We have discussed that indirect band gap materials have a lower absorption coefficient than direct band gap materials, due to the fact that the charge carriers need a change in energy AND momentum in order to be excited. If both Si and Ge are indirect band gap materials, why does Ge have a much higher absorption coefficient than Si in the visible wavelength range?
To understand why germanium (Ge) has a higher absorption coefficient than silicon (Si) in the visible wavelength range, even though both are indirect band gap materials, we need to consider a few factors.
First, it is important to note that while both Si and Ge are considered indirect band gap materials, they still have some differences in their electronic band structures. The energy difference (band gap) between the valence band and the conduction band plays a crucial role in determining the absorption properties of a material.
In the case of Si and Ge, Ge has a smaller band gap compared to Si. Ge has a band gap of around 0.67 eV, while Si has a slightly larger band gap of about 1.1 eV. The smaller band gap of Ge means that it requires less energy to excite electrons from the valence band to the conduction band.
Secondly, the absorption coefficient is influenced by the density of available electronic states in the vicinity of the band edges. In indirect band gap materials, charge carriers require both a change in energy and momentum to be excited. This means that the absorption coefficient is lower compared to direct band gap materials where only a change in energy is needed. However, the density of states near the band edges can still have an impact on the absorption properties.
Ge has a higher density of states near the band edges compared to Si. This higher density of states increases the likelihood of absorption of photons falling within the visible wavelength range. Consequently, Ge exhibits a higher absorption coefficient in the visible wavelength range compared to Si, despite both being indirect band gap materials.
In summary, Ge has a higher absorption coefficient than Si in the visible wavelength range due to its smaller band gap and higher density of states near the band edges. These factors make it more likely for Ge to absorb photons in the visible spectrum, even though both materials are indirect band gap semiconductors.