I want to correlate band gap values got from two technique
1) Tauc plot which will give overall band gap
2) Scanning tunneling spectra (STS) or Scanning tunneling microscopy
There is difference between these two. Generally ( to my understanding) the Tauc plot give you the optical band gap. This means the min energy needed of a photon to be absorbed by the semiconductor. Here the exciton ( Electron -hole pair is bound). But in the case of electronic energy gap, the electron-hole pair is not bound and that is measured by the difference between the lowest unoccupied CB level highest occupied VB level. Normally optical band gap is less that the electronic band gap.
While surface electronic gap is mentioned in the literature referring to the top monolayers of the material. For example, in the case of chalogenides, the surface electronic gap of MoS2 and bulk band gap of MoS2 has completely different meaning. The electronic transitions are completely different.
so in your case, comparing the band gap ( for me it is bulk optical energy gap) with the surface electronic gap may not be correct.
In a perfectly periodic crystal, electrons propagate, and are modelled as Bloch waves.
Surface is a sharp transition from the solid to the vacuum, a discontinuity. This discontinuity, and the corresponding weakening potential, leads to the so called surface states, which are evanescent in nature.
This is the reason of the change of the electronic band structure in the few atomic layers close to the surface. Of course, this may affect the band gap of the material under study.
For more details you may refer to a solid state physic textbook, the Kittel Introduction to Solid State Physics for instance.
Let me add a comment on STS: In a band gap measurement using STS you can't directly distinguish between bulk- and surface band gaps.
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