MEASUREMENTS WITH THE THIN-TARGET METHOD

By using the thin-target with thick substrate method, the following effects should not be ignored: the effect of multiple scattering of incident electrons in the thin films, the effect of backscattering of incident electrons from the thick substrates, and the effect of bremsstrahlung photons produced by incident electrons in both thin films and thick substrates. These effects were corrected by Monte Carlo method. Here we give a brief description and the details can be found in Ref.[2].

Usually, the x-ray production cross-sections can be expressed as

(1)

where σ is the x-ray production cross-section, E_e is the incident electron energy, N is the net count of the characteristic x-ray peaks, A is the atomic weight, E_ph is the characteristic x-ray photon energy, N_A is the Avogadro constant, t is the thin film mass thickness, N_e is the number of incident electrons, ε(E_ph) is the intrinsic detection efficiency of the detector, and Ω is the solid angle subtended by the detector system. For K-shell ionization, the ionization cross-section can be easily deduced from the x-ray production cross-section by using the K-shell fluorescence yield ω_k.

In our experiment, the Eq. 1 should be corrected because of the effects mentioned above. We assume the count of the characteristic x-raypeaks contributed by these effects as

∆N, and define a K factor as the ratio of ∆N to N, then the x-ray production cross-section can be denoted as

(2)

here the definitions of symbols are the same as in Eq. 1.

We can use the Monte Carlo simulations to obtain the K factors. For example, the atomic L_α x-ray production cross-sections by electron-impact can be expressed as Eq. 3

4 ,

87 (3)

where A, N_e, N_A and t are same as in Eq.1, N_Lα,MC is the corresponding characteristic x-ray counts from the backscattered x-ray spectra generated by the Monte Carlo PENELOPE code.

The inner-shell ionization cross-sections of the optical-data model [10] and the other atomic parameters (e.g., fluorescence yields, Coster-Kronig transition probabilities, and x-ray emission rates) used in the Monte Carlo simulations can be obtained from the databases of the PENELOPE code, and they can be converted into the L_α, L_β and K-shell x-ray production cross-sections according to Eqs. 4–6 [11,12]

V , and V_Kare the L-subshell and K-shell ionization cross-sections by electron-impact; ω₁,ω_2, ω₃ and ω_K are the L-subshell and K-shell fluorescence yields; f₁₂, f₁₃, f₂₃ are the Coster-Kronig transition probabilities; Γij, Γi are the fractional and total x-ray emission rates for L-shell ionization, respectively. When the incident electron energyis larger than the K-shell ionization threshold energy, the vacancy transfers from the K shell to L subshells should be taken into account. Finally, we can obtain the K factors according to the Eq. 7

. The sensitivity of K factors to the K, L-shell ionization cross-sections used in the database of PENELOPE code has also been studied. The inner-shell ionization cross-sections of the PWBA-C-Ex theory [13,14] and of the Mayol and Salvat’s model [10] have been used to calculate the K factors. We found that the K factors are not sensitive to the inner-shell ionization cross-sections. The differences of the (1-K) factors calculated from the two sets of inner-shell ionization cross-sections are less than 3% although they are very different both in shape and in magnitude.The K- and L-shell x-ray production cross-sections can be obtained according to Eq. 2 with the calculated K factors.

By using the method of thin-target with thick substrate, we have measured the electron-impact inner-shell x-ray production cross-sections near the threshold energy for the following elements and shells: S-K, Cl-K, Ca-K, Zn-K, W-L_D, L_E, Bi-L_D, L_E, Ba-L_D and Gd-LD. We used the K-shell fluorescence yields to convert the K-shell x-ray production cross-sections to the K-shell ionization cross-cross-sections [15]. The experimental results are summarized in Tables 1-8, and the comparisons with the results of some theoretical models and empirical formulae are shown in Figs. 1-8. The experimental uncertainties come from several factors: values of the net peak counts (~5-9%), detection efficiency (~5%), target thickness (~5%), number of incident electrons (~1%), (1-K) factors (~3%) and inhomogenity of the target (~4%). The uncertainties of K-shell fluorescence yields should be considered for

2 ,

88

K- shell ionization cross-sections [15]. Therefore, the total uncertainties by quadratic addition are estimated to be ~10-15%.

