Abstract
This short survey of results concerning the applications of perturbation analysis in semiconductor device modeling is devoted mostly to problems that were solved using the method of composite asymptotic expansions or the, so-called, boundary function method. Thorough description of this approach can be found in Vasil’eva and Butuzov [17], [18], [19] and in O’Malley [13], [14]. The main ideas of the method are illustrated below on the example of the singularly perturbed problem for the Gunn diode. Here the construction of the leading order terms of the asymptotic solution is discussed. This gives the opportunity to obtain the main characteristics of the device to the zeroth order. More detailed analysis of the asymptotic approximation for the solution of the Gunn diode problem, including the construction of higher order terms, will be published later. To make the presentation more compact some cumbersome details of the solution algorithm have been omitted.
This research was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation.
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
M.P. Belyanin, Numerical-asymptotic solution of a nonstationary singularly perturbed problem from the theory of semiconductor devices (Russian), Diff. Uravneniya 21, No. 8, (1985), pp. 1436–1440.
M.P. Belyanin, Asymptotic solution of one model for p — n junction (Russian), Zh. Vichislit. Matem. i Matem. Fiziki 26, No. 2, translated into English in U.S.S.R. Comput. Math. and Math. Phys. (1986), pp. 306–311.
M.P. Belyanin, On the asymptotics in a one-dimensional model of some semiconductor devices, U.S.S.R. Comput. Math. and Math. Phys. 28, (1988), pp. 21–34.
M.P. Belyanin, L.V. Kalachev, E.V. Mamontov, Application of the boundary function method for the simulation of some semiconductor devices, to appear in Mat. Model.
M.P. Belyanin, A.B. Vasil’eva, On an inner transition layer in a problem of the theory of semiconductor films (Russian), Zh. tVichislit. Matem. i Matem. Fiziki 28, No. 2, translated into English in U.S.S.R. Comput. Math. and Math. Phys. (1988), pp. 223–236.
M.P. Belyanin, A.B. Vasil’eva, A.V. Voronov, A.V. Tikhonravov, An asymptotic approach to the problem of designing a semiconductor device (Russian), Mat. Model. 1, No. 9 (1989), pp. 43–63.
V.F. Butuzov, L.V. Kalachev, Asymptotic derivation of the ambipolar diffusion equation in the physics of semiconductors, submitted for publication in U.S.S.R. Comput. Math. and Math. Phys..
L.V. Kalachev, S.V. Kruchkov, I.A. Obukhov, Asymptotic analysis of the Poisson equation in semiconductors (Russian), Mat. Model. 1, No. 9 (1989), pp. 129–140.
L.V. Kalachev, I.A. Obukhov, Approximate solution of the Poisson equation for a model of a two-dimensional semiconductor structure, Vestnik Mosk. Universiteta, Fizika, 44, No. 3, translated into English (1989), pp. 63–68.
L.V. Kalachev, I.A. Obukhov, Asymptotic solution of the Poisson equation in a three-dimensional semiconductor structure, to appear in U.S.S.R. Comp. Math. and Math. Phys..
L.V. Kalachev, I.A. Obukhov, Asymptotic solution of the Poisson equation in the case of a large outer field, submitted for publication in Mat. Model.
P.A. Markowich, C.A. Ringhofer, C. Schmeiser, Semiconductor Equations, Springer-Verlag, Wien-New York (1990).
R.E. O’Malley Jr., Introduction to Singular Perturbations, Academic Press, New York (1974).
R.E. O’Malley Jr., Singular Perturbations Methods for Ordinary Differential Equations, Springer-Verlag, New York (1991).
M.P. Shaw, H.L. Grubin, P.R. Solomon, Gunn-Hilsum effect, Academic Press, New York (1979).
P. Szmolyan, Asymptotic analysis of the Gunn effect, IMA Preprint, Univ. of Minnesota (1989).
A.B. Vasil’eva, V.F. Butuzov, Asymptotic Expansions of the Solutions of Singularly Perturbed Equations (Russian), Nauka, Moscow (1979).
A.B. Vasil’eva, V.F. Butuzov, Singularly Perturbed Equations in the Critical Case (Russian), Moscow State University, Moscow (1978); translation into English (1980).
A.B. Vasil’eva, V.F. Butuzov, Asymptotic Methods in Singular Perturbation Theory, Visshaya Shkola, Moscow (1990).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag New York, Inc.
About this paper
Cite this paper
Kalachev, L.V. (1994). Some Applications of Asymptotic Methods in Semiconductor Device Modeling. In: Coughran, W.M., Cole, J., Lloyd, P., White, J.K. (eds) Semiconductors. The IMA Volumes in Mathematics and its Applications, vol 59. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8410-6_11
Download citation
DOI: https://doi.org/10.1007/978-1-4613-8410-6_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-8412-0
Online ISBN: 978-1-4613-8410-6
eBook Packages: Springer Book Archive