Transcript Document

Chapter 6 Selected Materials Processing Technologies
6.3. Gas-to Solid Processing
6.3.1. surface Heat Treating
Carburizing is a surface heat treating process in which the carbon content
of the surface of a steel is increased, usually to between 0.8 and 1 wt%, by
exposure to a gas atmosphere at an elevated temperature, often between
850 and 950°C . Subsequent rapid cooling allows the high-carbon surface
layer to transform to martensite, thus producing a hardened surface layer for
wear resistance, as shown in the gear in Fig. 6.3-1
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As illustrated in Fig. 6.3-2, the gas atmosphere can
be a mixture of CO and CO2 , with or without an inert
gas such as N2, to cause carburization by the
following reaction:
[6.3-1]
2CO(g)  CO2(g) + C(s)
The equilibrium constant for the reaction is as
follows
KP =
PCO2
P
2
aC
[6.3-2]
CO
Where PCO2 and PCO are the partial pressures of CO2 and CO in the gas mixture,
respectively. The activity of carbon aC is a function of the carbon concentration wC
as follows:
ac= fc wc
[6.3-3]
2
Where fc is the activity coefficient. The equilibrium constant KP has been
determined to be a function of temperature T as follows :
log K P =
-8918
+9.1148
T(K)
[6.3-4]
From Eqs. [6.3-2] through [6.3-4], it is seen that the surface carbon concentration
wC depends on both temperature T and parameter K defined by
P 2 CO
K=
PCO 2
[6.3-5]
Figure 6.3-3 can be used to find wC from T and K ; the total pressure of the gas
mixture is 1 atm. Similar information is also available for carburization by the
reaction
CH4(g)  2H2(g) + C(s)
[6.3-6]
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6.3.2. Semiconductor Device Fabrication
The fabrication of silicon devices is illustrated in Fig. 6.3-4
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6.3.2.1 Chemical Vapor Deposition
Chemical vapor deposition is a widely
used process illustrated in Fig. 6.3-5.
The Si wafer, placed on a rotatable
graphite susceptor to typically above
1000℃ with an induction heater. The
vapor does not deposit on the quartz
tube as quartz cannot be inductionheated.
The inlet gas is hydrogen containing a
controlled concentration of silicon
tetrachloride. The basic reaction is
SiCl4 ( g )  2H2 ( g )
Si(s)  4HCl ( g )
[6.3-7]
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The Si single-crystal thin film grows
on the substrate with the same lattice
structure and orientation as the
substrate；this is, epitaxial growth.
Chemicals containing the atoms to be
doped in the thin film are introduced in
the inlet gas；examples are phosphine
(PH3) for n-type doping and diborane
(B2H6) for P-type doping. Figure 6.3-6
illustrates the formation of a P-doped Si
film.
6.3.2.2 Thermal Oxidation
Thermal oxidation in Si device fabrication is to form a SiO2 layer (Fig. 6.3-4c)
that can protect the device surface and/or provide a mask for selective diffusion.
Either a dry or a steam oxidation process can be used, as shown by
Dry oxidation:
Steam oxidation:
Si(s)  O2 ( g )  SiO2 (s)
Si(s)  2H2O( g )  SiO2 (s)  2H2 ( g )
[6.3-8]
[6.3-9]
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The steam oxidation process is illustrated on Fig. 6.3-7. As shown in Fig. 6.3-8,
the growth mechanism of the SiO2 layer is such that the oxidant, either O2(g) or
H2O(g), diffuses through the layer to the SiO2/Si interface and react with Si to form
SiO2 .
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6.3.2.3. Thermal Diffusion
Thermal diffusion in semiconductor device fabrication consists of two steps:
predeposition and drive-in diffusion.
In predeposition the wafer is exposed briefly to a dopant-containing gas
atmosphere at an elevated temperature so that its surface is saturated with the
dopant, as illustrated in Fig. 6.3-9a. A
Fig. 6.3-10; the furnace temperature
ranges from 800 to 1200oC.The liquid
dopant source can be boron tribromide
BBr3 for boron diffusion in silicon. The
BBr3 vapor, which is produced by
bubbling an inert carrier gas (e.g., N2)
through the liquid source, is allowed to
react with oxygen according to the
following reaction:
4BBr3(g) + 3O2(g) 
2B2O3(g) + 6Br2(g)
[6.3-10]
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The gaseous B2O3 then reacts with silicon as follows:
2B2O3(g) + 3Si(s)  4B(s) + 3SiO2(g)
[6.3-11]
The boron so produced is incorporated into silicon, whereas the SiO2 forms a
thin layer on the surface. The concentration of the dopant at the surface of the
wafer is nominally equal to the solubility of the dopant in silicon, which is given
in Fig. 6.3-11 as a function of temperature for several dopants in silicon.
After predeposition, extended thermal diffusion can be applied to reduce the
surface dopant concentration and push the dopant deeper into the bulk of the
substrate. This step, called drive-in diffusion, is illustrated in Figs. 6.3-9b
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Chapter 9 Mass Transfer in Materials Processing
9.2 One-dimensional mass transfer
9.2.1 Surface heat treating: Carburizing
The surface of a carbon steel of an initial
carbon level wAi is to be carburized (Section
6.3.1). The steel is heated to the desired
temperature in a furnace. At time = 0 the steel
is exposed to a gas mixture containing CO2
and CO, which keeps its surface at a constant
carbon level wAS throughout carburizing, as
illustrated in Fig. 9.2-1. the carburized layer is
much thinner than the steel itself
and the latter can thus be considered
semiinfinite.
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We assume that the overall density
r and the diffusion coefficient of
carbon in steel DA are both constant.
Since the steel is stationary and there
are no chemical reactions in it, the
species continuity equation reduces to
the following Eq.
r A
2 r A
 DA
t
x 2
[9.2-1]
Since rA = rwA and r is constant, this equation becomes
wA
 2 wA
 DA
[9.2-2]
t
x 2
The initial and boundary conditions are
wA(0,t) =wAS
[9.2-4]
The solution is as follows:
wA(x,0) =wAi
[9.2-3]
wA(∞,t) =wAi
[9.2-5]
 x 
wA  wAS
 erf 

