The temperature dependence of evaporation field for Gomer-type field-evaporation mechanisms

Theoretical formulae are developed for the temperature dependence of the onset evaporation field F°, assuming a parabolic surface-atom bonding well and a Gomer-type mechanism for the escape process. Recent experimental results for tungsten and molybdenum, when replotted in the form $\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ versus $\text{1}\text{F}\text{°}$, exhibit linear behaviour in the range from about 60 to 150 K. Deviations occur below this (at 50 K for W, 35 K for Mo); the deviation temperatures are compatible with theoretical estimates of the critical temperature at which ion tunnelling effects become important. Values of the zero-Q evaporation field extrapolated from the linear regime (74 V/nm for W, 60 V/nm for Mo) are significantly higher than observed values of F° near 78 K or values of F^e derived from the Müller-Schottky formula; the difference can be explained by taking into account repulsive ion-surface and F² potential-energy terms. Our theoretical picture seems generally self-consistent at the classical level, and it is concluded that the low-temperature field-evaporation process for the more field-desorption-resistant metals is, at this level, now basically understood. Field evaporation may now be used to investigate atomic behaviour at charged surfaces, but greater care is needed over the standardization of evaporation conditions and the consistent choice of field calibration.