Plot the dopant concentration profile of a 2000 long silicon rod grown by the floatzone technique using P as a dopant in a core doping scheme for various lengths of the floating zone. Assume the dopant concentration in the core to be 10¹⁹ cm^-3 and the radius of the core to be four times smaller than that of the final rod. Which one results in a more uniform doping profile: a long float-zone or a short one?