Effect of kinematics and abrasive particle dynamics on material removal rate uniformity during polishing

Transcription

1 Effect of kinematics and abrasive particle dynamics on material removal rate uniformity during polishing Armin Saeedi Vahdat 1,2 and S V Babu 2 1 Dept. of Mechanical and Aeronautical Engineering 2 Center for Advanced Material Processing (CAMP) Clarkson University Potsdam, New York April16, 215 1

2 Motivation and Objective Scaling down the structures and increasing wafer size MRR uniformity becomes more challenging CMP kinematics based on slurry distribution and particle trajectories have a big impact on MRR profiles. (Pressure and temperature profiles are also very important) 2

3 Chemical Mechanical Polishing Kinematics y Pad ω p : Platen rotational/angular velocity ω w : wafer rotational/angular velocity Rotary Dynamics Y ω p t e t : Carrier oscillatory motion function Reciprocation Dynamics e : Distance between pad and wafer centers, e wafer ω w t e t r r : Wafer radius X, x 3

4 Velocity Field on Wafer Surface Relative velocity of a point on the wafer: r v r (e r e r r ) r r e r & A p t p t 2 2 &/ ( ) (1 ) / 1 / (1 ) / v e e e y e e e x e A p t p t where / w For typical rotary-type polishers: e& e, e e t p t p Y ω p t e y wafer ω w t r A e t r Pad X, x 2 2 v e y (1 ) / e 1 x(1 ) / e A p 4

5 Velocity Field on Wafer Surface When α = 1 (ω p = ω w ) va pe ( y (1 ) / e ) (1 x(1 ) / e ) v A e p Uniform velocity field all over the wafer Assuming uniform pressure distribution, Preston s equation suggests uniform MRR: MRR(x, y) k v (x, y) p(x, y) p A p p However experimental results suggests α = 1 is not a proper velocity ratio option in order to get uniform MRR profile. MRR(x, y) k p e cont. 5

6 Particle Trajectories and MRR Particles trapped between pad asperities and wafer are active particles active inactive Non active abrasives cause zero/negligible MRR Active particles trajectories distribution MRR uniformity depends on: Material removed along each trajectory (particle size) 6

7 Description of a Particle Location Initial location of each active particle of pad: X cos A R Y A sin Y y φ φ m R e A r Location of all Active particles participating in MRR on wafer follows these conditions X, x m R e r m m cos R e r 2Re 7

8 Description of a Particle Trajectory Time dependent trajectory of a particle in fixed/global coordinate: X (t) cos( t) A p R Y (t) sin ( p t) A Assumption: Particle leaves the wafer area and rotates with pad velocity and eventually reenters the wafer area.?? Y φ +ω p t R y e t A 8

9 Description of a Particle Trajectory Time-dependent particle locations in fixed and moving coordinates are related as: XA(t) xa(t) e et YA(t) ya(t) x (t) cos( t) sin( t) A p p xa(t) y (t) sin( p t) cos( p t) A ya(t) Y φ +ω p t y e +e t yʹ ω w t Carrier oscillatory motion is described using its amplitude and frequency: e A sin ( t) t e e Zhao, Dewen, et al. "Kinematic optimization for chemical mechanical polishing based on statistical analysis of particle trajectories." Semiconductor Manufacturing, IEEE Transactions on 26.4 (213): A x xʹ X 9

10 x Description of a Particle Trajectory Time dependent trajectory of a particle in local coordinate system can be expressed: (t) cos( t) sin( t) Rcos( t) ( e A sin ( t)) A p p p e e y (t) sin( p t) cos( p t) Rsin ( p t) A 1

11 Five Particle Trajectories (No Oscillation) 15 1 When α = 1 (ω p = ω w ) Five particles are located on pad asperities

12 Five Particle Trajectories (No Oscillation) 15 1 α= α= α= α=

13 Five Particle Trajectories (No Oscillation) 15 1 α= α= α= α=

14 Five Particle Trajectories (No Oscillation) 15 1 α= α= For α=.91,.93,.94,.97 the trajectories are better distributed all over the wafer surface. A ring with lower trajectory density is observed. 14

15 Five Particle Trajectories (No Oscillation) The observed ring is an artifact which is induced due to the initial particle locations

16 Five Particle Trajectories The trajectory distribution density at the center of the wafer can be improved by making the carrier oscillate No oscillation With Oscillation

17 1 Particle Trajectories When number of particles increase, the trajectory distribution appears uniform but it is not Therefore a quantitative technique is required to measure the distribution of particle trajectories across the wafer. 17

