Contents lists available atScienceDirect
Wear
j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / w e a r
Analyses and experimental confirmation of removal performance of silicon oxide
film in the chemical–mechanical polishing (CMP) process with pattern geometry
of concentric groove pads
Chin-Chung Wei
a,∗, Jeng-Haur Horng
a, An-Chen Lee
b, Jen-Fin Lin
c aDepartment of Power Mechanical Engineering, National Formosa University, Yunlin, TaiwanbDepartment of Mechanical Engineering, National Chiao Tung University, Shinchu, Taiwan cDepartment of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan
a r t i c l e i n f o
Article history: Received 29 March 2010
Received in revised form 3 September 2010 Accepted 20 October 2010
Available online 26 October 2010 Keywords: Chemical–mechanical polishing Surface topography Wear model Three-body abrasion Removal rate
a b s t r a c t
A Reynolds equation that considers both the smoothing hydrodynamic pressure and the pattern of sur-face topography at the polishing pads was used to solve the distribution of the hydrodynamic field. A three-body abrasion wear model for solving the removed thickness of silicon oxide films was also intro-duced to obtain the removal rate of SiO2film in a chemical–mechanical polishing (CMP) process. The suction hydrodynamic pressure field expands its region with increasing groove width and decreasing depth of grooves. The flow rate of the slurry was thus increased, and the removal rate also increased with an increased number of abrasive particles. The solid contact pressure was much higher than the hydrodynamic pressure. The three-body abrasion for the wear depth of a particle arises from the solid contacting pressure and is hence more important than the hydrodynamic pressure. The removal rate of the SiO2film was dominated by the number of abrasive particles, which was affected by the variation of the hydrodynamic pressure in addition to the wear depth controlled by the solid contact pressure. The thickness of the silicon oxide films removed increased with decreasing grooving width and depth.
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
The chemical–mechanical polishing process (CMP) is a key tech-nology in the semiconductor industry. A material, like silicon oxide, is etched by using chemicals and then polished using a mechani-cal process until it has a smooth and uniform surface. The removal rate and uniformity are important properties that vary with several processing factors. These factors can be separated into three cate-gories: (i) operation conditions, including down force and rotation speeds of the wafer and polishing pad; (ii) properties of the slurry, including pH and the viscosity, size, and shape of wear particles; (iii) properties of the polishing pads, including pattern, asperities, and mechanical properties. The earliest study on the removal rate introduced Preston’s equation, R = KP|V|[1], where R is the removal rate, P is the down force, |V| is the absolute value of relative speed between a polishing pad and a wafer, and K is a constant. In this equation, the removal rate is a function of the down force and relative speed; the chemical and fluid effects are not considered. Many studies used this model to find the relationship between the removal rate and operating conditions. McFarlane and Tabor[2]
∗ Corresponding author. Tel.: +886 56315414; fax: +886 56312110. E-mail address:ccwei@nfu.edu.tw(C.-C. Wei).
discussed the influence of the adhesion effect of wear particles on the real contact area. Eringen[3]added the micro spinning effect of wear particles and the stress couple effect of the flow field to the micro-fluid analysis. Cook[4]replaced the pressure and velocity parts of Preston’s equation with the normal and shear stresses to find more correct results for the removal rate. Runnels and Eyman [5], Runnels[6], and Sundararajan et al. [7]studied the lubrica-tion parameters and wear rate of the CMP process by solving the Navier–Stokes equation or the Reynolds equation. This approach assumes slurry erosion to be responsible for the wear mechanism and neglects abrasion wear by particles entrapped in the surface of the polishing pad. The study of Seok et al.[8]described a multistage model for material removal. This model is based on the defor-mation of hyper-elastic asperities attached to a linear-elastic pad. Zhao and Chang[9]developed a model based on the elastic–plastic micro-contact mechanics and abrasive wear theory. The syner-getic effects of mechanical and chemical actions are included in the model. The model reveals some insights into the microcon-tact and wear mechanisms of the CMP process. Yu et al.[10,11], Murarka and Gutmann[12], and Lee et al.[13]established micro-contact models and analysed the micro-contact behaviour between the polishing pad and wafer with viscous-elastic and plastic contact models at two rough contacting surfaces. Tichy et al.[14]presented a one-dimensional model to predict the magnitude of measured
0043-1648/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2010.10.057
Nomenclature
FB back force applied by the wafer carrier (N)
FC contact force (N)
FD down force (N)
FL hydrodynamic force (N)
Mg wafer weight (N)
PB back pressure applied from the wafer carrier (Pa)
Pc solid contact pressure (Pa)
PL hydrodynamic pressure (Pa)
attack angle (rad)
, spinning angles of wafer and pad, respectively (rad) RC diameter of wafer (m)
ωp, ωc wafer and polishing pad angular speeds,
respec-tively (rpm)
P hydrodynamic pressure between two contact sur-faces (Pa)
