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

Abstract

The invention provides a method for determining the hydraulic distribution and the grinding removal rate of chemical mechanical polishing grinding liquid, which comprises the steps of giving the thickness of the grinding liquid between a wafer to be ground and a grinding pad, and determining the dynamic pressure distribution of the grinding liquid and the acting force of the wafer on the grinding liquid 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 polishing pad and the polishing particles on the wafer during polishing according to the properties of the polishing solution and the polishing pad; judging whether the acting force and the moment applied to the wafer are balanced or not by combining the external force applied to the wafer, if not, correcting the thickness of the liquid film, and re-determining the acting force applied to the wafer and the dynamic pressure distribution of the grinding fluid; if so, determining the grinding removal rate of the wafer. The method can predict the surface appearance of the wafer after chemical mechanical polishing, and provides guidance for CMP process modeling; meanwhile, the change characteristics of the grinding surface can be reflected, and modification suggestions are provided for the manufacturability design of the integrated circuit layout, so that the product yield is improved.

Description

Method for determining chemical mechanical polishing grinding liquid pressure distribution and grinding removal rate

Technical Field

The invention relates to the field of semiconductor manufacturing, in particular to a method for determining the hydraulic pressure distribution and the grinding removal rate of chemical mechanical polishing grinding liquid.

Background

In recent years, as the feature size of the IC (Integrated Circuit) manufacturing process is decreasing, the IC manufacturing technology has made more and more strict requirements on the device manufacturing process, and especially in the manufacturing process of semiconductor devices below 65nm, the flatness of the Circuit surface is an important factor affecting the lithography focus depth level and the yield. The wafer surface planarization technology is a critical IC process technology for removing the dielectric layer and the metal layer on the wafer surface during the wafer production process to make the wafer surface flat enough to achieve three-dimensional or multi-layer wiring, increase the wiring density and reduce the defect density.

Currently, the CMP (Chemical Mechanical Polishing) technology has become the most widely used planarization technology in the era of large-scale integrated circuits, and the complete CMP process includes two main processes, i.e., wafer Polishing and post-Polishing cleaning. In the process of wafer polishing, complex chemical and physical actions exist between a wafer to be polished and a polishing pad, polishing liquid and polishing particles, and interaction forces among multiple bodies have important influences on the polishing removal efficiency of the wafer surface, the surface flatness, the reduction of dielectric constant, etching, scraping and the like. In recent years, prediction of the CMP process and polishing results has become a hot spot of research at home and abroad. In summary, the CMP process mainly includes two directions, namely, the contact action between the wafer and the particle-polishing pad and the physical and chemical reaction action between the metal, the dielectric and the polishing solution, the contact action can be divided into four categories, namely direct contact, fluid contact, particle contact and mixed lubrication, and the related disciplines mainly include contact mechanics, tribology, hydromechanics, elastomechanics, partial differential equation, molecular (kinetic) mechanics, slurry chemistry and the like.

Although the prediction method of CMP has made a certain progress, the obtaining of the Removal Rate (MRR) of the polishing slurry on the wafer in the CMP process still remains in the empirical stage, and the results of the polishing of the wafer under the same polishing conditions are generally predicted by experimental results, and the prediction method ignores the influence of the polishing slurry, the polishing parameters and the like on the flatness and the Removal Rate of the polished wafer, and the prediction results cannot accurately represent the polishing results of CMP. Particularly in the fabrication of nanoscale IC devices, the flatness requirements of the wafer surface are extremely high, and the interaction of the polishing pad, slurry and particles with the wafer surface is an extremely complex process that cannot be described simply by empirical methods. In addition, the spatial pressure distribution of the polishing liquid during the CMP polishing process has an important influence on the material removal of the wafer surface, and the effect of the polishing liquid pressure distribution on the wafer removal cannot be ignored.

Disclosure of Invention

The invention provides a method for determining the hydraulic pressure distribution and the grinding removal rate of chemical mechanical polishing grinding liquid, which can accurately simulate the surface appearance of CMP grinding on the surface of a wafer.

