Hi ojim,
SN74AHCT1G02 (OR Gate) has typ. 2.4ns to 4.5ns switching times from input to output, but with the absence of heavy capacitive loads. Rise/fall times of the outputs are not defined, but should be inside these margins, input tr/tf must be inside 100ns.
ACT Logic has output transition times inside 3ns at 5V at output loads less than 50pF. But the ouput will over-/undershoot, if it is not terminated properly and the ipedance of the power supply is too high. Try a variable series resistor to dampen ringing.
Another solution would be an ultrafast current feedback amp with slew rates beyond 1000V/us. See Analog Devices AD8009. This provides bipolar voltages. The driver of this amplifier may be slower by the amp gain approximately.
Linear technology has published an picosecond-avalanche pulse generator in their application handbooks with higher voltages.
tiki