Note: A single specimen channel crack growth technique applied to brittle thin films on polymer substrates Free

Thin films are omnipresent in many technologies such as microelectronics, microelectromechanical systems, flexible electronics, and solar cells. Their mechanical stability is often a key devices.^1,2 Hence the cohesive fracture toughness, K_c, and fracture energy, G_c, of these thin films are the key material parameters to predict cracking. In addition, subcritical crack growth may occur even when the driving force for crack extension is lower than the critical value for instantaneous cracks, for materials that undergo environmentally assisted cracking.^3,4

There are currently two main techniques to measure the cohesive subcritical crack growth properties of thin films: the double cantilever beam (DCB) test⁵ and the channel crack growth technique.^6–8 The DCB specimen is prepared by sandwiching the thin film of interest in between two thick substrates.^1,5 The specimen is then pre-cracked (for example, using a dicing saw and a wedge, or by overloading) and must be done in a manner to have a crack propagating through the thickness of the thin film of interest to obtain a valid test (post-mortem chemical characterization of the two mating fracture surfaces can be done to validate the test). A preliminary DCB test can be done to measure G_c. Once G_c is characterized, a subcritical crack growth DCB test consists of increasing the applied load P up to a value corresponding to G ∼ G_c, at which point the crosshead displacement of the machine is fixed. Load relaxation occurs as a result of subcritical crack growth, and a full v-G curve can be obtained simply by measuring the load evolution over time. In contrast, the channel crack growth technique consists of observing under a microscope the extension of channel cracks that develop in a thin film under residual tensile stress on a substrate. Channel cracks can be introduced using indentation^6,7 or by scribing the sample.^8,9 The driving force G can be calculated knowing the residual stress in the thin film, $σres$⁠, the film thickness, h_f, the thin film plane strain elastic modulus, $Ef*$⁠, and the elastic modulus mismatch between the thin film and substrate, and is given by¹⁰ 

where $εres$ is the residual strain in the film, and Z is the dimensionless energy release rate which depends on the elastic mismatch between the film (⁠$Ef*$⁠) and substrate (⁠$Es*$⁠). A full v-G curve requires many specimens, typically of varying thickness and/or residual stress, each specimen providing one G value. Although sample preparation is much easier compared to the DCB tests, this technique only works provided the applied G can be large enough (at least to exceed the threshold value for environmentally assisted cracking and ideally to approach G_c). This technique may therefore not work for ultrathin films.^8,9,11,12 More importantly, this technique cannot work if the thin film is under residual compressive stresses. Residual stresses are mainly dictated by the thin film deposition conditions and thermal history, which in turn may affect as well the thin film microstructure and therefore the G_c value and the v-G curve. To circumvent these issues, we developed a channel crack growth technique that relies on applying a tensile load onto a specimen that consists of a brittle thin film onto a poly(ethylene terephthalate) (PET) substrate. This technique is especially well suited for testing thin films that may be used in flexible electronics and that may be deposited at low temperatures on such substrates. We recently demonstrated its feasibility, especially highlighting the fact that the substrate-relaxation-induced subcritical crack growth was negligible.¹³ In this technical note, we report further improvements in the technique such as to enable the characterization of a full v-K curve using only one specimen.

