N. Schwarzer

Steps towards a mechanical modeling of layered systems

Up to now the search for suitable film substrate combinations with respect to mechanical applications is mainly based on empirical approaches using results of hardness, scratch, wear or other tests. It is desirable to cut down this time consuming process by a higher degree of modeling. Steps towards this aim are presented using a novel methodology for the evaluation of the response of coated substrates to mechanical contact. This approach is based on the combination of a recently developed theoretical method (the method of image loads) and high-accuracy indentation experiments using spherical indenters. For different film substrate combinations it is shown how accurate and reliable values of mechanical film parameters like Youngs modulus and yield strength can be obtained, even for films below 100 nm thickness. Then the theoretical method is used for the calculation of critical loads to failure of film-substrate combinations in dependence on the radius of the counterpart. It is shown how the addition of an intermediate layer can improve the whole compound and which properties it should have. Finally the influence of an additional tangential load due to friction in a sliding motion on the stress fields is investigated. The conventional scratch test is discussed in the light of the latter results.

Mechanical properties of thin films in the ternary triangle B-C-N

Abstract We report on thin films in the ternary system B–C–N deposited by reactive magnetron sputtering of targets with different B/C ratio in an Ar/N 2 gas mixture. First, the proportion of nitrogen in the gas was varied from 0 to 100% with the substrate being at floating potential in order to change the incorporated amount of nitrogen in the films. Secondly, at 50% nitrogen in the gas a negative substrate potential was applied for ion bombardment of the growing film. The film composition was measured by elastic recoil detection analysis. The mechanical properties, Youngs modulus and hardness, were determined from nanoindentation measurements. All films were also investigated by Fourier-transformed infrared spectroscopy (FTIR). The mechanical properties show a great variation range in dependence on the film composition (up to a factor of three) and ion bombardment (up to a factor of two), which can be related to the bonding characteristics derived from the FTIR spectra.

Investigation of the elastic modulus of thin films using simple biaxial bending techniques

Abstract The increasing use of thin films in numerous applications has raised the interest in the mechanical behavior of thin films; particularly the hardness and the elastic modulus of these films. The aim of the present study is to evaluate a simple biaxial bending technique to measure the elastic modulus of films with thicknesses ranging from 0.1 to 2 μm. In this range, it can be difficult to use simple indentation techniques owing to the influence of the substrate, and in order to determine the performance of these systems it is often essential to be able to determine the elastic modulus unambiguously. Tests have been carried out on glass substrates, and magnetron sputtered metal films (copper and aluminium) have been deposited on glass discs to evaluate the film properties. The samples were loaded in biaxial flexure using a point load on the disc supported by three point supports. The bending apparatus uses a commercially available micromechanical probe (UMIS 2000) that enables the measurement of very low loads and small displacements. Comparison is made between the force-displacement response of the disc with and without the sputtered film. Analysis of the bending response gave values of the elastic modulus for the glass discs of E=54.7±0.4 GPa, while E=116±8 GPa for the copper films and E=84±5 GPa for the aluminium films.

Comparison between an elastic-perfectly plastic finite element model and a purely elastic analytical model for a spherical indenter on a layered substrate

Abstract The contact problem of an elastic sphere indenting an elastic-perfectly plastic substrate having an elastic layer is analysed using the finite element method and compared with a purely elastic analytical solution. The case of a layer stiffer and harder than the substrate is investigated and solutions for the contact pressure, subsurface stresses and strains are presented for various indentation depths. The results show good agreement until the threshold of plasticity is reached. Thereafter, as the system is subjected to higher penetrations, the two solutions diverge as plastic deformation initiates in the finite element model. The analysis also demonstrates that the influence of a deformable indenter upon the plastic solutions cannot be neglected.

