Measurements of K-shell ionization cross sections and L-shell X-ray production cross sections of Al, Ti, Cu, Ag, and Au thin films by low-energy electron impact

Li Bo; Li Ling; Zhu Jing-Jun; Lin Wei-Ping; An Zhu

doi:10.7498/aps.71.20220162

Abstract

The K-shell ionization cross sections of Al, Ti, Cu and L-shell characteristic X-ray production cross sections of Cu, Ag and Au (Lα, Lβ and Lγ subshells for Au) by electron impact at incident energy of 5–27 keV are determined experimentally. Thin films of the studied elements, deposited on thin carbon substrates, are employed as targets in the experiments. The thickness of the thin carbon substrate is 7 μg/cm², the targets are Al, Ti, Cu, Ag and Au and their thickness values are 5.5 μg/cm², 28 μg/cm², Cu 35.5 μg/cm², 44 μg/cm² and 44 μg/cm², respectively. The target thickness values are checked by using Rutherford Backscattering Spectrometry (RBS). The electron beam is provided by a scanning electron microscope (KYKY-2800B). The characteristic X-rays produced are recorded by a silicon drifted detector (XR-100SDD, Amptek), which has a C2 ultrathin window and can detect the low-energy X-rays down to boron Kα line (0.183 keV). The detector efficiency is calibrated by using the standard sources (⁵⁵Fe, ⁵⁷Co, ¹³⁷Cs and ²⁴¹Am) for X-ray energy larger than 3.3 keV while using the characteristic peak method (i.e. by measuring characteristic X-ray spectra produced by 20 keV electron impacting various thick solid targets) for X-ray energy less than 3.3 keV. The experimental results are corrected by the Monte Carlo code PENELOPE for the effects of target structure and Faraday cup. Meanwhile, the electron escape rates obtained from the Faraday cup and the signal pile-up effect are also considered. The results show that when the incident electron energy is low, the influences of electron energy loss and target thickness are significant. The thinner the target , the smaller the correction is. Experimental uncertainties for K-shell ionization cross sections of Al, Ti and Cu are about 5.0%, 5.6% and 5.1%, respectively; experimental uncertainties for L-shell X-ray production cross sections for Cu and Ag are about 5.3% and 4.0%, and for Lα,Lβ,and Lγ of Au are about 6.1%, 8.9% and 11.0%, respectively. The experimental L-shell characteristic X-ray production cross sections of Cu are given for the first time. Compared with the theoretical values of the semi-relativistic distorted-wave Born approximation (DWBA), most of the experimental values in this work are in good agreement within 7% deviation. The best agreement between the experimental results and the theoretical values is obtained for the K shell ionization cross section of Al, and the deviation is less than 1.7% for the data where the incident energy is above 10 keV. The least consistency with the theoretical values is the experimental L shell characteristic X-ray production cross sections of Cu, with a deviation being about 5–22%. The comparison of the experimental L shell characteristic X-ray production cross sections of Cu (including Ga and As elements) with those from the DWBA theory indicates that the theoretical calculations of L shell ionization cross sections of medium heavy elements and the corresponding atomic parameters (such as fluorescence yields and Coster-Kronig transition probabilities) need to be more accurately determined. According to the present results, the ionization cross sections or characteristic X-ray production cross sections measured by the thin target thin substrate, the thin target thick substrate and the thick target methods are equivalent to each other within the uncertainties.

Keywords:

Authors and contacts

Key Laboratory of Radiation Physics and Technology of Ministry of Education, Institute of Nuclear Science and Technology, Sichuan University, Chengdu 610064, China

Corresponding author: An Zhu, anzhu@scu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12175158).