Our thin film channel crack growth measurement technique relies on the in situ microscopy tensile testing of a 50-mm-long specimen (consisting of 125 μm thick heat stabilized PET (Dupont Teijin ST-505) substrate with a thin film deposited on top) using a microtensile testing stage (Linkam Scientific Instruments, TST350, with a 0.01 N load resolution and a 10 μm displacement resolution); see Figure 1(c). The stage allows testing under controlled environments by continuously flowing gas inside the chamber, as well as under controlled temperature. The crack growth observations during the tests are performed under an optical microscope for thick enough films (typically >100 nm) for which cracks can easily be detectable, or under a laser scanning confocal microscope (Olympus LEXT, OLS4100) for films as thin as 15 nm. A test consists of loading the specimen up to a strain $ε0$ at which several channel cracks develop and grow in a fast manner (corresponding to G₀ ∼ G_c). This first step allows the nucleation of many channel cracks whose growth will be tracked throughout the rest of the test. The applied strain is then decreased to a slightly lower value $ε1$ = $ε0$ − $Δε$ (the minimum $Δε$ is 0.02%), and the growth of several cracks is tracked for a maximum duration of 30 min (the choice for this value will be explained later) in order to obtain an average crack growth rate for this corresponding G₁ value. The process is then repeated to $ε2$⁠, $ε3$⁠, etc., until $εn$ for which no crack growth is detected within 30 min. Using a resolution of ∼1 $μm$ for crack tip detection with the optical microscope at a 10× magnification, the minimum measurable crack growth rate is 5.5 × 10⁻¹⁰ m/s. For a given applied strain, $εapplied$⁠, the driving force G can be calculated using the following equation:

The technique presented in this note is an improved version of our previously employed technique,¹³ whereby a specimen is directly loaded to a given strain (⁠$ε1$⁠, $ε2$⁠,…, $εn$⁠) and crack growth rates are only measured for that given strain. The former technique therefore required a larger number of specimens to obtain a v-G curve, as only one G value was tested per specimen.

Crack growth tests demonstrating this new technique were performed with 250-nm-thick plasma enhanced chemical vapor deposited (PECVD) SiN_x films deposited at 110 °C (see details in Ref. 13) on the heat stabilized PET substrate (exhibiting excellent dimensional stability up to 150 °C), which we previously demonstrated were susceptible to stress corrosion cracking.¹³ Using ellipsometry, the film thickness was h_f = 254 ± 1 nm. The elastic moduli of the SiN_x film and PET substrate were measured to be E_f = 123 ± 5.8 GPa and E_s = 4.07 ± 0.12 GPa, respectively, corresponding to the plane strain elastic moduli values of $Ef*$ = 131 ± 6.2 GPa and $Es*$ = 4.47 ± 0.25 GPa. The corresponding Z is 11.8 ± 2.2. A compressive residual strain of $εres$ = −0.15% ± 0.02% was measured in the SiN_x film.¹³ Based on a measured applied strain of 0.95% ± 0.02% at which fast channel crack propagation is observed, we calculated G_c = 25 ± 5 J/m² using Eq. (2), accounting for the errors associated with each term of that equation. This G_c value consists of an upper limit based on the measurement technique,¹³ and is in fact slightly larger than the reported G_c values (ranging from 5 to 15 J/m²)^14,15 for other PECVD SiN_x films (deposited under different conditions).

Figure 2 shows the v-G curves obtained with our technique for the 250-nm-thick SiN_x films for two different temperatures (25 and 85 °C) and two different environments (air and dry N₂). The driving force G was calculated using Eq. (2). The empty symbols represent the tests for which the specimens are only tested at a given strain value;¹³ the error bars associated with these tests represent the standard deviation from average rates calculated over typically 20-30 measured growing cracks. These data highlight environmentally assisted cracking in the SiN_x films,^13,16,17 which is a thermally activated phenomenon.^18–20 The solid symbols represent data from our improved technique, whereby one specimen is tested to provide a full v-G curve. Here the data are averaged over 2 or 3 tested specimens. The solid data match very well with the empty data (most of the solid data points are within the error bars of the empty data points), highlighting the fact that our improved technique is a fast and accurate way of obtaining a v-G curve with only one or two specimens. More importantly, the improved technique allows measuring crack growth rates below 10 nm s⁻¹, whereas the previous technique was limited to rates above 100 nm s⁻¹. The reason for this discrepancy is related to the number of growing cracks. By first loading the specimen at large strains at which many channel cracks nucleate, a large number of cracks can continue to grow under lower strains corresponding to lower G values. Hence, the improved technique provides an entire v-G curve, including importantly the threshold regime.

