# In-Situ Nanoindentation Surface Topography of Lead-Free Piezoelectric Thin Films
## 1 Introduction  
The selection of manufacturing parameters and processes has a direct impact on the surface morphologies and microstructures of materials, resulting in the generation of highly specific properties and functionalities [1, 2, 3, 4]. In the work of [PERSON] et al. [4], a correlation is demonstrated between larger grain structures and enhanced thermoelectric properties. Furthermore, it has been demonstrated that precise regulation of manufacturing process parameters facilitates recrystallization and size control of sub-nano regions, ultimately yielding materials with enhanced thermal conductivity and optimized performance [3]. More specifically, surface roughness is a critical characteristic that influences the response of many components in service. In the case of microelectromechanical systems (MEMS), their dynamic and electrostatic characteristics and their structural integrity partially depend on the surface roughness [5]. Surface roughness with positive skewness and sharp asperities (high kurtosis) is desirable to reduce adhesion. However, increasing surface roughness can cause contact loading to dominate adhesion forces, reducing the risk of permanent adhesion. It is important to find a compromise between reducing adhesion through sharp asperities and the structural reliability of the device. Numerous studies have focused on the influence of roughness on mechanical performance [6, 7, 8]. It is widely documented that an increase in roughness results in a significant discrepancy in the estimated values of hardness andYoung's modulus. This is due to the uncertainty inherent in the estimation of the contact area, which is more pronounced at shallow depth. Consequently, it is recommended to indent at a depth larger than the roughness, typically twenty times greater than the Ra parameter (ISO 14577-1 [9]). Alternatively, roughness can be reduced through polishing, although this may result in alterations to the mechanical properties [4]. For piezoelectric films, surface roughness plays an important role in the electromechanical behavior [10], e.g., the piezoelectric coefficient increases for lower roughness and more uniform surfaces [11]. When studying the mechanical properties of thin films, one of the main techniques used is nanoindentation, since it allows testing very small volumes of the material in an almost nondestructive way, providing the local intrinsic mechanical properties of the thin films [12]. Classically, atomic force microscopy (AFM) is used to measure the topography of surfaces after nanoindentation [13]. Some nanoindenters, notably Hysitron (Bruker, Billerica, MA, USA), include an in situ scanning probe microscope (SPM) to directly measure and study the indents [14]. In our work, the nanoindenter is directly used to measure the surface roughness of thin piezoelectric films. The study of surface roughness always represents a complex subject because roughness parameters depend on their evaluation methods, therefore on the scale of measurement [15]. We have previously studied and proposed different methodologies to determine the most relevant roughness parameters that characterize the surface morphology regarding a particular function, property, or application [16; 17]. This work firstly describes a methodology based on discriminant analysis to determine the most relevant roughness parameter. Then, we study which parameters provide a closer relationship with the mechanical properties by nanoindentation. Measuring the surface roughness in situ before and after nanoindentation tests with the nanoindentation probe offers the great advantage of obtaining topographic information of the sample at the same location of nanoindentation tests with a good precision. The interest of this work is to obtain direct information of the sample topography with the Berkovich indenter to distinguish between surfaces (thin lead-free piezoelectric films) and the combination with the mechanical properties.