r, cylindrical coordinates
˚r, ˚, flow factors along the r and directions, respectively
˚Sr shear flow factor in the r direction
viscous of slurry
coefficient of roughness of patterns
hrd, hg film thickness in and away from groove area
u1r, u2r, u1, u2 flow velocities along the r, directions at
upper (subscript 1) and lower (subscript 2) surfaces, respectively (m/s)
Rd distance between the centres of the wafer and
pol-ishing pad (m)
˛, ˇ flow rates along the r and directions, respectively PWP pressure produced by the contact load of a solid
applied at the real contact area (Pa)
AWP circular contact area of roughness peaks (m2)
ı deformation of roughness peaks (m) EWP effective elastic modulus (Pa)
EW, Ep, EA modulus of a wafer polishing pad, and particle of
slurry, respectively (Pa)
v
W,v
p,v
A Poisson’s ratio of a wafer polishing pad, andpar-ticle of slurry, respectively
Rp curvature radius of the roughness peaks on a
polish-ing pad (m)
(zs) Gaussian probability density function
aWP contract radius of roughness peak (m)
ıc critical yielding deformation (m)
HW surface hardness of a wafer (Pa)
AWAe, AWAp real elastic and plastic contact areas formed at
the wear particle and wafer contact region, respec-tively (m2)
RWA complex curvature radii of contact roughness peaks
existing at two contact surfaces (m)
RW, RA curvature radii of roughness peaks on a wafer and a
pad, respectively
FWAe, FWAp contact loads created by elastic and plastic
con-tact, respectively (N)
ha contact distance between the surface of a wafer and
a wear particle (m)
(za) probability density function of roughness peaks on
a pad along the altitude direction
FWA contact load created by a wear particle acting on a
wafer (N)
PWA real contact pressure of a wear particle (Pa)
AWA projection area of a wear particle (m2)
ıaw deformation created between the particle and wafer
(m)
ıap deformation created between the particle and pad
(m)
V relative sliding speed at two contact surfaces (m/s)
t process time (s)
k wear constant
r contact radius of contact roughness (m)
na concentration of particles of slurry (numbers/m3)
ε0 factor of chemical reaction
sub-ambient hydrodynamic pressure in the CMP process. The for-mation of a subambient hydrodynamic pressure region in part of the wafer lubrication area was found in the experimental results of Shan et al.[15]and Levert et al.[16]. An abrasive mechanism in solid–solid contact model was investigated in the model studied by Luo and Dornfeld[17]. This model developed for material removal considered the concentration of active abrasives in the slurry. The proposed model integrates the process parameters including pres-sure, velocity, and other important input parameters. The effects of particles size were investigated in the study of Jeng and Huang [18]. They proposed a CMP removal rate model based upon a micro-contact model which considered the effects of the abrasive particles located between the polishing interfaces. The roughness factor of the polishing pad and the wear particles in the CMP fluid analy-sis model have been extensively discussed by Thakurtaa et al.[19], Vlassak et al.[20], Qin et al.[21]and Wei et al.[22]. In this study, the model developed by Luo and Dornfeld[17]for the number of active abrasive particles was improved, and a micro-contact model was included. High subambient pressures are liable to generate in the use of a non-grooved pad. Therefore, a large suction force is formed between the wafer and the pad such that they are often difficult to separate from each other. The feasible way of lower-ing the subambient pressure is the applications of different groove patterns in the pad. In many engineering applications, surfaces are grooved into different patterns to enhance friction and lubrication performance. Lloy[23]reported that the patterns of grooves in wet clutch surfaces affect the drag loss during the disengaged state. Razzzaque and Kato[24]observed similar results in their exper-iments and attempted to incorporate grooving effects in squeeze film analysis. In the studies of Berger et al.[25]the groove effect in an engagement model was introduced in their analysis; however, only a small number of radial grooves were considered. Various pat-terns and shapes of polishing pad grooves can increase the removal rate and uniformity of wafers. Lin et al. studied analysis models of the slurry fluid field by using concentric and spot patterns of pol-ishing pads[26,27]. They solved CMP problem by developing the average Reynolds equation with flow factors to study the mixed lubrication arising at a cylindrical coordinate system. A theoretical abrasive and adhesive wear model was developed to evaluate the removal rate of the copper film. Subambient hydrodynamic pres-sure was predicted to be formed in part of the wafer’s lubrication area.
The present work extends the analyses of the CMP fluid field of Lin et al.[27]with a three body micro-contact model[28]to improve the model, and a well removal analysis is also introduced in the fluid analysing model. The removal rate and uniformity of wafers were found for several widths and depths of grooves in con-centric pattern pads. These analysis results were also confirmed with experimental data obtained from an industrial CMP device. A referenced tendency of pressure distribution of fluid field in the geometric design of concentric patterns of a CMP pad is also pro-vided to find the better design coefficients for removal rate and god uniformity of SiO2film.
Fig. 1. A sketch of a wafer and polishing pad at steady state.
