A potential field distribution calculation method, computer equipment and storage medium

Abstract

The application provides a potential field distribution calculation method, a computer device and a storage medium, which are used for simulation of a semiconductor device and include the following steps: dividing the semiconductor device model into a plurality of grids; equivalently regarding the semiconductor device model as a simulation combination of parallel capacitor plates and a plurality of dielectrics, and dividing the potential of each grid into a first potential generated by an external potential difference and a second potential generated by internal charge aggregation of the device; constructing a Poisson equation satisfied by the potential of each grid according to the simulation combination; calculating a homogeneous term component of the Poisson equation as the first potential; calculating a non-homogeneous term component of the Poisson equation as the second potential according to the difference of the homogeneous term component; and calculating the total potential of each grid according to the first potential and the second potential. The scheme can realize calculation of the potential field distribution by using a non-iterative method, thereby accelerating the solving speed and improving the simulation efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of simulation, and particularly relates to a potential field distribution calculation method, a computer device and a storage medium. BACKGROUND

[0002] In the simulation process of some semiconductor device models, the potential information inside the semiconductor needs to be calculated, and then the physical information such as carrier concentration and band gap is corrected to achieve high-precision simulation. However, the existing solving method usually needs to perform a large amount of iterative calculation, resulting in slow solving speed. Therefore, there is an urgent need for a calculation method capable of using a non-iterative method to calculate the potential field distribution, thereby accelerating the solving speed and improving the simulation efficiency. SUMMARY

[0003] The purpose of the present application is to provide a potential field distribution calculation method, a computer device and a storage medium, which realize the use of a non-iterative method to calculate the potential field distribution, thereby accelerating the solving speed and improving the simulation efficiency.

[0004] The technical solutions provided by the present application are as follows:

[0005] The present application provides a potential field distribution calculation method for the simulation of semiconductor devices, comprising the steps of:

[0006] dividing the semiconductor device model into a plurality of grids;

[0007] equivalent the semiconductor device model to an analog combination of parallel capacitor plates and multiple dielectrics, and dividing the potential of each grid into a first potential affected by the external potential difference and a second potential generated by the aggregation of internal charges of the device;

[0008] constructing a Poisson equation satisfied by the potential of each grid according to the analog combination;

[0009] calculating the homogeneous term component of the Poisson equation as the first potential;

[0010] calculating the non-homogeneous term component of the Poisson equation as the second potential according to the difference of the homogeneous term component;

[0011] calculating the total potential of each grid according to the first potential and the second potential.

[0012] The semiconductor device model is abstracted as parallel capacitor plates and multiple dielectrics, a Poisson equation of an equivalent simulation system is constructed, a homogeneous component of the Poisson equation is equivalent to a potential generated by a potential difference outside a grid, a non-homogeneous component is equivalent to a potential generated by a charge aggregation inside the grid, and a total potential of each grid is calculated by solving the two potentials. The calculation method can calculate the potential field distribution of the semiconductor device without iteration, thereby accelerating the solving speed and improving the simulation efficiency of the semiconductor device. The method is suitable for scenarios where the calculation accuracy of the potential field is not particularly high, such as dynamic simulation, and can have a good acceleration effect. Meanwhile, if the potential field provided by the simulation system outside is much larger than the potential field generated inside, the error of the total potential field generated by the calculation method can also be reduced to an acceptable range.

[0013] In some embodiments, the semiconductor device model is equivalent to a combination of parallel capacitor plates and multiple dielectrics, further comprising:

[0014] According to the parameter information of the semiconductor device model, the external potential V of each grid, the dielectric constant of the different dielectrics corresponding to each grid, and the size parameters of the simulation combination are determined 、 and .

[0015] In some embodiments, the potential of each grid satisfies the Poisson equation:

[0016] ,

[0017] wherein, is the charge density, is the specific inductive capacity; the equivalent cathode of the simulation combination is located at , and the equivalent anode is located at .

