Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
1998-07-20
2002-02-19
Teska, Kevin J. (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C703S013000, C702S084000, C117S201000
Reexamination Certificate
active
06349271
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention generally relates to a process simulating method, a process simulator, and a recording medium for recording a process simulation program. More specifically, the present invention is directed to such a process simulating method for simulating an oxidation process in a semiconductor device manufacturing step for an LSI and the like. Also, the present invention is directed to a process simulator for the above-described process simulating method, and also to a recording medium for recording a process simulation program.
2. Description of the Related Art
Conventionally, process simulators are practically available in order to predict internal physical amounts and shapes such as impurity profiles of various elements for constituting semiconductor devices such as LSIs by calculating an oxidation process, a diffusion process, an ion implantation process in manufacturing steps of these LSIs with employment of computers. When such a process simulator is employed, manufacturing processes of the respective elements for constituting the semiconductor device such as the LSI can be optimized as a desk plan in such a manner that the semiconductor device such as the LSI has a desirable electric characteristic. As a consequence, the manufacturing cost can be considerably reduced and the time can be largely shortened, as compared with the actual manufacture of the semiconductor device as a trial case.
To calculate the manufacturing steps for the various sorts of elements by using the computer, the model formulae have been installed in the process simulator with respect to each of the processes. Among these processes, as to the oxidation process, for example, the following simulation method is known. That is, the formula of Deal-Grove (see formula (22)) disclosed in Japanese publication “VLSI Designing/Manufacturing Simulation” written by M. MORISUE issued by CMC K. K., in 1987, pages 62 to 63 is differentiated with respect to time to thereby obtain the formula (23). Then, this formula (23) is solved to simulate the temporal change in the film thickness of the silicon oxide film (SiO
2
, simply referred to as an “oxide film” hereinafter).
In the formulae (22) and (23), symbol “t” indicates a time instant in the oxidation process, symbol “T
OX
” shows a film thickness of an oxide film at a present time instant, and symbol “T
P
OX
” indicates a film thickness of an oxide film at a preceding time instant, and also symbols “A” and “B” are parameters related to oxidation speed. The formula (23) is applied to an one-dimensional oxidation case such that a flux of an oxidizing agent does not depend upon a place:
T
OX
2
+AT
OX
=B
(
t+&tgr;
) (22)
ⅆ
T
OX
ⅆ
t
=
B
(
2
T
OX
P
+
A
)
(
23
)
On the other hand, very recently, in connection with the high integration in semiconductor devices such as LSIs and VLSIs, namely in conjunction with very fine structures of structural elements for constituting these semiconductor devices, these structural elements are isolated by employing LOCOS (Local Oxidation of Silicon) structures and trench structures in order to avoid electrical adverse influences caused by these structural elements. As a consequence, also in process simulators, oxide film shapes in these LOCOS structures and trench structures are required to be simulated. When these oxide film shapes are simulated, since fluxes of oxidizing agents differ from each other, depending on places, the simulation for the oxide film shapes should be carried out at least in the two-dimensional manner, which is completely different from the one-dimensional oxidation.
The two-dimensional oxidation simulation as to the LOCOS structure is disclosed in Japanese publication “Semiconductor Process Device Simulation Technique” written by S. ISOMAE, published by REALIZE publisher, in 1990, on pages 79 to 89. Also, the method for determining the time step “&Dgr;t” equal to the unit time of the oxidizing agent diffusion within the oxide film during the oxidation process is described in “Two-Dimensional Oxidation” by DAEJE CHIN et al., IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-30, No. 7, July 1983.
Now, the conventional two-dimensional oxidation process simulating method disclosed in the last-mentioned publication will be described with reference to a flow chart shown in FIG.
5
and a sectional structure view of an LSI under manufacture indicated in FIG.
6
.
In the flow chart of
FIG. 5
, at the first step SA
1
, the time instant variable “t” used to count up a time elapse in the oxidation process is set to zero. Subsequently, the simulating operation is advanced to the step SA
2
. At this step SA
2
, the Laplace equation indicated in the above-described formula (24) as to the oxide film
1
is solved to calculate oxidizing agent (oxidant) density C
S
OX
at the boundary surface between the oxide film
1
and the silicon substrate
2
(will be referred to as “a boundary surface between an oxide film/a silicon substrate” hereinafter). Then, the simulating operation is advanced to the further step SA
3
. In the following formula (24), symbol D
OX
shows the diffusion coefficient of the oxidizing agent within the oxide film
1
:
D
OX
∇
2
C
OX
=0 (24).
At the step SA
3
, the film thickness T
S
OX
of the oxide film
1
of the side wall in the LOCOS structure at the time instant “t” is calculated. Thereafter, the process operation is advanced to the step SA
4
.
At the step SA
4
, the calculated value of this film thickness T
S
OX
is substituted for the below-mentioned formula (25) so as to calculate the time step “&Dgr;t” equal to the unit time of the oxidizing agent diffusion within the oxide film
1
during the oxidation process. Subsequently, the simulating process is advanced to the step SA
5
. It should be understood that symbol “&Dgr;T
OX
” shown in the formula (25) is a desirable film thickness increase amount of the oxide film
1
per 1 time step &Dgr;t. This formula (25) is substantially same as the formula [23] disclosed in page 748 of the last-mentioned publication “Two-Dimensional Oxidation”.
Δ
t
=
(
2
T
OX
S
+
A
B
)
Δ
T
OX
(
25
)
At the step SA
5
, the time instant “t” is advanced only by the time step &Dgr;t. In other words, after the time step &Dgr;t is added to the time instant variable “t”, this simulating process is advanced to the step SA
6
.
At this step SA
6
, after the calculation is made of deformation in the shape of the oxidation film as to the time instant “t”, the simulating process is advanced to the further step SA
7
.
At this step SA
7
, the judgment is made as to whether or not the time instant “t” reaches an ending time instant of the oxidation process. If the judgment result is “NO”, then the simulating process is returned to the step SA
2
, at which the process operations defined from the step SA
2
to the step SA
6
are repeatedly performed. Then, in the case that the time instant “t” has reached the ending time instant of the oxidation process, since the judgement result of the step SB
8
becomes “YES”, a series of simulation work is accomplished.
As previously explained, in accordance with the conventional process simulating method, as indicated in
FIG. 6
, the time step “&Dgr;t” is determined in such a manner that the increased value of the film thickness T
S
OX
of the oxide film of the side wall in the LOCOS structure is continuously made equal to the film thickness &Dgr;T
OX
.
On the other hand, in the above-explained conventional process simulating method, the film thickness T
S
OX
of the side wall in the LOCOS structure is employed as the present film thickness of the oxide film
1
which is required to determine the time step “&Dgr;t”. As a consequence, this conventional process simulating method owns such a drawback that this process simulating method cannot be applied to any of the oxidation process simulation methods. That is, when the respective structural elements for constituting
Broda Samuel
NEC Corporation
Teska Kevin J.
LandOfFree
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