$4.$ An n$-$type Si wafer has been doped uniformly with $1017$ phosphorus $($P$)$ atoms cm$3.$ Calculate the position of the Fermi energy with respect to the Fermi energy EFi in intrinsic Si$.$ The above n$-$type Si sample is further doped with $51018$ boron atoms cm$3.$ Calculate the position of the Fermi energy with respect to the Fermi energy EFi in intrinsic Si at room temperature $(300$ K$),$ and hence with respect to the Fermi energy in the n$-$type case above.