The inverse modeling problem is to find the parameter values of the
diffusion model of arsenic in silicon, where a large number of
19 measurements ought to be matched. Table 15.1
shows the process conditions of the experiments for which measurements
were obtained. In the table the temperature of the wafer surface, the
time period where the wafer was exposed to arsenic, and the arsenic
concentration at the wafer surface are given. The last column
indicates if the measurement refers to the electrically active or
total concentration.
Table 15.1:
The 19 process conditions for which measurements of the
arsenic profile were performed.

Table 15.2:
Variable of the model to be determined, their intervals,
and their units.

Table 15.3:
Result using optimizer DONOPT (cf. Section 9.3.5)
with the above free variables yielding the respective values. The
value of the objective function at this point is .

Figure 15.1:
Measurement and resulting simulation corresponding to
parameter values shown in Table 15.3. The
measurements used are numbered 1, 2, 3, 6, 7, and 8 in
Table 15.1.

Table 15.4:
Result using optimizer DONOPT (cf. Section 9.3.5)
with the above free variables yielding the respective values. The
value of the objective function at this point is .

Figure 15.2:
Measurement and resulting simulation corresponding to
parameter values shown in Table 15.4. All 19
measurements from Table 15.1 were used.

The simulations were performed using TSUPREM4 [8]. The
model of diffusion of arsenic and of point defects, i.e., interstitials
and vacancies, in silicon depends on several variables. The variables
of the model to be determined are shown in
Table 15.2. Their meaning is as follows.
is a factor used in the preexponential constants of the
diffusivities. The diffusivity of arsenic with neutral interstitials
is given by
where
is the preexponential constant
and
the activation energy. The diffusivity of arsenic
with neutral vacancies is given by
The diffusivity of arsenic with singlynegative interstitials
is given by
and the diffusivity of arsenic with singlynegative vacancies
is given by
Thus the preexponential constants of the interstitials and the
vacancies add to unity in the two cases of neutral and charged
particles.
Finally
is the preexponential constant for the
clustering of arsenic,
its activation energy, and
its exponent of concentration.
Clemens Heitzinger
20030508