JP3123533B2 - 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, and more particularly to a process simulation method for performing a simulation in a process such as oxidation of a semiconductor device using a computer.

[0002]

2. Description of the Related Art A process simulator simulates an oxidation process, a diffusion process, an ion implantation process, and the like in a semiconductor device by performing calculations using a computer as if it were an actual operation. This is to predict the shape. If the process simulator is used to optimize the semiconductor device to exhibit the best electrical characteristics, the cost and the period can be significantly reduced as compared with actually producing LSl on a trial basis. In the process simulator, since the manufacturing processes of various semiconductor elements are calculated using a computer, a model formula is incorporated in each process. LS
In I, element isolation is performed by LOCOS (Local Oxidation of Silicon: selective oxidation method), a trench, or the like so that the elements do not electrically affect each other.

[0003] With the recent miniaturization of semiconductor elements, LO
It is also necessary to simulate element isolation such as COS and trench. For this reason, two-dimensional process simulation is being promoted. 2D LOCO
For the calculation method of S oxidation, see, for example, "Semiconductor Process Device Simulation Technology" (Realize)
pp. 79-89. The method described herein, the oxidation rate was calculated from the oxidant concentration, to calculate whether the Si / Si0 ₂ interface at a time interval is how much movement, and calculating the change in shape from its displacement.

By the way, when the oxidation rate is small at a low temperature and the time interval (simulation interval) is made small in order to guarantee the accuracy, the growth of the oxide film becomes very small. Further, 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 small near the nitride film, and the oxide film growth is very small. However, according to the method described in the above-mentioned literature, even when the oxide film growth is very small, the growth of the oxide film is always calculated to create a new interface (silicon oxide film boundary). You are doing the calculations.

The present inventors have proposed Japanese Patent Application No. 09-327616 as a process simulation method for preventing unnecessary oxidation calculations. In this method, in order to omit unnecessary oxidation calculations, if the oxide film thickness increasing weight ΔTox at the time interval Δt is less than a certain value, the oxidant concentration is stored, and the oxidant concentration is included at the next time. Then, at the next time, the oxidation calculation is performed in consideration of the oxide film thickness increment at the previous time.

FIG. 5 shows the processing of a conventional process simulation method in which unnecessary oxidation calculations are omitted. First, t = 0
(Step 501), the oxidation calculation is performed for each Δt (t = t + Δt) (Step 502), and the oxidant diffusion equation is solved to obtain the surface oxidant concentration (Step 503). Next, the oxidant concentration is reset according to the oxide film thickness grown by the oxidant concentration obtained in step 503 (step 50).
4). Further, a displacement vector is calculated using the oxidant concentration obtained in step 504 (step 50).
5) Create a new interface from the displacement vector (step 50)
6) Then, a deformation calculation is performed (step 507). The above procedure is repeatedly executed until the desired time comes (t = end) (step 508).

FIG. 6 shows the oxidane of step 504 of FIG.
The details of the method for resetting the concentration are shown. First, on the interface to be oxidized
(Step 601), and focus on each node
t₀ Oxidant concentration and current time t₁Oh
The oxidant concentration is added and the current time t₁Oxidane
(Step 602). Then step 6
Based on the oxidant concentration at the current time calculated in 02,
A growth oxide film thickness is calculated (step 603). further,
Determine whether the grown oxide film thickness is less than or equal to the comparison value ε
(Step 604). If the result of the judgment is that it is less than ε, the current
Time t₁(Step 60)
5). In step 605, the process of step 602 is performed next time.
Oxidant concentration for calculation
Save (copy) the data from the data storage device to the storage memory area. This
After the current time t in the register for calculation, etc.₁Oxy
The dant density is cleared (step 606). Steps
If it is determined in step 604 that ε is equal to or larger than ε, the process proceeds to step
Move to 7. After the process of step 606 is completed,
Steps 601 to 607 are applied to all nodes on the interface to be oxidized.
The process is executed (step 607). The processing of FIG. 6 is completed.
If so, the process returns to step 505 in FIG. 5 to execute the subsequent processing.
I do. By the processing of FIG. 6, unnecessary oxidation calculations can be omitted.
it can.

FIG. 7 shows a semiconductor device that has undergone a LOCOS process. Oxide film (SiO ₂ ) on the surface of the silicon substrate 1
2 is formed, and a nitride film (Si ₃ N) is formed on a part of the oxide film 2.
₄ ) 3 is formed. In FIG. 7, the right half where the oxide film 2 is thick is a portion where the oxide film is grown by selectively oxidizing the nitride film 3 (LOCOS treatment) after removing the nitride film 3. In addition, since the oxidizing agent diffuses into the lower portion of the nitride film 3 and enters the central portion, the nitride film 3 is curved upward.

