JPH10125612A - Simulation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain analysis of high precision in a narrow calculation region by setting the boundary condition of a region for simulation, in such a manner that impurities or point defect move across the boundary of the calculation region. SOLUTION: Diffusion time T is set to 0 (S 101). By calculating the diffusion. coefficients or the like at a diffusion temperature, a diffusion equation is set (S 102). The boundary of the simulation region, i.e., the boundary condition to a substrate bottom surface is so set, that it is allowed for impurities or point defects to exceed the boundary of the calculation region and move (S 103). After the boundary condition and the diffusion equation are set, analysis of the diffusion equation is obtained by using a numerical analysis method (S 104) Next, the diffusion time T is increased by ΔT (S 105). Whether the value excess the total diffusion time Tf is judged (S 106). When it exceeds Tf, the loop which starts from the setting of the diffusion equation is again executed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a simulation method and, more particularly, to a technique used for simulation of impurity or point defect diffusion in a semiconductor manufacturing process.

[0002]

2. Description of the Related Art As the degree of integration of integrated circuits increases, the number of manufacturing steps increases and the steps themselves become complicated. For this reason,
The number of prototypes has increased and the development cost has increased. In order to cope with such a situation, efforts have been made to narrow down trial production conditions in advance by using a simulator, reduce the number of trial productions, and shorten the trial production period. For example, in the case of process simulation, a process simulator is used to simulate ion implantation, oxidation / diffusion processes, etc., to predict the device shape and impurity distribution, and to narrow down the process conditions of the prototype so that the result is a desired value. Was out.

[0003] The process simulation has a problem that a large element area is simulated and a large amount of memory is required. Most of the calculation time and memory required for the process simulation are occupied by the impurity diffusion simulation. Therefore, if the calculation time and the amount of memory required for the simulation of impurity diffusion in a wide area can be reduced, the process simulation can be performed efficiently.

In order to perform an impurity diffusion simulation at high speed and with a small amount of memory, the simulation region may be limited to a necessary portion. However, in the conventional impurity diffusion simulation, since the reflection-type boundary condition is used at the boundary of the calculation region, if the calculation region is narrow, impurities are trapped within the boundary, and the accuracy of the solution is reduced. To simplify this, one of the well forming steps
A description will be given using a dimensional simulation as an example.

FIG. 3 shows that a silicon substrate is
It is a table | surface at the time of eV and the dose amount 3 * 10 < ¹³ > / cm < ² > ion implantation. The horizontal axis of this chart indicates the depth from the silicon substrate surface, and the vertical axis indicates the boron concentration. A dotted line A in the chart indicates a profile immediately after ion implantation. Also,
8 μm deep from the substrate surface to accurately calculate the boron profile when diffused at 1200 ° C. for 4 hours
The result calculated up to is shown by the broken line B.

Generally, most of the element characteristics are, for example, MO
To calculate the threshold value of the SFET, use a depth of 2 from the substrate surface.
Since it is sufficient to have a profile of μm, the calculation is often limited to this calculation area for reasons such as reduction of processing time. The profile in this case is indicated by a dashed line C. In either case, the reflection type is used as the boundary condition of the substrate bottom surface. As can be seen from the result of the dashed-dotted line C, the accuracy of the solution is very poor when the calculation region is narrowed from this figure.

[0007]

When the reflection type boundary condition is used for the boundary of the impurity diffusion simulation region as described above, there is a problem that the accuracy of the solution is reduced when the calculation region is narrowed. On the other hand, if the simulation area is widened for accurate simulation, there is a problem that the required memory amount increases and the calculation time becomes longer.

The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a simulation method capable of obtaining a highly accurate solution even in a narrow calculation area.

[0009]

According to a first aspect of the present invention, there is provided a method of simulating an impurity or a point defect diffusion in a semiconductor manufacturing process, the method comprising the steps of: Alternatively, it is characterized in that the setting is made so as to allow the point defect to move beyond the boundary of the calculation area.

According to a second aspect of the present invention, the boundary condition in the first aspect is such that the amount of movement of an impurity or a point defect passing through the boundary is equal to the amount of movement obtained when calculation is performed in a sufficiently wide area including the area. It is characterized in that the boundary condition of the boundary is determined as follows.

According to a third aspect of the present invention, the boundary condition in the first aspect is such that the boundary condition in which impurities move beyond the boundary is determined by using a differential coefficient of an impurity profile in a boundary normal direction near the boundary. Features.

According to a fourth aspect of the present invention, the boundary condition according to the first aspect is such that an impurity or point defect profile in a direction normal to the boundary in the vicinity of the boundary is approximated by a Gaussian function, so that the impurity or the point defect exceeds the boundary. It is characterized in that a moving boundary condition is determined.

[0013]

Embodiments of a simulation method according to the present invention will be described below in detail with reference to the drawings. In the following embodiments, a one-dimensional impurity diffusion simulation in a silicon substrate will be described for the sake of simplicity.