In order to achieve the above object, the present invention provides a method for determining the hydraulic pressure distribution and the grinding removal rate of a chemical mechanical polishing grinding fluid, comprising the steps of:

giving the thickness of a liquid film, wherein the thickness of the liquid film is the thickness of grinding liquid between a grinding pad and a wafer;

determining the dynamic pressure distribution of the grinding fluid according to the properties of the grinding fluid, the angular velocity of the grinding pad and the thickness of the liquid film; determining the acting force of the polishing pad and the polishing particles on the wafer during polishing according to the properties of the polishing solution and the polishing pad;

determining the acting force of the grinding fluid on the wafer during the chemical mechanical polishing according to the dynamic pressure distribution of the grinding fluid;

judging whether the acting force and the moment applied to the wafer are balanced or not by combining the external force applied to the wafer, if not, correcting the thickness of the liquid film, and re-determining the acting force applied to the wafer and the dynamic pressure distribution of the grinding fluid; if so, determining the grinding removal rate of the wafer.

Preferably, the given liquid film thickness may be expressed in a three-dimensional cartesian coordinate system as:

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

wherein h is₀Is the average height of the polishing pad, R_PIs the peak height of the trench, λ_xAnd λ_yThe wavelength is fluctuated along the horizontal direction of the groove.

Preferably, determining the force applied to the wafer by the polishing pad and the polishing particles during polishing according to the properties of the polishing solution and the polishing pad comprises:

determining the force F of the polishing pad transmitted to the wafer by the particles_T；

Determining the direct contact force F between the polishing pad and the wafer_DC。

Preferably, the force F of the polishing pad transmitted to the wafer by the particles is determined_TThe method specifically comprises the following steps:

determining the average particle contact pressure in the polishing slurry

The above-mentioned

Determined by the following equation:

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

wherein N is₀Number of particles per unit volume of polishing slurry, epsilon_STo average compressive stress, E_SIs modulus of elasticity, v_SIn order to obtain the poisson ratio,

pressure, phi, generated by contact of single abrasive particles with the wafer_p(r_p) Is a normal distribution probability density function;

determining the contact area A of the active particles in the polishing slurry_iSaid A is_iDetermined by the following equation:

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

determining the force F transmitted by the polishing pad to the wafer by the polishing particles_TDetermined by the following determination formula:

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

preferably, the direct contact force F between the polishing pad and the wafer is determined_DCThe method specifically comprises the following steps:

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

wherein epsilon is the average compressive stress; e_SIs the modulus of elasticity; v is_SIs the poisson ratio;

the pressure generated by the direct contact of the grinding pad and the wafer obtained by the finite element method; a is the difference between the total contact area and the movable particle contact area A =1-A_iArea of contact of the moving particles

Φ_p(r_p) Is a normally distributed probability density function.

Preferably, the determining of the dynamic pressure distribution of the polishing liquid according to the properties of the polishing liquid, the angular velocity of the polishing pad and the thickness of the liquid film is specifically as follows:

substituting the thickness of the liquid film into a two-dimensional Reynolds equation under a polar coordinate:

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

wherein mu is the dynamic viscosity of the grinding fluid, omega is the angular velocity of the backing plate, and p is the dynamic pressure distribution function of the liquid film;

and solving the two-dimensional Reynolds equation to determine a dynamic pressure distribution function p of the liquid film.

Preferably, the determining the acting force of the polishing solution on the wafer during the chemical mechanical polishing according to the dynamic pressure distribution of the polishing solution comprises:

determining the shearing stress F of the wafer along the horizontal direction_τThe concrete formula is as follows:

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

determining the normal pressure F of the slurry to the wafer_NThe specific method is to divide the liquid film dynamic pressure distribution function p along the whole wafer surface area to determine the normal pressure F_N。

Preferably, the determining the force applied to the wafer by the polishing particles during polishing according to the properties of the polishing solution and the polishing pad further comprises van der Waals force F applied to the wafer by contacting the active particles_VDW，F_VDWThe determination method specifically comprises the following steps:

by normally distributing the probability density function phi_p(r_p) Determining the number of active particles contacting with the wafer, specifically:

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

wherein N is₀The number of particles per volume of polishing slurry;

determining Van der Waals acting force of all contact moving particles on the wafer according to the Van der Waals acting force formula of the single particles and the surface of the rigid wafer; wherein the van der Waals acting force formula of the single particles and the rigid wafer surface is as follows:

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

the van der waals forces of all contacting mobile particles on the wafer are:

F_VDW=f_VDWN_cawherein A is_HIs the hamask constant.

