A good start would be to use UPS (Ultraviolet Photoelectron Spectroscopy) which can give you information about the valence electrons and molecular orbitals, particularly the work-function of a sample.

Can we use "current voltage and capacitance voltage measurements" for "electronic band gap" calculation?  

IV data from scanning tunneling microscope results electronic band gap but you can't calculate band gap from simple IV or CV data.

Agree with S.Yadav. Get a dI/dV spectra using lock-in measurements in STM.

Since you are talking specifically of an electronic band gap, I will not go into further details about measuring the optical band gap via UV-Vis spectroscopy.

However, I think you can do cyclic voltammetry of a thin film with a special AFM tip and setup.

Dear Mr. J. Vollbrecht can you please elaborated the theory for this....

The basic idea is the following:

While measuring a cyclic voltammogram, you have a three-electrode setup. But instead of having the typical CV measurement setup in solution, you have the thin film you want to characterize with a certain thickness on top of a conducting material (i.e. a smooth and conductive metal, or ITO). This substrate is one of your electrodes.

The second electrode is a modified tip of your AFM, it should also constist of a conducting material. The third electrode is the reference electrode.

The substrate, thin film, AFM tip and reference electrode are submersed in a conductive solution that should not be able to dissolve your thin film.

This is an unusual setup and I only saw it once. Unfortunately I do not have any papers at hand that could further illustrate this type of measurements.

Two methods can be:

photoluminescence spectra and spectral photoconductivity measurements.

Dear Dr. Trucchi I am grateful to you If you suggest me some research paper related to this method ...  

Dear Ravi,

sorry for the late reply, but I have been engaged during the last days.

Both the techniques are described in text-books for materials science characterization (i.e. UV-VIS and Photoluminescence Spectroscopy for Nanomaterials Characterization from Springer, etc.)

The difference among the two techniques is that the first is not invasive since you measure the photoluminescence induced by an over-bandgap radiation and impinging on your semiconducting material. The optical signal of luminescence will pass through a monochromator and measured by a callibrated detector. This will form a spectrum and it will give you information not only on bandgap, but also on density of defect states (if any).

The second one needs electric contacts on your material (usually planar, but in some cases also sandwich) to bias the semiconductor and measure the photocurrent. By changing the wavelength of the impinging radiation (thus it needs a monochromator for making the radiation monochromatic), you will be able to construct the photocurrent spectrum. It gives you information about bandgap and joint density of defect states.

As an example, please see the paper "Thin polycrystalline diamond for low-energy x-ray detection, J. Appl. Phys. 96 (2004) 6415" or "Temporal response of CVD diamond detectors to modulated low energy X-ray beams, phys. stat. sol. (a), 1– 4 (2004) / DOI 10.1002/pssa.200303915". In any case, you will find many examples in lthe literature by only typing the keywords "photoluminescence or photocunductivity spectra".

If you can get the C-V measurement data of a PN junction,you will obtain the dopant concentration of the lower doped region(Nd) and built-in voltage(phi0) of the PN junction.If you have hnown the dopant concentration of the heavier doped region(Na) of the PN junction when you make it,then you can easily get the intrinsic carrier concentration value of the materials you used to make the diode.From the data of  intrinsic carrier concentration,you may calculate the value of electronic energy band gap.I hope it will be helpful to you.

Use photoluminescence and/or photoconductivity spectra at variable monochromatic wavelengths.

In the first method, you use a overbandgap radiation (e.g. laser) on your semiconductor and measure the spectral distribution of the photoluminescence signal caused by the radiative recombination.

In the second you need to fabricate electric contacts (planar or sandwich configuration, it depends on your geometry). You make a monochromatic radiation impinge on the semiconducture and measure the photogenerated current (pre-amplified + lock-in amplifier are suggested for high-sensitivity measurements). You make the radiation wavelength vary and build a photocurrent spectrum. Divide the photocurrent by the lamp power spectrum and obtain responsivity. Multiply it by photon energy and you obtain quantum efficiency. From quantum efficiency it is simple to derive the electronic bandgap. Limitation of this method is if the film is very thin, since the generated signal depends on the active interaction volume.

Where to find additional informations: the techniques are widely discussed in university books and several scientific papers.

Here you can find good explanation and band gap calculator,

http://www.instanano.com/characterization/theoretical/uv-vis-spectroscopy-band-gap-calculation/