14. MODELLING OF TECHNOLOGICAL PROCESS OF
IC FABRICATION
14.1. Objective of the test
Knowledge of IC fabrication processes, simulation of the thermal
impurity diffusion process.
14.2. Theory and the main formulae
The diffusion process is described by Fick’s equations:
N
(14.1)
,
x
N
2N
(14.2)
D 2 ,
t
x
where J is impurity atom flow density, N – impurity concentration, D diffusion coefficient, x - co-ordinate, t – time.
The diffusion coefficient D strongly depends on temperature:
(14.2)
D  D0  exp  Wa kT  .
J ( x)   D
Here D0 is the coefficient which depends on a semiconductor
material, impurity type, diffusion direction and initial impurity
concentration; Wa – activation energy, k – Boltzmann’s constant, T –
absolute temperature.
Usually diffused junctions are fabricated using a two-step process
to improve the controllability of the impurity profile N (x) . Two steps
are called the predeposition and drive-in diffusion.
The number of impurity atoms taken in by the solid during the
predeposition step is linear related to the partial pressure of the
impurity species in the gaseous atmosphere. For a given impurity
there is a maximum impurity concentration that the solid can
accommodate at a given temperature. This concentration is called the
solid solubility.
Using the solid-solubility limit at the surface we can find the
solution of the diffusion equation (14.2) for the predeposition step.
The solution is given by
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N ( x, t )  N 0 erfc
x
2 Dt
.
(14.3)
Here N 0 is impurity concentration at the surface, erfc is the
complementary error function. It is given by
erfc y  1 
y
2
 exp(  y ) d y .
2

(14.4)
0
The term Dt 1 / 2 is called the diffusion length.
If we know N(x,t), we can find the impurity flux density through
the surface of the wafer. According to the first Fick’s law
J (0, t )   D
N ( x, t )
x
x 0 
D
N0
Dt
e( x / 2
Dt ) 2
x 0
 N0
D
. (14.5)
t
Now, using the last equation we can find the diffusion dose – the
total number of impurity atoms per unit surface diffusing into the
wafer during the predeposition step:
t

Q (t )  J (0, t ) d t  ...  2 N 0
0
Dt
.

(14.6)
After the predeposition step the surface impurity concentration is
nominally equal to the solid solubility at the diffusion temperature.
Frequently it is necessary to reduce the surface concentration and at
the same time push the impurity atoms further away from the surface
into the bulk of the wafer. This desirable impurity distribution can be
achieved by the drive-in step. In a practical system the surface of the
wafer is sealed off by a thin oxide layer during the drive-in step. That
prevents the escape of impurity through the surface and the number of
impurity atoms remains constant during the drive-in step.
The total impurity Q resulting from predeposition may be
assumed to be a delta function. Using this as the initial condition and
solving the diffusion equation we can find the solution given by
N ( x, t © ) 

x 2 
exp  
.
D' t '
 4 D' t ' 
Q
58
(14.7)
If it is necessary to form a pn junction as a result of the diffusion,
the previously doped wafer is used. Let us consider that the wafer has
been doped by p-type impurity and the n-type impurity was introduced during the drive-in step. Then we can find the depth of the pn
junction assuming that
 x 2pn 
N .
N D 0 exp  
A
 4 Dt 


(14.8)
Then
x 2pn  4Dt ln
N D0
.
NA
(14.9)
Using the last equation we can find the depth of the pn junction
or choose regime of the diffusion process (T and t) to have a certain
depth of the junction.



1.
2.
3.
4.
5.
6.
7.
8.
14.3. Preparing for the test:
Using lecture-notes and referenced literature [2, p. 90–118],
examine IC fabrication and thermal diffusion.
Consider section “14.4. In laboratory” of this test.
Prepare to answer the questions:
Explain the fabrication sequence of a semiconductor IC. Name
the following processes: epitaxy, oxidation, photolithography,
diffusion and metallization.
Explain the purpose and mechanism of the thermal impurity
diffusion.
How does the diffusion coefficient depend on temperature, and
why?
Comment on the predeposition step of the thermal impurity
diffusion.
Comment on the drive-in step of the thermal impurity diffusion.
What three processes follow after the epitaxy while manufacturing bipolar ICs?
Describe the ion implantation process.
For what are oxide and nitride films used? How are they formed?
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9. What processes are used before the metallization?
10. Describe the metallization process.
14.4. In laboratory:
1. Answer the test question.
2. According to specified data:
a) Calculate the diffusion profiles formed using the predeposition
step.
b) Calculate the dependence of the diffusion flow density and the
doping dose on the time for the predeposition step.
c) Calculate the diffusion profiles formed using drive-in diffusion
step.
d) Investigate the influence of the temperature deviations at
predeposition and drive-in steps on the pn junction depth.
e) Calculate the diffusion profiles of bipolar transistors fabricated
using double thermal impurity diffusion.
3. After necessary calculations plot graphs and examine the results.
4. Prepare the report.
1.
2.
3.
4.
5.
14.5. Contents of the report
Objectives.
Initial data.
Results of calculations.
Diagrams.
Conclusions (explanation of physical processes going on during
the investigated diffusion stages; results of investigation of
temperature variation; interpretation of the base and emitter
regions fabrication of a npn transistor).
60