18 Kinematics Parameters and Sliding Length n n Sliding distance of each particle inside each area element is calculated during polishing time. Particle 2 t=t + t Sliding distance L 11 n n Sliding n distance L 12 Particle 1 t=t + t Particle 1 t=t + 2 t Sliding n distance L 21 Sliding distance L 22 Particle 2 t=t + 2 t 18

19 Sliding Distance, MRR and WIWNU Material volume removed based on particle trajectory length: V ( x, y) k p( x, y) L( x, y) p V ( x, y) ( ) (, ) L( x, y) MRRv k p R p x y T T Uniform pressure profile Mono-dispersed particles p MRR v k p p ( R) p T p const L( x, y) Hence Sliding distance distribution is an indicator of WIWNU MRR L WIWNU (%) 1 1 MRR L mean mean 19

20 WIWNU vs Active Particle Number Using large number of particles in simulations is impractical So determine the number of active particles that leads to a realistic simulation WIWNU(%) n =1, is a good choice for number of particles Particles Number Zhao, Dewen, et al. "Kinematic optimization for chemical mechanical polishing based on statistical analysis of particle trajectories." Semiconductor Manufacturing, IEEE Transactions on 26.4 (213):

21 WIWNU Distribution Question: Whey does WIWNU converge a) to a constant value and b) that is still large? Answer: The MRR increases toward the edge of the wafer even when the whole wafer surface is covered by active particles Normalized Sliding Distance WIWNU(%) Particles Number

22 WIWNU (%) WIWNU vs α Parameter Mono-dispersed slurry is assumed α =.91 results in lowest WIWNU. α = 1 results in worst WIWNU results. Normalized Sliding Distance Normalized Sliding Distance

23 WIWNU vs Oscillatory Motion WIWNU(%) WIWNU(%) p / e A e / r Oscillatory motion e A sin ( t) t e e e A e p 6 r 5 WIWNU is improved WIWNU (%) 3.36% 23

24 Quantitative Example of CMP Kinematics For polishing of 3 mm wafers on a rotary-type polishing tool with mono-dispersed slurry: For 93 r / min e p 2mm WIWNU (%) 4% w p.9193 r/ min 85 r/ min p e 15 r / min 6 r Ae 3mm 5 Small variations in these numbers create a small change in the obtained WIWNU However, some special cases need to be avoided: 93 / min and A or p w r e e WIWNU (%) 18% 24

25 Large Particles Influence on WIWNU MRR depends on the size of the abrasives When film thickness is larger than particle penetration depth Film Small Particle Large Particle Particle size dependency of MRR is projected in the Preston s constant k ( ) p R R 2 When large particles are present in the slurry along with the nominal particle size Large and small particles effects will both be projected in the MRR profile. Qin, Kuide, Brij Moudgil, and Chang-Won Park. "A chemical mechanical polishing model incorporating both the chemical and mechanical effects." Thin Solid Films (24):

26 n Large Particles Influence on WIWNU Sliding distance n L R1 Small Particle Sliding distance L 22 Large Particle k p MRR R L ( R / R ) L ( R / R ) L... ( R / R ) L p v 1 R1 2 1 R2 3 1 R3 n 1 R T p MRR WIWNU (%) v 1 MRR T mean n 26

27 Effect of Large Particles The number of larger particles is assumed to be 1%-5% of the total number of active particles Trajectories of large particles are calculated while changing their position every 2 seconds

28 Large Particles Size and Concentration Effects WIWNU(%) % 2% 3% 4% 5% R L / R s Large particles size can drastically deteriorate WIWNU indicating the significance of a proper slurry filtration process. 28

29 Scratch Growth For the special case of α = 1 (ω p = ω w ), since each particle travels the same path over and over during the polishing Large particles and undesired debris can create major scratches on the wafer surface. Scratch growth on a constant path α = For α 1 (ω p ω w ), since each particle travels various paths during the polishing the effect of large particles is distributed across the wafer which may minimize their unwanted effects 29

30 Conclusions and Remarks A mathematical model to describe particle trajectories during polishing was developed. MRR and WIWNU were determined based on the extracted particle trajectories. The results showed that ω w =ω p uniformity. leads to the worst MRR When ω w =.91 ω p, the most uniform MRR is obtained. The oscillatory motion frequency and amplitude can also be optimized to improve MRR profile uniformity. This model is capable of explaining the effect of large particles on WIWNU and scratch growth. 3

31 Questions and Comments Life Before CMP Life After CMP Thank you for your attention. 31