Chapter 3
Stress Evolution during 3D IC Stacking using Open TSVs

In open TSVs the presence of high levels of mechanical stress is critical to the mechanical stability of the structure. During 3D IC stacking external mechanical stress acting on the TSV can be generated leading to accelerated circuit failure.

In this work an external force applied on an open TSV was reproduced using a model, which was implemented using FEM. The implemented model was calibrated using experimental data from an industrial partner. Subsequently the areas in the structure, in which a mechanical failure due to an external force is most likely, were localized. In these critical areas the probability of cracking or delamination is highest.

In the first part of this chapter a brief description of the approach used to reproduce an external force acting in open TSVs is provided. In the second part the results obtained from the FEM simulations are discussed.

3.1 Stress Generation during 3D IC Stacking

During the 3D IC stacking, dies and wafers are bonded to each other, either as die-to-die, die-to-wafer, or wafer-to-wafer [14]. Different sources of mechanical stress can be identified during stacking:

In this work, these stresses are considered as an external load acting on an open TSV. During the stacking process mechanical stress evolves in the TSV structure, generating mechanical instability.

3.2 Nanoindentation

The approach used in order to treat the potential presence of unintentional indenters during bonding with open TSVs was the nanoindentation. Usually, nanoindentation is employed to evaluate the elastic modulus, the strain-hardening exponent, the fracture toughness, and the viscoelastic properties [3855]. However, in this study, nanoindentation was differently used. It was employed to reproduce an external load acting in an open TSV. This external load can result in additional mechanical stress during the 3D IC stacking. Nanoindentation is a simple method which consists of contacting the material of interest (open TSV) with another material (indenter). In one of these two materials, the mechanical properties, such as elastic modulus and hardness, are unknown. In the other, the material properties are known.

The main goal of this work was to estimate the areas in which mechanical failure due to an external load can be expected. From the results, a better understanding of how to increase the mechanical stability of the system can be obtained.

During nanoindentation, an indenter is placed in contact with the surface of a sample in which a steadily increasing load is applied. This causes the indenter to penetrate into the sample. Indenters can be adapted to suit the parameters under investigation and can therefore have different shapes and can be composed of different materials. Indenters are identified as spherical, conical, Vickers, or Berkovich [3856]. The applied force at the indenter is usually in the millinewton range, and the depth of penetration is on the order of micrometers.

During nanoindentation experiments, both load and depth of penetration are recorded at each load increment, resulting in load-displacement curves. Following the measurement of the maximum load, the indenter is steadily removed and the penetration depth is recorded again. If a residual impression is left on the surface of the specimen, a plastic deformation in the material has occurred. In contrast, if the removal of the indenter does not leave an impression, the material has behaved elastically.

Figure 3.1 (a) depicts an example of a load-displacement curve. The top line represents the loading while the indenter is penetrating the sample. The bottom line, on the other hand, depicts the unloading during which the indenter is extracted from the sample. Since the unloading curve does not follow the loading curve the sample deforms plastically. The plastic response is detectable because the unloading curve does not return to its initial displacement value. Therefore, a residual impression due to plastic deformation of the material remains. Usually, the loading portion of the indentation cycle consists of an elastic response of the material at lower loads followed by plastic flow, or yield, within the sample at higher loads [38].

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Figure 3.1: (a) A sample of load displacement curve. (b) An indenter penetrating in to a sample.

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Figure 3.2: Examples of load-displacement (P-d) curves for different material responses and properties. The pop-in event in (e) indicates cracking or delamination.

Generally speaking the indentation stress-strain response of an elastic-plastic solid can be divided into three regimes. These regimes are defined by considering the mean contact pressure of the indenter pm, and the uniaxial compressive yield (or flow) stress Y of the sample. The contact pressure of the indenter is defined by

     (    *)
pm =   4E--  a-,
        2π   R

where E* is the reduced modulus that combines the Young’s modulus of the indenter E and that of the specimen E

            2         ′2
-1- = (1--ν--)+ (1---ν-).
E *      E         E ′

If the contacting bodies are two spheres, the indenter radius R is defined by

1    1     1
R-=  R--+ R--,
      1     2

where R

1indicatestheindenterradiusandR_2thesampleradius [57].RandaaredepictedinFigure 3.1(b).

