CN102509712B - Method for determining dynamic pressure distribution and grinding removal rate of chemical mechanical polishing grinding liquid - Google Patents

Abstract

The invention provides a method for determining the dynamic pressure distribution and grinding removal rate of chemical mechanical polishing grinding liquid. The method comprises the following steps of: with given thickness of the grinding liquid between a wafer to be ground and a grinding pad, determining the dynamic pressure distribution of the grinding liquid and the acting force of the grinding liquid on the wafer according to the property of the grinding liquid, the angular velocity of the grinding pad and the thickness of a liquid film; determining the acting force of the grinding pad and grinding particles on the wafer during the grinding according to the properties of the grinding liquid and the grinding pad; in combination with the external force on the wafer, judging whether theacting force on the wafer is in balance with the moment; if not, correcting the thickness of the liquid film, and re-determining the acting force on the wafer and the dynamic pressure distribution ofthe grinding liquid; otherwise, determining the grinding removal rate of the wafer. Through the invention, the surface topography of the wafer after the chemical mechanical grinding can be predicted so as to provide instruction for the CMP (chemical mechanical polishing) technological modeling; and meanwhile, the change characteristics of the grinding surface can be reflected, and modification suggestion can be provided for the manufacturing design of an integrated circuit board so as to improve the product yield.

Description

Chemical mechanical polishing liquid dynamic pressure and definite method of grinding clearance

Technical field

The present invention relates to field of semiconductor manufacture, the definite method that particularly relates to the chemical mechanical polishing liquid dynamic pressure and grind clearance.

Background technology

In recent years, along with IC(Integrated Circuit, integrated circuit) the continuous decline of manufacturing process characteristic size, the IC manufacturing technology has proposed more and more stricter requirement to the making technology of device, especially in the fabrication of semiconductor device below 65nm, the evenness of circuit surface is the key factor that affects photoetching depth of focus level and yields.The planarization of crystal column surface is as an important step in the semiconductor fabrication process, to remove crystal column surface dielectric layer and metal level in the wafer production process, make enough smooth solid or multilayer wirings of reaching of crystal column surface, promote distribution density, reduce a key IC process technique of defect concentration.

At present, CMP(Chemical Mechanical Polishing, chemico-mechanical polishing) technology has become most popular planarization of large scale integrated circuit epoch, and complete CMP technical process comprises grinding wafer and grinds rear two main process that clean.In the grinding wafer process, have complicated chemistry, physical action between wafer to be ground and grinding pad, lapping liquid and polishing particles, the interaction force between many bodies grinds the reduction of removing efficient, surface smoothness, dielectric constant and etching scraping etc. to crystal column surface and consists of material impact.In recent years, the prediction of CMP process and polish results has been become the focus of domestic and international research.Be summed up, the CMP process mainly comprises physical-chemical reaction effect two general orientation between contact action and metal, dielectric and lapping liquid between wafer-particle-grinding pad, contact action can be divided into direct contact, fluid contact, particle contact and mixed lubrication four classes, and the branches of learning and subjects that are mainly concerned with comprise contact mechanics, tribology, fluid mechanics, Elasticity, partial differential equation, molecule (moving) mechanics and slurries chemistry etc.

Although the Forecasting Methodology of CMP has obtained certain progress, but for grinding clearance (the Material Removal Rate of lapping liquid in the CMP process to wafer, MRR) acquisition still rests on the experience real example stage, general by experiment result predicts the grinding result of wafer under the identical grinding condition, this Forecasting Methodology has been ignored lapping liquid, abrasive parameters etc. to the evenness of grinding rear wafer and the impact of wafer clearance, and it predicts the outcome and can not accurately embody the grinding result of CMP.Especially in nanoscale IC device manufacturing processes, the evenness of crystal column surface requires high, and the interaction of grinding pad, lapping liquid and polishing particles and crystal column surface is an extremely complicated process, can not adopt simply the method for experience real example to describe.In addition, the space pressure of lapping liquid distributes the material of crystal column surface is removed important in the CMP process of lapping, and the effect that the lapping liquid dynamic pressure is removed wafer can not be ignored.

Summary of the invention

The definite method that the invention provides a kind of chemical mechanical polishing liquid dynamic pressure and grind clearance, the method can accurately be simulated the surface topography that crystal column surface CMP grinds.

For achieving the above object, the definite method that the invention provides a kind of chemical mechanical polishing liquid dynamic pressure and grind clearance comprises step:

Given thickness of liquid film, described thickness of liquid film are the thickness of lapping liquid between grinding pad and the wafer;

According to the character of lapping liquid, the angular speed of grinding pad and the dynamic pressure that described thickness of liquid film is determined lapping liquid; Wafer is subject to the active force of grinding pad and polishing particles when determining to grind according to the character of lapping liquid and grinding pad;

Wafer is subject to the active force of lapping liquid when determining chemico-mechanical polishing according to the dynamic pressure of described lapping liquid;

In conjunction with the external force that wafer is subject to, judge whether balance of the suffered effect force and moment of wafer, if not, revise described thickness of liquid film, redefine active force that wafer is subject to and the dynamic pressure of lapping liquid; If so, determine the grinding clearance of wafer.

Preferably, described given thickness of liquid film can be expressed as in three-dimensional cartesian coordinate system:

$h(x,y)=h_0+R_P\cos \frac{2\mathrm{\πx}}{{\mathrm{\λ}}_x}\cos \frac{2\mathrm{\πy}}{{\mathrm{\λ}}_y}$

Wherein, h ₀Be grinding pad average height, R _PBe groove peak height, λ _xAnd λ _yBe along continuous straight runs groove fluctuation wavelength.

