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					 Simulations of ‘Bottom-up’ Fill in Via
Plating of Semiconductor Interconnects
       Uziel Landau1, Rohan Akolkar1,
  Eugene Malyshev2, and Sergey Chivilikhin2



         1Department   of Chemical Engineering
       Case Western Reserve University
                Cleveland, OH 44106
                           and
                 2L-Chem,        Inc
               Beachwood, OH 44122
            Outline
• Significance and Objectives
• Parameters Controlling the Bottom-Up Fill
• Simulation Method
• Sample Simulations
• Conclusions
                  Prior Work
•   Andricacos, Uzoh, Dukovic, Horkans and Deligianni, IBM J. R&D 1998:
      - Additives blocking model
      - Adjustable Parameters + steady-state additives diffusion

•   Georgiadou, Veyret, Sani and Alkire, J. Electrochem. Soc. 2001:
       - Convective flow + additives transport

•   Cao, Taephaisitphongse, Chalupa and West, J. Electrochem. Soc., 2001:
       - Diffusion controlled additives transport + adsorption isotherms

•   Josell, Baker, Witt, Wheeler and Moffat, J. Electrochem. Soc., 2002:
       - Curvature enhanced SPS coverage
           Objectives
 Develop a Simulation for the Bottom-Up Fill
 Based on Experimental Data
 Without Adjustable Parameters & Without
  Invoking Extreme Assumptions
 Simulation should correlate experimental
  observations
                   Gap-Fill Modes

Pinch                Seam                




  Conventional           Conformal       Bottom-up
    Plating               Plating           Fill

  (unacceptable)        (unacceptable)    (Good!)
                            Stages in ‘Gap-Fill’

‘Conventional’
   Plating



                                                                Void


  Conformal
   Plating




                                                               Seam


  Bottom-up
    Plating




                 ~ 30 sec          ~ 50 sec        ~ 2.5 min    Fill
Variable Adsorption leads to Variable Kinetics and
to ‘Bottom-up’ fill:

                      ‘Enhancer’, e.g.
Suppressor,           Organic di-sulfide   Slow deposition
e.g. PAG




              Fast deposition
Variable Deposition Rates Due to Non-uniform Inhibition


                  Polarization Curves
       i
    [mA/cm2]

                                             Enhanced Kinetics (via)
           100




                                                  Suppressed Kinetics
                                                      (‘flat’ wafer)
            10

                                                  V
                                    300 mV
           Rapid Fill of Vias and Trenches




2-3 Min

< 50 Sec
  Transport Equations --
Nernst-Plank Equation (ionic transport):
    Cj
          D j C j   Z j F U jC j     V  C j
     t
               Diffusion        Electric       Convection
   Pseudo
                                Migration
   Steady
   -State

Navier-Stokes Equation (fluid-flow–momentum balance):
      V              
   
           V   V    P   2 V
                                                           C   (Boundary Layer)
       t             
Electroneutrality:
       Zj Cj = 0
 Scaling Analysis of the Nernst Plank Equation*:
      D j 2C j  Z j U j F C j   0
       Diffusion       Electric Migration

                            RT                                     Ohmic Control on
       L characteristic          0.5 mm  500 μm                 the Macro-Scale
                           n F iL
                                     (Laplace’s eqn.
                2    =0            for the potential
                                     is solved within
                                     the cell)           Thin
                                                                           2 = 0
                                                         boundary
                                                                            Cb
Boundary conditions:                                     layer

 Insulator: i = 0   (i = - κ  )      =0

 Electrode:  = V – E0 – ηa – ηC



* U. Landau, The Electrochem. Soc.        Thin Boundary Layer Approximation
  Proceedings Volume 94-9, 1994.
Scaling Analysis of the Nernst Plank Equation*:
   D j 2C j  Z j U j F C j   0
    Diffusion        Electric Migration

                         RT                                    Mass Transport
    L characteristic          0.5 mm  500 μm                Control on the
                        n F iL
                                                                Micro-Scale
                                     (Laplace’s eqn. for
             2 C = 0                the Concentration,
                                     solved in the
                                     boundary layer)     Boundary
                                                        layer
Boundary conditions:                                                   Cb

 outer edge of diffusion layer: y =     C = CB                       2 = 0
 Insulator: i = 0   (i = - κ  )       C=0

 Electrode: ηC = V – E0– ηa - 


* U. Landau, The Electrochem. Soc.
  Proceedings Volume 94-9, 1994.
            The Software Package
‘Cell-Design’ Features:
    Current Distribution + Fluid Flow (BEM + FD)
    Current Distribution: (BEM)
       • Macro-scale: 2 = 0
       • Micro-scale: 2 C = 0
          • Moving boundaries      Boundary Element   Finite Differences
          • Variable Kinetics           (BEM)                (FD)

    Fluid-Flow (FD):
       • Complete solution of the Navier-Stokes equation
       • Integrated with the electrochemical modeling
           • Solution of the Nernst-Plank equation
           • Export C
    Fast, Robust, Menu driven
Simulation of Deposit Propagation
      Variable kinetics + Moving boundaries

     Virtual electrode;
Outer edge of diffusion layer

                                                      2  =0
                           i = f (η)                                    C
                                                        2 C =0
  Passivated kinetics (PEG+SPS)
        [Measured, f(t)]


                    Variable kinetics
                [Partially passivated, f(t)]




                                               Accelerated kinetics (SPS)
  Flow Simulations
       Wafer Scale


60 RPM + 4 GPM Impinging Flow




                   ‘Cell-Design’ Simulations
                              Flow Simulations
                                  Micro-Scale




