新型超硬功能材料的设计与硼碳氮体系杂质行为的理论研究
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摘要
本工作采用第一性原理设计了两种新型B-C及C-N材料,并对其稳定性及其相关性质作了系统的研究;针对几种典型的B-C-N体系,研究了杂质行为及其压力效应,主要包括c-BN和c-BC_2N等超硬半导体材料中杂质的形成能、电子能级的位置等随压力的变化情况,研究了材料中可能存在的杂质或缺陷类型及其在压力下的稳定性问题.具体的研究工作介绍如下:
(一)由简立方C_20结构出发,通过取代设计了两种材料,C_3N_2和B_2C_3。研究结果表明,C_3N_2有α-C_3N_2和β-C_3N_2两个相,α-C_3N_2存在压力范围为0-1.2GPa,β-C_3N_2为C_3N_2的高压相。通过第一性原理硬度计算知道其韦氏硬度均约为86GPa,介于c-BN(68GPa)和金刚石(98GPa)之间;B_2C_3具有金属性质,在3K时可以转变为超导体相。
(二)研究了立方氮化硼中几种杂质在压力下的行为。(1)压力下立方氮化硼本征空位的研究。发现在富氮条件下硼空位的形成焓随压力的增加而减小,根据平衡杂质浓度公式,可以知道随压力的增加,硼空位的平衡浓度在增大;在富硼条件下,氮空位的形成焓随压力的增加而增加,其平衡浓度随压力的增加而减小。(2)立方氮化硼中碳取代硼或取代氮杂质行为的研究。结果表明在60GPa范围内碳取代硼的形成焓随压力的增加而减小,说明在压力下其更加稳定存在,平衡浓度也在增加;而碳取代氮的形成焓随压力的增加而增加,说明在压力下其变得不大稳定了且其平衡浓度变小。(3)立方氮化硼中氮或氧取代硼的研究。结果表明这两种取代杂质的形成焓都随压力的增加而减小,即在压力下其变的更加稳定,平衡浓度更大些。
(三)研究了立方BC_2N中本征杂质的行为。研究结果显示,在BC_2N体材料中,空位的形成能都比较高,则空位不能稳定存在于材料中。而取代杂质( BC II、N CI、C N)的形成能都比较低,甚至为负值,表明这几类替代杂质容易形成且能稳定存在于BC_2N材料中,其浓度比较高。
Diamond is the most well-known superhard material and searching for much more hard materials is always in pursuit of the goal of experimental and theoretical workers. It is reported that covalent solids composed of boron, carbon and nitrogen are excellent candidates for extraordinary hardness. Prediction and development of the novel superhard materials also benefit from the first-principles method. One chief goal of this thesis is to find novel superhard functional materials.
A real semiconductor invariably has either some defects due to heat treatment or impurities during the crystal growth process. The electronic quality of a semiconductor is largely determined by the nature and number of its native defects and impurities. Defects in semiconductors not only influence the electrical and optical properties of these materials, but also exhibit their own interesting physics. The identification and control of defects such as vacancies, interstitials, and impurities is a major field of research, with important applications in materials engineering. Density-functional theory (DFT) calculation based on pseudopotentials, a plane-wave basis set, and a supercell geometry is now regarded as a standard first-principles method for the studies of defects in semiconductors. To reveal the natural properties of impurities in these typical B-C-N systems is another important aim of this thesis.
