Yukub

First thing to remember, is that most enhanced energy weapons have line of sight ranges for thremal and radiation pulses. That means that a nuclear weapon detonated at 5,000 meters (about 16,000 feet) will irradiate or set alight anything within a radius of 50 miles. While that sounds large, it is less than one thousanddth of one percent of the planet's surface.

To do what you suggest, you need not one bomb, but severa scattered all over the planetl.

Back in the seventies, they envisioned a 'doomsday' device which consisted of 50 missiles each with a 100 megaton weapon with a cobalt/ thorium sheath set where prevailing winds would cause the maximum spread. The detonation would cause the thorium to suck up the raqdiation of the blast which would be transferred to the cobalt releasing cobalt isotopes with a half life of approximately fifty years as fallout.