I am new to this field and after going through some tutorials I was making band structure diagram of Silicon as shown in figure below, and the Fermi energy I got from SCF calculation is 6.208 eV. However in academic articles the Fermi energy in band structure lies at 0 on y-axis, same was said by my professor but how does that make sense if Fermi energy is 6.208 eV then, how it will be at 0 on y axis?
In electronic structure calculations of finite systems, there is a well-defined energy scale: 0 is the vacuum energy, and any electron with positive energy is unbound.
For materials, the story is different. There is no fixed vacuum level (it's obtainable from the work function for your material, but it differs depending on your system). If you were to calculate the band structure with different density functional approximations (LDA, PBE, HSE06, ...), different pseudopotentials, and so on, you'd get a different answer for the Fermi energy each time.
So for consistency across calculations (and, maybe even more so, across papers), it's traditional to offset the energy axis by some constant so that the Fermi energy, or the conduction band minimum, or whatever, is zero. That shift doesn't matter for energy differences, and there is no privileged absolute scale, so there isn't really a problem with doing so. In particular, for comparing (say) silicon band structure across calculation methods, it's nice to have one energy level that's the same across all the methods, so that you can see what's stretched, squeezed, and shifted by comparison.