1 Introduction

Copper and its oxides, cuprous oxide (Cu2O) and cupric oxide (CuO), are important materials used in many industrial applications. Due to high electrical and thermal conductivity and high corrosion resistance of copper (Ref 1) this metal is widely used in machines, electronic devices, e.g., integrated circuits and printed circuit boards, telecommunications equipment, heat exchangers, electrodes, high conductivity wires fabrication and other important industry. Cu foil has been reported as a potential substrate material in silicon-free solar cell units (Ref 2, 3). Moreover, antimicrobial applications of copper are well recognized (Ref 4, 5). Recently, nanostructured copper is also considered as one of the most effective catalysts in an electrochemical reduction in carbon dioxide into hydrocarbons and alcohols (Ref 6,7,8). The activity of single metallic Cu-based catalysts can be improved for bimetallic systems (Ref 9, 10). Copper oxides, especially as a thin films, have wide range of applications in energy harvesting and storage (Ref 11,12,13,14,15). Both Cu oxides are also widely used in various gas sensors (Ref 16, 17). The Cu2O is known as an attractive material in catalysis, sensors fabrication and as chemical templates. Its suitability in photodegradation reactions, e.g., water splitting, photo-reduction of carbon dioxide and organic synthesis have been reviewed by Sun et al. (Ref 18). Additionally, Cu2O can be used as a low-cost hole-transport material for stable perovskite solar cells (Ref 19, 20). Similarly, CuO has been considered as a p-type absorber material for inexpensive photovoltaic devices (Ref 21, 22). Furthermore, due to the lower band gap energy compared to Cu2O, cupric oxide can be used as an infrared photodetector (Ref 23). Hence, the structure composed of copper and its oxides, e.g., Cu/Cu2O and Cu/CuO, seems to be interesting in photovoltaic applications, especially when flexibility of thin copper foil and semiconducting properties of Cu oxides are considered.

Mechanical and thermodynamic properties of copper and its oxides have been intensively studied by experimental methods (Ref 24,25,26,27,28,29) and computation modeling (Ref 30,31,32,33,34,35,36,37,38). Among various parameters determined by both methods high attention has been given to investigation of yield stresses. In some cases an excellent agreement between calculated and experimental data has been achieved, confirming suitability of theoretical model (Ref 32).

Simulations of oxide structures by FEM are difficult due to the heterogeneous connection susceptibility to cracking. Additionally, getting reliable data requires application of suitable intermediate model, which is usually created based on available experimental data. Moreover, each simulation has some limitations since the model assumptions are usually limited to a few variables and do not include defects, which are common due to thermal stresses in the interface area. Assuming a hybrid approach, in which complex spatial experimental results are analyzed along with FEM, reduction in time-consuming calculations but with more qualitative approach to data analysis can be achieved.

The presence of abovementioned heterogeneous connections, e.g., metal/oxide, may lead to stress corrosion cracking of thin oxide layer. Stress corrosion cracking of coatings tightly covering the supporting material is of great importance due to uncontrolled crack propagation in industrial applications. The stress may result from differences in physicochemical and mechanical properties of materials, their resistance to environmental conditions and their stability. Thermal expansion mismatch between metallic substrate and covering layer, e.g., oxide films generates a temperature-induced strain at the interface. Similarly, improperly selected elasticity of both materials may cause the stress induced by deflection. Hence, consideration and evaluation of possible failures at the early stage of designing the particulate components applied for larger systems constructions is the challenge of modern industry. This issue is frequently address in various aspects of materials engineering, and widely discussed based on both, experimental and theoretical investigations.

