3.1 Nano-scratch behavior of the CeO2 tip on copper film
The residue depth as a function relation of the force with different radius of CeO2 tips scratching on copper film with constant mode is shown in Fig. 3(a). We can see that the residue depth increased with the increase of the normal force for all cases in this work. The curves rise slowly when the normal force below 20 µN (within in the elastic stage) and then linear increase when the normal force after that. This variation trend of the residue depth comfortably with our early work [32] and the residue depth is near zero in the elastic regime and near linearly increase of residue depth during the changing elastic-plastic regime and steady elastic-plastic regime. Furthermore, there is an obvious size effect of the residue depth curve after the normal force of 20 µN. And then this size effect becomes more and more obvious with the increasing of the normal force. The residue depth decreased with the increase of the tip radius under the same normal force. That is the smaller particle size of the CeO2 abrasive resulted in a greater scratch depth in the copper film under the same normal load. From the previous work [32], we know that the microscopic deformation of the copper surface transformed from the pure elastic, the variable elastic-plastic stages and pure plastic deformation as increasing the normal force during the nanoscratch process. Therefore, in the same situation, after the scratch test, the smaller the particle size, the greater the residual depth, which leads to the more serious plastic deformation of the copper surface. This can be attributed to the fact that smaller particles will cause higher compressive stress in the substrate under the same normal force. As we know, the removal rate of the chemical mechanical polishing almost in proportion to the normal force as reported by Cook in 1990 [34]. The experimental results demonstrate that in the micro-nano-scale wear process, under the same normal force, smaller abrasive particles can achieve higher removal rates.
At the same time, the variation of COF calculated with different tip radii on the normal force of copper film under the constant mode is shown in Fig. 3(b). It can be clearly seen that COF has a functional relationship with the change of normal force, and it can be divided into three stages, which are the adhesion, the ploughing, and the cutting regime as we reported previously [32]. Obviously, in the first regime, the three COF curves almost overlap each other. However, we should note that the first critical point of the COF curve doesn’t across at one normal force. The black, red, and blue solid points indicate the first critical point of the COF curves of the tip radius of 120 nm, 180 nm, and 270 nm as marked in Fig. 3(b), respectively. And we found that this trend also appeared at the second critical point of the COF curves, which is marked by the black, red, and blue hollow circles. And as shown in the hatched section in Fig. 3(b), we can see that the transformation of the critical point from the adhesion to the ploughing friction and from the ploughing to the cutting friction regime shift to the higher normal force with the increase of the tip radius. That is the size effect appears at the end of the adhesion regime and gets more significant after the adhesion regime and stable in the cutting regime in the COF plot. The COF has the potential to down with increasing of the tip radius.
In the previous study [32], two formulas in terms of the COF obtained via theory calculation and confirmed by our experimental data well. In the adhesion and ploughing regimes, the COF can be expressed by Eqs. (1) and (2), respectively.
(1)
(2)
where τa, τp and σp are the shear stress of in the adhesion regime, the shear stress and the yield stress of the ploughing regime, r and h are the tip radius and the scratch depth, the N is the normal force and the K is a constant that depends on Poisson's ratio and Young's model of the object material.
As we can see from Eq. (1), the COF goes to infinity by making the normal force (N) in the infinitely small. In the adhesion regime, the normal force slowly increases from zero and has a great impact on the COF, i.e. the particle size (r) seems to have no effect on the COF in this regime. That is the reason why there is no significant size effect in the first regime, which is consistent with the experimental results as shown in the overlap of the COF curve in Fig. 3(b). And the relationship between the COF and particle size (r) can be expressed by Eq. (2) when the nanoscratch moving into the second regime (the ploughing regime). From the experimental results, the COF strongly depends on the particle radius (r) during the ploughing regime in the nanoscrath. And we can see that the COF decreases with increasing the particle size when the scratch depth (h) less than the particle radius (r) and increases with increasing the particle size when the scratch depth (h) greater than the particle radius (r) by theoretical analysis of the Eq. (2). The scratch depth less than the tip radius used in this work, therefore the experimental results show that the COF decreases with the increase of the particle size in the ploughing regime as expected, i.e. the Eq. (2) obtained from theoretical simulation is only suitable for the case of the scratch depth less than the particle radius and no longer adaptable when the scratch depth increase further. When the nanoscratch goes into the last regime (the cutting regime), the COF is also influenced by the particle radius, but not by the normal force. And the COF in the cutting regime also shows the character of size effect and decreases with the increase of the particle radius.
