JP3298524B2 - Process simulation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a process simulation method for simulating an oxidation process and the like in a semiconductor device manufacturing process using a computer or the like.
The present invention relates to a process simulation method in which calculation time is reduced.

[0002]

2. Description of the Related Art Conventionally, a process simulator is used to calculate semiconductor transistor manufacturing processes such as an oxidation process, a diffusion process, and an ion implantation process using a computer and to predict internal physical quantities such as an impurity profile of a transistor and a shape. Is used. By optimizing transistors so that semiconductor devices exhibit the best electrical characteristics using a process simulator, costs and time are significantly higher than when prototypes of large-scale integrated circuits (LSIs) are actually manufactured. Can be reduced. In a process simulator, a model formula is incorporated in each process in order to calculate various semiconductor transistor manufacturing processes using a computer.

[0003] In an LSI, LOCOS is used to prevent devices from electrically affecting each other.
Element isolation is performed by an oxide film or a trench. With the recent miniaturization of devices, element isolation simulation such as formation of a LOCOS oxide film and formation of a trench is also required.
Dimensions are being promoted.

[0004] For example, as a calculation method of two-dimensional LOCOS oxidation, see “Semiconductor Process Device Simulation Technology” (published by Realize) pp. 79-89 and "First
Knitting process Chapter 2 Process simulation Section 3 2D oxidation simulation ". In these calculation methods, the oxidation rate is calculated from the oxidant concentration, how much the Si / SiO ₂ interface moves at a certain time interval is calculated, and the shape change is calculated from the displacement amount. Even when the oxide film growth is extremely small, the thickness of the grown oxide film is always calculated, and a new interface (silicon oxide film boundary) is obtained.
Has been created.

[0005]

However, in the above-mentioned conventional calculation method, there is a problem that unnecessary oxidation calculation is always performed and the calculation time is long. In other words, when the oxidation rate is low at a low temperature and the time interval is made small in order to guarantee the accuracy, the growth of the oxide film becomes extremely small. In the case of LOCOS oxidation, the oxidant introduced from the oxidizing atmosphere diffuses in the oxide film to reach the silicon surface, but the oxidant concentration is low near the nitride film, and the growth of the oxide film becomes extremely small. However, in the above-described conventional calculation method, even when the oxide film growth is extremely small, the calculation time is long because the grown film thickness of the oxide film is calculated and a new interface is created.

[0006] The present invention has been made in view of such a problem, and can reduce the calculation time,
An object of the present invention is to provide a process simulation method that can be performed with high accuracy.

[0007]

A process simulation method according to the present invention is a process simulation method for simulating a process of forming an oxide film on the surface of a semiconductor material at predetermined time intervals. wherein the step of calculating the surface Oki Shidanto concentration at the interface between the oxide film and the semiconductor material, the surface Oki Shidanto concentration value obtained by multiplying a predetermined coefficient to solve the oxidant diffusion equation showing the relation between the diffusion coefficient and the oxidant concentration
Calculating the displacement vector in the direction perpendicular to the interface, and selecting one node on the interface;
When the previous displacement vector at the previous time is stored
At the nodal point and the calculated prior displacement vector
The current displacement vector is the sum with the displacement vector,
If the pre-displacement vector has not been saved,
The displacement vector to be used as the current displacement vector.
The magnitude of the current displacement vector and the time from the previous time
A step of calculating the product of the elapsed time and the growth thickness of the oxide film; and
The new interface is calculated at the current time
If the current displacement is less than a predetermined amount,
Save the vector and delete the current displacement vector before saving,
When the growth film thickness is larger than the predetermined amount,
Calculating the new interface by adding the grown film thickness
By executing the all nodes, and having a step of determining the current displacement vector of the interface at the current time, the.

In the present invention, since the current displacement vector of the interface at the current time is obtained in association with the calculated displacement vector and the previous displacement vector at the previous time, the calculation time is reduced by eliminating extra oxidation calculations. It is possible to perform simulation with high accuracy.

