# Is there a formula for the sputtering yield of compound materials for ion beam milling?

I am aware of the theory of sputtering by Sigmund and of the formula he derived for calculating the sputtering yield in focused ion beam milling. The modern version (modified by Matsunami and Yamamura) goes as follow:

$Y(E)=\frac{3.56}{U_0} \frac{Z_t Z_p}{\sqrt{Z_t^{2/3} + Z_p^{2/3}}} \frac{M_p}{M_t+M_p} \alpha(M_t/M_p) S_n(E/E_{tp})$

where $p$ refers to "projectile" and $t$ to "target", $U_0$ is the surface binding energy, $Z$ are the atomic numbers of the materials, $M$ the atomic masses, $\alpha$ is an experimental formula and $S_n$ is the nuclear stopping power with $E_{tp}$ being a constant related to both projectile and target.

However I would love to be able to estimate the sputtering yield for compound material. I'm aware of the difficulty of such a thing, but it would be really helpful in my work if I could predict at least the range of the sputtering yield. If there is no such formula then my other thought would be to use Sigmund's formula but with the average atomic number of the compound instead of $Z_t$ and the average atomic mass of the compound instead of $M_t$.

Can I rely on that as a vague approximation or am I completely off? As an example a prediction I get calculating that way is that the sputtering yield of neon ions on silicon is 5 times higher than on gallium oxide.

• Compounds get complicated, since the energy transfer to the various elements are different, the surface binding energies are different, etc. Plus, you get differential sputtering, so the surface composition changes until the various sputtering rates all work out nicely. – Jon Custer Feb 15 '18 at 22:43
• So you think that it’s quicker to just go experimentally instead of trying to predict the range of the sputtering yield? As a side note I forgot to mention that I took the surface binding energy of the compound, that is about 21eV for Ga$_2$O$_3$ if I believe the source that I found on google. – Jxx Feb 15 '18 at 23:11