The active force that wafer is subject to grinding pad and polishing particles when preferably, determining to grind according to the character of lapping liquid and grinding pad comprises:

Determine that grinding pad passes to the directed force F of wafer by particle _T

Determine the direct contact action power F between grinding pad and wafer _DC

Preferably, determine that grinding pad passes to the directed force F of wafer by particle _TBe specially:

Determine the averaged particles contact pressure in the lapping liquid

Described

Determined by following formula:

$p_p^m=\frac{E_S{N}_0}{1-v_S^2}{\∫}_0^{\∞}2r_p{f}_p^p(-{\mathrm{\ϵ}}_S){\mathrm{\Φ}}_p\left(r_p\right){\mathrm{dr}}_p$

Wherein, N ₀Be the population of unit lapping liquid volume, ε _SBe mean pressure stress under compression, E _SBe modulus of elasticity, ν _SBe Poisson's ratio,

For single polishing particles contacts the pressure that produces, Φ with wafer _p(r _p) be normpdf;

Determine the movable particle contact area A in the lapping liquid _i, described A _iDetermined by following formula:

$A_i=N_0{\∫}_0^{\∞}2r_p\mathrm{\π}{r}_i^2(-{\mathrm{\ϵ}}_p){\mathrm{\Φ}}_p\left(r_p\right){\mathrm{dr}}_p$

Determine that grinding pad passes to the directed force F of wafer by polishing particles _T, determine by following definite formula:

$F_T=A_i{p}_p^m.$

Preferably, determine direct contact action power F between grinding pad and wafer _DCBe specially:

$F_{\mathrm{DC}}=\frac{E_S}{1-v_S^2}{\∫}_{{\mathrm{\ϵ}}_p^m}^{\∞}{p}_d^p(\mathrm{\ϵ}-{\mathrm{\ϵ}}_p)\frac{\mathrm{dA}}{\mathrm{d\ϵ}}\mathrm{d\ϵ}$

Wherein, ε is the mean pressure stress under compression; E _SBe modulus of elasticity; ν _SBe Poisson's ratio;

For the grinding pad that obtains by Finite Element Method directly contacts the pressure that produces with wafer; A is the difference A=1-A of total contact area and movable particle contact area _i, movable particle contact area

Φ _p(r _p) be normpdf.

Preferably, the angular speed of described character according to lapping liquid, grinding pad and the thickness of liquid film dynamic pressure of determining lapping liquid is specially:

With the two-dimentional Reynolds equation under the described thickness of liquid film substitution polar coordinates:

$\frac{\∂\left({\mathrm{rh}}^3\frac{\∂p}{\∂r}\right)}{\∂r}+\frac{1}{r}\frac{\∂\left(h^3\frac{\∂p}{\∂\mathrm{\θ}}\right)}{\∂\mathrm{\θ}}=6\mathrm{\μr\ω}\frac{\∂h}{\∂\mathrm{\θ}}$

Wherein, μ is the lapping liquid dynamic viscosity, and ω is backing plate angular speed, and p is liquid film dynamic pressure function;

Find the solution above-mentioned two-dimentional Reynolds equation, determine liquid film dynamic pressure function p.

The active force that wafer was subject to lapping liquid when preferably, described dynamic pressure according to described lapping liquid was determined chemico-mechanical polishing comprises:

Determine that the wafer along continuous straight runs is subject to the shear action stress F of lapping liquid _τ, concrete formula is:

$F_{\mathrm{\τ}}=\frac{\mathrm{\μr\ω}}{h}+\frac{h}{2}\frac{\∂p}{\∂\mathrm{\θ}}$

Determine that lapping liquid is to the normal pressure F of wafer _N, concrete grammar is for to determine normal pressure F with liquid film dynamic pressure function p along whole crystal column surface integration _N

The active force that wafer was subject to polishing particles when preferably, described character according to lapping liquid and grinding pad was determined to grind also comprises and contacts the activity particle to the model ylid bloom action power F of wafer _VDW, F _VDWThe method of determining specifically comprises:

By normpdf Φ _p(r _p) definite activity population that contacts with wafer, be specially:

$N_{\mathrm{ca}}=N_0{\∫}_{h/2}^{\∞}2r_p{\mathrm{\Φ}}_p\left(r_p\right){\mathrm{dr}}_p$

Wherein, N ₀Population for unit lapping liquid volume;

Determine that according to single-particle and rigidity crystal column surface model ylid bloom action power formula all contact the activity particle to the model ylid bloom action power of wafer; Wherein said single-particle and rigidity crystal column surface model ylid bloom action power formula are:

$f_{\mathrm{VDW}}=\frac{A_H{r}_p}{{6h}^2}$

All contact activity particles to the model ylid bloom action power of wafer are:

F _VDW=f _VDWN _Ca, A wherein _HBe the Ha Make constant.

