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Cu Interfaces in Advanced Vertical Interconnects
Computational Materials Science 158 (2019) 398–405
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Electron Transport Across Cu/Ta(O)/Ru(O)/Cu Interfaces in Advanced Vertical Interconnects
T
⁎
Nicholas A. Lanzilloa, , Benjamin D. Briggsa, Robert R. Robisona, Theo Standaerta, Christian Lavoieb a b
IBM Research at Albany Nanotech, 257 Fuller Road, Albany, NY 12203 USA IBM T.J. Watson Research Center, 1101 Kitchawan Road, Yorktown Heights, NY 10598 USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Interconnects Via resistance Oxidation Metal oxides Electron transport
The vertical resistance of Cu/Ta/Ru/Cu stacks is calculated using a combination of first-principles density functional theory (DFT) and a Non-Equilibrium Green’s Function (NEGF) formalism. The effects of oxidizing either one or both of the Ta and Ru layers are analyzed. These oxides can be either metallic (TaO and RuO2) or insulating (Ta2O5) in nature. Simulations indicate that for the metallic oxides, the presence of RuO2 results in more electron scattering than TaO. Complete oxidation of both Ta/Ru layers results in a ≈ 3× increase in resistance for Cu/TaO/RuO2/Cu relative to the un-oxidized structure, and a ≈ 8x increase in resistance for Cu/ Ta2O5/RuO2/Cu relative to the un-oxidized structure. Electron transmission/reflection coefficients as well as values of total resistance are reported for each interface structure. These results highlight the importance of identifying and controlling oxygen contamination in high-volume manufacturing in order to obtain low resistance vertical interconnects and favorable device performance.
1. Introduction The nature of electron scattering in vertical interconnects is crucial in determining overall device performance in advanced semiconductor technology nodes[1–3]. Vertical interconnects (referred to as vias) connect adjacent levels of horizontal interconnect wiring and are of crucial importance in rapidly delivering electrical signals to and from the active regions (transistors) to large-width metal levels higher up in the stack. In the recently developed 7nm technology node, back-end-ofline (BEOL) interconnect trenches were filled first with a thin layer of TaN (barrier material) and then by a thin layer of Ru (wetting material) before filling with Cu conductor[4–8]. The TaN and Ru layers served as diffusion barriers and wetting layers, respectively, for electroplated Cu in the interconnect trench. More recently, proposed integration schemes replace TaN diffusion barriers with pure Ta layers combined with in-situ dielectric nitridation, resulting in significantly lower via resistance[9–11]. A representative via structure is depicted schematically in Fig. 1 for a typical dual-damascene process flow. M(x) is a level of horizontal interconnect wiring and M(x+1) is the level directly above it. Both M(x) and M(x+1) are embedded in an inter-level dielectric (ILD) material. In order for an electron to get from the M(x) level to the M(x+1) level, it must penetrate thin (≈ 1nm )
⁎
Corresponding author. E-mail address: [email protected] (N.A. Lanzillo).
https://doi.org/10.1016/j.commatsci.2018.11.040 Received 22 October 2018; Accepted 21 November 2018 0927-0256/ © 2018 Published by Elsevier B.V.
layers of both Ta and Ru. The presence of these thin metallic layers increases the via resistance due to interfacial scattering as well as the shifts in electronic potential when transitioning from one region to another. This type of scattering is reminiscent of electron scattering in thin Cu/Co multilayers known for their magnetoresistive properties [12,13], except that Cu, Ru and Ta are all non-magnetic. Furthermore, since oxygen contamination poses a significant risk in many modern fabrication environments and oxygen incorporation introduces additional scattering sites metallic multi-layered stack, understanding the impact of oxygenation on via resistance is paramount from the standpoints of both fundamental physics as well as technology development. There are several possible sources of oxygen contamination in BEOL metals and interconnects. Any time a wafer or substrate is moved between different tools/chambers, the resulting air break offers the largest opportunity for oxidation to occur. If etching, barrier deposition, liner deposition and electroplating each occur in different tools, there are then three air breaks before an interconnect trench is even filled with Cu. Additional sources of oxygen include precursors to the atomic layer deposition (ALD) of barrier/liner metals[14,15,48], diffusion of oxygen from the surrounding dielectrics[10], and diffusion of oxygen along grain boundaries in Cu[16]. Since Ta is a known oxygen scavenger [17,18], any residual oxygen near the via in the Cu is likely to diffuse
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Fig. 1. Schematic 2D illustration of a vertical interconnect (via) connecting two adjacent levels of horizontal interconnect wiring, M(x) and M(x+1). Arrows indicate electrons traveling through the Cu/Ta/Ru/Cu interface.
on each atom were less than 0.05 eV/Å. The exchange-correlation functional was taken to be the generalized-gradient approximation (GGA) for all structures except for those containing Ta2O5, which required the use of a hybrid meta-GGA functional[39,40] in order to correctly predict the band gap. In the meta-GGA scheme, the exchange functional is given by the expression:
toward the barrier/liner interface. In addition, previous studies have shown that the formation of tantalum oxide is thermodynamically favorable to the formation of copper oxide at the Cu/Ta interface[16]. Spectroscopic analysis has also indicated that RuO2 can form from Ru thin films exposed to atomic oxygen even at room temperature[19]. In the case of oxidized Ta/Ru layers at an interconnect via, electrons would have to travel through the Cu/Ta(O)/Ru(O)/Cu interface. There exists an extensive body of work describing electron scattering mechanisms in interconnect metals from a first-principles perspective, including grain-boundary scattering[20–23], surface scattering[24–29] and electron-phonon scattering[30–34]. Only recently have ab initio methods been applied to study electron transport in vertical interconnects[11,35]. Furthermore, while the effects of Cu oxidation have been studied with respect to surface scattering[27], the impact of oxidized interfaces in vertical interconnects remains an open topic. In this work, the impact of oxidation on the barrier/liner metals at interconnect via is evaluated using first-principles calculations based on density functional theory and a Non-Equilibrium Green’s function (NEGF) formalism. Simulations suggest that the presence of RuO2 is more detrimental to via resistance than TaO, while the total via resistance increases by no more than ≈ 3× when both TaO and RuO2 are present. While both RuO2 and TaO are metallic in nature, Ta2O5 is an insulator which drastically impacts electron transport across the interface structures considered here. In particular, the presence of Ta2O5 results in a ≈ 8x increase in via resistance for Cu/Ta2O5/RuO2/Cu relative to the pristine, non-oxidized structure.
3c − 2 vxTB (→ r ) = cvxBR (→ r)+ π
4τ (→ r) 6ρ (→ r)
(1)
where the superscript “TB” refers to the Tran and Blaha functional[40] and the superscript “BR” refers to Becke-Roussel exchange functional [39]. τ (→ r ) is the kinetic energy density written in terms of Kohn-Sham r ) is the electronic density. The parameter c is adorbitals and ρ (→ justable in the model. It can either be self-consistently calculated according to the formula:
c=α+β
1 Ω
∫Ω
∇ρ (→ r) → dr ρ (→ r)
(2)
or simply held fixed so as to reproduce the experimentally-determined band gap. In self-consistent Eq. (2), Ω is the volume of the computational unit cell and α and β are constants with values of − 0.012 and 1.023 Bohr1/2, respectively. For the interface structure containing Ta2O5, the meta-GGA is only applied along the z-direction in which Ta atoms are present, while the regular GGA is applied elsewhere. In the NEGF scheme for the two-terminal set up, the electron conductance (per spin) is given by the linear response expression at zerobias (V=0):
2. Computational Details Simulations for all structures were performed using the QuantumWise Atomistix Toolkit[36–38]. The simulations employed a cutoff energy of 75.0 Hartree and k-point sampling of 5x5x1 for geometry optimizations and 11x11x101 for transmission calculations. By considering lateral k-point sampling densities of 1x1, 3x3, 5x5, 7x7, 9x9 and 11x11, we find the values of electron transmission to be wellconverged (changes less than 2%) for an 11x11 k-point grid. Likewise, we have checked k-point sampling along the direction of transport to tightly-converged (changes less than 1%) using 101 mesh points. The high k-point sampling density along the direction of transport is required in this particular software package in order to accurately describe the electronic structure in the semi-infinite electrode unit cells, which extend semi-periodically in either the positive or negative direction. The geometries of all structures were relaxed until the forces acting
G=
I 1 e2 = = Σi Ti ⎛⎜EF , V = 0⎞⎟ V R h ⎠ ⎝
(3)
where EF is the Fermi Energy and Ti is the transmission for the ith electronic channel. The Fermi Energy is calculated self-consistently for the interface structure(s). Since the electrode regions are metallic, as well as the Ta, TaO, Ru and RuO2 regions, transport is considered only at the EF . While Ta2O5 is not metallic, we restrict our analysis to transport at EF for consistency when comparing to the other interface structures. Given the output transmission (conductance), the corresponding resistance is calculated using Ohm’s law and then normalized by the cross-sectional area of the supercell. The final results are presented as specific resistivities with units of Ωcm2 , following the established literature convention[11,20,21,23,41,42]. Cu, Ta and Ru were considered in the face-centered-cubic (FCC), 399
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calculations are well-converged by placing 9 atoms of Cu on either side of the central scattering region. The first three atomic layers of Cu in the central region, as well as the electrodes, are held fixed at their bulk lattice positions while the remaining atoms in the supercell are allowed to relax. While electron transport is “horizontal” as calculated from the left electrode to the right electrode depicted in Fig. 2 , the terminology “vertical resistance” is used throughout this work to refer to the direction of current flow at a via in an actual integrated circuit. In addition, electron transmission was calculated for the Cu/Ta/Ru/Cu structure with the lateral supercell dimensions doubled in size, where it was confirmed that the area-normalized resistance was unchanged.