Preferably, the determining the force applied to the wafer by the polishing particles during polishing according to the properties of the polishing solution and the polishing pad further comprises an electric double-layer force F applied to the wafer by contacting the movable particles_DL，F_DLThe determination method specifically comprises the following steps:

by normally distributing the probability density function phi_p(r_p) Determining the number of active particles contacting with the wafer, wherein the number is specifically represented by the following formula:

wherein N is₀The number of particles per volume of polishing slurry;

determining electric double-layer force f between single particle and plane through Zeta potential energy function psi_DLSpecifically, the following formula is used:

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

determining the electrical double-layer forces F of all contact events on the wafer_DL，F_DL=f_DLN_ca。

Preferably, the determining the grinding removal rate of the wafer is specifically determining the wafer removal amount per unit time, and includes:

determining the removal of abrasive particles from a wafer

The determination method specifically comprises the following steps:

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

wherein N is₀Number of particles per volume of polishing slurry, R_fpAs a function of abrasive particle removal;

determining the amount of material removed by direct contact between the polishing pad and the wafer

The determination method specifically comprises the following steps:

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

wherein N is₀Number of particles per volume of polishing slurry, R_SIs the polishing pad roughness peak radius, d_wpWafer-pad balance spacing;

determining the amount of the polishing slurry flowing to shear the wafer

The determination method specifically comprises the following steps:wherein K is Preston coefficient.

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

the invention provides a method for determining the hydraulic distribution and the grinding removal rate of chemical mechanical polishing grinding liquid, which has the technical scheme that the liquid film thickness of the grinding liquid between a wafer to be ground and a grinding pad is preset, the acting force of the grinding pad and grinding particles on the wafer during grinding is determined according to the properties of the grinding liquid and the grinding pad, the dynamic pressure distribution of the grinding liquid is determined according to the properties of the grinding liquid, the angular velocity of the grinding pad and the liquid film thickness, the acting force of the grinding liquid on the wafer during grinding is determined according to the properties of the grinding liquid and the grinding pad, whether the acting force and the moment on the wafer are balanced or not is judged by combining the external force on the wafer, if not, the liquid film thickness is corrected, the acting force on the wafer and the dynamic pressure distribution of the grinding liquid are re-determined, and if. The invention comprehensively considers the multi-body action of the grinding fluid, the grinding particles and the grinding pad on the wafer, and determines the liquid film thickness between the wafer and the grinding pad, the dynamic pressure distribution of the grinding fluid and the grinding removal rate of the wafer during the CMP grinding through the cycle iteration. The method for determining the hydraulic pressure distribution and the grinding removal rate of the chemical mechanical polishing grinding liquid can accurately predict the CMP grinding result and provide guidance for the CMP process and modeling.

Meanwhile, the method for determining the chemical mechanical polishing grinding liquid pressure distribution and the grinding removal rate can predict the surface appearance of the wafer after CMP, and provides improvement suggestions for the manufacturability design of the integrated circuit layout, thereby improving the product yield.

Drawings

The above and other objects of the present invention will become more apparent from the accompanying drawings.

FIG. 1 is a flow chart of the method for determining the hydrodynamic pressure distribution and removal rate of CMP liquid according to the present invention;

FIG. 2 is a schematic diagram illustrating the applied force applied to a wafer during CMP polishing;

FIG. 3 is a flowchart of a determination method according to a first embodiment of the present invention;

FIG. 4 is a vertical schematic diagram of mesh generation by solving a two-dimensional Reynolds equation;

FIG. 5 is a flowchart of a determining method according to a second embodiment of the present invention.

Detailed Description

With the continuous decrease of the characteristic dimension of the IC manufacturing process, the IC manufacturing technology puts more and more strict requirements on the device manufacturing process, and particularly in the manufacturing process of semiconductor devices below 65nm, the flatness of the circuit surface is an important factor affecting the lithography focus depth level and the yield. CMP is a critical IC process technology in wafer production as an important part of semiconductor manufacturing process. At present, the process control of CMP still remains in the empirical stage, and the polishing mechanism is not uniformly determined so far.

