The “changeover field” in thermal-field shaping
This chapter provides the condition for field changeover from blunting to sharpening.
At sufficiently high temperatures, a field emitter will change shape, as a result of the migration of surface atoms. As discussed in [14Mil], the direction of change, as indicated by the relevant electrical Gibbs function, depends in principle on the applied voltage. If the voltage is sufficiently small, then the surface-energy term dominates, and the emitter will tend to become blunter and to “ball up”; if the voltage is sufficiently large, then the energy term relating to the capacitance between the emitter and its surroundings (and to the work done by the high-voltage generator) dominates, and the emitter will tend to “reach out toward its surroundings,” by becoming sharper or by the formation of nanoprotrusions.
Values of this changeover field for a tip radius of 100 nm are shown in the last column of Table 158.2[ https://doi.org/10.1007/978-3-662-53908-8_158] and are typically a few V/nm or less. Obviously, for a tip radius of 1 nm, the changeover fields would be higher by a factor of 10. Comparisons with predicted evaporation field values indicate that, for all except very small tip apex radii, in the vicinity of 1 nm, emitter sharpening is the expected TF-shaping tendency in atom-probe operating conditions.
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