Abstract
This paper is devoted to a class of inverse problems arising in the testing of semiconductor devices, namely the identification of doping profiles from indirect measurements of the current or the voltage on a contact. In mathematical terms, this can be modeled by an inverse source problem for the drift-diffusion equations, which are a coupled system of elliptic or parabolic partial differential equations.
We discuss these inverse problems in a stationary and a transient setting and compare these two cases with respect to their mathematical properties. In particular , we discuss the identifiability of doping profiles in the model problem of the unipolar drift-diffusion system. Finally, we investigate the important special case of a piecewise constant doping profile, where the aim is to identify the p-n junctions, i.e., the curves between regions where the doping profile takes positive and negative values.
Supported by the Austrian National Science Foundation FWF under project grants SFB F013 / 08 and P 13478-INF
Supported by the Austrian National Science Foundation through the Wittgenstein Award 2000
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
H.T.Banks, K.Kunisch, Estimation Techniques for Distributed Parameter Systems (Birkhäuser, Basel, Boston, 1989).
E.Beretta, S.Vessella, Stable determination of boundaries from Cauchy data, SIAM J. Math. Anal. 30 (1998), 220-232.
F.Brezzi, L.D.Marini, P.Pietra Two-dimensional exponential fitting and applications in drift-diffusion models, SIAM J. Numer. Anal. 26 (1989), 1342-1355.
M.Burger, H.W.Engl, P.Markowich, P.Pietra, Identification of doping profiles in semiconductor devices, Inverse Problems (2001), to appear.
M.Burger, P.Markowich, Identification of doping profiles from transient measurements, in preparation.
M.Cheney, D.Isaacson, J.C. Newell, Electrical impedance tomography, SIAM Review 41 (1999), 85-101.
H.W.Engl, O.Scherzer, Convergence rate results for iterative methods for solving nonlinear ill-posed problems, in D.Colton, H.W. Engl, A.Louis, J.McLauglin, W.Rundell, eds., Surveys on Solution Methods for Inverse Problems (Springer, Vienna, 2000).
M.Hinze, R.Pinnau, Optimal control of the drift-diffusion model for semiconductor devices , Math. Models and Methods in Applied Sciences (2001), to appear.
A.Jüngel, Quasi-hydrodynamic Semiconductor Equations, Progress in Nonlinear Differential Equations (Birkhäuser, Boston, Basel, 2001).
N.Khalil, ULSI Characterization with Technology Computer-Aided Design (PhD-Thesis, Technical University Vienna, 1995).
V.Isakov, Inverse Problems for Partial Differential Equations (Springer, New York, 1998).
P.A.Markowich, The Stationary Semiconductor Device Equations (Springer, Wien, New York, 1986).
P.A.Markowich, C.A.Ringhofer, Stability of the linearized transient semiconductor device equations, Z. Angew. Math. Mech. 67 (1987), 319-332.
P.A.Markowich, C.A.Ringhofer, C.Schmeiser, Semiconductor Equations (Springer, Wien, New York, 1990).
A.l.Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Annals of Mathematics 143 (1996), 71-96.
C.Schmeiser, Voltage-current characteristics of multi-dimensional semiconductor devices , Quarterly of Appl. Math. 4 (1991), 753-772.
S.Selberherr, Analysis and Simulation of Semiconductor Devices (Springer, Wien, New York, 1984).
M.Stockinger,R.Strasser, R.Plasun, K.Wild,S .Selberherr, A qualitative study on optimized MOSEET doping profiles, Proc. of SISPAD 98 (Springer, 1998), 77-80.
M.Stockinger, R.Strasser, R.Plasun, A.Wild, S.Selberherr, Closed-loop MOSEET doping profile optimization for portable systems, Proceedings Intl. Conf. on Modeling and Simulation of Microsystems, Semiconductors, Sensors, and Actuators (San Juan, 1999), 411-414.
W.R. Van Roosbroeck, Theory of flow of electrons and holes in germanium and other semiconductors, Bell Syst. Tech. J. 29 (1950), 560-607.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this paper
Cite this paper
Burger, M., Engl, H.W., Markowich, P.A. (2002). Inverse Doping Problems for Semiconductor Devices. In: Chan, T.F., Huang, Y., Tang, T., Xu, J., Ying, LA. (eds) Recent Progress in Computational and Applied PDES. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0113-8_3
Download citation
DOI: https://doi.org/10.1007/978-1-4615-0113-8_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-4929-7
Online ISBN: 978-1-4615-0113-8
eBook Packages: Springer Book Archive