body-centered-cubic (BCC) and hexagonal-close-packed (HCP) crystal structures, respectively. The interface structures are constructed such that electron transport is along Cu(111), Ta(100) and Ru(0001). The (111) orientation of Cu is motivated by experimental observations of (111) sidewall texture in damascene interconnects[43–45]. The metal oxides TaO, Ta2O5 and Ru2 crystallize in the tetragonal, orthorhombic and rutile crystal structures, respectively. Electron transport was calculated along the (100) direction of each metallic oxide. In each case, these orientations result in minimal interface strain and lattice mismatch between the adjacent crystals while keeping the sizes of the computational supercells reasonable (<200 atoms.) The Cu electrodes are held fixed at the bulk geometry, while the lattice strain of the interfacial metals is kept below 5% for all structures. In particular, the Ta, Ru, TaO, RuO2 and Ta2O5 layers are strained 4.8%, 3.7%, 1.3%, 1.4% and 2.8%, respectively. Interface structures were generated by first creating a semi-infinite planar interface between Cu(111) and either Ta or TaO such that Cu (111) extends infinitely in the negative x-direction and Ta(O) extends infinitely in the positive x-direction. This interface was then truncated after 1nm of Ta(O), and the resulting structure was interfaced with either Ru or RuO2, such that the Ru(O) region extends infinitely in the positive x-direction. Again, the resulting interface was truncated after 1nm of Ru(O). Lastly, the resulting structure was interfaced with a Cu (111) region, which extends semi-infinitely in positive x-direction. In this manner, each Cu electrode region extends infinitely in either the positive or negative x-direction, while finite 1nm thick regions of Ta(O) and Ru(O) are sandwiched in between. Cross-sectional images of the two-terminal setups for the metallic interface configurations considered are depicted in Fig. 2. The reference structure Cu/Ta/Ru/Cu is shown in Fig. 2(a), while structures containing either RuO2 or TaO are depicted in Fig. 2(b) and (c), respectively. The structure in which both RuO2 and TaO are present is depicted in Fig. 2(d), and this represents the “worst-case” scenario in which the entire barrier/liner region is oxidized. All supercells have cross-sectional areas of 5.11Å × 5.11Å . The electrode regions are 3atoms thick in the z-direction, and we find that the transport
3. Results and Discussion Since the electron transport characteristics depend on the nature of the electronic states at the Fermi level, it is worth examining the electronic structure of the various metals (Ta, Ru) and their oxides (TaO, RuO2). The calculated electronic density of states are shown in Fig. 3. It is unsurprising that both Ta and Ru show non-zero density of states at the Fermi Energy in Fig. 3 (a) and (b) since these are both metallic in the bulk phase. Both TaO and RuO2 also show metallic behavior in the bulk, as depicted in Fig. 3(c) and (d). These results are consistent with previous published work indicating that both TaO and RuO2 are metallic in nature[46,47], and confirm the validity of the computational approach adopted here in describing these materials. Due to the metallic nature of both TaO and RuO2, the electron scattering is not expected to be impacted as much as it would if there were an insulating barrier. The k-space-resolved transmission spectra at the Fermi Energy for the four structures shown in Fig. 2 are depicted in Fig. 4. For the reference structure (Cu/Ta/Ru/Cu), the transmission spectra in Fig. 4(a) shows a distinct circular symmetry manifest as a ring surrounding the center of the Brillouin Zone, which corresponds to the (nearly) spherical Fermi surface of Cu. The presence of the hightransmission regions extending horizontally along kA in Fig. 4(a) is the
Fig. 2. The two-terminal computational supercells used for the NEGF calculations for the metallic interfaces: (a) Cu(111)/Ta(100)/Ru(0001)/Cu(111) (b) Cu(111)/ Ta(100)/RuO2(100)/Cu(111) (c) Cu(111)/TaO(100)/Ru(0001)/Cu(111) and (d) Cu(111)/TaO(100)/RuO2(100)/Cu(111). 400
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(a)
(b) Ru
DOS (1/eV/atom)
DOS (1/eV/atom)
Ta
E-EF (eV)
E-EF (eV)
(d) TaO
DOS (1/eV/atom)
DOS (1/eV/atom)
(c)
Ta
O E-EF (eV)
RuO2
O
Ru
E-EF (eV)
Fig. 3. The electronic density of states calculated for bulk (a) Ta (b) Ru (c) TaO and (d) RuO2.
direct result of the strain induced in Ta when interfaced with Cu. In order to match the Cu(111) lattice, the Ta(100) lattice vector is stretched along the a-direction and compressed along the b-direction. This results in less dispersion along the stretched direction (a) and more dispersion along the compressed direction (b). Taking the transmission at the Fermi Energy and converting to an area-normalized value of resistance, we obtain a value of γ = 34.24 × 10−12Ωcm2 for this reference
structure. For the Cu/Ta/RuO2 structure, the transmission spectra shown in Fig. 4(b) shows the same dispersion effects as in Fig. 4.(a), but substantially reduced in magnitude. This is purely the result of replacing Ru with RuO2, which reduces overall electron transmission across the Cu/Ta/Ru(O)/Cu interface by 60% relative to the pristine Cu/Ta/Ru/ Cu interface. The resistance for this structure is 86.04 × 10−12Ωcm2 . For
Fig. 4. The k-resolved transmission spectra for (a) Cu(111)/Ta(100)/Ru(0001)/Cu(111) (b) Cu(111)/Ta(100)/RuO2(100)/Cu(111) (c) Cu(111)/TaO(100)/Ru (0001)/Cu(111) and (d) Cu(111)/TaO(100)/RuO2(100)/Cu(111). 401
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(c), there are also regions with high amplitude near the right electrode, corresponding to effective transmission across the metallic interfaces. The Cu/Ta/RuO2/Cu and Cu/TaO/RuO2/Cu structures, on the other hand, show very low amplitudes near the right electrode, indicating poor transmission across the interfaces. Next, the worst-case scenario of complete oxidation of both Ta and Ru layers is considered but with the insulating Ta2O5 rather than the metallic TaO. Bulk Ta2O5 has a calculated band gap of approximately 2.5 eV[46] and is expected to impact electron transmission across the interface much more strongly than metallic TaO. The geometric structure of the Cu(111)/Ta2O5(100)/RuO2(100)/Cu(111) interface is shown in Fig. 6(a), with approximately 1nm of both Ta2O5 and RuO2 included. The band gap is bulk Ta2O5 is accurately reproduced using a metaGGA exchange-correlation functional as implemented in the the ATK software package[36]. In particular, the value of the band gap varies with the choice of the adjustable c-parameter as shown in Figure Fig. 6(b). A value of c=2.0 accurately reproduces a band gap of 2.5 eV and is used for subsequent electron transport calculations. In Fig. 6(c), the k-resolved transmission spectra is plotted. It is evident in this plot that there are very few regions in k-space with high electron transmission. The resulting value of normalized interface resistance for this structure is γ = 266.2 × 10−12Ωcm2 , which is nearly an order of magnitude larger than the corresponding value for the pristine Cu/Ta/Ru/Cu interface. It is worth noting that we calculated the electron transport across the Cu/Ta2O5/Ru/Cu interface using values of c ranging from 1.5 to 2.5 and found no significant variation in the calculated transmission. This indicates that small changes in the electronic structure (and band gap) of the Ta2O5 region have a minimal impact on the resulting electron transport. The transmission eigenstates corresponding to the largest three transmission eigenvalues calculated at the Γ -point of the Cu/Ta2O5/Cu interface are plotted in Fig. 7. The first and third eigenstates (Fig. 7(a) and (c)) show significant reflection at the Cu/Ta2O5 interface, while the second eigenvalue shows significant reflection at the Ta2O5/RuO2 interface. None of the
the Cu/TaO/Ru/Cu interface, while the transmission spectra depicted in Fig. 4(c) doesn’t feature any of the high-transmission channels in the corners, it does show the preservation of the some of the circular symmetry surrounding the Γ -point, and likewise the transmission is only reduced by 33% relative to the Cu/Ta/Ru/Cu structure. The value of resistance for this structure is 51.29 × 10−12Ωcm2 . Lastly, for the transmission spectra in Fig. 4(d), the circular symmetry surrounding the Γ -point is largely destroyed and there are no high-transmission channels visible anywhere in the Brillouin Zone. The structure corresponding to this structure (Cu/TaO/RuO2/Cu) shows the lowest electron transmission across the interface (reduced by 67% relative to Cu/ Ta/Ru/Cu) and likewise the highest value of resistance out of any of the four metallic interfaces considered: 104.78 × 10−12Ωcm2 . In order to gain additional insight regarding the interfacial scattering mechanisms in the various Cu/Ta(O)/Ru(O)/Cu structures, we consider the transmission eigenstates calculated at the Γ -point for each metallic interface structure. Since transmission is calculated from the left electrode to the right electrode, the matrix t represents the coupling between the incoming states from the left electrode and the outgoing states at the right electrode. Diagonalization of the matrix t †t gives the transmission eigenvalues, which describe how many channels contribute to the total transmission as well as their relative magnitudes. The eigenstates represent the superposition of both incoming and reflected waves in the left-hand region and the outgoing wave in the right-hand region. In Fig. 5, these eigenstates are plotted for the three largest eigenvalues in each interface structure. The top eigenstate corresponds to the largest eigenvalue while the bottom eigenstate corresponds to the lowest of the three eigenvalue. We note that one could chose specific k-points based on the plots in Fig. 3 that show either vary high or very low transmission, but these k-points are different for each structure. In light of this, we examine the eigenstates at the Γ -point of each structure as a common point of comparison. All four structures exhibit localized regions with high amplitude near the left electrode. The interference effects generated by the superposition of the incoming and reflected waves are clearly visible. For the Cu/Ta/Ru/Cu and Cu/TaO/Ru/Cu structures shown in Fig. 5(a) and
(a) Cu/Ta/Ru/Cu
(b) Cu/Ta/RuO2/Cu
(c) Cu/TaO/Ru/Cu
(d) Cu/TaO/RuO2/Cu
Amplitude (
0.0
0.25
Å )
0.5
Fig. 5. The transmission eigenstates at the Γ -point calculated for the three largest eigenvalues at each interface: (a) Cu(111)/Ta(100)/Ru(0001)/Cu(111) (b) Cu (111)/Ta(100)/RuO2(100)/Cu(111) (c) Cu(111)/TaO(100)/Ru(0001)/Cu(111) and (d) Cu(111)/TaO(100)/RuO2(100)/Cu(111). 402
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(a)
(b)
Ta2O5 Band Gap (eV)
(c)
c Parameter Fig. 6. (a) The geometry of the Cu(111)/Ta2O5/RuO2/Cu(111) interface (b) The band gap of bulk Ta2O5 calculated using the meta-GGA exchange-correlation functional as a function of the adjustable c-parameter and (c) The k-space resolved transmission spectra of the Cu/Ta2O5/Cu interface.
