A Multiscale Simulation Study of the Structural Integrity of Damascene Interconnects in Advanced Technology Nodes

The structural stability of tight-pitched (18 nm and below) damascene interconnects for back-end-of-line (BEOL) technologies are analyzed using force-field-based molecular dynamics simulations and finite-element modeling. At these pitches surface energy-dominated effects come into the picture, which lead to structural instability. The candidate metals analyzed are beyond copper (Cu) interconnect metals-ruthenium (Ru), cobalt (Co), and tungsten (W); and Cu is analyzed for reference. Cohesive traction and normal bonding energy are calculated using force-field- based molecular dynamics simulations and then fed as input to a finite-element analysis (FEA) tool, where their dependence on the physical dimensions of the interconnect lines is studied. The parameters studied for the BEOL structures are sidewall angle, aspect ratio, the internal stress of the metal, and modulus of elasticity of the dielectric material around the metal to understand the sensitivity of these parameters to the structural stability of the interconnects. We observe that a lower aspect ratio and higher modulus of elasticity of the dielectric results in stable structures whereas, intrinsic stress of the metal and side wall angle have a minor impact on the overall stability. The stability is analyzed at the seed-layer deposition step and based on this study, Co is the most stable alternate metal amongst Ru, Co, and W.


I. INTRODUCTION
T HE time-dependent dielectric breakdown (TDDB) and electromigration characteristics of copper (Cu)-based interconnects require a robust barrier layer, which are traditionally tantalum (Ta)/Ta nitride (TaN), to improve TDDB, and liner layers such as cobalt (Co)/ruthenium (Ru) to improve electromigration and yield, in the current technology nodes [1]. For advanced technology nodes, these requirements of a diffusion barrier and a liner leave very little area for Cu to fill, thereby limiting its superior conductivity advantages. While work has been done to make these diffusion barriers thinner, eliminating them altogether is highly unlikely [2], [3], [4], [5]. So, at these advanced technology nodes, several other metals become potential candidates for back-end-ofline (BEOL) interconnect metal, based on the backend-of-line requirements of power, performance, area, and reliability [6], [7], [8]. At the forefront of these potential candidates are Ru, Co, and tungsten (W). Co and W are well-studied metals in the field of interconnects [9], [10], [11], [12]. Ru is a novel metal for this application but has been heavily studied over the last decade [13], [14], [15]. However, these cited examples are at larger interconnect pitches such as 64 and 36 nm. At interconnect pitches below 30 nm, the surface energy-dominated effects of conductors come into play, as observed by [16] and predicted by [17], [18], resulting in structural instability. Such structural instability can be a serious yield limiter, so, the cause of this instability must be modeled and investigated.
This article demonstrates that intrinsic stresses due to prior processing alone do not result in the structural instability observed. However, an initial model based on cohesive traction shows similar trends as the hardware (Fig. 1), suggesting the analysis of the contribution of parameters such as cohesive traction and the normal bonding energy toward structural instability in advanced node interconnects [16]. So, these parameters are calculated for the three alternate metals: 1) Ru; 2) Co; and 3) W, and Cu, using force-field-based molecular dynamics simulations and are fed to a finite-element analysis (FEA) tool to simulate the effects of these properties on the macroscale structures. The Cu properties are modeled as a reference point and presented where relevant. Section II discusses the methodology adopted for this study where the properties required by the finite-element model are calculated using force-field-based molecular dynamics simulations because these properties are not readily available in the literature for the materials studied. Section III presents the results and their implications and shows a pitch-based dependence of structural stability of W interconnects. Finally, these results and their implications on future interconnect technologies are discussed.

