# How to find the band gap for a compound?

I have processed a si/polymer hybrid using a silane coupling agent which I need to determine the energy gap / band gap. Would you please let me know the procedure to go about determining the band gap?

• The energy gap being asked about the band gap between the valence band and the conductance band of the material. It is roughly analogous to the HOMO-LUMO energy gap of small molecules. I am also slightly confused about the fabrication process, but the methods of determining these energy gaps are generally independent of the material and how it was made. Jul 17 '12 at 11:08
• People might be more familiar with the term "band gap" than they are with the term "energy gap," so I suggested an edit to that effect. Jul 17 '12 at 13:09
• "Band" is appropriate in case of bands, i e. for metals and semiconductors or insulators in general crystalline solids. user 423 has done some si/polymer thing, nobody knows what that is, not even whether the answer below is wisedom or speculation. I had asked here for more information from user423, but somebody erased my comment. Manisherth? Jul 17 '12 at 14:53
• Georg, polymers are usually considered to have "bands" also. In a conducting polymer, by the time you get to a degree of polymerization of 10 or more, the pi orbitals become so close in energy so as to begin to behave like bands in semiconductors. I agree that user433 could be clearer about what the material in question is, but that doesn't change the methodology used to determine a band (or HOMO-LUMO) gap, which is what the question asks. Jul 17 '12 at 20:05
• There is no information on the type of polymer and what that "si" means. Maybe some silicon polymer? or some polymer bound to a silicon wafer? Answerinf such vague questions reveals "eggboundedness". Jul 17 '12 at 21:31

There are two ways in which the band gap of a material: using optical spectroscopy and using electrochemistry. The way you go about analyzing the data to determine the band gap is independent of material, but the process of collecting the data is very specific to your material, and you should consult papers where others have made similar measurements on similar systems.

1. Optical spectroscopy.

You need to collect an absorbance spectrum of your material. Given what I can gather from your fabrication description, you will probably need to collect said spectrum in the solid state. The exact means of doing that vary somewhat by spectrometer model. Find someone who knows your spectrometer very well and ask them how to do it (or read the manual).

The absorbance process measures the energy difference between the ground state and the excited state as electromagnetic radiation is absorbed. Since there are a number of vibrational states associated with both the ground state and the excited state, the absorbance spectrum appears as a blob instead of a nice line. The "true" band gap, or $E_{00}$, the energy difference between the lowest vibrational states of the ground and excited states, is difficult to measure. However, the most commonly accepted approximation is the onset of absorption from the low energy side. The onset value is the intersection of the extrapolations of the linear parts of the spectrum. See the image below.

Once you have the wavelength (x) at that point, you can convert it into energy using the Planck relation: $$E(\text{J})=\dfrac{hc}{\lambda(\text{m})}$$ If you want your energy in electronvolts, you can convert directly: $$E(\text{eV})=\dfrac{1239.84187 \text{ eV nm}}{\lambda(\text{nm})}$$

1. Electrochemistry, specifically voltammetry

Voltammetry gives you the ability to determine the peak oxidation potential, $V_{\text{ox}}$, and the peak reduction potential, $V_{\text{red}}$, of your material. Both cyclic voltammetry and differential pulse voltammetry can give you these data, and both should work on solids, though you may want to find someone who has experience in such things.

The assumption that we operate under when using electrochemistry to determine HOMO-LUMO or bad gap, is that when we oxidize a molecule or material, we take the first electron out of the HOMO (or valence band). When we reduce the molecule or material, we put an electron into the LUMO (or conductance band). Thus, $V_{\text{ox}}$ tells us something about the HOMO (valence band) and $V_{\text{red}}$ tells us something about the LUMO (conductance band). The energy gap (in electronvolts) is simply the difference between the two potentials (in volts) multiplied the charge on the electron $e=-1 \text{ eV/V}$. $$E(\text{eV})=e(V_{\text{red}}-V_{\text{ox}})$$