A. Arnold, J. A. Carrillo, L. Desvillettes, J. Dolbeault, A. Jüngel et al., Entropies and equilibria of many-particle systems: an essay on recent research, Monatsh. Math, pp.142-177, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01583063

C. Bataillon, F. Bouchon, C. Chainais-hillairet, J. Fuhrmann, E. Hoarau et al., Numerical methods for the simulation of a corrosion model with moving oxide layer, Journal of Computational Physics, vol.231, issue.18, pp.231-6213, 2012.
DOI : 10.1016/j.jcp.2012.06.005

R. Belaouar, N. Crouseilles, P. Degond, and E. Sonnendrücker, An Asymptotically Stable Semi-Lagrangian scheme in??the Quasi-neutral Limit, Journal of Scientific Computing, vol.149, issue.3, pp.41-341, 2009.
DOI : 10.1007/978-3-662-05018-7
URL : https://hal.archives-ouvertes.fr/hal-00189383

N. B. Abdallah, P. Degond, and P. , On a hierarchy of macroscopic models for semiconductors, Journal of Mathematical Physics, vol.17, issue.7, pp.3306-3333, 1996.
DOI : 10.1016/0038-1101(94)90217-8

M. Bessemoulin-chatard, A finite volume scheme for convection???diffusion equations with nonlinear diffusion derived from the Scharfetter???Gummel scheme, Numerische Mathematik, vol.16, issue.1, pp.637-670, 2012.
DOI : 10.1109/T-ED.1969.16566
URL : https://hal.archives-ouvertes.fr/hal-00534269

Y. Brenier and E. Grenier, Limitesingulì ere du système de Vlasov- Poisson dans le régime de quasi neutralité: le cas indépendant du temps, C. R. Acad. Sci. Paris Sér. I Math, pp.318-121, 1994.

F. Brezzi, L. D. Marini, and P. Pietra, Two-Dimensional Exponential Fitting and Applications to Drift-Diffusion Models, SIAM Journal on Numerical Analysis, vol.26, issue.6, pp.1342-1355, 1989.
DOI : 10.1137/0726078

C. Chainais-hillairet, J. G. Liu, and Y. J. Peng, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis, ESAIM: Mathematical Modelling and Numerical Analysis, vol.7, issue.2, pp.319-338, 2003.
DOI : 10.1007/978-3-7091-6961-2

C. Chainais-hillairet and Y. J. Peng, FINITE VOLUME APPROXIMATION FOR DEGENERATE DRIFT-DIFFUSION SYSTEM IN SEVERAL SPACE DIMENSIONS, Mathematical Models and Methods in Applied Sciences, vol.16, issue.03, pp.461-481, 2004.
DOI : 10.1109/T-ED.1969.16566

C. Chainais-hillairet and M. H. Vignal, Asymptotic preserving schemes in the quasi-neutral limit for the drift-diffusion system Finite volumes for complex applications. VI. Problems & perspectives, Proceedings of the conference, pp.205-213, 2011.

M. Chatard, Asymptotic behavior of the Scharfetter-Gummel scheme for the drift-diffusion model Finite volumes for complex applications. VI. Problems & perspectives, Proceedings of the conference, pp.235-243, 2011.

I. Choquet, P. Degond, and C. Schmeiser, Energy-Transport Models for Charge Carriers Involving Impact Ionization in Semiconductors, Transport Theory and Statistical Physics, vol.32, issue.2, pp.99-132, 2003.
DOI : 10.1081/TT-120019039
URL : http://www.hyke.org/preprint/Asymptotic/ps/ChDeSc1.ps

S. Cordier and E. Grenier, Quasineutral limit of an euler-poisson system arising from plasma physics, Communications in Partial Differential Equations, vol.100, issue.5-6, pp.1099-1113, 2000.
DOI : 10.1002/(SICI)1097-0312(199709)50:9<821::AID-CPA2>3.0.CO;2-7

P. Crispel, P. Degond, and M. H. Vignal, An asymptotic preserving scheme for the two-fluid Euler???Poisson model in the quasineutral limit, Journal of Computational Physics, vol.223, issue.1, pp.208-234, 2007.
DOI : 10.1016/j.jcp.2006.09.004
URL : https://hal.archives-ouvertes.fr/hal-00635602