The analytical solution of the contact problem of spherical indenters on layered materials: application for the investigation of TiN films on silicon

Utilising an analytical solution of the contact problem of spherical indentation into layered materials we investigated TiN layers of various thicknesses on single-crystal silicon. We used Heaviside functions to describe the discontinuity of the mechanical parameters at the interface of the TiN-silicon compound. A spherical 5 μm diamond indenter was used to obtain the penetration depth-force curves. In spite of this small indenter we only obtained good utilizable results for film thicknesses of more than 0.8 μm. For thinner films the influence of failure effects such as roughness of the film, not an exactly known film thickness and substrate parameters, deviation of the shape of the diamond indenter from the ideal spherical one and the failure caused by the indentation apparatus themselves becomes too influential. Thus, here we show an investigation of a 1.4 and an 0.8 μm TiN layer on silicon including calculation of the films Youngs modulus and the stresses, and for an 0.4 and an 0.2 μm TiN layer on silicon a stress calculation only using estimated Youngs moduli from the thicker films. We paid special attention to the investigation of the non-elastic behaviour of the compounds utilising the von-Mises criterion.

Comparison between analytical and FEM calculations for the contact problem of spherical indenters on layered materials

Abstract An analytical solution and a finite element calculation have been utilised to investigate the contact stresses due to elastic spherical indentation into coating/substrate systems. Such calculated stress distributions may be used for the optimal design of layer systems as well as, together with experimental penetration-force curves, to determine quantitative measures for toughness and adhesion of the film. Both approaches were compared using various systems composed of a higher modulus surface coating on a relatively low modulus substrate. It was found that both methods agree very well and yield adequate stress distributions for various film thicknesses. Here we show the radial stress component Yγ = σ r for six different systems.

Determination of mechanical properties of thin films: a theoretical feasibility study

Abstract The aim of this work was to determine the principal mechanical parameters of a thin film on a substrate, i.e. Youngs modulus, Poissons ratio, intrinsic stress, and coefficient of linear thermal expansion. First, standard experiments possibly suitable for this purpose were investigated theoretically. The margin of error of the mechanical parameters determined was estimated as dependent on the geometrical conditions, substrate properties, and error in the respective measurements. In addition, the homogeneity and stability of the parameters were taken into account, for instance inhomogeneity of the film thickness and possible modification of substrate parameters during film growth. To obtain meaningful results, the accuracy of the measurements as well as the homogeneity and stability of several geometrical and physical parameters in general must be extremely high. However, the experimental conditions were found to fulfill these requirements.

Nanomechanical Testing : A usable concept for the indentation of thin porous films

Abstract The paper deals with the application of Pharrs concept of the effectively shaped indenter as well as an extension of that concept – referred to as extrapolation method – on the determination of the yield strength of porous thin films. As an example, a 1066 nm thick porous SiO2 xerogel film having a porosity of about 50% and an average pore size in the range 3 – 4 nm was investigated. Three different spherical indenters with radii of 1.4, 3.11 and 110 µm were used in this investigation. Depending on the indenter radius and the applied load the physical nature of the sample deformation was different eaking the one or the other of the two methods more suitable for analysis. We found that the data received with the large indenter could be well analysed using Pharrs concept, while for the twg smaller indenters the extrapolation method had to be used. The yield strength values obtained with the two methods were in remarkable agreement 109 vs. 99 MPa).

Neue Möglichkeiten zur Charakterisierung dünner Schichten mit Indentermethoden

A novel methodology for the evaluation of the response of coated substrates to mechanical contact is presented which is based on the combination of a new theoretical method and high-accuracy indentation experiments using a spherical diamond indenter, The concept may be extended in many respects and will be illustrated here only with few special examples: Using low loads, i.e. staying completely in the elastic region, the elastic parameters of film and substrate can be measured with high accuracy. When the indentation experiments is extended until failure of the coating substrate compound, the full stress and strain fields in three dimensions in the very moment of failure can be calculated. The knowledge of those fields enables one to draw conclusions on the relevant mechanisms. Once the failure mode has been identified, layer systems with optimum resistance to that failure mechanism can be found by theoretical simulations.