the cross-sectional area (perpendicular to the direction of electron transport) of the computational supercell. In addition, the transmission values in Table 1 represent the composite transmission spectra for all modes present at the Fermi Energy. Transmission is converted to re2e 2 1 sistance using the equation for conductance: G = h T = R and then divided by the cross-sectional area to obtain γ . In addition, a reference calculation of electron transport along bulk Cu(111) yields γ = 10.59 × 10−12Ωcm2 , which can then be used to calculate the normalized transmission coefficients using the formula:
eigenstates show significant transmission across the full interface. This visually explains the high resistance across the interface as the direct result of low electron transmission. For comparison, the calculated values of electron transmission at the Fermi Energy (T @ EF), the cross-sectional area of each computational supercell, the area-normalized vertical resistance (γ ) and the normalized transmission coefficient (t) for each structure are listed in Table 1. The raw values of calculated electron transmission (T @ EF) are not normalized by area and can be arbitrarily increased by increasing
Fig. 7. The eigenstates corresponding to the highest three eigenvalues ((a) through (c)) for the Cu/Ta2O5 structure calculated at the Γ -point.
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24p
T @ EF
Area [Å2]
γ (× 10−12Ωcm2 )
t
r
Cu(111) Cu/Ta/Ru/Cu Cu/Ta/RuO2/Cu Cu/TaO/Ru/Cu Cu/TaO/RuO2/Cu Cu/Ta2O5/RuO2/Cu
0.79 0.988 0.393 0.659 0.323 0.330
9.24 26.13 26.13 26.13 26.13 67.89
10.59 34.24 86.04 51.29 104.78 266.24
1.0 0.31 0.12 0.21 0.10 0.04
0.0 0.69 0.88 0.79 0.90 0.96
t=
γCu γinterface
30p 36p
48p
60p
Cu/Ta2O5/RuO2/Cu Cu/TaO/RuO2/Cu Cu/Ta/Ru/Cu
V
Structure
cal Resistance [ȍ]
Table 1 The total transmission at the Fermi Energy (T @ EF), the cross-sectional area of each supercell, the area-normalized vertical resistance (γ ) and the normalized transmission (t) and reflection (r) coefficients for each interface structure. In each structure, the Ta(O) and Ru(O2) regions are approximately 1nm thick.
(4)
where the corresponding reflection coefficients could be calculated by taking r = 1 − t . The value of bulk ballistic conductance for Cu obtained here in the appropriate units (10.59 × 10−12Ωcm2 → 1 0.94 × 1015 2 ) lies within the range previously reported in the literaΩm
1
Contact Area [nm2] Fig. 8. The interface contribution to the total vertical resistance as a function of contact area for the reference structure Cu/Ta/Ru/Cu and the two ”worst-case” structures Cu/TaO/RuO2/Cu and Cu/Ta2O5/RuO2/Cu.
1
ture(0.99 × 1015 2 to 1.2 × 1015 2 )[49,23]. Ωm Ωm Inspection of the numbers indicates that the presence of even a pristine Cu/Ta/Ru/Cu interface increases the via resistance by ≈ 3× relative to the barrier-free Cu(111) bulk. The formation of TaO increases the resistance by ≈ 1.5x relative to Cu/Ta/Ru/Cu, while the formation of RuO2 increases the resistance by ≈ 2.5x . The two worstcase scenario structures, corresponding to complete oxidation of both Ta and Ru layers, show resistance increased by either ≈ 3× or ≈ 8x , depending on the stoichiometry of the tantalum oxide. Inspection of the normalized reflection and transmission coefficients also highlights the dramatic differences between the various structures. These coefficients are cumulative in that they represent transmission/ reflection for the entire multi-interface structure, as opposed to transmission/reflection at a particular interface. For the case of pristine Cu/ Ta/Ru/Cu, 69% of incoming electrons are reflected relative to the baseline interface-free case of Cu(111). Inclusion of TaO increases this number to 79%, while inclusion of RuO2 increases this number of 88%. The inclusion of both TaO and RuO2 results in a net reflection coefficient of 90%, which is only marginally higher than the case of just including RuO2. Replacing TaO with Ta2O5 results in 96% of electrons getting reflected and only 4% of incoming electron successfully penetrating that Cu/Ta2O5/RuO2/Cu interface structure. In order to evaluate the actual impact on vertical resistance in realistically-sized interconnects, the values of interface resistance in Table 1 are divided by an effective contact area and plotted in Fig. 8 over a range of contact areas from 1000nm2 down to 100nm2. To put these contact areas into perspective, consider the recentlydeveloped 7nm technology node[4], in which BEOL interconnects are fabricated with a pitch of 36nm. Assuming symmetric line-to-line spacing, these interconnects would have a width of 18nm. A square-shaped vertical interconnect which joins two adjacent metal levels would then have an effective contact area of approximately 18nm × 18nm = 324nm2 . Similarly, estimates of effective contact areas for several representative BEOL pitches are shown as shaded regions in Fig. 8, including pitches of 60nm, 48nm, 36nm, 30nm and 24nm. For large enough dimensions, including the 48p and 60p cases, even the worst-case oxidation of the via results in a vertical resistance less than 50Ω. Beginning at 36p, the worst-case oxidation of the via results in values of vertical resistance approaching 100Ω, while for 24p structures the values are larger than 250Ω. Clearly, as physical dimensions in the BEOL continue to shrink, controlling and minimizing oxidization in vertical interconnects becomes increasingly important in maintaining low vertical resistance. As expected, the impact of electron scattering at the interfaces becomes more pronounced as the effective contact area is reduced. For the
reference structure (Cu/Ta/Ru/Cu) with no oxidation, the vertical resistance never exceeds 50Ω even down to a 100nm2 contact area. The Cu/TaO/RuO2/Cu structure results in a ≈ 3× higher resistance than the reference structure at a given cross-sectional area, which translates to vertical resistance values as high as 50-100Ω for contact areas for 200nm2 or smaller. The worst-case structure Cu/Ta2O5/RuO2/Cu results in dramatically high values of vertical resistance, which rapidly approach several hundred Ohms as the effective contact area shrinks to below a few hundred nm2. These results show that via resistance can fluctuate by as much as an order of magnitude depending on the size of the metal-to-metal contact area and the degree of oxidation in the barrier/liner materials.
