Subsections

• 8.1 Description of the Considered Deposition Processes Used by Investigations
• 8.2 Three-Dimensional Void Characteristics for the Prediction of Cracks
• 8.3 Summary

8. Applications of Three-Dimensional ELSA to Crack Prediction

Cracks may be created at any stage of a manufacturing process, but the deposition process step is generally the most problematic. The cracks are observed during the deposition of the passivation layers that cover IC chips in the areas where the top metalization layout geometry yields a three-dimensional profile for the deposition of the passivation layers.

To avoid such cracking and subsequent device failure, it is essential to characterize the deposition profile of the passivation layers as a function of the layout geometry. This characterization can then be used to establish a set of layout design rules to mitigate the formation of crack. An efficient and fast approach is the use of deposition simulation tools. Therefore, having a general purpose topography simulator capable of handling different physical etching and deposition models is essential. We present investigations during deposition of silicon nitride and silicon dioxide to gain insight into possible layout design rules that may be taken into account to avoid crack formation.

8.1 Description of the Considered Deposition Processes Used by Investigations

As mentioned in Section 6.2.1, the transport of particles is in the radiosity regime [80] for the considered processes. The deposition processes are governed by luminescent reflection. The deposited films are silicon nitride and silicon dioxide films.

Since measurements can only be made from cross sectional SEM images in two dimensions, for three-dimensional deposition simulations we have used the same parameters which were extracted with the optimization and calibration tool SIESTA [35] for two-dimensional simulations. The first set of parameters comes from the simulation results of the deposition of silicon nitride into interconnect lines as shown in [12] and the second set comes from the simulation results of the deposition of silicon dioxide from a TEOS process performed in [9]. These parameters led to very good agreement of simulation results with measurements in two dimensions.

8.2 Three-Dimensional Void Characteristics for the Prediction of Cracks

Figure 8.1 shows a schematic of three-dimensional structure used in our investigations. The geometrical parameters for which we obtain the void characteristics are line-to-line spacings ($S$), metal thickness ($T$), metal width ($W$), displacement parameter ($L$), and a diagonal parameter ($P$). The last two parameters result in pronounced three-dimensional effects.

Figure 8.1: Schematic of the investigated three-dimensional interconnect structure.

Figure 8.2: Initial structure for $T_{2}$, and $S=0.72\mathrm{\mu m}$.

Figure 8.3: Void formation during deposition into the structure as shown in Figure 8.2.

Figure 8.4: Simulation result for $S=1\mathrm{\mu m}$ and $T_{2}$.

Figure 8.5: A cross section of the simulation results shown in Figure 8.4.

Since our simulations [10] have shown that the metal width does not play an important role for void characteristics, it will be held constant during all investigations. The first set of simulations was performed for different line to line spacings holding the metal thicknesses at $T_{1}=0.845\mathrm{\mu m}$ and $T_{2}=1.045\mathrm{\mu m}$. As mentioned in Section 8.1 the deposited layers were silicon dioxide and silicon nitride with thicknesses of $D_{1}=0.1\mathrm{\mu m}$ and $D_{2}=0.9\mathrm{\mu m}$, respectively.

One of the initial structures considered for the first set of investigations can be seen in Figure 8.2. The simulation of the deposition processes into this structure has led to a result as shown in Figure 8.3. To analyze the cracking effects we introduce a parameter $C$ which is calculated as follows:

$$C(S,T,D,L,P)=T+D-Z_{void}(S,T,D,L,P)$$

where $Z_{void}$ (the $Z$ coordinate of top of the void) and $C$ are shown in Figure 8.3.

The simulations have generally shown that increasing $S$ shifts the void upwards while it simultaneously decreases $C$ as can be seen by a comparing Figure 8.3 and Figure 8.4. In addition, increasing $S$ causes the void to be wider. To see the formation of the void more clearly, a cross section of the simulation result shown in Figure 8.4 is given in Figure 8.5.

In order to find the influence of the metal thickness on $C$, we have performed another set of simulations. The dependence of $C$ on different metal thicknesses is illustrated in Figure 8.6. Whereas the metal thickness does not considerably affect $C$ for small $S$, its effect is stronger once $S$ crossed a threshold value, and the thicker the metal the larger is $C$.

So far we have presented three-dimensional simulations with results which could also have been estimated with two-dimensional simulations at the expense of a lower accuracy.

We now present investigations which can only be performed using three-dimensional simulations [8]. In a first attempt $L$ is varied while keeping the remaining parameters constant. Although increasing $L$ shifts the voids upwards, the dimensions of the voids do not increase as when increasing $S$.

Introducing a parameter $P$ and its variation results in pronounced three-dimensional effects. Because $P=\sqrt{S^{2}+L^{2}}$ is not a single-valued function of $S$ and $L$ as shown in Figure 8.1, considering the dependence of $C$ on $P$ is difficult. Therefore, it is very important to have a profile of $C$ depending on $S$ and $L$ that leads to the same value of $P$ with different combinations of $S$ and $L$.

Figures 8.7, 8.8, and 8.9 show three of many investigations for different $S$ and $L$. As in Figure 8.5 we show cross sections of simulation results shown in Figures 8.7, 8.8, and 8.9, in Figures 8.10, 8.11, and 8.12, respectively. These figures show that simultaneous increase of $S$ and $L$ results in three different effects. First, the voids are shifted upwards. Second, they will be wider. Finally, their height is decreased. These investigations have led to a profile of $C$ as shown in Figure 8.13. The important characteristic of Figure 8.13 is that there are different regions which guarantee a stable process, i.e., a large $C$. Using such profiles, $C$ can be predicted and therefore process engineers will be able to choose the optimal geometrical parameters to avoid cracks. The cracks are avoided by choosing $C$ as large as possible because the smaller $C$ the more probable is the formation of cracks.

Figure 8.6: Dependence of $C$ on $T_{1}$ and $T_{2}$. The lower and upper curve stand for $T_{1}$ and $T_{2}$, respectively.

Figure 8.7: Void formation for $T_{1}$ and $S=L=0.3\mathrm{\mu m}$.

Figure 8.8: Void formation for $T_{1}$ and $S=L=0.6\mathrm{\mu m}$.

Figure 8.9: Void formation for $T_{1}$ and $S=L=0.9\mathrm{\mu m}$.

Figure 8.10: A cross section of simulation result shown in Figure 8.7.

Figure 8.11: A cross section of simulation result shown in Figure 8.8.

Figure 8.12: A cross section of simulation result shown in Figure 8.9.

Figure 8.13: Dependence of $C$ on $S$ and $L$.

8.3 Summary

The void characteristics during the deposition of silicon dioxide and silicon nitride layers into interconnect lines are predicted. We have obtained a profile of $C$ which determines the probability of cracking effects. Process engineers can set layout design rules depending on geometrical parameters while they choose such parameters leading to larger $C$ because the smaller $C$ the more probable are cracking effects.