Another process simulation according to the present invention
The method includes forming an oxide film on the surface of a semiconductor material.
Process simulation to simulate at fixed time intervals
A method of diffusing an oxidant in said oxide film.
Oxidant diffusion showing the relationship between number and oxidant concentration
Solve the equation at the interface between the oxide film and the semiconductor material.
Calculating the surface oxidant concentration,
The value obtained by multiplying the oxidant concentration by a predetermined coefficient
Calculating a displacement vector in a direction perpendicular to the interface;
A step of selecting one node on the interface, at a previous time
When the previous displacement vector is stored,
And the calculated displacement vector
And the same size as the previous displacement vector.
The current displacement vector is the sum of
If the vector is not saved,
Making a displacement vector the current displacement vector;
The magnitude of the displacement vector and the time elapsed since the previous time
A product thickness of the oxide film, and the growth
Standard for determining whether to calculate a new interface at the current time for film thickness
If the current displacement vector is equal to or less than the predetermined amount, the current displacement vector is stored.
And the current displacement vector before storage is erased, and
When the thickness is larger than the predetermined amount, the growth film thickness is
In addition, the process of calculating a new interface is performed for all nodes on the interface.
The interface at the current time.
Obtaining the current displacement vector of
And

[0010]

[0011]

[0012]

[0013] The oxide film may be made of LOCO (LOCO).
S) It may be an oxide film.

[0014]

BEST MODE FOR CARRYING OUT THE INVENTION As a result of intensive experiments and research conducted by the present inventors to solve the above-mentioned problems, if the amount of increase .DELTA.Tox of the oxide film thickness at a time interval .DELTA.t is smaller than a predetermined value, The oxidant concentration at the time is stored, the oxidant concentration is added at the next time, and the oxidation calculation is performed at the next time taking into account the increase in the oxide film thickness at the previous time, thereby eliminating unnecessary oxidation calculations. I found what I could do. This simulation method will be described. FIG. 6 is a flowchart showing a process simulation method for storing the oxidant concentration.

In this process simulation method, first, the oxidation time is set to 0 (step S1).
1).

Next, the oxidation time is advanced by Δt (step S12).

Then, at each time of the oxidation calculation, the oxidant diffusion equation is solved to calculate the surface oxidant concentration (step S13).

Next, the oxidant concentration is reset based on the oxide film thickness grown by the oxidant concentration (step S14).

Next, a displacement vector is calculated using the oxidant concentration obtained by the resetting (step S).
15).

Thereafter, a new interface is created from the displacement vector (step S16).

Next, the deformation of the oxide film is calculated (step S17).

The above steps S11 to S17
Are repeated until a predetermined time is reached.

Next, the method of resetting the oxidant concentration in step S14 will be described in more detail. FIG. 7 is a flowchart showing a method for resetting the oxidant concentration in the process simulation method for storing the oxidant concentration.

In this method of resetting the oxidant concentration, after calculating the oxidant concentration in step S13, one node on the interface to be oxidized is selected (step S14-1).

Next, for the selected node, the sum of the oxidant concentration stored at the previous time and the oxidant concentration at the current time is calculated, and this is set as the oxidant concentration at the current time (step S14-2).

Thereafter, the growth film thickness is calculated from the oxidant concentration at the current time (step S14-3).

Then, it is determined whether or not the grown film thickness is equal to or smaller than a predetermined amount ε (step S14-4).

If the result of this determination is that the grown film thickness is equal to or smaller than the predetermined amount ε, the oxidant concentration at the current time is stored (step S14-5), and the oxidant concentration at the current time before storage is cleared (erased) (step S14-5). Step S14-6).

The above steps S14-1 to S14
Steps up to 14-6 are performed for all nodes on the interface to be oxidized.

Next, the operation of the above-described simulation method will be described. FIG. 8 is a sectional view showing a LOCOS oxide film to be simulated. Here, a description will be given assuming that a SiO ₂ film 2 is formed as a LOCOS oxide film on a Si substrate 1 and a Si ₃ N ₄ film 3 is formed thereon. FIG. 9 is a schematic diagram showing the operation of a simulation method for preserving the oxidant concentration. It is assumed that the oxidation proceeds from time t = t ₀ to t ₁ and t ₂ .

According to the above-described simulation method, it is not necessary to perform an unnecessary oxidation calculation as in the related art.
Calculation time is reduced. However, assuming that the direction of the displacement vector is a direction perpendicular to the interface at each node, as shown in FIG. 9, the interface is drawn as time passes, and the amount of movement of the node at the previous time is associated with only the oxidant concentration. Since the information is held, for example, at time t = t ₁ , information on the movement direction of the node at the previous time t ₀ is not held. Accordingly, since the interface only in the displacement vector V ₁ of the current time without moving direction of the node at the previous time t ₀ is taken into account is determined, there is a drawback that looseness of the interface is increased.