FIG. 8 shows a two-dimensional simulation in which a part of the LOCOS shape of the semiconductor device of FIG. 7 is enlarged. The direction of the displacement vector at time t = t1 is set to be the vertical direction of the node. In the conventional methods shown in FIGS. 5 and 6, since the movement amount of the node at the previous time t = t0 is stored as the oxidant concentration, the information of the movement direction of the node at the previous time is not stored. Therefore, the previous time t = t
Since the moving direction of 0 is not taken into account, the fluctuation (rattle) of the interface increases.

FIG. 9 shows another process simulation method previously proposed by the present inventors to reduce the fluctuation of the interface. First, the oxidation time is set to zero (step 901). Next, the oxidation time is updated every Δt (t =
Δt) (step 902). At each time of the oxidation calculation, the oxidant concentration is solved using the oxidant diffusion equation of Dox ▽ · ▽ Cox = 0 (Dox is the oxidant diffusion coefficient, Cox is the surface oxidant concentration), and the surface oxidant concentration Cox is obtained (step 903). . Next, a displacement vector V0 is calculated (step 904). The magnitude of the displacement vector V0 is calculated by the following equation.

| V0 | = ΔTox / Δt = K · Cox (where, ΔTox is the oxide film thickness that increases with Δt, and K is a proportional constant) The direction of the displacement vector is the vertical direction of the node.
Further, the displacement vector is reset according to the oxide film thickness grown by the displacement vector (step 905). Next, a new interface is created using the displacement vector obtained in step 905 (step 906). Thereafter, a deformation calculation is executed (step 907). The above processing is repeatedly executed until a desired time (t = end).

FIG. 10 shows the details of the method for resetting the displacement vector in step 905 shown in FIG. First, a certain node on the interface to be oxidized is targeted (step 1001). Then, the vector sum of the displacement vector V0 at the previous time and the displacement vector V1 at the current time is calculated, and this is set as the displacement vector V1 at the current time (step 1002). Then
The growth oxide film thickness ΔTox is calculated based on the displacement vector V1 (step 1003). Furthermore, when the grown oxide film thickness is ε
It is determined whether or not it is below (step 1004). As a result of the determination, if ε> ΔTox, to use in the next calculation,
The displacement vector at the current time is saved (copied) from a register for calculation or the like to a memory area for saving (step 100).
5). Thereafter, the current time t ₁ in a register for calculation or the like is used.
Is cleared (step 1006). If ΔTox> ε, the process proceeds to step 1007.
Subsequent processing is the same as that of FIG. 6. After the displacement vector at the current time is cleared from the memory area for calculation in step 1006, it is determined in step 1007 whether all the nodes on the interface have been checked. If there are still nodes to be checked, the process returns to step 1001 and the subsequent processes are repeatedly executed. If all the nodes have been checked, the process ends.

FIG. 11 shows a two-dimensional simulation in the process of FIG. 10, and the LOC of the semiconductor device shown in FIG.
A part of the OS shape is shown in an enlarged manner. The oxidation takes place at time t
Progresses as t0 → t1 → t2. First, a displacement vector V0 (magnitude: ΔTox / Δt, direction is the vertical direction of the node) at time t = t0 (previous time) is calculated. The product of the magnitude of the displacement vector V0 and the added value Δt of the oxidation time is calculated, and the grown oxide film thickness ΔTox at that time is calculated. The oxidation calculation is performed in the conventional manner for the nodes having the grown oxide film thickness of ε or more. At the node where the grown oxide film thickness is not more than ε, the displacement vector V0 at that node is stored, and the oxidation calculation at that time is not performed. The stored displacement vector V0 is the sum of the displacement vector V1 at the current time t1 and the displacement vector V1 at the current time t1, and is used as the displacement vector at the next time t2. The above procedure is executed for all nodes on the interface to be oxidized.

FIG. 12 shows another example of the method of resetting the displacement vector in step 905 of FIG. First, a certain node on the interface to be oxidized is selected as a target (step 1201).
Then, the magnitude (scalar amount) of the displacement vector at the current time is added to the displacement vector at the previous time to obtain a displacement vector at the current time (step 1202). From this displacement vector, a grown oxide film thickness is calculated (step 120).
3). Next, it is determined whether or not the grown oxide film thickness is equal to or smaller than ε (step 1204). If the grown oxide film thickness is equal to or smaller than ε, the displacement vector at the current time is saved (copied) from a register for calculation or the like to a memory area for saving (step 1205), and the displacement vector is reset. After this,
Clears the displacement vector at the current time existing in the calculation register and the like.