The invention provides a method for determining the pressure distribution and the grinding removal rate of a chemical mechanical polishing grinding fluid by comprehensively considering the contact and non-contact stress of the grinding fluid and a grinding pad on a wafer and the multiple influence of the grinding fluid on the wafer, wherein the flow chart of the method is shown in figure 1 and comprises the following steps:

giving the initial liquid film thickness between the wafer to be ground and the grinding pad;

determining the dynamic pressure distribution of the grinding fluid according to the properties of the grinding fluid, the angular velocity of the grinding pad and the thickness of the liquid film; determining the acting force of the polishing pad and the polishing particles on the wafer during polishing according to the properties of the polishing solution and the polishing pad;

determining the acting force of the grinding fluid on the wafer during grinding according to the properties of the grinding fluid and the grinding pad;

judging whether the acting force and the moment applied to the wafer are balanced or not by combining the external force applied to the wafer, if not, correcting the thickness of the liquid film, and re-determining the acting force applied to the wafer and the dynamic pressure distribution of the grinding fluid; if so, determining the grinding removal rate of the wafer.

The process of the method for determining the hydraulic pressure distribution and the grinding removal rate of the chemical mechanical polishing grinding fluid of the invention is described in detail in the following with reference to the specific embodiments.

In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.

The first embodiment is as follows:

in addition to the external forces applied to the wafer during the CMP process, there are many interactions between the rigid wafer, the rigid polishing particles and the random rough porous elastic surface polishing pad, and the force applied to the polished wafer 100 is schematically shown in FIG. 2. In a three-dimensional cartesian coordinate system, a wafer undergoing CMP moves relative to a polishing pad at a velocity V, and the wafer is subjected to forces comprising: external force F applied to the wafer_EThe force F transmitted by the polishing pad to the wafer through the polishing particles_TDirect contact force F between wafer and polishing pad_DC(including a positive pressure F perpendicular to the wafer_DCNAnd frictional force F to the wafer_DCF) And the shear stress F caused by the flow of the slurry on the wafer_τAnd normal pressure F_N. During the CMP polishing process, the wafer is subjected to multiple influences of the contact force of the polishing particles and the polishing pad and the action of the polishing liquid.

In order to determine the polishing liquid pressure distribution and the polishing removal rate of the wafer in the CMP process, the angular velocity of the polishing pad and the properties of the polishing liquid during CMP are required to be known, and the properties of the polishing liquid comprise the initial thickness of the polishing liquid, the concentration of polishing particles, the average compressive stress, the elastic modulus, the Poisson's ratio and the like. The technical scheme of the invention is as follows: according to the assumed thickness of the liquid film, the dynamic pressure distribution of the grinding fluid can be obtained, and further the shearing force and normal pressure applied to the wafer can be obtained. The force transmitted by the polishing pad to the wafer through the polishing particles and the force directly contacting the polishing pad with the wafer can be determined according to the properties of the polishing pad and the polishing solution. Judging whether the force and the moment borne by the wafer are balanced or not, if not, updating the thickness of the liquid film, and re-determining the dynamic pressure distribution of the grinding fluid and the acting force borne by the wafer; if the force and moment on the wafer are balanced, the mechanism of absorption and abrasion of abrasive particles is considered according to the thickness of the liquid film and the dynamic pressure distribution of the grinding liquid, and the grinding removal rate of the interaction among the complete wafer, the particles and the grinding pad can be determined by combining the removal of the particles on the wafer. The method of the present embodiment is described in detail below with reference to the accompanying drawings.

Fig. 3 is a flowchart of a CMP slurry dynamic pressure distribution and removal rate determining method according to the present embodiment, which includes the steps of:

first, an initial thickness of a polishing slurry between a wafer to be polished and a polishing pad is given.

The thickness of the liquid film is the thickness of the grinding fluid between the grinding pad and the wafer, and the grinding pad is a rough and porous elastic surface, so that the thickness of the liquid film is determined in a three-dimensional Cartesian coordinate system according to the following formula:

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

wherein h is₀The average height of the backing plate is the average height of the surface pattern of the grinding pad; r_PFor grinding the peak height of pad groove, lambda_xAnd λ_yThe wavelength is fluctuated along the horizontal direction of the groove.