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References

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[2]	Zhao J L, An Z, Zhu J J, Tan W J, Liu M T 2016 J. Phys. B: At. Mol. Opt. Phys. 49 065205 Google Scholar
[3]	Born M 1926 Z. Physik 38 803 Google Scholar
[4]	Truhlar D O, Rice J K, Kuppermann A, Trajmar S 1970 Phys. Rev. A 1 778 Google Scholar
[5]	Shelton W N, Leherissey E S, Madison D H 1971 Phys. Rev. A 3 242 Google Scholar
[6]	Madison D H, Shelton W N 1973 Phys. Rev. A 7 499 Google Scholar
[7]	Rainer H 1990 Phys. Lett. A 144 81
[8]	Bely O, Schmartz S B 1969 Astron. Astrophys. 1 281
[9]	Sampson D H 1986 Phys. Rev. A 34 986 Google Scholar
[10]	Fontes C J 1993 Phys. Rev. A 47 1009 Google Scholar
[11]	Segui S, Dingfelder M, Salvat F 2003 Phys. Rev. A 67 062710 Google Scholar
[12]	Colgan J, Fontes C J, Zhang H L 2006 Phys. Rev. A 73 062711 Google Scholar
[13]	Bote D, Salvat F 2008 Phys. Rev. A 77 042701 Google Scholar
[14]	Llovet X, Powell C J, Salvat F, Jablonski A 2014 J. Phys. Chem. Ref. Data 43 013102 Google Scholar
[15]	Shima K, Nakagawa T, Umetani K, Mikumo T 1981 Phys. Rev. A 24 72 Google Scholar
[16]	Shima K, Okuda M, Suzuki E, Tsubota T, Mikumo T 1983 J. Appl. Phys. 54 1202 Google Scholar
[17]	Llovet X, Merlet C, Salvat F 2000 J. Phys. B:At. Mol. Opt. Phys. 33 3761 Google Scholar
[18]	Bote D, Llovet X, Salvat F 2008 J. Phys. D:Appl. Phys. 41 105304 Google Scholar
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[22]	Merlet C, Llovet X, Fernandez-Varea J M 2006 Phys. Rev. A 73 062719 Google Scholar
[23]	Merlet C, Llovet X, Salvat F 2004 Phys. Rev. A 69 032708 Google Scholar
[24]	An Z, Li T H, Wang L M, Xia X Y, Luo Z M 1996 Phys. Rev. A 54 3067 Google Scholar
[25]	Luo Z M, An Z, He F Q, Li T H, Long X G, Peng X F 1996 J. Phys. B:At. Mol. Opt. Phys. 29 4001 Google Scholar
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[28]	Zhu J J, An Z, Liu M T, Tian L X 2009 Phys. Rev. A 79 052710 Google Scholar
[29]	Zhao J L, Tian L X, Li X L, An Z, Zhu J J, Liu M T 2015 Radiat. Phys. Chem. 107 47 Google Scholar
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[34]	Han J F, An Z, Zheng G Q, Bai F, Li Z H, Wang P, Liao X D, Liu M T, Chen S L, Song M J 2018 Nucl. Instrum. Methods Phys. Res. B 418 68 Google Scholar
[35]	Liu B, Ding W, An Z, Zhu J J, Zhang Z, Li L, Lin W P 2021 Fusion Eng. Des. 172 112751 Google Scholar
[36]	Sabbatucci L, Scot V, Fernandez J E 2014 Radiat. Phys. Chem. 104 372 Google Scholar
[37]	Salvat F, Fernández-Varea J, Sempau J 2008 PENELOPE-2008, A Code System for Monte Carlo Simulation of Electron and Photon Transport (Issy-les-Moulineau: OECD/NEA Data Bank)
[38]	Perkins S T, Cullen D E, Chen M H, Hubbell J H, Rathkopf J, Scofield J 1991 Report UCRL-50400 30 Lawrence Livermore National Laboratory, Livermore, CA
[39]	Mei C S, Wu Y, Yuan Y, Chang C H, Qian Z C, Zhu J J, Moharram K 2016 J. Phys. B: At. Mol. Opt. Phys. 49 245204
[40]	Silvina P L, Vasconcellos M A Z, Ruth H, Jorge C T 2012 Phys. Rev. A 86 042701 Google Scholar
[41]	He F Q, Peng X F, Long X G, Luo Z M, An Z 1997 Nucl. Instrum. Methods Phys. Res. B 129 445 Google Scholar
[42]	周长庚, 付玉川, 安竹, 罗正明 2000 强激光与粒子束 12 601 Zhou C G, Fu Y C, An Z, Luo Z M 2000 High Power Laser and Particle Beams 12 601
[43]	Zhao J L, An Z, Zhu J J, Tan W J, Liu M T 2016 Radiat. Phys. Chem. 122 66 Google Scholar
[44]	Campbell J L 2003 At. Data Nucl. Data Tables 85 291 Google Scholar
[45]	Wu Y, An Z, Liu M T, Duan Y M, Tang C H, Luo Z M 2004 J. Phys. B:At. Mol. Opt. Phys. 37 4527 Google Scholar
[46]	Sepúlveda A, Bertol A P, Vasconcellos M A Z, Trincavelli J, Hinrichs R, Castellano G 2014 J. Phys. B:At. Mol. Opt. Phys. 47 215006 Google Scholar
[47]	Campos C S, Vasconcellos M A Z 2002 Phys. Rev. A 66 012719 Google Scholar

