Barbara Abraham-Shrauner

Senior Professor

Office: 213 Cupples II
Tel. (314) 935-6134
Fax. (314) 935-7500
email: bas@ese.wustl.edu
Webpages: personal, research group

Education
Harvard University (A.M. 1957, Ph.D. 1962)
University of Colorado (B.A. 1956)

Postdoctoral
Université Libre de Bruxelles: AAUW Illinois Fellowship
NASA-Ames Research Center : NAS-NASA Fellowship

Memberships
IEEE
American Geophysical Union
American Physical
Society
AAUP

Honors
Senior Member, IEEE
Phi Beta Kappa
Eta Kappa Nu
Sigma Xi
Fellow, American Physical Society

Professor Abraham-Shrauner joined the faculty in 1966 at Washington University where she is now a Senior Professor in the Department of Electrical and Systems Engineering. She retired from full-time service as Professor in July, 2003.

    She continues her research activities part-time as a Senior Professor. She has done research in the past on space plasmas, on plasma theory, on charge effects in blood clotting, on high electric field transport in III-V semiconductors and on sputter depostion by plasmas of thin films such as GaAs for applications in infrared optoelectronics.
    Currently she is concentrating on theoretical models of plasma processing and symmetry analysis of nonlinear differential equations. The plasma processing models are of semiconductors used in the fabrication of integrated circuits. The models have included the etching of rectangular trenches and contact holes in silicon dioxide as well as in GaAs. More recently she has modeled the etching and deposition on silicon in a fluorocarbon plasma. The three regimes of reactive sputtering, fluorocarbon suppression and fluorocarbon deposition were treated with a multilayer model.
    The symmetry analysis continues extensive investigations of Lie point symmetries of plasma problems and especially hidden symmetries of nonlinear ordinary differential equations. Symmetries of differential equations may be used to simplify the differential equations and many analytic solutions are found as a result of symmetry analysis. Recent research has included the systematic solution of a model diffusion equation for a fractal system by Lie symmetries with attention to initial and boundary conditions. The analysis of hidden symmetries of linear and nonlinear partial differential partial equations has discovered a new type of hidden symmetry not seen in ordinary differential equations.

Selected Publications

B. Abraham-Shrauner, K.S. Govinder, "Provenance of Type II hidden symmetries from nonlinear partial differential equations," J. Nonl. Math. Phys . (to be published, 2006).

B. Abraham-Shrauner, K.S. Govinder and D.J. Arrigo, "Type-II hidden symmetries of the linear 2D and 3D wave equations," J. Phys A:Math. & Gen. . Vol. 39, pp. 5739-5747 , 2006.

B. Abraham-Shrauner, "Lie symmetry solutions for anomalous diffusion," J. Phys. A:Math. & Gen. Vol. 36, pp. 2547-2553, 2005

B. Abraham-Shrauner, "Simultaneous, multilayer plasma etching and deposition of fluorocarbon layers on silicon," J. Appl. Phys. Vol. 94, pp. 4776-4780 , 2003.

L.-H. Ouyang, D. L Rode, T. Zulkifli, B. Abraham-Shrauner, N. Lewis and M.R.Freeman, "Hydrogenated amorphous and microcrystalline GaAs Films prepared by radio-frequency magnetron sputtering," J. Appl. Phys. Vol. 91, pp. 3459-67, 2002.

C. Liu and B. Abraham-Shrauner, "Plasma Etching Model for SiO2 Contact Holes, " IEEE Trans. Plasma Sci. Vol. 30, pp, 1579-1586, 2002.

B. Abraham-Shrauner, "Hidden Symmetries, First Integrals and Reduction of Order of Nonlinear Ordinary Differential Equations," J. Nonlinear Math. Phys. 9, Supplement 2, pp. 1-9, 2002.

B. Abraham-Shrauner, "Plasma etch profiles of passivated open-area trenches," J. Vac. Sci. & Tech. B, Vol 19, pp. 711-721, 2001.

