Numerical Simulation of MOCVD Growth of Semiconductor

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Numerical Simulation of MOCVD Growth of Semiconductor Powered By Docstoc
					 Numerical Simulation of
  MOCVD Growth of
Semiconductor Compounds




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                                       2



            Contents

Simulation output.
Fluid flow and heat transfer models.
Gas and surface reactions models.
MOCVD reactor models.
Example of GaAs growth.
Example of GaN growth.
Rotating disk model.
                                         3



       Simulation output


Chemical species distributions in
reactor.
Gas flow pattern.
Temperature distribution.
Film deposition rates and composition.
Common impurity incorporation.
                                            4



                  Fluid Flow
1. Continuity equation

  ∂ρ
     = −∇ ⋅ ( ρV )
  ∂t

2. Momentum conservation


 ∂ ( ρV )
          = −∇ ⋅ ( ρVV ) + ∇ ⋅τ − ∇P + ρg
    ∂t
                                                5



   Heat and Species transfer
3. Energy Conservation

 ∂ (c p ρT )
               = −∇ ⋅ ( ρc pVT ) + ∇ ⋅ (λ∇T )
     ∂t


4. Species Transport


  ∂ ( ρω i )
             = −∇ ⋅ ( ρVω i ) − ∇ ⋅ ji + Si
      ∂t
                                               6



  Gas and Surface Reactions


Detailed gas phase reaction models for GaAs,
InP, InGaAsP, GaN and AlGaN materials.
Precursors: TMGa, TMAl, TMIn, TEGa, TBAs,
NH3, AsH3, TBP …
Well calibrated surface reaction models for
GaAs, InP, InGaAsP, GaN and AlGaN
materials.
                              7



    Built in Reactor Models


Horizontal reactor
Vertical reactor
Planetary reactor
Barrel reactor
                    8



User Friendly GUI
GaAs Growth in Horizontal
                                                                                                    9



        reactor




                                                                      Growth rate vs. temperature
 Growth rate (um/min)




                         0.1




                        0.01
                                         present theory
                                         other's theory
                                         expt.

                           0.6   0.8   1.0     1.2        1.4   1.6
                                        1000/T(K)
                                                                              10



 GaN Growth in Vertical Reactor




Growth rate vs. position on substrate   Temperature distribution in reactor
3D Simulation of GaAs Growth
                                                     11



    in Horizontal Reactor




     Reactor model in 3D, only half of it is shown
     because of symmetry of the reactor
                          12



GaAs Growth Rates in 3D
                                                   13



               Introduction
Rotating disk has great potential for highly
Rotating disk has great potential for highly
uniform film growth.
uniform film growth.

Commercial rotating disk reactors are common.
Commercial rotating disk reactors are common.

PROCOM uses a variable separation
PROCOM uses a variable separation
transformation to obtain good practical
transformation to obtain good practical
approximation for efficient gas flow solutions.
approximation for efficient gas flow solutions.

PROCOM combines rotating disk solution with
PROCOM combines rotating disk solution with
chemical reaction, mass transport, heat transfer
chemical reaction, mass transport, heat transfer
and multiple gas inlet boundaries models.
and multiple gas inlet boundaries models.
                      Simplified boundaries for                                               14


                              fuild flow
           the infinite-radius disk and inlet boundary
           the infinite-radius disk and inlet boundary
           conditions
           conditions                         Inlet boundary conditions
                                                          Forced flow with axial velocity
a facing, parallel,              Flow Inlet
porous, non-                         y
rotating surface




                                         W(y)                  a solid rotating surface
                                                   V(y)        of infinite extent in the r,
                                                u(y)           θ plane
                                                     r


                      RPM
                                                            15



               Equation systems
Conservation equations
Conservation equations
Mixture continuity:
              1 ∂ρ    ∂u      u ∂ρ
                   = − − 2V −      =0                 (1)
              ρ ∂t    ∂x      ρ ∂x
Radial momentum:
   ∂V  ∂ ⎛ ∂V ⎞      ∂V
                        − ρ (V − W ) −
                                       1 dpm
 ρ    = ⎜µ    ⎟ − ρµ
                              2   2
                                             =0       (2)
   ∂t ∂x ⎝ ∂x ⎠      ∂x                r dr
Circumferential momentum:

              ∂W   ∂ ⎛ ∂W    ⎞      ∂W                (3)
          ρ       = ⎜µ       ⎟ − ρµ     − 2 ρVW = 0
               ∂t  ∂x ⎝ ∂x   ⎠       ∂x
                                                                                 16


               Viscosity parameters
Viscosity of Gas mixture
Viscosity of Gas mixture
Viscosity of each gas species is defined by:


     2.6693 × 10−5 M i T
µi =                                          rewritten as
                                                             µi = δ1iT ψ    1i

