The built-in potential in a semiconductor equals the potential across the depletion region in thermal equilibrium. Since thermal equilibrium implies that the Fermi energy is constant throughout the p-n diode, the built-in potential equals the difference between the Fermi energies, EFn and EFp, divided by the electronic charge. It also equals the sum of the bulk potentials of each region, fn and fp, since the bulk potential quantifies the distance between the Fermi energy and the intrinsic energy. This yields the following expression for the built-in potential.

Example 2 | An abrupt silicon p-n junction consists of a p-type region containing 2 x 10^16 cm-3 acceptors and an n-type region containing also 10^16 cm-3 acceptors in addition to 10^17 cm-3 donors. 1. Calculate the thermal equilibrium density of electrons and holes in the p-type region as well as both densities in the n-type region. 2. Calculate the built-in potential of the p-n junction 3. Calculate the built-in potential of the p-n junction at 400 K.. |

Solution | where the instrinsic carrier density at 400 K was obtained from example1 1. The thermal equilibrium densities are: In the p-type region: p = Na = 2 x 10^16 cm-3 n = ni^2/p = 10^20/2 x 10^16 = 5 x 103 cm-3 In the n-type region n = Nd - Na = 9 x 10^16 cm-3 p = ni2/n = 10^20/(1 x 10^16) = 1.11 x 10^3 cm-3 2 The built-in potential is obtained from: 3.Similarly, the built-in potential at 400 K equals: |

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