II. SIMULATION METHODOLOGY
In our study, we model the analytical formulation of the cohesive traction-separation law as the simulation framework.
See https://www.ieee.org/publications/rights/index.html for more information. Here, the dielectric fins are 9 nm wide and the metal trench is also 9 nm wide at mid-trench CD. The aspect ratio (defined in Section III-D) is modeled to be two, the sidewall angle is 89 • , the stress in deposited metal is 100 MPa (an atomic layer deposition (ALD)-like process), and Young's modulus of the dielectric is modeled as 33 GPa. We notice a displacement of 1.5 nm toward each other after fin metal deposition.  [23], [24], [25], [26] We choose an exponential model, from several existing models, where the entire law can be expressed in terms of maximum normal traction and the normal bonding energy as described by the following equation [19], [20], [21]: where T n is the normal traction, n0 is the normal bonding energy, δ n is the normal separation, δ n0 is the characteristic separation, and σ max is the maximum normal traction. We use force-field-based molecular dynamics simulations to extract the maximum normal traction and the normal bonding energy for thin films of Ru, Co, W, and Cu. These simulations account for the interactions happening at a molecular level and feed into the finite element analysis. The following subsections provide a detailed description of the simulations performed.

A. Force-Field Based Molecular Dynamics Simulations
A force-field molecular dynamics study is performed using the Synopsys Quantum ATK software (R2020.09-SP1), where the normal traction is calculated using bins and local stresses (Fig. 2) [22]. The width of each bin is specified at 8 Å and the height is 20 Å. This is a type of embedded atom model (EAM) that takes the interatomic potentials of the material being studied into account. This potential energy is defined as below Here, ρ is a generalized density arising from the neighbor atoms, and φ is a repulsive pair potential. The potential models used in this study are listed in Table I. To build a surface, a unit cell configuration of the element being studied is specified, for example, Ru (0001), and then this unit cell is repeated in the x-z directions. Next, the cohesive traction study is set up by defining two anti-parallel surfaces with an initial separation of 15 Å. Once set up, these surfaces evolve in time such that the system is updated to a new configuration at each time step by solving Newton's equations of motion.
As this is a microcanonical ensemble, the acceleration of the atoms being studied is governed by the potentials defined initially, and the velocities defined using the Maxwell-Boltzmann distribution. The temperature is kept constant at 300 K then the simulation is run for a fixed number of steps defined by the user (50 000-60 000) or more. The normal traction is calculated using a custom script where the atoms on the edges are tagged to be in one of the five defined bins. Then the local stress on each atom and the displacement is calculated. The time step is set to be 1 fs. With each step, the two anti-parallel surfaces are moved incrementally closer to one another to simulate approaching surfaces, where this movement is dictated by Hooke's law. The results obtained are reported in Table II.

B. Finite Element Analysis
The cohesive traction-separation law is solved in conjunction with the intrinsic stresses due to thermal mismatch using Synopsys Sentaurus Interconnect software (R2020.09-SP1). The integration sequence modeled is informed by process conditions in a state-of-the-art 300 mm wafer processing environment. However, for the sake of a fair comparison, the same integration sequence is used for all the alternate metals, which is the formation of damascene trenches through reactive ion etch (RIE), deposition of 1 nm TaN for adhesion, and finally deposition of 2 nm metal using an ALD like process. Practically, most metal fills require a seed layer or a precursor prior to complete fill [27]. The 2 nm metal deposition is intended to model the same.
In this setup, the metal film deposited forms the surface, hence, the cohesive traction-separation law is applied to the metals only. Furthermore, the intrinsic stresses due to the temperatures applied during processing are considered and the final simulation performs a thermal relaxation from 250 • C to 25 • C, which mimics the relaxation of the structure to room Displacement produced in dielectric trenches after metal deposition with and without the application of the cohesive tractionseparation law. For this study, an aspect ratio of 2, a sidewall angle of 87 • , and a dielectric's modulus of 33 GPa are modeled. The intrinsic stress of the metal is varied. The solid lines show data points where the traction-separation law was applied to the structures, and the dashed lines show cases where is law was not applied. We observe that in the case this law was not applied, the displacement due to thermal mismatch stresses are minimal.
temperature. In addition to the thermal mismatch stresses, stress is also applied to the deposited metal film for a few modeling splits. This stress is representative of the stress induced in the metal during the deposition process itself. For example, a metal film deposited through physical vapor deposition (PVD) has different stress than a metal film deposited through chemical vapor deposition (CVD) [28]. The modulus of elasticity for the metal films and the dielectrics are obtained from existing repositories and studies [29], [30], [31].