Cited By

图 1 实验装置示意图

Figure 1. The schematic of experimental setup.

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图 2 SDD探测器的效率刻度曲线

Figure 2. The X-ray detection efficiency of the SDD detector.

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图 3 从上到下分别是能量为25 keV的电子束碰撞Cu, Au, Al, Ti, Ag 5种薄靶产生的X射线谱, 元素×N中的N为对应谱放大倍数, 虚线是轫致辐射本底

Figure 3. The experimental spectra for Cu, Au, Al, Ti, Ag target by 25 keV electron impact (from the top to the bottom). N in element ×N is the magnification of the corresponding spectrum. The dotted line is the bremsstrahlung background.

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图 4 能量为5—27 keV的电子碰撞5种薄靶K壳层电离截面或L壳层特征X射线产生截面修正系数

Figure 4. The correction factors K for K shell ionization cross sections or L shell characteristic X-ray production cross sections of five thin targets with 5–27 keV electron impact.

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图 5 能量为5—27 keV的电子碰撞Al靶K壳层电离截面. 实心形状为实验值; 实线为DWBA理论值

Figure 5. The K shell ionization cross sections of Al target by 5–27 keV electron impact. The solid shapes are experimental values. The solid line is DWBA theoretical value.

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图 7 能量为12—27 keV的电子碰撞Cu靶K壳层电离截面. 实心形状为实验值; 实线为DWBA理论值

Figure 7. The K shell ionization cross sections of Cu target by 12–27 keV electron impact. The solid shapes are the experimental values. The solid line is DWBA theoretical value.

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图 8 能量为5—27 keV的电子碰撞Cu靶L壳层特征X射线产生截面. 实心方点为实验值; 实线为DWBA理论值

Figure 8. The L shell characteristic X-ray production cross sections of Cu target by 5–27 keV electron impact. Solid squares are the experimental values. The solid line is DWBA theoretical value.

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图 10 能量为13—25 keV的电子碰撞Au靶L壳层特征X射线产生截面. 从上到下分别是Lα, Lβ和Lγ子壳层. 其中, 实心形状为实验值; 实线为DWBA理论值

Figure 10. The Lα, Lβ and Lγ shell characteristic X-ray production cross sections of Au target by 13–25 keV electron impact (from top to bottom). The solid shapes are the experimental values. The solid line is DWBA theoretical value.

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图 6 能量为7—25 keV的电子碰撞Ti靶K壳层电离截面. 实心形状为实验值; 实线为DWBA理论值

Figure 6. The K shell ionization cross sections of Ti target by 7–25 keV electron impact. The solid shapes are the experimental values. The solid line is DWBA theoretical value.