[0018] In some embodiments, the Poisson equation of the potential homogeneous component is:

[0019] ;

[0020] For a certain grid , the calculation result of the homogeneous component is: ,

[0021] wherein, is the grid length without oxygen vacancies along the direction, is the distance from the grid to the electrode on one side of the parallel capacitor plates.

[0022] In some embodiments, the Poisson equation of the non-homogeneous component of the electric potential is:

[0023] ,

[0024] The electric displacement vector satisfies the continuous boundary condition at the interface of the dielectric, i.e.

[0025] ,

[0026] ,

[0027] ,

[0028] wherein, and represent the normal component of the electric potential gradient in the dielectric on both sides of the interface; is the ratio of the dielectric constant , on both sides of the interface.

[0029] In some embodiments, the non-homogeneous component of the Poisson equation is calculated according to the difference of the homogeneous component, comprising:

[0030] Calculating the amount of charge accumulated at the interface of the dielectric for a certain grid :

[0031] ,

[0032] ,

[0033] Substituting the difference of the homogeneous component for , obtaining:

[0034] ,

[0035] wherein, is the length of the grid; then,

[0036] ,

[0037] The calculation result of the non-homogeneous component is:

[0038] ,

[0039] wherein, is the distance from the grid to the grid .

[0040] In some embodiments, the total electric potential of each grid is ​The sum of the homogeneous component and the non-homogeneous component is

[0041] .

[0042] In some embodiments, after the total electric potential of each grid is obtained, the method further comprises:

[0043] calculating the error of the total electric potential;

[0044] using an iterative method to correct the grid whose error of the total electric potential is greater than a preset error.

[0045] In a second aspect, the present application provides a computer device, comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the electric potential field distribution calculation method of the first aspect.

[0046] In a third aspect, the present application provides a computer storage medium, which stores a computer program or instructions, wherein the computer program or instructions are executed by a processor to implement the steps of the electric potential field distribution calculation method of the first aspect.

[0047] The electric potential field distribution calculation method, the computer device and the storage medium provided by the present application can abstract the semiconductor device model into parallel capacitive plates and multiple dielectrics, can construct the Poisson equation of the equivalent simulation system, can equivalently convert the homogeneous component of the Poisson equation into the electric potential generated by the potential difference outside the grid, can equivalently convert the non-homogeneous component into the electric potential generated by the charge aggregation inside the grid, and can solve the two electric potentials to obtain the total electric potential of each grid. The calculation method can obtain the electric potential field distribution of the semiconductor device without iterative calculation, so that the solving speed can be accelerated, and the simulation efficiency of the semiconductor device can be improved. BRIEF DESCRIPTION OF DRAWINGS

[0048] The above features, technical characteristics, advantages and implementation manners of the present application will be further described in the following preferred embodiments in a clear and understandable manner in combination with the accompanying drawings.

[0049] Figure 1 is a schematic diagram of the overall flow of one embodiment of the present application;

[0050] Figure 2 is a schematic diagram of the simulation combination of the semiconductor device model equivalent to parallel capacitive plates and multiple dielectrics according to one embodiment of the present application. DETAILED DESCRIPTION

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, specific implementations of the present application will be described below with reference to the drawings. Obviously, the drawings in the following description only represent some of the embodiments of the present application, and for those skilled in the art, other drawings can be obtained from these drawings without creative labor, and other embodiments can also be obtained.

[0052] In order to make the drawing simple, only the parts related to the present application are shown in each drawing, which does not represent the actual structure of the product. In addition, in order to make the drawing simple and easy to understand, in some drawings, only one of the components with the same structure or function is shown schematically, or only one of them is marked. In this paper, "one" not only means "only one", but also means "more than one".