Adhesion–delamination phenomena at the surfaces and interfaces have been extensively discussed in the literature (Ref 39,40,41,42). It was shown that thickness of coating layers, surface roughness and thermal treatment affected the resistance to delamination failure (Ref 40). Moreover, it is well known that residual stresses caused by thermal expansion mismatch between metal substrate and oxide coating can play an important role in degrading the adherence of oxide layer, e.g., the protective alumina scales (Ref 43, 44). Delamination failure leads to the damage of thin oxide layers, and thus, to destruction of metal–oxide structure. Srikanth et al. (Ref 45) examined adhesion of epoxy-based molding compound (EMC) and the copper leadframe, showing that copper oxide layers formation improved the surface roughness and enhanced the shear stresses in-plane direction. FEM studies of a traditional small outline IC package showed high shear stresses at the interfaces of EMC–leadframe with a stress of ~ 20.56 MPa for the chosen EMC type (Ref 45). Esa et al. (Ref 46) assigned delamination of copper oxides formed on copper alloy leadframe material to formation of micro-voids along the interface of copper to copper oxide, which at higher temperatures might cause complete separation of copper oxides. Yuan et al. (Ref 47) reported that increasing the surface roughness of the Cu substrate can effectively improve the oxide/substrate interfacial adhesion, resulting in better self-protection of the oxide film. The improved oxide/Cu interfacial adhesion was assigned to the concave shape of craters generated by Cu sandblasting, which produced a net downward force from the compressive stresses in the oxide film to force the film to adhere to the substrate (Ref 47).

Adhesion strength testing is usually performed by scratch test and nanoindentation technique (Ref 48, 49). Both methods are fast and simple, and they do not require sophisticated equipment. Indentation or nanoindentation tests measure the resistance to permanent deformation of a material when subjected to a particular combination of triaxial compressive stress and steep stress gradient, which provide a convenient and non-destructive means of estimating the strength properties of metals (Ref 50, 51). In the case of thin films and coatings, the nanoindentation test requires probing of a sample in such a way that properties of the substrate are excluded and the influence of the substrate is separated from the measurement data. Moreover, the surface quality (roughness) is extremely critical for determination of credible data (Ref 50, 51).

In this paper we analyzed some practical aspects of using microperforated copper sheets which would have use from the metal-oxide interface. The conducted analysis took into consideration the contact between copper and its oxide and impact of the microperforated holes which could enhance the range of applications and performance. As a base example in this work we analyzed the use of microperforated copper sheets with an oxide layer for the use in the photovoltaics. The simulations were performed for thin copper plates with equally distributed holes of 0.3 mm diameter, aiming to determine the upper limit of oxide cohesion. We used the stiffness matrix for individual materials and FEM analysis to obtain a viable decohesion criterium and macro stress analysis of the whole plate. The results were verified by a profilometer surface scan and a TEM/FIB imaging. The critical areas of maximum stresses are discussed in terms of simplifications introduced in applied model. Moreover, the influence of oxide layer thickness (Cu2O and CuO) on durability and delamination failure of examined structures is reported, as well. Thermal expansion and critical temperature leading to oxide layers damage are evaluated by simplified model using FEM.

The primary goal of conducted research aimed to find a solution of an engineering issue in which both the contact surface and the continuity of the oxide layer must be preserved in order to achieve maximum efficiency. Additionally, our aim was to evaluate the suitability of applied mathematical models (FEM) and compare the results obtained by both simulations and experimental method. There is no clear analysis in the available literature for the microperforated plates with thermal oxide layers. Despite larger specific surface there are issues concerning thermal gradients and expansion which enhance cracking.

2 Methodology

2.1 Oxide Analysis

The Pilling-Bedworth ratio can be calculated based on the formula:

$$R_{{{\text{PB}}}} = \frac{{M_{{{\text{oxide}}}} \times \rho_{{{\text{metal}}}} }}{{n \times M_{{{\text{metal}}}} \times \rho_{{{\text{oxide}}}} }}$$

where

M-atomic or molecular mass.ρ-densityn-number of atoms of metal per molecule of the oxide

Based on the atomic mass of copper (MCu = 63.546 u) and molecular masses of oxides (MCu2O = 143.09 u; MCuO = 79.545 u), the number of Cu atoms per oxide molecule (n = 2 for Cu2O, n = 1 for CuO), and density of each material (ρCu = 8920 kg/m3; ρCu2O = 6000 kg/m3; (ρCuO = 6315 kg/m3), the Pilling-Bedworth ratio for Cu-Cu2O and Cu-CuO systems is equal to:

$$R_{{{\text{PB}}}} \left( {{\text{Cu}} - {\text{Cu}}_{{2}} {\text{O}}} \right) = {1}.{67}$$
$$R_{{{\text{PB}}}} \left( {{\text{Cu}} - {\text{CuO}}} \right) = {1}.{77}$$

In both cases, the calculated PB ratio is higher than 1 and below 2 (1 < RPB < 2) which means that the oxide coating provides a protective effect against further surface oxidation. However, the calculated values are only theoretical ones and cannot be treated literally, especially when top Cu2O layer is covered with CuO layer, as in the case of Cu/Cu2O/CuO systems which may be present in our studies.

