2. In the fabrication of a p-type semiconductor, elemental boron is diffused a small distance into a solid crystalline silicon wafer. The boron concentration within the solid silicon determines the semiconducting properties of the material. A physical deposition process keeps the concentration of elemental boron at the surface of the water equal t

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2. In the fabrication of a p-type semiconductor, elemental boron is diffused a small distance into a solid crystalline silicon wafer. The boron concentration within the solid silicon determines the semiconducting properties of the material. A physical deposition process keeps the concentration of elemental boron at the surface of the water equal to

5.0 \times 1 0^{20}

atoms boron

/ cm^{3}

silicon. In the manufacture of a transistor, it is desired to produce a thin film of silicon doped to a boron concentration of at least

1.7 \times 1 0^{19}

atoms boron/

cm^{3}

silicon at a depth of

0.2 μ m

from the surface of the silicon wafer. It is desired to achieve this target within a 30 -min processing time. The density of solid silicon is

5.0 \times 1 0^{22}

atoms

Si / cm^{3}

solid. At what temperature must the boron doping process be operated? It is known that the temperature dependence of the diffusion coefficient of boron

(A)

in silicon

(B)

is given by:

D_{A B} = D_{0} e^{- Q_{0} / RT}

where

D_{0} = 0.019 cm^{2} / s

and

Q_{0} = 2.74 \times 1 0^{5} J / g

mol for elemental boron in solid silicon. The thermodynamic constant

R = 8.314 J / g mol / K

.

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