diffusion coefficient

The diffusion coefficient (D) quantifies how fast dopant atoms move through a material, depending strongly on temperature and the specific dopant-substrate combination. **Arrhenius relationship**: D = D0 * exp(-Ea/kT), where D0 is pre-exponential factor, Ea is activation energy, k is Boltzmann constant, T is absolute temperature. **Temperature sensitivity**: D changes by roughly 2-3x for every 25 C change. Extremely sensitive to temperature control. **Dopant comparison in Si**: Boron diffuses fastest among common dopants. Phosphorus intermediate. Arsenic slow. Antimony slowest. **Typical values at 1000 C**: B: ~2x10^-14 cm²/s. P: ~3x10^-14 cm²/s. As: ~5x10^-15 cm²/s. Sb: ~8x10^-16 cm²/s. **Mechanisms**: **Vacancy-mediated**: Dopant moves by exchanging with crystal vacancies (As, Sb). **Interstitial-mediated**: Dopant kicks out a Si atom and moves via interstitial sites (B, P). **Concentration dependence**: At high doping levels (>10^19/cm³), D becomes concentration-dependent. Electric field enhancement (built-in field) accelerates diffusion. **Transient Enhanced Diffusion (TED)**: Implant damage creates excess interstitials that temporarily increase B and P diffusivity by 10-1000x during initial anneal. **Material dependence**: D in SiO2 much lower than in Si for most dopants. Oxide blocks diffusion (except B through thin oxide). **Process implications**: Junction depth = f(D, time, temperature). All thermal steps contribute to total dopant diffusion.