In case of applied FEM analysis both oxides, Cu2O and CuO, were evaluated separately, and hence, the determined critical temperatures of decohesion listed in Table 2 were computed for individual Cu-Cu2O and Cu-CuO systems. In real conditions most probably more complex situation occurs, and both oxides are likely present forming the structure of Cu-Cu2O-CuO. The presence of Cu4O3 was neglected. Detail analysis of crystallographic phases corresponding to cuprite, tenorite, paramelconite or others by XRD technique could be informative but it was excluded from our research.

2.2 Nanoindentation Tests

The main difficulty in nanoindentation of thin film and coating that needs to be taken into consideration is to avoid probing the substrate properties and to separate the influence of the substrate from the measurement data. Thus, the maximum penetration depth during the test should be restricted to no more than 10% of the film thickness (Ref 50). However, such restriction leads to great errors in the test data due to application of very small load. In our case, the copper oxide layers were thick enough to achieve the reliable data. The image of the Cu heat-treated sample after nanoindentation test performed by Berkovich pyramid-shaped tip indenter is shown in Fig. 1. Based on the image and the conducted nanoindentation tests a computer model was developed. It is worth noting that the footprint geometry and forces are reassembled in the computer model.

Fig. 1
figure 1

Image of nanoindentation test by Berkovich pyramid-shaped tip indenter

Full size image

The plot showing relationship between applied force (F) and indenture depth (r) (Fig. 2) for all measuring points exhibits recurrent character. Curves show a clear difference in the course of loading and unloading the indenter. In the final loading area (applied force of 10 mN), a small range of displacements (c.a. 330-350 nm) is visible suggesting plasticization or local damage. The forces determined by using indenter in scratch and nanoindentation tests are comparable, reaching 10 mN. Moreover, the presence of hysteresis on nanoindentation plot enables calculation of strain energy. The latter is equal to the work (W) of the indenter performed during its penetration (r), and hence, can be determined by integrating the area under the force (F) plot according to Eq 1:

$$W = Fr = \mathop \smallint \limits_{0}^{{r_{\max } }} F{\text{d}}r - \mathop \smallint \limits_{{r_{\max } }}^{0} F{\text{d}}r$$
(1)
Fig. 2
figure 2

Nanoindentation plot: applied force vs. penetration depth. Red arrow points out the area of irreversible local displacements

Full size image

Different curves for loading and unloading suggest that the material was subjected to permanent deformation/damage in the entire volume. The measure of this deformation is a strain energy, based on which the global criteria of material damage can be estimated by Eq 2.

$$W = \int {\int_{0\,0}^{\varepsilon \,V} {\sigma d\varepsilon {\text{d}}V = \sigma \varepsilon V,\,\sigma = \frac{W}{\varepsilon V},\,\varepsilon = \frac{r}{h},\,V = Ah} }$$
(2)

where: σ, ε, r, h, V, and A denotes critical stress leading to deformation in MPa, strain (deformation), indentation depth, sample thickness, the volume of material under indenter, and head area of indenter, respectively. The model was verified according to the CAD model with the results shown in Fig. 3. The red shape represents the intender and the blue is the material oxide surface. The residual stress is generated at the junction as a result of stiff intender displacement (Fig. 2).

Fig. 3
figure 3

Displacement of indenter [nm]–verification of damage criteria

Full size image

In the experiment, 75 indentation tests were done in a straight line with a 10 μm intervals. The results shown in Fig. 4 revealed some scattering of individual sampling points varying from 189 to 226 MPa with an average value of 205 ± 5 MPa. This may indicate local differences in oxide layer structure, e.g., thickness and/or density, or most probably is related to experimental error of applied technique.

