alum gate grinding clearance whether meet pre-provisioning request, if so, then tentatively determine that the initial value of each concentration of component in described lapping liquid is each concentration of component in described lapping liquid;

D, according to the Changing Pattern of each concentration of component in each concentration of component in the described lapping liquid tentatively determined and lapping liquid to alum gate grinding clearance, finally determine each concentration of component in described lapping liquid.

Further, described judge the grinding of described alum gate whether clearance meet pre-provisioning request after, also comprise, if not, adjust each concentration of component initial value in described lapping liquid, circulation performs steps A to C.

Further, in described acquisition lapping liquid, the initial value of each concentration of component is specially:

${\mathrm{\υ}}_r\frac{\∂\left[A\right]}{\∂r}+{\mathrm{\υ}}_{\mathrm{\θ}}\frac{1}{r}\frac{\∂\left[A\right]}{\∂\mathrm{\θ}}+{\mathrm{\υ}}_z\frac{\∂\left[A\right]}{\∂z}{D}_{\left[A\right]}\frac{{\∂}^2\left[A\right]}{{\∂z}^2};$

Boundary condition is:

$\left\{\begin{array}{c}\left[A\right](r,\mathrm{\θ},z)={\left[A\right]}_0\\ -D_{\left[A\right]}\frac{\∂\left[A\right]}{\∂z}(r,\mathrm{\θ},0)=0\end{array}\right.;$

Wherein, [A] is the concentration of any one component in lapping liquid, D _[A]for the Reaction-diffusion terms coefficient of any one component in lapping liquid; [A] ₀for the bulk concentration of any one component in lapping liquid; R, θ, z are the coordinate variables of polar coordinate system, υ _r, υ _θ, υ _zthe flowing velocity of any one component on r, θ, z direction in lapping liquid.

An optimization method for layout design, comprises step:

A, provide a kind of initial domain;

B, described domain to be emulated, obtain Simulated metal dish value and the emulated media erosion value of described domain;

C, according to described Simulated metal dish value and emulated media erosion value, according to the rule preset, described domain to be checked, analyze the hot spot region affecting chip yield existed;

D, judge whether described hot spot region meets the coherence request of layout design rules and domain and circuit; If so, the optimization method of layout design terminates;

Wherein, adopt arbitrary emulation mode described above to emulate described domain, obtain Simulated metal dish value and the emulated media erosion value of domain.

Further, described judge whether described hot spot region meets the coherence request of layout design rules and domain and circuit after, also comprise: if not, the optimization filling algorithm according to layout design is repaired described hot spot region, and circulation performs step b to d.

Compared with existing alum gate CMP emulation mode, the model basis that Chemical Kinetics emulation mode provided by the invention adopts is the conventional formulation based on metal CMP lapping liquid, extract effective grinding composition that alum gate CMP process exists, chemically reaction mechanism carries out reasonable dismissal and surface elevation real-time simulation to the alum gate CMP in HKMG technique, inherently disclose the principle of work of alum gate CMP.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, be briefly described to the accompanying drawing used required in embodiment or description of the prior art below, apparently, accompanying drawing in the following describes is some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these accompanying drawings.

Fig. 1 is alum gate CMP Chemical Kinetics emulation mode process flow diagram in the present invention;

Fig. 2 is each concentration of component optimization method process flow diagram in the lapping liquid of alum gate CMP of the present invention;

Fig. 3 is the optimization method process flow diagram of layout design of the present invention.

Embodiment

For enabling above-mentioned purpose of the present invention, feature and advantage become apparent more, are described in detail the specific embodiment of the present invention below in conjunction with accompanying drawing.

Set forth a lot of detail in the following description so that fully understand the present invention, but the present invention can also adopt other to be different from alternate manner described here to implement, those skilled in the art can when without prejudice to doing similar popularization when intension of the present invention, therefore the present invention is by the restriction of following public specific embodiment.

Refer to Fig. 1.Fig. 1 is alum gate CMP Chemical Kinetics emulation mode process flow diagram in the present invention.

Each concentration of component in S101, optimization lapping liquid:

Based on alum gate CMP chemical reaction kinetic model, optimize each concentration of component in alum gate CMP lapping liquid.