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图 9 能量为7—27 keV的电子碰撞Ag靶L壳层特征X射线产生截面. 实心形状为实验值; 实线为DWBA理论值

Figure 9. The L shell characteristic X-ray production cross sections of Ag target by 7–27 keV electron impact. The solid shapes are the experimental values. The solid line is DWBA theoretical value.

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表 1 靶原子K壳层荧光产额及X射线分支比(提取自PENELOPE程序数据库)

Table 1. Fluorescence yields and X-ray branching ratios of K shell of target atoms (extracted from PENELOPE program database).

Elements	Fluorescence yields	X-ray branching ratios
Elements	ω_K	F_Kα	F_Kβ
Al	0.0371	0.9939	0.0061
Ti	0.2135	0.8979	0.1021
Cu	0.4338	0.8916	0.1084

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表 2 靶原子L壳层荧光产额及Coster-Kronig跃迁概率(提取自PENELOPE程序数据库)

Table 2. Fluorescence yields and Coster-Kronig transition coefficients of L shell of target atoms (extracted from PENELOPE program database).

Elements	Fluorescence yields			Coster-Kronig transition coefficients
Elements	ω_L1	ω_L2	ω_L3	f₁₂	f₁₃	f₂₃
Cu	0.0019	0.0092	0.0088	0.2402	0.5722	0.0089
Ag	0.0149	0.0547	0.0570	0.0921	0.6646	0.1604
Au	0.0823	0.3627	0.3183	0.0700	0.7034	0.1285

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表 3 靶原子L壳层X射线分支比(提取自PENELOPE程序数据库)

Table 3. X-ray branching ratios of L shell of target atoms (extracted from PENELOPE program database).

Elements	X-ray branching ratios
Elements	F_3α	F_1β	F_2β	F_3β	F₁_γ	F₂_γ
Cu	0.4933	0.9430	0.4821	0.0121	0.0000	0.0131
Ag	0.8159	0.8391	0.8509	0.0814	0.1494	0.0862
Au	0.7822	0.7466	0.7989	0.1702	0.2227	0.1786

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表 4 Al, Ti, Cu的K壳层电离截面实验结果

Table 4. Experimental results of K shell ionization cross sections of Al, Ti and Cu.

Incident energies/keV	K-shell ionization cross sections and uncertainties/b
Incident energies/keV	Al		Ti		Cu
5	11720	±580
7	12261	±616	689	±41
8	12378	±621	898	±53
10	12050	±588	993	±55	151	±8
12	10952	±546	1149	±64	219	±12
13	10526	±523	1191	±67	264	±15
15	9982	±488	1211	±67	324	±17
17	9258	±461	1236	±69	377	±20
18	9019	±449	1240	±70	399	±21
20	8495	±415	1256	±70	426	±22
22	7866	±390	1248	±70	448	±24
23	7629	±379	1243	±69	453	±24
25	7283	±355	1232	±68	458	±24
27	6923	±363			467	±25

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表 5 Cu, Ag和Au的L壳层特征X射线产生截面实验结果

Table 5. Experimental results of L shell characteristic X-ray production cross sections of Cu, Ag and Au.

Incident energies/keV	L-shell X-ray production cross sections and uncertainties/b
Incident energies/keV	Cu		Ag		Au-Lα		Au-Lβ		Au-Lγ
5	961	±49
7	883	±45	569	±23
8	842	±43	612	±25
10	770	±39	621	±24
12	719	±37	638	±26
13	704	±36	637	±26	36.9	±2.9	11.3	±1.9
15	653	±33	626	±25	79.1	±4.4	34.5	±2.5
17	601	±31	616	±25	112.9	±6.8	64.4	±4.6
18	587	±30	607	±25	130.5	±8.0	76.0	±5.5
20	558	±28	598	±24	148.7	±8.3	86.4	±5.2	11.6	±1.3
22	520	±27	579	±23	161.8	±9.5	100.5	±6.6	13.6	±1.8
23	505	±26	571	±23	168.8	±10.0	100.2	±6.5	13.8	±1.8
25	474	±24	555	±21	178.1	±9.5	110.9	±6.1	16.3	±1.4
27	452	±23	534	±21