The active force that wafer was subject to polishing particles when preferably, described character according to lapping liquid and grinding pad was determined to grind also comprises and contacts the activity particle to the electric double layer power F of wafer _DL, F _DLThe method of determining specifically comprises:

By normpdf Φ _p(r _p) definite activity population that contacts with wafer, be specially following formula:

Wherein, N ₀Population for unit lapping liquid volume;

Determine single-particle and interplanar electric double layer power f by Zeta potential-energy function Ψ _DL, be specially following formula:

$f_{\mathrm{DL}}=-2r_p\mathrm{\π}{\mathrm{\ϵ}}_0{\mathrm{\ϵ}}_r({\mathrm{\Ψ}}_1^2+{\mathrm{\Ψ}}_2^2)\frac{{\mathrm{\κe}}^{-\mathrm{\κh}}}{1-e^{-2\mathrm{kh}}}(\frac{2{\mathrm{\Ψ}}_1{\mathrm{\Ψ}}_2}{{\mathrm{\Ψ}}_1^2+{\mathrm{\Ψ}}_2^2}+e^{-\mathrm{kh}}),$ Wherein κ is the Debye length constant;

Determine that all contact activity particles are to the electric double layer power F of wafer _DL, F _DL=f _DLN _Ca

Preferably, the grinding clearance of described definite wafer is specially the wafer removal amount of determining the unit interval, comprising:

Determine that polishing particles is to the removal amount of wafer

The method of determining is specially:

${\mathrm{MRR}}_p^m=\left\{\begin{array}{c}{N}_0{\&Integral;}_{h/2}^{\&infin;}2r_p{R}_{\mathrm{fp}}{\mathrm{\&Phi;}}_p\left(r_p\right){\mathrm{dr}}_p,h>0\\ N_0{\&Integral;}_0^{\&infin;}2r_p{R}_{\mathrm{fp}}{\mathrm{\&Phi;}}_p\left(r_p\right){\mathrm{dr}}_p,h<0\end{array}\right.$

Wherein, N ₀Be the population of unit lapping liquid volume, R _FpFor polishing particles is removed function;

Determine that grinding pad directly contacts the material removal amount that causes with wafer

The method of determining is specially:

${\mathrm{MRR}}_d^m=N_0{\&Integral;}_{h_{\mathrm{wp}}}^{\&infin;}\mathrm{\&pi;}(z_S-d_{\mathrm{wp}})R_S{\mathrm{MRR}}_p^m\left(\frac{4E_p}{3\mathrm{\&pi;}(1-{\mathrm{\&upsi;}}_p^2)}{\left(\frac{z_S-d_{\mathrm{wp}}}{R_S}\right)}^{1/2}\right){\mathrm{\&Phi;}}_S\left(z_S\right){\mathrm{dz}}_S,$

Wherein, N ₀Be the population of unit lapping liquid volume, R _SBe grinding pad rough peak radius, d _WpBe wafer-grinding pad equilibrium spacing;

Determine that lapping liquid flows to wafer shear removal amount

The method of determining is specially: Wherein, K is the Preston coefficient.

Compared with prior art, the present invention has following advantages:

Chemical mechanical polishing liquid dynamic pressure provided by the invention and definite method of grinding clearance, technical scheme is, the thickness of liquid film of lapping liquid between wafer to be ground given in advance and the grinding pad, wafer is subject to the active force of grinding pad and polishing particles when determining to grind according to the character of lapping liquid and grinding pad, character according to lapping liquid, the angular speed of grinding pad and thickness of liquid film are determined the dynamic pressure of lapping liquid, wafer is subject to the active force of lapping liquid when determining to grind according to the character of lapping liquid and grinding pad, the external force that is subject in conjunction with wafer, judge whether balance of the suffered effect force and moment of wafer, if not, the opaquing fluid film thickness, redefine active force that wafer is subject to and the dynamic pressure of lapping liquid, if so, determine the grinding clearance of wafer.The present invention has considered the many bodies effect to wafer of lapping liquid, polishing particles and grinding pad, by loop iteration, and thickness of liquid film, the dynamic pressure of lapping liquid and the grinding clearance of wafer when having determined the CMP grinding between wafer and the grinding pad.Definite method of chemical mechanical polishing liquid dynamic pressure of the present invention and grinding clearance can be predicted the result that CMP grinds more exactly, provides guidance for CMP technique adds modeling.

Simultaneously, by chemical mechanical polishing liquid dynamic pressure of the present invention and definite method of grinding clearance, can predicting wafer CMP after surface topography, for the manufacturability design of integrated circuit diagram suggests improvements, thereby improve product yield.

Description of drawings

Shown in accompanying drawing, above-mentioned and other purpose of the present invention is more clear.

Fig. 1 is chemical mechanical polishing liquid dynamic pressure of the present invention and the definite method flow diagram that grinds clearance;

Fig. 2 is that wafer is carrying out being subjected to institute's force diagram when CMP grinds;

Fig. 3 is definite method flow diagram of first embodiment of the invention;

Fig. 4 carries out the vertical schematic diagram of mesh generation for finding the solution two-dimentional Reynolds equation;

Fig. 5 is definite method flow diagram of second embodiment of the invention.

Embodiment

Continuous decline along with IC manufacturing process characteristic size, the IC manufacturing technology has proposed more and more stricter requirement to the making technology of device, especially in the fabrication of semiconductor device below 65nm, the evenness of circuit surface is the key factor that affects photoetching depth of focus level and yields.CMP is key IC process technique in the wafer production process as an important step in the semiconductor fabrication process.At present, still rest on the experience real example stage for the process control of CMP, grinding mechanism is so far without unified final conclusion.

By consider that lapping liquid contacts wafer with grinding pad and noncontact is stressed and lapping liquid on the multiple impact of wafer active force, the definite method that the invention provides a kind of chemical mechanical polishing liquid dynamic pressure and grind clearance, the method flow chart is seen Fig. 1, comprises step:

Initial thickness of liquid film between given wafer to be ground and the grinding pad;

According to the character of lapping liquid, the angular speed of grinding pad and the dynamic pressure that thickness of liquid film is determined lapping liquid; Wafer is subject to the active force of grinding pad and polishing particles when determining to grind according to the character of lapping liquid and grinding pad;

Wafer is subject to the active force of lapping liquid when determining to grind according to the character of lapping liquid and grinding pad;

In conjunction with the external force that wafer is subject to, judge whether balance of the suffered effect force and moment of wafer, if not, the opaquing fluid film thickness redefines active force that wafer is subject to and the dynamic pressure of lapping liquid; If so, determine the grinding clearance of wafer.