Then, the force applied to the wafer by the polishing pad and the polishing particles during polishing is determined according to the properties of the polishing solution and the polishing pad.

Force F transmitted by the polishing pad to the wafer through the polishing particles_TThe direct contact force F is between the polishing pad and the wafer_DC。

The average particle contact pressure in the polishing liquid can be determined by the following equation:

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

wherein N is₀Number of particles per unit volume of polishing slurry, epsilon_SIs the average compressive stress; e_SIs the modulus of elasticity; v is_SIs the poisson's ratio;

the pressure generated for contacting the single abrasive particle with the wafer can be obtained by finite element method, phi_p(r_p) Is a normally distributed probability density function. The contact area of the active particles in the slurry can be given by the following equation:

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

determining the force F required to transmit the polishing pad to the wafer through the polishing particles_TIt can be determined by the following determination formula:

$F_T=A_i{p}_p^m$

the force transmitted to the wafer by the polishing pad is only considered when the active particles in the polishing liquid contacting with the wafer have force F on the wafer_DCIncluding a positive pressure F perpendicular to the wafer_DCNAnd frictional force F to the wafer_DCF，F_DCCan be determined by the 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 epsilon is the average compressive stress; e_SIs the modulus of elasticity; v is_SIs the poisson ratio;the pressure generated by the direct contact of the grinding pad and the wafer obtained by the finite element method; a is the difference between the total contact area and the movable particle contact area A =1-A_iArea of contact of the moving particlesΦ_p(r_p) Is a normally distributed probability density function.

The dynamic pressure distribution of the polishing liquid is determined according to the properties of the polishing liquid, the angular velocity of the polishing pad, and the thickness of the liquid film.

This step may be performed before the step of determining the force applied to the wafer by the polishing pad and the polishing particles during polishing based on the properties of the polishing slurry and the polishing pad.

There are various methods for determining the dynamic pressure distribution of the liquid, and in this embodiment, the dynamic pressure distribution of the polishing liquid during the CMP process is determined by solving the two-dimensional reynolds equation. The assumed liquid film thickness is substituted into the 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 mu is the dynamic viscosity of the grinding fluid, omega is the angular velocity of the backing plate, and p is the dynamic pressure distribution function of the liquid film. The rectangular coordinate system is converted into polar coordinates in the horizontal direction of grinding (XY plane in fig. 1), see fig. 4. In a polar coordinate system, the Reynolds equation is dimensionless, and the solving area is divided to initially determine grid points W_ijThen, the first order partial differential and the second order partial differential in the equation are subjected to differential dispersion by adopting a central differential format, and p is solved by adopting a cancellation method or an iteration method according to the boundary value condition_ijAnd obtaining the dynamic pressure distribution function p (r, theta) of the grinding fluid by the satisfied linear algebraic equation system. The dynamic pressure distribution function of the grinding fluid describes the spatial distribution of the pressure in the grinding fluid, and the pressure of the grinding fluid on each point on the surface of the wafer is visually displayed.

And determining the acting force of the grinding fluid on the wafer during the chemical mechanical polishing according to the dynamic pressure distribution of the grinding fluid. The acting force of the grinding fluid on the wafer comprises the shearing acting force F of the wafer along the horizontal direction by the grinding fluid_τAnd normal pressure F_N. Substituting the liquid film dynamic pressure distribution p (r, theta) into the following fluid shear stress equation:

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

determining the shearing force F applied to the wafer along the horizontal direction_τThe dynamic pressure distribution function p (of the liquid film)r, theta) along the entire surface area of the wafer to determine the normal pressure F of the slurry against the wafer_N。

When a wafer is polished by CMP, an external force F such as a weight is usually added to the wafer to improve the polishing efficiency of the wafer_EAnd (4) acting. The forces experienced by the wafer in fig. 2 should be balanced while satisfying the moment balance equation, i.e.:

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

if the wafer is subjected to an imbalance of forces and moments indicating that the assumed thickness of the liquid film is incorrect in the embodiment, the thickness of the liquid film should be corrected. The process of specifically correcting the thickness of the liquid film is realized by finely adjusting the average height h of the surface of the backing plate₀Trench peak height R_PHorizontal direction groove fluctuation wavelength lambda_xAnd λ_yTo correct the liquid film thickness. And repeating the steps to determine the acting force applied to the wafer until the force and moment balance conditions are met.