In a simulation method described in the following embodiments, a CPU for performing various processes, an input device such as a keyboard, a mouse, a light pen, or a flexible disk device, and an external storage device such as a memory device or a disk device are used. An ordinary computer system including a device and an output device such as a display device and a printer device is used. Note that the CPU includes an arithmetic unit that performs processing of each step described below, and a main storage unit that stores instructions for the processing.

First Embodiment FIG. 1 is a flowchart showing a processing operation of an impurity diffusion simulation according to the present embodiment. When the diffusion simulation is started, first, the diffusion time T is set to 0 (step S101). Then, a diffusion coefficient at the diffusion temperature, a segregation coefficient, and the like are calculated to set a diffusion equation (step S102).

Next, the boundary conditions are set as follows with respect to the boundary of the simulation region, that is, in this example, the bottom surface of the substrate (step S103).

F = -D∂ΔC / ∂x where D is the diffusion coefficient of the impurity, and C is the impurity concentration. This boundary condition means that impurities flow out of the simulation region by the flux F from the substrate bottom surface. In the conventional method, the reflection condition (F = 0) is set as the boundary condition here. For this reason, the impurity distribution that should spread due to diffusion is confined due to the reflective boundary condition set on the bottom surface, and the concentration becomes abnormally high. This problem can be avoided by setting the simulation area sufficiently wide, but the problem that the calculation time becomes long has occurred.

After setting the diffusion equation and the boundary conditions in this way, a solution of the diffusion equation is obtained by using a numerical solution (step S104). Next, the diffusion time T is increased by ΔT (step S105), and it is determined whether or not the value exceeds the total diffusion time Tf (step S106). Executes the loop that starts, otherwise ends the calculation.

Next, the effects of the present invention will be described with reference to a simulation of one-dimensional diffusion of boron in a silicon substrate. FIG. 2 is a chart in the case where 100 keV boron and a dose of 3 × 10 ¹³ / cm ² are implanted into a silicon substrate. The horizontal axis of this chart indicates the depth from the silicon substrate surface, and the vertical axis indicates the boron concentration. For the sake of simplicity, the calculations were performed on the assumption that no impurities were evaporated from the substrate surface. Here, the result of the diffusion at 1200 ° C. for 4 hours, the depth of the substrate was set to a sufficiently large value of 8 μm, and the calculation was performed with high accuracy is shown by the broken line B.
Shown in The dashed line C is the result of calculation using the conventional method while limiting the depth of the substrate to 2 μm. In the conventional method, since the reflection-type boundary condition is used as the boundary condition of the substrate bottom surface, boron is confined in the calculation region, and the boron concentration is significantly overestimated. on the other hand,
The results of calculations using the present invention with the substrate depth limited to 2 μm are shown by solid lines.

The result of the simulation method according to the present invention is shown by a bold line D. As shown in the figure, since the boundary conditions of the simulation boundary are appropriately given, the result of calculation with high accuracy over a sufficiently wide area (broken line B) is very good even though the simulation area is limited to 2 μm. . The element distribution is greatly affected by the impurity distribution near the substrate surface. As shown in FIG. 2, the present invention accurately calculates the impurity distribution in the vicinity of the substrate surface, so that highly accurate device characteristics can be obtained.

As described above, according to the present invention, a simulation can be performed with little loss of accuracy even if the simulation area is narrowed. In this example, the simulation area is reduced to a quarter, but it goes without saying that the amount of memory required for the simulation and the calculation time are also reduced to the same extent. As described above, by using the present invention, a process simulation can be performed at a higher speed with a smaller amount of memory than before.

Although the present embodiment has been described using a one-dimensional simulation for the sake of simplicity, it is apparent that the present invention can be applied to two-dimensional and three-dimensional simulations. In particular, it is apparent that the effect of reducing the amount of memory and the calculation time is remarkable in two-dimensional and three-dimensional simulations.

Second Embodiment In the first embodiment, the boundary condition is calculated using the differentiation of the impurity distribution in the setting of the boundary condition in step S103. What is necessary is just to set so that a close solution is obtained. For this reason, in the present embodiment, for example, in the case of a one-dimensional simulation, the profile of the impurity distribution near the boundary in the direction of the boundary normal is approximated by a Gaussian function a · exp [−b (xx− ₀ ) ² ]. Where x represents the depth from the substrate surface,
a, b, x ₀ is a constant. As is well known,
When the diffusion coefficient is constant, the Gaussian function becomes a solution of the diffusion equation. Therefore, the impurity distribution near the bottom surface of the simulation region can be accurately approximated by the Gaussian function. Then, assuming that the Gaussian function extends outside the region beyond the simulation boundary, the flux at the boundary is calculated, and this value is used as a boundary condition. If the boundary condition is calculated in this way, since the numerical differentiation is not used unlike the above-described embodiment, stable calculation can be performed without depending on the mesh interval or the like. As a result, a simulation result with higher accuracy than the conventional method can be obtained.

