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 deter mines semiconducting properties of the material. A physical vapor deposition process keeps the concentration of elemental boron at the surface of the wafer equal to 5.0 × 10²⁰atoms boron/cm³silicon. 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 × 10¹⁹atoms boron/cm³silicon at a depth of 0.20 microns (µm) 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 can be stated as 5.0 × 10²²atoms Si/cm³solid. 

a. 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 

where D_o = 0.0 19 cm2^/s and Q_o = 2.74 · 10⁵ J/gmole for elemental boron in solid silicon. The thermodynamic con stant R = 8.314 J/gmole · K. 

b. What is the flux of boron atoms at the silicon wafer surface at 10 min vs. 30 mm?

Transcribed Image Text:

|DAB = D¸·e-Qo/RT