2. Analysing the model and experiment
The hydrodynamic pressure of a slurry is formed between a wafer and polishing pad with a small angle of inclination between the wafer and polishing pad during the CMP process, which is called the attack angle, , as shown inFig. 1. This angle leads to hydrody-namic pressure at the contact surface and allows the slurry to flow smoothly into the gap between the pad and wafer. The attack angle cannot be directly controlled; it depends on the kinematical bal-ance of the CMP device, including force and moment equilibriums. Equivalent equations obtained from the forces are[27]:
−FB− FD− Mgcos + FL+ FC= 0 (1)
where Mgis the weight of a wafer, FBis the back force applied by the
wafer carrier, FDis the down force, FL is the hydrodynamic force,
and FCis a contact force. The equivalent equations for the moments
are[27]: (Mx)total=
2 0 RC 0 pL(r, )r2cos( − ) drd + 2 0 RC 0 pc(r, )r2cos( − ) drd − N i=1 ripBABcos( − i)= 0 (2) (My)total= 2 0 RC 0 pL(r, )r2sin( − ) drd + 2 0 RC 0 pc(r, )r2sin( − ) drd − N i=1 ripBABsin( − i)= 0 (3)where PLis the hydrodynamic pressure, Pcis the solid contact
pres-sure, PB is the back pressure applied by the wafer carrier, Rc is
diameter of the wafer, and and are the spinning angles of the wafer and pad, respectively. Eqs.(1)–(3)were used to calculate the minimum film thickness, its position, and the attack angle, which were then used as the initial values in the flow field model. Two cylindrical coordinates were used to describe the motions of the wafer and polishing pad, as shown inFig. 2. The wafer and polish-ing pad were rotated with angular speeds ωpand ωc, respectively,
in the counter-clockwise direction.
The depth of the groove is much greater than the surface rough-ness. The surface asperities can thus be ignored on the polishing pad in the region with grooves. The roughness effect in the flow field model is still considered for the region without grooves. From Lin et al.[27], a Reynolds equation that considers both the smooth-ing hydrodynamic pressure and the pattern effect at the polishsmooth-ing pads is: ∂ ∂r
H1 ∂p ∂r + H2 1 r ∂p ∂ + ∂ ∂ H3 ∂p ∂r + H4 1 r ∂p ∂ =∂r∂(F1)+ ∂ ∂(F2) (4) where H1= r˚rf (N, e, hrd) 12 h˛+ hˇ− ˇh˛− ˇh3rd h˛+ hˇ +rˇf (N, e, hg) 12 h˛+ h3rd h˛+ hˇ (5a) H2=r˚rf (N, e, hrd) 12 1− ˇ 1− ˛ˇ tan h˛− h3rd h˛+ hˇ +rˇf (N, e, hg) 12 1− ˇ 1− ˛tan h˛− h3rd h˛+ hˇ (5b) H3= −˚f (N, e, hrd) 12 1− ˛ 1− ˇ˛ cot hˇ− h3rd h˛+ hˇ +f (N, e, hg) 12 1− ˛ 1− ˇ˛ cot hˇ− h3rd h˛+ hˇ (5c) H4= −˚f (N, e, hrd) 12 h˛+ hˇ− ˛hˇ− ˛h3rd h˛+ hˇ +f (N, e, hg) 12 ˛ hˇ+ h3rd h˛+ hˇ (5d) F1= r(1 − ˇ) ¯h Trd 2 (u1r+ u2r)+ 2(u1r− u2r) ∂˚sr ∂r+ rˇhg 2(u1r+ u2r) −r˚rf (N, e, hrd) 12 ˇ(1− ˇ)tan m h˛+ hˇ +rf (N, e, hg) 12 ˇ(1− ˇ)tan m h˛+ hˇ (5e) F2= (1 − ˛) ¯h Trd 2 (u1+ u2)+ 2(u1− u2) ∂˚sr ∂
+ ˛hg 2(u1+ u2) +˚f (N, e, hrd) 12 ˛(1− ˛) m h˛+ hˇ −f (N, e, hg) 12 ˛(1− ˛) m h˛+ hˇ (5f) where the coefficients h˛, hˇ, and m and the function f(N, e, hrd) are
written as:
h˛= (1 − ˛)h3g+ (˛)h3rd (6a)
hˇ= (1 − ˇ)h3g+ ˇh3rd (6b)
m= [−6rωc(hg+ hrd)− 6ωp(r+ Rdcos )(hg+ hrd)]
+ 6(hg+ hrd)Rdωpsin cot (6c)
f (N, e, hrd)= h3rd+ 12e2hrd− 6Neh2TCoth
Nhrd
2e
(6d) Here, P is the hydrodynamic pressure formed between the wafer and polishing pad, r and are the cylindrical coordinates, ˚rand
˚are flow factors along the r and directions, respectively, ˚Sris
the shear flow factor in the r direction, is the viscous of slurry, and is the parameter of the roughness patterns. = 0.5r/ 0.5· 0.5r
and 0.5are the self-correlation functions of the surface asperities
along the r and directions, respectively. hgand hrdare the film
thicknesses at the regions with and without grooves, respectively. u1r, u2r, u1, and u2are the flow velocities along the r, directions at
upper and lower surfaces, respectively. Rdis the distance between
the centres of the wafer and polishing pad. ˛ and ˇ are flow rates along the r and directions, respectively; they were assumed to be equal. The boundary equation was given as follows: when the radius from the centre of the wafer, r, is equal to the radius of the wafer, Rc, the hydrodynamic pressure is equal to the atmosphere
pressure (1 atm). Based on Eq.(1), the hydrodynamic pressure can be obtained using the finite difference method. The fluid velocity and the flow rate at any position in the flow field can be obtained by using the gradient of the hydrodynamic pressure and the boundary velocity.