In this work, we suggest two hypothetical structures with C_3N_2 and B_2C_3 stoichiometry, by replacing of the carbon atoms with nitrogen or boron in the crystalline phase of simple cubic carbon (C_20), and have presented a completely theoretical analysis of the structural, elastic and electronic properties ofα-C_3N_2 andβ-C_3N_2 using first-principles method. We carry out density functional calculations on the self-vacancies, substitutional carbon and boron-related defects in c-BN and native defects in c-BC_2N using the strict convergence criteria and a large simulation cell. The defect formation enthalpy is a key quantity describing the behavior of defects and is calculated from the total energies of perfect and defected supercell. To check the stability of defects created under pressure, we calculate the formation enthalpies as a function of hydrostatic pressure. The main contents are as follows:
I. Recently, theoretical prediction and experimental synthesis of superhard materials are focuses of research. We suggest two new compoundsα-C_3N_2 andβ-C_3N_2 with cubic symmetry, which are derived from a simple cubic carbon (C_20) reported recently. Our first-principles calculations show that both the solids are highly incompressible with high bulk modulus (380 and 343 GPa), large shear modulus G (365 and 368 GPa), great elastic constant C44 (327 and 329 GPa), and high Vickers hardness Hv (both are 86 GPa), respectively. Accordingly we come to a conclusion that both the C_3N_2 phases are potentially superhard semiconductor materials. From the electronic partial density of state, it is found that the superhard character of the two phases is mainly attributed to the strong covalent bond between C and N. Theα-C_3N_2 is dynamically stable at pressures below 1.2 GPa, but unstable above 1.2 GPa because an optical branch softens to zero at theΓpoint. Theα-C_3N_2 will transform intoβ-C_3N_2 at about 1.2GPa which is energetically more stable. Both phonon dispersion and elastic constant calculations at zero and high pressures show that thisβ-C_3N_2 remains mechanically and dynamically stable in a pressure range from 0 GPa to at least 20 GPa. Based on ab initio phonons and electron-phonon coupling constants, we estimate the transition temperatures for B_2C_3 Tc cal≈3 K.
II. We investigate, through first-principles calculations, the pressure dependence on the formation enthalpy and electronic level positions of defects and impurities in c-BN. There are a lot of experimental and theoretical work about the doped c-BN, but up to now, a complete quantitative description of the formation enthalpy and energy-level positions of defects in different charge states under pressures is still lacking. In this part the effects of pressure on the self-vacancies、substitutional carbon and boron-related defects in c-BN have been extensively studied. Finding: a) The formation enthalpy of VB decreases with pressure and the equilibrium concentration of VB increases with pressure under nitrogen-rich condition; the formation enthalpy of VN increases with pressure and the equilibrium concentration of VN decreases with pressure under boron-rich condition. Bothe boron and nitrogen vacancies induce localized narrow“vacancy bands”in the energy gap region of c-BN. The partial defect energy levels of VN move up with an increase in pressure and intersect with the conduction band, showing pressure strengthens its conductivity, while for VB the position of defect energy levels remains almost unchanged relative to the valence-band edge, indicating a pressure effect that is not obvious. b) We have observed that the dependence of the formation enthalpy of CB on pressure is much stronger than that of CN on pressure. The formation enthalpy decreases with pressure for CB, which suggests that CB becomes much more stable and has a larger concentration with pressure increase. In contrast to CB, the formation enthalpy of CN impurities exhibits positive dependence on pressure, so the concentration of CN reduces with pressure. We think that the opposite trend for the formation enthalpies of CB and CN with pressure mainly originate in the enthalpies of the defect-contained supercell under different pressure. It is also observed that pressure may weaken its conductivity in the case of CN and CB in c-BN. Theses results are useful for making a boron nitride pn junction diode and an ultraviolet light-emitting diode under high pressure. c) We find that the nitrogen atoms surrounding the defect relax inward in the case of CB, while the nitrogen atoms relax outward in other cases. The formation volume of all boron-related impurities decrease with pressure, which means that the formation enthalpies decrease with pressure and the equilibrium concentration of boron-related impurities increase with pressure. Those results are in close agreement with the direct defect formation enthalpy calculations. The impurity CB+1 is found to have the lowest formation enthalpy and exhibit semiconductor and have higher bulk modulus than ideal c-BN, and suggest that the hardness of c-BN may be strengthen when a carbon atom substitute at a B site.
III. First-principles pseudopotential calculations have been performed to investigate intrinsic defects including vacancies and antisite defects in BC_2N crystals. All self-vacancies, namely, B-vacancy (VB), C-vacancies (VCI and VCII) and N-vacancy (VN), have high formation energies and are hence unstable. In contrast, carbon at boron and nitrogen sites (CB and CN) exhibit p-type and n-type properties, respectively, as well as low formation energies. The antisite defect BN does not change the semiconducting character of the BC_2N according to the band structures. The BCII and NCI in BC_2N have the lowest formation energies and are energetically favorable to form under B-rich and N-rich growth conditions, respectively. They also exhibit acceptor and donor properties, suggesting the formation of defect-induced p-type and n-type BC_2N.
