Ion Implantation Range Calculator

Reviewed By: Patrick Myers (BSME)

Enter the implant energy and stopping power into the calculator to estimate the projected range (Rp) of ion implantation. Note: this calculator uses a constant-stopping-power approximation; accurate implantation ranges are typically obtained from energy-dependent models/tables (for example SRIM/TRIM-style results).

Ion Implantation Range Calculator

Range (mass stopping power)

Simplified Range

Range & Straggle (Si/SiO2)

Enter any 3 values to calculate the missing variable (Rp ≈ E / (ρ · S_m))

Target material preset (sets Density) Implant orientation preset (for depth along surface normal) Projected Range (Rp)

Implant Energy (E)

Density of Target Material (ρ)

Mass Stopping Power (S_m)

Related Calculators

Ion Implantation Range Formula

The projected range (Rp) is typically found by integrating energy loss with depth. If you assume the stopping power is approximately constant over the energy interval (a rough approximation), you can estimate range using either of these equivalent forms:

R_p \approx \frac{E}{dE/dx} \approx \frac{E}{\rho\,S_m}

Variables:

Rp is the projected range (approximate mean depth along the ion’s travel direction)
E is the implant energy
dE/dx is the (linear) stopping power (energy loss per unit length)
ρ is the density of the target material
S_m is the mass stopping power (often tabulated in units like MeV·cm²/g), where dE/dx = ρ·S_m

To estimate Rp, divide the implant energy (E) by the stopping power. If you have mass stopping power values, multiply by density first (since dE/dx = ρ·S_m), then divide: Rp ≈ E/(ρ·S_m).

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 outline how to estimate the Ion Implantation Range using a constant stopping-power approximation.

Determine the implant energy (E).
Determine the stopping power: either linear stopping power (dE/dx) or mass stopping power (S_m).
If using mass stopping power, determine the target density (ρ) and compute dE/dx = ρ·S_m.
Compute the projected range using Rp ≈ E/(dE/dx) (equivalently Rp ≈ E/(ρ·S_m) when using mass stopping power).
After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge (mass stopping power form).

Implant Energy (E) = 150 keV

Density of Target Material (ρ) = 2.33 g/cm³

Mass Stopping Power (S_m) = 1500 MeV·cm²/g

Estimated Projected Range: Rp ≈ E/(ρ·S_m) = 0.150 MeV / (2.33×1500 MeV/cm) ≈ 4.29×10^-5 cm ≈ 0.429 µm