PARAMETERS THAT INFLUENCE DIFFUSIVITY

• Diffusion constant or diffusivity is a paramater that appears in Fick's first law , giving the dependence of flux on concentration gradient.
• Depends on:
• Diffusion mechanism - the interstitial mechanism is faster than substitutional (atomistic models of diffusion), due to the fact that the impurities can travel further through the interstitials without requiring much energy.
• Temperature - with increasing the temperature, the diffusivity increases, because the atoms thermal energy increases, thus they can diffuse faster
• Diffusivity depends on temperature following an Arhenius type formula:, where E_a is the activation energy = the energy required to break the bonds between the atoms. (see picture below)

• Type of crystal structure and crystal imperfections:

  • Interstitial diffusion easier in BCC than in FCC, due to a lower density in BCC

  • Defects and imperfactions enhance diffusion:

    • grain boundaries

    • dislocation lines

    • excess vacancies

• Concentration and type of diffusing species: P, As, B

  • Arsenic has a lower diffusion constant than phosphorous, thus it is used for low doping. It can be observed that a saturation appears, the concentration cannot be increased with increasing the temperature or surface concentration.

  • For high concentrations it can be observed a diffusion constant enhancement for As

  • There is a kink for phosporous doping profile noticeable, several explanations are possible

    In the lower picture were plotted several profiles for various dopants. It can be observed the different shape, due to different diffusivity and diffusion mechanism

• Other phenomena that influence the diffusion process:
  • Electric field (Impurities are charges that move due to the electric field created by charge gradient). The flow formula is then slightly changed:

• Due to oxidation or nitridization
  • B, P diffuse through interstitials - higher D at oxidation, when interstials are created
  • As diffuse through vacancies - higher D at nitridization, when vacancies are created