Method for calculating the capture cross section of defects in a semiconductor material

Abstract

The application provides a method for calculating a defect capture cross section in a semiconductor material, comprising the following steps: constructing a semiconductor material structure without defects and with defects, then specifying the charged states a, a-1 and a+1 of the material, optimizing the semiconductor material so that atoms are all in respective equilibrium positions; calculating the energy of the obtained semiconductor material structures; and calculating the capture cross section of the defects in the semiconductor material by using a formula. The application can quickly and accurately calculate the capture cross section in the semiconductor material by means of simulation calculation, so as to evaluate the radiation resistance of the semiconductor material, and solve the problems of long test period and low efficiency in the traditional capture cross section calculation process.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of condensed matter physics, and in particular, to a method for calculating a defect capture cross section in a semiconductor material. BACKGROUND

[0002] When a semiconductor device is in an extreme environment such as high-energy particle irradiation, the working stability and service life of the device will be greatly affected. High-energy particle irradiation can cause displacement damage or ionization damage to the microstructure of the device, and the accumulation of various defect structures will cause the device to fail temporarily or even permanently. Therefore, the research and development of radiation-resistant semiconductor materials are of great significance, and the research and development of radiation-resistant semiconductor materials requires a deep understanding of the mechanism of the correlation between the properties of irradiation defects and semiconductor materials.

[0003] Among them, the radiation defect is one of the factors that must be considered in the evaluation of the anti-radiation ability of electronic components, and the capture cross section of the defect is a essential physical property of the defect. The capture cross section can represent the trapping ability of the defect structure to non-equilibrium carriers in the semiconductor device, and can be divided into electron capture cross section and hole capture cross section according to the capture object. During the operation of the electronic component, due to the trapping and emission of non-equilibrium carriers by the defect, a series of problems such as the decline of the radio frequency performance of the device and the change of the channel resistance will occur. Therefore, the defect capture cross section is one of the necessary parameters for constructing the influence of the defect on the properties of the semiconductor material.

[0004] At present, the micro-mechanism of the relationship between the properties of defects caused by high-energy particles and the properties of semiconductor materials is mainly realized through experimental research and computer simulation, but the experimental research method has many limitations in studying the micro-mechanism, and the research efficiency is slow. In addition, although the computer simulation method has been widely used in the evaluation of the damage ability of electronic components, there is still no method for calculating the defect capture cross section in the semiconductor material through computer simulation, which leads to low calculation efficiency and poor accuracy of the defect capture cross section in the semiconductor material, and affects the research and development of radiation-resistant semiconductor materials. SUMMARY

[0005] The problem solved by the present application is how to provide a method for quickly and accurately calculating the defect capture cross section in a semiconductor material.

[0006] To solve at least one aspect of the above problems, the present application provides a method for calculating a defect capture cross section in a semiconductor material, comprising the following steps:

[0007] Step S1: constructing a defect-free semiconductor material structure, then specifying a charged state a of the material, and constructing a semiconductor material structure based on the charged state a in which an electron state a-1 and a hole state a+1 are obtained, and optimizing the semiconductor material so that all atoms are in their respective equilibrium positions;

[0008] Step S2: constructing a defective semiconductor material structure, then specifying a charge state a of the material, and constructing a semiconductor material structure based on the charge state a in which an electron state a-1 and a hole state a+1 are obtained, and optimizing the semiconductor material so that all atoms are in their respective equilibrium positions;

[0009] Step S3, calculating the energy of the several semiconductor material structures constructed in step S1 and step S2, respectively Represents the energy of different semiconductor material structures, where and They represent the energy of a defect-free semiconductor material structure under the conditions of charged states a-1, a and a+1, respectively. and They represent the energy of the defective semiconductor material structure under the conditions of charged states a-1, a and a+1 respectively;

[0010] Step S4, calculating the capture cross section of defects in the semiconductor material using the following formula:

[0011] First, calculate the energy barrier of an electron in the semiconductor material Δ E(a-1) and the energy barrier of a hole Δ E(a+1);

[0012]

[0013]

[0014] Then, according to Δ E(a-1) and Δ E(a+1) calculates the electron capture cross section σ - and the hole capture cross section σ + :

[0015]

[0016]

[0017] Among them, m * is the effective electron mass or effective hole mass, is the reduced Dirac constant.

[0018] Preferably, the semiconductor material comprises Si, SiC, GaAs or GaN.

[0019] Preferably, in the step S1 and the step S2, the semiconductor material is optimized by using the first-principle calculation software VASP.

[0020] Preferably, in the step S1, ISIF=2, IBRION=2, EDIFEG=-0.01, EDIEF=1e-6, until the atomic position and the electronic structure of the semiconductor material reach the convergence criterion, and the atoms are all in the respective equilibrium position.