wAi  wAs
 4 DAt 
[9.2-6]
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9.2.2 Semiconductor device fabrication: Dopant diffusion
Doping by diffusion is usually conducted in two steps: predeposition and drive-in.
Let us consider the predeposition of a dopant A into an initially dopant free substrate.
Assume that the diffusion coefficient of the dopant DA and the density r are constant,
and that the doped layer is much thinner than the substrate, that is, the substrate is
seminfinite. Since WAi=0, from Eq. [9.2-6]
 x 


 4 DAt 
[9.2-7]
 x 
wA  wAs [1  erf 
]
 4 DAt 
[9.2-8]
wA  wAS
 erf
0  wAs
or
Let M be the amount of dopant predeposited per unit area

M   r wAdx
0
[9.2-9]
Substituting Eq.[9.2-8] into [9.2-9]
M  r wAS 

0


x
) dx
1  erf (
4 DAt 

[9.2-10]
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M  r wAS 4 DAt 

0
using


x
x
1

erf
(
)
d
(
)


4 DAt 
4 DAt


 1  erf ( )d 
0
We obtain
M  r wAS
[9.2-11]
1

4DAt

[9.2-12]
[9.2-13]
Let us now consider the drive-in of dopant A. We assume that the depth of diffusion
in predeposition is much smaller that that in drive-in, and that the latter is in turn much
smaller than the thickness of the substrate. From Eq.[9.2-2]
wA
 2 wA
 DA
t
x 2
[9.2-14]
The initial and boundary conditions are
wA(x,0) =wAi
[9.2-15]
wA(∞,t) =wAi
[9.2-16]
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And the mass conservation requirement is

M   r w Adx
0
[9.2-17]
The solution is listed as follows
  x2 
M
wA 
exp 

4
D
t
r  DAt

A 
[9.2-18]
Where DA is the diffusion coefficient of the dopant at the drive-in temperature
and t is the drive-in time. Eq. [9.2-18] describes the concentration profile of
dopant A in the substrate. The amount of the dopant predeposited, M,
can be determined from Eq. [9.2-13].
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