JP2800722B2 - Terminal current calculation error evaluation method in semiconductor simulation - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION The present invention predicts a terminal current value by numerically obtaining a physical state inside a semiconductor device,
The present invention relates to a method of obtaining a calculation error of a terminal current and evaluating the same.

[0002]

2. Description of the Related Art In the development of semiconductor devices, semiconductor device simulators capable of predicting device operation by numerically obtaining the physical state inside the device are frequently used. For example, there is a method of performing a spatial discretization by a finite difference method (control volume method) on a partial differential equation describing an operation of a semiconductor element, numerically obtaining a physical state inside the semiconductor element, and predicting an element operation. However, in this method, the simulation does not present information to the user regarding the discretization error at the time of analysis, and the user creates a discretization grid based on his own experience.
Optimization has been performed.

[0003] Various methods have been devised as a method for creating error information for supporting this optimization work. For example, a method using an impurity concentration distribution inside a semiconductor element (Japanese Patent Laid-Open No. 3-101150), a method of mathematically estimating an error distribution of an electric field or a current density (Siam Journal on Numerical Analysis (SIAMj)) .
Numer. Anal. ), Vol. 15, No. 4,
pp. 736-754, 1978).

[0004]

Usually, the purpose of using a simulator is to predict a terminal current value in many cases.
Therefore, the user creates a discretized grid in which the error included in the terminal current value is reduced. Therefore, it is desirable that the error information indicates how much the terminal current error is. However, in the conventional error information generation method, it is possible to know an error distribution such as a current density, but there is a problem that an error included in a terminal current cannot be evaluated.

[0005]

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method for evaluating an error contained in a terminal current value based on an error distribution such as a current density.

[0006]

In the method of evaluating a terminal current calculation error according to the present invention, first, as shown in the flowchart of FIG. 1, element characteristics of a current density distribution inside the element are calculated (step S1). Then, the error distribution of the current density,
An error distribution of the unit positive charge generation rate obtained from the carrier generation and recombination rate is obtained (step S2). Next, a closed region including the interface between the electrode of the terminal and the element whose error is to be obtained is defined, and an amount obtained by integrating the error of the unit positive charge generation rate inside the closed region and the electrode interface on the surface of the closed region are removed. An error in the terminal current value is estimated from the difference from the amount obtained by integrating the error of the current density perpendicular to the surface and outward in the portion (step S3).

[0007]

In other words, as shown in FIG. 2, when a closed region Ω including the interface between the electrode and the element is defined, the boundary の of Ω, the amount of charge flowing out from the electrode interface and the amount of charge generated in Ω are Since they are equal, it can be seen that the current I flowing out of the electrode satisfies the following equation.

(Equation 2) Here, J is a current density, n is a unit direction vector perpendicular to Γ and outward, and G is a unit positive charge generation rate. When a negative charge is generated by the generation of electrons, G has a negative value.

From this equation, if the error of the current, the error of the current density, and the error of the charge generation rate are written as δI, δJ, δG, respectively,

(Equation 3) It turns out that it becomes.

In order to obtain δI, it is necessary to know the error in the current density and the charge generation rate. Transactions on Computer Aided Design (IEEE
Trans. CAD), Vol. 10, No. 10, p
p. 1251-1257, 1991) or a method of constructing an approximate solution by interpolation of the obtained current distribution or the like and treating it as an error therefrom (IEICE Transactions on Electronics (IEICE)
Trans. Electron. ), Vol. E77
-C, No. 2, pp. 214-217, 1994). The closed region Ω can be arbitrarily selected in principle, but in practical use, it is desirable to consider the consistency with the mesh used for the analysis of the electrical characteristics and the ease of detecting an error.