[0021] Preferably, in the step S2, the atomic force and the electronic energy are used as the convergence criterion, ISIF=2, IBRION=2, EDIFEG=-0.01, EDIEF=1e-6, until the atomic position and the electronic structure of the semiconductor material reach the convergence criterion, and the atoms are all in the respective equilibrium position.

[0022] Preferably, the charged state a is 0, a-1 is -1, and a+1 is +1.

[0023] Preferably, in the step S3, in the energy calculation process, ISIF=2, IBRON=-1, LHFCALC=T, HFSCREEN=0.2, and AEXX=0.31.

[0024] The present application constructs a defect-free material structure and a defective material structure respectively, specifies the charged state of the material, adds a state of obtaining one electron and a state of obtaining one hole on the basis of the specified charged state, then calculates the energy of the defect-free structure and the defective structure in different charged states respectively, and calculates the energy barrier of obtaining one electron or one hole through the energy of the defective structure, and finally calculates the result of the defect capture cross section through a formula; the present application can quickly and accurately calculate the capture cross section in the semiconductor material through simulation calculation, so as to evaluate the anti-radiation performance of the semiconductor material, and solve the problems of long experimental test period and low efficiency in the traditional capture cross section calculation process. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 The flow chart of the calculation method of the defect capture cross section in the semiconductor material in the embodiment of the present application is shown in the figure.

[0026] Figure 2 The GaN structure diagram of the defect-free structure in the embodiment of the present application is shown in the figure.

[0027] Figure 3 The GaN structure diagram of the defective structure in the embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0028] In order to make the above objectives, features and advantages of the present application more apparent, specific embodiments of the present application are described in detail below.

[0029] It should be noted that the features in the embodiments of the present application can be combined with each other without conflict. The terms "comprise", "include", "contain", "have" are non-limiting, i.e. other steps and other components can be added without affecting the results. The above terms encompass the terms "consist of" and "consist essentially of". Unless otherwise specified, the materials, devices, reagents are commercially available.

[0030] When calculating the defect capture cross section in a semiconductor material, it can be assumed that the recombination center in the semiconductor material is a sphere with a radius, and the cross-sectional area is σ, and the larger the cross-sectional area, the greater the probability that the carrier will be captured by the recombination center during movement. Therefore, σ can be used to represent the ability of the recombination center to capture carriers, which is called the capture cross section. The ability of the recombination center to capture holes and electrons is different, and can be represented by the electron capture cross section σ - and the hole capture cross section σ + .

[0031] The embodiment of the present application provides a calculation method for the defect capture cross section in a semiconductor material, as shown in Figure 1 , comprising the following steps:

[0032] Step S1, constructing a defect-free semiconductor material structure, then specifying the charged state a of the material, and constructing the semiconductor material structure of the state a-1 of obtaining one electron and the state a+1 of obtaining one hole on the basis of the charged state a, optimizing the semiconductor material so that the atoms are all in their respective equilibrium positions;

[0033] Step S2, constructing a semiconductor material structure with defects, then specifying the charged state a of the material, and constructing the semiconductor material structure of the state a-1 of obtaining one electron and the state a+1 of obtaining one hole on the basis of the charged state a, optimizing the semiconductor material so that the atoms are all in their respective equilibrium positions;

[0034] Step S3, calculating the energy of the several semiconductor material structures constructed in steps S1 and S2, respectively represented by representing the energy of different semiconductor material structures, wherein, and represent the energy of the defect-free semiconductor material structure under the conditions of the charged states a-1, a and a+1, respectively, and represent the energy of the semiconductor material structure with defects under the conditions of the charged states a-1, a and a+1, respectively;

[0035] Step S4, the capture cross section of the defects in the semiconductor material is calculated by using the following formula:

[0036] First, the energy barrier of an electron in the semiconductor material is calculated Δ E(a-1) and the energy barrier of a hole Δ E(a+1) is calculated.

[0037]

[0038]

[0039] Then, the capture cross section σ Δ of the electron and the capture cross section σ Δ of the hole are calculated according to - E(a-1) and + E(a+1) respectively:

[0040]

[0041]

[0042] where m * is the effective electron mass or the effective hole mass, is the reduced Dirac constant.

[0043] The semiconductor material includes Si, SiC, GaAs or GaN.

[0044] In step S1, the first principle software VASP is used to optimize the semiconductor material, and the optimization parameters are ISIF=2, IBRION=2, EDIFEG=-0.01, EDIEF=1e-6, until the atomic positions and electronic structures of the semiconductor material reach the convergence criteria, so that the atoms are all in their respective equilibrium positions.

