A square wave is just like a normal sinusoidal wave except that it has plenty of odd harmonics (each at the appropriate amplitude).
For example, if you're looking to create a square wave of 20MHz, then your circuits need to be able to handle at least 60MHz to produce a waveform that even looks slightly like a square wave. A 'nice' 20 MHz square wave would require harmonics well above 100 MHz.
The issue for you isn't really creating a nice 20 MHz square wave (that's easy) - the issue is creating a nice 20 MHz square wave that is capable of driving your cyclotron (I assume that is what you're up to...).
Which leads to the next question:
Are you sure you want a square wave?
Circular motion and sin waves are one in the same. If you're using the 10-20 MHz wave to drive the cyclotron, then you likely just need a nice easy sin wave (from any HF transmitter).
If you're going to be using much power, then choose an ISM frequency like 13.56 MHz (check the regs).