Be described in detail below in conjunction with definite procedure of embodiment to chemical mechanical polishing liquid dynamic pressure of the present invention and grinding clearance.

A lot of details have been set forth 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 and implement, those skilled in the art can be in the situation that do similar popularization without prejudice to intension of the present invention, so the present invention is not subjected to the restriction of following public specific embodiment.

Embodiment one:

In the CMP process of lapping, except the external force that wafer is subject to, there is many-body interaction power between rigidity wafer, rigidity polishing particles and the random rough poroelasticity polishing pad surface, be polished wafer 100 suffered power schematic diagrames and see Fig. 2.In three-dimensional cartesian coordinate system, carry out the relative grinding pad of wafer of CMP with speed V motion, the active force that wafer is subject to comprises: the external force F that puts on wafer _E, grinding pad passes to the directed force F of wafer by polishing particles _T, the direct contact action power F between wafer and the grinding pad _DC(comprise the normal pressure F perpendicular to wafer _DCNWith the frictional force F to wafer _DCF) and the mobile shear stress F that wafer is caused of lapping liquid _τAnd normal pressure F _NIn the CMP process of lapping, wafer is subject to the contact force of polishing particles and grinding pad and the multiple impact of lapping liquid effect.

In order to determine wafer lapping liquid dynamic pressure and grinding clearance in the CMP process, grind the angular speed of backing plate and the character of lapping liquid in the time that CMP need to being known, the character of lapping liquid comprises the original depth of lapping liquid, abrasive particle concentration, mean pressure stress under compression, modulus of elasticity, Poisson's ratio etc.Technical scheme of the present invention is: according to the thickness of liquid film of supposition, can obtain the dynamic pressure of lapping liquid, further obtain shear force and normal pressure that wafer is subject to.Can determine grinding pad passes to wafer by polishing particles active force and grinding pad and the direct contact action power of wafer according to the character of grinding pad and lapping liquid.Judge whether balance of the suffered force and moment of wafer, if uneven, then upgrade thickness of liquid film, redefine the dynamic pressure of lapping liquid and the active force that wafer is subject to; If the force and moment balance that wafer is subject to, dynamic pressure according to thickness of liquid film and lapping liquid, investigation comprises polishing particles absorption and wear mechanism, wafer is removed the grinding clearance that can determine complete wafer, particle, grinding pad interaction in conjunction with particle.Be described in detail below in conjunction with the method for accompanying drawing to the present embodiment.

Fig. 3 is the flow chart that the present embodiment CMP lapping liquid dynamic pressure and grinding clearance are determined method, and the method comprising the steps of:

At first, the original depth of lapping liquid between given wafer to be ground and the grinding pad.

Thickness of liquid film of the present invention is the thickness of lapping liquid between grinding pad and the wafer, because grinding pad is the elastic surface of rough porous, therefore, in the present invention, thickness of liquid film is determined according to following formula in three-dimensional cartesian coordinate system:

$h(x,y)=h_0+R_P\cos \frac{2\mathrm{\&pi;x}}{{\mathrm{\&lambda;}}_x}\cos \frac{2\mathrm{\&pi;y}}{{\mathrm{\&lambda;}}_y}$

Wherein, h ₀Being the backing plate average height, is the surfacial pattern average height of grinding pad; R _PBe grinding pad groove peak height, λ _xAnd λ _yBe along continuous straight runs groove fluctuation wavelength.

Wafer is subject to the active force of grinding pad and polishing particles when then, determining to grind according to the character of lapping liquid and grinding pad.

Grinding pad passes to the directed force F of wafer by polishing particles _T, direct contact action power F is arranged between grinding pad and the wafer _DC

Averaged particles contact in the lapping liquid is pressed and can be obtained by following formula:

$p_p^m=\frac{E_S{N}_0}{1-v_S^2}{\&Integral;}_0^{\&infin;}2r_p{f}_p^p(-{\mathrm{\&epsiv;}}_S){\mathrm{\&Phi;}}_p\left(r_p\right){\mathrm{dr}}_p$

Wherein, N ₀Be the population of unit lapping liquid volume, ε _SIt is the mean pressure stress under compression; E _SIt is modulus of elasticity; ν _SIt is Poisson's ratio;

For single polishing particles contacts the pressure that produces with wafer, can obtain by Finite Element Method Φ _p(r _p) be normpdf.Movable particle contact area in the lapping liquid can be given by the following formula:

$A_i=N_0{\&Integral;}_0^{\&infin;}2r_p\mathrm{\&pi;}{r}_i^2(-{\mathrm{\&epsiv;}}_p){\mathrm{\&Phi;}}_p\left(r_p\right){\mathrm{dr}}_p$

Determine that required grinding pad passes to the directed force F of wafer by polishing particles _T, can determine by following definite formula:

$F_T=A_i{p}_p^m$

Grinding pad passes to the active force of wafer by polishing particles, only consider that the movable particle that contacts with wafer in the lapping liquid has directed force F to wafer _DC, comprise the normal pressure F perpendicular to wafer _DCNWith the frictional force F to wafer _DCF, F _DCCan determine by following formula:

$F_{\mathrm{DC}}=\frac{E_S}{1-v_S^2}{\&Integral;}_{{\mathrm{\&epsiv;}}_p^m}^{\&infin;}{p}_d^p(\mathrm{\&epsiv;}-{\mathrm{\&epsiv;}}_p)\frac{\mathrm{dA}}{\mathrm{d\&epsiv;}}\mathrm{d\&epsiv;}$

Wherein, ε is the mean pressure stress under compression; E _SBe modulus of elasticity; ν _SBe Poisson's ratio; For the grinding pad that obtains by Finite Element Method directly contacts the pressure that produces with wafer; A is the difference A=1-A of total contact area and movable particle contact area _i, movable particle contact area Φ _p(r _p) be normpdf.