(一)由简立方C_20结构出发,通过取代设计了两种材料,C_3N_2和B_2C_3。研究结果表明,C_3N_2有α-C_3N_2和β-C_3N_2两个相,α-C_3N_2存在压力范围为0-1.2GPa,β-C_3N_2为C_3N_2的高压相。通过第一性原理硬度计算知道其韦氏硬度均约为86GPa,介于c-BN(68GPa)和金刚石(98GPa)之间;B_2C_3具有金属性质,在3K时可以转变为超导体相。
(二)研究了立方氮化硼中几种杂质在压力下的行为。(1)压力下立方氮化硼本征空位的研究。发现在富氮条件下硼空位的形成焓随压力的增加而减小,根据平衡杂质浓度公式,可以知道随压力的增加,硼空位的平衡浓度在增大;在富硼条件下,氮空位的形成焓随压力的增加而增加,其平衡浓度随压力的增加而减小。(2)立方氮化硼中碳取代硼或取代氮杂质行为的研究。结果表明在60GPa范围内碳取代硼的形成焓随压力的增加而减小,说明在压力下其更加稳定存在,平衡浓度也在增加;而碳取代氮的形成焓随压力的增加而增加,说明在压力下其变得不大稳定了且其平衡浓度变小。(3)立方氮化硼中氮或氧取代硼的研究。结果表明这两种取代杂质的形成焓都随压力的增加而减小,即在压力下其变的更加稳定,平衡浓度更大些。
(三)研究了立方BC_2N中本征杂质的行为。研究结果显示,在BC_2N体材料中,空位的形成能都比较高,则空位不能稳定存在于材料中。而取代杂质( BC II、N CI、C N)的形成能都比较低,甚至为负值,表明这几类替代杂质容易形成且能稳定存在于BC_2N材料中,其浓度比较高。
Diamond is the most well-known superhard material and searching for much more hard materials is always in pursuit of the goal of experimental and theoretical workers. It is reported that covalent solids composed of boron, carbon and nitrogen are excellent candidates for extraordinary hardness. Prediction and development of the novel superhard materials also benefit from the first-principles method. One chief goal of this thesis is to find novel superhard functional materials.
A real semiconductor invariably has either some defects due to heat treatment or impurities during the crystal growth process. The electronic quality of a semiconductor is largely determined by the nature and number of its native defects and impurities. Defects in semiconductors not only influence the electrical and optical properties of these materials, but also exhibit their own interesting physics. The identification and control of defects such as vacancies, interstitials, and impurities is a major field of research, with important applications in materials engineering. Density-functional theory (DFT) calculation based on pseudopotentials, a plane-wave basis set, and a supercell geometry is now regarded as a standard first-principles method for the studies of defects in semiconductors. To reveal the natural properties of impurities in these typical B-C-N systems is another important aim of this thesis.
