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