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Feature-scale to wafer-scale modelling and simulation of physical vapor deposition

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## Feature-scale to wafer-scale modelling and simulation of physical vapor deposition

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**Feature-scale to wafer-scale modelling and simulation of**physical vapor deposition Peter O’Sullivan work done with: Frieder Baumann, George Gilmer & Jacques Dalla Torre, Bell Labs., Lucent Technologies, Murray Hill, NJ In collaboration with: I. Petrov, C.-S. Shin and T.-Y. Lee Materials Research Lab, U. of Illinois, Urbana-Champaign Funded by an NSF/DARPA VIP grant through the University of Illinois**Multi-level interconnects / metallization for ICs**Tungsten (W) deposited in circular “vias” (plugs) using CVD Al lines (Cu electro-deposited in long trenches)**Cu diffuses into Si short circuit**• WF6 + 3H2O W + 3O + 6HF etches SiO2 • duringCVD fill of vias 2mm Must use “barrier” layers of Ti, TiN, Ta, TaN to to prevent diffusion or etch-damage Cu Ta SiO2 Si Thin Films for Metalization**Simulation of PVD into trench**Keyhole formation Low side-wall coverage Low bottom coverage**Micro-voids and grain boundaries**impinging atoms ~ 0.25mm 10nm Barrier failure • Metallic films are polycrystalline Columnar (rough) growth and pores more likely because of oblique incidence& low surface diffusivity ( Monte Carlo simulations by Jacques Dalla Torre & George Gilmer )**Objectives: 1. Predict film coverage across wafer**2. Optimize deposition process**Axisymmetric vias:**• Validation + analytic scaling with AR • Different angular distributions • Comparison with experiment (Ti and Ta) • General 3D: • Across-wafer non-uniformity • Modelling issues • Problems, challenges • Summary & conclusions Talk Outline • Physical model of low pressure PVD: • Feature-scale + reactor-scale • (continuum) (atomistic) • Numerics for moving interface: • Level sets**sputter target**Ti, Ta, Al, Cu, .... S N N S -V +V +V Ar+ plasma Ar P ~ 1 - 20 mTorr wafer 30 cm Low pressure PVD—DC magnetron sputtering Rotating magnetic field “traps” electrons => non-uniform target erosion**Must calculate flux at each surface point**• Target visibility/shadowing.................Ray tracing • Need to know: • Size and distance of target • Target erosion pattern (relative sputter rate across target) • Angular distribution of atoms from target, f(q) • Current assumption / applicability: • Sticking coeff. = 1 ..................... Ti, Ta • More complex surface kinetics under development • (reflection, resputtering etc.) Sputter Target bL bR n d Feature on wafer Physical Model of Sputter Deposition Advance using level sets**Continuum Modeling**• 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(N4—5) ray-tracing codes**Binary collision MC code gives resultant angular**distribution, f(q), just above wafer f(q) then used in level set code “virtual” target Low pressure PVD — Monte Carlo vapor transport code Rotating magnetic field “traps” electrons sputter target Ti, Ta, Al, Cu, .... -V S N N S +V plasma Ar+ +V Ar P ~ 1 - 20 mTorr wafer****w(r) f(q) cos g F3D(substrate) = dA r2 visible region DA discrete surface element on target f(q) Deposition rate given by: q r n 1.2 3D MD data for Al g Can use different angular distibutions: Nonlinear curve fit 1 Equivalent 2D flux f(q) = cos(q)(isotropic emission from target) f(q) = f(q) =· · · · · Cosq discrete surface element on substrate 0.8 w(r) = weight function from target erosion profile 0.6 ......from molecular dynamics calculations 0.4 q 0.2 ......Monte Carlo vapor transport code 0 0 10 20 30 40 50 60 70 80 90 q (deg) Computation of geometric 3D material flux**2R**q Z wafer g h w Via Geometry • 3D flux • finite target • 3D line-of- • sight model • Axisymmetric, but • with 3D shadowing AR = h / w Q = Z / R**}**Field = 250 Å } Field = 1250 Å BC = 100 b / t SWB = 100 s / t t s b Step coverage vs. AR : Circular Via Analytic AR = h / w Q = Z / R Analytic Bottom coverage ~AR–2 Side-wall coverage ~AR–3**1.2**Subcosine (ellipse) * 1.0 cosine Polar plot: 0.8 dN — 0.6 W d 0.4 Ti at 2mTorr (Varian M2000) MC vapor transport code 0.2 0.0 0 20 40 60 80 q (deg) Ti deposition into vias (which angular distribution?) * suggested by Malaurie & Bessaudou (Thin Solid Films v. 286, 1996)**Ti into vias**Deposition Start End cosine HRSEM f(q) from gas transport code Experimental data Subcosine (ellipse) BC vs AR for several angular distributions • Subcosine shows best agreement subcosine + scattering**cut-away viewfrom below**cut-away side view Complex 3D features 20cm wafer; 30cm target; depth = 0.8mm; AR = 2;deposited 0.4mm**0.4 mm**Target Plan view z wafer y z (mm) xoff x x y Off-axis circular via, depth = 0.85mm, aspect ratio, AR = 2.0, deposited 0.3mm Asymmetry in minimum step coverage ~ 10% LHS: Sees less of target LHS RHS: Shadowed by overhang Off-Axis Deposition**More experimental validation — long-throw deposition**(similar to ionized PVD)**R 3 cm**• Measured target erosion profile • modelled by w(r) 1.2 1.0 1.0 w(r) 0.8 • Simulation takes angular distribution • from vapor transport code dN — dW 0.6 ZT = 10 cm 0.4 P=1mTorr 0.2 0.0 r(cm) 20 40 60 80 q 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 r Low pressure Ta PVD (circular via) cosine**R 3 cm**ZT = 10 cm P = 1mTorr Experimental Cosine (no erosion) Erosion + scattering r Low pressure Ta PVD (circular via)**R 3 cm**ZT = 10 cm P = 1mTorr Amplitude = 4 D Amplitude = 8 D r D = 0.0025 mm (400 X 400) Columnar growth / roughness**Level set codeÞfast, accurate, predictive model for PVD**• of refractory metals • LS code coupled to MC code throughf(q)and “virtual” target • Validated LS code using analytic formulae • — Step coverage ~ AR–2 (trench) • — Step coverage ~ AR–3 (via) • 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) • Full 3D code • Strong non-uniformity in coverage across wafer Conclusions