The deformation of a polishing pad was assumed under the elas-tic limit. The contact pressure produced by the roughness of pads can thus be obtained by the elastic contact theory as[28]: PWP= 4 3 EWP (RP)1/2
∞ h (zs− h)1/2· (zs) dzs (7)where PWPis the pressure produced by the contact load of a solid
applied at the real contact area, AWP. ı is the compressible
defor-mation of the roughness peaks, ı = zs− h. EWPis the effective elastic
modulus: EWP=
1−v
2 W EW + 1−v
2 P EP −1 (8) where EWandv
Ware the modulus and the Poisson’s ratio of thepol-ished surface of the wafer, respectively. Epand
v
pare the modulusand the Poisson’s ratio of the roughness peaks on the polishing pad, respectively. Rpis the radius of curvature of the roughness peaks
on a polishing pad, and (zs) is the Gaussian probability density
function. (zs)= 1 √2exp
− zs2 22 (9) The contact radius of the surface roughness produced by the pad and wafer, aWP, is:aWP= (RP)1/2(ı)1/2 (10)
An elastro-plastic model was used to simulate wear particles contacting the wafer surface. Several assumptions were used to modify the behaviour of the wear particles. (1) Wear particles were distributed uniformly on the wafer and polishing pad; a surface roughness that consists of wear particles was homogeneous and independent of time. (2) The Gaussian distribution function was used to describe the distribution of wear particles on roughness peaks. (3) The contact behaviour of the roughness peaks between the wafer and pad was elastro-plastic contact. (4) The radii of cur-vature of the roughness peaks on the pad were assumed to be equal. (5) The roughness peaks were independent of each other. (6) The hydrodynamic pressure and fluid film did not exist in the contact
region. The Hertz contact theory was used to describe the contact behaviour of the roughness peaks[28]. Tabor[29]showed that for the elastic deformation formed at all roughness peaks of two rough-ness plates, the average contact stress was Pm= KcH, where H is the
hardness of the softer material and Kc is a constant. The critical
yielding deformation, ıc, can be written as:
ıc=
K cHW 2EWA2 RWA (11)
EAand
v
Aare the elastic modulus and the Poisson’s ratio of thewear particles, respectively. HWis the hardness of the wafer on the
polishing side. The real contact area formed by a particle in contact with a wafer surface can be written as[30]:
AWA(ha) = AWAe(ha)+ AWAp(ha) = RWA
ha+ıc ha (za− ha)w(za) dza + RWA ∞ ha+ıc w(2(za− ha)− ıc)(za) dza (12)where AWAe(ha) and AWAp(ha) are the real elastic and plastic contact
areas formed at the wear particle and wafer contact regions, respec-tively. RWAis the complex radius of curvature of the roughness
peaks and is written as: RWA=
1 RW + 1 RA−1 (13) where RWand RAare the radii of curvature of the roughness peaks
on the wafer and pad, respectively. The value of RAis half of the
secondary particle size. The elastro-plastic contact load of a wear particle is written as:
FWA(ha) = FWAe(ha)+ FWAp(ha) =43EWAR0.5WA
ha+ıc ha (za− ha)1.5(za) dza + KcHWRWA ∞ ha+ıc (2(za− ha)− ıc)(za) dza (14)where FWAe(ha) and FWAp(ha) are the contact loads created by elastic
and plastic contact, respectively, which act on the real contact area between the wafer and pad. hais the distance from the surface of a
wear particle to the wafer. (za) is the probability density function
of roughness peaks on a pad along the altitude direction.
The contact load created by a wear particle acting on the wafer, denoted as FWA, can be obtained by the contact pressure, PWA,
cre-ated by the contact between the wafer and pad, and the projection area of a wear particle, AWA. FWAcan thus be written as:
FWA= PWAAWA= PWA(RA)2 (15)
From this equation, the real contact pressure of a wear particle, PWA,
can thus be written as: PWA= FWA AWA= FWA (RA)2 (16) The removal rate of wafers, RR, is usually defined as the average removed thickness per unit time.Fig. 3shows a wear particle acting on a flat plate. x is the contact length of the particle and specimen. ıawis the deformation created by the particle and wafer. ıapis the
deformation created by the particle and pad when the removal area of a particle at the surface of the wafer, S, is very small. The wear volume of a particle is written as:
¯V= k SVt ≈ kVtıaw
Fig. 3. A sketch of the wear volume of a particle.