[0045] In step S2, the structure of the semiconductor material with defects is constructed, and then the charged state a of the material is specified, and the semiconductor material structure of the state a-1 with one electron and the state a+1 with one hole is constructed on the basis of the charged state a, and the semiconductor material is optimized so that the atoms are all in their respective equilibrium positions. Wherein, the atomic force and the electronic energy are used as the convergence criteria, and the optimization parameters are ISIF=2, IBRION=2, EDIFEG=-0.01, EDIEF=1e-6, until the atomic positions and electronic structures of the semiconductor material reach the convergence criteria, so that the atoms are all in their respective equilibrium positions.

[0046] It should be understood that the calculation method of the defect capture cross section of the semiconductor material provided by the embodiment of the present application is used to calculate the semiconductor, and in the process of constructing the defect model, the known defects are used to construct, or the defects of the material are obtained by other methods capable of determining the defect structure of the semiconductor material, and then the defect model is constructed.

[0047] In step S3, the parameters are set as ISIF=2, IBRON=-1, LHFCALC=T, HFSCREEN=0.2, and AEXX=0.31, and the energy of the semiconductor material with defects and without defects is calculated, and the energy of the semiconductor material without defects is E(a) represents the energy of the semiconductor material structure without defects, E(a-1) represents the energy of the semiconductor material structure without defects in the charged state of a-1, E(a+1) represents the energy of the semiconductor material structure without defects in the charged state of a+1. E(a) represents the energy of the semiconductor material structure with defects, E(a-1) represents the energy of the semiconductor material structure with defects in the charged state of a-1, and E(a+1) represents the energy of the semiconductor material structure with defects in the charged state of a+1.

[0048] For example, the charged state of the semiconductor material is a=0, a-1=-1, and a+1=+1.

[0049] In step S4, the capture cross section of the defect in the semiconductor material is calculated by the following formula:

[0050] First, the energy barrier of one electron of the semiconductor material is calculated as Δ E(a-1) and the energy barrier of one hole of the semiconductor material is calculated as Δ E(a+1);

[0051]

[0052]

[0053] The formula is obtained according to the reaction process of the semiconductor material capturing an electron and a hole according to the following defect structure, and the reaction process is as follows:

[0054] Bulk -1 +Defect 0 →Bulk 0 +Defect -1 ;

[0055] Bulk +1 +Defect 0 →Bulk 0 +Defect +1 ;

[0056] Then, according to Δ E(a-1) and ΔE(a+1) calculates the capture cross section of electron σ - and the capture cross section of hole σ + :

[0057]

[0058]

[0059] wherein m * is the effective electron mass or effective hole mass, is the reduced Dirac constant.

[0060] By constructing a defect-free and a defect structure respectively, and specifying the charge state of the material, and adding the state of obtaining an electron and the state of obtaining a hole on the basis of the specified charge state, then the energy of the defect-free structure and the defect structure under different charge states is calculated respectively, and the energy barrier of obtaining an electron or a hole of the defect structure is calculated by the energy, and finally the result of the defect capture cross section is calculated by the formula; the present application can quickly and accurately calculate the capture cross section in the semiconductor material by means of simulation calculation, so as to evaluate the radiation resistance of the semiconductor material, and solve the problems of long experimental test period and low efficiency in the traditional capture cross section calculation process.

[0061] The calculation method of the defect capture cross section in the semiconductor material will be introduced in combination with specific embodiments as follows:

[0062] Embodiment

[0063] 1.1, construct a GaN supercell structure composed of 128 atoms, then specify the charge state of the material as 0, and construct the state of obtaining an electron-1 and the state of obtaining a hole+1 on the basis of the charge state of 0, optimize it, the optimization parameters are ISIF=2, IBRION=2, EDIFEG=-0.01, EDIEF=1e-6, until the atomic position and electronic structure of the semiconductor material reach the convergence standard, so that the atoms are all in their respective equilibrium positions; wherein, Figure 2 is a structural schematic diagram of a gallium nitride supercell;

[0064] 1.2, construct a GaN defect structure in which a carbon atom replaces a nitrogen atom, such as Figure 3The charge state of the material is then specified as 0, and a GaN defect structure of state -1 for obtaining one electron and state +1 for obtaining one hole is constructed based on the charge state 0, which is optimized so that the atoms are in their respective equilibrium positions; wherein the atomic force and electron energy are used as convergence criteria, the optimization parameters are ISIF=2, IBRION=2, EDIFEG=-0.01, EDIEF=1e-6, until the atomic positions and electron structure of the semiconductor material reach the convergence criteria, so that the atoms are in their respective equilibrium positions;

