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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

Chapter 6 Selected Materials Processing Technologies

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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:

2CO(g) CO2(g) + C(s)[6.3-1]

The equilibrium constant for the reaction is as follows

2COP C2

CO

PK = a

P[6.3-2]

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]

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Where fc is the activity coefficient. The equilibrium constant KP has been determined to be a function of temperature T as follows :

P

-8918log K = +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

2

2CO

CO

PK=

P [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 wi℃th an induction heater. The vapor does not deposit on the quartz tube as quartz cannot be induction-heated.

The inlet gas is hydrogen containing a controlled concentration of silicon tetrachloride. The basic reaction is

4 2( ) 2 ( ) ( ) 4 ( )SiCl g H g Si s HCl 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 (B2

H6) 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:

2 2( ) ( ) ( )Si s O g SiO s

2 2 2( ) 2 ( ) ( ) 2 ( )Si s H O g SiO s H 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 H2

O(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 transfer9.2.1 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 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.

2

2A A

ADt x

2

2A A

A

w wD

t x

[9.2-1]

Since A = wA and is constant, this equation becomes

[9.2-2]

The initial and boundary conditions are wA(x,0) =wAi [9.2-3]

[9.2-4] [9.2-5]wA(0,t) =wAS wA(∞,t) =wAi

The solution is as follows:4

A AS

Ai As A

w w xerf

w w D t

[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 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]

0 4A AS

As A

w w xerf

w D t

[1 ]4

A As

A

xw w erf

D t

0 AM w dx

[9.2-7]

or

[9.2-8]

Let M be the amount of dopant predeposited per unit area

[9.2-9]

Substituting Eq.[9.2-8] into [9.2-9]

01 ( )

4AS

A

xM w erf dx

D t

[9.2-10]

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04 1 ( ) ( )

4 4AS A

A A

x xM w D t erf d

D t D t

0

11 ( )erf d

4 AAS

D tM w

[9.2-11]

using

We obtain

2

2A A

A

w wD

t x

wA(x,0) =wAi [9.2-15]

[9.2-16]wA(∞,t) =wAi

Let us now consider the drive-in of dopant A. We assume that the depth of diffusionin 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]

The initial and boundary conditions are

[9.2-14]

[9.2-13]

[9.2-12]

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And the mass conservation requirement is

0 AM w dx

2

exp4A

AA

M xw

D tD t

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].

[9.2-18]

[9.2-17]

The solution is listed as follows