### High Concentration

The above calculation assumes that the diffusivity is constant in time and space. This is often true for lower concentrations, but diffusivity usually varies spatially with high concentrations.### Predeposition

Because predeposition introduces dopants at solid-solubility concentration, the warning above nearly always applies to predepositions, which means that the actual predeposition will be deeper than given by this calculation, which is a solution to the diffusion equation (Fick's Law).**Advanced Predep Models**: These advanced (non-constant D) models for Boron, Arsenic and Phosphorus provide a more realistic diffusion profile, and also calculate the approximate diffusion depth and sheet resistance. Subsequent diffusion step is not performed on these profiles. Antimony model not available. Data should be considered approximate, but illustrates the magnitude of diffusion enhancement at high concentrations. Phosphorus model is not considered reliable.

### Implant Damage

Ion implants produce crystal damage, which leads to a temporal transient in diffusion. This transient can magnify the diffusivity by orders of magnitude for a time period following the implant. The effect is not accounted for in this calculation. This effect can be minimized by performing a rapid thermal anneal (RTA).### Concurrent Oxidation

Anealing in an oxidizing ambient (IE: growing an oxide during the anneal) will perturb the diffusion, and is not considered here.### Crystal Channeling

The implant produced in this calculation is a gaussian, which is a very good approximation to most real implant profiles. However it does not account for atoms travelling in crystal channels. Still, the ion implant is a reasonable approximation over a wide variety of conditions, usually with the <100>-oriented wafer tilted 7 degrees from normal. (often a default for ion implantation)

Yes. The implant prediction is reasonably accurate for a 7 degree implant. For a predep, you can be reasonably certain that the simple model is giving a lower limit of diffusion depth. If you need a junction deeper than a certain value, this calculation offers guidance. For the implant transient, likewise you can assume that the actual diffusion will be greater than predicted here if implant damage is present. An implant followed by a long time diffusion should produce reasonable results, and implant followed by a short RTA should be reasonable to first order.

Eric Perozziello ©2013-2014. All Rights Reserved.