FIG. 13 shows a two-dimensional simulation corresponding to the processing of FIG. 12, and the L of the semiconductor device shown in FIG.
A part of the OCOS shape is shown enlarged. First, a displacement vector V0 (magnitude: ΔTox /
Δt, the direction is the vertical direction of the node). The product of the displacement vector V0 and the step of the oxidation time is taken, and the grown oxide film thickness at that time is calculated. The oxidation calculation is performed for the nodes having the grown oxide film thickness of ε or more as described above. For a node having a growth oxide film thickness of ε or less, the displacement vector V0 at that node is stored, and the oxidation calculation at that time is not performed. The stored displacement vector is the current time (t = t1)
The displacement vector at the time is increased by | V1 | The above procedure is executed for all nodes on the interface to be oxidized.

[0016]

However, according to the conventional process simulation method, the first conventional method shown in FIGS. 5 and 6 has the disadvantage that the interface is not smooth and the fluctuation is large. Further, according to the second conventional method shown in FIGS. 9, 10 and 12, the fluctuation (rattle) of the interface can be reduced as compared with the first conventional method, but t = t1.
Since the direction of the displacement vector of the node is set to the bisecting angle direction of the line connected to the node, the fluctuation cannot be largely eliminated.

Accordingly, an object of the present invention is to provide a process simulation method which can reduce the fluctuation of the interface.

[0018]

According to the present invention, in order to achieve the above object, a displacement vector of each node on an interface between a semiconductor substrate and an oxide layer is calculated at predetermined time intervals based on an oxidant concentration at the interface. In the process simulation method for simulating a semiconductor device and then, it is determined whether two adjacent nodes adjacent on both sides of the moving node moved during the calculation of the oxidant concentration at the previous time have moved at the previous time, When one of the two adjacent nodes moves and the other does not move, a unit vector (a vector having a displacement amount of 1) of a displacement vector of the other adjacent node at the previous time and a displacement of the one adjacent node at the current time. The direction of the displacement vector of the moving node is corrected based on a combined vector obtained by combining the unit vectors of the vector, and the corrected displacement vector of the moving node is corrected. Based provides a process simulation method characterized by calculating the thickness of the oxide layer on the moving node to.

According to this method, with respect to a node that has moved when the simulation time has changed, if one of the nodes adjacent to the both sides of this node (adjacent node) has not moved, the moved node becomes the previous node. The combined vector of the direction of the unit vector of the displacement vector of the adjacent node (immobile adjacent node) not moving at the time and the direction of the unit vector of the displacement vector of the adjacent node (moving adjacent node) moved at the current time is Then, the direction of the displacement vector is corrected to the direction of the composite vector. As described above, the direction of the displacement vector at the current time is corrected in consideration of the direction of the displacement vector at the previous time, so that it is possible to reduce the fluctuation (wobbles) of the interface.

[0020]

Embodiments of the present invention will be described below with reference to the drawings. (First Embodiment) FIG. 1 shows a first embodiment of a process simulation method according to the present invention. First, a node i on the interface to be oxidized is selected (step 10).
1). Then, it is determined whether or not the node i has moved to the previous time by the oxidation deformation calculation (step 102). If the node i has not moved at the previous time, the magnitude (length) of the displacement vector at the current time is added to the magnitude (length) of the displacement vector at the previous time (step 103).
Move to.

If it is determined in step 102 that the node i has moved, then the node (i) adjacent to the node i
-1), (i + 1) none of it is determined whether to move to the previous time _{t 0} (step 104). If both the nodes (i−1) and (i + 1) have moved at the previous time t ₀ , the process proceeds to step 108. Then, the node (i-1), (i + 1) if only one of the moves (step 104), calculates the unit vector of the displacement vector at the previous time t ₀ in the adjacent node that has not moved (step 105 ), Calculate the unit vector of the displacement vector at the current time t1 at the moved adjacent node (step 106). Then, the direction of the displacement vector at the node i is corrected to the direction of the vector sum of the unit vectors obtained in steps 105 and 106 (step 107). Next, a grown oxide film thickness is calculated based on the magnitude of the displacement vector (step 108). Next, it is determined whether or not the grown oxide film thickness is equal to or smaller than the comparison value ε (Step 109). Is stored (copied) (step 110). After that, the displacement vector at the current time is deleted from the calculation register or the like (step 111). It is determined whether the above steps have been performed for all settings on the interface (step 11).
2) If all the steps have been executed, the process is terminated. If there is a node of the final examination, the process returns to step 101, and the subsequent processes are repeatedly executed.

