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Semi-empirical Material Removal Model with Modified Real Contact Area for CMP

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Abstract

Chemical mechanical polishing (CMP) is essential in semiconductor processing and has recently widened its scope of application. However, the study on its mechanisms is still in progress. Understanding the CMP process requires an understanding of the various physical and chemical reactions that occur at the pad-wafer interface. Moreover, understanding the real contact area (RCA) between the polishing pad and the wafer in the CMP process is essential for predicting the material removal rate (MRR) and understanding the overall process. In this study, a modified mathematical model for the RCA was developed and validated experimentally. The model of the RCA proposed in this study was used to establish the MRR model and predict the MRR under various pressure values and the effect of abrasive particle size and its distribution. Specifically, the experimentally obtained values were compared with the values obtained by the model and the comparison results were analyzed. Thereby, it was found that the RCA model and the MRR model proposed in this study were in good agreement with the experimental results, which shows that the MRR can be predicted by a mathematical model using the measurement of the RCA.

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Abbreviations

A r :

Real contact area (RCA) at Case I

C :

Constant from Qin’s research (C = 0.35)

R pa :

Average radius of pad’s asperities

σ pa :

Standard deviation of asperity heights

p :

Applied pressure

A w :

Apparent area of wafer

E pw :

Composite elastic modulus of pad and wafer

E p :

Elastic modulus of polishing pad

E w :

Elastic modulus of wafer

ν p :

Poisson’s ratio of polishing pad

ν w :

Poisson’s ratio of wafer

F :

Down force

A ′ r :

Real contact area at Case II

R r :

Radius of the real contact area at Case I

d :

Separation distance between two surfaces

z :

Asperity height at any given asperity

p(z):

Probability density function of asperity peak heights

A T w :

Apparent wafer-pad sliding area

n p :

Number of revolution of the polishing platen

r c :

Length between the center position of polishing pad and the center position of wafer

r w :

Radius of wafer

l :

Distance between particles

X :

Total slurry volume

ρ s :

Density of the slurry

ρ a :

Density of slurry particle

C a :

Weight concentration of slurry particle

N p :

Total number of slurry in slurry volume

φ :

Normal distribution function

q :

Area density of particles

n a :

Number of active particles

D i :

Particle diameter

σ D :

Standard deviation of particle size

δ p(D i):

Indentation depth of particle into pad

δ w(D i):

Indentation depth of particle into wafer

H w :

Wafer hardness

E ap :

Composite elastic modulus of particle and pad

V :

Relative velocity between wafer and polishing pad

m 4 :

Spectral moment

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Acknowledgements

This Research was supported by the Tongmyong University Research Grants 2017 (2017A016).

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  1. School of Mechanical Engineering, Tongmyong University, 428 Sinseonno, Nam-gu, Busan, 48520, Korea

    Hyunseop Lee

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Lee, H. Semi-empirical Material Removal Model with Modified Real Contact Area for CMP. Int. J. Precis. Eng. Manuf. 20, 1325–1332 (2019). https://doi.org/10.1007/s12541-019-00161-6

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