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Imaging Gas Adsorption in the Field Ion Microscope : Dependence in Tip Field Strength and Tip Temperature C

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Imaging Gas Adsorption in the Field Ion Microscope : Dependence in Tip Field Strength and Tip Temperature C IMAGING GAS ADSORPTION IN THE FIELD ION MICROSCOPE : DEPENDENCE IN TIP FIELD STRENGTH AND TIP TEMPERATURE C. de Castilho, D. Kingham To cite this version: C. de Castilho, D. Kingham. IMAGING GAS ADSORPTION IN THE FIELD ION MICROSCOPE : DEPENDENCE IN TIP FIELD STRENGTH AND TIP TEMPERATURE. Journal de Physique Colloques, 1988, 49 (C6), pp.C6-99-C6-104. 10.1051/jphyscol:1988617. jpa-00228114 HAL Id: jpa-00228114 https://hal.archives-ouvertes.fr/jpa-00228114 Submitted on 1 Jan 1988 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE Colloque C6, supplbment au n0ll, Tome 49, novembre 1988 IMAGING GAS ADSORPTION IN THE FIELD ION MICROSCOPE : DEPENDENCE IN TIP FIELD STRENGTH AND TIP TEMPERATURE C.M.C. de CASTILHO and D.R. KING-" Instituto de Fisica, UFBa. , Campus Universitario da ~edera~so, 40 210 Salvador, Bahia, Brazil 'VG Ionex Ltd., Charles Avenue, Maltings Park, GB-Burguess Hill RH15 9TQ, West Sussex, Great-Britain ~dsum&- Les conditions pour la formation dtune couche de gaz "imageant" adsorb; sur la surface dfun ;chantillon au Microscope Ignique de Champ sont recherchdes en utilisant un simple modGle thdorique pour le mouvement des moldcules du gaz. On conclue, alors, que la formation de cette couche n'est possible que pour une certaine gamme de valeurs dtintensit& du champ et de temp6rature. Abstract - The conditions for an imaging gas adsorbed layer in the Field Ion Microscope to be formed are investigated using a simple theoretical model for the imaging gas hopping motion. It is concluded that such a layer is formed just for a certain range of tip field (or voltage) values and tip temperatures. I ,INTRODUCTION The Imaging process in the Field Ion Microscope (FIM) /1, 2/ occurs through the ionization of gas molecules (usually single atoms) and their subsequent accelerated movement towards a screen (or equivalent device) as a result of an alectric field of order of few volts per angstrom. The sample to be imaged has a very narrow curvature radius at the apex (200 to 1000 W) and the structure of its surface is revealed by the local electric field strength at points,close to the sample /2, 3/ which is the region which is in fact imaged, since ionization is forbiden in a region a few angstroms wide from the sample surface /4, 5/. Ionization then occurs from that critical distance (x ) /4/, in a very narrow zone (ionization zone) of few tenths of angstroms fr8m x . ft has been noticed that image gas molecules are desorbed together with atoms of the sample /6/ as would be expe'cted with an adsorbed layer of the imaging gas molecules /7, 8/. Our aim is, by using a simple model for the imaging molecules motion before ionization /9/, to discuss the possibility of an imaging gas adsorbed layer formation for different tip fields and tip temperatures. We are' going to refer as adsorption the mechanism of accommodation of an imaging gas molecule to the tip temperature and its trapping between the critical distance and the tip surface. I1 THE MODEL We assume the metal tip shape as hyperboloidal so that the electric field in the region not very far away from the symmetry tip axis, x, can be written as /lo/: F(x) = F / [ 1 + (2x/Rt)] (1) 0 where F is the surface field strength, x is the distance to the tip apex and R t is tRe surface apex radius of curvature. An image gas molecule of electric polarizability a has a potential energy, due to the electric field, given by: @(x) = - 0.5 at ~(x) The gas molecuie' then drifts towards the tip with a velocity which is dependent on the local field and with a probability of being ionized at a point x dependent on F(x) and on its survival probability up to this p0in.t Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988617 C6-100 JOURNAL DE PHYSIQUE /lo/. As, under the normal operating conditions of the FIM, most of the ionization occurs in the narrow region just beyond the critical distance /4, 5/ we restrict, in our model, the ion production to this zone, with width -w, i. e., between x and x + w. Another simplification of the model is that the ionization zone is assumed to be laterally continuous instead of a set of "ionization disks" /2/, each one above the protruding atoms