FIG. 2 shows a two-dimensional simulation in the process of FIG. This simulation shows an enlarged part of the LOCOS shape of the semiconductor device of FIG.
In the following, description will be made mainly on the displacement at the node i. First, a displacement vector (magnitude is .DELTA.Tox / .DELTA.t, direction is a bisecting angle direction of the node) at time t = t0 (previous time) is calculated. The product of the displacement vector and the added value Δt of the oxidation time is taken, and the grown oxide film thickness at that time is calculated. For a node having a grown oxide film thickness of ε or more (here, node i), a conventional oxidation calculation is performed. Further, a node whose growth oxide film thickness is equal to or smaller than ε (here, the node (i
-1), hereinafter referred to as an immobile node) at the node (i-
The displacement vector in 1) is stored, and the oxidation calculation at that time is not performed. The stored displacement vector is the current time (t =
At (t1), the magnitude of the displacement vector at the current time t1 is added to the magnitude of the displacement vector at the previous time t0 to obtain a displacement vector at the node. The node (i, i + 1, i + 2,...) That has moved in the change from time t0 to t1
), At the node i having the fixed node (i-1) as an adjacent node, the direction of the unit vector p * (→) of the displacement vector at t = t1 of the fixed node (i-1) and the movement The direction of the displacement vector is corrected to the direction of the vector sum with the direction of the unit vector q * (→) of the displacement vector at t = t1 of the adjacent node (i + 1).

As described above, in the first embodiment, among the moved nodes (i, i + 1, i + 2,...), For the node i whose adjacent node has not moved, the t = Unit vector p of displacement vector at t0
The direction of the displacement vector is corrected in the direction of the vector sum of the direction of * (→) and the direction of the unit vector q * (→) of the displacement vector at t = t1 of the moving node. As a result, it is possible to reduce the fluctuation (rattle) of the interface shape due to the simulation.

(Second Embodiment) FIG. 3 shows a process simulation method according to a second embodiment of the present invention. In the present embodiment, a process (Step 307) for correcting the unit vector of the displacement vector at the current time at the moving adjacent node is added between Steps 106 and 107 of the above-described first embodiment, and At t = t1, the displacement vector is corrected in the unit vector q * direction. In the following, the displacement will be described focusing on the node i.

When a node i on the interface to be oxidized is to be calculated (step 301), whether or not the node i has moved to the previous time is determined by an oxidation deformation calculation (step 30).
2). If the node i has not moved at the previous time, the flow goes to step 303 to add the magnitude of the displacement vector at the current time t1 to the magnitude of the displacement vector at the previous time t0, and then goes to step 308. In step 302, node i
Has moved, the node (i−1,
It is determined whether any of (i + 1) has moved to the previous time (step 304). If it is determined in step 304 that both adjacent nodes (i-1, i + 1) have moved,
The process moves to step 309. If one of the adjacent nodes (here, i-1) does not move, a unit vector of the displacement vector at the previous time at the immovable adjacent node (i-1) is calculated (step 305), and the moving neighbor is calculated. The unit vector q '* of the displacement vector at the current time at the node is calculated (step 306). Further, the unit vector q of the displacement vector at the current time at the moving adjacent node
* Is corrected (step 307).

In step 308, steps 305 and 3
The direction of the displacement vector at the node i is corrected in the vector sum direction of the unit vectors p * and q * obtained in step 07. A grown oxide film thickness is calculated from the corrected magnitude of the displacement vector (step 309). Further, it is determined whether or not the grown oxide film thickness is equal to or smaller than the comparison value ε (step 310).
If the grown oxide film thickness is not more than ε, the displacement vector at the current time t1 is stored (copied) from a calculation register or the like into a storage memory area (step 311). After this,
The displacement vector at the current time is deleted from the calculation register and the like (step 312). The above series of processing is executed for all of the interfaces (step 313). If there is an unprocessed node, the process returns to step 301 and the subsequent processing is repeatedly executed. Thereafter, the processing after step 505 shown in FIG. 5 is executed to create a new interface.

