An Integrated Model for Si Etching

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					An Integrated Model
   for Si Etching
        Jiehui Wan
   Instructor: Dr. Tzeng
ELEC 7730       Dec 8, 2003

• What are the two models used here and
  what’s their relationship?

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• Introduction;
• Description of the models:
             • Hybrid Plasma Equipment Model (HPEM);
             • Surface Kinetics Module (SKM)
• C2F6etching of Si
             • Surface Reaction Mechanism
             • Results

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• Fluorocarbon (CmFn ) plasmas are widely used for Si/SiO2
  etching due to their favorable kinetic properties and high
• CFx radicals passivate the wafer surface and so influence
  etching behavior;
• The passivation thickness depends on wafer materials, plasma-
  wall interactions, and processing parameters;
• Active surface reactions occurring in fluorocarbon plasmas can
  also influence plasma properties by consuming or generating
  plasma fluxes;
• An Integrated plasma-surface model which was used to
  investigate surface reaction mechanisms in fluorocarbon plasma
  etching will be introduced.

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HPEM(Hybrid Plasma Equipment Model)
• HPEM (Hybrid Plasma Equipment Model): developed
  at the University of Illinois, a modular simulator
  addressing low temperature, low pressure plasmas;
• Three modules:
             • EMM (Electromagnetic Module) calculates electromagnetic
               fields and magneto-static fields;
             • EETM (Electron Energy Transport Module) computes electron
               impact source functions and transport coefficients;
             • FKM (Fluid-chemical Kinetic Module) derives the densities,
               momentum and temperature of plasma species;
• VPEM (Virtual Plasma Equipment Model) shell can
  be added to HPEM for process control.

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                                           Electron                                      Fluid-
        Electro-                           Energy
        Magnetic            E (r , z )                          S (r , z ), Te(r , z ) Chemistry
                                          Transport                                    Kinetics
        Module                                                       m( r , z )
                            B(r , z )       Module                                      Module
                                            (EETM)                                       (FKM)
                n(r , z )                           n(r , z )
     v( r , z )                         v( r , z ) 
               F (r , z )                          F (r , z )

                   VPEM: Sensors, Controllers, Actuators

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Electromagnetic Module
• The EMM computes time varying electric and
  magnetic fields for HPEM;
• For ICP, rf currents passing through the inductive
  coils generate azimuthal electric fields that are
  governed by Maxwell’s equations:
             1                               qe ne   1
              E   2E  iJ      
                                             me  me  i
• EMM also solves the magnetostatic fields:
              A  B                  A  j
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       1                                      2
   E   E  iJ      J c   E   qe ne   1

                                             me  me  i
• : permeability E : azimuthal electric field
  : frequency of the source current
  : permittivity    J : total currents
• qe: unit electron charge ne: electron density
  me: electron mass
  vme: momentum transfer collision frequency of
  : driving frequency

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 EETM (Electron Energy Transport Module)
• Electron Energy Transport Module was designed to
  simulate plasma kinetics and chemistry;
• Two methods: Monte Carlo Simulation &
      • Electron Energy Equation Method:
                             f e               e(E  v  B )            f 
       Boltzmann Equation:         v  r fe                 v fe   e 
                             t                     me                   t  collision
       Electron Energy Distribution Function (EEDF): Te                 f ( )    d

                 kTe    (eTe )  Pheating  Ploss

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FKM (Fluid-chemical Kinetic Module)
• In FKM, fluid equations, together with chemical
  reactions are solved to obtain plasma species
  densities and fluxes;
      N i
              i  Si
• The electrostatic fields are also computed by solving
  Poisson’s equation;
                   j  S   j   (-)

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Modular HPEM
                           E                   Boltzmann and
       Maxwell’s                               electron energy
                           B                  equations or Electron
       Equations                                  Monte Carlo
                                                  Simulation
               , j
                                           Te , S , 
                          FKS                           
                      Fluid equations                   Es , N
                   Poisson’s equation or

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HPEM Results I

             a) Azimuthal Electric Field; b) Total Power
             Deposition. Process conditions: Cl2, 10
             mTorr, 80 sccm gas flow rate, 800 W ICP
             power, 100v rf substrate bias
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HPEM Results II

 a) Cl2+ source function; b) Cl2+ density and fluxes; The arrows in (b) denote
 the relative magnitudes and directions of Cl2+ ion fluxes.

