N-Channel Enhancement Mode MOSFET Switching Speed
I'm not sure at what constant current you are driving your LED, but you have a 100 nF capacitor there. A constant current into a capacitor results in a linear voltage increase.

You might want to check if the math checks out.

The ramp looks like 4 V in 100 µs. So if I'm not doing it wrong:

$$ I = \frac{C*U}{t} = \frac{100 \text{nF}*4 \text{V}}{100 \text{µs}} = 4 \text{mA}$$

Sounds reasonable for a small LED - but at that drive level I'd probably not go through the trouble of a constant current source.