The theoretical direct-band-gap optical gain of Germanium nanowires

Abstract

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 radius 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 19 cm −3 when the doping concentration is zero, and a remarkable optical gain can be obtained when the injected carrier density is close to 1×10 20 cm −3 , 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.

The optical gain variation of Ge nanowires induced by L-valley splitting under the [110] direction stress

“…We adopt the same method as in Ref. 25 to calculate the electron energy levels at each L-valley under U 110 , and the convergence of the electron levels at the L-valley is guaranteed, which is also consistent with the results calculated by the sp 3 d 5 s * tight-binding model in Ref. 27.…”

“…Obviously, the shape of each electron state at the L 1 -valleys and L 2 -valleys in two figures is almost parabolic, and the reason has been analyzed in Ref. 25. According to Eq.…”

“…18. For the indirect [111] L-valley, we can write the effectivemass Hamiltonian of Ge nanowires grown along the [001] direction under the [110] direction stress U 110 as follows 25)  9) is the strained Hamiltonian introduced by the [110] direction stress, which can be expressed as 26) H I a a : 1 0…”

Synergistic Effects of B-F/B-S and Nitrogen Vacancy Co-Doping on g-C3N4 and Photocatalytic CO2 Reduction Mechanisms: A DFT Study

“…In contrast, B-F-N v is a direct bandgap structure with a value of 2.67 eV calculated by the HSE06 method, smaller than g-C 3 N 4 , as both VBM and CBM are located at point Gamma. The direct transition of electrons reduces the energy loss caused by electron relaxation, which means a higher energy conversion efficiency [ 52 , 53 , 54 ]. The loss of nitrogen atoms caused by vacancies destroys the π-conjugation of g-C 3 N 4 , leading to the reconstruction of the band structure and the formation of impurity states in the middle of the forbidden band.…”

Absorption spectra and exciton g factor of InAs1−x N x nanowires in a magnetic field

“…14. As we all know, for calculating the electronic structures of lowdimensional semiconductor structures, the effective-mass theory has been widely employed and verified by comparison with other methods such as sp 3 d 5 s * tight-binding model, [20][21][22] which indicates that the adopted method in the paper is reasonable.…”