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 of 4.0 h, which gives a junction depth x_j of 3.0 mm. Compute the predeposition diffusion time at 950°C if the surface concentration is maintained at a constant level of 2 × 10²⁵ atoms/m³. For the diffusion of Al in Si, values of Q_d and D₀ are 3.41eV and 1.38 × 10^-4 m²/s, respectively.