A method for calculating the off-site threshold energy of semiconductor materials

Abstract

The present invention provides a method for calculating the off-position threshold energy of a semiconductor material, comprising the following steps: constructing a supercell composed of semiconductor materials, and optimizing its structure so that each atom is in its own equilibrium position; taking a target atom as the center, selecting a velocity direction, setting the initial kinetic energy, and performing molecular dynamics simulation of the target atom's motion, and finally obtaining the kinetic energy corresponding to the Frankel defect through repeated attempts, that is, the minimum energy required for the target atom to leave its own position along the velocity direction to form a defect; analyzing the obtained data to obtain the off-position threshold energy of the target atom. The present invention constructs a supercell of semiconductor materials by a simulation method, and uniformly selects multiple velocity directions with the target atom as the sphere center, calculates the off-position threshold energy range of the target atom along different velocity directions, and reaches the set accuracy, obtains the off-position threshold energy of the target atom and the average off-position threshold energy data, and improves the calculation efficiency.

Description

Technical Field

[0001] The invention relates to the field of microelectronics and device technology, and in particular to a method for calculating off-site threshold energy of semiconductor materials. Background Art

[0002] The working environment of semiconductor devices is very complex. When semiconductor devices are located in extreme environments such as high-energy particle irradiation, high-energy particle irradiation can cause displacement damage or ionization damage to the microstructure of semiconductor devices, seriously affecting the working stability and service life of semiconductor devices. Therefore, it is necessary to develop new semiconductor devices that are resistant to high-energy particle irradiation to cope with extreme environments, and an in-depth understanding of the microscopic mechanism of the interaction between high-energy particles and semiconductor materials is the basis for the development of semiconductor devices that are resistant to high-energy particle irradiation. At present, the study of the microscopic mechanism of the interaction between high-energy particles and semiconductor materials is mainly carried out through experimental research and computer simulation, but experimental research is subject to many limitations in understanding the microscopic mechanism of the damage process, which affects the efficiency of microscopic mechanism research, while computer simulation has higher efficiency.

[0003] Among them, most of the damage caused by high-energy particles to semiconductor materials is displacement damage, while ionization damage accounts for a small proportion, and the main measurement indicator of displacement damage is the off-displacement threshold energy. Generally speaking, the larger the off-displacement threshold energy of a semiconductor material, the stronger its ability to resist high-energy particle radiation. Therefore, there is an urgent need for a method to quickly and accurately calculate the off-displacement threshold energy of semiconductor materials, to efficiently evaluate the radiation resistance of semiconductor materials, and to promote the development of radiation-resistant semiconductor materials. Summary of the invention

[0004] The problem solved by the present invention is how to provide a method for quickly and accurately calculating the off-state threshold energy of a semiconductor, so as to efficiently evaluate the radiation resistance of semiconductor materials.

[0005] In order to solve at least one aspect of the above problems, the present invention provides a method for calculating the off-site threshold energy of a semiconductor material, comprising the following steps:

[0006] Step S1, constructing a supercell composed of semiconductor materials, and optimizing its structure so that each atom is in its own equilibrium position;

[0007] Step S2, selecting an atom for which the off-position threshold energy needs to be calculated as the target atom, taking the target atom as the center, obtaining a spherical surface with a radius of 1 angstrom, selecting n uniformly distributed geometric points on the spherical surface, and then connecting lines from the center of the sphere to the n geometric points on the spherical surface respectively, and taking the direction from the center of the sphere to the geometric points on the spherical surface as the velocity direction of the target atom;

[0008] Step S3, selecting one of the speed directions, setting an initial kinetic energy of 1 eV, performing a molecular dynamics simulation of the target atom's motion, then gradually increasing the kinetic energy of the target atom, and repeating the molecular dynamics simulation until the target atom generates a Frankel defect, recording the last kinetic energy that does not generate a Frankel defect and the first kinetic energy that generates a Frankel defect in the process, and the delocalization threshold energy of the target atom along this speed direction is within this range;

[0009] Step S4, calculating the average of the last kinetic energy of the last Frankel defect that did not generate and the first kinetic energy of the first Frankel defect that generated, and using the average to perform molecular dynamics simulation of the target atom motion, and gradually increasing or decreasing the kinetic energy according to whether a Frankel defect is generated, repeating the above process, and gradually reducing the kinetic energy difference between the Frankel defect that can be generated and the Frankel defect that cannot be generated, until the set calculation accuracy is reached, and the kinetic energy corresponding to the Frankel defect that can be generated is finally obtained, that is, the minimum energy required for the target atom to leave its own position along the speed direction to form a defect;

[0010] Step S5, repeating steps S3 and S4 in different speed directions, respectively, to calculate the minimum energy required for the target atom to leave its own position along different speed directions to form a defect;

[0011] Step S6, analyzing the obtained data, wherein the values ​​of the minimum energy required for the target atom to form a defect at its own position along n different speed directions are compared, the minimum value is the off-location threshold energy of the target atom, and the average value of the minimum energy required for the target atom to form a defect at its own position along n different speed directions is the average off-location threshold energy.