The inventors of the present invention have conducted further studies and as a result, as a result of determining the displacement vector at the current time based on the displacement vector at the previous time, the calculation time is reduced while suppressing the rattling of the interface. I found what I could do.

Hereinafter, a process simulation method according to an embodiment of the present invention will be specifically described with reference to the accompanying drawings. FIG. 1 is a flowchart showing a process simulation method according to the first embodiment of the present invention.

In this embodiment, first, the oxidation time is set to zero.
(Step S1).

Next, the oxidation time is advanced by Δt (step S2).

Then, the surface oxidant concentration Cox is calculated by solving the oxidant diffusion equation represented by the following equation (1) (step S3).

[0037]

(Equation 1) Here, Dox is the oxidant diffusion coefficient, and Cox is the oxidant concentration at that time.

Next, calculate the displacement vector V _i (step S4). At this time, the magnitude of the displacement vector V _i | V _i
Is represented by the following equation (2).

[0039]

| V _i | = ΔTox / Δt = K · Cox where ΔTox is an oxide film thickness that increases with time Δt, and K is a proportional constant.

The direction of the displacement vector is a direction perpendicular to the interface at the node.

Thereafter, the displacement vector is reset based on the oxide film thickness grown by the displacement vector (step S5).

Next, a new interface is created using the displacement vector obtained by the resetting (step S6).

Next, the deformation of the oxide film is calculated (step S7).

Then, it is determined whether or not the time has reached a predetermined end time end (step S8). If the end time end has not been reached, the flow returns to step S2 to advance the oxidation time by Δt. That is, step S2
Are repeated until a predetermined end time is reached.

Next, the method of resetting the displacement vector in step S5 will be described in more detail. FIG. 2 is a flowchart showing a displacement vector resetting method according to the first embodiment of the present invention.

In the method for resetting the displacement vector in the first embodiment, after calculating the displacement vector in step S4, one node on the oxidized interface is selected (step S5-1).

Next, for the selected node, the previous time
Displacement vector V stored at _i-1And at the current time
Displacement vector V_iTo calculate the vector sum of
Displacement vector V at time_i(Step S5-
2). Note that the displacement vector V at the previous time is_i-1Is saved
If not, the displacement vector V_iIs as it is.

Thereafter, the displacement vector V _{i at the} current time is calculated.
Is used to calculate the growth film thickness ΔTox (step S5-
3).

Then, it is determined whether or not the grown film thickness ΔTox is equal to or smaller than a predetermined amount ε (step S5-4).

The result of this determination, the growth thickness ΔTox is equal to or less than a predetermined amount epsilon, stores the displacement vector V _i at the current time (step S5-5).

Next, the displacement vector V at the current time before storage is
_i is cleared (erased) (step S5-6).

Then, it is determined whether or not the necessity of resetting the displacement vector has been checked for all the nodes on the interface (step S5-7). If the result of determination in step S5-4 is that the growth film thickness ΔTox is larger than the predetermined amount ε, step S5-7 is immediately performed. If all nodes have not been reset,
Returning to step S5-1, a point on the interface for which the necessity of resetting has not yet been checked is selected. That is, step S
The steps from 5-1 to S5-6 are repeated until the resetting of the displacement vectors is completed for all the nodes.

Next, the operation of the above-described first embodiment will be described. Here, a simulation is performed on the growth of the LOCOS oxide film 2 shown in FIG. FIG. 3 is a schematic diagram showing the operation of the first embodiment of the present invention. It is assumed that the oxidation proceeds from time t = t ₀ to t ₁ and t ₂ .

[0054] First, the displacement vector V ₀ which each node at time t = t ₀ is calculated. The magnitude | V ₀ | of the displacement vector V ₀ is ΔTox / Δt, and the direction is a direction perpendicular to the interface at the node. Then, the product of each displacement vector V ₀ and the time Δt is obtained, and the growth oxide film thickness ΔTox at each node at the time t ₀ is calculated.

At the nodes where the grown film thickness is larger than the predetermined amount ε, the conventional oxidation calculation is performed. on the other hand,
For a node whose growth film thickness is equal to or smaller than the predetermined amount ε, the displacement vector V _{0 at} that node is stored, and the oxidation calculation at that time is not performed. Stored displacement vector V
₀ is the displacement vector V at this and the next time t = t _1
1 (shown by a broken line in FIG. 3), and
It is used for resetting the displacement vector V ₁ (shown by a solid line in FIG. 3) at the next time t = t ₁ . Such a process is performed for all nodes on the interface to be oxidized.

