banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02–200 keV
Rent this article for


Image of FIG. 1.
FIG. 1.

Comparison of the differential angular cross section (per atom) for 50 eV electrons in molecule (full circles) calculated using the data of Bettega et al. (Ref. 16) to those calculated using the tabulation of ICRU-77 (Ref. 14) in silicon (open triangles) and in carbon and sulfur (open squares). We use .

Image of FIG. 2.
FIG. 2.

The elastic IMFP in silicon as a function of electron energy.

Image of FIG. 3.
FIG. 3.

The IMFP for inelastic electron scattering in silicon as a function of electron energy . The full and dotted lines show the results of our calculations and those of Ziaja et al. (Ref. 29), respectively. The symbols are experimental data of Powell and Jablonski (Ref. 30) and Tanuma et al. (Ref. 31).

Image of FIG. 4.
FIG. 4.

The backscattering coefficients and for silicon (at normal incidence) as a function of . The two dashed curves for are our results for two separation energies and . The full line shows the results of Eq. (1). The circles and the crosses are for the experimental results of Martin et al. (Ref. 43) and Hoedl (Ref. 34), respectively. The diamonds and the triangles present the results of PENELOPE and GEANT4 simulations, respectively, taken from Ref. 43. The lower curve with open stars shows our calculated .

Image of FIG. 5.
FIG. 5.

The angular dependence of the backscattering coefficient for electrons with energies , 10, and 100 keV, incident on a silicon surface at different angles . The lines were computed using Eq. (2). The symbols show the results of our MC simulations.

Image of FIG. 6.
FIG. 6.

Illustration of the method to estimate the extrapolated ranges in silicon from the calculated electron transmission curve and the energy deposition curve scaled to its maximum. is the depth into the material. The plots are for 1 keV electrons normally incident on silicon.

Image of FIG. 7.
FIG. 7.

The different electron ranges in silicon described in the text as a function of incident electron energy . The dashed line demonstrates the asymptotic dependence proportional to at high energies.

Image of FIG. 8.
FIG. 8.

The ratio for silicon of calculated by Brigida et al. (Ref. 49) and our calculated using Eq. (6) to the experimental of Everhart and Hoff (Ref. 46) extended up to 200 keV.

Image of FIG. 9.
FIG. 9.

Energy dependence of the projected range in silicon scaled to its value at normal incidence for incidence directions of , 45°, 60°, and 80° from the normal.

Image of FIG. 10.
FIG. 10.

Transmission curve for 100 keV electrons normally incident on silicon face. Our simulated curve and the fit using Eq. (9) are shown as full and dashed lines, respectively. The curve with open squares is the EMID tabulation (Ref. 50). Note that here is in microns.

Image of FIG. 11.
FIG. 11.

Deposited energy distribution for 100 keV electrons in silicon. The full line and the dashed line show, respectively, our MC results and our fit using Eqs. (6) and (10)–(12). The curve with open squares is the EMID tabulation (Ref. 50).

Image of FIG. 12.
FIG. 12.

The cumulative spherical radial energy distributions in silicon scaled by the incident electron energy . The curves from the top to the bottom are for , 0.2, 0.5, 1, 2, 5, and 10 keV.

Image of FIG. 13.
FIG. 13.

Contour plots of in silicon for three values of incident electron energy: 100 eV (top), 1 keV (middle), and 10 keV (bottom).

Image of FIG. 14.
FIG. 14.

Deposited energy distributions as a function of depth of penetration in an infinite silicon medium for different incident electron energies: 100 eV and 1 keV (bottom and left axes) and for 10 keV (upper and right axes).

Image of FIG. 15.
FIG. 15.

Temporal evolution of the spectrum (per primary electron) of the first generation of -electrons, generated directly by a primary electron with energy of 5 keV in silicon. The -electron energy is with respect to the bottom of the conduction band. The arrows indicate the positions of the plasmon (denoted as 1), Si-LVV Auger (2), and Si-KLL Auger (3) peaks.

Image of FIG. 16.
FIG. 16.

The time dependence of the LVV Auger-electron yield (per primary electron) in the cascade process for different electron energies in silicon.

Image of FIG. 17.
FIG. 17.

The time dependence of the average energy and average number (both per incident electron) of cascading hot electrons (i.e., with energy of ) in an infinite silicon medium for different incident electron energies . The curves are (from top to bottom) for , 5, 1, 0.5, 0.2, 0.1, and 0.05 keV.

Image of FIG. 18.
FIG. 18.

The total number of cascading electrons , including those that have already stopped, in an infinite silicon medium for different values.

Image of FIG. 19.
FIG. 19.

Lateral electron density at different times due to a single electron with ejected by an energetic ion propagating in the -direction in an infinite silicon medium.

Image of FIG. 20.
FIG. 20.

The Debye length in silicon as a function of the radial distance from the track axis for 5 MeV/amu Xe and Ne ions at different times. The symbols are identical to those shown in Fig. 19.


Generic image for table
Table I.

The coefficients to be used in Eq. (10) to calculate the twice-scaled depth distribution for the deposited energy.


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02–200 keV