Modeling of dielectric reliability in copper damascene interconnect systems under BTS conditions P. Bělský 1, R. Streiter 2, H. Wolf 2, S. E. Schulz 1,2, O. Aubel 3, and T. Gessner 1,2 1 Chemnitz University of Technology, Reichenhainer Str. 70, 09126 Chemnitz, Germany 2 Fraunhofer ENAS, Technologie-Campus 3, 09126 Chemnitz, Germany 3 GLOBALFOUNDRIES Dresden Module One LLC & Co. KG, Wilschdorfer Landstraße 101, 01109 Dresden, Germany Email: petr.belsky@zfm.tu-chemnitz.de
Outline BTS experiments The Haase model Key aspects Basic equations Simulations based on the Haase parameters for the 90 nm data Modifications of the model and parameter fitting Influence of a defect and 2D implementation Simulations with the modified Haase model for the 45 nm data Temperature dependence Analysis of the dependence of lifetime on the electric field Comparison of the Haase-based model with the Poole-Frenkel lifetime model Comparison with another data set from the 45 nm technology Analysis of the second 45 nm data set Summary and conclusions
BTS experiments (90 nm and 45 nm technology) Test structure 90 nm technology Test conditions (90 nm): Constant voltage BTS test Line length (total) 2 cm Line distance 83 nm (estimated from the SEM picture) Bias voltage 40 V Field intensity 4.82 MV/cm Temperature 100 ºC I (A) BTS experiment 90 nm 40 V, 100 C 10-1 10 0 10 1 10 2 10 3 10 4 t (s) Test conditions (45 nm): Constant voltage BTS tests Line length (total) 2 cm Line distance (min.) 50 nm Data set A: Bias voltages 22, 25, 30 V Field intensity (max.) 4.4, 5.0, 6.0 MV/cm Temperature 100 C and 150 C at 22 V Data set B: Bias voltages 20-28 V Field intensity (max.) 4.0 5.6 MV/cm Temperature 100 C
The key aspects of the Haase model One type of shallow immobile neutral traps in the dielectric Conduction by transport of e - in the conduction band and tunneling between traps Injection of electrons from the cathode to the dielectric thermally and by FN tunneling Cu cathode Energy of e - Position φ B FN tunneling Conduction band of the metal Electron Unoccupied trap (neutral) Occupied trap (negatively charged)
Basic equations of the Haase model Electronic transport ρe, Mobile / ρe, Trapped = exp( ETrap, eff / kbt ) ρ e, Tunnel = ρe, Trapped J e = Ve ( ρe, Mobile + ρe, Tunnel ) D ρe, Mobile ρe, Total t = J e Tunneling _ Prob (continuity equation) mobile e - and e - in the traps are in thermodynamic equilibrium a fraction of trapped e - can tunnel (strong E-field dependence) transport in the conduction band tunneling between the traps ρ + e, Total = ρe, Mobile ρe, Trapped (total trapped and mobile e - density) Electric potential: ( ε V ) = q ρe, Total (Poisson equation) Trap generation: ρ Trap t = J e l 1 scat exp E k a, eff ' bte ρ Trap : strong influence on the tunneling probability between the traps Electron scattering length: l scat ρ 1/3 = Trap "An Alternative Model for Interconnect low-k Dielectric Lifetime Dependence on Voltage" G. S. Haase, 46th Annual IEEE International Reliability Physics Symposium Proceedings, p. 556-561, Phoenix, 2008.
Simulations based on the Haase parameters (for 90 nm data) J e (A/cm 2 ) 10 0 10-1 10-2 10-3 model curves: 4.75 MV/cm 4.82 MV/cm 4.90 MV/cm experimental data 10-7 10-5 10-3 10-1 10 1 10 3 10 5 10 7 Time (s) Test conditions: Line length 2 cm Line distance 83 nm Bias 40 V 4.82 MV/cm Temperature 100 ºC Parameters: Trap creation E a = 2.4 ev Trap depth E trap = 0.7 ev 1.1 ev Barrier Cu/low-k ϕ B = 1.7 ev Initial trap dens. ρ(0) = 3e17cm -3 Trap radius λ = 1.5 Å Increase of electron temperature by field p = 0.12 0.07 By an adjustment of only 2 Haase parameters the leakage level and the time of minimum current can be reproduced well. The rate of current decrease before breakdown and the rate of increase during breakdown are underestimated (the fast current drop is shifted to lower times).