P. Degond, F. Deluzet, L. Navoret, A. B. Sun, and M. H. Vignal, Asymptotic-Preserving Particle-In-Cell method for the Vlasov???Poisson system near quasineutrality, Journal of Computational Physics, vol.229, issue.16, pp.229-5630, 2010.
DOI : 10.1016/j.jcp.2010.04.001
URL : https://hal.archives-ouvertes.fr/hal-00359356

L. Desvillettes and K. Fellner, Exponential decay toward equilibrium via entropy methods for reaction???diffusion equations, Journal of Mathematical Analysis and Applications, vol.319, issue.1, pp.157-176, 2006.
DOI : 10.1016/j.jmaa.2005.07.003
URL : https://doi.org/10.1016/j.jmaa.2005.07.003

R. Eymard, J. Fuhrmann, and K. Gärtner, A finite volume scheme for nonlinear parabolic equations derived from one-dimensional local dirichlet problems, Numerische Mathematik, vol.102, issue.3, pp.463-495, 2006.
DOI : 10.1007/s00211-005-0659-5
URL : http://www.cmi.univ-mrs.fr/~gallouet/art.d/congres.d/equadiff.d/equadiff-egh.pdf

R. Eymard, T. Gallouët, and R. Herbin, Finite volume methods, Handbook of numerical analysis, pp.713-1020, 2000.

F. Filbet and S. Jin, An Asymptotic Preserving Scheme for the ES-BGK Model of the Boltzmann Equation, Journal of Scientific Computing, vol.120, issue.2, pp.46-204, 2011.
DOI : 10.1016/S0997-7546(00)01103-1

R. N. Franklin and J. R. Ockendon, Asymptotic matching of plasma and sheath in an active low pressure discharge, Journal of Plasma Physics, vol.1, issue.02, pp.371-385, 1970.
DOI : 10.1098/rspa.1950.0064

H. Gajewski, On Existence, Uniqueness and Asymptotic Behavior of Solutions of the Basic Equations for Carrier Transport in Semiconductors, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.294, issue.2, pp.101-108, 1985.
DOI : 10.1002/zamm.19850650210

H. Gajewski and K. Gärtner, On the Discretization of van Roosbroeck's Equations with Magnetic Field, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.16, issue.5, pp.247-264, 1996.
DOI : 10.1002/j.1538-7305.1950.tb03653.x

H. Gajewski and K. Gröger, On the basic equations for carrier transport in semiconductors, Journal of Mathematical Analysis and Applications, vol.113, issue.1, pp.12-35, 1986.
DOI : 10.1016/0022-247X(86)90330-6

K. Gärtner, Existence of Bounded Discrete Steady-State Solutions of the Van Roosbroeck System on Boundary Conforming Delaunay Grids, SIAM J. Sci. Comput, pp.31-1347, 2009.

I. Gasser, The initial time layer problem and the quasineutral limit in a nonlinear drift diffusion model for semiconductors, Nonlinear Differential Equations and Applications, vol.8, issue.3, pp.237-249, 2001.
DOI : 10.1007/PL00001447

I. Gasser, C. D. Levermore, P. A. Markowich, and C. Schmeiser, The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model, European Journal of Applied Mathematics, vol.12, issue.04, pp.497-512, 2001.
DOI : 10.1017/S0956792501004533

A. Glitzky, Exponential decay of the free energy for discretized electro-reaction???diffusion systems, Nonlinearity, vol.21, issue.9, pp.1989-2009, 2008.
DOI : 10.1088/0951-7715/21/9/003

A. Glitzky, Uniform exponential decay of the free energy for Voronoi finite volume discretized reaction-diffusion systems, Mathematische Nachrichten, vol.26, issue.17-18, p.21592174, 2011.
DOI : 10.1016/0362-546X(94)00297-U
URL : http://www.wias-berlin.de/preprint/1443/wias_preprints_1443.pdf

A. Glitzky and K. Gärtner, Energy estimates for continuous and discretized electro-reaction-diffusion systems, Nonlinear Anal, pp.788-805, 2009.
DOI : 10.1016/j.na.2008.01.015
URL : http://www.wias-berlin.de/preprint/1222/wias_preprints_1222.pdf