Described alum gate CMP chemical reaction kinetic model is:

$\mathrm{MRR}(x,y,t)=\frac{M}{{\mathrm{\ρ}}_0}\frac{(k_6{k}_2+k_2{k}_3[\mathrm{Oxi}\left](x,y,t)\right)\left(k_4\right[\mathrm{CA}](x,y,t)+k_5)}{k_2{k}_3\left[\mathrm{Oxi}\right](x,y,t)+(k_2+k_1[\mathrm{In}\left](x,y,t)\right)\left(k_4\right[\mathrm{CA}](x,y,t)+k_5)};$

Wherein, MRR (x, y, t) is alum gate grinding clearance, and M is the atomic mass of aluminium, ρ ₀for the density of aluminium, the concentration that [Oxi] (x, y, t) is oxygenant in lapping liquid, the concentration that [In] (x, y, t) is inhibitor in lapping liquid, the concentration that [CA] (x, y, t) is sequestrant in lapping liquid, k _i(i=1 ..., 6) be chemical reaction rate constant, x is selected coordinate system coordinate figure along the x-axis direction, and y is selected coordinate system coordinate figure along the y-axis direction, and t is the simulation time of alum gate CMP.

The process of establishing of above-mentioned alum gate CMP chemical reaction kinetic model is as follows:

1, alum gate CMP chemical reaction mechanism is:

(1) the inhibitor In reaction equation in aluminium and lapping liquid is:

(2) the oxygenant Oxi reaction equation in aluminium and lapping liquid is:

(3) the sequestrant CA reaction equation in aluminium and lapping liquid is:

2, polishing particles machinery cutting mechanisms is:

(1) polishing particles A removes the mechanism of the material such as oxide film, chelate:

(2) polishing particles A removes the mechanism of aluminium simple substance:

3, chemical rate equation is set up:

According to alum gate CMP chemical reaction mechanism, simultaneously based on above-mentioned chemical rate equation and polishing particles machinery cutting mechanisms, set up the dependence between aluminum particulate concentration changes with time rate and particle concentration:

$\left\{\begin{array}{c}\frac{\∂[\mathrm{Al}\·\mathrm{In}]}{\∂t}=k_1\left[\mathrm{Al}\right]\left[\mathrm{In}\right]-k_2[\mathrm{Al}\·\mathrm{In}]\\ \frac{\∂\left[{\mathrm{Al}}^{3+}\right]}{\∂t}=k_3\left[\mathrm{Al}\right]\left[\mathrm{Oxi}\right]-k_4\left[{\mathrm{Al}}^{3+}\right]\left[\mathrm{CA}\right]-k_5\left[{\mathrm{Al}}^{3+}\right]\end{array}\right.$

4, alum gate CMP chemical reaction kinetic model is determined:

According to mass balance principle, solve above formula chemical reaction equilibrium rate equation:

$\left\{\begin{array}{c}\frac{\∂[\mathrm{Al}\·\mathrm{In}]}{\∂t}=0\\ \frac{\∂\left[{\mathrm{Al}}^{3+}\right]}{\∂t}=0\end{array}\right.$

Again in conjunction with aluminium element surface composition relation: [Al] _t=[Al]+[Al ³⁺]+[AlIn]

And alum gate CMP grinds clearance:

$\mathrm{MRR}=\frac{M}{{\mathrm{\ρ}}_0}\frac{k_4\left[{\mathrm{Al}}^{3+}\right]\left[\mathrm{CA}\right]+k_5\left[{\mathrm{Al}}^{3+}\right]+k_6\left[\mathrm{Al}\right]}{{\left[\mathrm{Al}\right]}_T};$

Wherein, the removal speed of aluminium comprises chemical etch rate and mechanical lapping speed, therefore, obtains above-mentioned alum gate CMP chemical reaction kinetic model.

In constant CMP Mechanical course factor (as grinding pad rotating speed, wafer pressure etc.) and the environmental factor such as temperature, lapping liquid flowing velocity and under not changing lapping liquid composition (lapping liquid particle concentration, size etc.) prerequisite, based on alum gate CMP chemical reaction kinetic model described above, optimize each concentration of component in alum gate CMP lapping liquid one by one.

In the present embodiment, the method optimizing each concentration of component in alum gate CMP lapping liquid can be step as follows.Refer to Fig. 2.

