$5\mathrm{.}25$ Indium atoms are diffused into the silicon wafer through the two$-$step heat treatment of pre$-$deposition and inlay. It is known that the background concentration of indium in the silicon material is $2\backslash$times $1020$ atoms$/$m$^3.$ The inlay heat treatment was performed at $1175\backslash$deg C for $2\mathrm{.}0$ h$,$ and the inlay depth x was obtained at $2\mathrm{.}35$m$.$ If the surface concentration is maintained at $2\mathrm{.}5$x$1026$ atoms$/$m$^3,$ calculate the time required for pre$-$deposition diffusion at $925\backslash$deg C$.$ It is known that the diffusion of impurity in silicon is $3\mathrm{.}63$ eV$/$ atom; the value of Do is $7\mathrm{.}85\backslash$times $10-5$ m$^2/$s$.$