[0012] Preferably, the semiconductor material includes Si, SiC, GaAs or GaN.

[0013] Preferably, in step S1, the number of atoms in the supercell is ≥ 5000.

[0014] Preferably, in step S1, the molecular dynamics program LAMMPS is used to relax and optimize the atomic structure of the semiconductor material based on the BFGS algorithm so that the force on each atom in the semiconductor material is zero.

[0015] Preferably, in step S2, 200≤n≤300.

[0016] Preferably, in step S3, the kinetic energy is increased by 10 eV each time.

[0017] Preferably, in step S4, the increased kinetic energy is gradually reduced to achieve the purpose of gradually reducing the kinetic energy difference between the kinetic energy that can produce Frankel defects and the kinetic energy that cannot produce Frankel defects.

[0018] Preferably, the method for calculating the off-location threshold energy of the semiconductor material further comprises analyzing the off-location threshold energy of the target atom along different speed directions to find the regularity of the off-location threshold energy in the semiconductor material in different speed directions.

[0019] The present invention constructs a supercell of semiconductor materials through a simulation method, and uniformly selects multiple speed directions with a target atom as the center of the sphere, calculates the range of the off-position threshold energy of the target atom along different speed directions by gradually increasing the kinetic energy, and then gradually repeats the calculation multiple times to reach the set accuracy, and can obtain the off-position threshold energy and average off-position threshold energy data of the target atom according to the comparison of different speed directions, thereby avoiding the problems of repeated attempts, long test cycle and low efficiency in the off-position threshold energy of traditional semiconductor materials, and also reducing the loss of semiconductor materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a flow chart of a method for calculating the off-site threshold energy of a semiconductor material in an embodiment of the present invention;

[0021] Figure 2 Schematic diagram of the unit cell structure composed of Si atoms in an embodiment of the present invention;

[0022] Figure 3 Schematic diagram of the change of the delocalization threshold energy of Si atoms in different planes in an embodiment of the present invention;

[0023] Figure 4 This is an analysis diagram of the delocalization threshold energy of Si atoms along different crystal directions in an embodiment of the present invention. DETAILED DESCRIPTION

[0024] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below.

[0025] It should be noted that, in the absence of conflict, the features in the embodiments of the present invention can be combined with each other. The meanings of the terms "comprising", "including", "containing", and "having" are non-restrictive, that is, other steps and other ingredients that do not affect the results can be added. The above terms cover the terms "consisting of" and "essentially consisting of". Unless otherwise specified, materials, equipment, and reagents are commercially available.

[0026] The embodiment of the present invention provides a method for calculating the off-site threshold energy of a semiconductor material, such as Figure 1 As shown, the following steps are included:

[0027] Step S1, constructing a supercell composed of semiconductor materials, and optimizing its structure so that each atom is in its own equilibrium position;

[0028] Step S2, selecting an atom for which the off-position threshold energy needs to be calculated as the target atom, taking the target atom as the center, obtaining a spherical surface with a radius of 1 angstrom, selecting n uniformly distributed geometric points on the spherical surface, and then connecting lines from the center of the sphere to the n geometric points on the spherical surface respectively, and taking the direction from the center of the sphere to the geometric points on the spherical surface as the velocity direction of the target atom;

[0029] Step S3, selecting one of the speed directions, setting an initial kinetic energy of 1 eV, performing a molecular dynamics simulation of the target atom's motion, then gradually increasing the kinetic energy of the target atom, and repeating the molecular dynamics simulation until the target atom generates a Frankel defect, recording the last kinetic energy that does not generate a Frankel defect and the first kinetic energy that generates a Frankel defect in the process, and the delocalization threshold energy of the target atom along this speed direction is within this range;