P. G. L. Leach ,K. S. Govinder, and B. Abraham-Shrauner," Symmetries of First Integrals and Their Associated Differential Equations," J. Math. Analysis and Applications, Vol. 253, pp. 58-93, 1999.

W. Chen and B. Abraham-Shrauner and J. R. Woodworth, "Model etch profiles for ion energy distribution functions in an inductively coupled plasma reactor ," J. Vac. Sci. & Tech.B, Vol 17, pp. 2061-2069, 1999.

B. Abraham-Shrauner, K. J. Nordheden and Y. S. Lee, "Model for etch dependence on GaAs Via Diameter, " J. Vac. Sci. Tech. B Vol 17, pp. 961-964, 1999.

B. Abraham-Shrauner and N. Jagannathan, "Modification of Plaxma Etched Profiles by Sputtering," IEEE Trans. Plasma Sci., Vol 27, pp. 665-675, 1999.

B. Abraham-Shrauner, "Contact hole model for etch depth dependence," J. Vac. Sci. Tech,B Vol 17, pp. 158-161, 1999.

B. Abraham-Shrauner, "Model for Ion-Initiated Trench Etching," IEEE Trans, Plasma Science, Vol 2, pp 433-438, 1997.

B. Abraham-Shrauner and W. Chen, "The effects of ion sheath collisions on trench etch profiles," J. Appl. Phys,, Vol 81, pp. 2547-2554, 1997.

B. Abraham-Shrauner and W. Chen, "Neutral shadowing in circular cylindrical trench holes," J. Vac. Soc. & Tech,B, Vol 14, pp. 3492-3496, 1996.

B. Abraham-Shrauner, "Hidden symmetries and nonlocal group generators of ordinary differential equations," IMA J., Vol 56, pp. 235-252, 1996.

B. Abraham-Shrauner, "Lie Symmetries, Hidden Symmetries and Time-Dependent Invariants," Dynamical Systems and Applications, (World Scientific Publishing Company, Singapore, 1995), pp.1-10.

B. Abraham-Shrauner, "Analytic Models for Plasma-Assisted Etching of Semiconductor Trenches," J. Vac. Soc. & Tech. B, Vol 12, pp. 2347-2351, 1994.

B. Abraham-Shrauner, R. Zitter, and X. Zhang, "Current generated periodic space charge in semiconductor diodes and non-ohmic injection," J. Appl. Phys., Vol 75, pp. 373-376, 1994.

B. Abraham-Shrauner and Ann Guo, "Hidden Symmetries of Differential Equations," Lie algebras, cohomology and new applications to quantum mechanics, Cont. Math. Vol 160, (AMS, 1994) pp. 1-13.

B. Abraham-Shrauner, W. Weeks IV and R. N. Zitter, "Current-voltage curves for a spatially periodic Ge diode," J. Appl. Phys., Vol 73, pp. 8628-8632, 1993.

B. Abraham-Shrauner, "Hidden symmetries and linearization of the modified Painleve-Ince equation," J. Math. Phys., Vol 73, pp. 8628-8632, 1993.

B. Abraham-Shrauner, "Hidden symmetries and linearization of the modified Painleve-Ince equation," IMA J. Appl. Math., Vol 51, pp. 147-153, 1993.

B. Abraham-Shrauner and P. G. L. Leach, "Hidden Symmetries of Nonlinear Ordinary Differential Equations," in Lectures in Applied Mathematics. Vol Symmetry in Applied and Numerical Analysis, Providence: American Mathematical Society, 1993. pp. 1-10.

B. Abraham-Shrauner and Ann Guo, "Hidden and Nonlocal Symmetries of Nonlinear Differential Equations," Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, eds. N. H. Ibragimov, M. Torrissi and A. Valenti, Catania, (Kluwer, Dordrecht, 1993) pp. 1-5.