Xiong Wen, Wang Jian-Wei, Fan Wei-Jun, Song Zhi-Gang, Tan Chuan-Seng
Nanyang Technological University, School of EEE, 50 Nanyang Avenue, Singapore, 639798, Singapore.
Chongqing University, School of Physics, No. 55 South Road, University Town, Chongqing, 401331, People's Republic of China.
Sci Rep. 2020 Jan 8;10(1):32. doi: 10.1038/s41598-019-56765-5.
We calculate the electronic structures of Germanium nanowires by taking the effective-mass theory. The electron and hole states at the Γ-valley are studied via the eight-band k.p theory. For the [111] L-valley, we expand the envelope wave function using Bessel functions to calculate the energies of the electron states for the first time. The results show that the energy dispersion curves of electron states at the L-valley are almost parabolic irrespective of the diameters of Germanium nanowires. Based on the electronic structures, the density of states of Germanium nanowires are also obtained, and we find that the conduction band density of states mostly come from the electron states at the L-valley because of the eight equivalent degenerate L points in Germanium. Furthermore, the optical gain spectra of Germanium nanowires are investigated. The calculations show that there are no optical gain along z direction even though the injected carrier density is 4 × 10 cm when the doping concentration is zero, and a remarkable optical gain can be obtained when the injected carrier density is close to 1 × 10 cm, since a large amount of electrons will prefer to occupy the low-energy L-valley. In this case, the negative optical gain will be encountered considering free-carrier absorption loss as the increase of the diameter. We also investigate the optical gain along z direction as functions of the doping concentration and injected carrier density for the doped Germanium nanowires. When taking into account free-carrier absorption loss, the calculated results show that a positive net peak gain is most likely to occur in the heavily doped nanowires with smaller diameters. Our theoretical studies are valuable in providing a guidance for the applications of Germanium nanowires in the field of microelectronics and optoelectronics.
我们采用有效质量理论计算锗纳米线的电子结构。通过八能带k.p理论研究了Γ谷处的电子和空穴态。对于[111] L谷，我们首次使用贝塞尔函数展开包络波函数来计算电子态的能量。结果表明，L谷处电子态的能量色散曲线几乎是抛物线形的，与锗纳米线的直径无关。基于电子结构，我们还得到了锗纳米线的态密度，并且发现由于锗中有八个等效简并的L点，导带态密度主要来自L谷处的电子态。此外，我们研究了锗纳米线的光学增益谱。计算表明，当掺杂浓度为零时，即使注入载流子密度为4×10 cm，沿z方向也没有光学增益，而当注入载流子密度接近1×10 cm时，可以获得显著的光学增益，因为大量电子将倾向于占据低能量的L谷。在这种情况下，考虑到自由载流子吸收损耗随直径增加，会遇到负光学增益。我们还研究了掺杂锗纳米线沿z方向的光学增益随掺杂浓度和注入载流子密度的变化。考虑自由载流子吸收损耗时，计算结果表明，在直径较小的重掺杂纳米线中最有可能出现正的净峰值增益。我们的理论研究对于指导锗纳米线在微电子和光电子领域的应用具有重要价值。