A. Glitzky and R. Hünlich, Stationary solutions to an energy model for semiconductor devices where the equations are defined on different domains, Mathematische Nachrichten, vol.17, issue.12, pp.1676-1693, 2008.
DOI : 10.1002/mana.200710707
URL : https://onlinelibrary.wiley.com/doi/pdf/10.1002/mana.200710707

E. Grenier, Oscillations in quasineutral plasmas, Communications in Partial Differential Equations, vol.15, issue.1982, pp.363-394, 1996.
DOI : 10.1215/kjm/1250520925

A. M. , Il'in, A difference scheme for a differential equation with a small parameter multiplying the highest derivative, Mat. Zametki, vol.6, pp.237-248, 1969.

S. Jin, Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations, SIAM Journal on Scientific Computing, vol.21, issue.2, pp.441-454, 1999.
DOI : 10.1137/S1064827598334599

A. , Numerical Approximation of a Drift-Diffusion Model for Semiconductors with Nonlinear Diffusion, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.46, issue.10, pp.783-799, 1995.
DOI : 10.1007/978-1-4899-3614-1

A. , Quasi-hydrodynamic semiconductor equations, Progress in Nonlinear Differential Equations, 2001.
DOI : 10.1007/978-3-0348-8334-4

A. , Transport equations for semiconductors, Lect. Notes Phys, 2009.

A. Jüngel and Y. J. Peng, A hierarchy of hydrodynamic models for plasmas. Quasi-neutral limits in the drift-diffusion equations, Asymptot. Anal, vol.28, pp.49-73, 2001.

A. Jüngel and P. Pietra, A Discretization Scheme for a Quasi-Hydrodynamic Semiconductor Model, Mathematical Models and Methods in Applied Sciences, vol.07, issue.07, pp.935-955, 1997.
DOI : 10.1142/S0218202597000475

A. , QUALITATIVE BEHAVIOR OF SOLUTIONS OF A DEGENERATE NONLINEAR DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS, Mathematical Models and Methods in Applied Sciences, vol.05, issue.04, pp.497-518, 1995.
DOI : 10.1142/S0218202595000292

R. D. Lazarov, I. D. Mishev, and P. S. Vassilevski, Finite Volume Methods for Convection-Diffusion Problems, SIAM Journal on Numerical Analysis, vol.33, issue.1, pp.31-55, 1996.
DOI : 10.1137/0733003

M. Lemou and L. Mieussens, A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit, SIAM Journal on Scientific Computing, vol.31, issue.1, pp.31-334, 2008.
DOI : 10.1137/07069479X
URL : https://hal.archives-ouvertes.fr/hal-00348594

P. A. Markowich, The stationary semiconductor device equations, Computational Microelectronics, 1986.

P. A. Markowich, C. A. Ringhofer, and C. Schmeiser, Semiconductor equations, 1990.

M. S. Mock, An Initial Value Problem from Semiconductor Device Theory, SIAM Journal on Mathematical Analysis, vol.5, issue.4, pp.597-612, 1974.
DOI : 10.1137/0505061

A. Prohl and M. Schmuck, Convergent discretizations for the Nernst???Planck???Poisson system, Numerische Mathematik, vol.39, issue.4, pp.591-630, 2009.
DOI : 10.1007/978-3-642-79987-7

D. L. Scharfetter and H. K. , Large-signal analysis of a silicon Read diode oscillator, IEEE Transactions on Electron Devices, vol.16, issue.1, pp.64-77, 1969.
DOI : 10.1109/T-ED.1969.16566

M. Slemrod and N. Sternberg, Quasi-Neutral Limit for Euler-Poisson System, Journal of Nonlinear Science, vol.11, issue.3, pp.193-209, 2001.
DOI : 10.1007/s00332-001-0004-9

H. Sze, J. Benford, W. Woo, and B. Harteneck, Dynamics of a virtual cathode oscillator driven by a pinched diode, Physics of Fluids, vol.27, issue.11, pp.29-3873, 1986.
DOI : 10.1063/1.864811

S. M. Sze, Physics of Semiconductor Devices, 1969.

W. Van-roosbroeck, Theory of the flow of electrons and holes in germanium and other semiconductors, Bell System Tech, J, vol.29, pp.560-607, 1950.