where V is the relative sliding speed, t is the wear time, and k is a constant of wear. With the use of Eq.(17), the removal rate is: RR= ¯V na Ant = kVıau
ıauxna An (18) where nais the concentration of particles. Xie and Williams[31]introduced the attack angle, , formed between a particle and wafer as shown inFig. 3, which affects the wear volume. When the attack angle, , is less than 15◦, and the pressed depth of a wear particle is assumed to be very small compared to the diameter of a particle, the wear constant k can be written as:
k≈3
ıaw
x (19)
The removal rate can be rewritten as[30]: RR= 3ε0Vı2aw An aAud
Xmax Xmax−ıap a(x) dx (20)where a is the number of particles of contact area. a(x) is the
Gauss density function. ε0is introduced as a chemical factor in the
removal rate function, RR. If the chemical factor ε0= 1, which means
that non-chemical effect occurring at the contact area. 3. Results and discussion
The numerical calculation flow chart is shown inFig. 4. The force and moment equations were used to solve for the minimum slurry film thickness, spinning angle ϕ, and attack angle as initial con-ditions. The Reynold’s equation, considering both the smoothing hydrodynamic pressure and the pattern of the pad, was solved to obtain the hydrodynamic pressure distribution, and the solid con-tact pressure was used to obtain the applied normal load. Then the force balance equation was iterated until it converged. The wear theory of particles was then used to obtain the distribution of the removal rate of the silicon oxide film, which varied with the pattern of concentric pads in the radial direction. All coeffi-cients of the material and the operating conditions are shown in detail inTables 1 and 2, respectively. In the analysis model, sev-eral parameters were obtained from experimental measurements, including the hardness of the wafer and pad and particle size and concentration in the slurry. The experiment was conducted on a commercial CMP device. The rotational speed of the pad and wafer carrier was 90 rpm counter-clockwise. The down force was 1 psi, or about 6.896 kPa. The polishing duration time for each wafer was 40 s. Because slurry filled in the clearance between the wafer and pad, the fluid behaviour of slurry in this gap between the wafer and pad can be considered as a fully developed flow.
Many factors affect the removal rate and uniformity of the sili-con oxide film treated by the CMP process. A new theoretical model was established and presented to analyse the fluid field, removal rate and uniformity, which varied with the groove depth and width
Input operating data of CMP process
Reynold’s equation considered both with smoothing hydrodynamic pressure and pattern effect in polishing pads.
Balance equations of forces and moments used to solve the minimum film thickness, spinning angle, and attacking angle.
Wear theory used to obtain the removing rate of a silicon oxide film
Average contact pressure of roughness peaks of a pad
The deformation theory of polishing pads Kept iteration until solutions converged
Output data, including hydrodynamic pressure, solid contacting pressure, and removal rate.
Fig. 4. Flow chart of the CMP model.
Table 1
The material properties and conditions used in the numerical calculation.
Nanohardness of the SiO2film wafer without a passivation layer,
Ew(GPa)
10.88 Young’s modulus of the SiO2film wafer without a passivation
layer, Ew(GPa)
72.4 Poisson’s ratio of the SiO2film, w 0.2
Young’s modulus of abrasive particles (Al2O3), Ea(GPa) 393
Poisson ratio of abrasive particles (Al2O3), a(GPa) 0.27
Mean radius of abrasive particles (Al2O3), Ra(m) 0.2
Young’s modulus of pad’s asperities, Ep(MPa) 100
Poisson ratio of pad’s asperities and substrate, pand ps 0.3
Young’s modulus of pad’s substrate, Eps(MPa) 2.4
Viscosity of the slurry (Ns/m2) 0.001
Standard deviation of pad’s roughness heights (m) 15 Mean radius of curvature for pad’s roughness heights, Rp(m) 50
Pad’s asperity density, s(1/m2) 4.3× 107
Distance between the centres of wafer and pad, Rd (m) 0.6096
Wafer radius, Rc(m) 0.3048
Density of the slurry before dilution, s(g/mm3) 1× 10−3
Density of abrasives, a(g/mm3) 4× 10−3
Average volume of a single abrasive, ¯Va(m3) 1.4× 10−2
Mean height of a single asperity, l (m) 1.5× 10−5
Table 2
The operation conditions used in the study.
Polishing pad Rodel Politex Regular E (IC1400) Down-force pressure 6.896 kPa
Back Pressure 10.34 kPa
Platen speed 90 rpm
Carrier speed 90 rpm
Slurry flow rate 150× 10−6m3/min
Plating temperature 37◦C
Polishing time 40 s
Pre-wet duration 20 s
Pre-wet flow rate 300× 10−6m3/min
Fig. 5. Contour diagram of hydrodynamic pressure varying with different conditions of concentric grooves on a dimensionless wafer area: (a) width is 0.7 mm, depth is 1.7 mm, groove pitch is 4 mm, and area ratio of grooves on a pad is 17.15%; (b) width is 1.2 mm, depth is 1.7 mm, groove pitch is 4 mm, and area ratio of grooves on a pad is 29.36%; (c) width is 1 mm, depth is 1.2 mm, groove pitch is 6 mm, and area ratio of grooves on a pad is 16.06%; (d) width is 1 mm, depth is 2.3 mm, groove pitch is 6 mm, and area ratio of grooves on a pad is 16.06%; (e) width is 1 mm, depth is 1.2 mm, groove pitch is 4 mm, and area ratio of grooves on a pad is 24.48%.
