Abstract
In this work we present the mathematical modeling and the simulation of the diffusive transport of an electron gas confined in a nanostructure. A coupled quantum-classical system is considered, where the coupling occurs in the momentum variable: the electrons are like point particles in the direction parallel to the gas, while they behave like waves in the transverse direction. A drift-diffusion description in the transport direction is obtained thanks to an asymptotic limit of the Boltzmann transport equation for confined electrons. The system is used to model the transport of charged carriers in a nanoscale Double-Gate MOSFET. Simulations of transport in such a device are presented.
Similar content being viewed by others
References
Bastard, G.: Wave mechanics applied to semiconductor heterostructures, Les éditions de Physique (1996)
Davies, J.H.: The Physics of Low Dimensional Semiconductors. Cambridge Univ. Press, Cambridge (1998)
Ferry, D.K., Goodnick, S.M.: Transport in Nanostructures. Cambridge Univ. Press, Cambridge (1997)
Balestra, F., Cristoloveanu, S., Benachir, M., Brini, J., Elewa, T.: Double gate silicon-on-isolator transistor with volume inversion: A new device with greatly enhanced performance. IEEE Electron Device Lett. EDL-8, 410–412 (1987)
Polizzi, E., Ben Abdallah, N.: Subband decomposition approach for the simulation of quantum electron transport in nanostructures. J. Comput. Phys. 202, 150–180 (2005)
Ben Abdallah, N., Polizzi, E., Mouis, M., Méhats, F.: Simulation of 2D quantum transport in ultrashort DG-MOSFETs: a fast algorithm using subbands. Proceedings of the SISPAD Conference 2003, IEEE product TH8679-TBR, pp. 267–270 (2003)
Mock, M.S.: Analysis of Mathematical Models of Semiconductor Devices. Advances in Numerical Computation, Series 3. Boole Press, Dublin (1983)
Markowich, P.A., Ringhofer, C.A., Schmeiser, C.: Semiconductor Equations. Springer, Vienna (1990)
Selberherr, S.: Analysis and Simulation of Semiconductor Devices. Springer, Vienna (1984)
Jungemann, C., Grasser, T., Neinhüs, B., Meinerzhagen, B.: Failure of moments-based transport models in nanoscale devices near equilibrium. IEEE Trans. Electron Devices 52(11), 2404–2408 (2005)
Nekovee, M., Geurts, B.J., Boots, H.M.J., Schuurmans, M.F.H.: Failure of extended–moment–equation approaches to describe ballistic transport in submicrometer structures. Phys. Rev. B 45(12), 6643–6651 (1992)
Baccarani, G., Reggiani, S.: A compact double-gate MOSFET model comprising quantum-mechanical and nonstatic effects. IEEE Trans. Electron Devices 46(8), 1656 (1999)
Negulescu, C., Ben Abdallah, N., Polizzi, E., Mouis, M.: Simulation Schemes in 2D nanoscale MOSFETs: a WKB based method. J. Comput. Electron., to appear in special issue for the ICWE 10
Ancona, M.G., Iafrate, G.J.: Quantum correction to the equation of state of an electron gas in a semiconductor. Phys. Rev. B 40, 7347 (1989)
Casssano, G., De Falco, C., Giulianetti, Cl., Sacco, R.: Numerical simulation of tunneling effects in nanoscale semiconductor devices using quantum corrected drift-diffusion models. Comput. Methods Appl. Mech. Eng. 195(19–22), 2193–2208 (2006)
Curatola, G., Iannaccone, G., Fiori, G.: Effective Bohm Quantum Potential for device simulators based on drift-diffusion and energy transport, 1–4 September “SISPAD 2004”, Munich, Germany, pp. 275–278
Degond, P., Méhats, F., Ringhofer, C.: Quantum energy-transport and drift-diffusion models. J. Stat. Phys. 118(3–4), 625–665 (2005)
Gallego, S., Méhats, F.: Numerical approximation of a quantum drift-diffusion model. C.R. Acad. Sci. Paris, Ser. I 339, 519–524 (2004)
Pirovano, A., Lacaita, A., Spinelli, A.: Two dimensional Quantum Effects in Nanoscale MOSFETs. IEEE Trans. Electron Devices 49(1), 25–31 (2002)
De Falco, C., Gatti, E., Lacaita, A.L., Sacco, R.: Quantum-corrected drift-diffusion models for transport in semiconductor devices. J. Comput. Phys. 204(2), 533–561 (2005)
Jüngel, A., Pinnau, R.: Convergent semidiscretization of a nonlinear fourth order parabolic system. Math. Mod. Num. Anal. 37, 277–289 (2003)
Nier, F.: A stationary Schrödinger-Poisson system arising from the modelling of electronic devices. Forum Math. 2(5), 489–510 (1990)
Seeger, K.: Semiconductor Physics. An Introduction, 6th edn. Springer, Berlin (1997)
Vinter, B., Weisbuch, C.: Quantum Semiconductor Structures. Academic Press, San Diego (1991)
Golse, F., Poupaud, F.: Limite fluide des équations de Boltzmann des semiconducteurs pour une statistique de Fermi-Dirac. Asymptot. Anal. 6, 135–169 (1992)
Poupaud, F.: Diffusion approximation of the linear semiconductor Boltzmann equation: analysis of boundary layers. Asymptot. Anal. 4, 293–317 (1991)
Ben Abdallah, N., Méhats, F., Vauchelet, N.: Diffusive transport of partially quantized particles: existence uniqueness and long time behaviour. Proc. Edinb. Math. Soc. 49, 513–549 (2006)
Vauchelet, N.: Diffusive limit of a kinetic system of partially quantized particles in two dimensions, submitted
Pöschel, J., Trubowitz, E.: Inverse Spectral Theory. Academic Press, San Diego (1987)
Ben Abdallah, N., Tayeb, M.L.: Diffusion approximation for the one dimensional Boltzmann-Poisson system. Multiscale Model. Simul. 4(3), 896–914 (2005)
Bouchut, F., Golse, F., Pulvirenti, M.: Kinetic Equations and Asymptotic Theory. Series in Appl. Math. Gauthiers-Villars, Paris (2000)
Scharfetter, D.L., Gummel, H.K.: Large signal analysis of a silicon Read diode oscillator. IEEE Trans. Electron Devices ED-16, 64–77 (1969)
Brezzi, F., Marini, L.D., Pietra, P.: Méthodes d’éléments finis mixtes et schéma de Scharfetter-Gummel. C.R. Acad. Sci. Paris Sér. I 305, 599–604 (1987)
Caussignac, Ph., Zimmermann, B., Ferro, R.: Finite element approximation of electrostatic potential in one dimensional multilayer structures with quantized electronic charge. Comput. 45, 251–264 (1990)
Gummel, H.K.: A self-consistent iterative scheme for one-dimensional steady state transistor calculations. IEEE Trans. Electron Devices 11(10), 455 (1964)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pietra, P., Vauchelet, N. Modeling and simulation of the diffusive transport in a nanoscale Double-Gate MOSFET. J Comput Electron 7, 52–65 (2008). https://doi.org/10.1007/s10825-008-0253-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10825-008-0253-z