纤锌矿半导体电子能带结构和光学性质：第一性原理研究
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摘要
本文针对以氮化铟和石墨烯为代表的纤锌矿半导体在电子能带结构,及其光学性质,以及它们的掺杂结构所体现出来的特殊的物理性质,进行了系统地研究。首先,我们利用了第一性原理基于密度泛函理论研究了氮化铟的声子色散谱线和其在剩余射线区域内的光学性质,给出了其光学特性参数与横纵光学支频率之间的变化关系。其次,我们基于密度泛函理论,采用GGA+U(p+d)的近似方法,修正了第一性原理计算氮化铟带隙的不足,给出了与实验相符的结果,并且修正了电子能带结构,进一步的研究了In1-xGaxN的能带结构,以及掺杂原子对能带结构的影响和每个原子轨道对能带结构的贡献。最后,利用第一性原理研究了本征手扶椅式石墨烯纳米带的能带结构,以及氢修饰和锂掺杂后的能带结构和掺杂原子对费米能级附近能带的影响。
计算结果表明,氮化铟具有半金属的性质,因此,容易产生电子跃迁,更加适合应用于光学器件的制造。计算结果也表明在ωTO<ω<ωLO区域内,反射谱可以达到最大值,且接近于1。消光系数谱中,在ω=ωTO处,产生了一个尖锐的峰值。这些光学性质的产生都说明了,在ωTO<ω<ωLO区域内,能量反射和损失是非常明显的,在该区域内发生了电场与晶格振动之间的相互作用,声子的产生和消失对电磁波能量变化产生了重要的影响。
其次,利用GGA+U(p+d)的近似方法,修正了能带结构,得到氮化铟带隙值0.78eV与实验值一致,并且修正了能带结构。当镓掺杂氮化铟后,随着掺杂组分的增加,带隙发生了蓝移,即反斯托克斯移动。通过分波态密度分析可以看出,当掺杂镓原子后,p-d轨道之间的排斥作用减弱,Ga-4s, Ga-4p的态密度贡献均向导带移动,并且与In-5s,5p发生了强烈的杂化效应,促使带隙升高,发生了反斯托克斯移动。
最后,通过计算本征手扶椅式石墨烯纳米带的能带结构,分析表明它是间接带隙半导体,并且能带结构主要是由C-2p轨道的电子贡献的。进一步研究其氢修饰和锂掺杂不同位置的结构,结果表明氢修饰石墨烯纳米带为直接带隙半导体,带隙为1.68eV,手扶椅式石墨烯纳米带经过掺杂调制后具有了金属的性质。而且,单边掺杂具有最低的形成能,即结构稳定,因此可以预测该位置最适合掺杂。从分波态密度结果中可以清楚地了解到,锂掺杂后,Li-2s,2p轨道的电子在费米能级附近的贡献明显,并与C-2p电子发生了强烈的杂化作用,导致了手扶椅式石墨烯纳米带具有了金属性质。
For electronic energy band structure and optical properties of the wurtzite InN and graphene are studied. And unique physical properties for doped InN and graphene are investigated detaily. Firstly, the phonon spectra and optical properties of wurtzite InN in the reststrahlen region are studied by the first-principle calculations based on the density functional theory. Secondly, the band gap of wurtzite InN is corrected using GGA+U in density functional theory. Furthermore, the electronic band structures, density of states (DOS) and projected density of states (PDOS) of the wurtzite In1-xGaxN are studied. The calculations of phonon spectra are based on the Generalized-Gradient Approximation (GGA). Finally, the charge density, electronic energy band and density of states of bare, H terminated and Li doped armchair graphene nanoribbons (AGNRs) are investigated using the local density approximation based on density function theory.
The calculation indicates that InN has metal-like behavior. Also, Our calculation shows the reflectivity R at ω close to ωLO is nearly zero and R-1at ωTO<ω<ωLO.In the dispersion curves, there are a strong absorption peak of k(ω) at the resonance frequency ω=ωTO.These results show the fundamental vibration has dipole moment and is therefore infrared active in wurtzite structure semiconductors.
Secondly, our calculations suggest that in the case of wurtzite InN it is important to apply GGA+U(p+d) in order to recover the correct bang gap and obtain a reliable description of InN band structure. The methodology is applied to study the electronic properties of the wurtzite In1-xGaxN. The increases in the band-gap and valence band width show that an anti-Stokes shift occurs with the band-gap variations due to the composition fluctuations. It was confirmed that the increases of the band gap and the valence-band width stem from the repulsion of p-d electrons and strong hybridizations during of the Ga-4,s, In-5s and Ga-4p, In-5p electrons.