According to the character of lapping liquid, the angular speed of grinding pad and the dynamic pressure that thickness of liquid film is determined lapping liquid.

This step also can be when determining to grind according to the character of lapping liquid and grinding pad wafer be subject to carrying out before the active force step of grinding pad and polishing particles.

It is multiple that the dynamic pressure of liquid determines that method has, and adopts in the present embodiment the method for finding the solution two-dimentional Reynolds equation to determine the dynamic pressure of lapping liquid in the CMP process.Bring the thickness of liquid film of supposition into following Reynolds equation:

$\frac{\&PartialD;\left({\mathrm{rh}}^3\frac{\&PartialD;p}{\&PartialD;r}\right)}{\&PartialD;r}+\frac{1}{r}\frac{\&PartialD;\left(h^3\frac{\&PartialD;p}{\&PartialD;\mathrm{\&theta;}}\right)}{\&PartialD;\mathrm{\&theta;}}=6\mathrm{\&mu;r\&omega;}\frac{\&PartialD;h}{\&PartialD;\mathrm{\&theta;}}$

Wherein, μ is the lapping liquid dynamic viscosity, and ω is backing plate angular speed, and p is liquid film dynamic pressure function.In the horizontal direction (XY plane among Fig. 1) of grinding rectangular coordinate system is converted into polar coordinates, referring to Fig. 4.In polar coordinate system, with the Reynolds equation nondimensionalization, Domain is divided the initial grid point W of determining _Ij, then adopt central difference schemes that the single order in the equation, Second Order Partial differential are carried out difference discrete, adopt elimination approach or solution by iterative method p according to boundary value condition _IjThe linear algebraic equation group that is satisfied, the dynamic pressure function p (r, θ) of acquisition lapping liquid.The dynamic pressure function representation of lapping liquid the spatial distribution of pressure in the lapping liquid, shown intuitively the pressure of the suffered lapping liquid of crystal column surface each point.

Wafer is subject to the active force of lapping liquid when determining chemico-mechanical polishing according to the dynamic pressure of described lapping liquid.Described lapping liquid comprises that to the active force of wafer wafer is subject to the shear force F of lapping liquid along continuous straight runs _τWith normal pressure F _NWith the following fluid shear stress formula of liquid film dynamic pressure p (r, θ) substitution:

$\mathrm{\&tau;}=\frac{\mathrm{\&mu;r\&omega;}}{h}+\frac{h}{2}\frac{\&PartialD;p}{\&PartialD;\mathrm{\&theta;}}$

Determine the shear force F that the wafer along continuous straight runs is subject to _τ, liquid film dynamic pressure function p (r, θ) can be determined lapping liquid to the normal pressure F of wafer along whole crystal column surface integration _N

Wafer in order to improve the grinding efficiency of wafer, can increase at wafer the external force F such as counterweight usually when carrying out the CMP grinding _EEffect.Suffered active force should balance in Fig. 2 for wafer, satisfies simultaneously torque equilibrium equation, that is:

$\underset{X,Y,Z}{\mathrm{\&Sigma;}}{F}_i=0,\underset{X,Y,Z}{\mathrm{\&Sigma;}}{M}_i=0$

If the active force that wafer is suffered and moment unbalance show that the thickness of liquid film of supposition is incorrect in an embodiment, should correct thickness of liquid film.The process of concrete corrigendum thickness of liquid film is, by fine setting backing plate surface average height h ₀, groove peak height R _P, horizontal direction groove fluctuation wavelength X _xAnd λ _yCorrect thickness of liquid film.Repeat again above-mentioned steps and determine the process of the suffered active force of wafer, until satisfy the force and moment equilibrium condition.

Thickness of liquid film and lapping liquid dynamic pressure when so far, having determined the suffered active force of wafer and equalising torque.

At last, determine the grinding clearance of wafer.

Grinding clearance is the grinding removal amount of unit interval wafer, because wafer is subject to the acting in conjunction of grinding pad and polishing particles, need to considers the absorption of polishing particles and wear mechanism and obtain grinding removal amount in the CMP process.Removal amount comprises that polishing particles is to the removal amount of wafer

Grinding pad directly contacts the material removal amount that causes with wafer With the mobile removal amount that produces that wafer is sheared of lapping liquid Wherein,

With

Can determine according to following formula:

${\mathrm{MRR}}_p^m=\left\{\begin{array}{c}{N}_0{\&Integral;}_{h/2}^{\&infin;}2r_p{R}_{\mathrm{fp}}{\mathrm{\&Phi;}}_p\left(r_p\right){\mathrm{dr}}_p,h>0\\ N_0{\&Integral;}_0^{\&infin;}2r_p{R}_{\mathrm{fp}}{\mathrm{\&Phi;}}_p\left(r_p\right){\mathrm{dr}}_p,h<0\end{array}\right.$

Wherein, R _FpRemove function for polishing particles, can pass through R _Fp=k _wf _NV _r/ H _wProvide k _wFor grinding coefficient, f _NFor the wafer particle method to contact force, V _rBe the relative sliding velocity of particle and wafer, H _wBe wafer hardness.