Fig. 4
figure 4

Maximum stress measurement by Berkovich indenter at a given point

Full size image

Simulations of thermal resistivity of oxide layers covering perforated plates provide an important information in terms of metal–oxide structures applications in photovoltaics.

2.3 Computing Models

The Finite Element Method (FEM) simulations were performed using ANSYS 11 software, based on plates and shells theory (Ref 52,53,54,55). According to the latter, thin plate assumption was applied since the ratio of thickness (0.1 mm and 0.3 mm) to the edge (156 mm) is lower than 0.1. The proposed model used in modeling of mechanical properties of copper plates is based on fixed geometry of square shaped samples of dimensions of 156 mm × 156 mm. The total sample area is equal to 243.36 cm2 corresponding to the standard area of a solar cell unit. Moreover, each plate has a series of holes of a diameter of 0.3 mm equally distributed on the entire surface. The holes are spaced from the outer plate edges and from each other by the distance of 1 mm as shown in Fig. 5(b) Since the initial square plate has two symmetry axes equally dividing the opposite sides, the model can be simplified to a quarter of the former, and thus, the smaller section represents the entire surface, which may be further enlarged. The thickness of metal plates varies from 0.1 mm to 0.3 mm. Additionally, top surface of each plate is covered by a thin Cu2O or CuO film (thickness of 1-3 μm) corresponding to 1-3% of total thickness. Both oxides are considered as a promising p-type materials in solar cells applications (Ref 12). Further replacement of silicon by metal substrate enables fabrication of silicon-free solar cells. Moreover, application of perforated plates may enhance the efficiency of the latter. The impact of the film presence on mechanical properties is not considered; however, it will be encountered in thermal expansion analysis. Due to the in-plane stresses in thin layer oxide structures, the stresses on metal/oxide interfaces, which affect adhesion of thin oxide layers, can be ignored in performed simulations.

Fig. 5
figure 5

Geometry used in simplified model (a) the main dimensions (b)

Full size image

Two types of boundary conditions were taken into consideration. First, it was assumed that the support point is limited to the outer edges only (out of plane distortions, Ux, Uy, Uz = 0). In the second case, the freedom of movement on the plate surface is restricted (out-of-plane distortions and rotations, Ux, Uy, Uz = 0; Rotx, Roty, Rotz = 0). Because of the small distance of the holes from the outer edges (1 mm), proposed span of the support surface is equal to 0.5 mm from the edges. Furthermore, it was assumed that the loading is due to plates weight only (q(x,y) = 9.81 [m·s−2] × m). Mechanical properties of copper used in simulations are presented in Table 1.

Table 1 Mechanical properties of copper used in simulations
Full size table

In the simplified model three rows of holes closest to the outer edges in the vicinity of each symmetry axis were attained as shown in Fig. 5(a). Computing grid was also simplified (Fig. 5b) leaving the same number of elements close to the holes as in extended model. Thus, simplified model uses 11,500 elements compared to 255,000 applied in starting simulations. Other parameters has not been changed.

Simplified model has been used for modeling the thermal properties of metal–oxide structures composed of Cu plates covered on top by Cu2O or CuO thin films. Thermal expansion and critical temperature causing oxide layers delamination failure derived from simulations are discussed in terms of mechanical properties of component materials. In simplified model 2 oxide layers thicknesses, namely 1 μm and 3 μm, have been considered. Due to less rigid structure of thinner plates (thickness of 0.1 mm) leading to higher stresses experienced by metal samples, all modeling configurations are limited to this plate thickness. Besides of plate weight, an additional loading is introduced by temperature, which evenly increases from reference value of 293 K to critical one, corresponding to oxide layers damage. Additionally, in simplified model freedom of outer edges movement is frozen. In simulations, temperature dependence of density [ρ(T)], Young’s modulus [E(T)], tensile test curves and thermal expansion coefficient [α(T)] of copper plates in the temperature range of 273-573 Kwas taken into consideration (Ref 56). Thermal expansion of copper shows some deviation from linearity resulting in rather narrow variability of this parameter. It varies between c.a. 1.65 × 10−5 K−1 at 273 K and c.a. 1.90 × 10−5 K−1 at 573 K In case of support layers bi-linear model with isotropic holder enabling plastic distortions and support accommodation are assumed. The limit of plasticity is temperature dependent.