III. RESULTS AND DISCUSSION
Stresses due to prior processing are known to cause line bending or pattern collapse in BEOL structures [32]. While a lot of these stresses from processing have been alleviated over time with process refinement or material innovation, they must always be accounted for in any structural stability study. So, the first result we show is that of displacement caused by metallization when the cohesive traction-separation law (or zipping forces) is applied to the deposited metals, in addition to the intrinsic stresses, and when this physics is removed from the study (Fig. 3). We see that the addition of the zipping forces results in additional displacement in the case of W, Co, and Ru, whereas minimal change in displacement is observed in the case of Cu. This behavior may be attributed to the lower normal-bonding energy and lower maximum normal traction values for Cu-which are the two major inputs into the cohesive traction-separation finite-element modeling simulations. Having established that these forces do play a role at advanced interconnect nodes like the 18-nm pitch, we further analyze the factors that make this effect better or worse for alternate metals.

A. Maximum Normal Traction
Normal traction versus separation is plotted for Cu, Ru, Co, and W, using force-field-based molecular dynamics simulations, and the maximum normal traction is extracted. The traction vector can be defined as a ratio between forces applied to the surface and the area of the surface, as the area tends to zero, as denoted by equation below Here, ⃗ t is the traction vector, ⃗ P denotes forces applied, which in this case are the interatomic forces, and A denotes the area of the solid being deformed. Let n denote a unit vector normal to the surface then normal traction is given by equation below For all the alternate metals, the value of maximum traction is in a similar range (14.3-15.5 GPa), as shown in Table II. However, these values are almost an order of magnitude higher than that for Cu. So, we can expect these alternate metals to behave differently from Cu but like each other.

B. Normal Bonding Energy
The normal bonding energy is defined as the binding energy per unit area or the force per unit length (dyn/cm). Physically, this term is equivalent to the spring constant, as in Hooke's law. The normal bonding energy is derived for Cu, Ru, Co, and W using force-field-based molecular dynamics simulations as explained in Section II-A. From Table II, we can see that W has the highest normal bonding energy followed by Ru, Co, and Cu. However, all these values are in the same order of magnitude, so we expect to see subtle differences based on this parameter alone.
If we do consider the subtleties in behavior based on this parameter, W and Ru have a larger normal bonding energy than Co and Cu. It must be noted here that this bonding energy is directly proportional to the change in electrostatic energy as the two metal surfaces come closer together (Fig. 4). So, it is representative of the tendency of the metal to form bonds with itself. A similar trend is observed when we look at the bulk values for Young's modulus for these metals, Ru and W have a much higher value, that of 414 and 400 GPa, as opposed to 211 and 110 GPa for Co and Cu, respectively. However, there's no direct correlation, because W has a higher value for normal bonding energy than Ru, but a lower Young's modulus than Ru. This highlights the fact that taking factors such as the normal bonding energy into account can highlight nuances of the thin-film behavior of these metals that are different from bulk behavior. The following subsections analyze the effects of normal bonding energy and maximum normal traction on trenches of different shapes and sizes. Fig. 4. Drop in potential energy as two W surfaces come closer to each other. When the two surfaces are far apart, they do not interact with one another, and thus the energy stays constant. As they get closer, bonds begin to form, which lowers the energy. Of all metals, we see the largest drop in potential energy for W, meaning it the most energetically favorable for W to form surfaces. This is followed by Ru, Co, and Cu, respectively.

