Aluminum atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of Al in this silicon material is known to be 3× 1019 atoms/m3. The drive-in diffusion treatment is to be carried out at 1050°C for a period of4.0 h, which gives a junction depth xj of 3.0 μm. Compute the predeposition diffusion time at950°C if the surface concentration is maintained at a constant level of 2 × 1025 atoms/m3. Forthe diffusion of Al in Si, values of Qd and D0 are 3.41 eV and 1.38 × 10-4 m2/s, respectively.