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HPEM Results III
                                     The plasma possesses a uniform
                                     potential in the bulk region due to
                                     its high conductivity. The rf bias
                                     produces a negative dc
                                     component on the substrate
                                     because of the large difference in
                                     the areas for the biased surface
                                     and the grounded surface. This
                                     results in the sheath voltage drop
                                     peaking above the wafer,
                                     contributing to the energetic ion
                                     bombardment of the wafer

             Electric Potential of the ICP plasma

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             SKM (Surface Kinetics Module)
•   The Surface Kinetics Model (SKM) is an integrated module of the
•   Before SKM, HPEM used a fixed boundary condition at the plasma-
    solid interface:
     – The reflecting flux of some species back to the bulk plasma from
        the mth material is    R
                                   im    (1  Sim )  

     I im flux of species I to the surface m,
    Sim reaction probability for the ith plasma species and mth surface
     R im reflecting flux of species I from the surface m;
     – Incident species may produces other species on the surface

                             R ijm   I im  fijm
     f ijm fractional generation rate
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SKM (Surface Kinetics Module)
• The SKM
   –   uses reactant fluxes from the HPEM
   –   applies a user defined reaction mechanism
   –   updates surface sticking and product reflection coefficient for the HPEM
   –   calculates surface coverages and etch rates

                                   Reaction Mechanism

                        (1  Si ) i
             HPEM                          SKM                  Etch Rate
                         f j j

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Integrated plasma-surface Model

 Surface Reaction       Incident             Initial          Surface
   Mechanism         Species/Fluxes        Conditions       Composition


               Reflecting                     Surface
             Species/Fluxes                Species/Fluxes

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SKM: Energy Dependence of Reaction
•   All surface reactions involving ion reactants in the SKM allow for ion
    energy dependence;
•   Ions are accelerated to the surface through the sheath, arriving on the
    surface with energy of:
                                Eion  Qf (r )Vsh (r )
    Q: ion charge.
    f(r):Ratio of ion mean free path to sheath thickness.
    Vsh(r): Sheath voltage drop;
•   Surface Reaction have a general energy dependence given by
                        k  k0 ( Eion  Eth ) /(Eref  Eth )
                                   n      n      n       n

    Where    Eion   : Incident ion energy;
             k0      : Etching yield or reaction probability for ion with energy Eref.
             Eth     : Threshold energy for the process;
                     : reaction probability for an ion with energy Eion.
•   Ions with higher bombarding energy produces higher etch yield.
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• During Si/SiO2 etching by fluorocarbon plasmas, a CmFn
  polymer layer will simultaneously deposit on the surface of the
  wafer and the reactor wall;
• The SKM allows the growth of the passivation layer by CFx
  radical polymerization on the surface. F atoms etching and
  energetic ion sputtering can consume the layer;
• The steady state passivation thickness is reached when the film
  generation and consumption rates are balanced;
• SKM uses passivation thickness dependent rates for mass and
  energy transfers through the layer.

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C2F6 Etching of Si

•A CxFy polymer layer is formed on the Si surface in coincidence
with Si etching. The steady state passivation layer thickness is a
balance of CFx deposition, ion sputtering and F etching of the layer;
•Si etching precursor (F) needs to diffuse through the passivation
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• Representative gas phase reactions:
   e + C2F6 CF3+ + CF3 + e + e        e + C2F6 CF3 + CF3 + e
   e + CF3 CF2 + F + e                e + CF3 CF2 + F + F-
   e + CF4 CF2 + F + F + e e + CF4 CF3+ + F + e + e
   F + F + M F2 + M           CF3 + CF3 + M C2F6 + M
   CF2 + F2 CF3 + F           CF3 + F2 CF4 + F
   CF2 + CF3 C2 F 5           C2 F5 + F CF3 + CF3
   CF3 + F CF4                CF2 + F CF6