The initial value of each concentration of component in S201, acquisition lapping liquid:

Process engineer empirically or other modes obtain the initial value of each concentration of component in lapping liquid.Each component in this lapping liquid mainly to the effective main abrasive component of alum gate CMP, as inhibitor, oxygenant and sequestrant.Under normal circumstances, in the lapping liquid that process engineer obtains, the initial value of each concentration of component is the bulk concentration of each component in lapping liquid, but, due to the diffusion of lapping liquid, in lapping liquid, the bulk concentration of each component is different from the concentration of chip surface diverse location, so, in order to obtain the initial value of each concentration of component in lapping liquid more accurately, the concentration value of lapped face diverse location can be obtained by solving mass transfer equation.Mass transfer equation is:

${\mathrm{\υ}}_r\frac{\∂\left[A\right]}{\∂r}+{\mathrm{\υ}}_{\mathrm{\θ}}\frac{1}{r}\frac{\∂\left[A\right]}{\∂\mathrm{\θ}}+{\mathrm{\υ}}_z\frac{\∂\left[A\right]}{\∂z}{D}_{\left[A\right]}\frac{{\∂}^2\left[A\right]}{{\∂z}^2};$

Boundary condition is:

$\left\{\begin{array}{c}\left[A\right](r,\mathrm{\θ},z)={\left[A\right]}_0\\ -D_{\left[A\right]}\frac{\∂\left[A\right]}{\∂z}(r,\mathrm{\θ},0)=0\end{array}\right.;$

Wherein, [A] is the concentration of any one component in lapping liquid, D _[A]aM is the Reaction-diffusion terms coefficient of any one component in lapping liquid; [A] ₀for the bulk concentration of any one component in lapping liquid; The coordinate variable of R, θ, z polar coordinate system, υ _r, υ _θ, υ _zthe flowing velocity of any one component on r, θ, z direction in lapping liquid.

S202, acquisition alum gate grinding clearance:

Based on alum gate CMP chemical reaction kinetic model, adopt the initial value of each concentration of component of lapping liquid provided in step S201 to obtain alum gate CMP and grind clearance.

S203, judge described alum gate grinding clearance whether meet pre-provisioning request, if so, tentatively determine each concentration of component in lapping liquid:

Judge whether the alum gate grinding clearance of above-mentioned acquisition meets pre-provisioning request, namely whether grind clearance with the alum gate in actual process close, if so, execution step S204; If not, upgrade the initial value of lapping liquid parameter, and keep other related process parameters constant, circulation performs step S201 ~ S203, until the alum gate in the alum gate grinding clearance obtained and actual process to grind clearance close.

S204, tentatively determine that selected lapping liquid initial parameter value is lapping liquid parameter:

According to above-mentioned judged result, if meet pre-provisioning request, then tentatively determine that selected lapping liquid initial parameter value is lapping liquid parameter.

S205, finally determine each concentration of component of described lapping liquid:

In fact, because lapping liquid component is more, the concentration adjusting each component reaches after preset standard can not ensure the adjustment of all components concentration still can reach optimization criteria, therefore, step S201 to S204 is initial adjustment, also need to adjust further according to the Changing Pattern of lapping liquid concentration of component to alum gate grinding clearance, the final preferred version obtaining one group of each concentration of component configuration of assisted milling liquid.

In CMP process, all there is the average abrasive clearance that realistic.When only changing lapping liquid concentration of component, slip-stick artist obtains suitable grinding clearance by each concentration of component of adjustment lapping liquid, but is in course of adjustment, and need carry out related experiment, cause the technique adjustment cycle to increase.And the lapping liquid concentration of component of adjustment only need be input to the grinding clearance that this alum gate CMP chemical reaction kinetic model can obtain alum gate CMP by the method that the present invention optimizes lapping liquid concentration of component, thus the method for optimization lapping liquid concentration of component provided by the invention ancillary works's teacher rapid Optimum can grind clearance, accelerates Process configuration adjustment cycle.

S102, alum gate to be emulated, the variable quantity on prediction alum gate surface:

Based on above-mentioned alum gate CMP chemical reaction kinetic model and the alum gate CMP lapping liquid concentration of component after optimizing, alum gate is carried out to the emulation of predetermined amount of time, remove rate equation in conjunction with grinding, the variable quantity of prediction alum gate surface elevation.The length of this schedule time is determined by technician.Such as, this schedule time can be identical with the Process configuration time, in order to check simulation result whether accurate, also can be set to multiple different time period the schedule time, like this can the pattern change on detecting real-time alum gate surface, and then pass judgment on alum gate surface and whether meet the requirements.

