Estimate ion implantation path length from implant energy and stopping power, or calculate a Gaussian dopant concentration profile from Rp and straggle.

E/S is a constant-stopping path-length estimate. It does not predict the projected implant depth Rp from ion and target properties. Use traceable transport data for Rp and straggle.

Related Calculators

Ion Implantation Range Formula

Integrating inverse stopping power over energy estimates CSDA path length, not projected depth. Ion scattering makes projected range a separate transport quantity. With a constant positive stopping power S (a rough approximation), the path length L is:

L โ‰ˆ (E) / (S) โ‰ˆ (E) / (ฯ Sโ‚˜)

Variables:

  • L is the path-length estimate; it is not the projected range Rp along the initial direction
  • E is the implant energy
  • S = โˆ’dE/ds is positive linear stopping power (energy lost per unit path length)
  • ฯ is the density of the target material
  • Sm is the mass stopping power (often tabulated in units like MeVยทcmยฒ/g), where S = ฯยทSm

To estimate constant-stopping path length L, divide ion energy by positive linear stopping power. If using mass stopping power, multiply by density first: S = ฯยทSm, then L โ‰ˆ E/(ฯยทSm). Projected Rp and straggle for the Gaussian mode must come from a measurement, table or transport model.

What is Ion Implantation?

Ion implantation is a process used in semiconductor device fabrication to introduce impurities into a substrate, typically silicon, to modify its electrical properties. This is achieved by accelerating ions to high velocities and directing them into the substrate. The depth and concentration of the implanted ions can be precisely controlled, making ion implantation a critical step in the manufacturing of integrated circuits and other semiconductor devices. The projected range (Rp) is an important parameter in ion implantation, as it describes the approximate depth at which the ions come to rest within the target material.

How to Calculate Ion Implantation Range?

The following steps estimate constant-stopping path length. They do not predict projected implant depth from ion and target properties.

  1. Determine the implant energy (E).
  2. Determine the stopping power: either linear stopping power (dE/dx) or mass stopping power (Sm).
  3. If using mass stopping power, determine target density and compute positive linear stopping power S = ฯยทSm in compatible units.
  4. Compute path length using L โ‰ˆ E/S. The energy and stopping inputs must refer to the same ion, target and energy interval.
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following illustrative values (mass stopping power form). The linear stopping input is 349.5 eV/nm; this is not a tabulated ion/material prediction.

Implant Energy (E) = 150 keV

Density of Target Material (ฯ) = 2.33 g/cmยณ

Mass Stopping Power (Sm) = 1500 MeVยทcmยฒ/g

Estimated constant-stopping path length: L โ‰ˆ E/(ฯยทSm) = 0.150 MeV / (2.33ร—1500 MeV/cm) โ‰ˆ 4.29ร—10-5 cm โ‰ˆ 0.429 ยตm