shown in the FIM micrographs. The imaging gas molecules have a kinetic energy in a range such that it is possible to treat their collisions with the tip classically /12/, with the accommodation coefficient a defined as ac = (E~- E~)/(E~ - ET) (3) where E - incident kinetic energy of the molecule at a certain collision, Ei - scattered, or reflected, kinetic energy corresponding to the same I- collision as Ei, ET - average value of Er for a gas beam scattered at the tip temperature T , i. e., E would be the average energy of molecules T fully accommo8.ated to the tip temperature. On average several collisions with the tip are expected for a molecule and since the forces between collisions are conservative the scattered energy of a molecule after the n th collision would correspond to the incident energy for the (n+l) th collision. Denoting by En the kinetic energy of a gas molecule just after the n th collision (Eo is the kinetic energy just before the first collision) and using eq. 3, we obtain: The collision of one molecule with incident kinetic energy E and n scattered energy E can be formally treated as a "destruction" of one n+l ' particle of energy E and a "creation" of another one with energy E Thus n n+l' we transform the collision process into a "destruction/creation" one. The relation between E and En is as expressed by eq. 4. Thus, the "life11of n one molecule lasts, at mosg, between two successive collisions or, when ionization occurs, between one collision and the ionization time. This is equivalent to separating the distribution function f into an infinite sum of terms f., each one corresponding to the fraction of the molecules with energy compati61e -with the occurence of i collisions. Thus: f=lfi i=O with fo - particles which have not suffered any collision, and which will disappear at the first collision or before if ionized when crossing the ionization zone; fl - particles originating from the first collision which will last, at most, up to the next collision. fn - particle originating from the n th collision. We assume for now that all particles are originally "created" at x a with the same energy E . Thus, at a point x, a particle has a defite momentum (in modulus) which is 8ependent on the position, on the value of E and on a the number of collisions it has suffered. So, th Denoting the total energy of a molecule by E, its value after the i E~, i i. f = c(Ea, i) which enables collision, is dependent on and Ea, e., i us to write eq. 7 as p = pl(x, ci). Denoting by n(x, E ) the number of particles at z, with all values of momentum but with the regtriction that all particles were l1createdVtwith energy E we have: a' Expressing the distribution function as in eq. 6 and the total energy after the ith collision as E,, we have where the delta function assures the correct relation between momentum, total energy and coordinate x. Up to this point we have considered that all particles were tlcreatedll with the same kinetic energy, which is quite unrealistic. In fact, Ea is the kinetic energy of the gas molecule far away from the tip, so it ranges according to a distribution appropriate to the local gas temperature. Hence, the gas density at a point x must take this into account so that the density at a point x, D(x), can be written as where W(E ) is a weight function for the number of particles created with a kinetic energy Ea at xa ( with momentum -pa ). We assume a Boltzmann distribution for the energy of the gas molecules far away from the tip, at a temperature Te and then: W(Ea) = [ (2nN)/(nkB TB)3'2 (~~1"~exp ( -E~/~~T~) where kB is the Boltzmann constant and N is the total number of particles. I11 NUMERICAL RESULTS We have considered helium and neon as the imaging gases and a W metal surface. We solve eq. 10 numerically. The integration in the range of energies E is made from zero to un upper limit which was taken as 10 times the a average value of Ea, given by: No significant change was observed if we take the superior limit as, for example, 20 or 30 times the average value of E,. Figure 1, a and b, represent the enhancement factor of the gas- concentration, normalised to the concentration at x=x-, i. e., we represent X, defined as: x(x) = Gas........................ Concentration at x Gas Concentration at x The ratio between the gas atom eelocities just after and before a collision tends to 1.0 as the number of collisions suffered by a molecule increases.
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