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map

[1]	Powell C J 1976 Rev. Mod. Phys. 48 33 Google Scholar
[2]	Zhao J L, An Z, Zhu J J, Tan W J, Liu M T 2016 J. Phys. B: At. Mol. Opt. Phys. 49 065205 Google Scholar
[3]	Born M 1926 Z. Physik 38 803 Google Scholar
[4]	Truhlar D O, Rice J K, Kuppermann A, Trajmar S 1970 Phys. Rev. A 1 778 Google Scholar
[5]	Shelton W N, Leherissey E S, Madison D H 1971 Phys. Rev. A 3 242 Google Scholar
[6]	Madison D H, Shelton W N 1973 Phys. Rev. A 7 499 Google Scholar
[7]	Rainer H 1990 Phys. Lett. A 144 81
[8]	Bely O, Schmartz S B 1969 Astron. Astrophys. 1 281
[9]	Sampson D H 1986 Phys. Rev. A 34 986 Google Scholar
[10]	Fontes C J 1993 Phys. Rev. A 47 1009 Google Scholar
[11]	Segui S, Dingfelder M, Salvat F 2003 Phys. Rev. A 67 062710 Google Scholar
[12]	Colgan J, Fontes C J, Zhang H L 2006 Phys. Rev. A 73 062711 Google Scholar
[13]	Bote D, Salvat F 2008 Phys. Rev. A 77 042701 Google Scholar
[14]	Llovet X, Powell C J, Salvat F, Jablonski A 2014 J. Phys. Chem. Ref. Data 43 013102 Google Scholar
[15]	Shima K, Nakagawa T, Umetani K, Mikumo T 1981 Phys. Rev. A 24 72 Google Scholar
[16]	Shima K, Okuda M, Suzuki E, Tsubota T, Mikumo T 1983 J. Appl. Phys. 54 1202 Google Scholar
[17]	Llovet X, Merlet C, Salvat F 2000 J. Phys. B:At. Mol. Opt. Phys. 33 3761 Google Scholar
[18]	Bote D, Llovet X, Salvat F 2008 J. Phys. D:Appl. Phys. 41 105304 Google Scholar
[19]	Moy A, Merlet C, Llovet X, Dugne O 2013 J. Phys. B:At. Mol. Opt. Phys. 46 115202 Google Scholar
[20]	Qian Z C, Wu Y, Chang C H, Yuan Y, Mei C S, Zhu J J, Moharram K 2017 EPL 118 13001 Google Scholar
[21]	Liang S, Wu Y, Zhao Z, Xia X G, Ke Z X, Pan M, Wang B Y, Zhang P 2021 Radiat. Phys. Chem. 180 109321 Google Scholar
[22]	Merlet C, Llovet X, Fernandez-Varea J M 2006 Phys. Rev. A 73 062719 Google Scholar
[23]	Merlet C, Llovet X, Salvat F 2004 Phys. Rev. A 69 032708 Google Scholar
[24]	An Z, Li T H, Wang L M, Xia X Y, Luo Z M 1996 Phys. Rev. A 54 3067 Google Scholar
[25]	Luo Z M, An Z, He F Q, Li T H, Long X G, Peng X F 1996 J. Phys. B:At. Mol. Opt. Phys. 29 4001 Google Scholar
[26]	Zhao J L, An Z, Zhu J J, Tan W J, Liu M T 2017 Radiat. Phys. Chem. 134 71 Google Scholar
[27]	Zhao J L, Bai S, An Z, Zhu J J, Tan W J, Liu M T 2020 Radiat. Phys. Chem. 171 108722 Google Scholar
[28]	Zhu J J, An Z, Liu M T, Tian L X 2009 Phys. Rev. A 79 052710 Google Scholar