Thus, the liquid film thickness and grinding liquid pressure distribution when the acting force and the moment on the wafer are balanced are determined.

And finally, determining the grinding removal rate of the wafer.

The removal rate is the amount of removal of the wafer by polishing per unit time, and since the wafer is subjected to the combined action of the polishing pad and the polishing particles, the polishing particles need to be comprehensively consideredTo obtain the amount of abrasive removal during CMP. The removal amount includes the removal amount of the wafer by the abrasive particles

Amount of material removed by direct contact of polishing pad and waferAnd the amount of removal by shearing of the wafer by the slurry flowWherein,

and

can be determined according to the 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 is_fpAs a function of abrasive particle removal, can be determined by R_fp=k_wf_NV_r/H_wGive k_wIs the coefficient of abrasion, f_NIs the wafer particle normal contact force, V_rIs the relative slip velocity of the particles and the wafer, H_wIs the wafer hardness.

Determining the amount of material removed by direct contact between the polishing pad and the wafer

The determination method specifically comprises the following steps:

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

wherein R is_SIs the polishing pad roughness peak radius, d_wpWafer-pad balance spacing;

determining the amount of the polishing slurry flowing to shear the wafer

The determination method specifically comprises the following steps:

wherein K is Preston coefficient.

Example two:

the wafer for CMP polishing moves at a speed V relative to the polishing pad, and the wafer is subjected to an action force other than an external force F_EThe force F transmitted by the polishing pad to the wafer through the polishing particles_TDirect contact force F between wafer and polishing pad_DC(including a positive pressure F perpendicular to the wafer_DCNAnd frictional force F to the wafer_DCF) And the shear stress F caused by the flow of the slurry on the wafer_τAnd normal pressure F_NIn addition, when a wafer is subjected to CMP polishing, the distance between polishing particles in a polishing liquid and the surface of the wafer is very close, and van der Waals forces F also exist between the polishing particles and the wafer_VDWAnd electric double layer force F_DL。

Fig. 5 is a flowchart of a CMP slurry hydraulic pressure distribution and polishing removal rate determining method according to the present embodiment, where the determining method includes the steps of:

first, an initial thickness of a polishing slurry between a wafer to be polished and a polishing pad is given.

Then, the force applied to the wafer by the polishing pad and the polishing particles during polishing is determined according to the properties of the polishing solution and the polishing pad. Determining the direct contact acting force of the grinding pad and the wafer, the acting force of the grinding pad transmitted to the wafer through grinding particles, the van der Waals force of movable grinding particles to the wafer and the electric double-layer force according to the property of the grinding liquid, the angular velocity of the grinding pad and the thickness of the liquid film, and solving a two-dimensional Reynolds equation to obtain the dynamic pressure distribution of the liquid film.

Then, the shearing force and normal pressure of the polishing liquid received by the wafer are determined according to the properties of the polishing liquid and the polishing pad.

The thickness h (r, θ) of the liquid film and the force F transmitted to the wafer by the polishing pad via the polishing particles_TDirect contact force F between wafer and polishing pad_DC(including a positive pressure F perpendicular to the wafer_DCNAnd frictional force F to the wafer_DCF) And the shear stress F caused by the flow of the slurry on the wafer_τAnd normal pressure F_NThe determination method in this embodiment is the same as that in the first embodiment, and will not be repeated here.

The van der Waals forces F of the active abrasive particles on the wafer are described in detail below_VDWAnd electric double layer force F_DLThe determination method of (1):

the active particles in the slurry act on the wafer through the normal distribution probability density function phi_p(r_p) Determining the number of active particles in contact with the wafer according to the 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 is₀The number of particles per unit volume of the polishing slurry. According to the van der Waals force formula of the surfaces of the single particles and the rigid wafer flat plate

Determining the van der Waals forces F of all contact mobile particles on the wafer_VDW=f_VDWN_caWherein A is_HIs the hamask constant.