[0053] In the simulation process of some semiconductor device models, the electric potential information inside the semiconductor needs to be calculated, and then the carrier concentration, band gap and other physical information are corrected to achieve high-precision simulation. However, the existing solving method usually needs to perform a large number of iterative calculations, resulting in slow solving speed. Considering that, on the one hand, for some application scenarios, for example, dynamic simulation, the calculation accuracy of the electric field is not very high, only a reasonable electric field distribution is given, which can ensure the first-order continuity of the electric field and the relative accuracy of the electric field intensity direction; on the other hand, for complex electrode structure devices, or there are multiple dielectrics inside the capacitor device, we can abstract it as a parallel capacitor plate plus multiple dielectrics, and directly calculate the electric potential field through this simulation system. Although the calculation accuracy is lower than that of the iterative method, the calculation speed is greatly improved, which can save a lot of time, and for some scenes with low precision requirements, it can be completely applicable. Therefore, the present scheme proposes a calculation method for calculating the electric potential field distribution using a non-iterative method, thereby speeding up the solving speed and improving the simulation efficiency. Next, the present scheme will be described in detail in combination with the drawings:

[0054] In one embodiment, with reference to the drawings Figure 1 The present application provides an electric potential field distribution calculation method for simulation of semiconductor devices, comprising the steps of:

[0055] S100, dividing the semiconductor device model into a plurality of grids.

[0056] When solving the electric field Poisson equation, the grid needs to be divided first, and then the difference of the grid point is used to replace the Laplace differential in the Poisson equation for solving. In theory, the grid shape can be divided arbitrarily, but when the edges of the grid are parallel to the spatial coordinate axes, the calculation will be more convenient. The present application takes a square grid in an orthogonal coordinate system as an example for introduction.

[0057] S200, equivalent the semiconductor device model to the simulation combination of parallel capacitor plates and multiple dielectrics, and divide the electric potential of each grid into a first electric potential affected by the external potential difference and a second electric potential caused by the internal charge aggregation.

[0058] For a complex electrode structure device or a capacitor type device, there are multiple dielectrics inside, which can be uniformly abstracted as the case of parallel capacitor plates plus multiple dielectrics. At the same time, in order to solve the Poisson equation, the electric potential can be divided into a homogeneous component and a non-homogeneous component , wherein the homogeneous component can be understood as the electric potential caused by the external potential difference (i.e., the first electric potential), and the non-homogeneous component can be understood as the electric potential caused by the internal charge aggregation (i.e., the second electric potential).

[0059] In one specific implementation, equivalent the semiconductor device model to the combination of parallel capacitor plates and multiple dielectrics, further comprising:

[0060] determining the external potential V suffered by each grid, the dielectric constant of the different dielectrics corresponding to each grid, and the size parameters of the simulation combination according to the parameter information of the semiconductor device model , and . Refer to the attached Figure 2 In one actual example, equivalent the semiconductor device model to the combination of parallel capacitor plates and two dielectrics, after dividing the semiconductor device model into a plurality of grids, the size of the grid (grid) i is , the distance from the electrode plate of the parallel capacitor plate is , the dielectric constant of the medium 1 is , and the dielectric constant of the medium 2 is . Build an orthogonal coordinate system for the simulation system, and the three axes are x, y, and z. The size parameters of the simulation combination are , and .

[0061] S300, construct the Poisson equation satisfied by the electric potential of each grid according to the simulation combination.

[0062] The Poisson equation satisfied by the electric potential of each grid is:

[0063] ,

[0064] wherein is the charge density, is the specific inductive capacity; the equivalent cathode of the simulation combination is located at , and the equivalent anode is located at ​Location. To solve the Poisson equation, the electric potential can be divided into two parts: a homogeneous component and a non-homogeneous component. The homogeneous component can be understood as the potential generated by an external potential difference, while the non-homogeneous component can be understood as the potential generated by the accumulation of internal charges. Next, we will solve for these two terms separately.

[0065] S400. Calculate the homogeneous component of the Poisson equation as the first potential.

