As ronsimpson says, you need a resistor to ground.
The LED in the circuit diagram is large, with a rated current of 1.5 A, but it's being run at far less than that. The Vf of the LED at full current is more than the supply voltage, so it's difficult to estimate what current and Vf you'll get.
Is that the actual LED being used?
The reason that I'm asking is that the LED may be acting as a photocell and generating a voltage when it's illuminated. All LEDs that I've tested this on produce some voltage in the forward direction when illuminated, so current will actually flow through them in reverse in that condition. The voltage will always be less than Vf, but in this case it only needs 1 V for the PF240D25 to remain on, and virtually no current is needed.
There may be leakage from the transistor as well.
The waveform doesn't have a voltage scale, so I don't know how low the voltage is going, but it doesn't drop sharply. That indicates that there should be something to pull the voltage down to ensure that the PF240D25 turns off.