The only place where I find this answer documented is in Ben Eater's video "Using an EEPROM to replace combinational logic" at this particular time linked here.
This needs to be shown in schematics. I happen to want his ~600ns pulse width in my application too, so I use his exact values for R6 = 680 ohm and C3 = 1 nF for a 680 ns pulse. And the R5 resistor is there to re-charge the capacitor. Please excuse that I am showing the schematics in a certain application of a ramp generator that I'm building. Falling edge of a counter is supposed to reset the ramp. But the circuit in question here is all aroun R5, R6, C3, and D1, along with the rectangle wave from V2. The gate of M1 is simply the output pulse I want.
I added D1 to Ben Eater's circuit to chop off the +10V pulse on the rising edge. It may not matter with my MOSFET application, but it probably does matter on a TTL input pin to run it out of spec.
Here is the detail view of the negative pulse, and don't worry about the red trace, which is the charging of C1.
Here is the trace showing the positive edge pulse too, chopped off by D1. The problem of this is that it works with the switch application that Ben Eater uses, but it might not work driven directly by a TTL device since the momentary current it needs to sink to discharge C3 (a whopping full ampere) is not possible with a TTL device.
So I wonder if I need to deploy another MOSFET, an n-channel to do the discharging.
and this seems to work. Not sure if it is the simplest solution, but it is doable.
without that n-MOSFET M2 the resistance of the pulse generator would not be enough to generate that negative pulse.