[0030] Step S4, calculating the average of the last kinetic energy of the last Frankel defect that did not generate and the first kinetic energy of the first Frankel defect that generated, and using the average to perform molecular dynamics simulation of the target atom motion, and gradually increasing or decreasing the kinetic energy according to whether a Frankel defect is generated, repeating the above process, and gradually reducing the kinetic energy difference between the Frankel defect that can be generated and the Frankel defect that cannot be generated, until the set calculation accuracy is reached, and the kinetic energy corresponding to the Frankel defect that can be generated is finally obtained, that is, the minimum energy required for the target atom to leave its own position along the speed direction to form a defect;

[0031] Step S5, repeating steps S3 and S4 in different speed directions, respectively, to calculate the minimum energy required for the target atom to leave its own position along different speed directions to form a defect;

[0032] Step S6, analyzing the obtained data, wherein the values ​​of the minimum energy required for the target atom to form a defect at its own position along n different speed directions are compared, the minimum value is the off-location threshold energy of the target atom, and the average value of the minimum energy required for the target atom to form a defect at its own position along n different speed directions is the average off-location threshold energy.

[0033] A supercell of semiconductor material is constructed through simulation method, and multiple speed directions are uniformly selected with the target atom as the center of the sphere. The range of the target atom's off-location threshold energy along different speed directions is calculated by gradually increasing the kinetic energy, and then repeated many times to gradually reach the set accuracy. The off-location threshold energy and average off-location threshold energy data of the target atom can be obtained by comparison according to different speed directions, avoiding the problems of repeated attempts, long test cycle and low efficiency in the off-location threshold energy of traditional semiconductor materials, and also reducing the loss of semiconductor materials.

[0034] The semiconductor material includes Si, SiC, GaAs or GaN. Si, SiC, GaAs and GaN are all commonly used semiconductor materials, and the off-position threshold energy can be calculated by the method provided by the present invention.

[0035] In step S1, a supercell composed of semiconductor materials is constructed, and its structure is optimized so that each atom is in its own equilibrium position, wherein the number of atoms in the supercell exceeds 5000, which can reduce the error caused by the size effect.

[0036] Specifically, under the Linux system environment, the molecular dynamics program LAMMPS is used to relax and optimize the atomic structure of the semiconductor material based on the BFGS algorithm, so that the force on each atom in the semiconductor material is zero, that is, at this time, the atoms in the semiconductor material are in their respective equilibrium positions.

[0037] In step S2, the atom for which the delocalization threshold energy needs to be calculated is selected as the target atom, and a radius of 1 angstrom is obtained with the target atom as the center. spherical surface, select n uniformly distributed geometric points on the spherical surface, and then connect the n geometric points on the spherical surface from the center of the sphere, and use the direction from the center of the sphere to the geometric points on the spherical surface as the velocity direction of the target atom, where 200≤n≤300. The smaller the value of n, the rougher the obtained off-position threshold energy data, and the larger the value of n, the more accurate the obtained off-position threshold energy data, but the amount of calculation will also increase accordingly. In order to balance the accuracy of the off-position threshold energy data and the amount of calculation, the value of n is selected between 200-300.

[0038] In step S3, one of the speed directions is selected, the initial kinetic energy of 1 eV is set, and the molecular dynamics simulation of the target atom's motion is performed. Then, the kinetic energy of the target atom is gradually increased, and the molecular dynamics simulation is repeated until the target atom generates a Frankel defect. The last motion speed that does not generate a Frankel defect and the kinetic energy of the first one that generates a Frankel defect are recorded. The delocalization threshold energy of the target atom along this speed direction is within this range.

[0039] Specifically, one of the speed directions is selected, and the initial kinetic energy of 1eV is set to perform molecular dynamics simulation of the target atom's movement. When the initial kinetic energy is small, it is difficult for the target atom to produce Frankel defects. Then the kinetic energy of the target atom is gradually increased by 10eV each time, and the molecular dynamics simulation is repeated until the target atom produces Frankel defects. The range between the last movement speed that does not produce Frankel defects and the first kinetic energy that produces Frankel defects is the range of the target atom's delocalization threshold energy along this speed direction.

[0040] For example, when one of the speed directions is selected, the initial kinetic energy of 1eV is set, the target atom does not produce Frankel defects, the kinetic energy of the target atom is gradually increased by 10eV, and the molecular dynamics simulation is repeated. If the target atom does not produce Frankel defects when the kinetic energy is 21eV, but the target atom produces Frankel defects when the kinetic energy is 31eV, it means that the delocalization threshold energy of the target atom along this speed direction is between 21eV-31eV.