Third Embodiment In the above embodiment, the diffusion of impurities in a silicon substrate has been described. However, the present invention can be applied to a simulation of diffusion of point defects and impurities. Since impurity diffusion is affected by point defects, the diffusion equation incorporating point defects is
The impurity diffusion can be described more accurately than the diffusion equation of the impurity alone.

However, the point defect has a much higher diffusion rate than the impurity, so that the conventional method requires a very large simulation area. For example, the usual M
In the process simulation of the OSFET, the calculation region may have a depth of about 10 μm from the substrate surface, but when a point defect is introduced, a depth of about 100 μm is required. For this reason, a large amount of memory is required to perform a simulation incorporating the point defect diffusion, and the calculation time is very long.

However, for example, a calculation region necessary for diffusion of the impurity alone is set, and the boundary condition is applied to the point defect by the method used for the impurity in the first embodiment. In this way, a simulation can be performed even in a region as narrow as the case where only impurity diffusion is handled, and the required memory amount and calculation time can be significantly reduced.

As described above, by using the embodiments of these simulation methods, it is possible to perform a process simulation of a semiconductor device only in a necessary region. Therefore, it is possible to perform a simulation at a higher speed with a smaller amount of memory than before. In addition, in the conventional method, the accuracy of the calculation result obtained when the simulation region is narrow was sometimes very poor. However, according to the present invention, the decrease in the calculation accuracy is suppressed even when the simulation region is narrow, so that the accuracy is low. The possibility of being confused by poor calculation results.

As described in the first embodiment, if the boundary conditions are calculated using the derivative of the impurity profile in the direction of the boundary normal, the effects of the present invention can be realized by slightly modifying the conventional program. Can be. Also, the calculation time required for calculating the boundary condition is almost negligibly short compared to the calculation time required for the simulation.

As described in the second embodiment,
The boundary condition approximates the boundary normal profile of the impurity distribution near the boundary with a Gaussian function, calculates the flux at the boundary assuming that this function extends outside the boundary, and sets the boundary condition using this . In this way, since the boundary conditions can be set without using the numerical differentiation, it is possible to set the boundary conditions that are less dependent on the mesh used for the numerical calculation.

Further, as described in the third embodiment, the present invention can be applied not only to impurity diffusion but also to point defect and impurity diffusion simulation. Since point defects have a remarkably high diffusion rate of impurities, the conventional method requires a very large simulation area. For this reason, a large amount of memory was required to perform the simulation incorporating the point defect diffusion, and the calculation time was very long. However, by applying the present invention, simulation can be performed even in a small area, and the required memory amount and calculation time can be significantly reduced.

Note that a program for implementing the above-described simulation method can be stored in a recording medium. This recording medium is read by a computer system, and the above-described simulation method can be realized while controlling the computer by executing the program. Here, the recording medium is a memory device,
Devices that can record programs, such as a magnetic disk device and an optical disk device, are included.

[0032]

As described above, according to the simulation method of the present invention, when simulating impurity diffusion and point defects in a semiconductor manufacturing process, a high-precision solution can be obtained even in a narrow calculation area. Can be obtained.

[Brief description of the drawings]

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

FIG. 2 is a chart showing a well impurity distribution when a process simulation is performed by the simulation method of the embodiment. The horizontal axis shows the depth from the substrate surface,
The vertical axis indicates the boron concentration.

FIG. 3 is a chart showing impurity distribution in a well when a conventional process simulation method is used. The horizontal axis shows the depth from the substrate surface, and the vertical axis shows the boron concentration.

[Explanation of symbols]

A Boron concentration distribution immediately after ion implantation B Boron concentration distribution calculated to a depth of 8 μm C Boron concentration distribution calculated to a depth of 2 μm D Depth 2 using the simulation method of the present embodiment
Boron concentration distribution calculated to μm

Claims (4)

[Claims] 1. A method of simulating the diffusion of an impurity or a point defect in a semiconductor manufacturing process, comprising the steps of:
A simulation method including setting to allow an impurity or a point defect to move beyond a boundary of a calculation region. 2. The boundary condition is set such that the amount of movement of an impurity or a point defect passing through the boundary is equal to the amount of movement obtained when calculation is performed in a sufficiently large area including the area. The simulation method according to claim 1, wherein the determination is performed. 3. The simulation according to claim 1, wherein the boundary condition is determined by using a derivative of an impurity profile in a boundary normal direction in the vicinity of the boundary to move the impurity beyond the boundary. Method. 4. The method according to claim 1, wherein the boundary condition is such that an impurity or point defect profile in the direction of the boundary normal in the vicinity of the boundary is approximated by a Gaussian function to determine a boundary condition at which the impurity or point defect moves beyond the boundary. The simulation method according to claim 1, wherein: