Germanium ($\mathrm{Ge}$) has the potential to be incorporated into the next generation of electronic and optoelectronic devices due to its quasidirect band gap and high carrier mobility. With $\mathrm{Ge}$ as the primary semiconductor, it is essential to engineer the energy-band structure and optical properties. To understand alterations in the band structure and variations in optical response, three distinct conditions were investigated via spectroscopic ellipsometry: defect density, buffer-layer thickness, and substrate orientation and offcut angles. As the threading-dislocation density in $\mathrm{Ge}$ is increased from $5\times {10}^3{\mathrm{cm}}^{-2}$ to ${10}^{10}{\mathrm{cm}}^{-2}$, a characteristic redshift in the indirect and direct band gaps and optical critical points (CPs; $E_0$, $E_0+{\mathrm{\Delta }}_0$, $E_1$, and $E_1+{\mathrm{\Delta }}_1$) was observed, along with a significant increase in the absorption onset. In the case of lattice-matched epitaxial $\mathrm{Ge}$ on an $\mathrm{Al}\mathrm{As}$ buffer, the band gaps are redshifted with increasing $\mathrm{Al}\mathrm{As}$ thickness, which is attributed to surface local fields. A similar trend is observed in the direct-band-gap CPs ($E_0$ and $E_0+{\mathrm{\Delta }}_0$), while the high-energy CPs ($E_1$ and $E_1+{\mathrm{\Delta }}_1$) remain unchanged. Deviating from this trend, the $\mathrm{Ge}$ sample grown on a $\mathrm{Ga}\mathrm{As}$ ($100/6^{\circ }$ offcut) substrate exhibits a redshift in its $E_0$ and $E_0+{\mathrm{\Delta }}_0$ CPs, which is attributed to superior growth quality due to the $6^{\circ }$ offcut substrate. In this case, it is observed that the $\mathrm{Ge}$ on $\mathrm{Ga}\mathrm{As}$ ($100/6^{\circ }$ offcut) has the highest direct-band-gap CPs ($E_0$ and $E_0+{\mathrm{\Delta }}_0$) and $\mathrm{Ge}$ on $\mathrm{Ga}\mathrm{As}$ ($100/2^{\circ }$ offcut) has the lowest. In contrast, the $\mathrm{Ge}$ on $\mathrm{Ga}\mathrm{As}$ (110), with the highest unintentional doping of approximately ${10}^{19}$, exhibits a high absorption onset, potentially compensating for the Burstein-Moss (BM) effect due to band-gap narrowing (BGN); however, the $\mathrm{Ge}$ sample grown on a $\mathrm{Ga}\mathrm{As}$ ($100/2^{\circ }$ offcut) substrate exhibits a blueshift in its indirect band gap, which can be attributed to the BM effect overpowering the BGN effect. A significant redshift in the $E_0$ and $E_0+{\mathrm{\Delta }}_0$ CPs is observed with changes in substrate orientation, while the $E_1$ and $E_1+{\mathrm{\Delta }}_1$ CPs remain the same. Thus, our findings indicate that the optical response in the epitaxial $\mathrm{Ge}$ layer is sensitive to defects, the $\mathrm{Al}\mathrm{As}$ buffer-layer thickness, and substrate orientation.

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• Band gap
• Defects
• Dielectric properties
• Epitaxial strain
• Optoelectronics
• Elemental semiconductors
• Ellipsometry
• Materials modeling