## 4 Conclusions  
A numerical adhesive contact model for the TFC slider-disk interface based on the Lifshitz theory, capable of handling various recording status including the flying state, lubricant contact state and solid contact state, is established in this paper. The adhesive contact characteristics of the HDI in the presence of thin lubricant and DLC layers are examined, and effects of the TP height, lubricant thickness and DLC thickness on the interaction force and _FH_ (or _HMS_) are investigated. The main conclusions are as follows.  
Figure 12: DLC thickness versus adhesion force and _HMS_ for **(a)** flying height of 11 nm; **(b)** flying height of 10 nm; (c) flying height of 7 nm; **(d)** DLC thickness versus contact force for flying height of 7 nm, under \(l_{\rm c}=10\) nm, \(t_{\rm hub}=2\) nm.  
(1) Unstable regions exist when the status of the slider transits from the flying state to the TP-lube contact state and from the TP-lube contact state to the TP-DLC contact state, which should be avoided in the operation of the HDD.  
(2) At the TP-DLC contact state, adhesive interactions occur near the TP-DLC contact edge and near the periphery of the TP-lube contact zone, which are more remarkable than those at the flying state or the TP-lube contact state. At the TP-DLC contact center, strong repulsive interactions exhibit when the TP comes into proximity with the disk and the \(F\!H\) is difficult to be further reduced.  
(3) The adhesion force of the HDI using the TFC technology is smaller than that without applying the TFC technology under the same \(F\!H\) at the flying state.  
(4) Under the fixed nominal flying height, the \(F\!H\) can be reduced through suitably increasing the TP height at the flying state or the TP-lube contact state with only a slight increase in the adhesion force. However, at the TP-DLC contact state, increasing the TP height can not only render the \(F\!H\) almost unchangeable, but also increase the contact force and contact zone which influence the friction and wear properties of the HDI.  
(5) The \(H\!MS\) can be reduced by decreasing the lubricant thickness when the slider operates under the flying state or the TP-lube contact state, while, at the TP-DLC contact state, the \(H\!MS\) cannot be further reduced through decreasing the lubricant thickness.  
(6) The decrease in the DLC thickness on the disk is beneficial in reducing the \(H\!MS\), but can increase the adhesive interaction of the HDI. The thickness of the DLC layer on the slider has negligible effects on the \(H\!MS\), thus a relatively thick layer is more beneficial since it reduces the adhesion at the HDI.  
Conceptualization, Y.Z. and W.Y.; Methodology, Y.Z.; Software, L.J.; Validation, W.Y.; Formal Analysis, Q.Y.; Investigation, Y.Z.; Resources, W.Y.; Data Curation, C.M.; Writing--Original Draft Preparation, Y.Z.; Writing--Review and Editing, C.M.; Visualization, L.J.; Supervision, Q.Y.; Project Administration, C.M.; Funding Acquisition, Y.Z. and W.Y. All authors have read and agreed to the published version of the manuscript.  
The authors would like to express their gratitude to the financial support from the National Natural Science Foundation of China (No. 51805269), the Youth Science and Technology Innovation Foundation of Nanjing Forestry University (No. CX2017007), and the Postdoctoral Foundation of China (No. 2019M660449).  
The authors declare no conflict of interest.