3.2 Scratches on the TEOS film with CeO2 tips
In order to confirm that the observed size effect of the COF is a general phenomenon rather than an accidental phenomenon, we conducted the nanoscratch experiment with a homemade CeO2 tip on the TEOS film. We know the hardness of the CeO2 tip and TEOS film are 7.35 GPa and 6.0 GPa as measured by TI 950. However, because the hardness of the tip is similar to that of the SiO2 film, the CeO2 tip is no longer suitable for use as a rigid particle in this system, i.e. the CeO2 tip will inevitably be worn when scratched on the TEOS film. That is the size of the CeO2 tip radius will become lager and lager with the progress of the nanoscratch procedure. However, that is good news for us, since the size of the tip radius can be regarded as increasing continuously in the nanoscratch test. As shown in Fig. 4, COF is a function of the normal force with CeO2 tip scratches the silicon dioxide film under the ramp mode. The CeO2 tip was worn after the nanoscratch test, and the morphology before and after the wear is shown in Fig. 4. It is considered that there are four different sizes of tips (160 nm, x nm, y nm, and 1000 nm, 160 nm < x < y < 1000 nm) scratched the TEOS film in turns under the ramp mode, respectively. As shown in Fig. 4, the three friction regimes between the four curves of TEOS film and the COF curve on copper film are in good agreement. We can see that as the tip radius increases, the critical point between the three regimes, especially the critical point between the ploughing and cutting regime, shifts to a higher normal force. An obvious size effect of the COF appears at the beginning of the ploughing regime. At the same time, the ploughing regime (between the first and second critical points) expanded with increasing the tip radius. As shown in Fig. 4, for the tip radius of 160 nm, the second critical point is 350 µN, and for the 1000 nm, the second critical point is2 500 µN. And when the tip radius increases from 160 to 1000 nm, the range of the ploughing regime expands from 250 to 2250 µN.
From our previous work [32], we pointed out that the ploughing regime is a key stage to CMP due to the tunable material removal rate and the gentle scratching. From this work, we can conclude that by increasing the size of abrasive particles within the restricted range, the range in which the normal force affects the material removal efficiency can be expanded. In the past few decades, many scholars have studied the response of COF to the material removal rate by the in-situ CMP process monitor [35, 36], and there is a good correlation between COF and material removal rate. It can be concluded that the removal rate of CMP could be controlled by adjusting the COF between the abrasive and wafer. And we can adjust the COF by adjusting the size of the abrasive particles and the normal force of the nano-scratch experiment.
3.3 Mechanical properties of CeO2 abrasives
We believe that the size effect of abrasive mechanical properties could be related to the results of nanoscratch experiments. Therefore, the mechanical performance of abrasives were tested using the displacement control method of the PI85 test system, i.e. the displacement of the indenter during the in-situ compression experiment was set to half of the particle’s equivalent diameter, and then the abrasive was loaded and unloaded to obtain the corresponding loading and unloading curves. Figure 5 shows the positive force-compression displacement curves of CeO2 particles with particle sizes of 80.8 nm, 90.0 nm, and 94.6 nm during the nanoindentation process. When the compression depth is about 10 nm, these three curves basically coincide. At this time, the particle size has no effect on the mechanical curve. And when the indentation depth further increases, the curve begins to diverge, showing a certain size effect, and this tendency becomes more and more obvious as the compression progresses. Finally, after unloading, all three particles have some degree of plastic deformation. The slope of the force-displacement curve shows a downward trend as the particle size increases, meaning that as the abrasive size decreases, the force required during compression also increases. By calculating the slope of the unloading section of the effective stress-strain curve, we can obtain the effective modulus of the particles. Figure 6 shows the effective stress-strain curve for particles with an equivalent diameter of 80.8 nm. The black line segment in the figure is obtained by fitting the unloading section of the curve, and the slope of the black line segment is the effective modulus of the particle. For the particle sizes of 80.0 nm, 90.0 nm, and 94.6 nm, the effective modulus of particles are 68.71 GPa, 56.11 GPa, and 54.67 GPa, respectively. The mechanical properties of nanoparticles exhibit a certain size effect and follow the "The smaller the stronger" principle [36].
The experimental results show that the size effect does exist and affects the mechanical properties of the abrasive, which will guide the improvement of the material removal rate.