[0065] 1.3, the parameters are set as ISIF=2, IBRON=-1, LHFCALC=T, HFSCREEN=0.2, AEXX=0.31, and the energy of the defect-free and defective GaN structures is calculated, and the energy of the defect-free GaN structure is calculated as represent the energy of different GaN structures, wherein, and represent the energy of the defect-free GaN structure under the condition of charge state -1, 0 and +1, respectively, and represent the energy of the defective GaN structure under the condition of charge state -1, 0 and +1, respectively, and the calculation results are shown in Table 1:

[0066] Table 1 Energy calculation results of different GaN structures

[0067]

[0068] 1.4, the capture cross section of the defect in the semiconductor material is calculated by the following formula:

[0069] First, the energy barrier of the semiconductor material to obtain one electron Δ E(-1) and the energy barrier of one hole Δ E(+1) are calculated;

[0070]

[0071]

[0072] Then, the capture cross section σ - of the electron and the capture cross section σ + of the hole are calculated according to Δ E(-1) and Δ E(+1), respectively:

[0073]

[0074]

[0075] wherein m * is the effective electron mass or effective hole mass, is the reduced Dirac constant, the calculated results are shown in Table 2:

[0076] Table 2 Capture cross-section calculation results of GaN defect structures

[0077] Calculation parameter Value Unit Δ E(-1) ​ -2.38 eV Δ E(+1) ​ 0.008 eV - ]]> ​ 2.5×10-15 cm 2 ]] <![CDATA[σ + ]]> 7.45×10-14 cm 2 ]]

[0078] Although the present disclosure is disclosed as above, the protection scope of the present disclosure is not limited to this. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present disclosure, and these changes and modifications will fall within the protection scope of the present disclosure.

Claims

1. A method of calculating a defect capture cross section in a semiconductor material, characterized in that, The method comprises the following steps: Step S1, constructing a defect-free semiconductor material structure, then specifying the charged state a of the material, and constructing the semiconductor material structure of the state a-1 of obtaining one electron and the state a+1 of obtaining one hole on the basis of the charged state a, optimizing the semiconductor material so that the atoms are in their respective equilibrium positions; Step S2, constructing a defective semiconductor material structure, then specifying the charged state a of the material, and constructing the semiconductor material structure of the state a-1 of obtaining one electron and the state a+1 of obtaining one hole on the basis of the charged state a, optimizing the semiconductor material so that the atoms are in their respective equilibrium positions; Step S3, calculating the energy of the several semiconductor material structures constructed in step S1 and step S2, respectively, as representing the energy of different semiconductor material structures, wherein, and respectively represent the energy of the semiconductor material structure without defects under the condition of the charged state of a-1, a and a+1, and respectively represent the energy of the semiconductor material structure with defects under the condition of the charged state of a-1, a and a+1; Step S4, calculating the capture cross section of the defect in the semiconductor material by using the following formula: First, the energy barrier for a semiconductor material to get an electron Δ E(a-1) and a hole Δ E(a+1); Then, the capture cross section σ Δ E(a-1) and Δ E(a+1) are calculated, respectively, for the capture of an electron σ - and a hole σ + : where m * is the effective electron mass or effective hole mass, is the reduced Dirac constant.

2. The method of calculating a defect capture cross section in a semiconductor material according to claim 1, wherein, The semiconductor material comprises Si, SiC, GaAs or GaN.

3. The method of calculating a defect capture cross section in a semiconductor material according to claim 1, wherein, In the step S1 and the step S2, the first principle calculation software VASP is used to optimize the semiconductor material.

4. The method of calculating a defect capture cross section in a semiconductor material according to claim 3, wherein, In the step S1, ISIF=2, IBRION=2, EDIFEG=-0.01, EDIEF=1e-6, until the atomic position and the electronic structure of the semiconductor material reach the convergence criterion, so that the atoms are in their respective equilibrium positions.

5. The method of calculating a defect capture cross section in a semiconductor material according to claim 3, wherein, In the step S2, the atomic force and the electronic energy are used as the convergence criterion, ISIF=2, IBRION=2, EDIFEG=-0.01, EDIEF=1e-6, until the atomic position and the electronic structure of the semiconductor material reach the convergence criterion, so that the atoms are in their respective equilibrium positions.

6. The method of calculating a defect capture cross section in a semiconductor material according to claim 1, wherein, The charged state a is 0, a-1 is -1, and a+1 is +1.

7. The method of calculating a defect capture cross section in a semiconductor material according to claim 1, wherein, In the step S3, in the energy calculation process, ISIF=2, IBRON=-1, LHFCALC=T, HFSCREEN=0.2, and AEXX=0.

31. In the step S3, in the energy calculation process, ISIF=2, IBRON=-1, LHFCALC=T, HFSCREEN=0.2, and AEXX=0.31.

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