[0066] homogeneous potential components The Poisson equation is:

[0067] ;

[0068] For a certain grid The calculation results of the homogeneous components are as follows: ,

[0069] in, For along The grid length has no oxygen vacancies in the direction. This is the distance from the grid to one electrode on the parallel capacitor plate.

[0070] S500. Calculate the non-homogeneous components of the Poisson equation based on the difference between the homogeneous components, and use them as the second potential.

[0071] The Poisson equation for the non-homogeneous components of the electric potential is:

[0072] ,

[0073] We can consider this non-homogeneous component as a Coulomb interaction. Next, we begin to estimate its magnitude. At the interface of the dielectric, the electric displacement vector continuity boundary condition is satisfied, i.e.

[0074] ,

[0075] ,

[0076] ,

[0077] in, and This represents the normal component of the potential gradient within the dielectric on both sides of the interface. , where is the dielectric constant on both sides of the interface. , The ratio of .

[0078] Assume that charge mainly accumulates at the interface of the dielectric (the degree of accumulation depends on the difference in dielectric constant). Calculate the charge at a specific grid point at the interface of the dielectric. Accumulated charge :

[0079] ,

[0080] ,

[0081] Replacing the difference of the homogeneous component with a difference of the non-homogeneous component , and assuming that the charge density inside the grid is a constant (for a grid, since its size is small, the charge density inside can be considered as a constant), we can get:

[0082] ,

[0083] where, is the length of the grid; then,

[0084] ,

[0085] Next, the non-homogeneous component of the grid potential can be calculated using the Coulomb potential generated by the charge gathered at the interface edge, and since is a small quantity that can be ignored, the calculation result of the non-homogeneous component is:

[0086] ,

[0087] where, is the distance from the grid to the grid .

[0088] S600, calculating the total potential of each grid according to the first potential and the second potential.

[0089] The total potential of each grid is the sum of the homogeneous component and the non-homogeneous component, that is,

[0090] .

[0091] The semiconductor device model is abstracted as parallel capacitor plates and multiple dielectrics in the application, and the Poisson equation of the equivalent simulation system can be constructed. The homogeneous component of the Poisson equation is equivalent to the potential generated by the potential difference outside the grid, and the non-homogeneous component is equivalent to the potential generated by the charge aggregation inside the grid. The total potential of each grid can be calculated by solving the two potentials. The calculation method can calculate the potential field distribution of the semiconductor device without iteration, thereby accelerating the solving speed and improving the simulation efficiency of the semiconductor device. The method is suitable for scenarios where the calculation accuracy of the potential field is not particularly high, such as dynamic simulation, and can have a good acceleration effect. At the same time, if the potential field given by the simulation system outside is much larger than the potential field generated inside, the error of the total potential field generated by the calculation method can also be reduced to an acceptable range.

[0092] To verify whether the calculation method is feasible, the potential field distribution of the semiconductor device calculated by the iteration method is compared with the calculation method. Taking a two-dimensional model as an example, the potential calculated by the existing iteration method can be expressed as:

[0093] ,

[0094] The potential calculated by the approximate method of the application is:

[0095] ,

[0096] The result of the iteration method is:

[0097] ,

[0098] Therefore, the relative error is:

[0099] ,

[0100] Continuing the Taylor expansion can obtain:

[0101] .

[0102] For some scenarios where the calculation accuracy of the potential field is not particularly high, such as dynamic simulation, or the potential field given by the simulation system outside is much larger than the potential field generated inside, the error can be acceptable. Of course, in order to expand the application range and make the error as small as possible, the following improvements can be made: the sum is as small as possible, that is, the charge aggregation area is as small as possible, and the dielectric constant difference of different dielectrics is large; The grid length is as large as possible, that is, the position far away from the charge aggregation area.

[0103] Therefore, when the combination model of the present application is used, the following should be ensured as much as possible: the difference between the dielectrics on both sides of the interface is large; the distance between the potential calculation region and the interface is far; other more accurate algorithms are used in the region near the interface or a correction is added. Specifically, after the total potential of each grid is calculated, the following steps are further included:

[0104] calculating the error of the total potential; and using an iterative method to correct the grid where the error of the total potential is greater than a preset error.

