Cuadro de cargas

In the past, there has been a considerable effort to measure the quantum yield ηdetector of a given CEM detector, and to calibrate a particular CEM detector within a detection system with absolute efficiency values. Nevertheless, until today there is still no generally agreed response function for the quantum yield ηdetector =ηdetector(Ekin) of a CEM detector to the kinetic energy Ekin of an incident primary particle. In the literature, there are numerous efficiency calibrations of CEM detectors in pulse counting mode for the detection of incident electrons [48, 89–94], various species of positive ions (for low energy ions Ekin < 10 keV [89, 91, 95–106], for highly-energetic ionsEkin >10 keV [95, 107]), for negative ions [101, 104, 108], photons [80, 109–115], and for neutral atoms [116, 117]. However, all these individual calibration attempts display at least partially huge discrepancies in the observed efficiency values [48]. Moreover, even as identical CEM models are used in several of the calibration measurements, the particular experiments still show a large variety in the observed quantum yield values of the individual CEM detectors (see, e.g., compilation by [48] for identical CEM models).

Although the individual experimental systems differ significantly from each other, the ob- served deviations in ηdetector can basically be attributed to two possible error sources in the calibration measurements: (a) the accidental simultaneous influence of ηcol in addition to the actual quantum yield ηdetector of the bare CEM detector (eq. 2.8), i.e., unintentionally measuring the varying product ηcolηdetector instead of the isolated raw quantum yieldηdetector of the CEM detector as stated by eq. 2.6, (b) the efficiency determination methodology used itself, i.e., in most cases the accuracy of a relative calibration of the unknown detector to a specific precalibrated source or detector (see section 5.1).

Concerning the collection efficiency ηcol for the calibration measurements, in many of the above systems a reduced collection efficiency ηcol < 1 is accidentally introduced in the cali- bration measurements. Such a reduced collection efficiency is given, e.g., by the application of a biased grid18 in front of the CEM detector. Additionally, in many experimental systems the parameters ηcol andηdetector are often not even properly specified or generally ill defined. Consequently, in particular the impact position of the primary particle in the CEM and the therewith attributed kinetic energyEkin at primary particle impact remain comparably unde- fined in many systems. In addition, for low kinetic particle energiesEkin at cone entrance19, the internal field of the CEM caused by the gain voltage UCEM will macroscopically affect the kinetic energy Ekin of the primary particle at impact in the CEM surface (see subsec-

18

For the transmission of a metal grid structure, the technically maximum attainable open surface area peaks at approximately95 %, correspondingly reducing the collection efficiency down to this value.

19_{In the literature, for the quantum yield responseη}

detector =ηdetector(Ekin)of a CEM detector, the kinetic

tion 4.3.4). A comparison of the efficiency values of any such system is therefore generally difficult, even for identical CEM models [48].

Referring to the second of the above mentioned error sources, one should note that al- most all published calibration measurements are based on relative measurements only, not on an absolute measurement method (see section 5.1). As a consequence, many of the above systems are referenced only relatively to a precalibrated particle source, or a second precal- ibrated detector (see subsection 5.1.1). Strictly speaking therefore, in all these calibration measurements no absolute efficiency values or an explicit quantum yieldηdetector as expressed by eq. 2.6 can be stated. On the contrary, the described CEM detection system of this thesis will rely on an absolute efficiency calibration method based on coincident counting of two simultaneously generated ionisation fragments (see section 5.1). As the collection efficiency ηcol of this detection system is assumed to be one (see subsection 4.4.3), the CEM detectors can be calibrated to absolute efficiency values.

Linear approach and reduced yield curve approach

Although there is no generally agreed response function of the quantum yield ηdetector = ηdetector(Ekin)of a CEM detector, in the literature there are two phenomenological approaches for ηdetector in correspondence to the kinetic energy of the incident primary particle. Both approaches are based on fundamental considerations20 of the subsequent kinetic emission of secondary electrons out of a surface after the impact of an incident primary particle [64, 65, 118–120]. As a result, both approaches relate the CEM quantum yield ηdetector to the primary emission yieldδ0 of the incident primary particle at primary particle impact in the CEM (fig. 2.1, primary particle hit).