TABLE 1. MEASURED K-SHELL IONIZATION CROSS-SECTIONS FOR S ELEMENTS (E˖keV; V_KAND ERROR: cm²)

TABLE 2. MEASURED K-SHELL IONIZATION CROSS-SECTIONS FOR Cl ELEMENT (E˖keV; V_KAND ERROR: cm²)

TABLE 3. MEASURED K-SHELL IONIZATION CROSS-SECTIONS FOR Ca ELEMENT (E: keV; V_KAND ERROR: cm²)

89 TABLE 4. MEASURED K-SHELL IONIZATION CROSS-SECTIONS FOR Zn ELEMENT

(E: keV; V_KAND ERROR: cm²)

TABLE 5. MEASURED L-SHELL X-RAY PRODUCTION CROSS-SECTIONS FOR W ELEMENT

TABLE 6. MEASURED L-SHELL X-RAY PRODUCTION CROSS-SECTIONS FOR Bi ELEMENT

90

TABLE 7. MEASURED L-SHELL X-RAY PRODUCTION CROSS-SECTIONS FOR Ba ELEMENT

TABLE 8. MEASURED L-SHELL X-RAY PRODUCTION CROSS-SECTIONS FOR Gd ELEMENT

91

0 7 14 21 28 35

0.00E+000 1.50E-021 3.00E-021 4.50E-021 6.00E-021 7.50E-021 9.00E-021

This work PWBA-C-Ex Hombourger Casnati Luo and Joy V (cm2 )

E (keV) S K shell

FIG. 1. The present experimental data of K-shell ionization cross-sections by electron-impact for S element are compared with the results from the PWBA-C-Ex theory [13,14] and the Luo and Joy’s theory [16,17] as well as the results from the empirical formulae of Casnati and co-workers [18] and of Hombourger [19].

0 7 14 21 28 35

0.00E+000 1.00E-021 2.00E-021 3.00E-021 4.00E-021 5.00E-021 6.00E-021

Cl K shell This work PWBA-C-Ex Luo and Joy Casnati et al Hombourger

V (cm2 )

E (keV)

FIG. 2. The present experimental data of K-shell ionization cross-sections by electron-impact for Cl element are compared with the results from the PWBA-C-Ex theory [13,14] and the Luo and Joy’s theory [16,17] as well as the results from the empirical formulae of Casnati and co-workers [18] and of Hombourger [19].

92

0 5 10 15 20 25 30 35

0.0 5.0x10^-22 1.0x10^-21 1.5x10^-21 2.0x10^-21 2.5x10^-21 3.0x10^-21

Ca K shell

This work Shevelko PWBA-C-Ex Luo and Joy Casnati Hombourger

V (cm2 )

E (keV)

FIG. 3. The present experimental data of K-shell ionization cross-sections by electron-impact for Ca element are compared with the results from the PWBA-C-Ex theory [13,14] and the Luo and Joy’s theory [16,17] as well as the results from the empirical formulae of Casnati and workers [18] and of Hombourger [19]. The experimental data of Shevelko and co-workers [20] for Ca element are also plotted for comparison.

10 15 20 25 30 35

0.00E+000 1.00E-022 2.00E-022 3.00E-022 4.00E-022 5.00E-022

6.00E-022 This work Tang et al Tang' correct PWBA-C-Ex Casnati Hombourger Gryzinski Luo and Joy V(cm2 )

E (keV) Zn K shell

FIG. 4. The present experimental data of K-shell ionization cross-sections by electron-impact for Zn element are compared with the results from the PWBA-C-Ex theory [13,14] and the Luo and Joy’s theory [16,17] as well as the results from the empirical formulae of Casnati and co-workers [18] and of Hombourger [19] and of Gryzinski [21]. The experimental data of Tang and co-workers [22,23] for Zn element are also plotted for comparison.

93

FIG. 5. The present experimental data of L_α, L_β x-ray production cross-sections by electron-impact for W element are compared with the PWBA-C-Ex theory[13,14] and the experimental data of Campos et al. [24].

FIG. 6. The present experimental data of L_α, L_β x-ray production cross-sections by electron-impact for Bi element are compared with the PWBA-C-Ex theory [13,14].

6 12 18 24 30

FIG. 7. The present experimental data of L_α x-ray production cross-sections by electron-impact for Ba element are compared with the PWBA-C-Ex theory [13,14].

10 15 20 25 30 35 40

94

FIG. 8. The present experimental data of L_α x-ray production cross-sections by electron-impact for Gd element are compared with the PWBA-C-Ex theory [13,14].