4. Conclusion This work calculates effective electron transmission/reflection coefficients as well as values of specific resistivity for oxidized, Cubased vertical interconnect structures far more complicated than the Cu-based interfaces previously reported in the literature (such as twin grain boundaries and pristine Cu interface structures), thereby extending the applicability of NEGF calculations to realistic structures likely to be found in modern fabrication environments. The scattering mechanisms considered in this work include both interfacial electron scattering as well as scattering due to modulations in electronic potential in the intermediate metal regions. The impact of tantalum and ruthenium oxidation on the vertical resistance of Cu/Ta/Ru/Cu stacks has been evaluated using first-principles calculations and an NEGF formalism. While both TaO and RuO2 are metallic in nature, layers of either increase the vertical resistance by 1.5x and 2.5x, respectively, relative to the reference Cu/Ta/Ru/Cu structure. When both TaO and RuO2 are present in the stack, the vertical resistance is increased by ≈ 3×. The formation of insulating Ta2O5, however, results in a dramatic ≈ 8x increase in vertical resistance relative to the pristine Cu/Ta/Ru/Cu structure. These results indicate that interface quality and composition must be tightly controlled in order to minimize vertical resistance in next-generation interconnect technology. The authors would like to thank the Rensselaer Polytechnic Institute (RPI) Computational Center for Innovation (CCI) for providing computational resources. This work was performed by the Research Alliance Teams at various IBM Research and Development Facilities. The raw data required to reproduce these findings are available upon request to any of the authors. 404
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References
[22] B. Feldman, S. Park, M. Haverty, S. Shankar, S. Dunham, Physica Status Solidi B 247 (2010) 1791. [23] N. Lanzillo, Journal of Applied Physics 121 (2017) 175104. [24] Y. Zhou, S. Sreekala, P. Ajayan, S. Nayak, Journal of Physics: Condensed Matter 20 (2008) 095209. [25] B. Feldman, S. Dunham, Applied Physics Letters 95 (2009) 222101. [26] N. Kharche, S. Manjari, Y. Zhou, R. Geer, S. Nayak, Journal of Physics Condensed Matter 23 (2011) 085501. [27] S. Jones, A. Sanchez-Soares, J. Plombon, A. Kaushik, R. Nagle, J. Clarke, J. Greer, Physical Review B 92 (2015) 115413. [28] J. Roberts, A. Kaushik, and J. Clarke, IEEE International Interconnect Technology Conference p. 341 (2015). [29] N. Lanzillo, T. Standaert, C. Lavoie, Journal of Applied Physics 121 (2017) 194301. [30] S. Savrasov, D. Savrasov, Physical Review B 54 (1996) 16487. [31] Z. Lin, L. Zhigilei, Physical Review B 77 (2008) 075133. [32] K. Sankaran, S. Clima, M. Mees, G. Pourtois, ECS Journal of Solid State Science and Technology 4 (2015) N3127. [33] N. Lanzillo, J. Thomas, B. Watson, M. Washington, S. Nayak, Proceedings of the National Academy of the Sciences 111 (2014) 8712. [34] A. Simbeck, N. Lanzillo, N. Kharche, M. Verstraete, S. Nayak, ACS Nano 6 (2012) 10449. [35] T. Zhou, N. Lanzillo, P. Bhosale, D. Gall, R. Quon, AIP Advances 8 (2018) 055127. [36] Atomistix Toolkit version 2016.0, QuantumWise A/S, URL www.quantumwise.com. [37] J. Soler, E. Artache, J. Gale, A. Garcia, J. Junquera, P. Ordejon, D. Sanchez-Portal, Journal of Physics: Condensed Matter 14 (2002) 2745. [38] M. Brandbyge, J. Mozos, P. Ordejon, J. Taylor, K. Stokbro, Physical Review B 65 (2002) 165401. [39] A. Becke, M. Roussel, Physical Review A 39 (1989) 3761. [40] F. Tran, P. Blaha, Physical Review Letters 102 (2009) 226401. [41] H. Dixit, C. Niu, M. Raymond, V. Kamineni, R. Pandey, A. Konar, J. Fronheiser, A. Carr, P. Oldiges, P. Adusumilli, et al., IEEE Transactions on Electron Devices 64 (2017) 3775. [42] N. Lanzillo, H. Dixit, E. Milosevic, C. Niu, A. Carr, P. Oldiges, M. Raymond, J. Cho, T. Standaert, V. Kamineni, Journal of Applied Physics 123 (2018) 154303. [43] L. Vanasupa, Y.-C. Joo, P. Besser, Journal of Applied Physics 85 (1999) 2583. [44] C. Lingk, M. Gross, W. Brown, Applied Physics Letters 74 (1999) 682. [45] O. Chyan, T. Arunagiri, T. Ponnuswamy, Journal of the Electrochemical Society 150 (2003) C347. [46] G.-S. Park, Y. Kim, S. Park, X. Li, S. Heo, M.-J. Lee, M. Chang, J. Kwon, M. Kim, U.I. Chung, et al., Nature Communications 4 (2013) 2382. [47] Y. Ze-Jin, G. Yun-Dong, L. Jin, L. Jin-Chao, D. Wei, C. Xin-Lu, Y. Xiang-Dong, Chin. Phys. B. 19 (2010) 077102. [48] S.M. Rossnagel, A. Sherman, F. Turner, J. Vac. Sci. Tech. B. 18 (2000) 2016. [49] K. Schep, P. Kelly, G. Bauer, Physical Review B 57 (1998) 205406.
[1] International Technology Roadmap for Semiconductors (ITRS), Interconnects Section, Semiconductor Industry Associate (2013). [2] J.-C. Chen, N. LiCausi, E. Ryan, T. Standaert, and G. Bonilla, Interconnect Technology Conference / Advanced Metallization Conference (IITC/AMC) (2016). [3] N. Lanzillo, K. Motoyama, T. Hook, and L. Clevenger, IEEE International Interconnect Technology Conference pp. 70–72 (2018a). [4] T. Standaert, G. Beique, H.-C. Chen, S.-T. Chen, B. Hamieh, J. Lee, P. McLaughlin, J. McMahon, Y. Mignot, F. Mont, et al., Interconnect Technology Conference / Advanced Metallization Conference (IITC/AMC) (2016). [5] T. Nogami, X. Zhang, J. Kelly, B. Briggs, H. You, R. Patlolla, H. Huang, P. McLaughlin, J. Lee, H. Shobha, et al., Symposium on VLSI Technology pp. T148–T149 (2017). [6] P. Bhosale, J. Maniscalco, N. Lanzillo, T. Nogami, D. Canaperi, K. Motoyama, H. Huang, P. McLaughlin, R. Shaviv, M. Stolfi, et al., IEEE International Interconnect Technology Conference pp. 43–45 (2018). [7] H. Huang, N. Lanzillo, T. Standaert, K. Motoyama, C. Yang, H. Shobha, J. Maniscalco, T. Nogami, J. Li, T. Spooner, et al., IEEE International Interconnect Technology Conference pp. 13–15 (2018). [8] K. Motoyama, O. van der Straten, J. Maniscalco, H. Huang, Y. Kim, J. Choi, J. Lee, C.-K. Hu, P. McLaughlin, T. Standaert, et al., IEEE International Interconnect Technology Conference pp. 40–42 (2018). [9] C.-C. Yang, T. Spooner, W. Wang, J. Maniscalco, P. McLaughlin, C.-K. Hu, E. Liniger, T. Standaert, D. Canaperi, R. Quon, et al., 2016 IEEE International Interconnect Technology Conference (2016). [10] C.-C. Yang, T. Spooner, P. McLaughlin, R. Quon, T. Standaert, D. Edelstein, IEEE Electron Device Letters 38 (2017) 115. [11] N. Lanzillo, O. Restrepo, P. Bhosale, E. Cruz-Silva, C.-C. Yang, B. Kim, T. Spooner, T. Standaert, C. Child, G. Bonilla, et al., Applied Physics Letters 112 (2018) 163107. [12] M. Hall, B. Hickey, M. Howson, C. Hammond, M. Walker, D. Wright, D. Greig, N. Wiser, Journal of Physics: Condensed Matter 4 (1992). [13] B. Elsafi, F. Trigui, Z. Fakhfakh, Journal of Applied Physics 109 (2011). [14] T. Aaltonen, P. Alen, M. Ritala, M. Leskela, Chemical Vapor Deposition 9 (2003) 45. [15] O.-K. Kwon, J.-H. Kim, H.-S. Park, S.-W. Kang, Journal of the Electrochemical Society 151 (2004) G109. [16] K.-M. Yin, L. Chang, F.-R. Chen, J.-J. Kai, C.-C. Chiang, G. Chuang, B. Ding, P. Chin, H. Zhang, F. Chen, Thin Solid Films 388 (2001) 27. [17] H. Wu, X. Li, M. Wu, F. Huang, Z. Yu, H. Qian, IEEE Electron Device Letters 35 (2014) 39. [18] X. Zhong, I. Rungger, P. Zapol, H. Nakamura, Y. Asai, O. Heinonen, Physical Chemistry Chemical Physics 18 (2016) 7502. [19] A. McCoy, J. Bogan, A. Brady, G. Hughes, Thin Solid Films 597 (2015) 112. [20] M. Cesar, D. Liu, D. Gall, H. Guo, Physical Review Applied 2 (2014) 044007. [21] M. Cesar, D. Gall, H. Guo, Physical Review Applied 5 (2016) 054018.
