JPH05121740A - Method of simulating semiconductor device - Google Patents

Abstract

PURPOSE:To calculate accurately the impurity distribution in a region, whose diffusion coefficient is small, in the vicinity of the interface of the region and another region whose diffusion coefficient is large and considerably different from the coefficient of the small diffusion coefficient region, even if the mesh of the small diffusion coefficient region is rough in the vicinity of the interface. CONSTITUTION:First and second regions having small and large diffusion coefficients respectively forms an interface. Digitizing meshes are used for one-dimensional simulation of the process of manufacturing a semiconductor device. If the mesh of the area of the first region is rough in the vicinity of the interface, the amount of transportation of an impurity at the interface between the regions is given using an analytical formula. In the case where after a diffusion process is performed, an ion-implantation is performed and a diffusion process is further performed, another value of the amount of the transportation of the impurity found applying the analytical formula to the increment of the impurity concentration at the interface due to the ion-implantation is added to the former amount of transportation of the impurity, and the sum is used as the simulated amount of transportation of the impurity. Accordingly, even in the case where the meshes in an oxide film is rough, the boron concentration in the surface of a substrate can be calculated accurately. The boron concentration in the surface of the substrate of (a) is calculated abnormally low by a conventional method.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to semiconductor device simulation, and more particularly to semiconductor device simulation for performing an approximate solution of an impurity diffusion equation.

[0002]

2. Description of the Related Art In semiconductor device process simulation, the impurity distribution in the silicon substrate near the oxide film interface has a great influence on the electrical characteristics of the device, for example, the threshold value of the MOSFET. Therefore, the impurity distribution in this region can be accurately calculated. There is a need to.

However, the diffusion coefficient of impurities serving as acceptors or donors, such as boron, in the oxide film is only about 1/1000 of the diffusion coefficient in the substrate, and the transport coefficient at the interface is very large, so that the impurity distribution can be accurately measured. In order to calculate well, it is necessary to make the mesh for discretizing the diffusion equation fine enough in the oxide film.

However, the mesh used in the ordinary one-dimensional simulator is often rougher in the oxide film than in the substrate due to the volume expansion accompanying oxidation. For this reason, the amount of impurities transported at the interface becomes abnormally large, which may cause a large numerical error in the impurity distribution near the interface.

In the case of one-dimensional simulation, control of mesh density is relatively easy, and if the mesh is made finer, the calculation accuracy improves but the calculation time increases. In the case of a two-dimensional simulation using a triangular mesh, it is very difficult to control the density of the mesh, and a triangle having a desired size cannot often be obtained. If an attempt is made to make the mesh fine only in the oxide film in order to improve the calculation accuracy, obtuse triangles may be generated, which may rather reduce the accuracy. If the mesh in the oxide film and the mesh in the substrate are both fine, the occurrence of obtuse triangles can be prevented and the calculation accuracy improves, but the calculation time increases.

For this reason, there is an approximation method, for example, as in document [1], in which the transport coefficient at the interface is modulated with time to maintain numerical accuracy. However, this method cannot be applied to a composite process that appears in an actual device manufacturing process, such as performing an ion implantation process and then performing a diffusion process after the diffusion process. [Reference 1] Kenji Nishi, Jun Ueda, IEICE Technical Report CPM89-5
6, p. 31.

[0007]

As described above, in the conventional solution of the diffusion equation, when the mesh in the oxide film is rough, it is difficult to accurately calculate the impurity distribution in the silicon substrate near the oxide film interface. However, there is a problem that the calculation time increases if the mesh in the oxide film is made fine. Further, there is a problem that the above-mentioned approximation method [Reference 1] for solving this problem cannot be applied to a composite process that appears in an actual device manufacturing process.

According to the present invention, in the vicinity of the interface of a region having a large diffusion coefficient, even if the mesh near the interface of a region having a small diffusion coefficient is coarse, the numerical accuracy of the impurity distribution near the interface of the region having a large diffusion coefficient is deteriorated. It is an object of the present invention to provide a semiconductor device simulation method that can perform calculations without any need and can repeatedly perform diffusion and ion implantation process simulations.

[0009]

In order to achieve the above object, the present invention provides a method of numerically solving an impurity diffusion equation by using a discretized mesh, in which the diffusion coefficient in the vicinity of an interface in a region where the diffusion coefficient greatly differs. When the mesh in the vicinity of the interface in a small area is rough, the amount of impurity transport at the interface is given using an analytical formula, the impurity distribution near the interface in the area with a large diffusion coefficient is calculated, and the diffusion and ion implantation process simulations are repeated. Is characterized by.

[0010]

According to the present invention, in the interface of the region where the diffusion coefficient is largely different, when the mesh in the vicinity of the interface of the region where the diffusion coefficient is small is rough, the impurity transport amount at the interface is given by using an analytical expression. After performing the diffusion process, ion implantation is performed,
When the diffusion process is further performed, the impurity transport amount is obtained by adding the transport amount obtained by applying the analytical formula to the interface concentration increment by ion implantation to the above-described impurity transport amount.

[0011]

EXAMPLES Examples of the present invention will be described below. First, for example, the amount of impurities transported per unit time at the interface between two regions with different impurity diffusion coefficients

[0012]

[Equation 1]

It is given by. Where t is the diffusion time, C _s (C
_L) is small impurity diffusion coefficient (greater) surface concentration at the start of the diffusion in the region, m is the segregation coefficient, D _s is the diffusion coefficient in a small area of the impurity diffusion coefficient.

The following one-dimensional simulation was performed to confirm the effect of the present invention. First, an oxide film having a thickness of 200 angstrom is formed on a silicon substrate having a thickness of 1 micron, and boron of 50 keV is ion-implanted at 1.10 ¹³ / cm ² . Next, a diffusion process is performed at 900 degrees for 30 minutes.
At this time, the mesh in the oxide film is set to a width of 1, 10, 20, 5
Diffusion simulation is performed using the present invention and the conventional method while changing the value to 0, 100, 200 angstroms.

On the other hand, the mesh in the silicon substrate has a width of 20.
Angstrom. It can be said that this mesh width is sufficiently fine considering the diffusion coefficient of boron in the silicon substrate. FIG. 1 shows the substrate surface concentration of boron thus obtained as a graph of the mesh width of the oxide film. (A) is the substrate surface concentration obtained by the present invention,
(B) is the substrate surface concentration obtained by the conventional method.

As can be seen from this figure, when the approximate solution method of the present invention is used, the substrate surface concentration of boron can be accurately calculated even when the mesh in the oxide film is rough, but when the mesh is rough by the conventional method. The substrate surface concentration of boron is calculated to be abnormally low. When the diffusion process and the ion implantation process are repeatedly performed, the above-mentioned analytical formula may be applied to the increment of the interface concentration due to the ion implantation.

[0017]

As described above, according to the present invention, even if the mesh of the region having a small impurity diffusion coefficient is coarse, the impurity concentration distribution in the vicinity of the interface of the region having a large impurity diffusion coefficient is increased without increasing the calculation time. Can be calculated accurately.

[Brief description of drawings]

FIG. 1 is a diagram comparing substrate surface concentrations obtained using the present invention and a conventional simulation method.

Claims (1)

[Claims] 1. When numerically solving an impurity diffusion equation using a discretized mesh, when the mesh near the interface of a region having a large diffusion coefficient is rough and the mesh near the interface of a region having a small diffusion coefficient is rough, impurities at the interface are A method for simulating a semiconductor device, characterized in that an amount of transport is given using an analytical expression, an impurity distribution near an interface in a region having a large diffusion coefficient is calculated, and a diffusion and ion implantation process simulation is repeated.