The three regimes during the nanoindentation are defined as [58]:

During these three regimes different physical phenomena may occur in the sample. Non-linear events, such as phase transformation (Figure 3.2 (d)), cracking, and delamination (Figure 3.2 (e)) are identifiable in the load displacement curves. The presence of discontinuities in the load displacement curves suggest the appearance of cracks or delamination (Figure 3.2).

3.3 FEM Approach

The mechanical reliability of TSVs is strongly connected to the material properties and the size of the device. Materials behave differently under mechanical stress, which affects the mechanical stability of the entire system. The bottom portion of an open TSV can be composed of different material layers. During the deposition processes and subsequent fabrication steps (die bonding, etc.), new mechanical stresses can be generated leading to mechanical instability. Mechanical stresses, in turn, determine the formation of new defects or the propagation of existing defects in the structure. Therefore, the material properties and the device geometry must be optimized in order to minimize mechanical stresses and to improve reliability [59].

FEM was used to simulate the application of an external load on an open TSV, as shown in Figure 3.3. From the simulation results, information regarding the development of mechanical stress in the device are obtained. In these simulations the bottom part of the open TSV was mechanically fixed laterally at the Si sidewall. The bottom area was thereby “free” to bend in the y-axis direction (red arrow in Figure 3.3). The figure corresponds to a structure used for optical sensor applications [2960] at the step in the fabrication process prior to die bonding. During the fabrication process, a critical mechanical stress can be generated. High concentrations of mechanical stress can cause failure in the form of cracking and delamination in the layers which make up the bottom of the TSV.

The bottom of the TSV under consideration consists of a multilayer structure which corresponds to the Al based interconnect structure for CMOS technology [29]. These layers are materials with different thicknesses and mechanical properties. In the following, this many-layered structure is diagrammatically depicted as a single layer, denoted as “multilayer” in Figure 3.3 and it corresponds to oxide, nitride, and aluminium layers.

Figure 3.3: Two-dimensional representation of a TSV structure and an indenter. The dashed line indicates the axis of symmetry. Only a quarter of the system is represented. Al is shown in yellow, W in black, SiO2 in orange, and Si in red. The multilayer consists of different materials. The indenter is spatially external to the TSV (the via height and width of the TSV in the figure do not represent the real size, under consideration).

The mechanical and electromechanical properties of the materials play an important role for the reliability of devices. Mechanical properties of thin films should be accurately measured at the length scale of the devices under consideration, since their properties are different from those of bulk materials. These differences can be due to size effects, grain structures, and processing [61]. Unfortunately material properties for thin materials employed in open TSV are not available in literature.

3.3.1 Simulation Setup

In an open TSV, the indenter can be placed at two different locations, either internal or external to the TSV. These two locations will produce a different distribution of mechanical stress inside the TSV. In this work an indenter acting external to an open TSV, as shown in Figure 3.3, was considered. A spherical diamond indenter with a radius of 50 μm, a Young’s modulus of 1100 GPa, and a Poisson’s ratio of 0.07 was used. The TSV aspect ratio is 1:2.5 and the TSV diameter is 100 μ[29]. The layers which line the inside of the TSV have thicknesses of 1 μm for SiO2, 1 μm for the Al layer, and 0.2 μm for W.

The simulations were performed by accounting for each material of the multilayer, rather than considering a single artificial one (Figure 3.3). The materials used in an open TSV have a polycrystalline or amorphous structure. An isotropic behavior can therefore be assumed which leads to a simplification of the simulation, such as allowing to use a two-dimensional axis-symmetric simulation environment. Because of the location of the indenter, the mechanical stress is mainly generated in the multilayer area and not along the Si in the sidewall. Therefore it is assumed that Si is isotropic and that it does not significantly influence the mechanical stability of the multilayer. Only a negligible influence of the anisotropy of the Si on the final results is expected.

FEM simulation requires a contact condition between indenter and sample to recreate the interaction between TSV bottom and indenter during penetration. In the implemented model, this condition was reproduced by employing the contact pressure penalty method [3862].

Accurate results are obtainable by modeling the contact areas of the indenter and the TSV with a very fine mesh. In general, all geometries would benefit from a fine mesh, but this would lead to excessively long simulation times. A mapped mesh with a minimum element size of 0.5 μm was employed for the layer in contact with the indenter. Along the edge of the indenter in contact with the TSV, a maximum element size of 0.06 μm was used.

A stationary parametric sweep study was performed. The movement of the indenter was emulated using the prescribed displacement as variable. This was repeated for increasing displacement, until the maximum measured displacement from the experimental data was reached.

The TSV structure was mechanically fixed at a single point, the top of the TSV sidewall. For the outer-rightmost Si region, a so-called roller constraint was chosen, which allows the material to move tangential to the boundary but not perpendicular to it. On the other edges, the TSV was free to move, allowing for a reproduction of the real conditions of the device.

3.3.2 Plasticity Simulation

In the implemented model, the elastic-plastic behavior of the materials was considered. The elastic behavior was reproduced with Hooke’s law (2.37). The plastic behavior was described by employing an isotropic hardening law [6263].

An elastic-plastic material is usually modeled under the assumption that the strains ε and strain increments dε formed by the elastic and plastic part can simply be added together  (2.36). By coupling the elastic part εe, described by Hooke’s law, and the plastic part εp in (2.36), the stress σ in a material can be described as [363744]

σ  = C : εe = C : (ε - εp),

where C is the elasticity tensor.

When considering an isotropic plastic material, the strain increment is studied by using the plastic potential Qp, which is a function of the three invariants of the Cauchy stress tensor

Qp(σ) = Qp (I1(σ),J2(σ),J3(σ)),

where the three invariants are defined by

I =  σ  + σ   + σ  ,
 1    xx    yy    zz
J2 = 1(σiiσjj - σijσji),and
J3 = σxxσyyσzz + 2σxyσyzσzx - σ2xyσzz - σ2yzσxx - σ2zxσyy.

An increment of the plastic strain tensor ε˙p can therefore be decomposed as

              (                              )
      ∂Qp-      ∂Qp-∂I1-  ∂Qp- ∂J2-  ∂Qp-∂J3-
˙εp = λ ∂σ  = λ  ∂I1  ∂σ +  ∂J2 ∂σ  + ∂J3  ∂σ  ,

where λ is the plastic multiplier, which depends on the current state of the stress and the load history. The "dot" in ˙εp does not indicate a true time derivative, but rather it indicates the rate at which the plastic strain tensor changes with respect to ∂Qp∕∂σ. The employed measure of the plastic deformation is the effective plastic strain rate ε˙pe, which is defined as

     ∘ --------
˙εpe =   2˙εp :ε˙p.

In the theory of plasticity, it is possible to describe yielding in the terms of σ only by means of a yield function. Therefore, a yield function can be used to define the onset of the plastic behavior. Given a yield function Fy(σys), which defines the limits of the elastic regimes, when Fy(σys) < 0 the material reacts elastically and when Fy(σys) 0 it begins to deform plastically [63].

σys(εpe) is the current yield stress which evolves during plastic flow and is described by an isotropic hardening law. The isotropic hardening law under consideration is a linear equation described by

σys(εpe) = σys0 + 1- ETsioεpe,

where σys0 is the initial yield stress (a material property), which indicates the stress level at which plastic deformation occurs. As can be seen in (3.9) σys(εpe) is determined by the isotropic tangent modulus ETiso and the effective plastic strain εpe. The yield level increases proportionally with the effective plastic strain εpe [6263]. In Figure 3.4 the σys0 and ETiso necessary to describe the plastic behavior are represented in a stress-strain plot.

The yield function is defined as

Fy = σmises - σys(εpe),  Qp = Fy,

where σmises is the Von Mises stress.

Not only do the material parameters influence the load-displacement curves, but nanoindentation is also sensitive to the level of residual stress in the layers. The results of experimental indentation are therefore the sum of two contributions: plastic deformation and residual stress.

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Figure 3.4: Stress-strain curve showing the elastic part before reaching the σys0. At σys0 the plastic deformation begins.

3.4 Results and Discussions

The model calibration can permit to understand how mechanical stress develops within the different layers (multilayer) as the force applied by the indenter increases. The presented model was calibrated using experimental data from an industrial partner. The experimental data were obtained for a displacement of the indenter into the surface up to approximately 3 μm. During the experiment, the process of unloading was not recorded.

In Figure 3.5 the simulation result shows the indenter at the highest prescribed indentation displacement. The movement of the indenter causes it to penetrate approximately 3 μm into the multilayer, which results in the displacement and deformation of the materials therein. The highest displacement is found at the center of the device. The deformation of the sample develops around the contact point between indenter and sample, and increases as the load is applied.

From the experimental data it was possible to obtain the load-displacement curve. The loading plot provides information about the mechanical properties, as well as the failure of the device.


Figure 3.5: FEM result, illustrating the displacement (μm) of the indenter inside of the TSV. The displacement peaks at about 3 μm.

In Figure 3.6 the red and black lines indicate the experimental and simulation, respectively. Due to the complex, multilayered architecture of TSVs, the experimental results do not represent the behavior of only one material, but rather the behavior of a multilayer structure. In the experimental data shown in Figure 3.6 we can identify an initial elastic regime which corresponds to an indentation displacement between 0 and 0.25 μm, followed by a plastic regime for indentation displacements above 0.25 μm. An aberration is notable around an indentation displacement of 2.5 μm, assumed to be due to a failure in the device, such as cracking or delamination [38].

The results of the simulation are in good agreement with experimental data, as can be seen in Figure 3.6. It is particularly important to have a good fit for low loads of the indenter, in the range of 0 to 0.1×F/F0 because, in this range, only the elastic behavior of the materials influences the result. The fitting of the plastic regime requires much more effort because the bottom of the TSV consists of different materials. Each material could exhibit plasticity, which can occur when different sufficiently high loads are applied. Furthermore, the plastic properties of thin layers employed in TSV structures are not reported in the literature. The plastic response of plastic materials during loading was described in (3.9), where the yield stress and isotropic tangent modulus are the fitting parameters [646566]. The results of the simulation depend on the values of the yield stress and the isotropic tangent modulus of the materials. To fit the model with the experimental data, the values of the yield stress and the isotropic tangent modulus of the plastic materials of the multilayer which were in contact with the indenter during indentation were modified. By changing these parameters, a good match with the experimental data was found. The deviation between the experimental results and the simulations is due to the multilayer structure for which the composition between layers and the non-bulk character can have an influence on the plastic behavior, which the model does not take into account.


Figure 3.6: The loading part of the nanoindentation process is plotted and it illustrates a comparison between the FEM simulation and experimental data.

During the deposition processes, residual stresses develop in the layers of the multilayer structure. These stresses can influence the nanoindentation test [38]. Different values of residual stress [67] were attempted in thin films of the multilayer in order to assist the calibration process. However, these tests did not improve the fitting; therefore, the influence of the residual stress was not considered.

Figure 3.7 depicts the normalized Von Mises stress due to the penetration of the indenter in the TSV. Two locations with high mechanical stress can be seen. The first is above the indenter and the second is located at the bottom corner around the TSV sidewall. The first interaction with the indenter generates a critical mechanical stress only at this location. As the indenter penetrates into the TSV, the mechanical stress develops and becomes high at the bottom corner around the TSV sidewall.


Figure 3.7: This image depicts normalized Von Mises stress development in the TSV. Two physical regions with high mechanical stress can be identified. The first is located in the TSV area above the indenter and the second is at the corner of the TSV. This perspective of the structure differs from Figure 3.3 in order to highlight those areas with a high concentration of mechanical stress.


Figure 3.8: Normalized Von Mises stress versus displacement into surface.

An increase in the displacement of the indenter increases the stress in the TSV. The inset in Figure 3.7 depicts in detail the distribution of the Von Mises stress in the W layer.

From the simulations stress values at different locations were determined allowing to deduce which mode of failure is most likely to occur. The highest stresses were found at the corner of the TSV sidewall, in particular:

The Figure 3.8 illustrates the Von Mises stress development in the SiO2 layer and at the interface between SiO2/W at the corner of the TSV sidewall. This result indicates a continuous increase in the SiO2. The stress behaves differently in the SiO2 layer and at the SiO2/W interface. The stress at the SiO2/W interface initially grows continuously, but at a smaller slope than the stress at the SiO2 surface. After an indentation of approximately 0.5 μm, the slope is further reduced. This does not indicate that the failure will be confined to the SiO2 layer; the SiO2/W interface could be experiencing a reduced stress behavior due to defects or a small interface fracture toughness, which can strongly contribute the failure at the interface.

3.5 Summary

In this chapter the stress development in the layers of open TSVs, during the application of an external force, was investigated. The implemented model permits to simulate the penetration of an indenter into the bottom of the TSV, reproducing the extra mechanical stress which might appear during the 3D IC stacking. The simulations were calibrated with experimental data, provided by an industrial partner. The model was fitted qualitatively by altering the plasticity parameters of the material under test. The simulations can predict the areas of the device in which there is increased stress and thereby a higher probability of failure. The following scenarios were found:

The model can be used to identify the way in which geometric and material properties influence the mechanical stability of TSVs during 3D IC stacking.