Can we find potential difference of a P-N junction by connecting voltmeter across diode terminals? I know the answer is no but i don't know how.
The correct way to measure a diode is with a I-V curve tracer. The barrier potential occurs at the "knee" voltage in the forward bias. This is the point at which current increases greatly compared to the applied voltage.
I found a video of how to do this cheaply. 2 If you are student your electronics lab may have something like a Tektronix 370A somewhere you can use.
If you are wondering "why" this is you are asking a physics question and the answer is that the barrier potential is not really a "voltage". A diode is still a passive device like a resistor. You have to apply a voltage/current to get a meaningful output. 3
I think you are referring to the diffusion voltage across the pn junction, correct? No - it is not possible to measure or even to use this voltage because each electrical contact at the collector resp. emitter terminals will produce the opposite effect (voltage with opposite sign) because each of these contacts acts like a Schottky junction (metal-semiconductor).