Effect of Potassium Persulfate as an Additive On Chemical Mechanical Polishing Performance on C-, A- and R-Plane Sapphire

Under the same conditions, the lattice structure is the decisive factor for achieving different MRR of different planes sapphire wafers. The lattice of sapphire (α-Al₂O₃) is composed of Al³⁺ and O²⁻. There is mainly ionic bonding for the bond in α-Al₂O₃, so it is the forces of electrostatic interactions that have the greatest effect on the bond energy. In the lattice of α-Al₂O₃ crystal, the electrostatic energy q between per pairs of ions can be defined as follows²⁴:

$$\begin{eqnarray}&&q=\displaystyle \frac{A{z}_{1}{z}_{2}{e}^{2}}{r}\end{eqnarray} \tag{ 2 }$$

where A, a numerical quantity, is termed as the Madelung constant, ${z}_{1}e$ and ${z}_{2}e$ are considered as point charges, representing a pair of ions and r is the distance of per pairs of ions. Obviously, the greater the distance r, the smaller the electrostatic energy.

Consequently, it can be deduced that the lattice bond energy of adjacent atomic layers that belong to different crystal orientations is inversely proportional to the interplanar spacing d of different crystal planes. The distance between adjacent atomic layers of C-, A- and R-plane sapphire substrates can be obtained from the interplanar spacing d for planes (006), (220), and (036) respectively, as shown in Fig. 3.²⁴ For the hexagonal crystal system, the interplanar spacing d for the plane (hkl) is given as follows:

$$\begin{eqnarray}&&{d}_{hkl}=\displaystyle \frac{1}{\sqrt{\displaystyle \frac{4\left({h}^{2}+{k}^{2}+hk\right)}{3{a}^{2}}+\displaystyle \frac{{l}^{2}}{{c}^{2}}}}\end{eqnarray} \tag{ 3 }$$

where the lattice constants of sapphire are a = 4.758 Å and c = 12.992 Å at 300 K. The calculated d values of C-, A- and R-plane sapphire plates are 2.177 Å, 1.190 Å, 1.160 Å, respectively.²⁵ The interplanar spacing d of different crystal planes is in the order of C-plane > A- plane > R-plane. As mentioned above, the lattice bond energy of adjacent atomic layers is inversely proportional to the interplanar spacing. Therefore, the bonding energy for different crystal planes of sapphire is in the order of C-plane < A- plane < R-plane. The smaller the bonding energy is, the more easily the material to remove, thus, the material removal rate of sapphire with different planes is in the order of C-plane > A- plane > R-plane.

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The thermodynamic reaction energy of sapphire and K₂S₂O₈ in the slurry during the polishing processes was investigated, which can judge whether the chemical reactions can occur spontaneously or not. It was gradually discovered that the changes of entropy(S) and enthalpy(H) were not sufficient to determine whether a reaction could occur spontaneously. Afterwards, Gibbs function, G was defined as follows:

$$\begin{eqnarray}&&G=H-TS\end{eqnarray} \tag{ 4 }$$

According to the principle of minimum free energy, the reaction always moves in the direction that the Gibbs free energy decreases, and the change of Gibbs free energy (∆G) becomes the criterion for determining whether the reaction can occur autonomously.²⁶

Based on chemical thermodynamics, HSC chemistry software was used to calculate the ${\rm{\Delta }}G$ as a function of temperature (T) for each reaction. The standard molar Gibbs free energy change of reaction was calculated as follows:

$$\begin{eqnarray}&&{\rm{\Delta }}{G}_{T}^{\theta }={\displaystyle \sum \left({n}_{i}{\rm{\Delta }}{G}_{f}^{\theta }\right)}_{resultant}-{\displaystyle \sum \left({m}_{i}{\rm{\Delta }}{G}_{f}^{\theta }\right)}_{reactant}\end{eqnarray} \tag{ 5 }$$

At constant temperature and pressure, chemical reaction isotherm which shows the relationship between the change of Gibbs free energy in any state and the standard molar Gibbs free energy change is as follows²⁷:

$$\begin{eqnarray}&&{\rm{\Delta }}{G}_{T}={\rm{\Delta }}{G}_{T}^{\theta }+RT\,\mathrm{ln}\,Q\,\end{eqnarray} \tag{ 6 }$$

where R is a constant, Q is termed as Reaction Quotient. If the value of ${\rm{\Delta }}G$ was less than zero, the chemical reactions can occur spontaneously. The possible chemical reactions are expressed in the following equations:

$$\begin{eqnarray}&&A{l}_{2}{O}_{3}+3{H}_{2}O=2Al{\left(OH\right)}_{3}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&A{l}_{2}{O}_{3}+{H}_{2}O=2AlO\left(OH\right)\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&A{l}_{2}{O}_{3}+2Si{O}_{2}+2{H}_{2}O=A{l}_{2}S{i}_{2}{O}_{7}\cdot 2{H}_{2}O\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&\begin{array}{l}6{K}_{2}{S}_{2}{O}_{8}+4Al{\left(OH\right)}_{3}=6{K}_{2}S{O}_{4}+2A{l}_{2}{\left(S{O}_{4}\right)}_{3}+3{O}_{2}\uparrow \\ \,+\,6{H}_{2}O\end{array}\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&6{K}_{2}{S}_{2}{O}_{8}+2A{l}_{2}{O}_{3}=6{K}_{2}S{O}_{4}+2A{l}_{2}{\left(S{O}_{4}\right)}_{3}+3{O}_{2}\uparrow \end{eqnarray} \tag{ 11 }$$

During the polishing process, these reaction products were calculated based on the Gibbs free energy, as shown in Fig. 4.

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These findings show that the polishing temperature of the thermodynamic calculation is between 0 °C and 60 °C. Figure 4 indicates the value of ${\rm{\Delta }}G$ is less than zero, all these chemical reactions can occur spontaneously.

In order to improve the MRR and surface quality of different plane sapphire substrates, K₂S₂O₈ was used as an additive in the sapphire slurry. The ratio of deionized water to nano-SiO₂ sol was 1:1. The nonionic surfactant isobutanol polyoxyethylene ether (JFCE) was used, whose volume fraction was 0.2 vol%. K₂S₂O₈ with different concentrations of 0.0 wt%–0.5 wt% was added to the slurry. Finally, the slurry pH value was adjusted to 10.5 with KOH.

It can be seen from Fig. 5, which the MRRs of C-, A- and R-plane sapphire increase significantly with the enhancing of K₂S₂O₈ concentration. Otherwise, the MRR of sapphire with different planes is in the order of C-plane > A-plane > R-plane, which identifies the previous theoretical foundation for different planes of sapphire. As the K₂S₂O₈ concentration increases from 0 to 0.2 wt%, the MRRs of C-, A- and R-plane increase sharply to 6.722μm h⁻¹, 3.051μm h⁻¹, and 2.927μm h⁻¹, respectively. However, with the K₂S₂O₈ concentration continues to increase, the MRRs begin to show a downward trend. Moreover, it can be speculated that when the concentration of K₂S₂O₈ is 0.2 wt%, the mechanical action and chemical action reach the dynamic equilibrium, optimum removal occurs. When the concentration is greater than 0.2 wt%, the chemical action is greater than the mechanical action, insufficient removal will occur, and lower removal rate and lower removal rate and surface quality will be obtained. Therefore, the optimal K₂S₂O₈ concentration was selected at the inflection point 0.2 wt% to obtain higher MRRs.

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Moreover, the changes of zeta potential and pH value with the standing time of the slurry containing 0.2 wt% K₂S₂O₈ were measured, as shown in Fig. 6. Within seven days, the zeta potential and pH value slightly changed. It is generally considered that the colloid is stable when the absolute value of the zeta potential is greater than 30 mV, and the larger the absolute value, the more stable the colloid is. When the absolute value of the zeta potential is less than 30 mV, the repulsion between particles is weakened, which will cause collisions between particles to increase particle size and reduce CMP slurry stability.²⁸ As shown in Fig. 7, the measured results show that slurry performances have fluctuated slightly. It also indicates that the slurry can be stable at least seven days, which meets the conditions for industrial production.

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Meanwhile, good surface morphology was achieved after polishing with 0.2 wt% K₂S₂O₈ slurry, as shown in Fig. 8. When 0.2 wt% K₂S₂O₈ was added into the slurry, MRR and Sq of sapphire substrate with different planes are shown in Table II.

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From Table II, it can be seen when adding K₂S₂O₈ in the slurry, the removal rates of different planes all increase, which should be the enhancement of mechanical or chemical action. Firstly, the effect of K₂S₂O₈ on abrasive was verified. The variation of mean particle size was measured under the condition of different K₂S₂O₈ concentrations, as shown in Fig. 9. From Fig. 9, it can be found that the K₂S₂O₈ concentration has almost no effect on the mean particle size in the slurry, which indicates there is nearly no change in mechanical action. Accordingly, it can be inferred that the addition of K₂S₂O₈ enhanced the chemical action.