Because of porous structure, oxides exhibit lower density, however, computing simulations were performed for strictly adopted copper density. Thermal expansion coefficients (α) temperature dependence of Cu2O and CuO in the range of 273-573 K are derived from literature data reported by Liu et al. (Ref 30). Their studies by first-principles calculations employing pseudo-potential plane-waves (PP-PW) approach based on density functional theory (DFT) with the generalized gradient approximation (GGA) showed that calculated thermal expansion coefficients of Cu and Cu2O, 17.7 × 10−6 K−1 and 2.7 × 10−6 K−1, correlated with experimental data determined at 298 K, 17 × 10−6 K−1 and 1.9 × 10−6 K−1 (Ref 30), respectively. Moreover, the calculated α of Cu were larger than that of Cu2O and CuO. In case of copper(II) oxide thermal expansion coefficient increased with temperature in the range of 273-573 K from 1.21 × 10−5 K−1 to c.a. 1.36 × 10−5 K−1. Under the same conditions, Cu2O exhibited smaller α in the range of 2.4 × 10−6-2.6 × 10−6 K−1 (Ref 30). Moreover, it has been reported (Ref 30) that oxides exhibit orthotropic mechanical properties. Hence, the elastic stiffness coefficients which are the proportionality coefficients linking applied strain to the computed stress can be defined as σi = Cij × εij. The elastic behavior of a crystal is completely described by elastic constants Cij in the stiffness matrix (Ref 33).

To define properly material properties it is necessary to address none constants denoted in the stiffness matrix. However, due to rhombic symmetry of CuO crystal, complete description of oxide matrix requires determination of 6 different coefficients. Hence, theoretical model of CuO is based on a stiffness matrix given below obtained from the following article (Ref 57). The given Eq values were used in the computer model. For CuO Eq 3 and for the Cu2O Eq 4 were applied. The thermal expansions and the data for technical copper was obtained from Ansys built in data base.

$$C = \left[ {\begin{array}{*{20}c} {196.41} & {122.63} & {114.64} & 0 & { - 26.99} & 0 \\ {122.63} & {125.01} & {96.89} & 0 & { - 27.85} & 0 \\ {114.64} & {96.89} & {293.70} & 0 & { - 48.95} & 0 \\ 0 & 0 & 0 & {20.28} & 0 & { - 1.15} \\ { - 26.99} & { - 27.85} & { - 48.95} & 0 & {30.07} & 0 \\ 0 & 0 & 0 & { - 1.15} & 0 & {56.44} \\ \end{array} } \right]10^{3} {\text{MPa}}$$
(3)
$$C = \left[ {\begin{array}{*{20}c} {127.46} & {107.07} & {107.07} & 0 & 0 & 0 \\ {107.07} & {127.46} & {107.07} & 0 & 0 & 0 \\ {107.07} & {107.07} & {127.46} & 0 & 0 & 0 \\ 0 & 0 & 0 & {9.21} & 0 & 0 \\ 0 & 0 & 0 & 0 & {9.21} & 0 \\ 0 & 0 & 0 & 0 & 0 & {9.21} \\ \end{array} } \right]10^{3} {\text{MPa}}$$
(4)

2.4 Experimental Methodology

The microperforated sheets were obtained from 0.2 ETP Cu sheet using photochemical machining method which enables an accuracy of up to ± 5 μm without any influence on the material structure with a very fine mirror-like roughness. The method is used in precise engineering for the mass production of integrated circuits (Ref 58).

Two Cu ETP 0.2 mm sheets without and with perforation were annealed in an Ohm’s furnace in the temperature of 523 K for 4 h with consecutive furnace cooling. The applied conditions enabled formation of 3 μm thick oxide film on the copper surface. Furthermore, extreme conditions (temperature of 573 K) were chosen to monitor any potential defects.

The surface of the sheets were tested using a 3d Veeco profilometer in the VSI mode. The array size was 640 × 480 with varying magnifications.

