Excitonic effects in the optical absorption of gapless semiconductor α-tin near the direct bandgap

Stefan Zollner
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Abstract

Most cubic semiconductors have threefold degenerate p-bonding valence bands and nondegenerate s-antibonding conduction bands. This allows strong interband transitions from the valence to the conduction bands. On the other hand, intervalence band transitions within p-bonding orbitals in conventional p-type semiconductors are forbidden at k=0 and, therefore, weak, but observable. In gapless semiconductors, however, the s-antibonding band moves down between the split-off hole band and the valence band maximum due to the Darwin shift. This band arrangement makes them three-dimensional topological insulators. It also allows strong interband transitions from the s-antibonding valence band to the p-bonding bands, which have been observed in α-tin with Fourier-transform infrared spectroscopic ellipsometry [Carrasco et al., Appl. Phys. Lett. 113, 232104 (2018)]. This manuscript presents a theoretical description of such transitions applicable to many gapless semiconductors. This model is based on k→⋅p→ theory, degenerate carrier statistics, the excitonic Sommerfeld enhancement, and screening of the transitions by many-body effects. The impact of nonparabolic bands is approximated within Kane’s 8×8k→⋅p→-model by adjustments of the effective masses. This achieves agreement with experiments.
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直接带隙附近无隙半导体 α-锡光学吸收中的激子效应
大多数立方半导体都有三重退化的 p 键价带和非退化的 s 反键导带。这使得从价带到导带的带间跃迁很强。另一方面,在传统的 p 型半导体中,p 键轨道内的带间转换在 k=0 时是被禁止的,因此转换很弱,但可以观察到。然而,在无间隙半导体中,由于达尔文偏移,s-反键带在空穴带和价带最大值之间向下移动。这种带排列使它们成为三维拓扑绝缘体。它还允许从 s 反键价带到 p 键带的强烈带间跃迁,傅立叶变换红外光谱椭偏仪已在α-锡中观察到这种跃迁[Carrasco 等人,Appl. Phys. Lett.本手稿介绍了适用于许多无间隙半导体的此类跃迁的理论描述。该模型基于 k⋅p→ 理论、变性载流子统计、激子索默费尔德增强以及多体效应对跃迁的屏蔽。在凯恩的 8×8k→⋅p→ 模型中,通过调整有效质量来近似考虑非抛物带的影响。这实现了与实验的一致。
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