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Electron Transport Across Cu/Ta(O)/Ru(O)/Cu Interfaces in Advanced Vertical Interconnects
T
⁎
Nicholas A. Lanzilloa, , Benjamin D. Briggsa, Robert R. Robisona, Theo Standaerta, Christian Lavoieb a b
IBM Research at Albany Nanotech, 257 Fuller Road, Albany, NY 12203 USA IBM T.J. Watson Research Center, 1101 Kitchawan Road, Yorktown Heights, NY 10598 USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Interconnects Via resistance Oxidation Metal oxides Electron transport
The vertical resistance of Cu/Ta/Ru/Cu stacks is calculated using a combination of first-principles density functional theory (DFT) and a Non-Equilibrium Green’s Function (NEGF) formalism. The effects of oxidizing either one or both of the Ta and Ru layers are analyzed. These oxides can be either metallic (TaO and RuO2) or insulating (Ta2O5) in nature. Simulations indicate that for the metallic oxides, the presence of RuO2 results in more electron scattering than TaO. Complete oxidation of both Ta/Ru layers results in a ≈ 3× increase in resistance for Cu/TaO/RuO2/Cu relative to the un-oxidized structure, and a ≈ 8x increase in resistance for Cu/ Ta2O5/RuO2/Cu relative to the un-oxidized structure. Electron transmission/reflection coefficients as well as values of total resistance are reported for each interface structure. These results highlight the importance of identifying and controlling oxygen contamination in high-volume manufacturing in order to obtain low resistance vertical interconnects and favorable device performance.
1. Introduction The nature of electron scattering in vertical interconnects is crucial in determining overall device performance in advanced semiconductor technology nodes[1–3]. Vertical interconnects (referred to as vias) connect adjacent levels of horizontal interconnect wiring and are of crucial importance in rapidly delivering electrical signals to and from the active regions (transistors) to large-width metal levels higher up in the stack. In the recently developed 7nm technology node, back-end-ofline (BEOL) interconnect trenches were filled first with a thin layer of TaN (barrier material) and then by a thin layer of Ru (wetting material) before filling with Cu conductor[4–8]. The TaN and Ru layers served as diffusion barriers and wetting layers, respectively, for electroplated Cu in the interconnect trench. More recently, proposed integration schemes replace TaN diffusion barriers with pure Ta layers combined with in-situ dielectric nitridation, resulting in significantly lower via resistance[9–11]. A representative via structure is depicted schematically in Fig. 1 for a typical dual-damascene process flow. M(x) is a level of horizontal interconnect wiring and M(x+1) is the level directly above it. Both M(x) and M(x+1) are embedded in an inter-level dielectric (ILD) material. In order for an electron to get from the M(x) level to the M(x+1) level, it must penetrate thin (≈ 1nm )
⁎
Corresponding author. E-mail address: [email protected] (N.A. Lanzillo).
https://doi.org/10.1016/j.commatsci.2018.11.040 Received 22 October 2018; Accepted 21 November 2018 0927-0256/ © 2018 Published by Elsevier B.V.
layers of both Ta and Ru. The presence of these thin metallic layers increases the via resistance due to interfacial scattering as well as the shifts in electronic potential when transitioning from one region to another. This type of scattering is reminiscent of electron scattering in thin Cu/Co multilayers known for their magnetoresistive properties [12,13], except that Cu, Ru and Ta are all non-magnetic. Furthermore, since oxygen contamination poses a significant risk in many modern fabrication environments and oxygen incorporation introduces additional scattering sites metallic multi-layered stack, understanding the impact of oxygenation on via resistance is paramount from the standpoints of both fundamental physics as well as technology development. There are several possible sources of oxygen contamination in BEOL metals and interconnects. Any time a wafer or substrate is moved between different tools/chambers, the resulting air break offers the largest opportunity for oxidation to occur. If etching, barrier deposition, liner deposition and electroplating each occur in different tools, there are then three air breaks before an interconnect trench is even filled with Cu. Additional sources of oxygen include precursors to the atomic layer deposition (ALD) of barrier/liner metals[14,15,48], diffusion of oxygen from the surrounding dielectrics[10], and diffusion of oxygen along grain boundaries in Cu[16]. Since Ta is a known oxygen scavenger [17,18], any residual oxygen near the via in the Cu is likely to diffuse
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Fig. 1. Schematic 2D illustration of a vertical interconnect (via) connecting two adjacent levels of horizontal interconnect wiring, M(x) and M(x+1). Arrows indicate electrons traveling through the Cu/Ta/Ru/Cu interface.
on each atom were less than 0.05 eV/Å. The exchange-correlation functional was taken to be the generalized-gradient approximation (GGA) for all structures except for those containing Ta2O5, which required the use of a hybrid meta-GGA functional[39,40] in order to correctly predict the band gap. In the meta-GGA scheme, the exchange functional is given by the expression:
toward the barrier/liner interface. In addition, previous studies have shown that the formation of tantalum oxide is thermodynamically favorable to the formation of copper oxide at the Cu/Ta interface[16]. Spectroscopic analysis has also indicated that RuO2 can form from Ru thin films exposed to atomic oxygen even at room temperature[19]. In the case of oxidized Ta/Ru layers at an interconnect via, electrons would have to travel through the Cu/Ta(O)/Ru(O)/Cu interface. There exists an extensive body of work describing electron scattering mechanisms in interconnect metals from a first-principles perspective, including grain-boundary scattering[20–23], surface scattering[24–29] and electron-phonon scattering[30–34]. Only recently have ab initio methods been applied to study electron transport in vertical interconnects[11,35]. Furthermore, while the effects of Cu oxidation have been studied with respect to surface scattering[27], the impact of oxidized interfaces in vertical interconnects remains an open topic. In this work, the impact of oxidation on the barrier/liner metals at interconnect via is evaluated using first-principles calculations based on density functional theory and a Non-Equilibrium Green’s function (NEGF) formalism. Simulations suggest that the presence of RuO2 is more detrimental to via resistance than TaO, while the total via resistance increases by no more than ≈ 3× when both TaO and RuO2 are present. While both RuO2 and TaO are metallic in nature, Ta2O5 is an insulator which drastically impacts electron transport across the interface structures considered here. In particular, the presence of Ta2O5 results in a ≈ 8x increase in via resistance for Cu/Ta2O5/RuO2/Cu relative to the pristine, non-oxidized structure.
3c − 2 vxTB (→ r ) = cvxBR (→ r)+ π
4τ (→ r) 6ρ (→ r)
(1)
where the superscript “TB” refers to the Tran and Blaha functional[40] and the superscript “BR” refers to Becke-Roussel exchange functional [39]. τ (→ r ) is the kinetic energy density written in terms of Kohn-Sham r ) is the electronic density. The parameter c is adorbitals and ρ (→ justable in the model. It can either be self-consistently calculated according to the formula:
c=α+β
1 Ω
∫Ω
∇ρ (→ r) → dr ρ (→ r)
(2)
or simply held fixed so as to reproduce the experimentally-determined band gap. In self-consistent Eq. (2), Ω is the volume of the computational unit cell and α and β are constants with values of − 0.012 and 1.023 Bohr1/2, respectively. For the interface structure containing Ta2O5, the meta-GGA is only applied along the z-direction in which Ta atoms are present, while the regular GGA is applied elsewhere. In the NEGF scheme for the two-terminal set up, the electron conductance (per spin) is given by the linear response expression at zerobias (V=0):
2. Computational Details Simulations for all structures were performed using the QuantumWise Atomistix Toolkit[36–38]. The simulations employed a cutoff energy of 75.0 Hartree and k-point sampling of 5x5x1 for geometry optimizations and 11x11x101 for transmission calculations. By considering lateral k-point sampling densities of 1x1, 3x3, 5x5, 7x7, 9x9 and 11x11, we find the values of electron transmission to be wellconverged (changes less than 2%) for an 11x11 k-point grid. Likewise, we have checked k-point sampling along the direction of transport to tightly-converged (changes less than 1%) using 101 mesh points. The high k-point sampling density along the direction of transport is required in this particular software package in order to accurately describe the electronic structure in the semi-infinite electrode unit cells, which extend semi-periodically in either the positive or negative direction. The geometries of all structures were relaxed until the forces acting
G=
I 1 e2 = = Σi Ti ⎛⎜EF , V = 0⎞⎟ V R h ⎠ ⎝
(3)
where EF is the Fermi Energy and Ti is the transmission for the ith electronic channel. The Fermi Energy is calculated self-consistently for the interface structure(s). Since the electrode regions are metallic, as well as the Ta, TaO, Ru and RuO2 regions, transport is considered only at the EF . While Ta2O5 is not metallic, we restrict our analysis to transport at EF for consistency when comparing to the other interface structures. Given the output transmission (conductance), the corresponding resistance is calculated using Ohm’s law and then normalized by the cross-sectional area of the supercell. The final results are presented as specific resistivities with units of Ωcm2 , following the established literature convention[11,20,21,23,41,42]. Cu, Ta and Ru were considered in the face-centered-cubic (FCC), 399
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calculations are well-converged by placing 9 atoms of Cu on either side of the central scattering region. The first three atomic layers of Cu in the central region, as well as the electrodes, are held fixed at their bulk lattice positions while the remaining atoms in the supercell are allowed to relax. While electron transport is “horizontal” as calculated from the left electrode to the right electrode depicted in Fig. 2 , the terminology “vertical resistance” is used throughout this work to refer to the direction of current flow at a via in an actual integrated circuit. In addition, electron transmission was calculated for the Cu/Ta/Ru/Cu structure with the lateral supercell dimensions doubled in size, where it was confirmed that the area-normalized resistance was unchanged.