FIG. 4 shows a two-dimensional simulation in the processing of FIG. 3, and specifically shows correction of the unit vector of the displacement vector at the current time in step 307. In the first embodiment, the direction of the unit vector of the displacement vector at t = t1 of the node i is 2
It was in the equal angle direction. On the other hand, in the second embodiment, the unit is not in the bisecting direction of the node but in the direction of the length ratio (m: n) of the line segments m and n connected to both sides of the node i. The direction of the vector is oriented.

[0028]

As described above, according to the process simulation method of the present invention, when one of the nodes located on both sides of the node whose displacement is to be calculated does not move, the node adjacent to the node that did not move is For the moved node, the direction of the displacement vector is set to the vector direction obtained by combining the unit vector direction of the displacement vector at the previous time of the node that has not moved and the unit vector direction of the displacement vector at the current time of the moved adjacent node. Since the setting is made, it is possible to reduce the fluctuation (rattle) of the interface shape due to the simulation. Further, unnecessary calculation can be omitted, so that calculation time can be reduced.

Further, by correcting the direction of the composite vector according to the ratio of the line segments on both sides of the node between the node that has not moved and the node that has moved, it is possible to further reduce the fluctuation of the interface shape by simulation. it can.

[Brief description of the drawings]

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

FIG. 2 is an explanatory diagram showing a two-dimensional simulation in the processing of FIG. 1;

FIG. 3 is a flowchart illustrating a process simulation method according to a second embodiment of the present invention.

FIG. 4 is an explanatory diagram showing a two-dimensional simulation in the processing of FIG. 3;

FIG. 5 is a flowchart showing processing of a conventional process simulation method in which unnecessary oxidation calculations are omitted.

FIG. 6 is a flowchart showing details of a method for resetting the oxidant concentration in FIG. 5;

FIG. 7 is a cross-sectional view showing the semiconductor device after the LOCOS step.

8 is an explanatory diagram illustrating a two-dimensional simulation in which a part of the LOCOS shape of the semiconductor device in FIG. 7 is enlarged.

FIG. 9 is a flowchart showing a conventional process simulation method for reducing the fluctuation of the interface.

FIG. 10 is a flowchart showing details of a displacement vector resetting method in FIG. 9;

FIG. 11 is an explanatory diagram showing a two-dimensional simulation in the processing of FIG. 10;

FIG. 12 is a flowchart showing another example of the resetting method of the displacement vector of FIG. 9;

FIG. 13 is an explanatory diagram illustrating a two-dimensional simulation corresponding to the processing in FIG. 12;

[Explanation of symbols]

Reference Signs List 1 silicon substrate 2 oxide film (SiO ₂ ) 3 nitride film (Si ₃ N ₄ )

──────────────────────────────────────────────────続 き Continued on the front page (58) Field surveyed (Int.Cl. ⁷ , DB name) H01L 21/205 H01L 21/31 H01L 21/316 H01L 21/94 G06F 17/50

Claims (4)

(57) [Claims] 1. A process simulation method for simulating a semiconductor device by calculating a displacement vector of each node on the interface at predetermined time intervals based on an oxidant concentration at an interface between a semiconductor substrate and an oxide film layer, It is determined whether two adjacent nodes adjacent on both sides of the moving node moved at the time of calculating the oxidant concentration at the previous time have moved at the previous time, and one of the two adjacent nodes moves and the other moves. If not, the direction of the displacement vector of the moving node is corrected based on a combined vector obtained by combining the unit vector of the displacement vector of the other adjacent node at the previous time and the unit vector of the displacement vector of the one adjacent node at the current time. Calculating the thickness of the oxide layer on the moving node based on the corrected displacement vector of the moving node. Scan simulation method. 2. The method according to claim 1, wherein the step of calculating the thickness of the oxide film layer includes the step of calculating a new interface deformation without performing a new interface deformation calculation when the thickness obtained by the calculation is smaller than a predetermined thickness. 2. The process simulation method according to claim 1, further comprising the step of adding the magnitude of the displacement vector at the current time to the magnitude of the displacement vector at the previous time to obtain the displacement vector of the moving node. 3. The step of correcting the displacement vector of the moving node includes setting the displacement vector of the moving node in a bisecting direction of an angle formed by two line segments connecting the one and the other adjacent nodes. 2. The process simulation method according to claim 1, further comprising the step of: 4. The step of correcting the displacement vector of the moving node includes changing an angle formed by two line segments connecting the one and the other adjacent nodes to an angle formed by the two line segments. 2. The process simulation method according to claim 1, further comprising: setting a displacement vector of the moving node in a direction divided by a ratio of a length of a line segment.