Finally, the bare AGNRs are an indirect band gap semiconductor. And the upper valence-band and conduction band are mainly dominated by C-2p states for the bare AGNRs. The H terminated AGNRs is direct band gap semiconductor with band gap1.68eV. The Fermi level crosses the conduction band and the ribbon becomes metallic for Li doped AGNRs. The one-edge Li-doped AGNRs have the lowest formation energy for other different doping configurations. So we can predict that one-edge Li-doped AGNRs is an energetically favorable practice for different doping configurations. The project density of states is calculated and reveals that the localization and hybridization between C-2p and Li-2p electronic states are much stronger in the conduction band group.
计算结果表明,氮化铟具有半金属的性质,因此,容易产生电子跃迁,更加适合应用于光学器件的制造。计算结果也表明在ωTO<ω<ωLO区域内,反射谱可以达到最大值,且接近于1。消光系数谱中,在ω=ωTO处,产生了一个尖锐的峰值。这些光学性质的产生都说明了,在ωTO<ω<ωLO区域内,能量反射和损失是非常明显的,在该区域内发生了电场与晶格振动之间的相互作用,声子的产生和消失对电磁波能量变化产生了重要的影响。
其次,利用GGA+U(p+d)的近似方法,修正了能带结构,得到氮化铟带隙值0.78eV与实验值一致,并且修正了能带结构。当镓掺杂氮化铟后,随着掺杂组分的增加,带隙发生了蓝移,即反斯托克斯移动。通过分波态密度分析可以看出,当掺杂镓原子后,p-d轨道之间的排斥作用减弱,Ga-4s, Ga-4p的态密度贡献均向导带移动,并且与In-5s,5p发生了强烈的杂化效应,促使带隙升高,发生了反斯托克斯移动。
最后,通过计算本征手扶椅式石墨烯纳米带的能带结构,分析表明它是间接带隙半导体,并且能带结构主要是由C-2p轨道的电子贡献的。进一步研究其氢修饰和锂掺杂不同位置的结构,结果表明氢修饰石墨烯纳米带为直接带隙半导体,带隙为1.68eV,手扶椅式石墨烯纳米带经过掺杂调制后具有了金属的性质。而且,单边掺杂具有最低的形成能,即结构稳定,因此可以预测该位置最适合掺杂。从分波态密度结果中可以清楚地了解到,锂掺杂后,Li-2s,2p轨道的电子在费米能级附近的贡献明显,并与C-2p电子发生了强烈的杂化作用,导致了手扶椅式石墨烯纳米带具有了金属性质。
For electronic energy band structure and optical properties of the wurtzite InN and graphene are studied. And unique physical properties for doped InN and graphene are investigated detaily. Firstly, the phonon spectra and optical properties of wurtzite InN in the reststrahlen region are studied by the first-principle calculations based on the density functional theory. Secondly, the band gap of wurtzite InN is corrected using GGA+U in density functional theory. Furthermore, the electronic band structures, density of states (DOS) and projected density of states (PDOS) of the wurtzite In1-xGaxN are studied. The calculations of phonon spectra are based on the Generalized-Gradient Approximation (GGA). Finally, the charge density, electronic energy band and density of states of bare, H terminated and Li doped armchair graphene nanoribbons (AGNRs) are investigated using the local density approximation based on density function theory.
The calculation indicates that InN has metal-like behavior. Also, Our calculation shows the reflectivity R at ω close to ωLO is nearly zero and R-1at ωTO<ω<ωLO.In the dispersion curves, there are a strong absorption peak of k(ω) at the resonance frequency ω=ωTO.These results show the fundamental vibration has dipole moment and is therefore infrared active in wurtzite structure semiconductors.
Secondly, our calculations suggest that in the case of wurtzite InN it is important to apply GGA+U(p+d) in order to recover the correct bang gap and obtain a reliable description of InN band structure. The methodology is applied to study the electronic properties of the wurtzite In1-xGaxN. The increases in the band-gap and valence band width show that an anti-Stokes shift occurs with the band-gap variations due to the composition fluctuations. It was confirmed that the increases of the band gap and the valence-band width stem from the repulsion of p-d electrons and strong hybridizations during of the Ga-4,s, In-5s and Ga-4p, In-5p electrons.
Finally, the bare AGNRs are an indirect band gap semiconductor. And the upper valence-band and conduction band are mainly dominated by C-2p states for the bare AGNRs. The H terminated AGNRs is direct band gap semiconductor with band gap1.68eV. The Fermi level crosses the conduction band and the ribbon becomes metallic for Li doped AGNRs. The one-edge Li-doped AGNRs have the lowest formation energy for other different doping configurations. So we can predict that one-edge Li-doped AGNRs is an energetically favorable practice for different doping configurations. The project density of states is calculated and reveals that the localization and hybridization between C-2p and Li-2p electronic states are much stronger in the conduction band group.
引文
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