RG Nonlinear dynamics and controlCurrent filaments in low-temperature impurity breakdown

## Current filaments in low-temperature impurity breakdown

 J. Murawski, G. Schwarz, V. Novák, W. Prettl, E. Schöll: Simulation of longitudinal instabilities in filamentary current flow during low-temperature impurity breakdown in semiconductors J. Appl. Math. Mech. (ZAMM) 85, 823 (2005) G. Schwarz, C. Lehmann, A. Reimann, E. Schöll, J. Hirschinger, W. Prettl, V. Novák: Current filamentation in n-GaAs thin films with different contact geometries Semicond. Sci. Technol. 15, 593 (2000) G. Schwarz, E. Schöll, R. Nürnberg, H. Gajewski: Simulation of current filamentation in an extended drift diffusion model in Proc.\ Equadiff 99, edited by B. Fiedler, K. Gröger, J. Sprekels (World Scientific Publishing, Singapore, 2000) G. Schwarz, C. Lehmann, E. Schöll: Self-organized symmetry-breaking current filamentation and multistability in Corbino disks Phys. Rev. B 61, 10194 (2000) G. Schwarz, C. Lehmann, E. Schöll: Symmetry-breaking multiple current filamentation in n-GaAs Physica B 272, 270 (1999) E. Schöll: Nonlinear spatio-temporal dynamics in semiconductors Braz. J. Phys. 29, 627 (1999) E. Schöll, F. -J. Niedernostheide, J. Parisi, W. Prettl, H. G. Purwins: Formation of Spatio-Temporal Structures in Semiconductors in Evolution of spontaneous structures in dissipative continuous systems, edited by F. H. Busse, S. C. Müller (Springer, Berlin, 1998) E. Schöll: Impact phenomena and nonlinear spatiotemporal dynamics of hot electrons in semiconductors in Hot electrons in semiconductors: physics and devices, edited by N. Balkan (Oxford University Press, Oxford, 1998) , vormals SCH97c G. Schwarz, E. Schöll: Simulation of Current Filaments in Semiconductors with Point Contacts and Corbino Disks Acta Techn.\ CSAV 42, 669 (1997) K. Kunihiro, M. Gaa, E. Schöll: Influence of external circuits on filamentary current flow during impurity breakdown in n-type GaAs Electronics Letters 33, 1261 (1997) K. Kunihiro, M. Gaa, E. Schöll: Formation of current filaments in n-type GaAs under crossed electric and magnetic fields Phys. Rev. B 55, 2207 (1997) R. E. Kunz, E. Schöll, H. Gajewski, R. Nürnberg: Low-temperature impurity breakdown in semiconductors: an approach towards efficient device simulation Sol. State El. 39, 1155 (1996) M. Gaa, E. Schöll: Traveling carrier density waves in n-GaAs at low-temperature impurity breakdown Phys. Rev. B 54, 16733 (1996) M. Gaa, E. Schöll, W. Eberle, J. Hirschinger, W. Prettl: Spatial structure of impact-ionization induced current filaments in n-GaAs films Semicond. Sci. Technol. 11, 1646 (1996) M. Gaa, E. Schöll: Dynamics of nascent current filaments in low-temperature impurity breakdown Phys. Rev. B 53, 15971 (1996) M. Gaa, E. Schöll: Spatio-temporal dynamics of filament formation induced by impurity impact ionization in GaAs in Proc. 9th Int. Conf. on Hot Carriers in Semiconductors, edited by K. Hess, J. P. Leburton, U. Ravaioli (Plenum, New York, 1996) R. E. Kunz, E. Schöll: Dynamics of stochastically induced and spatially inhomogeneous impurity breakdown in semiconductors Z. Phys. B 99, 185 (1996) H. Kostial, M. Asche, R. Hey, K. Ploog, B. Kehrer, W. Quade, E. Schöll: Low temperature breakdown and current filamentation in n-type GaAs with homogeneous and partially ordered Si doping Semicond. Sci. Technol. 10, 775 (1995) B. Kehrer, W. Quade, E. Schöll: Monte Carlo simulation of impact-ionization-induced breakdown and current filamentation in $\delta$-doped GaAs Phys. Rev. B 51, 7725 (1995) B. Kehrer, W. Quade, E. Schöll: Monte Carlo Simulation of Low Temperature Impurity Breakdown and Current Filamentation in $\delta$-doped GaAs in Proc. 22nd Int. Conf. Phys. Semicond., Vancouver 1994, edited by D. J. Lockwood (World Scientific, Singapore, 1995) W. Quade, G. Hüpper, E. Schöll, T. Kuhn: Monte Carlo simulation of the nonequilibrium phase transition in p-type Ge at impurity breakdown Phys. Rev. B 49, 13408 (1994) T. Kuhn, G. Hüpper, W. Quade, A. Rein, E. Schöll, L. Varani, L. Reggiani: Microscopic analysis of noise and nonlinear dynamics in p-type Germanium Phys. Rev. B 48, 1478 (1993) G. Hüpper, K. Pyragas, E. Schöll: Complex spatiotemporal dynamics of current filaments in crossed electric and magnetic fields Phys. Rev. B 48, 17633 (1993) G. Hüpper, K. Pyragas, E. Schöll: Complex dynamics of current filaments in the low temperature impurity breakdown regime of semiconductors Phys. Rev. B 47, 15515 (1993) R. E. Kunz, E. Schöll: Globally coupled dynamics of breathing current filaments in semiconductors Z. Phys. B 89, 289 (1992) L. Schimansky-Geier, Ch. Zülicke, E. Schöll: Growth of domains under global constraints Physica A 188, 436 (1992) L. Schimansky-Geier, Ch. Zülicke, E. Schöll: Domain formation due to Ostwald ripening in bistable systems far from equilibrium Z. Phys. B 84, 433 (1991) E. Schöll, D. Drasdo: Nonlinear dynamics of breathing current filaments in n-GaAs and p-Ge Z. Phys. B 81, 183 (1990) E. Schöll: Theoretical Approaches to Nonlinear and Chaotic Dynamics of Generation-Recombination Processes in Semiconductors Appl. Phys. A 48, 95 (1989) E. Schöll, P. T. Landsberg: Generalised equal areas rules for spatially extended systems Z. Phys. B 72, 515 (1988) E. Schöll: Equal Areas Rules for Filamentation in SNDC Elements Sol. State El. 29, 687 (1986) E. Schöll: Influence of Boundaries on Dissipative Structures in the Schlögl Model Z. Phys. B 62, 245 (1986) E. Schöll: Stability of Generation-Recombination Induced Dissipative Structures in Semiconductors Z. Phys. B 52, 321 (1983) E. Schöll: Current Layers and Filaments in a Semiconductor Model with an Impact Ionization Induced Instability Z. Phys. B 48, 153 (1982)