Abstract
In this Chapter we shall formulate the system of partial differential equations, which describes potential distribution, carrier concentrations and current flow in semiconductor devices. We shall supplement the system by boundary conditions representing the interaction of the device with the outer world and discuss the modeling of physical parameters appearing in the system. Also, various choices of dependent variables, which are useful for analytical purposes, will be presented. Finally, we shall scale the physical quantities and put the system of equations and the boundary conditions into a dimensionless form appropriate for further mathematical and numerical investigations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Antoniadis, D. A., Hauser, S. E., Dutton, R. W.: SUPREM II: A Program for IC Process Modeling and Simulation. Report 5019–2, Stanford University, Cal., U.S.A., 1978.
Antoniadis, D. A., Dutton, R. W.: Models for Computer Simulation of Complete IC Fabrication Processes. IEEE J. Solid State Circuits SC-14, No. 2, 412–422 (1979).
De Mari, A.: An Accurate Numerical Steady State One-Dimensional Solution of the P—N Junction. Solid State Electron., 11, 33–58 (1968).
De Mari, A.: An Accurate Numerical One-Dimensional Solution of the P—N Junction under Arbitrary Transient Conditions. Solid State Electron. 11, 1021–2053 (1968).
Furikawa, S., Matsumura, H., Ishiwara, H.: Theoretical Considerations on Lateral Spread of Implanted Ions. Jap. J. Appl. Phys. 11, No. 2, 134–142 (1972).
Franz, G. A., Franz, A. F., Selberherr, S.: Cylindrically Symmetric Semiconductor Device Simulation. Report, Institut für Allgemeine Elektrotechnik, Technische Universität Wien, Austria, 1983.
Hall, R. N.: Electron-Hole Recombination in Germanium. Physical Review 87, 387 (1952).
Hofmann, H.: Das elektromagnetische Feld, 2. Aufl. Wien—New York: Springer 1982.
Jüngling, W.: Hochdotierungseffekte in Silizium. Diplomarbeit, Technische Universität Wien, Austria, 1983.
Jüngling, W., Guerrero, E., Selberherr, S.: On Modeling the Intrinsic Number and Fermi Levels for Device and Process Simulation. COMPEL 3, No. 2., 79–105 (1984).
Lin, C. C., Segel, L. A.: Mathematics Applied to Deterministic Problems in the Natural Sciences. New York: Macmillan 1974.
Markowich, P. A.: A Qualitative Analysis of the Fundamental Semiconductor Device Equations. COMPEL 2, No. 3, 97–115 (1983).
Markowich, P. A., Ringhofer, C.: A Singularly Perturbed Boundary Value Problem Modeling a Semiconductor Device. SIAM J. Appl. Math. 44, No. 2, 231–256 (1984).
Mock, M. S.: Analysis of Mathematical Models of Semiconductor Devices. Dublin: Boole Press 1983.
Schütz, A.: Simulation des Lawinendurchbruchs in MOS-Transistoren. Dissertation, Technische Universität Wien, Austria, 1982.
Selberherr, S.: Analysis and Simulation of Semiconductor Devices. Wien—New York: Springer 1984.
Selberherr, S., Griebel, W., Pötzl, H.: Transport Physics for Modelling Semiconductor Devices, Proceedings, Conference “Simulation of Semiconductor Devices”, Swansea, 1984.
Shockley, W., Read, W. T.: Statistics of the Recombination of Holes and Electrons. Physical Review, 87, No. 5, 835–842 (1952).
Smith, R. A.: Semiconductor, 2nd ed. Cambridge: Cambridge University Press 1978.
Sze, S. M.: Physics of Semiconductor Devides, 2nd ed. New York: J. Wiley 1981.
Van Roosbroeck, W. V.: Theory of Flow of Electrons and Holes in Germanium and Other Semiconductors. Bell Syst. Tech. J. 29, 560–607 (1950).
Vasileva, A. B., Butuzow, V. F.: Singularly Perturbed Equations in the Critical Case. MRC—TSR 2039, Math. Res. Center, University Wisconsin-Madison, U.S.A., 1980.
Vasileva, A. B., Stelmakh, V. G.: Singularly Disturbed Systems of the Theory of Semicon-ductor Devices. USSR Comput. Math. Phys. 17, 48–58 (1977).
Zimam, J. M.: Electrons and Phonons. London: Clarendon Press 1963.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag Wien
About this chapter
Cite this chapter
Markowich, P.A. (1986). Mathematical Modeling of Semiconductor Devices. In: The Stationary Semiconductor Device Equations. Computational Microelectronics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-3678-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-7091-3678-2_2
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-99937-0
Online ISBN: 978-3-7091-3678-2
eBook Packages: Springer Book Archive