David R. Kingham

The post-ionization of field evaporated ions: A theoretical explanation of multiple charge states

Abstract It is shown theoretically that post-ionization of field evaporated ions may occur, whereby a positive ion being accelerated away from a metal surface in a strong electric field loses one or more electrons by tunnelling into the substrate. Calculations reported here, based on a physically realistic model potential, predict the probability of post-ionization as a function of field strength for all elements of interest in field evaporation. This theory of post-ionization is consistent with all known experimental observations of the charge states for field evaporated ions and can explain both the variation of ion charge state with changing evaporation conditions and the occurrence of highly charged ions. Field evaporation may thus be viewed as a two-stage process of initial evaporation and subsequent post-ionization.

Field ion energy deficit calculations for liquid metal ion sources

Ionisation distributions of field-ionised ions from liquid metal ion sources are calculated. Various shapes for the emitter region, a range of currents and a range of electric field strengths at the liquid surface are considered. Their effects on the energy deficit distribution of the ions is presented through a numerical calculation for gold and gallium.

Field ionization theory: A new, analytic, formalism

Abstract A new formalism for the calculation of field ionization rate-constants near a model metal surface is derived. Approximate analytic formulae are given for the ionization rate-constant of an atom as a function of distance from the metal surface, for the total probability of ionization on a single pass through the ionization zone and for the width of the ionization zone. Theoretical estimates of best image fields are given for gas atoms of interest in field ion microscopy. The clarity of approach and computational ease of the method is shown to be compatible with the production of acceptably accurate results.

Calculations of field ionization in the field ion microscope

Abstract The ionization of a gas atom as it occurs in the field ion microscope is discussed. A wide range of values for the electric field intensity at the metal surface are considered in calculating the ionization occurring both far away from and close to the tip. Ionization distribution curves are calculated and electric fields strengths are determined at points where the distributions peak. Calculations of ionization zone widths and best image conditions are made and a new interpretation of best image conditions is considered. A new field calibration method is suggested.

On the charge state of tungsten ions in the pulsed-field atom probe

Abstract Observations of the charge state of field evaporated tungsten ions in the atom-probe are reported. In addition to pure W we present data from one material with higher binding energy, WC, and one with lower binding energy, a W containing high speed steel. Electric fields up to 64 V nm −1 at the pulse maximum have been successfully used and ion charge states as high as W 5+ have been observed. The observed relative abundance of different charge states of W is compared with our theoretical calculations and with the experimental results of Kellogg. A simple post-ionization model is able to explain adequately the charge state of field evaporated W ions.

Effects of local field variations on the contrast of a field-ion microscope

Both the gas concentration and the electron transition rate constant (for ionisation) of the imaging gas may be important factors determining the contrast in the field-ion microscope. It is demonstrated that the field dependent variation in the electron transition rate constant may be sufficient to explain the observed contrast, and that simple application of Boltzmann statistics gives implausibly large differences in gas concentration particularly at temperatures <20K.

Resolution of the field ion microscope

Equations for resolution in the field ion microscope are reviewed and modifications are suggested. Calculations are made of each contributing term, based on a proposed model for the electric field variation. Comparison with experimental results is made. The revised equations strongly indicate that thermal accommodation of He imaging gas prior to ionisation is almost complete. Instead of the gas temperature being 6.5 to 7.3 times the tip temperature as estimated by Chen and Seidman (1971) a factor of only 1.3 to 1.5 now seems plausible.

Model calculations of tunnelling and thermal evaporation rate constants relating to field evaporation

Tunnelling and thermal evaporation rate constants are compared for model potential barriers relating to field evaporation. Previous calculations of the temperature below which tunnelling becomes appreciable are shown to be model dependent. Distinctive features of different shaped barriers are found which might be experimentally observable and this could provide a means to distinguish between charge-hopping, charge-draining and image-hump models of field evaporation. The experimental results of Wada et al. (1980), who measured the temperature dependence of the evaporation field of W and Mo at constant evaporation rate, are shown to be consistent with the occurrence of ionic tunnelling below 60K.

Resolution and contrast in the field ion microscope

Abstract Resolution and contrast in the field ion microscope (FIM) are considered. The imaging of protruding atoms and the anomalous extra magnification of small planes are analysed by considering variations in local electric field strength and critical distance. A comparison is made between the FIM and the scanning tunnelling microscope (STM) and the possibility of sub-atomic resolution in the FIM is discussed.

Imaging gas concentration in the field ion microscope: a theoretical analysis

Abstract A Boltzmann equation method for calculating the gas concentration in the field ion microscope is proposed. A simple model for the molecules bouncing movement is presented. Numerical results are given and the formation of an imaging gas adsorbed layer is discussed. Within this model, no evidence is found which suggests that local variation in imaging gas concentration is the basic mechanism of image formation in the FIM. The results show limits on the values of tip field and or tip temperature, for which an adsorbed layer can be formed.