## Abstract

In this paper the vanishing Debye length limit (space charge neutral limit) of bipolar time-dependent drift-diffusion models for semiconductors with p-n junctions (i.e., with a fixed bipolar background charge) is studied in one space dimension. For general sign-changing doping profiles, the quasi-neutral limit (zero-Debye-length limit) is justified rigorously in the spatial mean square norm uniformly in time. One main ingredient of our analysis is the construction of a more accurate approximate solution, which takes into account the effects of initial and boundary layers, by using multiple scaling matched asymptotic analysis. Another key point of the proof is the establishment of the structural stability of this approximate solution by an elaborate energy method which yields the uniform estimates with respect to the scaled Debye length.

Original language | English (US) |
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Pages (from-to) | 1854-1889 |

Number of pages | 36 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 37 |

Issue number | 6 |

DOIs | |

State | Published - Feb 2006 |

Externally published | Yes |

## Keywords

- Classical energy methods
- Drift-diffusion equations
- Multiple scaling asymptotic expansions
- Quasi-neutral limit
- Singular perturbation
- λ-weighted Liapunov-type functional

## ASJC Scopus subject areas

- Analysis
- Computational Mathematics
- Applied Mathematics