Why it is not possible to measure the built-in voltage of a PN junction using a voltmeter?

  The built-in voltage of a PN junction can be considered as the contact potential between two dissimilar metals. When the leads of a voltmeter are contacted to either side of a PN junction, the contact potential between the voltmeter lead and P-type material, contact potential of the PN junction, and the contact potential between the N-type material and the voltmeter lead form a closed loop. Since the sum of all contact potentials in a closed loop is zero, the built-in voltage can not be measured by a voltmeter. (Reference: Operation and Modeling of the MOS Transistor, chapter 1, 2^nd edition, by Y. Tsividis).

Ref:http://eds.ieee.org/questeds/question-and-answer-page.html#Semi