# Numerical Study on the Dependency of Microstructure Morphologies of Pulsed Laser Deposited TiN Thin Films and the Strain Heterogeneities during Mechanical Testing

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Modelling of the PLD Process

#### Formulation of the kMC PLD Deposition Model

- (1)
- Creation of a list of all possible events in the system and calculation of a likelihood of their occurrence ${r}_{i}$.
- (2)
- Calculation of the sum of probabilities of all events $R={\displaystyle \sum}_{j=0}^{i}{r}_{j}$.
- (3)
- Random selection of a number in a range 〈$0,R$).
- (4)
- Each event is placed on a stack. Graphically (Figure 3), the height of a particular event represents its probability of occurrence. An overall height stack is thus equal to a cumulated probability of all considered events—$R$. A randomly chosen number $u$ unambiguously indicates the event, which will be applied to the system. Selection of the event is shown in Figure 3.
- (5)
- Transposition of the system to a new state by applying the selected event.
- (6)
- Updating the time counter by $\Delta t=1/R$.

- Adding events, which become possible;
- Removing obsolete events;
- Updating probabilities of all events, which could be affected by a previous change in the system.

## 3. Kinetic Monte Carlo Simulations of the PLD Process

## 4. Experimental Investigation

^{−2}, a pulse width of 20 ns, and a repetition rate of 10 Hz. The target was a disc with 2.54 cm in the diameter and 0.5 cm in the thickness. The initial pressure in the chamber was set to 5 × 10

^{−7}Torr. The silicon substrate was subjected to an ultrasonic cleaning procedure for 10 min in acetone and 10 min in methanol and finally, etched for 5 min in 10% HF. The substrate was placed parallel to the target material surface at a distance of 5 cm. The deposition temperature and nitrogen partial pressure were 200 °C and 1 × 10

^{−5}Torr, respectively [9,29]. Process settings closely replicated the conditions selected during numerical modelling presented earlier.

## 5. Numerical Nanoindentation Test Based on the Explicit Representation of Thin Films Morphologies

## 6. Discussion

## 7. Conclusions

- The kinetic Monte Carlo method is an adequate and feasible technique for numerical simulation of the PLD process and provides a reliable digital representation of microstructure morphology;
- The presented kMC PLD model can be adjusted to design the deposition processes of different nanolayered structures;
- The digital material representation model of the deposited thin films allows predicting of inhomogeneities in stress/strain fields under deformation conditions;
- Predicted local heterogeneities, especially in the interface area and along columns boundaries, can be further used to study fracture initiation and propagation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Procedure of choosing particles, and which interrelated events probabilities could be affected (marked as green) after applying a surface diffusion to the system (marked as yellow).

**Figure 6.**(

**a**) position of the cross-section in the final DMR sample, (

**b**) illustration of columns at particular cross-sections, and (

**c**) diagram representing areas of subsequent columns at particular cross-sections.

**Figure 10.**Distribution of (

**a**) equivalent stress (MPa) in the model from the side view and, (

**b**) equivalent stress (MPa), (

**c**) displacement (mm) from the top view.

**Figure 12.**Equivalent stress distribution within the DMR (Digital Material Representation) model after nanoindentation test.

**Figure 14.**SEM images (Quanta 3D 200i, FEI, Hillsboro, OR, USA) revealing fractures in the (

**a**) Si substrate and (

**b**) TiN thin film after nanoindentation test with force–displacement curves received during test.

Parameter | Value |
---|---|

Domain edge length | 90 nm |

Elementary cell size | 1 nm |

Substrate melting temperature | 1414 °C |

Substrate temperature | 200 °C |

Binding energy | 0.8 eV |

Deposition rate | 0.05 nm/s |

Vibration frequency | 1 × 10^{13} Hz |

Dimension Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Size (nm) | 15.1 | 25.9 | 89.1 | 24.8 | 33.1 | 94.4 | 23.6 | 30.5 | 87.6 | 30.8 | 53 | 93.6 |

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**MDPI and ACS Style**

Perzynski, K.; Cios, G.; Szwachta, G.; Bała, P.; Madej, L.
Numerical Study on the Dependency of Microstructure Morphologies of Pulsed Laser Deposited TiN Thin Films and the Strain Heterogeneities during Mechanical Testing. *Materials* **2021**, *14*, 1705.
https://doi.org/10.3390/ma14071705

**AMA Style**

Perzynski K, Cios G, Szwachta G, Bała P, Madej L.
Numerical Study on the Dependency of Microstructure Morphologies of Pulsed Laser Deposited TiN Thin Films and the Strain Heterogeneities during Mechanical Testing. *Materials*. 2021; 14(7):1705.
https://doi.org/10.3390/ma14071705

**Chicago/Turabian Style**

Perzynski, Konrad, Grzegorz Cios, Grzegorz Szwachta, Piotr Bała, and Lukasz Madej.
2021. "Numerical Study on the Dependency of Microstructure Morphologies of Pulsed Laser Deposited TiN Thin Films and the Strain Heterogeneities during Mechanical Testing" *Materials* 14, no. 7: 1705.
https://doi.org/10.3390/ma14071705