As described above, in the present embodiment, for a node whose growth film thickness is equal to or less than the predetermined amount ε, the displacement vector at the node is stored and the oxidation calculation at that time is not performed, but the storage at the next time is performed. Since the vector sum of the calculated displacement vector and the displacement vector at the next time is taken and reset as the displacement vector at the next time, the calculation time can be shortened by omitting unnecessary oxidation calculations, and By maintaining the moving direction of the interface at the time, the rattling of the oxide film shape can be reduced.

Next, a second embodiment of the present invention will be described. The second embodiment differs from the first embodiment in the method of resetting the displacement vector, but the other steps are the same as those of the first embodiment. FIG. 4 is a flowchart showing a displacement vector resetting method according to the second embodiment of the present invention.

In the method for resetting the displacement vector in the second embodiment, after calculating the displacement vector in step S4, one node on the interface to be oxidized is selected (step S5-11).

Next, for the selected node, the previous time
Displacement vector V stored at _i-1And the same as this
And the displacement vector V at the current time_iSize of
｜ V_iCalculate the vector sum with the vector having |
The displacement vector V at the current time_i(Step
S5-12). Note that the displacement vector V at the previous time is_i-1But
If not, the displacement vector V_iIs as it is
You.

Thereafter, the displacement vector V _{i at the} current time is calculated.
Is calculated from the equation (step S5-1).
3).

Then, it is determined whether or not the grown film thickness ΔTox is equal to or smaller than a predetermined amount ε (step S5-14).

[0062] As a result of this determination, the growth thickness ΔTox is equal to or less than a predetermined amount epsilon, stores the displacement vector V _i at the current time (step S5-15).

Next, the displacement vector V at the current time before storage is
_i is cleared (erased) (step S5-16).

Then, it is determined whether or not the necessity of resetting the displacement vector has been checked for all the nodes on the interface (step S5-17). If the result of determination in step S5-14 is that the growth film thickness ΔTox is larger than the predetermined amount ε, step S5-17 is immediately performed. If the investigation of the necessity of resetting has not been performed for all the nodes, the process returns to step S5-11 to select one point on the interface that has not yet been investigated. That is, steps S5-11 to S5-16 are repeated until the investigation of resetting of the displacement vector is completed for all the nodes.

Next, the operation of the above-described second embodiment will be described. Here, a simulation is performed on the growth of the LOCOS oxide film 2 shown in FIG. FIG. 5 is a schematic diagram showing the operation of the second embodiment of the present invention. It is assumed that the oxidation proceeds from time t = t ₀ to t ₁ and t ₂ .

[0066] First, the displacement vector V ₀ which each node at time t = t ₀ is calculated. The magnitude | V ₀ | of the displacement vector V ₀ is ΔTox / Δt, and the direction is a direction perpendicular to the interface at the node. Then, the product of each displacement vector V ₀ and the time Δt is obtained, and the growth oxide film thickness ΔTox at each node at the time t ₀ is calculated.

At the nodes where the grown film thickness is larger than the predetermined amount ε, the conventional oxidation calculation is performed. on the other hand,
For a node whose growth film thickness is equal to or smaller than the predetermined amount ε, the displacement vector V _{0 at} that node is stored, and the oxidation calculation at that time is not performed. Stored displacement vector V
₀ is the displacement vector V at this and the next time t = t _1
1 (. In FIG. 5, indicated by a broken line) and the same size | V ₁ | vector sum of the displacement vector V ₀ the same direction as the vector has is taken, the displacement vector V ₁ at the next time t = t ₁ (Indicated by a solid line in FIG. 5). Such a process is performed for all nodes on the interface to be oxidized.

As described above, in the present embodiment, for a node whose growth film thickness is equal to or smaller than the predetermined amount ε, the displacement vector at that node is stored, and the oxidation calculation at that time is not performed, but is stored at the next time. Since the displacement vector of the next time is reset based on the displacement vector, the calculation time can be reduced by omitting unnecessary oxidation calculations, and the shape of the oxide film can be reduced by maintaining the movement direction of the interface at the previous time. The rattling can be reduced.

