1. Feature-scale to wafer-scale modelling and simulation of physical vapor deposition Peter O’Sullivan Funded by an NSF/DARPA VIP grant through the University of Illinois In collaboration with: I. Petrov, C.-S. Shin and T.-Y. Lee Materials Research Lab, U. of Illinois, Urbana-Champaign work done with: Frieder Baumann, George Gilmer & Jacques Dalla Torre, Bell Labs., Lucent Technologies, Murray Hill, NJ

2. Background

3. Multi-level interconnects / metallization for ICs Tungsten (W) deposited in circular “vias” (plugs) using CVD Al lines (Cu electro- deposited in long trenches)

4. Thin Films for Metalization Cu Ta SiO 2 Si WF 6 + 3H 2 O  W + 3O + 6 HF etches SiO 2 during CVD fill of vias Cu diffuses into Si  short circuit Must use “barrier” layers of Ti, TiN, Ta, TaN to to prevent diffusion or etch-damage 2m2m

5. Simulation of PVD into trench Low bottom coverage Keyhole formation Low side-wall coverage

6. Barrier failure Metallic films are polycrystalline Micro-voids and grain boundaries Columnar (rough) growth and pores more likely because of oblique incidence & low surface diffusivity 10nm impinging atoms ~ 0.25  m ( Monte Carlo simulations by Jacques Dalla Torre & George Gilmer )

7. Objectives: 1. Predict film coverage across wafer 2. Optimize deposition process

8. Talk Outline Physical model of low pressure PVD: Feature-scale + reactor-scale (continuum) (atomistic) Axisymmetric vias: Validation + analytic scaling with AR Different angular distributions Comparison with experiment (Ti and Ta) Summary & conclusions General 3D: Across-wafer non-uniformity Modelling issues P roblems, challenges Numerics for moving interface: Level sets

9. Low pressure PVD—DC magnetron sputtering Rotating magnetic field “traps” electrons => non-uniform target erosion sputter target Ti, Ta, Al, Cu,.... +V SN SN wafer -V-V Ar + Ar P ~ 1 - 20 mTorr +V plasma 30 cm

10. Target Feature on wafer Sputter LL RR n  Need to know: Size and distance of target Target erosion pattern (relative sputter rate across target) Angular distribution of atoms from target, f(  ) Must calculate flux at each surface point Target visibility/shadowing.................Ray tracing Current assumption / applicability: Sticking coeff. = 1..................... Ti, Ta More complex surface kinetics under development (reflection, resputtering etc.) Physical Model of Sputter Deposition Advance using level sets

11. Objectives: Compute bottom / sidewall step coverage in high aspect ratio trenches, vias, etc. Predict across-wafer non-uniformity of coverage — Simulate feature-scale film profile evolution in 3D Study effects of macroscopic reactor variables on coverage — target erosion — angular distribution of different materials — gas pressure Incorporate important physical effects as determined from complementary Monte Carlo simulators and experimental data Develop efficient algorithms for O(N 4—5 ) ray-tracing codes Continuum Modeling

12. Low pressure PVD — Monte Carlo vapor transport code SN SN wafer sputter target Rotating magnetic field “traps” electrons -V-V Ar + Ar Ti, Ta, Al, Cu,.... P ~ 1 - 20 mTorr +V plasma +V Binary collision MC code gives resultant angular distribution, f(  ), just above wafer f(  ) then used in level set code “virtual” target

13. Computation of geometric 3D material flux 0 0.2 0.4 0.6 0.8 1 1.2 0102030405060708090  (deg) 3D MD data for Al Nonlinear curve fit Equivalent 2D flux Cos  f(  AA g q r discrete surface element on target discrete surface element on substrate n Deposition rate given by: w(  ) f(  ) cos   r 2r 2 dA visible region F 3D ( substrate ) = w(  ) = weight function from target erosion profile f(  cos(   (isotropic emission from target) f(  f(    ......from molecular dynamics calculations Can use different angular distibutions:......Monte Carlo vapor transport code

14. Code / model validation

15. Via Geometry 3D flux finite target 3D line-of- sight model Axisymmetric, but with 3D shadowing AR = h / w Q = Z / R 2R h  w Z wafer 

16. Step coverage vs. AR : Circular Via Side-wall coverage Analytic Bottom coverage AR = h / w Q = Z / R Analytic Field = 250 Å } } Field = 1250 Å b s t BC = 100 b / t SWB = 100 s / t ~AR –3 ~AR –2

17. Ti deposition into vias (which angular distribution?) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 020406080  (deg) Polar plot: cosine Subcosine (ellipse) * Ti at 2mTorr (Varian M2000) MC vapor transport code dN d  — * suggested by Malaurie & Bessaudou (Thin Solid Films v. 286, 1996)

18. Deposition StartEnd HRSEM Ti into vias cosine f(  ) from gas transport code Experimental data Subcosine (ellipse) BC vs AR for several angular distributions Subcosine shows best agreement  subcosine + scattering

19. Full 3D — Across-wafer non-uniformity

20. 20cm wafer; 30cm target; depth = 0.8  m; AR = 2; deposited 0.4  m cut-away side view cut-away view from below Complex 3D features

21. Off-axis circular via, depth = 0.85  m, aspect ratio, AR = 2.0, deposited 0.3  m z (  m)  m yx Plan view x y Target wafer x off z LHS: Sees less of target RHS: Shadowed by overhang LHS Asymmetry in minimum step coverage ~ 10% Off-Axis Deposition

22. More experimental validation — long-throw deposition (similar to ionized PVD)

23. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.00.51.01.52.02.53.0  w(  )   (cm) Low pressure Ta PVD (circular via) Simulation takes angular distribution from vapor transport code Measured target erosion profile modelled by w(  )  Z T = 10 cm R  3 cm P=1mTorr 1.0 0.0 dN — d  20406080  cosine

24. Low pressure Ta PVD (circular via) Cosine (no erosion) Experimental Erosion + scattering  Z T = 10 cm R  3 cm P = 1mTorr

25. Columnar growth / roughness  Z T = 10 cm R  3 cm P = 1mTorr Amplitude = 8  Amplitude = 4   m (400 X 400)

26. Conclusions Level set code  fast, accurate, predictive model for PVD of refractory metals Validated LS code using analytic formulae — Step coverage ~ AR –2 (trench) — Step coverage ~ AR –3 (via) LS code coupled to MC code through f(  ) and “virtual” target Full 3D code Strong non-uniformity in coverage across wafer Quantitative comparison w/ experiment Ti data: Subcosine distribution improves agreement — Need more data for ang. dist. + vapor transport Ta data: Can predict bottom coverage — Need to incorporate more physics to predict closing of feature (breadloafing)