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In order to further reveal the existing chemical form of the removed Al and the forming reaction products after polishing, the sapphire wafers soaked in K₂S₂O₈ sol were analyzed by XPS. All XPS data in the experiment were carbon calibrated.

XPS spectrums of element Al 2p, O 1s, and S 2p of the sapphire surface are presented in Fig. 10. The binding energy of the different substances is shown in Tables III–V. The black line shows the real total intensity measured by XPS and the olive line shows the total intensity after curve fitting using the Casa XPS software. The closer between the real result (black line) and the fitting result (olive line) means more accurate measurement results.

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It can be observed from the fitting drawings of Fig. 10a, that there are three peaks of Al(2p) and binding energies of different peaks are 73.01 eV, 74.89 eV and 73.60 eV corresponding to Al(2p) in Al₂O₃/Al²⁹ state, Al₂(SO₄)₃³⁰ state and Al(OH)₃³¹ state respectively. Seeing from fitting drawings of Fig. 10b, the binding energy at 530.06 eV and 531.82 eV in the XPS spectra of O(1s) is consistent with Al₂O₃³² state and Al(OH)₃³¹ state. From Fig. 10c, the peaks at the binding energy of 169.60 eV consisted with S 2p in Al₂(SO₄)₃³⁰ and the peak at the binding energy of 167.93 eV corresponds to S 2p in K₂SO₄.³³

Therefore, the chemical reactions did occur between sapphire and K₂S₂O₈ sol, and the equations are deduced as follows:

$$\begin{eqnarray}&&A{l}_{2}{O}_{3}+3{H}_{2}O\rightleftharpoons 2Al{\left(OH\right)}_{3}\end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&\begin{array}{l}6{K}_{2}{S}_{2}{O}_{8}+4Al{\left(OH\right)}_{3}=6{K}_{2}S{O}_{4}+2A{l}_{2}{\left(S{O}_{4}\right)}_{3}+3{O}_{2}\uparrow \\ \,+\,6{H}_{2}O\end{array}\end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray}&&6{K}_{2}{S}_{2}{O}_{8}+2A{l}_{2}{O}_{3}=6{K}_{2}S{O}_{4}+2A{l}_{2}{\left(S{O}_{4}\right)}_{3}+3{O}_{2}\uparrow \end{eqnarray} \tag{ 14 }$$

At the same time, the Gibbs free energy (${\rm{\Delta }}G$) of the reaction 13 and 14 are −95.814 kcal and −92.062 kcal at 20 °C in the previous part, so that the reaction 13 occurs easier than 14 when the reactants are enough, that is to say, K₂S₂O₈ will react with Al(OH)₃ at first precedence when Al(OH)₃ and Al₂O₃ exist simultaneously. However, Al(OH)₃ was an absence in the beginning, hence the reactions may occur in the following sequence. Firstly, reaction 14 occurred. At the same time, Al(OH)₃ was generated in reaction 12. Afterward, K₂S₂O₈ reacted with Al(OH)₃, which caused the reaction 12 to go forward to the direction of positive reaction.

From reaction 13 and 14, it can be well perceived the transformation from S₂O₈²⁻ to SO₄²⁻ occurred. It can be observed from Fig. 11a that the valence of S and O can be inferred, which contributes to speculate the mechanism of the reactions. One O–O bond, four S=O bonds, four S–O bonds exist in the structural formula of S₂O₈²⁻. O shows −1 valence in the O–O bond, and in the S=O and S–O bonds, O shows −2 valence, hence S shows +6 valence. Thus, during the process of the transformation from S₂O₈²⁻ to SO₄²⁻, there was no change in the valence of S element, instead of the O element in the O–O bond changed to 0 and −2 valence and according to this, O₂ and SO₄²⁻ are produced. What is more, it can be seen from Fig. 12, the O–O bond in S₂O₈²⁻ is broken to generate SO₄²⁻, which further indicates the accuracy of the analysis above.

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Based on these results, it can be deduced that the improvement of MRR in sapphire substrate is attributed to the concurrently chemical reactions between sapphire surface and slurry during polishing, and the products are Al₂(SO₄)₃ and K₂SO₄. Meanwhile, the reaction products Al₂(SO₄)₃ and K₂SO₄ are soluble and easy to be removed. Otherwise, Fig. 13 shows the schematic illustration of the chemical reaction model in the CMP process. The reaction between K₂S₂O₈ and Al(OH)₃ increases the consumption of OH⁻, which causes the reaction 11 to go in the direction of positive reaction, ensuring the continuous production of Al₂(SO₄)₃ and K₂SO₄.

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