Page 223 - Semiconductor Manufacturing Handbook

Geng(SMH)_CH15.qxd 04/04/2005 19:53 Page 15.8

EPITAXY

15.8 WAFER PROCESSING

1. k << h : The growth mode is reaction limited and since the reactions are thermally activated
s g
or of the Arrhenius type, the growth rate is given by
Gr ≈ CM k with k = k e − EkT)
a /
(
T
N s s 0
where E = reaction activation energy (E ≈ 1.6 for silicon)
a a
k = Boltzman constant
T = temperature
k = constant independent of temperature
0
In this regime, the growth rate is highly temperature dependent and will increase until the mass
flow limits the process.
2. h < k : The growth process is mass transport or gas-phase diffusion controlled and the growth
g s
rate equation is reduced to
Gr ≈ C g h with h = D g
N g g d
b
where D is the diffusion coefficient through the boundary layer δ .
g b
In practice, the mass-transport-limited regime is preferred since it is practically independent of
the growth temperature and primarily driven by a square root dependence on the bulk flow, thus
allowing for high growth temperature for high-quality epilayers. Figure 15.7 shows the growth
regime as a function of the deposition temperature.
However, the mass transport regime depends strongly on the boundary layer thickness, which in
turn depends on the reactor geometry leading to restrictions on the reactor chamber design. Horizontal-
type reactors provide the ability to control the boundary layer structure by maintaining the lowest pos-
sible height-to-width aspect ratio of the reaction chamber.
11
According to the boundary layer theory, δ is given by
b
d =  Dx  / 12 with Re = Dvp
b   
 Re m
where D = reaction tube diameter
x = distance along the reactor
Re = Reynolds numbers

= k exp(−E /kT)
k s 0 a h g = constant
Growth rate (log scale)

Mass transfer Reaction
controlled Mixed controlled
I/T
FIGURE 15.7 Growth regimes as a function of deposition
temperature.

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