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Properties (Plasma and Surface)

   Plasma and surface properties for the base case as a function of radius. (a)
   Fluxes of CF3 + , CF2 and F to the wafer. (b) Polymer layers and etch rates.
   The etch rate is constrained by the diffusion of F atoms through the polymer
   layer, giving rise to a minimum at the center of the wafer where the polymer
   layer is thickest.
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             CF2 density distributions at (a)
             30, (b) 50, and (c) 70 mTorr. All
             cases are at 250 V biases and 30
             sccm. The labels on the contour
             lines denote the percentage of
             the value shown at the top of
             each figure. Increasing pressure
             localizes sources closer to the
             powered electrode.

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Wall Conditions

Influences of reactor wall condition on plasma properties. (a) Experimental
data of normalized CF2 and F densities as a function of the reactor wall
temperature. (b) Simulated results of normalized CF2 and F densities as a
function of (1 - SCF2), where SCF2 is the sticking coefficient of CF2 on the wall
and it decreases with increasing reactor wall temperature.
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 Simulated CF2 normalized
 density as a function of
 sticking coefficient of CF2
 radicals on the reactor walls.
 Experimental results of
 Shaepkens et al. are shown
 plotted as a function of
 T(wall)1/2 . A decreasing
 sticking coefficient for CF2
 increases its gas phase

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Surface Properties

  Surface properties as a function of CF2 sticking coefficient (SCF2)
  on the walls of the reactor. (a) Polymer layers as a function of
  radius for different sticking coefficients. (b) Etch rates for different
  sticking coefficients.
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Etch Rate

     Polymer layers, CF2 flux, and etch rate at the center of the
     wafer as a function of SCF2.

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Etch Rate

Polymer thickness and etch rate at the center of the wafer as a function of
sheath potential. Increased sputtering of the polymer layer with increasing
bias decreases its thickness and increases the etch rate.
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Properties (Plasma and Surface)

  Plasma and surface properties as a function of dilution with argon in
  an Ar/C2F6 gas mixture. (a) Fluxes of CF2, F atoms and the ratio of
  the ion flux to the CF2 flux. (b) Etch rate and polymer thickness. The
  etch rate increases with decreasing polymer thickness until the F atom
  flux is insufficient to fully passivate silicon sites.
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• Ar/C2F6 etching of Si in a high-plasma-density ICP reactor was
  simulated using Integrated modeling;
• Results show that with a decreasing CF2 sticking coefficient on
  the reactor wall, the bulk CF2 density increases, which leads to
  a thicker polymer layer on the wafer and a lower Si etch rate;
• Higher biases produce larger sputtering rates and thinner
• Both the magnitude and radial dependence of the etch rate
  depend on the rate of ion activated desorption of etch products;
• For conditions where ion-desorption is not rate limiting, etch
  rates generally vary inversely with polymer thickness; For
  conditions where the ion-desorption is rate limiting, the etch rate
  and its spatial dependence vary with ion flux.

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•   M. Schaepkens, R. C. M. Bosch, T. E. F. M. Standaert, and G. S.
    Oehrlein, J. Vac. Sci. Technol. A 16, 2099 (1998);
•   Zhang Da, PhD thesis, 2002;
•   Da Zhang, Mark J. Kushner, Journal of Applied Physics, 87,3(2000),
•   Da Zhang, Mark J. Kushner, J. Vac. Sci. Technol. A 19(2), Mar/Apr
•   Da Zhang, Mark J. Kushner, J. Vac. Sci. Technol. A 18(6), Nov/Dec

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• The integrated model is composed of HPEM
  and SKM. SKM accepts fluxes of reactants
  from the HPEM then implement a modified
  surface site balance algorithm at all points
  along the plasma-surface boundary and
  produces surface coverages, effective
  reactive sticking coefficients, and the identity
  of species returning to the plasma.

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