Introduction and Theory of Milling Rate of Materials in FIB

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Introduction and Theory of Milling Rate of Materials in FIB

The milling rate in FIB milling process is defined as the ratio of the volume of the milled material to the product of the beam current and irradiation time, given by,

            Milling Rate of Materials in FIB ---------------------------- [2454a]
            ---------------------------- [2454b]
where,
           d - The milled depth,
           A - The milled area,
           I - The beam current,
           t - The beam irradiation time,
           q - The electronic charge,
           D - The ion dose.

Therefore, the milling rate of materials depends on many factors, including the ion flux, the probability of sputtering per incident ion, the re-deposition of the sputtered material, and the angle of incidence of the ions with the sample surface. Table 2455 lists some examples of milling rates of different materials in FIB.

The correlation between the milling rate and the sputtering yield is given by,

            Milling Rate of Materials in FIB ---------------------------- [2454c]
where,
           N_t - The atomic density of the target material,
           Y_S(E,Θ) - The sputtering yield,
           t - The beam irradiation time.

The user interfaces on the FIB systems normally have some configured files for sputtering of different materials. In these files, the beam dwell times and overlap have been calibrated for the specific materials in order to obtain the highest sputtering rates.

angle (θ) of incidence with respect to the target normal

Figure 2454a. The angle (θ) of incidence with respect to the target normal.

Figure 2454b shows the relationship between material removal rates, and the angles of incidence of 30 keV Ga ions for Si and SiC.

Relationship between material removal rates and the angle of incidence of 30 keV Ga ions for Si and SiC

Figure 2454b. Relationship between material removal rates, and the angles of incidence of 30 keV Ga ions for Si and SiC. [1, 2]

[1] S.K.P. Veerapandian, S. Beuer, M. Rumler, F. Stumpf, K. Thomas, L. Pillatsch, J. Michler, L. Frey, M. Rommel, Comparison of silicon and 4H silicon carbide patterning using focused ion beams, Nuclear Instruments and Methods in Physics Research B, 365, 44–49, 2015.
[2] C. Lehrer, L. Frey, S. Petersen, H. Ryssel, Limitations of focused ion beam nanomachining, J. Vac. Sci. Technol. B Microelectron. Nanometer. Struct. 19 (6) (2001) 2533–2538.

Practical Electron Microscopy and Database

An Online Book, Second Edition by Dr. Yougui Liao (2006)

Introduction and Theory of Milling Rate of Materials in FIB