Determining electric double-layer force f between single particle and plane through Zeta potential energy function psi_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; determining the electrical double-layer forces F of all contact events on the wafer_DL=f_DLN_ca。

And judging whether the acting force and the moment on the wafer are balanced or not, if the acting force and the moment on the wafer are unbalanced, indicating that the given liquid film thickness is incorrect in the embodiment, updating the liquid film thickness, and repeating the process of the acting force on the wafer until a force and moment balance equation is satisfied.

And finally, determining the grinding removal rate of the wafer.

The method for determining the polishing removal rate of the wafer in this embodiment is the same as that in the first embodiment, and will not be repeated here.

Therefore, the thickness of a liquid film between a wafer and a grinding pad during CMP grinding, the dynamic pressure distribution of grinding liquid and the grinding removal rate are determined, the grinding process of CMP can be predicted, and guidance is provided for the actual process of CMP. Meanwhile, the method for determining the chemical mechanical polishing grinding liquid pressure distribution and the grinding removal rate can also predict the surface appearance of the wafer, and provides modification suggestions for the manufacturability design of the integrated circuit layout.

The foregoing is illustrative of the present invention and is not to be construed as limiting thereof in any way. The method for determining the acting force of the polishing pad and the polishing solution on the wafer can also adopt other different modes.

Although the present invention has been described with reference to the above embodiments, the present invention is not limited thereto. Those skilled in the art can make possible variations and modifications to the invention using the methods and techniques disclosed above, or to modify equivalent embodiments with equivalent variations, without departing from the scope of the invention. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention, without departing from the content of the technical solution of the present invention, still belong to the protection scope of the technical solution of the present invention.

Claims (10)

1. The method for determining the hydraulic pressure distribution and the grinding removal rate of the chemical mechanical polishing grinding liquid is characterized by comprising the following steps of:

giving the thickness of a liquid film, wherein the thickness of the liquid film is the thickness of grinding liquid between a grinding pad and a wafer;

determining the dynamic pressure distribution of the grinding fluid according to the properties of the grinding fluid, the angular velocity of the grinding pad and the thickness of the liquid film;

determining the acting force of the polishing pad and the polishing particles on the wafer during polishing according to the properties of the polishing solution and the polishing pad;

determining the acting force of the grinding fluid on the wafer during the chemical mechanical polishing according to the dynamic pressure distribution of the grinding fluid;

judging whether the acting force and the moment applied to the wafer are balanced or not by combining the external force applied to the wafer, if not, correcting the thickness of the liquid film, and re-determining the acting force applied to the wafer and the dynamic pressure distribution of the grinding fluid; if so, determining the grinding removal rate of the wafer.

2. The method for determining the hydrodynamic pressure distribution and the removal rate of polishing slurry in chemical mechanical polishing according to claim 1, wherein the given liquid film thickness in a 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 is₀Is the average height of the polishing pad, R_PIs the peak height of the trench, λ_xAnd λ_yThe wavelength is fluctuated along the horizontal direction of the groove.

3. The method for determining the hydraulic pressure distribution and the removal rate of a chemical mechanical polishing slurry according to claim 1 or 2, wherein the determining the forces applied to the polishing pad and the polishing particles on the wafer during polishing according to the properties of the polishing slurry and the polishing pad comprises:

determining the effect of the polishing pad on the waferForce F_T；

Determining the direct contact force F between the polishing pad and the wafer_DC。

4. The method of claim 3, wherein the force F of the polishing pad transmitted to the wafer by the particles is determined_TThe method specifically comprises the following steps:

determining the average particle contact pressure in the polishing slurry

The above-mentionedDetermined by the following equation:

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

wherein N is₀Number of particles per unit volume of polishing slurry, epsilon_STo average compressive stress, E_SIs modulus of elasticity, v_SIn order to obtain the poisson ratio,

pressure, phi, generated by contact of single abrasive particles with the wafer_p(r_p) Is a normal distribution probability density function;

determining the contact area A of the active particles in the polishing slurry_iSaid A is_iDetermined by the following equation:

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

determining the force F transmitted by the polishing pad to the wafer by the polishing particles_TDetermined by the following formula:

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

5. the method of claim 3, wherein determining the direct contact force F between the polishing pad and the wafer_DCThe method specifically comprises the following steps:

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

wherein epsilon is the average compressive stress; e_SIs the modulus of elasticity; v is_SIs the poisson ratio;

the pressure generated by the direct contact of the grinding pad and the wafer obtained by the finite element method; a is the difference between the total contact area and the movable particle contact area A =1-A_iArea of contact of the moving particles

Φ_p(r_p) Is a normally distributed probability density function.