1) Model changes: Modifications of the model and parameter fitting Not every collision with a hot electron leads to a trap creation introduction of a probability of trap creation (f Trap ) in the Haase equation for the trap generation rate: ρ Trap t = J e l 1 scat E exp k a, eff ' bte ρ t Trap = J e l 1 scat exp Introduction of a temperature dependence of the scattering length l scat : E k a, eff ' bte f Trap 1/3 l ρ ( ) 1 scat 1/3 = Trap l scat = ρ T / T Trap 0 2) Parameter fitting The following 5 Haase parameters and the new trap creation factor f Trap have been fitted to reach a good agreement with the experimental data: Haase: our fit: Activation energy for trap formation: E a 2.4 ev 1.9 ev Energy depth of traps: E Trap 0.7 ev 1.37 ev Transition barrier metal-dielectric: ϕ B 1.7 V 1.45 V Initial trap density: ρ Trap, 0 3e17 cm -3 3e15 cm -3 Factor for field-induced electron heating: p 0.12 0.50 Trap creation probability: f Trap 1.0 1e-5
Simulations based on modified assumptions and fitted parameters 10 0 Test conditions: 10-1 start of intensive trap creation (decreasing scattering length reduces the electron mobility) Line length 2 cm Line distance 83 nm Bias 40 V 4.82 MV/cm Temperature 100 ºC J e (A/cm 2 ) 10-2 10-3 4.75 MV/cm 4.82 MV/cm 4.90 MV/cm intensive tunneling between traps Parameters: Trap creation E a = 1.9 ev Trap depth E trap = 1.37 ev Barrier Cu/low-k ϕ B = 1.45 ev initial trap dens. ρ(0) = 3e15 cm -3 Trap radius λ = 1.5 Å Increase of electron temperature by electric field p = 0.50 Trap creation factor f Trap = 1e-5 10-7 10-5 10-3 10-1 10 1 10 3 10 5 10 7 Time (s) By fitting the parameters, single BTS curves can be reproduced very well with the modified Haase model.
Analysis of the influence of a defect on the BTS curves ρ Trap, 0 (cm -3 ) 10 20 10 19 10 18 10 17 10 16 10 15 10 14 Initial spatial distribution of traps for the case of a defect 0 10 20 30 40 50 60 70 80 Position (nm) ρ Trap (cm -3 ) J e (A/cm 2 ) 10 20 10 19 10 18 10 17 10 16 10 15 10-2 a) b) experiment without defect with defect (inside it) 10-3 10-4 10-3 10-2 10-1 10 0 10 1 10 2 10 3 10 4 10 5 t [s] The defect is modeled as a cluster of traps. At the place of the defect the trap concentration grows much slower than elsewhere (shorter mean free path of electrons). Thus, the spatial distribution of traps gets equalized after a short time. The defect has practically no influence on the course of the leakage current.
2D implementation of the modified Haase model Motivation: To find out the influence of a defect (cluster of traps) in 2D. 1D: a series connection no important effect of such a defect 2D: concentration of electric field in the defect? acceleration of the BTS process? y PBC Initial spatial distribution of traps (with a defect) 0 V Computational domain (dielectric) pos. bias Cu PBC x Cu
2D implementation of the modified Haase model - results The results are analogous to the 1D case: The trap density inside the defect equalizes fast with the density outside the defect. Density of traps (with defect) The influence of the defect on the leakage current course is negligible. Conclusion: A defect consisting of a cluster of traps has practically no influence on the TDDB behavior according to the Haase model. Leakage current (without defect) Leakage current (with defect) A small change of the course All time dependences for the middle of the dielectric (x = x /2 = 42 nm).
Simulations with the modified Haase model for the 45nm data I (A) - experiment 10-3 Experiment: Model: 10-4 22V, 100 C 22V, 100 C 22V, 150 C 22V, 150 C 10-5 25V, 100 C 25V, 100 C 30V, 100 C 30V, 100 C 10-6 10-7 10-8 10-9 10-10 10-11 Log [ Time ] 10 6 10 5 10 4 10 3 10 2 10 1 10 0 10-1 J e (A/cm 2 ) - model All model curves were obtained with one single parameter set. The model dependence of the lifetime on the E-field agrees very well with the experiment. The dependence of the leakage current level on the E-field is overestimated by the model.
