# How to calculate mass of nanomaterial grown on a substrate

I'm growing graphene on copper substrates and need to know the mass. The graphene is grown via chemical vapor deposition; amounts of reactants are not completely known. The best approach I've thought of is recording the mass of the substrate before and after using an analytical balance, but with the nature of the material being nano, this method may be elusive. What other method could I use to find the mass?

• Is it a graphene monolayer? If so, then weighing will likely not work; monolayer graphene weighs $\mathrm{0.8\ mg\ m^{-2}}$. Also, does the graphene have to stay adhered to the copper? And to what precision do you need the mass to be determined? Do you know the shape/area the graphene layer has, or could you somehow mask it (i.e. measure the area covered in graphene and use the areal density to obtain the mass)? – Nicolau Saker Neto Jun 26 '15 at 23:45
• It's vertically grown graphene. We're calculating specific capacitance using cyclic voltammetry. It doesn't have to be extremely precise; just enough to do basic calculations. – John Snow Jun 26 '15 at 23:52
• Oh, not at all the type of layer I had in mind. Quite a pretty image! Depending how tall and dense that graphene forest (coral?) is, weight may work. Unfortunately it's a rather irregular layer of material, so now I'm having a hard time thinking of alternatives. If a destructive method is allowed, maybe you can oxidize the carbon to $\ce{CO2}$ and measure that with, say, gas chromatography? – Nicolau Saker Neto Jun 27 '15 at 0:03
• Ah, I don't think destruction of it is something we would be trying to do. And yes, I think its a great image. Wish it were mine. – John Snow Jun 27 '15 at 0:05

## 1 Answer

One possible option for thin film thickness measurement is by Energy Dispersive Spectroscopy (EDS) in a scanning electron microscope (SEM). There exist commercial packages for this such as LayerProbe by Oxford and STRATAGem (I have no financial interest in Oxford or SAMx). If your campus/research facility has an SEM with an EDS (many do), but not a commercial package, you can still work it out yourself. If I were tackling this in my own lab, I would probably do something along the following lines:

Option #1:

Obtain a spectrum from a known thickness of carbon on your Cu substrate. This can be any method such as sputtering or evaporation so long as the thickness is known by other means. Most geology labs have the ability to do this kind of deposition since they need reproducible carbon thicknesses on their samples.

For example, geo labs will typically place a polished brass object next to the sample to be coated in an evaporative coater. The change in the color of the brass corresponds to the thickness of the carbon: e.g. blue is 250 Å but bluish green is 300 Å (Kerrick, D. M., et al., 1973). So something like 25 % accuracy is possible this way.

Then you measure that thickness in the SEM using an exact beam current, size, distance from the objective lens. Then you measure your graphene in the SEM using the exact same conditions. If your sample is less than about 200 nm thick, then the number of counts/second is proportional to the number of carbon atoms present in the layer. Using the mass for your standard layer, (assume a density of graphite), then you can compute the mass of your graphene.

If your thickness is more than about 200 nm, then you may need to do an absorption correction – i.e. the photons are being absorbed on their way out and your count rate is no longer proportional to the number of atoms. You can compute attenuation coefficients using the CXRO calculator (and a couple other places if you google). Then you can do a thin film correction. At 200 nm, your error from ignoring the thin film correction is probably about 5–10 %, which is likely a bit less than the error in the determination of the standard film using the color method. So you can think with that for your sample.

Option #2:

You can measure the mass directly using an oscillating crystal. Commercial systems comprise a quartz crystal with electronics set to find the resonant frequency. You place the quartz crystal in your chamber alongside your Cu substrate. As your reaction happens, it grows both onto your Cu and onto the quartz crystal. The resonant frequency of the crystal changes as mass is added. These are sold commercially, though a bit pricey. For example, at TedPella (again, no financial interest). The resolution is typically billed as 1 Å thickness resolution (assuming you know the density of your material.)

For your application, you would have to be sure that the graphite grows on your monitor crystal the same as on your Cu substrate. That may require checking in an SEM, and it may require prepping the crystal somehow. Hence, I offer this as suggestion #2.

Finally, you could also figure this out using a focused ion beam and sectioning the sample from the side. If this is too complex, there also exist labs where one can hire them to do this kind of measurement.

I hope one of these solutions works for you!

Ref:

Kerrick, D. M., Eminhizer, L. B., & Villaume, J. F. (1973). The Role of Carbon Film Thickness in Electron Microprobe Analysis. American Mineralogist, 58, 920–925.