## 3 Results and Discussions
### Analysis of The Adhesive Contact Characteristics at The HDI  
To illustrate the adhesive contact characteristics of the HDI, Figure 6 shows a schematic of the adhesion force \(F_{\text{a}}\), contact force \(F_{\text{c}}\), net force \(F\) and flying height \(FH\) as a function of the nominal flying height \(z_{\text{r}}\). In regard to the results of this figure, five sub-regions, I-V, can be divided. In region I, the slider flies sufficiently away from the disk, and the net force depends entirely on the adhesion force as no contact occurs. In this region, the magnitude of the net force (\(|F|\)) increases and the \(FH\) decreases with the nominal flying height. When the nominal flying height decreases to the value at point A in region II, the attractive interaction increases abruptly and the TP jumps into contact with the lubricant, as evidenced by the sudden decrease in \(FH\) to the equilibrium distance \(z_{01}\). If the nominal flying height is now increased, the net force follows the A'B branch as far as point B but then jumps to point B', implying that the TP jumps out of contact with the lubricant. In region III, the slider is at the TP-lube contact state, and the net force is still determined totally by the adhesion force. As the nominal flying height decreases, it causes the magnitude of the net force to increase accompanied by a decrease in the \(FH\). In region IV, the TP jumps from point C to point C', at which it comes into contact with the DLC layer and the \(FH\) decreases to \(z_{02}\)-\(l_{\text{lub}}\), and jumps out of contact from point D to point D'. \(z_{02}\) stands for the equilibrium distance between two parallel surfaces having properties of the slider and the disk across the lubricant. In region V, the slider is at the TP-DLC contact state. During this full contact regime, both the adhesion force and the contact force increase with the decreasing nominal flying height, while the \(FH\) is almost unchangeable. Due to the combined effect of the adhesion force and the contact force, the magnitude of the net force increases firstly until reaching a maximum value and then decreases. Three important results can be extracted from the above contact characteristics of the HDI. First, the operation status of the slider can be approximately determined in light of the \(FH\). The slider is  
Figure 6: Variations of force and flying height with the nominal flying height under \(l_{\text{c}}\) = 10 nm, \(t_{\text{lab}}\) = \(t_{\text{DLC-disk}}\) = \(t_{\text{DLC-slider}}\) = 2 nm: (**a**) Adhesion force \(F_{\text{a}}\), Contact force \(F_{\text{c}}\), Net force \(F\) and (**b**) Flying height \(FH\). at the flying state when \(FH>z_{01}\), at the TP-lube contact state when \(z_{02}\)-\(t_{\text{hub}}<FH\leq z_{01}\), and at the TP-DLC contact state when \(FH\leq z_{02}\)-\(t_{\text{hub}}\). Second, jump-in and jump-out phenomena occur in regions II and IV, which can influence the stability of the slider and should be avoided during the operation of the HDD. Third, at the TP-DLC contact state, the adhesive interaction is remarkable compared with that at the flying or TP-lube contact states. The \(FH\) is difficult to be reduced further due to the strong repulsive interaction of the HDI at the small distance. The distribution of interaction pressure \(P\) for three nominal flying heights \(z_{\text{r}}\) = 11 nm, 9 nm and 8 nm corresponding to the flying state, the TP-lube contact state and the TP-DLC contact state is shown in Figure 7 in conjunction with the distance \(h\) in the section of \(y=0\). It can be seen that the pressure is almost zero and the surface is basically undeformed at the flying state (for example \(z_{\text{r}}\) = 11 nm). When the TP is in contact with the lubricant (for example \(z_{\text{r}}\) = 9 nm), the adhesive interaction near the contact edge between the TP and the lubricant becomes remarkable. At the TP-DLC contact state (for example \(z_{\text{r}}\) = 8 nm), the local pressure is positive at the contact center, together with the obvious surface deformation.