JP3070640B2 - Device simulation method and device simulator - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to relates to a device simulator for analyzing the semiconductor operation, device simulation how to analyze particular a three-dimensional device structure two-dimensionally
Method and device simulator.

[0002]

2. Description of the Related Art P.S. 4-P. As shown in FIG. 9, in a general device simulator, a method is used in which an initial value is given to an electrode and a Poisson equation, an electron current continuous equation, and a hole current continuous equation are solved for all regions other than the electrode.

A device simulator for calculating response characteristics of a transient device is disclosed in P.T. As indicated by reference numerals 124 to 125, a method of changing the analysis time and solving the Poisson equation or the current conservation equation, the electron current continuation equation, and the hole current continuation equation is used.

Next, a conventional analysis method for analyzing a charge transfer device (CCD: Charge Coupled Device) having a three-dimensional structure using a two-dimensional device simulator will be described.

[0005] As shown in FIG. 2, in the CCD, carriers generated by light incident on the photodiode unit 1 are:
Depending on the potential applied to the transfer gate 2, the vertical CCD unit 3
Is forwarded to The carrier transferred to the vertical CCD unit 3 is transferred in the depth direction of the CCD by the potential difference applied in the depth direction of the CCD (the direction perpendicular to the paper surface of FIG. 2).

In the conventional method, when analyzing the potential distribution under the transfer gate 2, Kawazoe et al.'S document "Application of a two-dimensional device simulator for developing a CCD image sensor".
(Spring 1990, The 37th Annual Meeting of the Japan Society of Applied Physics, Proceedings of the Related Lectures, Vol. 0, P.1208), Kitamura et al., "Simulation of sensitivity of frame transfer (FT) CCDs" As described in the second volume of the proceedings of the JSAP Conference, p.629)
A virtual electrode is provided in the vertical CCD section, and a voltage is applied to the virtual electrode until a region including the virtual electrode is sufficiently depleted,
The physical quantity distribution inside the semiconductor was examined by performing a simulation, then removing the virtual electrode and performing the simulation again.

In the device simulation method of Akiyama (Japanese Patent Application No. 3-36924), a Fermi level fixed region is provided in an analysis region, and a potential change in a CCD vertical direction is detected using the Fermi level in the Fermi level fixed region. It was a method of expressing using Fermi level.

[0008]

However, the conventional two-dimensional device simulation method of Kawazoe and Kitamura et al. Described above uses an electrode virtually provided as a carrier transfer section to a vertical CCD section in order to check the internal physical quantity. Since the simulation was carried out with the sensor removed, there was no place to absorb the carrier transferred from the photodiode to the vertical CCD section, so current could not flow, and the carrier generated by the photodiode was transferred to the vertical CCD. There was a problem that analysis was not possible.

Further, even in the two-dimensional device simulation method of Akiyama, since the Fermi level of the Fermi fixed region cannot be changed with time, a transient response inside the device such as how much carrier transfer efficiency cannot be examined.

In view of the above drawbacks, the technical problem of the present invention is to provide a device simulation method and a device simulation method for accurately simulating a carrier transfer state in a semiconductor device.
And device simulators.

[0011]

According to the present invention, a step of setting a predetermined potential to an electrode, a step of advancing a time, a step of setting a predetermined Fermi level in a predetermined area, and a formula of current conservation are provided. , Solving the electron current continuity equation for all regions other than the Fermi level setting region, obtaining the electron concentration from the Boltzmann distribution in the Fermi level setting region, Solving the hole current continuity equation, obtaining the hole concentration from the Boltzmann distribution in the Fermi level setting region, determining whether these solutions converge, and determining whether the time has reached the analysis end time. The steps to determine whether
Device simulation side, characterized in that to perform
The law is obtained.

Further, according to the present invention, there is provided a photodiode unit for generating carriers by receiving light, a transfer gate unit for transferring the carriers, and a vertical CCD unit for transferring the carriers in a depth direction different from the transfer direction. Fermi level setting means is provided in the vertical CCD section which is a sink area of the carrier, and the Fermi level is temporally changed. In the Fermi level setting area, a current storage formula and a carrier A device simulator characterized in that the carrier concentration is obtained based on the solution to the Boltzmann distribution equation is obtained.

[0013] Specifically, the Fermi level setting function device simulation method of the present invention, solves the semiconductor basic equations using numerical analysis of difference method or the like, to analyze the semiconductor device in two dimensions.

[0014]

In contrast to the above-described conventional two-dimensional device simulation method, the present invention can accurately change the transfer of carriers from a photodiode to a vertical CCD because the Fermi level can be changed with time. Can be.

[0015]

Next, embodiments of the present invention will be described with reference to the drawings. FIG. 1 shows a flowchart of a device simulator with a Fermi level setting function according to the first embodiment. The processing procedure of FIG. 1 will be described.

An arbitrary potential is set to the electrode by means 1 and the time is advanced by means 2. Means 3 sets an arbitrary Fermi level in an arbitrary area, and means 4 solves a current conservation equation. The determining means D1 determines whether or not the area is the Fermi level setting area. If the area is not the Fermi level setting area, the means 5 solves the electron current continuity equation for all areas other than the Fermi level setting area. On the other hand, in the Fermi level setting region, the electron concentration is obtained from the Boltzmann distribution by the means 6.

