I know that it takes about 0.6V-0.7V for a pn-junction diode to be on in forward biased conditions, but what about reversed-biased? I mean is it never called "on"? Here is the specific question that my general one stems from. A pn junction diode will be turned on when 1.5 V of an external voltage is applied to the n- side of the diode while the p-side is grounded – T or F ?
It depends on its history, and what you mean by 'on'.
Forward biasing a PN junction fills it with carriers.
When you apply a reverse current, the carriers get swept out. During that time, the diode is still conducting, and the voltage across the junction is low. Is it 'on' then?
This charge storage time limits the switching speed of junction diodes used as rectifiers.
Eventually, the charge in the junction will be depleted, and the junction voltage will rise rapidly. This is certainly off.
The turning off process happens very rapidly, and this feature is used in so called 'step recovery diodes', usually to interrupt a current flowing in an inductor, to generate a very sharp voltage transient.
A diode can be in forward bias or reverse bias based on the polarity of the bias voltage applied. There is a definite forward voltage at which the diode starts to conduct significantly, known as the cut-in voltage. Which is usually 0.6-0.7V in case of Silicon diodes. This voltage changes as material changes.
Now if you are assuming cut-in voltage as the threshold for 'on' condition, then the diode will be 'on' if it is forward biased with voltage higher than the cut-in voltage.
Current can flow in reverse bias also. A small saturation current flows in reverse bias. If the reverse bias is high, break down can occur and large current can flow as in zener diode.
So if 'on' means presence of current flow, then diode can be 'on' in reverse bias also.