C. Stress in Deposited Metal
As the conducting metal is deposited into the dielectric trenches, the method of deposition induces some stress into the metal itself [34], [35]. This stress can either be tensile, compressive, or close to zero, based on the method of deposition. In general, an ALD process is associated with low stresses, whereas a PVD process may induce tensile stress of 1 GPa [27]. The effects of such stresses are analyzed in conjunction with the cohesive traction study (Fig. 5). For these experiments, a sidewall angle of 87 is maintained along with an aspect ratio of 2. The width of the metal trench is 9 nm at mid-metal height. The modulus of the dielectric is modeled to be 33 GPa.
No significant change in displacement of the trenches is observed when the stress in deposited metal is varied between 1 and −1 GPa. We also observe that the W trenches collapse completely for all three cases and that Ru shows higher displacement than Co in all three cases. W and Ru have a similar modulus of elasticity, but W has higher normal bonding energy and maximum normal traction. This is possibly the reason that W trenches stick to each other resulting in complete collapse, whereas Ru trenches show a displacement, but not complete collapse.

D. Young's Modulus of the Dielectric
The industry moved toward low-k dielectrics to provide an RC benefit at current technology nodes. However, as we move toward smaller pitches and alternate metals, the structural stability of the BEOL interconnects becomes a concern, so a material with a higher dielectric constant may be better suited for the application. While the above analyses were performed using a 33 GPa dielectric, this sub-study analyses the effect of a weaker or stronger modulus of elasticity of the dielectric material.
We see that the structural stability decreases if we use a material with a lower dielectric constant, and it improves if the dielectric constant is increased. However, keeping the RC delays in mind, a value above the lowest k but not as high as 330 GPa is suggested for future nodes. Moreover, higherk dielectrics will have a smaller RIE-induced damage layer, Fig. 5. Stability of trenches with intrinsic stress of the deposited metal varying between −1 and 1 GPa for Ru, Co, and W at 18 nm pitch. The midline CD is maintained at 9 nm, the aspect ratio is 2, the sidewall angle is maintained at 87 • , and the dielectric's modulus of elasticity is kept constant at 33 GPa. W shows a complete collapse in all three cases, whereas Ru shows higher displacement than Co. which helps mitigate the capacitance penalty. Porous low-k dielectrics can have damage layers as thick as 2 nm, which mitigate much of the capacitance benefit they provide.

E. Sidewall Angle of Metal Trenches
The sidewall angle is the angle formed between the base of the trench and the sidewall. Values of 85 • , 87 • , and 89 • are studied. The intention of this study is to analyze whether changes in the adjacent metal wall profile results in better or worse stability. Here also the dielectric modulus is maintained at 33 GPa, the internal stress of the metal is kept at 100 MPa, and an aspect ratio of 2 is studied.
We observe that for W, all sidewall angles result in complete pattern collapse, whereas for Ru and Co a sidewall angle of 89 • results in slightly larger displacement than sidewall angles of 85 • and 87 • . However, the margin of displacement between the three sidewall angles is very small and may be attributed to numerical noise rather than an actual indication of a trend. Largely, the sidewall angle plays a minor role in the overall stability of the structures.