Fig. 6. Contour diagram of solid contact pressure varying with different conditions of concentric grooves on a dimensionless wafer area: (a) width is 0.7 mm, depth is 1.7 mm,
groove pitch is 4 mm, and area ratio of grooves on a pad is 17.15%; (b) width is 1.2 mm, depth is 1.7 mm, groove pitch is 4 mm, and area ratio of grooves on a pad is 29.36%; (c) width is 1 mm, depth is 1.2 mm, groove pitch is 6 mm, and area ratio of grooves on a pad is 16.06%; (d) width is 1 mm, depth is 1.2 mm, groove pitch is 4 mm, and area ratio of grooves on a pad is 24.48%.
and the area ratio of the concentric groove pads. The area ratio is the area of the grooves divided by the area of the whole pad. A high area ratio indicates that a higher groove area existed on a pad, the real contact area formed at a wafer and pad. In this study, the removal rate varied with the radii of the wafer according to the theoreti-cal analyses and was confirmed with the experimental data, which provided the correction of the numerical data.
3.1. The hydrodynamic pressure
Particles in slurry move with the flow direction of the fluid field, which varies with the gradient of the hydrodynamic pres-sure. When the variation of the hydrodynamic pressure is large, the motion of particles is violent, and a good uniformity of a polished wafer can thus be obtained. The distribution of the hydrodynamic pressure formed at the contact area affects the flow direction of the slurry; the number of abrasive particles at the contact area thus varies with it.Fig. 5shows the contour graphs of hydrodynamic pressures varying with grooving width, depth, pitch, and area ratio. The area ratio of a pad varies with the groove width and the pitch of
the grooves. InFig. 5, the distribution of the hydrodynamic pressure can be separated into negative and positive fields. In the positive pressure field formed at the contact area between the wafer and pad, the fluid pressure forms to separate these two contact sur-faces; the slurry can thus flow into the contact area. Otherwise, the negative hydrodynamic pressure, also named the suction pressure, allows these two contact surfaces, that is, the wafer and polishing pad, to be in contact, and thus the abrasive particles can remove material. The polishing behaviour thus occurs mainly at the neg-ative pressure field. Contour lines formed several eddies at and near the centre of the pad; the flow rate of the slurry thus became lower than that in the other area. Neither the negative nor the positive hydrodynamic pressure regions nor the pressure gradient increased with grooves of greater width, as shown inFig. 5(a) and (b), or shallower depth, as shown inFig. 5(c) and (d). These phenom-ena indicate that a narrow groove width means the slurry cannot flow out smoothly. Deeper grooving depth also let the slurry stay at the groove for a longer time instead of flowing out. The slurry thus filled the gap between the wafer and pad, and the suction and pos-itive pressures were hence decreased.Fig. 5(c) and (e) shows that
the hydrodynamic pressure varies with different groove pitches, which vary with the area ratio of the pad. Comparing these two figures, the distributions of the hydrodynamic pressure seem sim-ilarly, and the flow of the slurry does not vary significantly with different groove pitches.
3.2. The solid contacting pressure
Fig. 6shows the distributions of that solid contacting pressures varying with groove width, depth, pitch, and area ratio of the con-centric grooved pad on the dimensionless contact area of the wafer. Different groove widths, depths, and pitches only slightly affect the distribution of the solid contacting pressure. However, their val-ues are much higher than the hydrodynamic pressure, as shown in Fig. 5. Because the total pressure applied at the contact area is the sum of the solid contacting pressure and the hydrodynamic pres-sure, the abrasive effect for the wear depth of a particle due to the solid contacting pressure is hence more important than hydrody-namic pressure. However, the removal rate is also affected by the number of abrasive particles in the slurry, which increases with increasing gradient of hydrodynamic pressure.
