Home Knowledge Base Arrhenius relationship

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.

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