One step of the manufacturing of silicon solar cells is the molecular diffusion (doping) of elemental phosphorous (P) into crystalline silicon to make an n-type semiconductor. This Pdoped layer needs to be at least 0.467 μm into the 200-μm thick wafer. The present diffusion process is carried out at 1000^oC. Data for the total amount of phosphorous atoms loaded into the silicon wafer vs. time at 1000^oC are presented in the figure below. The maximum solubility of phosphorous within crystalline silicon is 1.0 × 10²¹P atoms/cm³at 1000^oC. The square silicon wafer has a surface area of 100 cm²(10 cm/side). Initially, there is no phosphorous impurity in the crystalline silicon. What is the concentration of P atoms (atoms P/cm³) doped into the silicon at a depth of 0.467 μm after 40 min, based on the data provided?

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6.0E+18 5.0E+18 4.0E+18 3.0E+18 2.0E+18 1.0E+18 0.0E+00 100 20 40 60 80 t1/2 (sec)2 ma(t) (total atoms P in silicon)