Coupling of Quantum and Electrothermal Effects in Semiconductor Device Simulation
by
Carlo de Falco
Bergische Universitaet Wuppertal, Gaußstr. 20 D-42119 Wuppertal, Germany
Coauthors: Joseph W. Jerome, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730, USA and Riccardo Sacco,Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy

According to the ITRS predictions, self-heating and mutual-heating effects will gain increasing importance in the near future especially in emerging SOI and thin-film CMOS technologies, where single device cooling is going to become a serious limitation. Furthermore, due to off-state leakage currents caused by quantum electrostatic effects, even steady-state power consumption will become an important factor affecting device and chip performance. This scenario imposes severe requirements on the development of mathematical models and numerical simulation methods. On the one hand, simulation tools to handle both quantum and heating effects are in order. On the other hand, the increasing complexity of the device geometries and the demand for the concurrent simulation of larger chip areas require models with low computational cost to achieve reasonable efficiency.

Based on the above considerations, in this communication we present a hierarchy of Quantum Corrected Electro Thermal (QCET) models that include:

• quantum electrostatic mechanisms (source-to-drain tunneling, energy quantization effects due to strong confinement, equivalent oxide thickness) through the use of different corrections of the carrier state equations, ranging from the Improved Modified Local Density Approach [5] to the Density-Gradient model [2] or to the direct solution of the Schrödinger equation [2];

• carrier and lattice heating via a full Thermo Energy Balance (THEB) model [1] or its simplified version (STHEB) [4, 6].

For the numerical solution of the resulting systems of nonlinearly coupled PDEs, we adapt the functional iteration and discretization techniques developed and thouroughly investigated in [2] and currently under theoretical analysis in [3]. Furthermore, we propose an approach based on heterogeneous domain decomposition (HDD) for thermal coupling of neighbouring devices, and a reduced-order version based on the use of lumped parameter thermal elements to reduce the discrete problem size [6].

References

[1] A. Benvenuti and W. M. Coughran and M. R. Pinto, A thermal-fully hydrodynamic model for semiconductor devices and applications to III-IV HBT simulation, IEEE Thans. El. Dev., 44 (9), 1349 (1997).

[2] C. de Falco and E. Gatti and A.L. Lacaita and R. Sacco, Quantum-Corrected Drift-Diffusion models for transport in semiconductor devices, J. Comp. Phys. 204 (2), 533 (2005).

[3] C. de Falco and J.W. Jerome and R. Sacco, Quantum Corrected Drift-Diffusion Models: Solution Fixed Point Map and Finite Element Approximation, in preparation (2007).

[4] H. Hayashi and R. Dang, A non-isothermal device simulator for MOSFET analysis, IEEE Trans. Magn., 29, 101 (1993).

[5] C. Jungermann and C. Nguyen and B. Neinhüs, S. Decker and B. Meinerzhagen, Improved modified local density approximation for modeling of size quantization in NMOSFETs, in Tech. Proc. of the 2001 Intern. Conf. on Modeling and Simulation of Microsystems, 458, (2001).

[6] E. Medina and M. Pagani, Multiphysics modeling and numerical simulation of electrothermal effects in semiconductor devices, Master's thesis, Politecnico di Milano, (2006).

Date received: June 27, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavg-97.