Determine that grinding pad directly contacts the material removal amount that causes with wafer

The method of determining is specially:

${\mathrm{MRR}}_d^m=N_0{\&Integral;}_{h_{\mathrm{wp}}}^{\&infin;}\mathrm{\&pi;}(z_S-d_{\mathrm{wp}})R_S{\mathrm{MRR}}_p^m\left(\frac{4E_p}{3\mathrm{\&pi;}(1-{\mathrm{\&upsi;}}_p^2)}{\left(\frac{z_S-d_{\mathrm{wp}}}{R_S}\right)}^{1/2}\right){\mathrm{\&Phi;}}_S\left(z_S\right){\mathrm{dz}}_S,$

Wherein, R _SBe grinding pad rough peak radius, d _WpBe wafer-grinding pad equilibrium spacing;

Determine that lapping liquid flows to wafer shear removal amount

The method of determining is specially:

Wherein, K is the Preston coefficient.

Embodiment two:

Carry out the relative grinding pad of wafer of CMP grinding with speed V motion, the active force that wafer is subject to is except external force F _E, grinding pad passes to the directed force F of wafer by polishing particles _T, the direct contact action power F between wafer and the grinding pad _DC(comprise the normal pressure F perpendicular to wafer _DCNWith the frictional force F to wafer _DCF) and the mobile shear stress F that wafer is caused of lapping liquid _τAnd normal pressure F _NOutward, because wafer is carrying out CMP when grinding, the polishing particles in the lapping liquid and the distance of crystal column surface are very near, also have model ylid bloom action power F between polishing particles and wafer _VDWAnd electric double layer power F _DL

Fig. 5 is the flow chart that the present embodiment CMP lapping liquid dynamic pressure and grinding clearance are determined method, and this determines that method comprises step:

At first, the original depth of lapping liquid between given wafer to be ground and the grinding pad.

Wafer is subject to the active force of grinding pad and polishing particles when then, determining to grind according to the character of lapping liquid and grinding pad.Pass to the active force of wafer, movable polishing particles to Van der Waals force and the electric double layer power of wafer according to the angular speed of the character of lapping liquid, grinding pad and direct contact action power that thickness of liquid film is determined grinding pad and wafer, grinding pad by polishing particles, and find the solution the dynamic pressure that two-dimentional Reynolds equation obtains liquid film.

The dynamic pressure that wafer is subject to the active force of lapping liquid and liquid film when then, determining to grind according to the character of lapping liquid and grinding pad is determined shear force and the normal pressure of the lapping liquid that wafer is subject to.

The grinding pad that the described thickness of liquid film h of the present embodiment (r, θ), wafer are subject to passes to the directed force F of wafer by polishing particles _T, the direct contact action power F between wafer and the grinding pad _DC(comprise the normal pressure F perpendicular to wafer _DCNWith the frictional force F to wafer _DCF) and the mobile shear stress F that wafer is caused of lapping liquid _τAnd normal pressure F _NIdentical with definite method among the embodiment one at the present embodiment, no longer repeat here.

Below detailed description activity polishing particles to the Van der Waals force F of wafer _VDWWith electric double layer power F _DLDefinite method:

Movable particle in the lapping liquid has active force to wafer, by normpdf Φ _p(r _p) determine that the activity population contact with wafer calculates according to following formula:

$N_{\mathrm{ca}}=N_0{\&Integral;}_{h/2}^{\&infin;}2r_p{\mathrm{\&Phi;}}_p\left(r_p\right){\mathrm{dr}}_p$

Wherein, N ₀Population for unit lapping liquid volume.According to single-particle and rigidity wafer planar surface model ylid bloom action power formula

Determine that all contact activity particles are to the model ylid bloom action power F of wafer _VDW=f _VDWN _Ca, A wherein _HBe the Ha Make constant.

Determine single-particle and interplanar electric double layer power f by Zeta potential-energy function Ψ _DL:

$f_{\mathrm{DL}}=-2r_p\mathrm{\&pi;}{\mathrm{\&epsiv;}}_0{\mathrm{\&epsiv;}}_r({\mathrm{\&Psi;}}_1^2+{\mathrm{\&Psi;}}_2^2)\frac{{\mathrm{\&kappa;e}}^{-\mathrm{\&kappa;h}}}{1-e^{-2\mathrm{kh}}}(\frac{2{\mathrm{\&Psi;}}_1{\mathrm{\&Psi;}}_2}{{\mathrm{\&Psi;}}_1^2+{\mathrm{\&Psi;}}_2^2}+e^{-\mathrm{kh}}),$

Wherein κ is the Debye length constant; Determine that all contact activity particles are to the electric double layer power F of wafer _DL=f _DLN _Ca

Judge whether balance of effect force and moment that wafer is subject to, if the active force that wafer is suffered and moment unbalance show that given in the present embodiment thickness of liquid film is incorrect, should upgrade thickness of liquid film, repeat the process of the suffered active force of above-mentioned wafer, until satisfy the force and moment equilibrium equation.

At last, determine the grinding clearance of wafer.

Identical in the present embodiment among definite method of the grinding clearance of wafer and the embodiment one here no longer repeated.

So far, the thickness of liquid film when having determined CMP and grinding between wafer and the grinding pad, the dynamic pressure of lapping liquid and grind clearance, and then can predict the process of lapping of CMP, for the CMP actual process provides guidance.Definite method of the chemical mechanical polishing liquid dynamic pressure that while the present invention proposes and grinding clearance is measurable crystal column surface pattern also, is the manufacturability design proposition suggestion for revision of integrated circuit diagram.