[0041] In step S4, the average value of the last kinetic energy without generating Frankel defects and the first kinetic energy generating Frankel defects is calculated, and the molecular dynamics simulation of the target atom motion is performed with the average value, and the kinetic energy is gradually increased or decreased according to whether Frankel defects are generated, and the above process is repeated to gradually reduce the kinetic energy difference between the Frankel defects that can be generated and the Frankel defects that cannot be generated, until the set calculation accuracy is reached, and the kinetic energy corresponding to the Frankel defects that can be generated is finally obtained, that is, the minimum energy required for the target atom to leave its own position along the speed direction to form a defect. And in order to achieve the set accuracy, the increased kinetic energy is gradually reduced during the repetition process.

[0042] For example, when the last target atom without Frankel defect has a kinetic energy of 21eV and the first target atom with Frankel defect has a kinetic energy of 31eV, the average of the two is calculated to be 26eV, and the molecular dynamics simulation of the target atom motion is performed using the kinetic energy of 26eV. If the target atom has Frankel defect, the kinetic energy is gradually reduced, and the molecular dynamics simulation of the target atom motion is performed again. Otherwise, the kinetic energy is gradually increased. In this process, the amplitude of the kinetic energy increase is gradually reduced, thereby gradually reducing the range of the off-position threshold energy and improving the accuracy of the off-position threshold energy.

[0043] In addition, the calculation method of the semiconductor material delocalization threshold energy also includes analyzing the delocalization threshold energy of the target atom along different speed directions, and finding the law of the delocalization threshold energy in the semiconductor material in different speed directions. Analyzing the obtained results can obtain the law of the delocalization threshold energy of the target atom in the semiconductor material in different speed directions, and provide ideas and directions for the development of high-energy particle radiation resistant devices.

[0044] The following is a method for calculating the off-site threshold energy of semiconductor materials in conjunction with a specific embodiment:

[0045] Example

[0046] 1.1. Construct a supercell consisting of 8000 Si atoms, where Figure 1 The unit cell structure is composed of 8 Si atoms. Under the Linux system environment, the molecular dynamics program LAMMPS is used to relax and optimize the atomic structure of the semiconductor material based on the BFGS algorithm, so that the force on each atom in the semiconductor material is zero;

[0047] 1.2. Select an atom in the supercell as the target atom, and get a spherical surface with a radius of 1 angstrom with the target atom as the center. Select 240 uniformly distributed geometric points on the spherical surface, and then connect the 240 geometric points on the spherical surface from the center of the sphere. The direction from the center of the sphere to the geometric point on the spherical surface is taken as the velocity direction of the target atom. There are 240 velocity directions in total.

[0048] 1.3. Select one of the speed directions, set the initial kinetic energy of 1eV, perform molecular dynamics simulation of the target atom's motion, then gradually increase the kinetic energy of the target atom by 10eV each time, and repeat the molecular dynamics simulation until the target atom generates a Frankel defect. Record the last motion speed that does not generate a Frankel defect and the kinetic energy of the first one that generates a Frankel defect. The delocalization threshold energy of the target atom along this speed direction is within this range.

[0049] 1.4. Calculate the average of the kinetic energy of the last Frankel defect that does not generate and the kinetic energy of the first Frankel defect that generates, and use the average to perform molecular dynamics simulation of the target atom's motion, and gradually increase or decrease the kinetic energy according to whether a Frankel defect is generated. Repeat the above process to gradually reduce the kinetic energy difference between the Frankel defect that can be generated and the Frankel defect that cannot be generated until the set calculation accuracy is reached. The kinetic energy corresponding to the Frankel defect that can be generated is the minimum energy required for the target atom to leave its own position along the speed direction to form a defect.

[0050] 1.5. Repeat steps 1.3 and 1.4 at different speeds to calculate the minimum energy required for the target atom to leave its position and form a defect along different speeds.

[0051] 1.6. Analyze the obtained data, wherein the values ​​of the minimum energy required for the target atom to form a defect at its own position along 240 different speed directions are compared, the minimum value is the off-position threshold energy of the target atom, and the average value of the minimum energy required for the target atom to form a defect at its own position along 240 different speed directions is the average off-position threshold energy;

[0052] 1.7. Analyze the delocalization threshold energy of the target atoms along different speed directions, and find the law of the delocalization threshold energy in semiconductor materials in different speed directions.

[0053] in, Figure 3 Figure 3 is the relationship between the delocalization threshold energy of Si atoms in the xoy, yoz and zox planes and their directions. It can be seen from the figure that the delocalization threshold energy in the three planes has roughly the same law. Taking the xoy plane as an example, the delocalization threshold energy in the 45° direction is 10eV, while the delocalization threshold energy in the 75° direction is 25eV. Relatively speaking, atoms are more likely to form defects in the 45° direction.

