Electrostatic lenses

It is easiest to discuss the electron optics of a TEM instrument by addressing the instrument from top to bottom. Refer again to the schematic in F ure la. At the top of the TEM column is an electron source or gun. An electrostatic lens is used to accelerate electrons emitted by the filament to a h potential (typically 100-1,000 kV) and to focus the electrons to a cross-over just above the anode (the diameter of the cross-over image can be from 0.5 to 30 Mm, depending on the type of gun ). The electrons at the cross-over image of the filament are delivered to the specimen by the next set of lenses on the column, the condensers. 

In 1951Castaing8 published results to show that an electron microscope could be converted into a useful x-ray emission spectrograph for point-to-point exploration on a micron scale. The conversion consisted mainly in adding a second electrostatic lens to obtain a narrower electron beam for the excitation of an x-ray spectrum, and adding an external spectrometer for analysis of the spectrum and measurement of analytical-line intensity. Outstanding features of the technique were the small size of sample (1 g cube, or thereabouts) and the absence of pronounced absorption and enhancement effects, which, of course, is characteristic of electron excitation (7.10). Castaing8 gives remarkable quantitative results for copper alloys the results in parentheses are the quotients... 

The ECAP incorporates an electrostatic lens in the time-of-flight spectrometer in order to improve the mass resolution by compensating for small spreads in the energies of the ions evaporated from the specimen under the pulsed electric field. A lens design by Poschenrieder or a reflectron type of electrostatic lens is used for this purpose, and is standard equipment for metallurgical or materials applications of APFIM. These typically improve the mass resolution at full width half maximum (FWHM) from m/Am 250 to better than 2000. 

Figure 6. Diagram of our 1-atm ion mobility spectrometer (IMS) apparatus (a) stainless steel source gas dilution volume, (b) septum inlet, (c) needle valve, (d) Nj source gas supply, (e) source and drift gas exhaust, (f) flow meter, (g) pressure transducer, (h) insulated box, (i) drift tube, (j) ion source, (k) Bradbury-Nielson gate, (I) Faraday plate/MS aperture, (m) drift gas inlet, (n) universal joint, (o) electrostatic lens element, (p) quadrupole mass filter, (q) 6"-diffusion pump, (r) first vacuum envelope, (s) channeltron electron multiplier, (t) second vacuum envelope, (u) 3"-dif-fusion pump, (v) Nj drift gas, (w) leak valve, (x) on/off valves, (y) fused silica capillary, (z) 4-liter stainless steel dilution volume, (aa) Nj gas supply.

Fig. 3.11 Poschenrieder ion flight time focusing scheme which uses a 163° spherical electrostatic lens.

The data presented here were taken with an apparatus similar to the one recently described by Parker and Eppink [25], The difference between it and the original photofragment imaging apparatus of Chandler and Houston [23] is that the flat screens, through which the ions or electrons are projected were replaced by a series of concentric electrodes. These form an electrostatic lens that, when the appropriate voltages are applied, will focus... 

Referring again to Figure 2.4, the slow positrons emitted from the boron were accelerated and focussed by the electrostatic lens system... 

The passage of electrons or other particles with charge q and mass m through an electrostatic lens system is governed by their motion under the action of the electric field. In the case considered here, cylindrical symmetry around the optical axis (z-axis) and paraxial rays will be assumed. Of the cylindrical coordinates only the transverse radial coordinate p and the distance coordinate z are of relevance, and the electrostatic potential of the lens is given by q>(p, z). As shown in Section 10.3.1, in the paraxial approximation the potential q>(p, z) is fully determined by the potential symmetry axis. Hence, the equations of motion and the fundamental differential equation of an electrostatic lens depend only on this potential. The fundamental lens equation is given by (see equ. (10.38))... 

Figure 4.31 Data for the characterization of an electrostatic lens, (a) Positions of the focal and principal planes (left-hand and right-hand sides are indicated by the subscripts Y and r respectively) and their distances (optical sign conventions are disregarded, i.e., the distances are described only by their lengths). (b) Geometrical construction applied to image the arrow ye by means of characteristic asymptotic trajectories, (c) Geometrical construction for an asymptotic ray with a pencil angle a,e. The shaded areas are needed for the derivation of the linear and angular magnification factors of the lens. For details see main text.

Due to the Helmholtz-Lagrange relation, no greater flexibility in the parameters determining the image is possible. However, lenses with even more elements than four can have other advantages, such as lower aberration or a more extended operation range. (See, for example, the movable electrostatic lens in [Rea83].)... 

Figure 4.34 The relationship between the voltage ratios V Vv and V3/Pl of an asymmetric electrostatic lens with the apertures calculated for A/D = 1 and two values of the mid-object and mid-image distances P/D and Q/D which are labelled (P/D, Q/D) on the curves. The solid and dashed curves belong to two different solutions for the potential V2 applied to the middle electrode. From [Rea70].

In order to derive the optical properties of an electrostatic lens, one has to establish and solve the equations of motion for a transmitted particle of mass m and charge q. Since the particle moves in the lens under the action of an electric field which can be derived from a potential cylindrical symmetry around the optical axis (z-axis) and treating paraxial rays only, the potential cylindrical coordinates p and z. It can be expanded as a power series in p with z-dependent coefficients. Due to the rotational symmetry, only even powers of p appear in the expansion, and one has the ansatz... 

R radius of the first aperture of the electrostatic lens system... 

XPS Equipment Operated with an Electrostatic Lens System... 

FIGURE 5 XPS equipment with electrostatic lens system. 

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