The above only is embodiments of the invention, is not the present invention is done any pro forma restriction.Definite method that definite wafer is subject to the active force of grinding pad and lapping liquid among the present invention can also adopt other different modes.

Although the present invention discloses as above with embodiment, yet is not to limit the present invention.Any those of ordinary skill in the art are not breaking away from the technical solution of the present invention scope situation, all can utilize the method for above-mentioned announcement and technology contents that technical solution of the present invention is made possible change and modification, or be revised as the equivalent embodiment of equivalent variations.Therefore, every content that does not break away from technical solution of the present invention to any simple modification, equivalent variations and modification that above embodiment does, still belongs to the scope of technical solution of the present invention protection according to technical spirit of the present invention.

Claims (10)

1. definite method of chemical mechanical polishing liquid dynamic pressure and grinding clearance is characterized in that, comprises step:

Given thickness of liquid film, described thickness of liquid film are the thickness of lapping liquid between grinding pad and the wafer;

According to the character of lapping liquid, the angular speed of grinding pad and the dynamic pressure that described thickness of liquid film is determined lapping liquid;

Wafer is subject to the active force of grinding pad and polishing particles when determining to grind according to the character of lapping liquid and grinding pad;

Wafer is subject to the active force of lapping liquid when determining chemico-mechanical polishing according to the dynamic pressure of described lapping liquid;

In conjunction with the external force that wafer is subject to, judge whether balance of the suffered effect force and moment of wafer, if not, revise described thickness of liquid film, redefine active force that wafer is subject to and the dynamic pressure of lapping liquid; If so, determine the grinding clearance of wafer.

2. definite method of chemical mechanical polishing liquid dynamic pressure according to claim 1 and grinding clearance is characterized in that, described given thickness of liquid film in three-dimensional cartesian coordinate system is:

$h(x,y)=h_0+R_P\cos \frac{2\mathrm{\&pi;x}}{{\mathrm{\&lambda;}}_x}\cos \frac{2\mathrm{\&pi;y}}{{\mathrm{\&lambda;}}_y}$

Wherein, h ₀Be grinding pad average height, R _PBe groove peak height, λ _xAnd λ _yBe along continuous straight runs groove fluctuation wavelength.

3. chemical mechanical polishing liquid dynamic pressure according to claim 1 and 2 and definite method of grinding clearance is characterized in that, the active force that wafer is subject to grinding pad and polishing particles when determining to grind according to the character of lapping liquid and grinding pad comprises:

Determine that grinding pad passes to the directed force F of wafer by particle _T

Determine the direct contact action power F between grinding pad and wafer _DC

4. definite method of chemical mechanical polishing liquid dynamic pressure according to claim 3 and grinding clearance is characterized in that, determines that grinding pad passes to the directed force F of wafer by particle _TBe specially:

Determine the averaged particles contact pressure in the lapping liquid

Described Determined by following formula:

$p_p^m=\frac{E_S{N}_0}{1-v_S^2}{\&Integral;}_0^{\&infin;}2r_p{f}_p^p(-{\mathrm{\&epsiv;}}_S){\mathrm{\&Phi;}}_p\left(r_p\right){\mathrm{dr}}_p$

Wherein, N ₀Be the population of unit lapping liquid volume, ε _SBe mean pressure stress under compression, E _SBe modulus of elasticity, ν _SBe Poisson's ratio,

For single polishing particles contacts the pressure that produces, Φ with wafer _p(r _p) be normpdf;

Determine the movable particle contact area A in the lapping liquid _i, described A _iDetermined by following formula:

$A_i=N_0{\&Integral;}_0^{\&infin;}2r_p\mathrm{\&pi;}{r}_i^2(-{\mathrm{\&epsiv;}}_p){\mathrm{\&Phi;}}_p\left(r_p\right){\mathrm{dr}}_p$

Determine that grinding pad passes to the directed force F of wafer by polishing particles _T, determine by following formula:

$F_T=A_i{p}_p^m.$

5. definite method of chemical mechanical polishing liquid dynamic pressure according to claim 3 and grinding clearance is characterized in that, determines the direct contact action power F between grinding pad and wafer _DCBe specially:

$F_{\mathrm{DC}}=\frac{E_S}{1-v_S^2}{\&Integral;}_{{\mathrm{\&epsiv;}}_p^m}^{\&infin;}{p}_d^p(\mathrm{\&epsiv;}-{\mathrm{\&epsiv;}}_p)\frac{\mathrm{dA}}{\mathrm{d\&epsiv;}}\mathrm{d\&epsiv;}$

Wherein, ε is the mean pressure stress under compression; E _SBe modulus of elasticity; ν _SBe Poisson's ratio;

For the grinding pad that obtains by Finite Element Method directly contacts the pressure that produces with wafer; A is the difference A=1-A of total contact area and movable particle contact area _i, movable particle contact area

Φ _p(r _p) be normpdf.

6. definite method of chemical mechanical polishing liquid dynamic pressure according to claim 2 and grinding clearance is characterized in that, the angular speed of described character according to lapping liquid, grinding pad and described thickness of liquid film determine that the dynamic pressure of lapping liquid is specially:

With the two-dimentional Reynolds equation under the described thickness of liquid film substitution polar coordinates:

$\frac{\&PartialD;\left({\mathrm{rh}}^3\frac{\&PartialD;p}{\&PartialD;r}\right)}{\&PartialD;r}+\frac{1}{r}\frac{\&PartialD;\left(h^3\frac{\&PartialD;p}{\&PartialD;\mathrm{\&theta;}}\right)}{\&PartialD;\mathrm{\&theta;}}=6\mathrm{\&mu;r\&omega;}\frac{\&PartialD;h}{\&PartialD;\mathrm{\&theta;}}$

Wherein, μ is the lapping liquid dynamic viscosity, and ω is backing plate angular speed, and p is liquid film dynamic pressure function;

Find the solution above-mentioned two-dimentional Reynolds equation, determine liquid film dynamic pressure function p.