[0054] Figure 4 The delocalization threshold energy diagram along different crystal directions shows that Si <100> , <101> , <110> and <111> There is anisotropy in four directions. In single crystal Si, Si atoms are anisotropic along <101> and <110> The delocalization threshold energy along <100> and <111> The delocalization threshold energy in the direction and the direction of the line connecting the two is larger.

[0055] Although the disclosure is disclosed as above, the protection scope of the disclosure is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the disclosure, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A method for calculating the off-site threshold energy of a semiconductor material, characterized in that: The following steps are involved: Step S1, constructing a supercell composed of semiconductor materials, and optimizing its structure so that each atom is in its own equilibrium position; Step S2, selecting an atom for which the off-position threshold energy needs to be calculated as the target atom, taking the target atom as the center, obtaining a spherical surface with a radius of 1 angstrom, selecting n uniformly distributed geometric points on the spherical surface, and then connecting lines from the center of the sphere to the n geometric points on the spherical surface respectively, and taking the direction from the center of the sphere to the geometric points on the spherical surface as the velocity direction of the target atom; Step S3, selecting one of the speed directions, setting an initial kinetic energy of 1 eV, performing a molecular dynamics simulation of the target atom's motion, then gradually increasing the kinetic energy of the target atom, and repeating the molecular dynamics simulation until the target atom generates a Frankel defect, recording the last kinetic energy that does not generate a Frankel defect and the first kinetic energy that generates a Frankel defect in the process, and the delocalization threshold energy of the target atom along this speed direction is within this range; Step S4, calculating the average value of the last kinetic energy of the non-Frankel defect and the first kinetic energy of the Frankel defect, and using the average value to perform molecular dynamics simulation of the motion of the target atom, and gradually increasing or decreasing the kinetic energy according to whether a Frankel defect is generated, repeatedly calculating the average value of the last kinetic energy of the non-Frankel defect and the first kinetic energy of the Frankel defect, and using the average value to perform molecular dynamics simulation of the motion of the target atom, and gradually increasing or decreasing the kinetic energy according to whether a Frankel defect is generated, gradually reducing the kinetic energy difference between the Frankel defect that can be generated and the Frankel defect that cannot be generated, until the set calculation accuracy is reached, and the kinetic energy corresponding to the Frankel defect that can be generated is finally obtained, that is, the minimum energy required for the target atom to leave its own position along the speed direction to form a defect; Step S5, repeating steps S3 and S4 in different speed directions, respectively, to calculate the minimum energy required for the target atom to leave its own position along different speed directions to form a defect; Step S6, analyzing the obtained data, wherein the values ​​of the minimum energy required for the target atom to form a defect at its own position along n different speed directions are compared, the minimum value is the off-location threshold energy of the target atom, and the average value of the minimum energy required for the target atom to form a defect at its own position along n different speed directions is the average off-location threshold energy.

2. The method for calculating the off-site threshold energy of semiconductor materials according to claim 1, characterized in that: The semiconductor material includes Si, SiC, GaAs or GaN.

3. The method for calculating the off-site threshold energy of semiconductor materials according to claim 1, characterized in that: In the step S1, the number of atoms in the supercell is ≥5000.

4. The method for calculating the off-site threshold energy of semiconductor materials according to claim 1, characterized in that: In the step S1, the molecular dynamics program LAMMPS is used to relax and optimize the atomic structure of the semiconductor material based on the BFGS algorithm, so that the force on each atom in the semiconductor material is zero.

5. The method for calculating the off-site threshold energy of semiconductor materials according to claim 1, characterized in that: In the step S2, 200≤n≤300.

6. The method for calculating the off-site threshold energy of semiconductor materials according to claim 1, characterized in that: In step S3, the kinetic energy is increased by 10 eV each time.

7. The method for calculating the off-site threshold energy of semiconductor materials according to claim 6, characterized in that: In step S4, the increased kinetic energy is gradually reduced to achieve the purpose of gradually reducing the kinetic energy difference between the kinetic energy that can produce Frankel defects and the kinetic energy that cannot produce Frankel defects.

8. The method for calculating the off-site threshold energy of semiconductor materials according to claim 1, characterized in that: It also includes analyzing the delocalization threshold energy of the target atoms along different speed directions, and finding the law of the delocalization threshold energy in semiconductor materials in different speed directions.

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