[0069]

As described in detail above, according to the present invention,
Since the current displacement vector of the interface at the current time is obtained in association with the calculated displacement vector and the previous displacement vector at the previous time, the extra oxidation calculation conventionally performed can be eliminated. For this reason, the calculation time can be reduced. In addition, since the previous displacement vector at the previous time is taken into consideration, the simulation can be performed with high accuracy.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a process simulation method according to a first embodiment of the present invention.

FIG. 2 is a flowchart illustrating a displacement vector resetting method according to the first embodiment of the present invention.

FIG. 3 is a schematic view showing the operation of the first embodiment of the present invention.

FIG. 4 is a flowchart illustrating a displacement vector resetting method according to a second embodiment of the present invention.

FIG. 5 is a schematic view showing the operation of the second embodiment of the present invention.

FIG. 6 is a flowchart illustrating a process simulation method for storing an oxidant concentration.

FIG. 7 is a flowchart showing a method for resetting the oxidant concentration in a process simulation method for storing the oxidant concentration.

FIG. 8 is a sectional view showing a LOCOS oxide film to be simulated;

FIG. 9 is a schematic diagram illustrating the operation of a simulation method for preserving the oxidant concentration.

[Explanation of symbols]

Reference Signs List 1: Si substrate 2: SiO ₂ film 3: Si ₃ N ₄ film

──────────────────────────────────────────────────続 き Continuation of the front page (56) References Monthly Semiconductor World, Japan, January, 140-143 Sharp Technical Report, Japan, No. 45, 37-42 IEEE TRANSONS ON ELECTRON DEVICE ES, USA, IEEE, ED-32, No. 2,132-140 (58) Field surveyed (Int.Cl. ⁷ , DB name) H01L 21/31 G06F 17/50 H01L 21/00 H01L 21/76

Claims (3)

(57) [Claims] 1. A process simulation method for simulating a process of forming an oxide film on a surface of a semiconductor material at predetermined time intervals, wherein the oxidant indicates a relationship between a diffusion coefficient of the oxidant in the oxide film and an oxidant concentration.
Calculating a surface Oki Shidanto concentration at the interface between the oxide film solves the diffusion equation and the semiconductor material, and the surface Oki Shidanto magnitude the value obtained by multiplying a predetermined coefficient to the concentration of
Calculating a displacement vector in a direction perpendicular to the interface; selecting one node on the interface;
When the previous displacement vector is stored
And the calculated displacement vector at
The current displacement vector is the sum of the current displacement vector and the previous displacement vector.
The change at the node if the
Making the current displacement vector the current displacement vector;
Between the magnitude of the position vector and the elapsed time from the previous time
Making the product a growth thickness of the oxide film, and the growth film
The criterion for determining whether or not to calculate a new interface at the current time
Save the current displacement vector if it is less than
Then, the current displacement vector before storage is erased, and the
If the amount is larger than the predetermined amount, the growth film thickness is added to the interface.
The process of calculating a new interface is described for all nodes on the interface.
By executing Te, process simulation method characterized by comprising a step of determining the current displacement vector of the interface at the current time, the. 2. A process for forming an oxide film on a surface of a semiconductor material.
Process simulation that simulates an experiment at predetermined time intervals
Oxidizing the oxidant in the oxide film.
Oxidant showing the relationship between dispersion coefficient and oxidant concentration
Solve the diffusion equation to find the interface between the oxide film and the semiconductor material.
Calculating the surface oxidant concentration in the
The value obtained by multiplying the surface oxidant concentration by a predetermined coefficient
Calculating a displacement vector in a direction perpendicular to the interface
And selecting one node on the interface,
When the previous displacement vector is stored
And the calculated displacement vector at
Torque and the same direction as the previous displacement vector
The current displacement vector is the sum of
If the position vector is not saved,
Making the displacement vector the current displacement vector,
The magnitude of the recorded displacement vector and the time since the previous time
The product of the thickness and the growth thickness of the oxide film, and
Whether the growth thickness should calculate a new interface at the current time
The current displacement vector when the value is equal to or less than a predetermined reference amount
Is stored, and the current displacement vector before the storage is deleted.
When the thickness is larger than the predetermined amount, the growth film is formed on the interface.
Calculating the new interface by adding the thickness to all nodes on the interface
By executing for, the said at the current time
Obtaining a current displacement vector of the interface.
A featured process simulation method. Wherein the oxide film, process simulation method according to claim 1 or 2, characterized in that the LOCOS oxide film.