6. The method for determining the hydraulic distribution and the grinding removal rate of the chemical mechanical polishing grinding liquid according to claim 2, wherein the determining the hydraulic distribution of the grinding liquid according to the properties of the grinding liquid, the angular velocity of the grinding pad and the thickness of the liquid film is specifically as follows:

substituting the thickness of the liquid film into a two-dimensional Reynolds equation under a polar coordinate:

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

wherein mu is the dynamic viscosity of the grinding fluid, omega is the angular velocity of the backing plate, and p is the dynamic pressure distribution function of the liquid film;

and solving the two-dimensional Reynolds equation to determine a dynamic pressure distribution function p of the liquid film.

7. The method for determining the hydraulic distribution and the grinding removal rate of the chemical mechanical polishing grinding fluid according to claim 6, wherein the step of determining the acting force of the grinding fluid on the wafer during the chemical mechanical polishing according to the hydraulic distribution of the grinding fluid comprises the following steps:

determining the shearing stress F of the wafer along the horizontal direction_τThe concrete formula is as follows:

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

determining the normal pressure F of the slurry to the wafer_NThe specific method is to divide the liquid film dynamic pressure distribution function p along the whole wafer surface area to determine the normal pressure F_N。

8. The method of claim 1, wherein determining the force exerted by the polishing slurry on the wafer during polishing based on the properties of the polishing slurry and the polishing pad further comprises van der Waals forces F on the wafer by the active particles_VDW，F_VDWThe determination method specifically comprises the following steps:

by normally distributing the probability density function phi_p(r_p) Determining the number of active particles contacting with the wafer, specifically:

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

wherein N is₀The number of particles per volume of polishing slurry;

determining Van der Waals acting force of all contact moving particles on the wafer according to the Van der Waals acting force formula of the single particles and the surface of the rigid wafer; wherein the van der Waals acting force formula of the single particles and the rigid wafer surface is as follows:

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

the van der waals forces of all contacting mobile particles on the wafer are:

F_VDW=f_VDWN_cawherein A is_HIs the hamask constant.

9. The method for determining hydraulic pressure distribution and grinding removal rate of chemical mechanical polishing grinding liquid according to claim 1, wherein said method is characterized in thatDetermining the force exerted by the polishing particles on the wafer during polishing based on the properties of the polishing slurry and the polishing pad further includes contacting the active particles with an electrical double layer force F on the wafer_DL，F_DLThe determination method specifically comprises the following steps:

by normally distributing the probability density function phi_p(r_p) Determining the number of active particles contacting with the wafer, wherein the number is specifically represented by the following formula:

wherein N is₀The number of particles per volume of polishing slurry;

determining electric double-layer force f between single particle and plane through Zeta potential energy function psi_DLSpecifically, the following formula is used:

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

determining the electrical double-layer forces F of all contact events on the wafer_DL，F_DL=f_DLN_ca。

10. The method for determining the hydrodynamic pressure distribution and the removal rate of polishing in chemical mechanical polishing according to claim 1, wherein the determining the removal rate of polishing of a wafer is specifically determining the removal amount of the wafer per unit time, and comprises:

determining the removal of abrasive particles from a wafer

The determination method specifically comprises the following steps:

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

wherein N is₀Number of particles per volume of polishing slurry, R_fpAs a function of abrasive particle removal;

determining direct contact between the polishing pad and the waferResulting amount of material removed

The determination method specifically comprises the following steps:

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

wherein R is_SIs the polishing pad roughness peak radius, d_wpWafer-pad balance spacing;

determining the amount of the polishing slurry flowing to shear the wafer

The determination method specifically comprises the following steps:

wherein K is Preston coefficient.

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