If the resistance of a p-n junction ( both contacts are taken from the top of the p semiconductor ) continuously increases with a fixed applied voltage then what is the reason behind it?
If you take two lateral metal contacts on the p-type semiconductor only then it is surely not the resistance of the p-n junction as you have mentioned. To obtain the junction resistance characteristics a potential barrier has to be created between p- and n-type semiconductors.. So, you need to make one metal contact on p-type and the other on n-type semiconductor.
About the continuous increase of resistance of p type semiconductor measured across the two metal contacts on p-type semiconductor my presumption is the effect of environment i.e the ambient temperature & the surrounding atmosphere. The adsorption of some gaseous species & moisture present in the atmosphere may be responsible for this continuous increase of resistance since it is a p-type semiconductor. You can confirm it by doing the measurement after keeping your sample in a vacuum chamber and evacuating the chamber,
I agree with the view of Dr. Sanat Kumar Mishra provided the metal contacts are made across the junction. but it was mentioned in the query that both the contacts were taken from the top of p-type semiconductor. This is really confusing !!!