Compared to the DCB test, the sample preparation is much simpler and only requires depositing the thin film of interest onto the PET substrate. One challenge associated with the DCB test is to pre-crack the specimen such that the crack tip lies within the thickness of the thin film of interest. This may be especially challenging for ultrathin films (such as thickness below 50-100 nm) for which the interfaces (with the substrates and/or glue required for the “sandwich” preparation) would be in close proximity to the crack tip; if the crack tip deviates onto one of these interfaces, the cohesive fracture energy of the thin film cannot be measured. This requirement can only be checked with post-mortem chemical characterization of the fracture surfaces for each test. In addition, the DCB test does not provide direct visualization of the crack front. Instead, the crack size (and therefore crack growth rate) is approximated through an analytical model of the specimen’s compliance which relies on a uniform crack front.^1,5 In contrast, the channel crack growth technique relies on simple specimen preparation and direct observations of the cracks to measure the growth rates. By applying an external load to drive crack propagation, a residual tensile stress in the thin film of interest to provide a large enough driving force is not required. Our technique therefore increases significantly the range of thin films for which the crack growth rates can be characterized, including ultrathin films and films with compressive residual stresses. We also demonstrated that a full v-G curve can be obtained by varying the applied strain during a single test, similar to what is done with the DCB test and unlike the residual-stress-driven channel crack growth technique which requires as many specimens as data points of the v-G curve.

The main particularity of the external-load-assisted channel crack growth technique is that it requires a polymer substrate to allow loading to large strains (up to 1% for the present tests) without substrate fracture. In comparison, the residual stress driven channel crack growth technique typically uses stiff substrates such as silicon,^6,7,9 and the DCB specimens are typically made of a stiff substrate (such as glass).^5,21 Hence there are several restrictions associated with our technique (in addition to the ones already existing for the channel crack growth technique¹²) that relate to the plastic and/or viscoplastic deformation of the substrate. First, the driving force for channel crack growth must be properly evaluated, for example, using finite element models, as Eq. (2) may be inaccurate in the case of local yielding in the substrate. Our finite element model of the SiN_x/PET system revealed that Eq. (2) is reasonably accurate (within 3.6%) for an applied strain of 1%,¹³ whereas the shear lag model of Hu and Evans²² significantly overestimated the effect of local yielding on G. Second, the viscoplastic behavior of the polymer substrate must be such that it does not induce significant time-dependent crack growth. Indeed, Suo and co-workers demonstrated that time-dependent cracking of an elastic film made of a material that does not undergo any subcritical cracking can still occur if a viscous underlayer or substrate is present.^23–25 Finite element models can also be used to quantify the amount of increase in G as a result of stress relaxation in the polymer substrate. Our model showed that for an applied strain of 0.95%, the increase in G due to substrate relaxation over a period of 30 min is only 0.8% (from 25.2 at t = 0 to 25.4 J/m² at t = 30 min),¹³ and therefore plays a negligible role in the fast crack growth behavior observed in Figure 2. Our results therefore demonstrate the feasibility of the technique on PET for applied strains up to 1%. If larger strains are required (for example, for thinner films (per Eq. (2)) or if a different polymer substrate/testing temperature is used, finite element models should be performed as well to address this issue and further validate the technique. Last but not least, the driving force calculation (Eq. (2)) is only accurate for a channel crack lying at the thin film/substrate interface.¹⁰ It is often the case for a thin film on a stiffer substrate, as the driving force G decreases as a crack reaches the interface.²⁶ However, for a stiff thin film on a compliant substrate, the driving force increases as a crack reaches the interface,²⁶ which may lead to some amount of substrate cracking depending on the fracture energy or time dependent fracture properties of the substrate. For example, in our case, we observed some cracking of the PET (several micrometers deep) for a specimen held at 0.7% for 5 days.¹³ However, no cracking of the PET was observed when held for 30 min, which is the reason why the specimens were only held for a maximum duration of 30 min at a given strain to measure the crack growth rates. It is therefore important to perform post-mortem examination (in our case, cross section SEM imaging) to ensure the proper cracking configuration.