Ion implantation profile calculator (Rp, peak concentration, junction depth)
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KEY POINTS
An implanted dopant profile can be approximated by a Gaussian centered on the projected range Rp with standard deviation ΔRp. The peak concentration is about 0.4 × dose / ΔRp, and the junction depth is where the profile meets the substrate doping. At the same 100 keV, boron's Rp is about 300 nm and arsenic's about 60 nm, five times apart; shallow junctions often use BF₂⁺ to cut the effective boron energy to 11/49.
Inputs
Concentration profile
The Gaussian is a first-order approximation. Real boron profiles have a tail on the deep side (Pearson IV distribution), and channeling along crystal directions extends the tail further. Activation annealing broadens the profile by diffusion, so the junction depth here is the as-implanted value.
Projected range Rp / ΔRp (nm)
| Energy | Boron | Phosphorus | Arsenic |
|---|---|---|---|
| 5 keV | 17 / 10 | 8 / 4 | 6 / 2 |
| 10 keV | 33 / 17 | 14 / 7 | 10 / 4 |
| 20 keV | 66 / 28 | 25 / 12 | 16 / 6 |
| 50 keV | 161 / 50 | 61 / 26 | 32 / 12 |
| 100 keV | 299 / 71 | 124 / 46 | 58 / 21 |
| 200 keV | 523 / 96 | 254 / 78 | 110 / 38 |
Reading an implant profile
Implanted ions lose energy through collisions with silicon atoms until they stop. The spread of stopping depths is roughly normal; its mean is the projected range Rp and its standard deviation ΔRp. Light boron goes deep and spreads out, while heavy arsenic stops shallow and sharp, so at the same energy boron's Rp is about five times that of arsenic.
Taking dose Φ as the area under the distribution, the peak concentration is about 0.4Φ/ΔRp. Lowering the energy is the basic way to make shallow junctions, but low-energy boron beams deliver little current, so heavier BF₂⁺ is often used to cut the energy carried by the boron to 11/49.
FAQ
Why use BF₂⁺ instead of B⁺ for shallow junctions?
The boron atom carries only 11/49 of the BF₂⁺ ion's energy, so a shallow implant can be done at a higher beam energy, where beam current is easier to obtain.
Is the Gaussian profile accurate?
It is a first-order approximation. Real boron profiles have a deep tail (Pearson IV), channeling extends it further, and annealing broadens the profile by diffusion.
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Last updated: October 23, 2026