3 Results and Discussion

3.1 Modeling of Thermal Expansion and Critical Temperatures for Metal–Oxide Structures

Preliminary studies were done to analyze the stiffness of the metal sheet. Wang et al. (Ref 59) reported numerical model of cracks propagation in thin copper oxide layers. To determine the influence of oxide film thickness and the type of copper oxide on their resistance to delamination failure, 6 configurations were applied. Simulations have been carried out for copper sheets with Cu2O or CuO layers of thicknesses of 1 μm or 3 μm, respectively, with and without perforations. The results were obtained as a stress maps along the plate thickness.

Figure 6 shows the stress distribution in the copper sheet with an oxide layer on top. In analyzed cases the stress was concentrated in a very thin region of metal-oxide contact. By changing the temperature and comparing the values with the decohesion criterion we obtained the stability ranges of oxides (Table 2). Based on simulation results it seems that the more oxide-rich phase of CuO was more susceptible to cracking. Furthermore, the thicker the layer the more susceptible to thermal cracking, most probably due to the limited ability to accommodate stress in the oxide region. It is worth noting that the changes in the critical temperature are a result of differences in thermal expansion and slightly different stiffnesses according to matrixes given in Eq 3 and 4. Additionally, the CuO has a more anisotropic structure which is also visible in additional non-zero values in Eq 3. This acumulates with layer thickness which results in lower thermo-mechanical resistance shown in Table 2.

Fig. 6
figure 6

Stress concentration in the interlayer of the copper plate covered with Cu2O

Full size image
Table 2 Critical temperatures of decohesion of examined Cu–oxide structure configurations
Full size table

For thicker oxide layer an increase in maximum stress is observed. However, this increase is of minor importance, more likely resulting from numerical method error of 1%. It is reasonable due to slight difference in oxide layers thickness. Similar effect has been observed for Cu–copper oxides films formed on copper surfaces as a corrosion products in ammoniacal solution (Ref 59). This observation indicated that a thicker and softer corrosion product films (CPF) (corresponding to a smaller CPF Young’s modulus) resulted in higher stress in the copper substrate, and hence, the CPF-induced stress was superimposed on the applied stress to enhance the emission and motion of dislocations, and then, the initiation and propagation of stress corrosion cracking(Ref 59). For the Cu-Cu2O structure the critical temperature remains constant independently of Cu2O film thickness (Table 2). It shows better thermal stability and durability of Cu-Cu2O system as a consequence of the difference in thermal expansion coefficients of copper (αCu ≈ 1.88 × 10−5 K−1) and cuprous oxide (αCu2O = 2.6 × 10−6 K−1).

The influence of oxide layer properties on stress distribution is unequivocal. The oxide layer thickness does not play a significant role in stress distribution on the plate surface. Similarly, change of Cu2O on CuO in Cu-oxide structure caused decrease in critical temperature. Simultaneously, the influence of CuO film thickness is more pronounced, since for thinner film critical temperature decreased to 468 K while for 3 μm CuO layer delamination temperature of 483 K was computed. Increase in film thickness for Cu-CuO structure resulted in consecutive increase in stresses in outer parts of the plate and revealed the presence of local maxima. Due to the lower differences of thermal expansion of metal support and oxide layers, maximum temperature and thermal stresses increased.

4 Experimental Verification

To verify the results of computation model an experimental investigation was conducted in order to achieve some qualitative insights and quantitative practical implications. First, the mismatch of material properties resulted from differences in the thermal expansion was manifested in the form of torn out oxides flakes and an increase in surface roughness. The thermal stresses were present mostly at the interface leading to the delamination of oxide layers, as shown in Fig. 7. In the case of micro-perforated samples this effect was also visible but in a lesser degree. Individual flakes can be seen, although, there was no separation from the metal surface and the contact between individual layers was preserved (Fig. 7b). Considering practical applications this is a crucial findings in terms of electrical conductivity and Ohmic contact (Ref 60, 61). Furthermore, the microperforated structure may have a practical use due to the increase in the working area, decreased weight, and reduced copper consumption (which can be reused from the photochemical manufacturing process). The results obtained for individual sheets are presented in Table 3. The spread of roughness were similar in both cases which suggests that the degradation mechanism is the same, however, slightly lower values for microperforated samples may be a result of thermal stress sinkholes. On the opposite, additional cracks are seen in inner surface which deteriorates the properties of the microperforated sheet.

Fig. 7
figure 7

Perforated (a, b) and non-perforated (c, d) Cu sheets surface analysis by profilometer

Full size image
Table 3 Roughness of the Cu-ETP sheets used in the experiment
Full size table

It is worth to note that both test plates were subjected to the same initial processes and were heated in the same conditions. Despite the fact that these are not purely quantitative studies in assessing the defect concentration they show relatively large qualitative differences which confirmed the purposefulness of the perforation of the sheets.

The complementary analysis of the decohesion of copper oxides was done using FIB TEM, as shown in Fig. 10. According to Jiang et al. (Ref 62) holes may increase the peeling effect between the oxide layer and the metal surface. However, it is worth noting that with higher radius the effect is more profound and it may cause an initial crack that could grow and reach a critical value. When thermal loadings continue, the edge cracks may coalesce with the interface creating an uncontrolled propagation of the crack. This is further increased with the Kirkendale effect in which the diffusion of oxygen along the grain boundaries creating paths of intergranular cracking (Ref 63). Moreover, according to the literature data (Ref 64) thermal fatigue in the interface region after several cycles causes fatigue cracking.

Analyzing the individual sheets it seems that cracks occur inside the holes (Fig. 8). On the opposite, the region in the upper sheet seems to be crack free which suggests that any microcracks and peeling are preferential inside the hole rather than at the outside.

Fig. 8
figure 8

SEM micrograph of holes after heat treatment

Full size image

The results from Fig. 8 were additionally compared to a computer model for a small area near the inner of the hole (Fig. 9). It seems that there is a large deformation build up in the inner of the hole. The deformation capacity of the oxides are very small which contracts the base metal material this results in cracks which are shown in Fig. 8 with red arrows.

Fig. 9
figure 9

Simulation for the inner of the hole region the analyzed region (a) and deformation maps (b)

Full size image

By analyzing individual micrographs, it seems that the cracks occur at the grain boundaries which further evolves into significant voids (Fig. 10a, b, c, and d). Furthermore, it seems that a build-up of wavy pattern appears leading to consecutive periodical cracking. The last stage is seen at 573 K (Fig. 10e). At this temperature a clear crack growth along the whole cross section is observed. Overall, both the perforated and non-perforated specimens are almost indistinguishable, although, it seems that the impact of the hole presence is limited to a relatively small volume which was not researched in detail. Various microcracks are visible in Fig. 10(f) mainly at the phase boundaries of oxides and metal. First of all, a near wavy pattern, which stacks up is observed. There are distinguishable areas where local loss of coherence between the layer and the metal causes cracks.

Fig. 10
figure 10

FIB TEM analysis of the metal-oxides interface at temperature of 473 K (a) and (b), 523 K (c) and (d), and 573 K (e) and (f), respectively, for the perforated and non-perforated sheet

Full size image

5 Conclusions

The model used for simulations of thermal analysis of metal–oxide structures, Cu-Cu2O and Cu-CuO, showed that the thickness of oxide layer had only minor influence on simulated stress distribution while delamination failure of Cu2O or CuO films was assigned to differences in thermal expansion coefficients of corresponding oxide and metal substrate. Higher disproportion of the latter led to decreasing of critical temperature. The highest critical temperatures of 513 K were achieved for Cu2O oxide structures due to comparable thermal expansion properties.

The microperforated Cu sheet showed lower surface roughness although the peeling effect was observed inside the holes. In the case of the non-perforated samples a more significant effect of decohesion was observed since the oxide layer delaminated easily from the metal support. In terms of practical applications, the microperforated sheets allowed to reduce some of the macroscopic thermal stresses improving the overall quality of the metal–oxide structure essential in repeatability of the Ohmic contact. Moreover, an increase in working surface area due to micro-perforations and the simultaneous decrease in material consumption obtained by the recuperation of the applied solution in the photomechanical machining seems to be a promising strategy of rational management of materials.