In the semiconductor device simulation, the current density at the midpoint of the mesh side of the analysis mesh is approximately determined, and the current density on the vertical bisecting plane of the mesh side is assumed to be constant at this value, and the current amount between the mesh points is determined. Is approximated. Therefore, it is advisable to form the boundary で by connecting the perpendicular bisectors of the mesh sides so that the current density in the vertical direction can be easily calculated. In addition, if the current density error is accurately obtained, the terminal current error can be estimated irrespective of how to select Ω.However, since the reliability of the current density error generally differs depending on the location, the current density error should be observed. It is also important to set a region that is easy to cross by Γ in order to increase the accuracy of current error estimation.

[0011]

Next, the present invention will be described with reference to the drawings. This will be described by taking the MIS structure shown in FIG. 3 as an example. This MIS structure element has a gate insulating film 5 and a gate electrode 4 on a semiconductor substrate 9, and has a source / drain diffusion layer 8 on the main surface of the semiconductor substrate 9. The source electrode 6 and the drain electrode 7 are formed on these diffusion layers 8 in a generally known configuration. Here, the interface (line segment AE) between the drain electrode 7 and the diffusion layer 8 and the broken line ABC
A closed region surrounded by a boundary さ れ る represented by DE is defined as Ω. When the analysis grid is an orthogonal grid, by forming the boundary Γ with only the horizontal and vertical sides in this way, it becomes easy to evaluate the current density orthogonal to the boundary Γ.

If the error distribution of the unit positive charge generation rate inside the closed region Ω and the current density error orthogonal to the boundary Γ on the boundary Γ are estimated by a known method, the drainage can be obtained by using the equation (1) as it is. The current error can be determined. However, it is also possible to use a more simplified expression. Of the boundary Γ, between AB, the current passing through the gate insulating film 5 is usually much smaller than the drain current, and the device simulator does not usually consider this current component;
Since the reflection type boundary is used in the device simulator between DEs, there is no outflow of carriers in the calculation, so there is no need to evaluate the current density error.

(Equation 4) Becomes

Further, the influence of δG on the drain current is extremely small, and between CDs, the current is mainly caused by the generation of electron-hole pairs in the drain depletion layer and the holes generated by the impact ionization phenomenon. Since it is extremely small compared to the drain current, in reality,

(Equation 5) Makes it possible to estimate δI.

[0014]

As described above, according to the present invention, a closed region including an interface between a terminal electrode for which an error is to be determined and an element is determined, and an amount obtained by integrating the error of the unit positive charge generation rate within the closed region, Since the terminal current error can be obtained from the difference between the area of the closed area surface excluding the electrode interface and the area in which the current density error perpendicular to the surface and outward is integrated, the simulator user can analyze with sufficient accuracy It can be clearly determined whether or not was performed. Even if the grid is slightly coarse, it is possible to obtain a highly accurate value by correcting the terminal current value using the method of the present invention.

[Brief description of the drawings]

FIG. 1 is a flowchart showing processing steps of a terminal current error evaluation method of the present invention.

FIG. 2 is a schematic diagram for illustrating a closed region including an electrode surface and a surface of a closed region excluding the electrode surface.

FIG. 3 is a schematic diagram showing a MIS structure element and a closed region for evaluating a drain current error.

[Explanation of symbols]

 Reference Signs List 1 electrode 2 closed region Ω 3 closed region surface excluding electrode surfaceΓ 4 gate electrode 5 gate insulating film 6 source electrode 7 drain electrode 8 diffusion layer (source / drain) 9 semiconductor substrate

Claims (1)

(57) [Claims] 1. A numerically determine the physical state of the semiconductor device by performing spatial discretization by the finite difference method the partial differential equations describing the operation of the semiconductor device, the semiconductor simulation to predict device operation, current A closed area including the interface between the terminal electrode and the element for which an error is to be determined is defined, and the amount obtained by integrating the error of the unit positive charge generation rate inside this closed area and the surface of the closed area surface excluding the electrode interface are determined. Calculating a terminal current value error from a difference between an amount of integration of a current density error in a vertical direction and a terminal current error in a semiconductor simulation.