GPR-based Sputtering Yield Prediction


Sputtering yield which is a number of atoms removed from material's surface per an incident ion, is one of the most important parameters in various studies such as plasma-material interactions. Measurements of the yields have been performed by many authors for various combinations of substrates and incident ions, and the published values are available from literature. This web page provides sputtering yields at normal incident angle, which are predicted by a machine learning technique called Gaussian process regression (GPR) using those published yields as a learning dataset.

If you are new to use this page, please see Notes first to consider whether the model here is reasonable for your parameter (energy and sputtering yield) range or not.


1H 2He
3Li 4Be 5B 6C 7N 8O 9F 10Ne
11Na 12Mg 13Al 14Si 15P 16S 17Cl 18Ar
19K 20Ca 21Sc 22Ti 23V 24Cr 25Mn 26Fe 27Co 28Ni 29Cu 30Zn 31Ga 32Ge 33As 34Se 35Br 36Kr
37Rb 38Sr 39Y 40Zr 41Nb 42Mo 43Tc 44Ru 45Rh 46Pd 47Ag 48Cd 49In 50Sn 51Sb 52Te 53I 54Xe
55Cs 56Ba 72Hf 73Ta 74W 75Re 76Os 77Ir 78Pt 79Au 80Hg 81Tl 82Pb 83Bi 84Po 85At 86Rn
87Fr 88Ra 104Rf 105Db 106Sg 107Bh 108Hs 109Mt 110Ds 111Rg 112Cn 113Nh 114Fl 115Mc 116Lv 117Ts 118Og
57La 58Ce 59Pr 60Nd 61Pm 62Sm 63Eu 64Gd 65Tb 66Dy 67Ho 68Er 69Tm 70Yb 71Lu
89Ac 90Th 91Pa 92U 93Np 94Pu 95Am 96Cm 97Bk 98Cf 99Es 100Fm 101Md 102No 103Lr
Single yield calculation
Plot the yields
*If input values are empty, the graph is automatically scaled.
Show Data Inline
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Download as a File (txt)



  • If you use the GPR prediction data above in your publication, please refer to this web site
    as well as the paper
    Kino et al.: Phys. Plasmas 28, 013504 (2021).
  • References of learning data
    • S. Tachi and S. Okudaira: J. Vac. Sci. Technol. B 4(2), 459-467 (1986).
    • Y. Yamamura and H. Tawara: Atomic Data and Nuclear Data Tables 62, 149-253 (1996).
    • R. P. Doerner, D. G. Whyte, and D. M. Goebel: J. Appl. Phys. 93(9), 5816-5823 (2003).
    • R. D. Kolasinski, J. E. Polk, D. Goebel, and L. K. Johnson: J. Vac. Sci. Technol. A 25(2), 236-245 (2007).
    • T. Ito and K. Karahashi: Si sputtering yields by halogen (F, Cl, Br) ions (private communications)
    • S. Taira, T. Ito, and K. Karahashi: Mn sputtering yields by noble gas (Ne, Ar) ions (private communications)
  • Dataset property
    Number of learning data points : 5687
    Substrate element range : Be - U
    Incident ion element range : H - Pb
  • Histograms of learning data
    If the parameter range you would like to use is completely off from these learning dataset range, predicted sputtering yields may be much less accurate.
  • Prediction model development

    The prediction model has been developed based on Gaussian process regression (GPR), which is a non-parametric regression method. The code of our model is written in python with GPy for GPR. The RBF kernel is used as a kernel function, and maximum likelihood estimation method and 10-fold cross validation (CV) have been applied for tuning of hyperparameters.

    Descriptors of the created model consist of atomic numbers and masses of substrate and incident ion elements, and an incident ion energy, additionally melting temperature of a substrate is also one of them.

    The observed-predicted plot of the model for all learning data is shown here. The prediction ability in the range of the dataset is quite nice, such as that R2 coefficient is 0.98 and the root mean square error (RMSE) is 0.15 for test of CV with the best parameters.

    Regression has been done for all dataset at once, so this model can predict sputtering yields even for combinations of no data by using similar conditions of descriptors.

  • Versions
    Environment on development
    python : 3.8.3
    GPy : 1.9.9
    numpy : 1.19.5
    prediction model : 0.0.3 (developed on )
    web page : 0.2.2 (last updated on )
  • Recommended screen width: 1024px and more.

Contact us

Kazumasa Ikuse, Ph.D.
ikuse☆ (Please replace "☆" in the e-mail address with "@".)

We would appreciate it if you could share your sputtering yield data of single-element substrates sputtered by single-element incident ions, not used as training data in this model yet. Your data will be added with proper references.