MOSFET for switching single LED
Why not use a charge pump?



V1 is a square wave source, for example the output of a PWM, can be buffered by a logic gate.

"X1" is a dual diode, make sure the two Vf in series reduce output voltage enouhgh so the LED is off when it needs to.

This is a somewhat constant current driver. If R2 and C2 are large enough to smooth the LED current well, then it will have a constant voltage output at VCC minus the two diode Vf. In this case R2 sets the current across LED Vf dispersion.

However if we remove C2 and set R2 so that C1 is discharged at each cycle then each cycle pumps an amount of charge equal to C1 times (Vcc minus one diode drop). Charge times frequency is current, so it makes a constant current drive. It's a bit more efficient than the one above, but the LED will blink at PWM frequency.