[29]	Zhao J L, Tian L X, Li X L, An Z, Zhu J J, Liu M T 2015 Radiat. Phys. Chem. 107 47 Google Scholar
[30]	Wu Y, Liang Y, Xu M X, Yuan Y, Chang C H, Qian Z C, Wang B Y, Kuang P, Zhang P 2018 Phys. Rev. A 97 032702 Google Scholar
[31]	李颖涵, 安竹, 朱敬军, 李玲 2020 69 133401 Google Scholar Li Y H, An Z, Zhu J J, Li L 2020 Acta Phys. Sin. 69 133401 Google Scholar
[32]	Li L, An Z, Zhu J J, Lin W P, Williams S 2021 Nucl. Instrum. Methods Phys. Res. B 506 15 Google Scholar
[33]	樊启文, 许国基, 杜英辉, 张榕 2008 原子能科学技术 42 925 Fan Q W, Xu G J, Du Y H, Zhang R 2008 Atom. Energ. Sci. Technol 42 925
[34]	Han J F, An Z, Zheng G Q, Bai F, Li Z H, Wang P, Liao X D, Liu M T, Chen S L, Song M J 2018 Nucl. Instrum. Methods Phys. Res. B 418 68 Google Scholar
[35]	Liu B, Ding W, An Z, Zhu J J, Zhang Z, Li L, Lin W P 2021 Fusion Eng. Des. 172 112751 Google Scholar
[36]	Sabbatucci L, Scot V, Fernandez J E 2014 Radiat. Phys. Chem. 104 372 Google Scholar
[37]	Salvat F, Fernández-Varea J, Sempau J 2008 PENELOPE-2008, A Code System for Monte Carlo Simulation of Electron and Photon Transport (Issy-les-Moulineau: OECD/NEA Data Bank)
[38]	Perkins S T, Cullen D E, Chen M H, Hubbell J H, Rathkopf J, Scofield J 1991 Report UCRL-50400 30 Lawrence Livermore National Laboratory, Livermore, CA
[39]	Mei C S, Wu Y, Yuan Y, Chang C H, Qian Z C, Zhu J J, Moharram K 2016 J. Phys. B: At. Mol. Opt. Phys. 49 245204
[40]	Silvina P L, Vasconcellos M A Z, Ruth H, Jorge C T 2012 Phys. Rev. A 86 042701 Google Scholar
[41]	He F Q, Peng X F, Long X G, Luo Z M, An Z 1997 Nucl. Instrum. Methods Phys. Res. B 129 445 Google Scholar
[42]	周长庚, 付玉川, 安竹, 罗正明 2000 强激光与粒子束 12 601 Zhou C G, Fu Y C, An Z, Luo Z M 2000 High Power Laser and Particle Beams 12 601
[43]	Zhao J L, An Z, Zhu J J, Tan W J, Liu M T 2016 Radiat. Phys. Chem. 122 66 Google Scholar
[44]	Campbell J L 2003 At. Data Nucl. Data Tables 85 291 Google Scholar
[45]	Wu Y, An Z, Liu M T, Duan Y M, Tang C H, Luo Z M 2004 J. Phys. B:At. Mol. Opt. Phys. 37 4527 Google Scholar
[46]	Sepúlveda A, Bertol A P, Vasconcellos M A Z, Trincavelli J, Hinrichs R, Castellano G 2014 J. Phys. B:At. Mol. Opt. Phys. 47 215006 Google Scholar
[47]	Campos C S, Vasconcellos M A Z 2002 Phys. Rev. A 66 012719 Google Scholar

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Vol. 71, Issue 17 - 2022-09-05

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