           σ i2Ω µi
Viscosity of gas mixture is calculated with the Wilkes correlation:
                           n
                               ⎛          n
                                                  ⎞
                 µmix   = ∑ ⎜ xi µi
                               ⎜         ∑ xiΦ ij ⎟
                                                  ⎟
                          i =1 ⎝         j =1     ⎠

           [
    Φ ij = 1 + (µi µ j )        (M       M j)      ] [8 + 8 M       M j]
                                                                       12
                           12                  14 2
                                     i                          i
                                         17




      Example of GaN growth
in vertical reactor with Rotating-Disk
                                                                              18
                              Structure
                              Structure


Flow inlet
Flow inlet




                                                                Flow outlet
                                                                Flow outlet

Rotating substrate
Rotating substrate


             Vertical reactor described by cylindrical coordinate
                                                                                      19
                   Effects of rotating disk
                   Effects of rotating disk




      Rotating rate=0 rpm
      Rotating rate=0 rpm                          Rotating rate=1000 rpm
                                                   Rotating rate=1000 rpm


Rotating disk increases GaN growth rate especially near the center of the substrate
Rotating disk increases GaN growth rate especially near the center of the substrate
                                                                                20
                Performace Compared
                Performace Compared




   Rotating rate=0 rpm
   Rotating rate=0 rpm                            Rotating rate=1000 rpm
                                                  Rotating rate=1000 rpm


More mass fraction of species tend to concentrate at center for rotating disk
More mass fraction of species tend to concentrate at center for rotating disk
                                                                    21
          Performace Compared
          Performace Compared




Rotating rate=0 rpm
Rotating rate=0 rpm                        Rotating rate=1000 rpm
                                           Rotating rate=1000 rpm


     The rotating disk attracts the flow towards disk center.
     The rotating disk attracts the flow towards disk center.
        Performace Compared                                           22




                         Most of GaCH3 gathers and takes part in
                          Most of GaCH3 gathers and takes part in
                         the chemical reaction in the region of
                          the chemical reaction in the region of
Rotating rate=1000 rpm
Rotating rate=1000 rpm   a rotating substrate.
                          a rotating substrate.


                         Nevertheless, lots of it flow out from the
                         Nevertheless, lots of it flow out from the
                         outlet with a immobile substrate.
                         outlet with a immobile substrate.




   Rotating rate=0 rpm
   Rotating rate=0 rpm
          Performace Compared                                            23




                         More TMG*NH3 flows to the region of
                          More TMG*NH3 flows to the region of
                         substrate under the rotation than
                          substrate under the rotation than
Rotating rate=1000 rpm
Rotating rate=1000 rpm   that without the effect, which is beneficial
                          that without the effect, which is beneficial
                         to the growth of GaN.
                          to the growth of GaN.




  Rotating rate=0 rpm
  Rotating rate=0 rpm
                                            Performace Compared                                  24


                                     36
                                     34
                                                                          0 rpm
                                     32
                                     30
                                                                          200 rpm
                                     28                                   400 rpm

           Growth rate ( µm / hr )
                                     26                                   700 rpm
                                     24                                   1000 rpm
                                     22                                   1500 rpm
                                     20                                   2000 rpm
                                     18                                   2500 rpm
                                     16
                                     14
                                     12
                                     10
                                      8
                                      6
                                      4
                                      2
                                      0.0    0.5   1.0   1.5       2.0       2.5     3.0   3.5
                                                               X ( cm )

Remark: At lower RPM, rotation increases growth rates of GaN by attracting species to the
Remark: At lower RPM, rotation increases growth rates of GaN by attracting species to the
   disk center. At higher RPM, larger radial velocity leads to more species leaking
    disk center. At higher RPM, larger radial velocity leads to more species leaking
   towards the outlet without having a chance to be deposited on substrate.
    towards the outlet without having a chance to be deposited on substrate.

                                     Pressure_gradient_const=0.01, RPM_ref=1500 rpm
                                     Pressure_gradient_const=0.01, RPM_ref=1500 rpm
                                                     25



                 Summary
PROCOM offers a comprehensive model of MOCVD
PROCOM offers a comprehensive model of MOCVD
process taking into account fluid dynamics, mass
process taking into account fluid dynamics, mass
and heat transports, and non-equilibrium gas-gas,
and heat transports, and non-equilibrium gas-gas,
gas-surface chemical reactions.
gas-surface chemical reactions.

Rather comprehensive GUI tools are developed to
Rather comprehensive GUI tools are developed to
handle geometry, mesh and chemical reaction
handle geometry, mesh and chemical reaction
design controls.
design controls.

The rotating disk model is efficient and clearly
The rotating disk model is efficient and clearly
demonstrates the benefits of using a rotating disk
demonstrates the benefits of using a rotating disk
in MOCVD.
in MOCVD.