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The built-in potential is generated because of the diffusion of the mobile charges across the junction which leaves back the uncompensated immobile charges near the junction. The number of charges diffusing across the junction is equal to the number of immobile charges left back. The mobile charges diffuse in the p or n type material and follow a negative exponential distribution with the distance from the junction. Therefore between the terminals of the device these charge are distributed and inside the device in total, the net charge is zero. Therefore we do not we get any potential between the two terminals. Had we have the scope to measure the voltage difference just across the junction we could have measured the built-in potential. When we try to measure the voltage difference between the two terminalr the diffused charges cause a contact potential at the point of contact with the lead which beacuse of the charge neutrality mentioned above is equal in magnitude and opposite in sign witht the contact potential. So we measure 0 voltage across the device.
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