[0105] In an embodiment, on the basis of the foregoing embodiment, the present application provides a computer device, which comprises a memory, a processor, and a computer program stored in the memory, and the processor executes the computer program to implement the steps of the potential field distribution calculation method of the foregoing embodiment.

[0106] In an embodiment, on the basis of the foregoing embodiment, the present application provides a computer storage medium, which stores a computer program or instructions, and the computer program or instructions are executed by a processor to implement the steps of the potential field distribution calculation method of the foregoing embodiment.

[0107] The potential field distribution calculation method of the present application can be implemented by program codes executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be respectively made into individual integrated circuit modules, or a plurality of modules or steps among them can be made into a single integrated circuit module to implement. Thus, the present application is not limited to any particular combination of hardware and software.

[0108] It should be noted that the foregoing embodiments can be freely combined as needed. The above only describes the preferred embodiments of the present application, and it should be noted that, for those skilled in the art, several improvements and refinements can be made without departing from the principles of the present application, and these improvements and refinements should also be considered as the protection scope of the present application.

Claims

1. A method for calculating electric potential field distribution, characterized in that, Simulation of semiconductor devices includes the following steps: The semiconductor device model is divided into several grids; The semiconductor device model is equivalent to a simulated combination of parallel capacitor plates and various dielectrics, and the potential of each grid is divided into a first potential generated by the influence of external potential difference and a second potential generated by the accumulation of charge inside the device. Based on the simulation combination, construct the Poisson equation satisfied by the potential of each grid. The homogeneous component of the Poisson equation is calculated as the first potential; The non-homogeneous component of the Poisson equation is calculated as the second potential based on the difference between the homogeneous components. The total potential of each grid is calculated based on the first potential and the second potential. The method of equating the semiconductor device model to a combination of parallel capacitor plates and various dielectrics further includes: Based on the parameter information of the semiconductor device model, determine the external potential V of each grid, the dielectric constant of the different dielectrics corresponding to each grid, and the size parameters of the simulation assembly. , and ; Electric potential of each grid The Poisson equation that is satisfied is: ， in, For charge density, The permittivity; the equivalent cathode of the simulated combination is located at Location, equivalent anode is located at Location; homogeneous component of electric potential The Poisson equation is: ； For a certain grid The calculation results of the homogeneous components are as follows: , in, For along The grid length has no oxygen vacancies in the direction. The distance from the grid to one electrode of the parallel capacitor plate; The Poisson equation for the non-homogeneous components of the electric potential is: ， At the interface of the dielectric, the boundary condition of continuous electric displacement vector is satisfied, that is... ， ， ， in, and This represents the normal component of the potential gradient within the dielectric on both sides of the interface. , where is the dielectric constant on both sides of the interface. , The ratio; The method of calculating the non-homogeneous components of the Poisson equation based on the differences of the homogeneous components includes: Calculate a mesh at the interface of the dielectric. Accumulated charge : ， ， The difference of the homogeneous term components is used instead. ,get: ， in, Let be the length of the grid; then, ， The calculation results for the non-homogeneous components are as follows: ， in, For grid To grid The distance.

2. The method for calculating the electric potential field distribution according to claim 1, characterized in that, Total potential of each grid It is the sum of homogeneous and non-homogeneous components, i.e. 。 3. The method for calculating the electric potential field distribution according to claim 1, characterized in that, After calculating the total potential of each grid, the process also includes: Calculate the error of the total potential; An iterative method is used to correct the error in the total potential at grid points where the error exceeds a preset error.

4. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the electric potential field distribution calculation method according to any one of claims 1-3.

5. A computer storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by the processor, they implement the steps of the electric potential field distribution calculation method according to any one of claims 1-3.

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