At the beginning try to read this three work. I think, they have a lot of answers on your questions.

1. Raman spectroscopy of graphene and graphite: Disorder, electron–phonon coupling, doping and nonadiabatic effects Andrea C. Ferrari http://www.sciencedirect.com/science/article/pii/S0038109807002967#

2. G′′ band Raman spectra of single, double and triple layer graphene

J.S. Park, A. Reina, R. Saito, J. Kong, G. Dresselhaus, M.S. Dresselhaus http://www.sciencedirect.com/science/article/pii/S000862230900030X#

3. Raman imaging of graphene D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, L. Wirtz http://www.sciencedirect.com/science/article/pii/S0038109807002979

Tuinstra-Koenig relation.. Many excellent review articles on this topic by Dresselhaus.

With addition of references given by Dr. Alexander,

Raman spectroscopy as a versatile tool for studying the properties of graphene

Andrea C. Ferrari & Denis M. Basko. Nature Nanotechnology 8,235–246 (2013)

doi:10.1038/nnano.2013.46

Thanks for your reply

the number of layers can be derived from the ratio of peak intensities, I2D/IG, as well as the position and shape of these peaks. in case of chemical exfoliation(like Hummers method) we don't have 2D peak for graphene. what should we do in such samples?

Yes for GO, we don't have G'(2D) peak. But after reduction , you can see the improvement of G' peak. Here truly speaking, the number of layer can't be find out from usual relation, like position and shape and intensity ratio. But still you can find out reported article, where they have mentioned monolayer graphene (GO). I don't know about the correctness to claim that. Waiting for the logical answer. Or you can ask author of that particular article.

Here is some references, where they reported manolayer GO. Yo can go through and ask corresponding author.

Chang et al. confirming the monolayer GO by measuring the AFM cross-section thickness.

1. Ultrasonic-assisted self-assembly of monolayer graphene oxide for rapid detection

of Escherichia coli bacteria. Chang et al.

http://pubs.acs.org/doi/pdf/10.1021/nn101781v

2. Mechanical Properties of Monolayer Graphene Oxide

http://pubs.rsc.org/en/content/articlelanding/2013/nr/c3nr00141e#!divAbstract

I saw one of your question in RG (https://www.researchgate.net/post/How_we_can_measure_density_of_graphene)

Your answer regarding to estimate the no. of layers of GO is hiding in Mazdak's comment.

we can not see 2D peak in graphene even after reduction. if you use CVD, we have 2D peak in raman but for example in hummers method, we don't have this peak. I asked some professors but I didn't get answer.

Kindly go through the following article :-

One-pot reduction of graphene oxide at subzero temperatures

Chem. Commun., 2011,47, 12370-12372, DOI: 10.1039/C1CC15569E

As Subrata Ghosh said a good reference to understand Raman spectra of graphene is" Raman spectroscopy as a versatile tool for studying the properties of graphene

Andrea C. Ferrari & Denis M. Basko." But when you analize your data you have to consider many things. Most of references are related to exfoliated graphene on SiO2, if you have graphene growth by CVD on a different substrate (specially if you have graphene on a metal) you would find differences respect to the bibliography due to the diferent interactions between graphene and the diferent subtrates. Generally CVD graphene is not AB stacked, then we can not characterize the number of layers by Raman spectroscopy due to the strong dependence of the spectrum with the relative rotated angle between adjacent layers ( Raman Spectroscopy Study of Rotated Double-Layer Graphene: Misorientation-Angle Dependence of Electronic Structure

Phys. Rev. Lett. 108, 246103 – Published 14 June 2012 )

Regarding to the GO I have not worked on it, but if I found a Graphene spectrum without 2D peak I would think that it is some amorphous carbon or GO, so maybe the reduction was not sufficient.

I hope I have been of some help

Can we use raman for estimating the thick of graphene layers?

Dear Zahra,

I too am not getting a prominent 2D peak after reduction of GO.The intensity of that peak seems to be related to the number of layers.More the number, lesser the intensity.So, I was wondering if sonicating the prepared graphene will exfoliate the layers and give a 2D peak.

This link is really useful,

http://www.instanano.com/characterization/experimental/raman-graphene/

Dear Dheeraj 

Thanks for the link. Brief but comprehensive.

I have written an application note on the topic: 

https://tools.thermofisher.com/content/sfs/brochures/AN52252_E%201111%20LayerThkns_H_1.pdf

Peak shift of G Band: Method) Care must be taken with the first method, G band peak position. There need to be not strain present as that will shift the peak to lower wavenumber and any presence of doping will also influence the peak position.

Method 2) 2D:G band ratio will give a good indication of single layer graphene with the ratio being around 2 or higher. The band shape however may distort the shape of the 2D band causing broadening. This is particularly evident for Bernal stacking of layers that is seen in HOPG graphene that has been exfoliated. In regards to CVD grown graphene the 2D:G may be more appropriate.

I have seen that exfoliated Graphene layer thickness follows a linear trend in G band intensity at upto 19 layers presenting a very good way to determine layer thickness for those samples. 

Let me know if this is helpful.

In the Aforementioned Papers for calculating the number of layers of Graphene, SiO2/Si, SiO2 were the substrates. What are the I(2D)/I(G) and FWHM values of 2D peak for Cu Substrate ? Can anyone suggest any papers.

Tejas,

When growing on Cu substrate the Cu substrate will act as a catalyst for growth of the graphene layer. It will self terminate when the cu layer is covered thus their should be little or no multi layer growth when CVD deposition is used to obtain graphene. The Intensity ratio of the 2D to G band may vary due to doping.

This link is very useful to find out the number of layers in graphene

http://www.instanano.com/characterization/experimental/raman-graphene/