Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
2000-05-22
2004-01-20
Jones, Hugh (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C703S006000, C703S013000
Reexamination Certificate
active
06681201
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to a simulation method of a breakdown, for simulating a phenomenon of impact ionization, which occurs in series.
In a conventional method, as shown by a dotted line D of
FIG. 3
, an impact ionization coefficient &agr;(E) is calculated from a magnitude of an electric field. Here, this impact ionization coefficient &agr;(E) is a coefficient on the assumption that a carrier is instantaneously accelerated. In the conventional method, by using this impact ionization coefficient, generation G
II
, of a carrier is calculated in accordance with an equation 6 described below (by means of an ISE manual):
G
II
=&agr;
n
·n·&ngr;
n
+&agr;
p
n·&ngr;
p
[Eq.
6
]
And, the generation of a carrier is calculated from the calculated impact ionization coefficient, and the generated carrier is combined with an original electric current, and the current increases, and a calculation of a phenomenon in which the impact ionization is also caused by the increased electric current is automatically obtained by calculating the drift diffusion model. Here, in
FIG. 3
, a solid line E indicates electric field strength, and a broken line F indicates an impact ionization coefficient in case that a process in which a carrier is accelerated is taken into account.
In the above-described conventional method, the electric field strength and the impact ionization coefficient are made to be a one-to-one function, and accordingly, if an electric field exists, a carrier is fully accelerated in the field.
Accordingly, compared with an actual fact, in the calculation, the impact ionization occurs too much. Such a task occurs because, as mentioned above, the electric field strength and the impact ionization coefficient are made to be a one-to-one function.
In the conventional model, in case that an electric field exists, a carrier is fully accelerated in the field and impact ionization occurs. However, actually, for accelerating a carrier, it is necessary that the carrier runs quite a long distance.
Accordingly, in the conventional model, since the impact ionization occurs greater than a reality, the calculation is not conducted correctly. Also, due to that, a breakdown voltage becomes to be smaller than a reality. As a result, in the conventional method, the impact ionization (or the breakdown) cannot be estimated correctly.
SUMMARY OF THE INVENTION
The present invention is made to solve the above-mentioned problems.
Moreover, the objective is to provide a simulation method of a breakdown, in which the impact ionization (or the break down) cannot be estimated correctly.
In accordance with the present invention, in a simulation method of a breakdown, an electric field distribution is calculated by means of a drift diffusion model, and a one-dimensional electric field distribution is taken out from a result of the calculation, and the electric field distribution which was taken out is provided to a one-dimensional Monte Carlo device simulation to calculate a distribution of impact ionization coefficients, and G
n
(x) is calculated by using an equation 1 to an equation 5 which are described in the above-described scope of claim for patent, and as a result of this calculation, it is determined that a breakdown does not occur in case that, as n becomes to be large, G
n
(x) converges to a constant value, and final electric current density is calculated, and it is determined that a breakdown occurs in case that G
n
(x) becomes to be large as n increases.
G
1
(
x
)
=
1
q
i
n
0
·
α
n
,
(
x
0
)
(
x
)
+
1
q
i
p
0
·
α
p
,
(
x
ω
)
(
x
)
+
∫
x
0
x
ω
G
0
(
x
′
)
α
n
,
(
x
′
)
(
x
)
ⅆ
x
′
+
∫
x
0
x
ω
G
0
(
x
′
)
α
p
,
(
x
′
)
(
x
)
ⅆ
x
′
[
Eq
.
1
]
G
2
(
x
)
=
∫
x
0
x
ω
G
1
(
x
′
)
α
n
,
(
x
′
)
(
x
)
ⅆ
x
′
+
∫
x
0
x
ω
G
1
(
x
′
)
α
p
,
(
x
′
)
(
x
)
ⅆ
x
′
[
Eq
.
2
]
G
n
+
1
(
x
)
=
∫
x
0
x
ω
G
n
(
x
′
)
α
n
,
(
x
′
)
(
x
)
ⅆ
x
′
+
∫
x
0
x
ω
G
n
(
x
′
)
α
p
,
(
x
′
)
(
x
)
ⅆ
x
′
[
Eq
.
3
]
∫
x
0
x
ω
G
n
(
x
′
)
α
n
,
(
x
′
)
(
x
)
ⅆ
x
′
[
Eq
.
4
]
∑
i
=
1
N
G
n
(
x
i
)
α
n
,
(
x
i
)
(
x
)
Δ
x
i
[
Eq
.
5
]
Here, the above-described electric field distribution is calculated by conducting a simulation by means of the above-described drift diffusion model, in which an inverse bias is applied to a semiconductor element including an element isolating region.
Also, the above-described semiconductor element has a device structure including a two-dimensional diode structure, for example.
In addition, the above-described semiconductor element has a device structure including a three-dimensional diode structure, for example.
Furthermore, the above-described element isolating region may be formed of a LOCOS (Local Oxidation of Silicon).
Also, the above-described one-dimensional electric field distribution is taken out by cutting out a part in an electric field direction in one dimension, which has the largest electric field out of the calculated electric field distribution.
In this case, the above-described part which has the largest electric field is, for example, an end portion of the element isolating region formed of the above-described LOCOS.
REFERENCES:
patent: 5627772 (1997-05-01), Sonoda et al.
patent: 5912824 (1999-06-01), Sawahata
patent: 5933359 (1999-08-01), Sawahata
Jones Hugh
NEC Electronics Corporation
Scully Scott Murphy & Presser
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