Next, the judging means D2 also judges whether or not the area is the Fermi level setting area. If the area is not the Fermi level setting area, the means 7 determines whether the area is the Fermi level setting area. Solve.
On the other hand, in the case of the Fermi level setting area, the hole concentration is obtained by the means 8 from the Boltzmann distribution in the Fermi level setting area. Subsequently, it is determined whether or not the solution obtained by the means 9 is a correct value , in other words, whether or not the solution converges. If the solution is correct , the procedure shifts to the means 10; And means 10
It is determined whether the time has advanced to the analysis end time, and if the time has not advanced to the analysis end time, the process returns to the means 2 to advance the time.

FIG. 3 shows processing means according to a second embodiment of the present invention. The method of FIG. 1 uses a decoupling method that separately solves the current conservation equation, the electron current continuation equation, and the hole current continuation equation. In the second embodiment shown in FIG. 3, the Fermi level setting function is incorporated in the couple method for solving the Poisson equation, the electron current continuity equation, and the hole current continuity equation collectively.

The processing procedure of FIG. 3 will be described. Means 3
1 sets an arbitrary potential on the electrode, and means 32 advances the time. By means 33, an arbitrary Fermi level is set in a predetermined area. The determining means D31 determines whether or not the area is a Fermi level setting area. If the area is not a Fermi level setting area, the means 34 determines a Poisson equation for an area outside the Fermi level setting area,
Solve the continuous current formula for electrons and the continuous current formula for holes. On the other hand, in the case of the Fermi level setting area, the means 35 solves the Poisson equation and the equation expressing the relationship between the carrier concentration and the potential by a Boltzmann distribution in the Fermi level setting area.

Next, it is determined whether or not the solution obtained by the means 36 is a correct value , that is, whether or not the solution converges. If the solution is correct , the procedure shifts to the means 37. And means 37
It is determined whether the time has advanced to the analysis end time, and if the time has not advanced to the analysis end time, the process returns to the means 2 to advance the time.

Here, as a third embodiment, in the first embodiment, the timing at which the time of the means 2 is advanced is set after the Fermi level of the means 3 is set or before the means 1 for setting an arbitrary potential to the electrode. You can also move it. When the means 2 is brought after the means 3, it is possible to analyze the transient response inside the device after fixing the Fermi level to a certain value. When the means 2 is brought before the means 1, it is possible to analyze the transient response when the potential on the electrode and the Fermi level in the Fermi level fixed region are simultaneously changed at each time.

Next, as a fourth embodiment, in the first embodiment, the means 1 for setting an arbitrary potential to the electrode and the means 3 for setting the Fermi level can be replaced. When the means 1 and the means 3 are replaced, after setting the Fermi level in the Fermi level fixed region, the transient response inside the device when the potential on the electrode is changed at each time can be analyzed.

[0023]

As described above, according to the present invention, when a three-dimensional structure such as a CCD is analyzed using a two-dimensional device simulator, the Fermi level is set and the analysis is performed. It is possible to accurately analyze how carriers are transferred from the CCD to the vertical CCD.

[Brief description of the drawings]

FIG. 1 is a flowchart showing a processing procedure according to a first embodiment of the present invention.

FIG. 2 is a schematic sectional view of a CCD.

FIG. 3 is a flowchart illustrating a processing procedure according to a second embodiment of the present invention.

[Explanation of symbols]

 1 photodiode section 2 transfer gate 3 vertical CCD section

Claims (3)

(57) [Claims] 1. A step of setting a predetermined potential on an electrode, a step of advancing time, a step of setting a predetermined Fermi level in a predetermined area, a step of solving a current conservation equation, and a step other than a Fermi level setting area. Solving the electron current continuity equation for the entire region of; and obtaining the electron concentration from the Boltzmann distribution in the Fermi level setting area; and solving the hole current continuity equation for the entire area other than the Fermi level setting area. In the Fermi level setting area, a step of obtaining a hole concentration from the Boltzmann distribution, a step of determining whether or not the obtained solutions converge, and a step of determining whether the time has reached the analysis end time are executed. Device simulation
Solution method . And a photodiode section for generating carriers by receiving light, a transfer gate section for transferring the carriers, and a vertical CCD section for transferring the carriers in a depth direction different from the transfer direction. sink area der of
The vertical CCD section is provided with a Fermi level setting means, and the Fermi level is changed with time. In this Fermi level setting region, the Fermi level is set based on the solution of the current conservation equation and the Boltzmann distribution equation of the carrier. A device simulator for determining a carrier concentration. 3. A step of setting a predetermined potential on an electrode.
Advancing the time, and setting a predetermined Fermi level in a predetermined area
And Poisson for all areas except the Fermi level setting area
Equations, the electron current continuous equations, the hole current continuous batch
And solving in the Fermi level setting region, Poisson equation, electron
The Boltzmann distribution equation for holes and the Boltzmann distribution equation for holes
And a step to determine whether these solutions converge.
And a step for determining whether the time has reached the analysis end time.
Device simulator for performing step and step
Solution method.