Abstract
The design of semiconductor devices is an important and challenging task in modern microelectronics, which is increasingly being carried out via mathematical optimization with models for the device behavior. The design variable (and correspondingly the unknown in the associated optimization problems) is the device doping profile, which describes the (charge) density of ion impurities in the device and is therefore modeled as a spatially inhomogeneous function. The optimization goals are usually related to the device characteristics, in particular to outflow currents on some contacts. This is also the typical setup we shall confine ourselves to in this chapter, namely to (approximately) achieve a certain goal related to the outflow current on a contact (e.g., a maximization or just an increase of the current), ideally with minimal change of the doping profile to some given reference state.
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. Burger, R. Pinnau, Fast optimal design of semiconductor devices, SIAM J. Appl. Math. 64, 108–126 (2003).
H. Gajewski, J. Sommrey, On the uniqueness of solutions of van Roosbroeck equations, ZAMM 72, 151–153 (1992).
[HP02a] M. Hinze, R. Pinnau, Optimal control of the drift-diffusion model for semiconductor devices, in: K.H. Hoffmann, G. Lengering, J. Sprekels, and F. Trottzch (eds.): Optimal Control of Complex Structures, Birkhäuser, Basel (2002), 95–106.
[HP02b] M. Hinze, R. Pinnau, An optimal control approach to semiconductor design, Math. Mod. Meth. Appl. Sci. 12, 89–107 (2002).
M. Hinze, R. Pinnau, Mathematical tools in optimal semiconductor design, to appear in TTSP (2005).
M. Hinze, R. Pinnau, A second order approach to optimal semiconductor design, to appear in JOTA (2006).
A. Jüngel, Y.J. Peng, A model hierarchy for semiconductors and plasmas, Nonlin. Anal. 47 (2001), 1821–1832.
C.T. Kelley. Iterative Methods for Linear and Nonlinear Equations. SIAM, Philadelphia, 1995.
P.A. Markowich, C.A. Ringhofer, and C. Schmeiser, Semiconductor Equations, Springer, Wien, New York, 1990.
R. Plasun, M. Stockinger, R. Strasser, and S. Selberherr, Simulation based optimization environment and its application to semiconductor devices, in: Proceedings IASTED Intl. Conf. on Applied Modelling and Simulation, 1998, pp. 313–316.
M. Stockinger, Optimization of ultra-low-power CMOS transistors, PhD Thesis, Technical University Vienna, 2000.
M. Stockinger, R. Strasser, R. Plasun, A. Wild, and S. Selberherr, A Qualitative Study on Optimized MOSFET Doping Profiles, in: Proceedings SISPAD 98 Conf., Leuven, 1998, pp. 77–80.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Birkhäuser Boston
About this chapter
Cite this chapter
Burger, M., Hinze, M., Pinnau, R. (2007). Optimization models for semiconductor dopant profiling. In: Cercignani, C., Gabetta, E. (eds) Transport Phenomena and Kinetic Theory. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4554-0_5
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4554-0_5
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4489-5
Online ISBN: 978-0-8176-4554-0
eBook Packages: EngineeringEngineering (R0)