A chip design calls for a phosphorus-doped layer reaching about into a silicon wafer…

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Condensed Matter Physics, Ch Real crystals: vacancies, dislocations and the strength of metals

Problem

A chip design calls for a phosphorus-doped layer reaching about

150\ \mathrm{nm}

into a silicon wafer after a single drive-in anneal at

1050\,{}^\circ\mathrm{C}

. Phosphorus in silicon has

D_0 = 3.85\ \mathrm{cm^2\,s^{-1}}

and

Q = 3.66\ \mathrm{eV}

(Section 13.3). Using the order-of-magnitude convention

\sqrt{Dt}

for the diffusion distance, estimate how long the anneal must run.

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