The first approach is associated to the potential and kinetic emission of secondary electrons depending on the impact velocity of the primary particle, and the incident primary particle type. This initial approach is based on calculations of [121], and results in a linear increase of the secondary electron emission yieldδ0(vkin, vthres)∼k·(vkin−vthres)with increasing impact velocity vkin of the incident particle (e.g., reviews by [62, 122]). The secondary electron emission starts at a minimum threshold velocity vthres under which no secondary electrons are emitted from the active CEM surface. The quantum yield of the CEM is then stated to be linearly proportional to the velocity of the incident particle as [122]

ηdetector(vkin, vthres)∼δ0(vkin, vthres)·Z =k·(vkin−vthres)·Z, (2.9) whereZ is the atomic number of the incident particle,δ0 is the primary emission yield, and kdenotes a constant.

Although this approach is successful for the description of the quantum yieldηdetector and its associated primary emission yieldδ0 within a certain range of velocitiesvkin, the response of δ0(vkin) is significantly different to a linear increase for considerable low values next to the threshold velocityvthres[62]. Moreover, for high values ofvkin, saturation of the primary emission yieldδ0 is observed experimentally [62, 81–83, 118], but cannot be described by this

20

In the secondary emission theory, after interaction with the incident primary particle there is a certain probability for a secondary electron to leave the bulk material without being re-adsorbed by the solid. By theory, the emission probability of a secondary electron is generally associated with the skin depth lλ of

the primary particle in the solid, i.e. the depth in the solid where the secondary electron is liberated by the primary particle.

2.4. Absolute detection efficiency

particular approach. Consequently, the linear approximation21 of the quantum yield of the CEM detector as stated by eq. 2.9 is only applicable to a certain, reduced range of kinetic energies for the incident primary particle. Although used in the literature [122, 124], it seems that the linear approach is only a limiting special case relating to a more general description of the quantum yield of a CEM detector. In the following, we will therefore focus on the second approach only.

The second approach for the CEM efficiency response goes back to theoretical work of [119, 125]. It introduces a universal reduced secondary emission yield curve for the primary emission yield δ0(Ekin), and to δ(Ekin), according to the kinetic energy of the incident par- ticle. Remarkably, the global shape of this universal reduced yield curve is assumed to be applicable to any type of incident primary particle, and for any secondary emitting surface [125]. Furthermore, the reduced yield curve characteristic describes quantitatively the global shape of many different primary emission yield measurements for different materials, and different incident primary particles [62, 81, 82, 118]. With respect to the CEM efficiency response of this approach, the second approach is based on two parts [48, 92]. The first part consists of the cascaded continuous dynode CEM model as introduced in section 2.1. The second part incorporates the global characteristic of the universal reduced yield curve of the secondary emission yield δ0(Ekin, Eδ0,max, δ0,max), and δ(Ekin, Eδ,max, δmax), respectively, into

the quantum yieldηdetector =ηdetector(δ0, δ) of the CEM detector, as stated by eq. 2.6. In more detail, the first part of the CEM efficiency response approach is associated with the maximum attainable quantum yield ηdetector = 1 −Pm(0), where the compound loss probability Pm(0) of all subsequent stages g1..m for the secondary electron avalanche in the CEM is defined by eq. 2.5. Note that the loss probabilityPm(0)and therefore the associated quantum yieldηdetector=ηdetector(δ0, δ)is expressed only in terms of the emission parameters δ0 andδ [92]. In the second part of the CEM efficiency response approach, the two secondary emission parameters δ0 and δ at any cascade stage gm are now individually characterised by the reduced yield curve according to the kinetic particle energy Ekin of the incident primary particle at impact [48].

