An abrupt p-n junction in thermal equilibrium is shown in Fig. The built-in potential Vbi is given as:
4) An abrupt p-n junction in thermal equilibrium is shown in Fig. The built-in potential Vbi is given as:
(1) qVn + qVp
(2) Eg − (qVn + qVp)
(3) Eg + (qVn + qVp)
(4) Eg − (qVn − qVp)
Solution:
From the band diagram, we observe the vertical relationships between energy levels:
- The total energy difference between Ec and Ev is the bandgap, Eg.
- On the p-side, the conduction band energy relative to the Fermi level is:
(Ec − EF)p = Eg − qVp - On the n-side, the conduction band energy relative to the Fermi level is:
(Ec − EF)n = qVn - The built-in potential energy qVbi is the shift in Ec between the two sides:
qVbi = (Ec − EF)p − (Ec − EF)n
qVbi = (Eg − qVp) − (qVn)
qVbi = Eg − (qVn + qVp)
Thus, option (2) is correct.
Further Reading:
GATE EC Previous Year Papers with Solutions