1- n-type semiconductor has an absorption spectra
2-Dye has an absorption spectra
3- Semiconductor+ Dye has an absorption spectra
4- Can I calculate the band gap of of SC, Dye and SC+Dye using Tauc equation
The bands of a semiconductor represent extended electronic states, and the band gap represents the energy gap between filled (conduction) and empty states. doping in the crystal lattice introduces localised defect states, which change the extended electronic wavefunction, and effectively reduces the band gap. These states also affect the absorption spectrum. Adding dye molecules does not have the same effect, unless the electronic wavefunctions interact in some way. Otherwise, the optical absorption, is simply the sum of the absorption spectrum of the two, and does not represent any interaction.
You can calculate the band gap energy of each element and make the energy band diagram of your semiconductor and dye for better understanding. The addition of dye will not change the band gap of semiconductor. However, dye (which has narrower band gap) is very useful to help exciting the electron from VB to CB due to its low band gap energy.
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