body-centered-cubic (BCC) and hexagonal-close-packed (HCP) crystal structures, respectively. The interface structures are constructed such that electron transport is along Cu(111), Ta(100) and Ru(0001). The (111) orientation of Cu is motivated by experimental observations of (111) sidewall texture in damascene interconnects[43–45]. The metal oxides TaO, Ta2O5 and Ru2 crystallize in the tetragonal, orthorhombic and rutile crystal structures, respectively. Electron transport was calculated along the (100) direction of each metallic oxide. In each case, these orientations result in minimal interface strain and lattice mismatch between the adjacent crystals while keeping the sizes of the computational supercells reasonable (<200 atoms.) The Cu electrodes are held fixed at the bulk geometry, while the lattice strain of the interfacial metals is kept below 5% for all structures. In particular, the Ta, Ru, TaO, RuO2 and Ta2O5 layers are strained 4.8%, 3.7%, 1.3%, 1.4% and 2.8%, respectively. Interface structures were generated by first creating a semi-infinite planar interface between Cu(111) and either Ta or TaO such that Cu (111) extends infinitely in the negative x-direction and Ta(O) extends infinitely in the positive x-direction. This interface was then truncated after 1nm of Ta(O), and the resulting structure was interfaced with either Ru or RuO2, such that the Ru(O) region extends infinitely in the positive x-direction. Again, the resulting interface was truncated after 1nm of Ru(O). Lastly, the resulting structure was interfaced with a Cu (111) region, which extends semi-infinitely in positive x-direction. In this manner, each Cu electrode region extends infinitely in either the positive or negative x-direction, while finite 1nm thick regions of Ta(O) and Ru(O) are sandwiched in between. Cross-sectional images of the two-terminal setups for the metallic interface configurations considered are depicted in Fig. 2. The reference structure Cu/Ta/Ru/Cu is shown in Fig. 2(a), while structures containing either RuO2 or TaO are depicted in Fig. 2(b) and (c), respectively. The structure in which both RuO2 and TaO are present is depicted in Fig. 2(d), and this represents the “worst-case” scenario in which the entire barrier/liner region is oxidized. All supercells have cross-sectional areas of 5.11Å × 5.11Å . The electrode regions are 3atoms thick in the z-direction, and we find that the transport
3. Results and Discussion Since the electron transport characteristics depend on the nature of the electronic states at the Fermi level, it is worth examining the electronic structure of the various metals (Ta, Ru) and their oxides (TaO, RuO2). The calculated electronic density of states are shown in Fig. 3. It is unsurprising that both Ta and Ru show non-zero density of states at the Fermi Energy in Fig. 3 (a) and (b) since these are both metallic in the bulk phase. Both TaO and RuO2 also show metallic behavior in the bulk, as depicted in Fig. 3(c) and (d). These results are consistent with previous published work indicating that both TaO and RuO2 are metallic in nature[46,47], and confirm the validity of the computational approach adopted here in describing these materials. Due to the metallic nature of both TaO and RuO2, the electron scattering is not expected to be impacted as much as it would if there were an insulating barrier. The k-space-resolved transmission spectra at the Fermi Energy for the four structures shown in Fig. 2 are depicted in Fig. 4. For the reference structure (Cu/Ta/Ru/Cu), the transmission spectra in Fig. 4(a) shows a distinct circular symmetry manifest as a ring surrounding the center of the Brillouin Zone, which corresponds to the (nearly) spherical Fermi surface of Cu. The presence of the hightransmission regions extending horizontally along kA in Fig. 4(a) is the
Fig. 2. The two-terminal computational supercells used for the NEGF calculations for the metallic interfaces: (a) Cu(111)/Ta(100)/Ru(0001)/Cu(111) (b) Cu(111)/ Ta(100)/RuO2(100)/Cu(111) (c) Cu(111)/TaO(100)/Ru(0001)/Cu(111) and (d) Cu(111)/TaO(100)/RuO2(100)/Cu(111). 400
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(a)
(b) Ru
DOS (1/eV/atom)
DOS (1/eV/atom)
Ta
E-EF (eV)
E-EF (eV)
(d) TaO
DOS (1/eV/atom)
DOS (1/eV/atom)
(c)
Ta
O E-EF (eV)
RuO2
O
Ru
E-EF (eV)
Fig. 3. The electronic density of states calculated for bulk (a) Ta (b) Ru (c) TaO and (d) RuO2.
direct result of the strain induced in Ta when interfaced with Cu. In order to match the Cu(111) lattice, the Ta(100) lattice vector is stretched along the a-direction and compressed along the b-direction. This results in less dispersion along the stretched direction (a) and more dispersion along the compressed direction (b). Taking the transmission at the Fermi Energy and converting to an area-normalized value of resistance, we obtain a value of γ = 34.24 × 10−12Ωcm2 for this reference
structure. For the Cu/Ta/RuO2 structure, the transmission spectra shown in Fig. 4(b) shows the same dispersion effects as in Fig. 4.(a), but substantially reduced in magnitude. This is purely the result of replacing Ru with RuO2, which reduces overall electron transmission across the Cu/Ta/Ru(O)/Cu interface by 60% relative to the pristine Cu/Ta/Ru/ Cu interface. The resistance for this structure is 86.04 × 10−12Ωcm2 . For
Fig. 4. The k-resolved transmission spectra for (a) Cu(111)/Ta(100)/Ru(0001)/Cu(111) (b) Cu(111)/Ta(100)/RuO2(100)/Cu(111) (c) Cu(111)/TaO(100)/Ru (0001)/Cu(111) and (d) Cu(111)/TaO(100)/RuO2(100)/Cu(111). 401
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(c), there are also regions with high amplitude near the right electrode, corresponding to effective transmission across the metallic interfaces. The Cu/Ta/RuO2/Cu and Cu/TaO/RuO2/Cu structures, on the other hand, show very low amplitudes near the right electrode, indicating poor transmission across the interfaces. Next, the worst-case scenario of complete oxidation of both Ta and Ru layers is considered but with the insulating Ta2O5 rather than the metallic TaO. Bulk Ta2O5 has a calculated band gap of approximately 2.5 eV[46] and is expected to impact electron transmission across the interface much more strongly than metallic TaO. The geometric structure of the Cu(111)/Ta2O5(100)/RuO2(100)/Cu(111) interface is shown in Fig. 6(a), with approximately 1nm of both Ta2O5 and RuO2 included. The band gap is bulk Ta2O5 is accurately reproduced using a metaGGA exchange-correlation functional as implemented in the the ATK software package[36]. In particular, the value of the band gap varies with the choice of the adjustable c-parameter as shown in Figure Fig. 6(b). A value of c=2.0 accurately reproduces a band gap of 2.5 eV and is used for subsequent electron transport calculations. In Fig. 6(c), the k-resolved transmission spectra is plotted. It is evident in this plot that there are very few regions in k-space with high electron transmission. The resulting value of normalized interface resistance for this structure is γ = 266.2 × 10−12Ωcm2 , which is nearly an order of magnitude larger than the corresponding value for the pristine Cu/Ta/Ru/Cu interface. It is worth noting that we calculated the electron transport across the Cu/Ta2O5/Ru/Cu interface using values of c ranging from 1.5 to 2.5 and found no significant variation in the calculated transmission. This indicates that small changes in the electronic structure (and band gap) of the Ta2O5 region have a minimal impact on the resulting electron transport. The transmission eigenstates corresponding to the largest three transmission eigenvalues calculated at the Γ -point of the Cu/Ta2O5/Cu interface are plotted in Fig. 7. The first and third eigenstates (Fig. 7(a) and (c)) show significant reflection at the Cu/Ta2O5 interface, while the second eigenvalue shows significant reflection at the Ta2O5/RuO2 interface. None of the
the Cu/TaO/Ru/Cu interface, while the transmission spectra depicted in Fig. 4(c) doesn’t feature any of the high-transmission channels in the corners, it does show the preservation of the some of the circular symmetry surrounding the Γ -point, and likewise the transmission is only reduced by 33% relative to the Cu/Ta/Ru/Cu structure. The value of resistance for this structure is 51.29 × 10−12Ωcm2 . Lastly, for the transmission spectra in Fig. 4(d), the circular symmetry surrounding the Γ -point is largely destroyed and there are no high-transmission channels visible anywhere in the Brillouin Zone. The structure corresponding to this structure (Cu/TaO/RuO2/Cu) shows the lowest electron transmission across the interface (reduced by 67% relative to Cu/ Ta/Ru/Cu) and likewise the highest value of resistance out of any of the four metallic interfaces considered: 104.78 × 10−12Ωcm2 . In order to gain additional insight regarding the interfacial scattering mechanisms in the various Cu/Ta(O)/Ru(O)/Cu structures, we consider the transmission eigenstates calculated at the Γ -point for each metallic interface structure. Since transmission is calculated from the left electrode to the right electrode, the matrix t represents the coupling between the incoming states from the left electrode and the outgoing states at the right electrode. Diagonalization of the matrix t †t gives the transmission eigenvalues, which describe how many channels contribute to the total transmission as well as their relative magnitudes. The eigenstates represent the superposition of both incoming and reflected waves in the left-hand region and the outgoing wave in the right-hand region. In Fig. 5, these eigenstates are plotted for the three largest eigenvalues in each interface structure. The top eigenstate corresponds to the largest eigenvalue while the bottom eigenstate corresponds to the lowest of the three eigenvalue. We note that one could chose specific k-points based on the plots in Fig. 3 that show either vary high or very low transmission, but these k-points are different for each structure. In light of this, we examine the eigenstates at the Γ -point of each structure as a common point of comparison. All four structures exhibit localized regions with high amplitude near the left electrode. The interference effects generated by the superposition of the incoming and reflected waves are clearly visible. For the Cu/Ta/Ru/Cu and Cu/TaO/Ru/Cu structures shown in Fig. 5(a) and
(a) Cu/Ta/Ru/Cu
(b) Cu/Ta/RuO2/Cu
(c) Cu/TaO/Ru/Cu
(d) Cu/TaO/RuO2/Cu
Amplitude (
0.0
0.25
Å )
0.5
Fig. 5. The transmission eigenstates at the Γ -point calculated for the three largest eigenvalues at each interface: (a) Cu(111)/Ta(100)/Ru(0001)/Cu(111) (b) Cu (111)/Ta(100)/RuO2(100)/Cu(111) (c) Cu(111)/TaO(100)/Ru(0001)/Cu(111) and (d) Cu(111)/TaO(100)/RuO2(100)/Cu(111). 402
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(a)
(b)
Ta2O5 Band Gap (eV)
(c)
c Parameter Fig. 6. (a) The geometry of the Cu(111)/Ta2O5/RuO2/Cu(111) interface (b) The band gap of bulk Ta2O5 calculated using the meta-GGA exchange-correlation functional as a function of the adjustable c-parameter and (c) The k-space resolved transmission spectra of the Cu/Ta2O5/Cu interface.
