Physics of Semiconductor Devices Lecture 6 Ideal P-N

Physics of Semiconductor Devices Lecture 6. Ideal P-N Junction. A. V. Sogoyan

Contents: • 1. Ideal p-n junction in equilibrium • 2. Ideal p-n junction out of equilibrium

Ideal p-n junction in equilibrium a) two semiconductors far apart b) two semiconductors in intimate contact

Ideal p-n junction in equilibrium

Ideal p-n junction in equilibrium

Ideal p-n junction in equilibrium Do depletion approximation: Volume charge density: Electric field:

Ideal p-n junction in equilibrium Do depletion approximation: Electric field: Electrostatic potential [select φ(x =0) =0]:

Ideal p-n junction in equilibrium Two unknowns: xn and xp. • demand overall charge neutrality: • potential difference across structure must be φbi: Solve for xn and xp: Total SCR width:

Ideal p-n junction in equilibrium Total SCR width: Maximum electric field: Symmetric junction: NA = ND: Strongly asymmetric junction: i. e. p+-n junction NA >> ND: the lowly-doped side controls everything

Ideal p-n junction out of equilibrium Apply voltage across: • forward bias: p-region positive with respect to n-region • reverse bias: p-region negative with respect to n-region Voltage can drop in five distinct regions: • ohmic contact to n-region • quasi-neutral n-region • space-charge region • quasi-neutral p-region • ohmic contact to p-region

Ideal p-n junction out of equilibrium Electrostatics Application of voltage splits Fermi levels: In forward and reverse bias:

Ideal p-n junction out of equilibrium Electrostatics Qualitatively, electrostatics unchanged out of equilibrium, but SCR widens and shrinks, as needed use equilibrium equations:

Ideal p-n junction out of equilibrium Depletion capacitance

Ideal p-n junction out of equilibrium Depletion capacitance For p+-n junction: Capacitance dominated by lowly-doped side

Conclusions