7. chemical mechanical polishing liquid dynamic pressure according to claim 6 and definite method of grinding clearance is characterized in that, the active force that wafer was subject to lapping liquid when described dynamic pressure according to described lapping liquid was determined chemico-mechanical polishing comprises:

Determine that the wafer along continuous straight runs is subject to the shear action stress F of lapping liquid _τ, concrete formula is:

$F_{\mathrm{\&tau;}}=\frac{\mathrm{\&mu;r\&omega;}}{h}+\frac{h}{2}\frac{\&PartialD;p}{\&PartialD;\mathrm{\&theta;}}$

Determine that lapping liquid is to the normal pressure F of wafer _N, concrete grammar is for to determine normal pressure F with liquid film dynamic pressure function p along whole crystal column surface integration _N

8. chemical mechanical polishing liquid dynamic pressure according to claim 1 and definite method of grinding clearance, it is characterized in that, the active force that wafer was subject to polishing particles when described character according to lapping liquid and grinding pad was determined to grind also comprises and contacts the activity particle to the model ylid bloom action power F of wafer _VDW, F _VDWThe method of determining specifically comprises:

By normpdf Φ _p(r _p) definite activity population that contacts with wafer, be specially:

$N_{\mathrm{ca}}=N_0{\&Integral;}_{h/2}^{\&infin;}2r_p{\mathrm{\&Phi;}}_p\left(r_p\right){\mathrm{dr}}_p$

Wherein, N ₀Population for unit lapping liquid volume;

Determine that according to single-particle and rigidity crystal column surface model ylid bloom action power formula all contact the activity particle to the model ylid bloom action power of wafer; Wherein said single-particle and rigidity crystal column surface model ylid bloom action power formula are:

$f_{\mathrm{VDW}}=\frac{A_H{r}_p}{{6h}^2}$

All contact activity particles to the model ylid bloom action power of wafer are:

F _VDW=f _VDWN _Ca, A wherein _HBe the Ha Make constant.

9. chemical mechanical polishing liquid dynamic pressure according to claim 1 and definite method of grinding clearance, it is characterized in that, the active force that wafer was subject to polishing particles when described character according to lapping liquid and grinding pad was determined to grind also comprises and contacts the activity particle to the electric double layer power F of wafer _DL, F _DLThe method of determining specifically comprises:

By normpdf Φ _p(r _p) definite activity population that contacts with wafer, be specially following formula:

Wherein, N ₀Population for unit lapping liquid volume;

Determine single-particle and interplanar electric double layer power f by Zeta potential-energy function Ψ _DL, be specially following formula:

$f_{\mathrm{DL}}=-2r_p\mathrm{\&pi;}{\mathrm{\&epsiv;}}_0{\mathrm{\&epsiv;}}_r({\mathrm{\&Psi;}}_1^2+{\mathrm{\&Psi;}}_2^2)\frac{\mathrm{\&kappa;}{e}^{-\mathrm{\&kappa;h}}}{1-e^{-2\mathrm{kh}}}(\frac{2{\mathrm{\&Psi;}}_1{\mathrm{\&Psi;}}_2}{{\mathrm{\&Psi;}}_1^2+{\mathrm{\&Psi;}}_2^2}+e^{-\mathrm{kh}}),$ Wherein κ is the Debye length constant;

Determine that all contact activity particles are to the electric double layer power F of wafer _DL, F _DL=f _DLN _Ca

10. definite method of chemical mechanical polishing liquid dynamic pressure according to claim 1 and grinding clearance is characterized in that, the grinding clearance of described definite wafer is specially the wafer removal amount of determining the unit interval, comprising:

Determine that polishing particles is to the removal amount of wafer

The method of determining is specially:

${\mathrm{MRR}}_p^m=\left\{\begin{array}{c}{N}_0{\&Integral;}_{h/2}^{\&infin;}2r_p{R}_{\mathrm{fp}}{\mathrm{\&Phi;}}_p\left(r_p\right){\mathrm{dr}}_p,h>0\\ N_0{\&Integral;}_0^{\&infin;}2r_p{R}_{\mathrm{fp}}{\mathrm{\&Phi;}}_p\left(r_p\right){\mathrm{dr}}_p,h<0\end{array}\right.$

Wherein, N ₀Be the population of unit lapping liquid volume, R _FpFor polishing particles is removed function;

Determine that grinding pad directly contacts the material removal amount that causes with wafer

The method of determining is specially:

${\mathrm{MRR}}_d^m=N_0{\&Integral;}_{h_{\mathrm{wp}}}^{\&infin;}\mathrm{\&pi;}(z_S-d_{\mathrm{wp}})R_S{\mathrm{MRR}}_p^m\left(\frac{4E_p}{3\mathrm{\&pi;}(1-{\mathrm{\&upsi;}}_p^2)}{\left(\frac{z_S-d_{\mathrm{wp}}}{R_S}\right)}^{1/2}\right){\mathrm{\&Phi;}}_S\left(z_S\right){\mathrm{dz}}_S,$

Wherein, R _SBe grinding pad rough peak radius, d _WpBe wafer-grinding pad equilibrium spacing;

Determine that lapping liquid flows to wafer shear removal amount

The method of determining is specially:

Wherein, K is the Preston coefficient.

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