crystal growth and semiconductor epitaxy fafn15 (lth) fyst35
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Crystal growth and semiconductor epitaxy
FAFN15 (LTH) FYST35 (PHY) Spring 2013
Lecture (11)
Reaction zones in CVD
Zone 1: homogeneous reaction in gas phase Zone 2: heterogeneous reactions determine deposition rate and the properties of film Zone 3-5: solid state reactions including phase transformations, recrystallization etc. Zone 4: diffusion zone
Stagnant boundary layer
Film
substrate
zone 1
zone 2
zone 3
zone 4
zone 5
main gas flow
Laminar flow
Parabolic velocity profile (Poiseuille flow)
Reynolds number (Re) is the ratio of inertial forces to viscous forces. At Re<1, laminar flow At Re>1200, turbulent flow
Non-parabolic flow patterns •This complicated flow pattern can be caused by abrupt changes in flow path or by steep T gradients.
• Lower half: For gradual expansion of the supply line and a small u at the point of gas injection , parallel flow patterns are achieved.
• Upper half: In case of rapid expansion or high u, there is the ‘Hamel-flow’ vortex which is different from a turbulent flow.
•Hamel-flow vortices cause:
• increasing the reactant residence time
• longer switching time
• excessive homogeneous reaction
• Upon encountering the susceptor, the flow pattern changes again.
• u must decrease to zero at susceptor surface, but the parabolic profile is
restored after a few L lengths (at low Re).
Non-parabolic flow patterns
Axisymmetric flow Boundary layers
• Laminar boundary layer not relevant for CVD
• Velocity boundary layer (v):
• Radial velocity boundary layer (vr)
• Axial velocity boundary layer (vz)
• Concentration boundary layer (n)
• The boundary layer we are interested in is where the reactant transport changes from convective to diffusive.
• Rotating the susceptor disk, decreases the thickness of the velocity boundary layer and this boundary layer is not dependent on rs anymore.
CV
D
Free convection
• Grashof number (Gr) determines the degree of free convection and relates the ratio of buoyancy force to viscous force and Re. For high Gr, convection occurs.
• Gr depends on the reactor geometry, susceptor rotation and the amount of forced convection.
• The flow pattern is bistable over some range of Gr and uz.
• Reducing pressure is the most effective way of reducing Gr. Also susceptor rotation decreases Gr.
In absence of uz Large uz
CVD
Precursors → Film material + Gaseous products
Chemical reaction
• Chemical equilibrium considerations – Which reactions are possible
• Reaction rate and gas-phase diffusion – How far does the reactions proceed
CVD phase diagram
Reaction kinetics • Deposition of Si from silane (overall reaction):
SiH4(g) Si(c) + 2H2 (g)
• Overall reaction rate: the slowest step in the fastest pathway
polymerization
Gas-phase diffusion
• Gradual transition: convection → diffusion
• Surface reaction: concentration boundary layer (n)
• Concentration gradient derives
the reactant diffusion flux, JA
𝐽𝑟 = 𝐽𝐴 = −𝐷𝑛𝑧 − 𝑛0
𝛿𝑛
Fractional depletion of reactant:
𝑓0 =𝑛𝑧 − 𝑛0
𝑛𝑧=
𝐽𝑟
𝐷𝑛𝑧/𝛿𝑛
Two cases:
• Reaction control 𝑓0 → 0 Batch reactors
• Diffusion control 𝑓0 → 1
Axisymmetric reactor
Concentration boundary layer
Gas-phase diffusion
𝐽𝑟 =
𝑘𝑎𝑛𝑧
1 +𝑘𝑎
𝐷/𝛿𝑛
Two cases:
• Reaction control 𝑘𝑎 ≪ 𝐷/𝛿𝑛
• Diffusion control 𝑘𝑎 ≫ 𝐷/𝛿𝑛
𝑙𝑜𝑔𝑘𝑎 ∝1
𝑇𝑠, Arrhenius dependence
Slope=−𝐸𝑎
𝑅
Reaction control
Diffusion control
Onset of re-evaporation
The slope change with T in segement 3 is due to a change in the rate-limiting reaction step to one with a higher Ea.
Higher Jr