3.3. The removal rate and uniformity of SiO2film
Fig. 7shows the removed thickness of the SiO2film varying with
the dimensionless radius of the wafer area and the geometrical parameters of the polishing pads, including groove width, depth, pitch, and area ratio.Fig. 7(a) and (b) are the groove pitches of 4 mm and 6 mm, respectively. These two figures show that the results of analysis and experiments are well matched, especially inFig. 7(a). The value of the removed thickness near the centre of the wafer is lower than those at other positions. This is due to the distribution of the hydrodynamic pressure, which forms several eddies near the centre, which let the slurry quickly flow into the area and thus decreases the number of abrasive particles. The removal rate was also affected by the effective density of particles and not only by the wear depth controlled by the solid contacting pressure. The removed thickness of silicon oxide films increased with decreasing width and depth of grooves, as shown inFig. 7(a) and (b). A narrow groove decreases the area ratio of grooves on a pad and increases the contact area of wear particles. A shallow groove lets more slurry and particles stay on the pad surface, making the slurry flow more violent due to a higher gradient of the hydrodynamic pressure field, as shown inFig. 5(c) and (d). In the study of Lin et al.[27], the application of concentric grooves in general lowered the suc-tion pressure (negative pressure) formed between the pad and the wafer, elevated the removal rate and reduced the non-uniformity. However, the influences of the groove depth on the removal rate and non-uniformity become insignificant when the depth is exces-sively large because the operating speed was 35 rpm in the study of Lin et al.[27], but the machine here was operated at 90 rpm, which is twice as high. The distribution of the hydrodynamic pressure anal-ysed at 35 rpm in Lin’s study[27]varied more smoothly than that obtained at the speed of 90 rpm, as shown inFig. 5. They also indi-cated that the removal rate was reduced by increasing the groove width such that it finally approached the result of a non-grooved pad, which is the same as our findings, as shown inFig. 7(a) and (b). Several situations were not considered in the proposed model, like the flatness of the polishing pad and the starvation effect without grooves. This may be a result of the assumption that the slurry must fill in the clearance between the wafer and pad. In a wide pitch pad, starvation may decrease the hydrodynamic pressure, but this phe-nomenon cannot be found inFig. 5(c) and (e). However, starvation behaviour was not considered in the proposed CMP model, which led to estimation error in the removal rate calculation results. More calculation error can be found inFig. 7(b).Fig. 7shows that the
opti-0 0.2 0.4 0.6 0.8 1 Dimensionless Radius 1000 1500 2000 2500 3000 3500
a
b
Removed Thickness (A)
Pitch of Groove 4mm W=0.7 mm ; D=1.7 mm ; AR = 17.15% W=1.0 mm ; D=1.2 mm ; AR = 24.48% W=1.0 mm ; D=2.2 mm ; AR = 24.48% W=1.2 mm ; D=1.7 mm ; AR = 29.36% W=0.7 mm ; D=1.7 mm ; AR = 17.15% W=1.0 mm ; D=1.2 mm ; AR = 24.48% W=1.0 mm ; D=2.2 mm ; AR = 24.48% W=1.2 mm ; D=1.7 mm ; AR = 29.36% Experiments Analyzing Results 0 0.2 0.4 0.6 0.8 1
Dimensionless Radius
1000 1500 2000 2500 3000 3500Removed Thickness (A)
Pitch of groove 6mm W=0.7 mm ; D=1.7 mm ; AR = 11.25% W=1.0 mm ; D=1.2 mm ; AR = 16.06% W=1.0 mm ; D=2.2 mm ; AR = 16.06% W=1.2 mm ; D=1.7 mm ; AR = 19.26% W=0.7 mm ; D=1.7 mm ; AR = 11.25% W=1.0 mm ; D=1.2 mm ; AR = 16.06% W=1.0 mm ; D=2.2 mm ; AR = 16.06% W=1.2 mm ; D=1.7 mm ; AR = 19.26% Experiments Analyzing Results
Fig. 7. Removal rates varied with different geometrical conditions of concentric
grooves were obtained from experiments and theoretical analyses and comparing with each other: (a) groove pitch is 4 mm, and (b) groove pitch is 6 mm.
mum conditions of a concentric pad for silicon oxide polishing are a width of 1 mm, a depth of 1.2 mm, and a pitch of 4 mm for a removal rate of 3100 A/min and a non-uniformity of under 5%.
4. Conclusion
The design factors of concentric grooves, including width, depth, and pitch, were considered in this study. A CMP analysis model was developed and compared with experimental results. Several conclusions were obtained:
1. The value of the solid contact pressure is much higher than that of hydrodynamic pressure. The experimental and analytical results show that the removal rate was also dominated by the effective density of particles, which was affected by the gradient of hydro-dynamic pressure variation and did not only arise from the effect of the wear depth, which was dominated by the solid contact pressure.
2. The suction hydrodynamic pressure field expands its region with increasing width and decreasing depth of grooves. The flow rate
of the slurry was thus increased, also increasing the number of abrasive particles.
3. The analytical results were consistent with the experimental results when the grooving pitch was 4 mm. The removed thick-ness of the silicon oxide film increased with decreasing width and depth of grooves. The optimum conditions of a concentric pad for silicon oxide polishing are a width of 1 mm, a depth of 1.2 mm, and a pitch of 4 mm for a removal rate of 3250 A/min and a non-uniformity of under 5%.
Acknowledgements
The authors would like to thank the Jui-Shin Technology Com-pany for providing help with experimental data analyses and providing polishing pads. This study was supported by the National Science Council of Taiwan, R.O.C., under grant NSC-96-2218-E-150-003.
References
[1] F.W. Preston, The theory and design of plate glass polishing machines, J. Soc. Glass Technol. 11 (1927) 214–247.
[2] J.S. McFarlane, D. Tabor, Relation between friction and adhesion, Proc. Roy. Soc., Lond., Series A 202 (1950) 244–253.
[3] A.C. Eringen, Theory of micropolar fluids, J. Math. 16 (1966) 1–18.
[4] L.M. Cook, Chemical process in glass polishing, J. Non-Cryst. Solid 120 (1990) 152–171.
[5] S.R. Runnels, L.M. Eyman, Tribology analysis of chemical–mechanical polishing, J. Electrochem. Soc. 141 (1994) 1698–1701.
[6] S.R. Runnels, Featured-scale fluid-based erosion modeling for chemical–mechanical polishing, J. Electrochem. Soc. 141 (1994) 1900–1905. [7] S. Sundararajan, D.G. Thakurta, D.W. Schwendeman, S.P. Murarka, W.N.
