The band gap of composite material cannot be calculated directly from the band gaps of its constituent materials. The reason is that the band gap of a composite material depends not only on the properties of its constituents but also on how these constituents are arranged, including their size, morphology, interfaces, and spatial distributions.
However, there are experimental and computational methods to determine the band gap of composite material:
Experimentally: The most common method to measure a material's band gap is absorption or reflectance spectroscopy. You can determine the band gap energy by shining light of various energies on the material and measuring how much light is absorbed or reflected. When the energy of the light matches the band gap, the light will be absorbed, and electrons will be excited from the valence band to the conduction band. A plot of absorption or reflectance versus energy (or wavelength) will show a step increase in the band gap energy, which can be used to determine its value.
Computational Modelling: For theoretically predicting the band gap of composite materials, computational methods based on quantum mechanics, such as Density Functional Theory (DFT) or time-dependent DFT (TDDFT), are often used. These methods require substantial computational resources and expertise in computational physics or materials science. They can account for the material's detailed atomic structure and interactions, and provide a prediction of the band gap. But it should be noted that standard DFT often underestimates the band gap, and a more accurate method may need to be used.
Effective Medium Approximations: In some specific cases where the size of the constituents is much smaller than the wavelength of light, and the constituents are randomly distributed, one might be able to estimate the effective band gap using models like the Maxwell Garnett or the Bruggeman effective medium approximations. However, these models have their own limitations and may not give accurate predictions in many cases.
It is essential to note that these are complex procedures requiring careful implementation and interpretation.