Handbook of Modern Coating Technologies

Multiplets of quadrupole lenses

Quadrupole lenses represent one more type of ion-optical elements for beam formation in SNMPs that are attracting the attention of physicists. Such lenses ensure strong focusing because the focusing field is normal to the beam axis, in contrast to axially symmetric lenses in which only the tangential field component contributes to the focusing. The optical power of electrostatic and magnetic quadrupole lenses (MQLs) is due to dimensionless excitation of pole tips k_E and k_M, respectively. The optical power of a MQL depends on the geometric and physical characteristics of both the lens and the beam, whereas that of an electrostatic quad- rupole depends only on the same parameters of the lens:

where Lf is the effective length of the lens field;q, m, T, and V are the particle charge, mass, energy, and the potential difference passed by the beam particles, respectively; B_p is the magnetic induction at a pole of the magnetic quadrupole; V_p is the pole potential of an elec­trostatic quadrupole, and r_a is the lens aperture radius.

A distinctive feature of quadrupole lenses is focusing in one transverse direction and defocusing in the other one. Therefore a system of lenses is needed to ensure focusing in both directions. By the late 1960s quadrupoles were applied in high-energy beam transport systems where higher order aberration effects were negligibly small. Therefore their use in PFSs was a novelty and there were concerns that aberrations and technical complexities would hamper probe formation with the desired characteristics. In the same period, theoreti­cal studies of the systems of quadrupole lenses were carried out in the framework of the development of high-voltage electron microscopes [53,54]. Soviet scientists proposed using a system of four quadrupole lenses with two independent power supplies [55,56]. It was shown in this work that such a system with the quadrupoles connected antisymmetrically to power supplies is analogous to an axially symmetric lens due to the equality of reduction factors in both transverse directions. In later publications, this system of quadrupole lenses became known by the name "Russian quadruplet.” It served as a PFS for the first SNMP of the Harwell Research Centre, UK, constructed by Cookson and coworkers in the late 1960s [57]. The authors used an MQL with an aperture diameter of 76 mm that had been previously used in the beamtransport system (the resolution achieved was 15 X 15 ^m² at a current of ~15 nA). Still later, special lenses with an aperture diameter of 38 mm were manufactured, and a resolution of 4 X 4 ^m² was reached at a current density of 30 pA/^m². Thus great progress was made in comparison with PFSs based on the beam collimation principle.

The successful creation of the first SNMP exceeded all expectations and gave impetus to the development of similar facilities in many laboratories worldwide with the use of various types of MQL multiplets (one-, three-, and four-lens systems with different power supplies). One such nuclear microprobe based on the Russian quadruplet of the MQL was designed and constructed in the city of Tomsk, Soviet Union [58]. Later on, a nuclear microprobe with an MQL doublet was commissioned at the Kharkov Physical-Technical Institute [59] and a 3.0 X 5.0-^m² proton beam was obtained at the target with a 4-nA current and an energy of

• The common drawback of both facilities is the impossibility of electromagnetic scanning and the absence of a synchronized data acquisition system, which essentially restricts their capabilities. In CIS countries, the first SNMP was created at the NASU IAP, Sumy. When operated in the microanalysis mode, it has a resolution of 2 pm and a beam current «100 pA [60,61]. The PFS of this microprobe constitutes an optimized, distributed Russian quadruplet with two integrated MQL doublets [62] and five MQL [63] of an essen­tially new design. The creation of this SNMP was preceded by a series of theoretical studies on the optimization of nonlinear beam-forming processes in quadrupole-based PFSs [64] that revealed the dependence of beam characteristics at the sample surface on the number of lenses and their positioning geometry.

The doublet of quadrupole lenses is the simplest system of this type among various PFSs. The lenses, located as close to the sample surface as possible, are fed by different power sup­plies and show alternating focusing—defocusing properties in each transverse direction (x and y). Special mention should be made of the recent work [65] describing the upgrade of PFS elements for the SNMP that allowed achieving a resolution of 0.4 X 0.4 pm² at a proton beam current of ~10 pA with an energy of 3 MeV. This resolution was estimated by linear scanning over the edge of the standard calibration grid in the x- and y-directions, and analyz­ing the secondary electron yield. The PFS based on the doublet of a precision MQL has the following parameters: total length of the system l = 6 m, working distance g = 26 cm, and reduction factors D_x X D_y = — 35 X —9, brightness of the output beam as it leaves the Dynamitron electrostatic accelerator b = 10 pA/pm² mrad² MeV with a maximum voltage of

• MV, and the energy spread of the beam particles AE/E = 6 X 10^—4.