S103, acquisition Simulated metal dish value and erosion medium resistance value:

Based on predicting the variable quantity of alum gate surface elevation obtained, calculate the difference in height between aluminum metal and restraining barrier, dielectric layer, final Simulated metal dish value and the emulated media erosion value obtaining alum gate surface.

The alum gate CMP chemical kinetics emulation mode that the present embodiment provides, its basic model is extracted effective grinding composition of alum gate CMP process, eliminate the fluctuating factor less to chemical reaction mechanism effect, considered effective polishing particles machinery remove and lapping liquid to interactions such as the chemical kinetics removal of chip surface and lapping liquid quality transmission, disclose inhibitor in aluminium and lapping liquid, the chemical reaction mechanism of oxygenant and sequestrant, this emulation mode chemically reaction mechanism has carried out reasonable dismissal to HKMG technique alum gate CMP process, inherently disclose the principle of work of alum gate CMP.

Based on above-mentioned alum gate CMP Chemical Kinetics emulation mode, the invention provides a kind of optimization method of layout design.Refer to Fig. 3.

S301, provide a domain:

A domain to be optimized is provided.

S302, described domain to be emulated, obtains metal dish value and the erosion medium resistance value of described domain:

Adopt alum gate CMP Chemical Kinetics emulation mode described above to emulate described domain, obtain Simulated metal dish value and the emulated media erosion value of this domain.

S303, described domain to be checked, analyzes the hot spot region affecting chip yield existed:

According to Simulated metal dish value and emulated media erosion value, check according to the rule preset, analyze the hot spot region affecting chip yield that may exist, and these hot spot regions are marked.

This rule designed in advance can be such as: 1) relative different of alum gate height and dielectric layer height is greater than 10nm and thinks hot spot region; 2) ratio of alum gate height and whole chip surface average height is greater than 1.1 or be less than 0.9 and think hot spot region; 3) alum gate surface elevation is greater than or less than chip surface average height 20nm and thinks hot spot region.

S304, judge whether described hot spot region meets the coherence request of layout design rules and domain and circuit; If so, step S305 is performed; If not, repair hot spot region, circulation performs step S302 ~ S304;

Judge whether described hot spot region meets the coherence request of layout design rules and domain and circuit, whether the described domain geometry of main inspection meets layout density and circuit design requirements, if met the demands, perform step S305: the optimization method of layout design terminates.

If above-mentioned judgement does not meet the demands, the optimization filling algorithm according to layout design carries out dynamic restoring to described hot spot region, and circulation performs step S302 ~ S304, until domain meets the coherence request of design rule and domain and circuit.Described optimization filling algorithm is closely-related with original layout figure, considers the thickness of local areal density and inter-level dielectric, and redundant filling density and the position of permission Local grid are distinct, and such filling has more specific aim.This optimization filling algorithm can adopt existing ripe algorithm, as the filling algorithm that density based drives and timing performance drives, also oneself can propose new intelligent algorithm.

The optimization method of S305, layout design terminates:

According to above-mentioned steps, as the hot spot region in fruit chip meets the coherence request of layout design rules and domain and circuit, then this layout design optimization completes.

Based on the layout design optimization method of alum gate CMP Chemical Kinetics emulation mode, fast and effeciently can optimize domain, for the manufacturability design of chip provides optimisation strategy.

The above is only preferred embodiment of the present invention, not does any pro forma restriction to the present invention.Although the present invention discloses as above with preferred embodiment, but not to limit the present invention.Any those of ordinary skill in the art, do not departing under technical solution of the present invention ambit, the Method and Technology content of above-mentioned announcement all can be utilized to make many possible variations and modification to technical solution of the present invention, or be revised as the Equivalent embodiments of equivalent variations.Therefore, every content not departing from technical solution of the present invention, according in technical spirit of the present invention to any simple modification made for any of the above embodiments, equivalent variations and modification, all still belong in the scope of technical solution of the present invention.