Temperature dependence comparison of Haase model with experiment 10 0 I(A) - experiment 10-7 10-8 10-9 w/o T dependence of L scat with T dependence of L scat 22V, 100 C - experiment 22V, 150 C - experiment 10-1 10-2 10-3 J e (A/cm 2 ) - model 10-10 10-1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 Time (s) The temperature dependence of lifetime is strongly underestimated by the original Haase model. The introduction of a temperature-dependent electron scattering length leads to a stronger dependence on the temperature. l scat = ρ 1/3 Trap 1 ( T T ), T = 373.15 K ( = 100 C) / 0 0 10-4
The dependence of lifetime on the electric field (45 nm) 1 year time to failure (ttf) time of minimum current (tmin) The Poole-Frenkel lifetime model: ttf (1 / E ) exp β 0 PF = e 3 / πε ε r ( β E / kt ) PF Log [ Time ] PF fit to ttf for ε r = 2.5 Haase-based model (tmin) 0 1 2 3 4 5 6 7 Electric field (MV/cm) operating conditions (~ 0.22 MV/cm) The Haase-based model describes the experimental lifetime dependence well. The Poole-Frenkel lifetime model cannot be excluded, either. Both the PF fit and the Haase model predict a practically infinite lifetime (whereas Haase is much more progressive than PF) Data for lower E-fields enabling a decision between the two mechanisms were not available.
The dependence of lifetime on the electric field (45 nm) Comparison with another 45 nm data set Log [ Time (s) ] 1 year PF fit (ttf) to data set A, for ε r = 2.5 Haase-based model (tmin) for data set A PF fit to data set B giving ε r = 16 Schottky fit to data set B giving ε r = 3.0 ttf, 45nm data set A tmin, 45nm data set A ttf, 45nm data set B 0 1 2 3 4 5 6 7 operating conditions Electric field (MV/cm) (~ 0.22 MV/cm) The Poole-Frenkel lifetime model: ttf (1 / E ) exp β 0 PF = e 3 / πε ε r ( β E / kt ) PF ε r = 16 (data set B) The Schottky lifetime model: ttf exp ( β E / kt ) S 2 3 βs = β PF / 2 = e / 4πε 0ε r ε r = 3.0 (data set B) The Haase-based model does not agree with the data set B at all. The Poole-Frenkel fit results to an unrealistic dielectric constant of ε r =16 for data set B. The Schottky model agrees well with the data and gives a reasonble ε r = 3.0. However, based on temperature dependence (not shown here), the Schottky effect can be excluded. There seem to be two different TDDB mechanisms in action.
Schottky-like Poole-Frenkel effect? Li, Groeseneken, Maex, and Tökei in IEEE Transactions on Device and Materials Reliability, Vol. 7, No. 2, June 2007, pp. 252-258: Fast voltage sweeps in selected times during constant voltage BTS experiments measured: Voltage Time (linear scale) The I-E dependences determined from these U-I characteristics obeyed the conduction model very well: E ( E kt ) I leak exp β / For the Poole-Frenkel conduction mechanism it should hold β = β PF = e 3 / πε0ε r which was true at the beginning of the BTS experiment. During the BTS experiment β exp dropped always from about β PF nearly exactly on the half of the initial value, β PF /2 This looks like a transition from the PF to the Schottky mechanism (β S = β PF /2). The authors conclude however: This phenomenon is probably caused by the so called anomalous Poole-Frenkel effect that can occur when both acceptor and donor states are present in the dielectric. Remark: The diagrams on this page are just illustrative.
Analysis of the lifetime dependence - the second 45nm data set Comparison of the PF and anomalous PF lifetime models Log [ Time ] 1 year ttf, 45nm data set B Poole-Frenkel fit --> resulting to ε r = 16 or to ε r = 4.0 for the anomalous PF! The Poole-Frenkel effect: ttf (1 / E ) exp β 0 PF = e 3 / πε ε r ε r = 16 ( β E / kt ) PF The anomalous Poole-Frenkeleffect: ttf (1 / E ) exp ( β E / 2kT ) PF ε r = 4.0 0 1 2 3 4 5 6 7 Electric field (MV/cm) operating conditions (~ 0.22 MV/cm) The breakdown most probably occurs in the interface layer a higher dielectric constant of ε r = 4.0 than that in the dielectric bulk (2.5 3.0) can be reasonable. The extrapolation of lifetime to operating conditions (0.22 MV/cm) results to about 16 years. However, the extrapolation is too far and the error is big, but data for lower electric fields were not available.
Conclusions 1) The evaluation of experimental data shows that different degradation mechanisms are in action. 2) One 45 nm data set is well described by the modified Haase model with regard to both the I-t characteristics and the dependence of lifetime on the electric field and temperature. 3) Another 45 nm data set can be well explained by the anomalous Poole-Frenkel effect. 4) The prevailing degradation mechanism probably depends on the process conditions and technology. A better identification of these mechanisms requires further measurements at lower electric fields.
Acknowledgements Thanks to the German Federal Ministry of Education and Research for the financial support of the project SIMKON (Project No. 13N10346). Thanks to Kristof Croes for helpful discussions and cooperation.