the cross-sectional area (perpendicular to the direction of electron transport) of the computational supercell. In addition, the transmission values in Table 1 represent the composite transmission spectra for all modes present at the Fermi Energy. Transmission is converted to re2e 2 1 sistance using the equation for conductance: G = h T = R and then divided by the cross-sectional area to obtain γ . In addition, a reference calculation of electron transport along bulk Cu(111) yields γ = 10.59 × 10−12Ωcm2 , which can then be used to calculate the normalized transmission coefficients using the formula:
eigenstates show significant transmission across the full interface. This visually explains the high resistance across the interface as the direct result of low electron transmission. For comparison, the calculated values of electron transmission at the Fermi Energy (T @ EF), the cross-sectional area of each computational supercell, the area-normalized vertical resistance (γ ) and the normalized transmission coefficient (t) for each structure are listed in Table 1. The raw values of calculated electron transmission (T @ EF) are not normalized by area and can be arbitrarily increased by increasing
Fig. 7. The eigenstates corresponding to the highest three eigenvalues ((a) through (c)) for the Cu/Ta2O5 structure calculated at the Γ -point.
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24p
T @ EF
Area [Å2]
γ (× 10−12Ωcm2 )
t
r
Cu(111) Cu/Ta/Ru/Cu Cu/Ta/RuO2/Cu Cu/TaO/Ru/Cu Cu/TaO/RuO2/Cu Cu/Ta2O5/RuO2/Cu
0.79 0.988 0.393 0.659 0.323 0.330
9.24 26.13 26.13 26.13 26.13 67.89
10.59 34.24 86.04 51.29 104.78 266.24
1.0 0.31 0.12 0.21 0.10 0.04
0.0 0.69 0.88 0.79 0.90 0.96
t=
γCu γinterface
30p 36p
48p
60p
Cu/Ta2O5/RuO2/Cu Cu/TaO/RuO2/Cu Cu/Ta/Ru/Cu
V
Structure
cal Resistance [ȍ]
Table 1 The total transmission at the Fermi Energy (T @ EF), the cross-sectional area of each supercell, the area-normalized vertical resistance (γ ) and the normalized transmission (t) and reflection (r) coefficients for each interface structure. In each structure, the Ta(O) and Ru(O2) regions are approximately 1nm thick.
(4)
where the corresponding reflection coefficients could be calculated by taking r = 1 − t . The value of bulk ballistic conductance for Cu obtained here in the appropriate units (10.59 × 10−12Ωcm2 → 1 0.94 × 1015 2 ) lies within the range previously reported in the literaΩm
1
Contact Area [nm2] Fig. 8. The interface contribution to the total vertical resistance as a function of contact area for the reference structure Cu/Ta/Ru/Cu and the two ”worst-case” structures Cu/TaO/RuO2/Cu and Cu/Ta2O5/RuO2/Cu.
1
ture(0.99 × 1015 2 to 1.2 × 1015 2 )[49,23]. Ωm Ωm Inspection of the numbers indicates that the presence of even a pristine Cu/Ta/Ru/Cu interface increases the via resistance by ≈ 3× relative to the barrier-free Cu(111) bulk. The formation of TaO increases the resistance by ≈ 1.5x relative to Cu/Ta/Ru/Cu, while the formation of RuO2 increases the resistance by ≈ 2.5x . The two worstcase scenario structures, corresponding to complete oxidation of both Ta and Ru layers, show resistance increased by either ≈ 3× or ≈ 8x , depending on the stoichiometry of the tantalum oxide. Inspection of the normalized reflection and transmission coefficients also highlights the dramatic differences between the various structures. These coefficients are cumulative in that they represent transmission/ reflection for the entire multi-interface structure, as opposed to transmission/reflection at a particular interface. For the case of pristine Cu/ Ta/Ru/Cu, 69% of incoming electrons are reflected relative to the baseline interface-free case of Cu(111). Inclusion of TaO increases this number to 79%, while inclusion of RuO2 increases this number of 88%. The inclusion of both TaO and RuO2 results in a net reflection coefficient of 90%, which is only marginally higher than the case of just including RuO2. Replacing TaO with Ta2O5 results in 96% of electrons getting reflected and only 4% of incoming electron successfully penetrating that Cu/Ta2O5/RuO2/Cu interface structure. In order to evaluate the actual impact on vertical resistance in realistically-sized interconnects, the values of interface resistance in Table 1 are divided by an effective contact area and plotted in Fig. 8 over a range of contact areas from 1000nm2 down to 100nm2. To put these contact areas into perspective, consider the recentlydeveloped 7nm technology node[4], in which BEOL interconnects are fabricated with a pitch of 36nm. Assuming symmetric line-to-line spacing, these interconnects would have a width of 18nm. A square-shaped vertical interconnect which joins two adjacent metal levels would then have an effective contact area of approximately 18nm × 18nm = 324nm2 . Similarly, estimates of effective contact areas for several representative BEOL pitches are shown as shaded regions in Fig. 8, including pitches of 60nm, 48nm, 36nm, 30nm and 24nm. For large enough dimensions, including the 48p and 60p cases, even the worst-case oxidation of the via results in a vertical resistance less than 50Ω. Beginning at 36p, the worst-case oxidation of the via results in values of vertical resistance approaching 100Ω, while for 24p structures the values are larger than 250Ω. Clearly, as physical dimensions in the BEOL continue to shrink, controlling and minimizing oxidization in vertical interconnects becomes increasingly important in maintaining low vertical resistance. As expected, the impact of electron scattering at the interfaces becomes more pronounced as the effective contact area is reduced. For the
reference structure (Cu/Ta/Ru/Cu) with no oxidation, the vertical resistance never exceeds 50Ω even down to a 100nm2 contact area. The Cu/TaO/RuO2/Cu structure results in a ≈ 3× higher resistance than the reference structure at a given cross-sectional area, which translates to vertical resistance values as high as 50-100Ω for contact areas for 200nm2 or smaller. The worst-case structure Cu/Ta2O5/RuO2/Cu results in dramatically high values of vertical resistance, which rapidly approach several hundred Ohms as the effective contact area shrinks to below a few hundred nm2. These results show that via resistance can fluctuate by as much as an order of magnitude depending on the size of the metal-to-metal contact area and the degree of oxidation in the barrier/liner materials.
