Section: 12 | Electron Stopping Powers |

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ELECTRON STOPPING POWERS

Cedric J. Powell

Numerical data are given for mass collision electron stopping powers in 41 elemental solids for energies between 100 eV and 30 keV. These stopping powers were determined with an algorithm that utilizes experimental optical data for each solid.

The stopping power for electrons and other charged particles in matter is often needed in calculations of electron transport in a medium, particularly in radiation physics and in descriptions of signal generation in analytical techniques such as electron-probe microanalysis and Auger electron spectroscopy. The stopping power is defined as the average rate at which the charged particles lose energy at any point along their trajectories. For electrons, it is customary to separate the total stopping power into two components, the collision stopping power due to inelastic-scattering events of the electrons in a medium and the radiative stopping power due to the emission of bremsstrahlung in the electric field of the atomic nucleus and atomic electrons (Ref. 1). For electron energies less than 30 keV, the radiative stopping power is less than 1% of the collision stopping power (Ref. 1) and is neglected in the numerical data given here.

Numerical data for collision and radiative stopping powers at electron energies between 10 keV and 1 GeV have been published for materials of interest in radiation physics and dosimetry (Ref. 1). Similar data can also be obtained from a Web site of the National Institute of Standards and Technology (Ref. 2). The collision stopping powers were calculated from the theory of Bethe (Refs. 3,4) and recommended values of the one material-dependent parameter, the mean excitation energy (Ref. 1). While the Bethe theory is expected to be valid for electron energies much larger than the largest K-shell binding energy of atoms in the particular material, the Bethe stopping-power equation is frequently utilized to calculate stopping powers for energies of 10 keV and above (Refs. 1,2). Detailed analyses of the Bethe stopping-power theory have been published (Refs. 1, 4).

The table below gives mass collision stopping powers for 41 elemental solids at energies between 100 eV and 30 keV (Ref. 5). The mass collision stopping power is the collision stopping power divided by the mass density of the solid. The mass collision stopping powers in the table were determined by interpolation with a clamped cubic spline from the published data (Ref. 5), which had been calculated with an algorithm that utilizes experimental optical data for each solid. Comparisons with collision stopping powers from the Bethe stopping-power equation showed root-mean-square differences of 9.1% and 8.7% for energies of 9.897 keV and 29.733 keV, respectively (Ref. 5). This level of agreement was considered satisfactory on account of uncertainties of the algorithm and optical data used for the calculations as well as uncertainties of the mean excitation energies used with the Bethe equation. The mass collision stopping powers in the table are given in units of MeV cm²/g for a range of relativistic kinetic energies. The elemental solids are listed in order of element symbol.

References

Stopping Powers for Electrons and Positrons, ICRU Report 37 (International Commission on Radiation Units and Measurements, Bethesda, MD, 1984).
Berger, M. J., Coursey, J. S., Zucker, M. A., and Chang, J., Stopping-Power and Range Tables for Electrons, Positrons, and Helium Ions, Version 1.2.3, 2005 <http://www.nist.gov/pml/data/star/index.cfm>.
Bethe, H., Ann. Physik 5, 325, 1930. [https://doi.org/10.1002/andp.19303970303]
Inokuti, M., Rev. Mod. Phys. 43, 297, 1971. [https://doi.org/10.1103/RevModPhys.43.297]
Shinotsuka, H., Tanuma, S., Powell, C. J., and Penn, D. R., Nucl. Instr. Methods Phys. Res. B 270, 75, 2012. [https://doi.org/10.1016/j.nimb.2011.09.016]

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Mass Collision Stopping Powers in MeV cm²/g for the Indicated Relativistic Electron Kinetic Energies (Ref. 5)

Element	Name	100 eV	200 eV	300 eV	400 eV	500 eV	1000 eV	1500 eV	2000 eV	3000 eV	4000 eV	5000 eV	10000 eV	15000 eV	20000 eV	30000 eV
Continued on next page...
Ag	Silver	66.9	94.9	95.5	87.0	78.7	54.7	44.3	38.5	31.1	26.2	22.8	14.3	10.7	8.71	6.54
Al	Aluminum	187.6	142.8	127.1	118.1	110.7	83.8	67.5	56.7	43.4	35.5	30.2	18.2	13.5	10.9	8.08
Au	Gold	41.7	52.1	49.7	45.5	41.7	31.1	26.0	22.8	18.7	16.0	14.1	9.21	7.12	5.94	4.58
Be	Beryllium	342.2	257.8	210.0	183.5	165.7	113.5	87.4	71.6	53.3	42.9	36.2	21.0	15.2	12.1	8.82
Bi	Bismuth	47.8	56.8	56.1	51.9	47.5	34.2	28.2	24.6	20.2	17.4	15.3	10.0	7.65	6.34	4.87
C^a	Carbon	251.3	218.8	183.9	158.4	139.8	92.5	73.9	62.4	48.1	39.4	33.6	20.0	14.7	11.8	8.60
C^b	Carbon (graphite)	343.5	296.1	246.2	210.6	184.6	118.9	92.1	76.2	57.5	46.7	39.5	23.2	16.9	13.5	9.84
C^c	Carbon (diamond)	262.2	249.6	212.4	183.6	162.0	106.1	83.0	69.0	52.4	42.7	36.2	21.4	15.6	12.5	9.12
Co	Cobalt	82.0	97.7	96.4	90.8	84.7	62.3	49.5	41.5	32.1	26.8	23.3	14.7	11.0	8.96	6.67
Cr	Chromium	97.4	104.1	96.9	88.5	81.0	57.4	45.3	38.1	30.1	25.5	22.3	14.0	10.5	8.51	6.34
Cs	Cesium	80.3	63.5	59.6	58.1	54.1	37.8	29.8	25.1	19.8	16.9	14.9	9.90	7.60	6.26	4.74
Cu	Copper	68.1	76.4	76.5	73.9	70.7	55.5	45.3	38.5	30.0	25.0	21.8	13.9	10.5	8.60	6.43
Dy	Dysprosium	75.7	78.4	70.3	63.6	58.6	43.9	35.6	30.3	23.8	19.8	17.2	11.1	8.52	7.02	5.32
Fe	Iron	80.4	86.2	83.7	78.7	73.7	54.8	43.9	37.0	28.9	24.4	21.3	13.6	10.2	8.31	6.20
Gd	Gadolinium	72.2	66.5	58.9	53.4	49.8	37.8	30.7	26.2	20.6	17.3	15.0	10.0	7.74	6.42	4.89
Ge	Germanium	90.4	79.3	73.7	69.8	66.5	53.6	44.7	38.4	30.2	25.1	21.7	13.8	10.5	8.55	6.41
Hf	Hafnium	42.6	51.0	48.0	44.7	41.9	32.9	27.7	24.2	19.6	16.6	14.5	9.48	7.39	6.15	4.72
In	Indium	62.6	74.7	75.4	69.7	63.4	43.7	34.7	29.5	23.9	20.5	18.1	11.7	8.88	7.27	5.50
Ir	Iridium	39.3	47.0	44.6	40.9	37.9	29.4	25.1	22.2	18.3	15.7	13.9	9.07	7.04	5.88	4.53

^a Glassy carbon
^b Graphite
^c Diamond

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ELECTRON STOPPING POWERS

References