In this work, we suggest two hypothetical structures with C_3N_2 and B_2C_3 stoichiometry, by replacing of the carbon atoms with nitrogen or boron in the crystalline phase of simple cubic carbon (C_20), and have presented a completely theoretical analysis of the structural, elastic and electronic properties ofα-C_3N_2 andβ-C_3N_2 using first-principles method. We carry out density functional calculations on the self-vacancies, substitutional carbon and boron-related defects in c-BN and native defects in c-BC_2N using the strict convergence criteria and a large simulation cell. The defect formation enthalpy is a key quantity describing the behavior of defects and is calculated from the total energies of perfect and defected supercell. To check the stability of defects created under pressure, we calculate the formation enthalpies as a function of hydrostatic pressure. The main contents are as follows:
I. Recently, theoretical prediction and experimental synthesis of superhard materials are focuses of research. We suggest two new compoundsα-C_3N_2 andβ-C_3N_2 with cubic symmetry, which are derived from a simple cubic carbon (C_20) reported recently. Our first-principles calculations show that both the solids are highly incompressible with high bulk modulus (380 and 343 GPa), large shear modulus G (365 and 368 GPa), great elastic constant C44 (327 and 329 GPa), and high Vickers hardness Hv (both are 86 GPa), respectively. Accordingly we come to a conclusion that both the C_3N_2 phases are potentially superhard semiconductor materials. From the electronic partial density of state, it is found that the superhard character of the two phases is mainly attributed to the strong covalent bond between C and N. Theα-C_3N_2 is dynamically stable at pressures below 1.2 GPa, but unstable above 1.2 GPa because an optical branch softens to zero at theΓpoint. Theα-C_3N_2 will transform intoβ-C_3N_2 at about 1.2GPa which is energetically more stable. Both phonon dispersion and elastic constant calculations at zero and high pressures show that thisβ-C_3N_2 remains mechanically and dynamically stable in a pressure range from 0 GPa to at least 20 GPa. Based on ab initio phonons and electron-phonon coupling constants, we estimate the transition temperatures for B_2C_3 Tc cal≈3 K.
II. We investigate, through first-principles calculations, the pressure dependence on the formation enthalpy and electronic level positions of defects and impurities in c-BN. There are a lot of experimental and theoretical work about the doped c-BN, but up to now, a complete quantitative description of the formation enthalpy and energy-level positions of defects in different charge states under pressures is still lacking. In this part the effects of pressure on the self-vacancies、substitutional carbon and boron-related defects in c-BN have been extensively studied. Finding: a) The formation enthalpy of VB decreases with pressure and the equilibrium concentration of VB increases with pressure under nitrogen-rich condition; the formation enthalpy of VN increases with pressure and the equilibrium concentration of VN decreases with pressure under boron-rich condition. Bothe boron and nitrogen vacancies induce localized narrow“vacancy bands”in the energy gap region of c-BN. The partial defect energy levels of VN move up with an increase in pressure and intersect with the conduction band, showing pressure strengthens its conductivity, while for VB the position of defect energy levels remains almost unchanged relative to the valence-band edge, indicating a pressure effect that is not obvious. b) We have observed that the dependence of the formation enthalpy of CB on pressure is much stronger than that of CN on pressure. The formation enthalpy decreases with pressure for CB, which suggests that CB becomes much more stable and has a larger concentration with pressure increase. In contrast to CB, the formation enthalpy of CN impurities exhibits positive dependence on pressure, so the concentration of CN reduces with pressure. We think that the opposite trend for the formation enthalpies of CB and CN with pressure mainly originate in the enthalpies of the defect-contained supercell under different pressure. It is also observed that pressure may weaken its conductivity in the case of CN and CB in c-BN. Theses results are useful for making a boron nitride pn junction diode and an ultraviolet light-emitting diode under high pressure. c) We find that the nitrogen atoms surrounding the defect relax inward in the case of CB, while the nitrogen atoms relax outward in other cases. The formation volume of all boron-related impurities decrease with pressure, which means that the formation enthalpies decrease with pressure and the equilibrium concentration of boron-related impurities increase with pressure. Those results are in close agreement with the direct defect formation enthalpy calculations. The impurity CB+1 is found to have the lowest formation enthalpy and exhibit semiconductor and have higher bulk modulus than ideal c-BN, and suggest that the hardness of c-BN may be strengthen when a carbon atom substitute at a B site.
III. First-principles pseudopotential calculations have been performed to investigate intrinsic defects including vacancies and antisite defects in BC_2N crystals. All self-vacancies, namely, B-vacancy (VB), C-vacancies (VCI and VCII) and N-vacancy (VN), have high formation energies and are hence unstable. In contrast, carbon at boron and nitrogen sites (CB and CN) exhibit p-type and n-type properties, respectively, as well as low formation energies. The antisite defect BN does not change the semiconducting character of the BC_2N according to the band structures. The BCII and NCI in BC_2N have the lowest formation energies and are energetically favorable to form under B-rich and N-rich growth conditions, respectively. They also exhibit acceptor and donor properties, suggesting the formation of defect-induced p-type and n-type BC_2N.
引文
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