Although theglobal shape of the universal reduced yield curve is independent on surface or incident particle type [125], to obtain explicit yield values δ0 and δ, the individual emission properties for a particular surface are specified by two material associated parameters δ0,max and Eδ0,max. Accordingly, the parameter δ0,max is the maximum primary particle emission

yield δ0,max ≈ δ0(Eδ0,max) with the corresponding kinetic energy value Ekin ≈ Eδ0,max at

primary particle impact. For kinetic particle energies Ekin lower or higher than the latter energy, the primary emission yield δ0 will generally decrease with respect to the maximum attainable value at Eδ0,max as observed in various primary emission experiments (see, e.g.,

compilation by [62], or [76, 81, 82, 118, 120, 126]). Although extensively measured for electrons as incident primary particles, for incident ions it appears that both parameters Eδ0,max and

δ0,max are shifted to considerably higher values [62, 127], respectively.

Combining both previously introduced parts of the second approach, the response of the quantum yield ηdetector =ηdetector(δ0, δ) according to the kinetic energy Ekin of the primary particle at primary impact in the representation of [48, 66] reads

21_{In the past, there have been attempts to expand the linear approach by a Taylor series in the velocity}

component into a polynomial description of the primary emission yield δ0(vkin, v2kin, ...) [73, 105, 123].

Although some observations are quantitatively well described by the individual fittings, the polynomial approach lacks a universal description of the observed phenomena, with the obtained parameters more or less referring only to the individual characteristic of the particularly measured data set.

cone channel primary particle i ii q (a) 0 15 30 45 60 75 90 0 20 15 10 5

angle of incidence [deg.]

d ( q ) 0 85 75 70 65 60 2 6 10 14 80 (b)

Figure 2.8:(a) CEM cone hitiin contrast to a channel hitiiat grazing incident angleθof the primary particle at surface impact (primary particle hit, stageg1, fig. 2.1). Inset: Zoom of shaded area displaying the definition of the incident angle θ. (b) Relative dependency of the primary emission yield δ0(0◦)according to the angle of incidence θ to the surface normal as stated by eq. 2.12. For comparison, a common CEM cone impact under an angle of θ= 60◦ is indicated by the dashed line. Inset: Zoom for relative values fromθ= 60◦−85◦.

ηdetector(δ0, δ) = 1−exp[δ0(−1 + exp[δ(−1 +...+ exp[−δ])])...

| {z }

)], m−1

(2.10)

where

δ0=δ0(Ekin, Eδ0,max, δ0,max) =

1−exp[−z1.35]

0.725z0.35 ·δ0,max, (2.11) andδ=δ(Ekin, Eδ,max, δmax), correspondingly. In eq. 2.10, the parameterδ0 is the primary emission yield, δ denotes the generalized secondary emission yield of all subsequent stages g2..m of amplification, and m is the number of amplification stages in the CEM until the generation of a macroscopic pulse at the CEM end. In eq. 2.11, the parameterEkinrepresents the kinetic energy of the primary particle at impact in the secondary emitting surface of the CEM, and δ0,max is the maximum emission yield δ0,max = δ0(Eδ0,max) with the energy

value Ekin = Eδ0,max (correspondingly, δmax = δ(Eδ,max) where Ekin = Eδ,max). Note that

the explicit value in the parameterz= 1.8431Ekin/Eδ0,max in eq. 2.11 represents a generally

accepted, experimental fit parameter for the global reduced yield curve characteristic from various independent emission experiments [48, 125]. Nevertheless, although the obtained parameter quantitatively describes the universal emission yield properties of many metal, semiconducting, and isolating surfaces, this introduced parameter leaves the second approach of the CEM efficiency response as stated by eq. 2.10 still basically phenomenological. Further note that for calculations, the parametermin eq. 2.10 is chosen to bem= 25[48]. Moreover, assuming that the collection efficiencyηcolattains unity as introduced in subsection 2.4.1, the absolute detection efficiencyηdet of the individual CEM detector in the joint CEM detection system of this thesis is given byηdet≡ηdetector(δ0, δ) (eq. 2.8).

2.4. Absolute detection efficiency