The study of multiplet configurations of two to four MQLs [66] revealed that triplets of magnetic quadrupoles with highly excited poles have certain advantages over other systems with compact positioning of the lenses. Such a system permits increasing reduction factors with a decreasing of working distance in both the x- and y-directions without a substantial change in their ratio.

Taken together, these modifications resulted in the highest SNMP resolution to date based on such a PFS known as the "Oxford type triplet” in a microanalysis mode [67]: probe size of 0.29 X 0.45 pm at an H¹ beam current of ~50 pA. These data were obtained by linear scanning of the edge of the standard calibration grid in the x- and y-directions, and analyzing the yield of characteristic X-ray emission. The PFS of SNMP at the Center of Ion Beam Application (CIBA), Singapore University, has the following parameters: total length of the system l« 7 m, working distance g = 16 cm, reduction factors D_x X D_y = 88 X—24, beam brightness at the exit from the Singletron electrostatic accelerator b = 74 pA/pm² mrad² MeV with a maximum voltage of 3.5 MV, and the energy spread of the beam particles AE/ E = 10^—5. The spot size of 35 X 75 nm² at a 1-fAH⁺₂ current [67] was also obtained at CIBA for a PFS with the following parameters: total length of the system l« 7 m, working distance g = 7 cm, and reduction factors D_x X D_y = 228 X —60 at the same characteristics of the high- voltage ion gun. The probe parameters result from linear scanning over the edge of the square 1-pm aperture in the x- and y-directions, and analyzing H⁺₂ ion intensity in the scan­ning transmission ion microscopy (STIM) mode.

Further progress in the development of SNMPs was expected to be made using paramet­ric MQL multiplets with the number of lenses and geometry of their location as parameters.

This implied theoretical research on PFSs based on four-quadrupole systems fed by Russian quadruplet type power supplies with the first two lenses positioned freely along the optical path. As shown in Ref. [68], the first and the second lenses must be coupled into a doublet and moved in search for the optimal position. The results of Refs. [69—71] gave reason for optimism, since the studied systems of the distributed Russian quadruplet permitted consid­erably increasing both reduction factors and system's acceptance. Major approaches to over­coming the resolution limit of 1 mm in the microanalysis mode are considered in Ref. [72] emphasizing a number of positive factors related to the presence of additional parameters influencing ion-optical properties and possibly improving resolution of the PFS based on dis­tributed MQL multiplets. A distinctive feature of the distributed Russian quadruplet is the isolated location of the first two lenses. The highest resolution in a PFS of this type was obtained for a probe size of 0.34 pm at a proton beam current of ~10 pA [73] by the linear scanning of the edge of the standard calibration grid in the x- and y-directions. The PFS of an SNMP (LIPSION, Leipzig, Germany) with which these results were achieved has the fol­lowing parameters: total length l & 9 m, working distance g = 30 cm, reduction factors D_x X D_y = 82 X 82, beam brightness b = 20 pA/pm² mrad² MeV at the exit from the singletron electrostatic accelerator with a maximum voltage of 3.5 MV, and the energy spread of the beam particles AE/E = 10^_s.

Studies of distributed PFSs based on the Russian quadruplet and their successful realiza­tion in experimental setups gave an impetus to the search for ways to improve SNMPs. One of the ways was the introduction of accessory lenses. As mentioned earlier, an important characteristic of SNMPs, besides the resolving power depending on the spot size at the tar­get, is the strength of the beam current concentrated in the probe. This parameter deter­mines sensitivity of microanalysis, all other detection conditions being equal.

The aim of the work reported in Ref. [74] was to create a high-acceptance PFS operating at a beam current from 0.1 to 20 nA with a resolution of 1—3 pm, that is, allowing a radical increase in the current, while only slightly enlarging the probe size. This circumstance is of importance for the detection of impurities in samples at a relative concentration of 0.1 ppm that does not yet cause radiation damage of materials or radiation-induced diffusion of microelements. A five-lens PFS was designed to accomplish the assigned task [75]. The total length of the system, l = 4.7 m, was limited by the floor space needed to install the SNMP. Special MQLs were developed to ensure the minimal working distance g = 8 cm. The follow­ing experimental values were obtained: probe size d = 1.3 pm at a proton beam current I~0.5 nA;d = 1.8 pm, I = 8 nA;d = 2 pm, I = 10 nA;d = 3 pm, and I = 20—25 nA. A PFS for SNMP (CSIRO GEMOC, Sydney, Australia) had the following parameters: reduction factors D_x X D_y = —65 X 69, and beam brightness at the output of the tandem electrostatic accelera­tor b = 1 pA/pm² mrad² MeV.