F. Aspect Ratio of Lines
Aspect ratio is defined as the ratio between the total metal height of the trench and the midline critical dimension (CD) of the trench. An analysis across all alternate metals for metal trenches with an aspect ratio of 1-3 shows that all metal trenches are relatively stable for an aspect ratio of 1 at 18 nm pitch, where the midline CD of the metal trench is 9 nm. These trenches show a displacement of less than 1.5 nm which does not result in complete pattern collapse. W trenches show complete pattern collapse for aspect ratios of 2 and 3, with a displacement greater than 3.5 nm [ Fig. 6(c)]. For a 9 nm midline CD, any displacement greater than 3.5 nm represents complete pattern collapse.
This pattern collapse at high aspect ratios can be attributed to the cohesive traction-separation law itself, which works on adjacent surfaces. A higher aspect ratio gives rise to a larger surface area of the metal walls, resulting in stronger  6. (a) Displacement in trenches with an aspect ratio of 1-3 for Ru, Co, and W at 18 nm pitch. The midline CD is maintained at 9 nm, the sidewall angle is 87 • , and the internal stress of the metal is modeled to be 0 GPa. The modulus of elasticity of the dielectric material is modeled to be 33 GPa. W shows complete pattern collapse for aspect ratios of 2 and 3. (b) Stability of trenches with sidewall angles of 85 • , 87 • , and 89 • for Ru, Co, and W at 18 nm pitch. The midline CD is maintained at 9 nm, the aspect ratio is 2, and the internal stress of the metal is modeled to be 100 MPa. The modulus of elasticity of the dielectric material is modeled to be 33 GPa. W shows a complete collapse in all three cases, whereas Ru shows higher displacement than Co. (c) Stability of trenches with dielectric's modulus of elasticity of 3.3, 33, and 330 GPa for Ru, Co, and W at 18 nm pitch. The midline CD is maintained at 9 nm, the aspect ratio is 2, the sidewall angle is maintained at 87 • , and the internal stress of the metal is modeled to be 100 MPa.
cohesive forces. For these experiments, the dielectric material is assumed to be a carbon and hydrogen-enriched silicon nitride with a modulus of elasticity of 33 GPa. The sidewall angle is kept constant at 87 • , and stress in the deposited metal is assumed to be 100 MPa.

G. Pitch-Based Line Wiggling Dependence of W
We observe that W is highly unstable in the above experiments at 18 nm pitch. However, we have seen manufactured examples of W interconnects in recent technology nodes [10]. To further investigate this behavior of W, we performed a pitch-based study where pitches from 28 to 18 nm were analyzed for an aspect ratio of 2, and a sidewall angle of 87 • . The young's modulus of the dielectric was maintained Fig. 7. Displacement of W as a function of pitch, where the pitch is varied from 18 to 28 nm. We observe that the W trenches completely collapse at 18 nm pitch. However, for pitches of 22 nm and above, these trenches are relatively stable. This drastic change in behavior based on the pitch can be attributed to the proximity of the adjacent metal surface at lower pitches, which triggers the cohesive forces to dominate and result in complete pattern collapse. As shown in Fig. 7, we observe that the W trenches completely collapse at 18 nm pitch. However, for pitches of 22 nm and above, these trenches are relatively stable, with 20 nm pitch showing a large displacement. This drastic change in behavior based on the pitch can be attributed to the proximity of the adjacent metal surface at lower pitches, which triggers the cohesive forces to dominate and result in complete pattern collapse for W.

IV. CONCLUSION
In summary, the cohesive traction versus separation and the normal bonding energy of Cu, Ru, Co, and W are calculated using a force field molecular dynamic simulation. All alternate metals show higher maximum normal traction and higher normal bonding energy than Cu. This implies that these metals have a lower tendency for electromigration, reducing liner requirements, but it also implies that these metals have a higher tendency to bond with themselves, if two adjacent surfaces are separated by a very small distance. This tendency results in partial or complete pattern collapse, or line bending, which is undesirable for large-scale manufacturing. An FEA study on varying geometrical aspects of the metal trench such as the aspect ratio shows that a lower aspect ratio produces more stable structures. An analysis of the modulus of elasticity of the dielectric material shows that materials with lower dielectric constants result in higher line bending, hence are not ideal for these future interconnects. The intrinsic stresses of the metals and a few different sidewall angles are also modeled, but no significant impact on structural stability is observed due to these factors. This study presents a new dimension in analysis of metals that are being studied to replace Cu in advanced technology nodes, where the intrinsic properties of these metals and surrounding dielectrics result in potentially unstable structures. It also shows that strict control over parameters like the aspect ratio can result in stable structures, thereby meeting the demands of future technology nodes.