       Transport within the via
       is due to diffusion

‘Cell-Design’ Simulations
Concentration Map




                    ‘Cell-Design’ Simulations
                   Steady-State Polarization Data
       50
                                            SPS
                                          (Stagnant)
                                                                         PEG
       40                                                              (Stagnant)




   i   30
[mA/cm2]

       20



       10



           0
               0    0.05     0.1   0.15     0.2    0.25   0.3   0.35     0.4    0.45

                           Activation Overpotential, a, [V]
                              Polarization Transients: PEG + SPS
                              80
                                      SPS steady state
                                      PEG+SPS unsteady state
                              70
                                          steady state
                                      PEG Initial state
Current Density, i [mA/cm ]
2




                                                              t=50ss t=20s
                                                                50 20 s
                              60              SPS                            10 sec
                                                                             t=10s
                                             Steady-
                              50              state                             t=0s
                                                                              0 sec
                                                       slow SPS                 (PEG)
                                                                                (PEG)
                                                       activity
                              40
                                                        Time
                              30


                              20


                              10


                               0
                               0.00   0.05     0.10    0.15       0.20   0.25         0.30
                                      Activation Overpotential, a [V]
                                          PEG Penetration Depth
PEG Penetration Depth, z*=z/h   1.0



                                0.8
                                                                          Slow PEG
                                                                          transport to the
                                                                          via-bottom
                                0.6



                                0.4
                                                Fast PEG transport to
                                                upper via sidewalls
                                0.2                        Short time
                                                          PEG coverage

                                                            Short time
                                0.0
                                                           SPS coverage
                                      0     2         4           6           8          10
                                                     Time, t (s)
                                          PEG Penetration Depth
PEG Penetration Depth, z*=z/h   1.0



                                0.8
                                                                        Slow PEG
                                                                        transport to the
                                                                        via-bottom
                                0.6



                                0.4
                                                Fast PEG transport to        Longer time
                                                                            PEG coverage
                                                upper via sidewalls
                                0.2
                                                         Slow SPS
                                                       depolarization


                                0.0                               Longer time
                                      0     2         4          SPS coverage 8
                                                                   6                       10
                                                     Time, t (s)
Via Fill Simulation
Fill Time: 47 sec.
                                         Electrolyte
Overpotential: - 124 mV
                               47 sec

                               44 sec


Bottom:
                               40 sec



i = 60 mA/cm2                  32 sec

i0 = 1.12 mA/cm2   C = 0.83
                                24 sec

Top & Sidewalls:                             SiO2
i = 0.24 mA/cm2  3.4 mA/cm2   16 sec


Depolarization by SPS:
                               12 sec


i0 = 3.1 μA/cm2  46 μA/cm2
                                 8 sec


C = 0.9
                                 4 sec
                                 2 sec




                                           ‘Cell-Design’ Simulations
Via Fill Simulation
                                         Electrolyte
Fill Time: 49 sec.
                                50 sec

Overpotential: - 124 mV
                               42 sec

Bottom:
i = 60 mA/cm2                  32 sec

i0 = 1.12 mA/cm2   C = 0.83
                                22 sec         SiO2
Top & Sidewalls:
i = 0.24 mA/cm2  6.8 mA/cm2
                               16 sec



Depolarization by SPS:         10 sec


i0 = 3.1 μA/cm2  92 μA/cm2     6 sec


C = 0.9                       2 sec




                                         ‘Cell-Design’ Simulations
Via Fill Simulation
                                                           Electrolyte
                                                           Electrolyte
Variable Kinetics along the Sidewalls

Fill Time: 48 sec.
Overpotential: - 124 mV
Bottom:
i = 60 mA/cm2
i0 = 1.12 mA/cm2   C = 0.83
                                                               SiO2
                                                               SiO2
Top:
i = 0.24 mA/cm2  3.4 mA/cm2
Depolarization by SPS:
i0 = 3.1 μA/cm2  46 μA/cm2
C = 0.9                                      1 sec
                                              time
Sidewalls: Interpolated kinetics              intervals
between Top and Bottom

                               ‘Cell-Design’ Simulations
 Via Fill Simulation
Current density has been lowered:                            Electrolyte
       No Bottom-Up Fill
Plating Time: ~147 sec.
Overpotential: - 80 mV
Bottom:
i = 10 mA/cm2
i0 = 1.12 mA/cm2   C = 0.83
Top:                                         Seam                SiO2
i = 0.05 mA/cm2  4.8 mA/cm2
High Depolarization by SPS:
i0 = 3.1 μA/cm2  0.28 mA/cm2                    1 sec
C = 0.9                                         time
                                                 intervals
Sidewalls: Interpolated kinetics
between Top and Bottom
                               ‘Cell-Design’ Simulations
      Deposit Propagation in Feature
       Clusters and Wide Features



                            Wide             Cluster
                            Feature




Flat regions - Passivated: i0 =5x10-4 A/cm2 A 1.7 c  0.3
Bottom – Pure copper:       i0 =10-3 A/cm2   A 1.5   c  0.5
Side-walls - interpolated                                         ‘Cell-Design’ Simulations
               Conclusions
   Simulation of bottom-up fill has been carried w/o
    invoking arbitrary assumptions
   Simulation is based on, and implements ‘variable‘
    kinetics = f(time, position)
   A commercial CAD program that accomodates moving
    boundaries and variable kinetics was used
   Different process parameters have been explored:
     Transport and adsorption kinetics of inhibiting and
      depolarizing additives must match process
     Operating conditions (i, V) must be within range
Acknowledgements
• Yezdi Dordi – Applied materials
• Peter Hey    – Applied Materials
• Andrew Lipin – L-Chem
Thank you for
your attention

				
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