4. Conclusion This work calculates effective electron transmission/reflection coefficients as well as values of specific resistivity for oxidized, Cubased vertical interconnect structures far more complicated than the Cu-based interfaces previously reported in the literature (such as twin grain boundaries and pristine Cu interface structures), thereby extending the applicability of NEGF calculations to realistic structures likely to be found in modern fabrication environments. The scattering mechanisms considered in this work include both interfacial electron scattering as well as scattering due to modulations in electronic potential in the intermediate metal regions. The impact of tantalum and ruthenium oxidation on the vertical resistance of Cu/Ta/Ru/Cu stacks has been evaluated using first-principles calculations and an NEGF formalism. While both TaO and RuO2 are metallic in nature, layers of either increase the vertical resistance by 1.5x and 2.5x, respectively, relative to the reference Cu/Ta/Ru/Cu structure. When both TaO and RuO2 are present in the stack, the vertical resistance is increased by ≈ 3×. The formation of insulating Ta2O5, however, results in a dramatic ≈ 8x increase in vertical resistance relative to the pristine Cu/Ta/Ru/Cu structure. These results indicate that interface quality and composition must be tightly controlled in order to minimize vertical resistance in next-generation interconnect technology. The authors would like to thank the Rensselaer Polytechnic Institute (RPI) Computational Center for Innovation (CCI) for providing computational resources. This work was performed by the Research Alliance Teams at various IBM Research and Development Facilities. The raw data required to reproduce these findings are available upon request to any of the authors. 404
Computational Materials Science 158 (2019) 398–405
N.A. Lanzillo et al.
References
[22] B. Feldman, S. Park, M. Haverty, S. Shankar, S. Dunham, Physica Status Solidi B 247 (2010) 1791. [23] N. Lanzillo, Journal of Applied Physics 121 (2017) 175104. [24] Y. Zhou, S. Sreekala, P. Ajayan, S. Nayak, Journal of Physics: Condensed Matter 20 (2008) 095209. [25] B. Feldman, S. Dunham, Applied Physics Letters 95 (2009) 222101. [26] N. Kharche, S. Manjari, Y. Zhou, R. Geer, S. Nayak, Journal of Physics Condensed Matter 23 (2011) 085501. [27] S. Jones, A. Sanchez-Soares, J. Plombon, A. Kaushik, R. Nagle, J. Clarke, J. Greer, Physical Review B 92 (2015) 115413. [28] J. Roberts, A. Kaushik, and J. Clarke, IEEE International Interconnect Technology Conference p. 341 (2015). [29] N. Lanzillo, T. Standaert, C. Lavoie, Journal of Applied Physics 121 (2017) 194301. [30] S. Savrasov, D. Savrasov, Physical Review B 54 (1996) 16487. [31] Z. Lin, L. Zhigilei, Physical Review B 77 (2008) 075133. [32] K. Sankaran, S. Clima, M. Mees, G. Pourtois, ECS Journal of Solid State Science and Technology 4 (2015) N3127. [33] N. Lanzillo, J. Thomas, B. Watson, M. Washington, S. Nayak, Proceedings of the National Academy of the Sciences 111 (2014) 8712. [34] A. Simbeck, N. Lanzillo, N. Kharche, M. Verstraete, S. Nayak, ACS Nano 6 (2012) 10449. [35] T. Zhou, N. Lanzillo, P. Bhosale, D. Gall, R. Quon, AIP Advances 8 (2018) 055127. [36] Atomistix Toolkit version 2016.0, QuantumWise A/S, URL www.quantumwise.com. [37] J. Soler, E. Artache, J. Gale, A. Garcia, J. Junquera, P. Ordejon, D. Sanchez-Portal, Journal of Physics: Condensed Matter 14 (2002) 2745. [38] M. Brandbyge, J. Mozos, P. Ordejon, J. Taylor, K. Stokbro, Physical Review B 65 (2002) 165401. [39] A. Becke, M. Roussel, Physical Review A 39 (1989) 3761. [40] F. Tran, P. Blaha, Physical Review Letters 102 (2009) 226401. [41] H. Dixit, C. Niu, M. Raymond, V. Kamineni, R. Pandey, A. Konar, J. Fronheiser, A. Carr, P. Oldiges, P. Adusumilli, et al., IEEE Transactions on Electron Devices 64 (2017) 3775. [42] N. Lanzillo, H. Dixit, E. Milosevic, C. Niu, A. Carr, P. Oldiges, M. Raymond, J. Cho, T. Standaert, V. Kamineni, Journal of Applied Physics 123 (2018) 154303. [43] L. Vanasupa, Y.-C. Joo, P. Besser, Journal of Applied Physics 85 (1999) 2583. [44] C. Lingk, M. Gross, W. Brown, Applied Physics Letters 74 (1999) 682. [45] O. Chyan, T. Arunagiri, T. Ponnuswamy, Journal of the Electrochemical Society 150 (2003) C347. [46] G.-S. Park, Y. Kim, S. Park, X. Li, S. Heo, M.-J. Lee, M. Chang, J. Kwon, M. Kim, U.I. Chung, et al., Nature Communications 4 (2013) 2382. [47] Y. Ze-Jin, G. Yun-Dong, L. Jin, L. Jin-Chao, D. Wei, C. Xin-Lu, Y. Xiang-Dong, Chin. Phys. B. 19 (2010) 077102. [48] S.M. Rossnagel, A. Sherman, F. Turner, J. Vac. Sci. Tech. B. 18 (2000) 2016. [49] K. Schep, P. Kelly, G. Bauer, Physical Review B 57 (1998) 205406.
[1] International Technology Roadmap for Semiconductors (ITRS), Interconnects Section, Semiconductor Industry Associate (2013). [2] J.-C. Chen, N. LiCausi, E. Ryan, T. Standaert, and G. Bonilla, Interconnect Technology Conference / Advanced Metallization Conference (IITC/AMC) (2016). [3] N. Lanzillo, K. Motoyama, T. Hook, and L. Clevenger, IEEE International Interconnect Technology Conference pp. 70–72 (2018a). [4] T. Standaert, G. Beique, H.-C. Chen, S.-T. Chen, B. Hamieh, J. Lee, P. McLaughlin, J. McMahon, Y. Mignot, F. Mont, et al., Interconnect Technology Conference / Advanced Metallization Conference (IITC/AMC) (2016). [5] T. Nogami, X. Zhang, J. Kelly, B. Briggs, H. You, R. Patlolla, H. Huang, P. McLaughlin, J. Lee, H. Shobha, et al., Symposium on VLSI Technology pp. T148–T149 (2017). [6] P. Bhosale, J. Maniscalco, N. Lanzillo, T. Nogami, D. Canaperi, K. Motoyama, H. Huang, P. McLaughlin, R. Shaviv, M. Stolfi, et al., IEEE International Interconnect Technology Conference pp. 43–45 (2018). [7] H. Huang, N. Lanzillo, T. Standaert, K. Motoyama, C. Yang, H. Shobha, J. Maniscalco, T. Nogami, J. Li, T. Spooner, et al., IEEE International Interconnect Technology Conference pp. 13–15 (2018). [8] K. Motoyama, O. van der Straten, J. Maniscalco, H. Huang, Y. Kim, J. Choi, J. Lee, C.-K. Hu, P. McLaughlin, T. Standaert, et al., IEEE International Interconnect Technology Conference pp. 40–42 (2018). [9] C.-C. Yang, T. Spooner, W. Wang, J. Maniscalco, P. McLaughlin, C.-K. Hu, E. Liniger, T. Standaert, D. Canaperi, R. Quon, et al., 2016 IEEE International Interconnect Technology Conference (2016). [10] C.-C. Yang, T. Spooner, P. McLaughlin, R. Quon, T. Standaert, D. Edelstein, IEEE Electron Device Letters 38 (2017) 115. [11] N. Lanzillo, O. Restrepo, P. Bhosale, E. Cruz-Silva, C.-C. Yang, B. Kim, T. Spooner, T. Standaert, C. Child, G. Bonilla, et al., Applied Physics Letters 112 (2018) 163107. [12] M. Hall, B. Hickey, M. Howson, C. Hammond, M. Walker, D. Wright, D. Greig, N. Wiser, Journal of Physics: Condensed Matter 4 (1992). [13] B. Elsafi, F. Trigui, Z. Fakhfakh, Journal of Applied Physics 109 (2011). [14] T. Aaltonen, P. Alen, M. Ritala, M. Leskela, Chemical Vapor Deposition 9 (2003) 45. [15] O.-K. Kwon, J.-H. Kim, H.-S. Park, S.-W. Kang, Journal of the Electrochemical Society 151 (2004) G109. [16] K.-M. Yin, L. Chang, F.-R. Chen, J.-J. Kai, C.-C. Chiang, G. Chuang, B. Ding, P. Chin, H. Zhang, F. Chen, Thin Solid Films 388 (2001) 27. [17] H. Wu, X. Li, M. Wu, F. Huang, Z. Yu, H. Qian, IEEE Electron Device Letters 35 (2014) 39. [18] X. Zhong, I. Rungger, P. Zapol, H. Nakamura, Y. Asai, O. Heinonen, Physical Chemistry Chemical Physics 18 (2016) 7502. [19] A. McCoy, J. Bogan, A. Brady, G. Hughes, Thin Solid Films 597 (2015) 112. [20] M. Cesar, D. Liu, D. Gall, H. Guo, Physical Review Applied 2 (2014) 044007. [21] M. Cesar, D. Gall, H. Guo, Physical Review Applied 5 (2016) 054018.
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