Claims (6)

1. an emulation mode for alum gate CMP Chemical Kinetics, is characterized in that, comprises step:

Based on alum gate CMP chemical reaction kinetic model, optimize each concentration of component in the lapping liquid of alum gate CMP;

Based on each concentration of component in the lapping liquid of the described alum gate CMP after described alum gate CMP chemical reaction kinetic model and optimization, alum gate is carried out to the emulation of predetermined amount of time, the variable quantity of prediction alum gate surface elevation;

Based on the variable quantity predicting the described alum gate surface elevation obtained, obtain Simulated metal dish value and the emulated media erosion value on alum gate surface;

Described alum gate CMP chemical reaction kinetic model is:

$\mathrm{MRR}(x,y,t)=\frac{M}{{\mathrm{\ρ}}_0}\frac{(k_6{k}_2+k_2{k}_3[\mathrm{Oxi}\left](x.y.t)\right)\left(k_4\right[\mathrm{CA}](x,y,t)+k_5)}{k_2{k}_3\left[\mathrm{Oxi}\right](x.y.t)+(k_2+k_1[\mathrm{In}\left](x,y,t)\right)\left(k_4\right[\mathrm{CA}](x,y,t)+k_5)};$

Wherein, MRR (x, y, t) is alum gate grinding clearance, and M is the atomic mass of aluminium, ρ ₀for the density of aluminium, the concentration that [Oxi] (x, y, t) is oxygenant in lapping liquid, the concentration that [In] (x, y, t) is inhibitor in lapping liquid, the concentration that [CA] (x, y, t) is sequestrant in lapping liquid, k _ifor chemical reaction rate constant, i=1 ..., 6, x is selected coordinate system coordinate figure along the x-axis direction, and y is selected coordinate system coordinate figure along the y-axis direction, and t is the simulation time of alum gate CMP.

2. emulation mode according to claim 1, is characterized in that, in the lapping liquid of described optimization alum gate CMP, each concentration of component is specially:

The initial value of each concentration of component in A, acquisition lapping liquid;

B, based on described alum gate CMP chemical reaction kinetic model, adopt each concentration of component in described lapping liquid initial value obtain alum gate grinding clearance;

C, judge described alum gate grinding clearance whether meet pre-provisioning request, if so, then tentatively determine that the initial value of each concentration of component in described lapping liquid is each concentration of component in described lapping liquid;

D, according to the Changing Pattern of each concentration of component in each concentration of component in the described lapping liquid tentatively determined and lapping liquid to alum gate grinding clearance, finally determine each concentration of component in described lapping liquid.

3. emulation mode according to claim 2, is characterized in that, described judge the grinding of described alum gate whether clearance meet pre-provisioning request after, also comprise, if not, adjust each concentration of component initial value in described lapping liquid, circulation performs steps A to C.

4. emulation mode according to claim 2, is characterized in that, in described acquisition lapping liquid, the initial value of each concentration of component is specially:

$v_r\frac{\∂\left[A\right]}{\∂r}+v_{\mathrm{\θ}}\frac{1}{r}\frac{\∂\left[A\right]}{\∂\mathrm{\θ}}+v_z\frac{\∂\left[A\right]}{\∂z}=D_{\left[A\right]}\frac{{\∂}^2\left[A\right]}{{\∂z}^2};$

Boundary condition is:

$\left\{\begin{array}{c}\left[A\right](r,\mathrm{\θ},z)={\left[A\right]}_0\\ -D_{\left[A\right]}\frac{\∂\left[A\right]}{\∂z}(r,\mathrm{\θ},0)=0\end{array}\right.;$

Wherein, [A] is the concentration of any one component in lapping liquid, D _[A]for the Reaction-diffusion terms coefficient of any one component in lapping liquid; [A] ₀for the bulk concentration of any one component in lapping liquid; R, θ, z are the coordinate variables of polar coordinate system, υ _r, υ _θ, υ _zthe flowing velocity of any one component on r, θ, z direction in lapping liquid.

5. an optimization method for layout design, is characterized in that, comprises step:

A, provide a kind of initial domain;

B, described domain to be emulated, obtain Simulated metal dish value and the emulated media erosion value of described domain;

C, according to described Simulated metal dish value and emulated media erosion value, according to the rule preset, described domain to be checked, analyze the hot spot region affecting chip yield existed;

D, judge whether described hot spot region meets the coherence request of layout design rules and domain and circuit; If so, then the optimization method of layout design terminates;

Wherein, adopt the emulation mode described in any one of claim 1-4 to emulate described domain, obtain Simulated metal dish value and the emulated media erosion value of domain.

6. optimization method according to claim 5, it is characterized in that, described judge whether described hot spot region meets the coherence request of layout design rules and domain and circuit after, also comprise: if not, optimization filling algorithm according to layout design is repaired described hot spot region, and circulation performs step b to d.