Gill, Two-dimensional wafer-scale chemical–mechanical planarization mod-els based on lubrication theory and mass transport, J. Electrochem. Soc. 146 (1999) 761–766.
[8] J. Seok, C.P. Sukam, A.T. Kim, J.A. Tichy, T.S. Cale, Multiscale material removal modeling of chemical mechanical polishing, Wear 254 (2003) 307–320. [9] Y. Zhao, L. Chang, A. Micro-Contact, Wear model for chemical–mechanical
pol-ishing of silicon wafers, Wear 252 (2002) 220–226.
[10] T.K. Yu, C.C. Yu, M. Orlowski, A statistical polishing pad model for chemical mechanical polish, IEDM Tech. Dig. (1993) 865–868.
[11] T.K. Yu, C. Chris, M.O. Lee, Combined asperity contact and fluid flow model for chemical mechanical polishing, in: Proc. Int. Workshop on Numerical Modeling
of Processes and Devices for Integrated Circuits: NUPAD V, Honolulu, HI/New York, NY, 1994, pp. 29–32.
[12] S.P. Murauka, R. Gutmann, Annual Report of the New York State Scoe, Semi-conductor Research Corporation, Research Triangle Park, NC, 1994. [13] W. Lee, D.W. Shin, M. Tomozawa, S.P. Murarka, The effect of the polishing pad
treatments on the chemical mechanical polishing of SiO2films, Thin Solid Films
270 (1995) 601–606.
[14] J. Tichy, J.A. Levert, L. Shan, S. Danyluk, Contact mechanics and lubrication hydrodynamics of chemical mechanical polishing, J. Electrochem. Soc. 146 (1999) 1523–1528.
[15] L. Shan, J. Levert, L. Meade, J. Tichy, S. Danyluk, Interfacial fluid mechanics and pressure prediction in chemical mechanical polishing, ASME J. Tribol. 122 (2000) 539–543.
[16] J.A. Levert, S. Danyluk, J. Tichy, Mechanism for subambient interfacial pressure while polishing with liquids, ASME J. Tribol. 122 (2000) 450–457.
[17] J. Luo, D.A. Dornfeld, Material removal mechanism in chemical mechanical pol-ishing: theory and modeling, IEEE Trans. Semicond. Manuf. 14 (2001) 112–133. [18] Y.R. Jeng, P.Y. Huang, Impact of abrasive particles on the material removal rate
in CMP, Electrochem. Solid-State Lett. 7 (2004) G40–G43.
[19] D.G. Thakurtaa, D.W. Schwendemanc, R.J. Gutmannb, S. Shankare, L. Jiange, W.N. Gill, Three-dimensional wafer-scale copper chemical mechanical pla-narization model, Thin Solid Films 414 (2002) 78–90.
[20] J.J. Vlassak, A model for chemical mechanical polishing of a material surface based on contact mechanics, J. Mech. Phys. Solids 52 (2004) 847–873. [21] K. Qin, B. Moudgil, C.W. Park, A chemical mechanical polishing model
incorpo-rating both the chemical and mechanical effects, Thin Solid Films 446 (2004) 277–286.
[22] C. Wei, G. Yongjin, C. Abhijit, B. Ashraf, A scratch intersection model of material removal during chemical mechanical planarization (CMP), ASME J. Manuf. Sci. Eng. 127 (2005) 545–554.
[23] F.A. Lloy, Parameters contributing to power loss in disengaged wet clutches, SAE Technical Paper Series, 1974, Paper No. 740676.
[24] M.M. Razzzaque, T. Kato, Effects of groove orientation on hydrodynamic behaviour of wet clutch coolant films, ASME J. Tribol. 112 (1999) 409–414. [25] E.J. Berger, F. Sadeghi, C.M. Krousgrill, Finite element modeling of engagement
of rough and grooved wet clutches, ASME J. Tribol. 118 (1996) 137–146. [26] J.F. Lin, J.D. Chern, Y.H. Chang, P.L. Kuo, M.S. Tsai, Analysis of the
tribologi-cal mechanisms arising in the chemitribologi-cal mechanitribologi-cal polishing of copper-film wafers, ASME J. Tribol. 126 (2004) 185–199.
[27] J.F. Lin, S.C. Chen, Y.L. Ouyang, M.S. Tsai, Analysis of the tribological mechanisms arising in the chemical mechanical polishing of copper-film wafers when using a pad with concentric grooves, ASME J. Tribol. 128 (2006) 445–459. [28] S.P. Timoshenko, J.N. Goodier, Theory of Elastic, McGraw-Hill, New York, 1951,
pp. 1–404.
[29] D. Tabor, The Hardness of Metals, Oxford University Press, 1951.
[30] J.H. Horng, J.S. Lee, D.C. Du, Three-body microcontact model of rough surfaces and its application on polishing of wafer, Mater. Sci. Forum (2006) 507–513. [31] Y. Xie, J.A. Wilfams, The prediction of friction and wear when a soft surface
