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Volterra Integral Equation Models for Semiconductor Devices
Author(s) -
Unterreiter Andreas
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199604)19:6<425::aid-mma744>3.0.co;2-m
Subject(s) - volterra integral equation , mathematics , integral equation , diode , semiconductor device , limit (mathematics) , control theory (sociology) , mathematical analysis , physics , computer science , materials science , quantum mechanics , layer (electronics) , control (management) , artificial intelligence , composite material
Van Roosbroeck's bipolar drift diffusion equations cover the qualitative behaviour of many semiconductor devices. The complexity of the model equations however prevents efficient implementations needed in circuit simulations. Under close‐to‐thermal‐equilibrium biasing conditions (zero space charge assumption, low injection limit) the van Roosbroeck system can be replaced by a system of coupled non‐linear Volterra integral equations of the second kind. Involving only the macroscopic quantities current, applied voltage and serial resistance this Volterra system can be handled with comparably little effort. Volterra integral equations models are formulated for a large class of semiconductor devices with abrupt pn‐junctions. The model equations are made explicit for diodes, transistors and thyristors. A survey on various results concerning Volterra models describing the switching behaviour of pn‐diodes is given. The integral equation model allows to recover all relevant properties of the voltage–current characteristics.