Voltage-current characteristics of multidimensional semiconductor devices
Author:
Christian Schmeiser
Journal:
Quart. Appl. Math. 49 (1991), 753-772
MSC:
Primary 35Q60; Secondary 78A55, 82D99
DOI:
https://doi.org/10.1090/qam/1134751
MathSciNet review:
MR1134751
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Abstract: The steady state drift-diffusion model for the flow of electrons and holes in semiconductors is simplified by perturbation techniques. The simplifications amount to assuming zero space charge and low injection. The limiting problems are solved and explicit formulas for the voltage-current characteristics of bipolar devices can be obtained. As examples, the $pn$-diode, the bipolar transistor and the thyristor are discussed. While the classical results of a one-dimensional analysis are confirmed in the case of the diode, some important effects of the higher dimensionality appear for the bipolar transistor.
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S. M. Sze, Physics of Semiconductor Devices, 2nd ed., Wiley , New York, 1981
A. B. Vasil’eva and V. G. Stelmakh, Singularly disturbed systems of the theory of semiconductor devices, USSR Comput. Math. Phys. 17, 48–58 (1977)
F. Brezzi, A. Capelo, and L. Gastaldi, A singular perturbation analysis of reverse biased semiconductor diodes, SIAM J. Math. Anal. 20, 372–387 (1989)
J. Henry and B. Louro, Singular perturbation theory applied to the electrochemistry equations in the case of electroneutrality, Nonlinear Analysis TMA 13, 787–801 (1989)
P. A. Markowich, A singular perturbation analysis of the fundamental semiconductor device equations, SIAM J. Appl. Math. 44, 896–928 (1984)
P. A. Markowich, The Stationary Semiconductor Device Equations, Springer-Verlag, Vienna-New York, 1986
P. A. Markowich and C. Ringhofer, A singularly perturbed boundary value problem modelling a semiconductor device, SIAM J. Appl. Math. 44, 231–256 (1984)
P. A. Markowich, C. Ringhofer, and C. Schmeiser, An asymptotic analysis of one-dimensional semiconductor device models, IMA J. Appl. Math. 37, 1–24 (1986)
P. A. Markowich , C. Ringhofer, and C. Schmeiser, Semiconductor Equations, Springer-Verlag, Vienna-New York, 1990
P. A. Markowich and C. Schmeiser, Uniform asymptotic representation of solutions of the basic semiconductor device equations, IMA J. Appl. Math. 36, 43–57 (1986)
R. E. O’Malley and C. Schmeiser, The asymptotic solution of a semiconductor device problem involving reverse bias, SIAM J. Appl. Math. 50, 504–520 (1990)
C. P. Please, An analysis of semiconductor P-N junctions, IMA J. Appl. Math. 28, 301–318 (1982)
C. Schmeiser, On strongly reverse biased semiconductor diodes, SIAM J. Appl. Math. 49, (1989) 1734–1748
C. Schmeiser, A singular perturbation analysis of reverse biased pn-junclions, SIAM J. Math. Anal. 21, 313–326 (1990)
C. Schmeiser, Free boundariers in semiconductor devices, Proc. Free Boundary Problems: Theory and Applications, Montreal, 1990, to appear
C. Schmeiser and R. Weiss, Asymptotic analysis of singular singularly perturbed boundary value problems, SIAM J. Math. Anal. 17, 560–579 (1986)
W. Shockley, The theory of p-n junctions in semiconductors and p - n junction transistors, Bell Syst. Tech. J. 28, 435 (1949)
J. W. Slotboom, Iterative scheme for 1- and 2-dimensional D.C.-transistor simulation, Electron. Lett. 5, 677–678 (1969)
H. Steinrück, A bifurcation analysis of the one-dimensional steady-state semiconductor device equations, SIAM J. Math. 49, 1102–1121 (1989)
S. M. Sze, Physics of Semiconductor Devices, 2nd ed., Wiley , New York, 1981
A. B. Vasil’eva and V. G. Stelmakh, Singularly disturbed systems of the theory of semiconductor devices, USSR Comput. Math. Phys. 17, 48–58 (1977)
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Article copyright:
© Copyright 1991
American Mathematical Society
