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CMCS at EPFL

Fluid models for the simulation of charge transport in submicron and nanometric device structures - Consolidated research activities

1. Numerical solution of the 2D Drift-Diffusion (DD) transport model using stabilized mixed finite volume methods.
Participants:
Stefano Micheletti, Fausto Saleri - MOX, Politecnico di Milano
Riccardo Sacco - Dipartimento di Matematica, Politecnico di Milano

A stable and accurate discretization has been devised introducing proper quadrature formulae into the dual-mixed formulation of the decoupled DD system. This technique yields a mixed finite volume approach which enjoys the same conservation and accuracy properties of the mixed method with a considerable saving of computational effort. The next figures show the geometry of a 1-micron MOS device with the computed I-V characteristics and the computed distributions of electric potential and electron concentration (in logarithmic scale).

 
Authors: R. Sacco, F. Saleri

 
Authors: R. Sacco, F. Saleri

Relevant publications:
[NMPDE97] , [EastWest97] , [CWIQuar97] , [SISC01]

2. Numerical solution of the 2D Energy-Balance (EB) transport model using stabilized mixed finite volume methods.
Participants:
Stefano Micheletti, Fausto Saleri - MOX, Politecnico di Milano
Riccardo Sacco - Dipartimento di Matematica, Politecnico di Milano

The methods introduced in the solution of the DD equations have been generalized to deal with the EB model. The next figures show the computed electron concentration (in logarithmic scale) and electron temperature in the same device as in the previous example. Notice the effect of thermal diffusion around the drain junction and the corresponding broadening of the inversion layer. Notice also the considerable carrier heating at the drain end of the channel.

 
Authors: S. Micheletti, R. Sacco, F. Saleri

Relevant publications:
[CVS99]

3. Numerical solution of the 1D and 2D Hydrodynamical (HD) transport model using upwinded finite differences.

Participants:
Stefano Micheletti - MOX, Politecnico di Milano
Riccardo Sacco - Dipartimento di Matematica, Politecnico di Milano
PhD students:
Luca Ballestra


Robust and accurate first and second order discretizations have been proposed for the simulation of submicron devices using both full Navier-Stokes and Euler descriptions of charge transport. The next figures show the electron velocity and concentration in a 1D n+-n-n+ structure modeling the conducting channel of a submicron MOS device with length equal to 0.4 micron. Notice the formation of a shock wave corresponding to electron velocity overshoot at the entrance of the channel, and the considerable carrier heating at the exit of the channel due to high-field acceleration across the submicron-sized region.

 
Authors: L. Ballestra, S. Micheletti, R. Sacco, F. Saleri

The next figures show the results of the simulation of a 2D MESFET submicron device, including the geometry of the device and the computed electron concentration (in log-10 scale), spatial distribution of the Mach number and electron temperature. Notice the extremely sharp boundary layer in the neighborhood of the gate contact, the onset of supersonic regions leading to the formation of truly 2D shock waves in the semiconductor and the considerable carrier heating around the drain junction.

 
Authors: L.Ballestra, S.Micheletti, R.Sacco, F.Saleri

 
Authors: L.Ballestra, S.Micheletti, R.Sacco, F.Saleri

Relevant publications:
[CVS01] , [PhD02] , [CMAME02]

4. Numerical solution of the 1D Quantum-Drift-Diffusion (QDD) transport model.

Participants:
Stefano Micheletti - MOX, Politecnico di Milano
Riccardo Sacco - Dipartimento di Matematica, Politecnico di Milano
Degree students:
Paolo Simioni


This is a very recent research area of relevant impact in modern nanometric semiconductor device structures. In the study of such devices, it is mandatory to consider quantum effects to model effectively charge transport. Here we deal with a perturbation of the standard DD model including a dispersive relation into the definition of the current density. The next figures show the geometry and the potential barrier profile of a 1D nanometer-sized heterostructure, and the computed I-V characteristics and electron concentration (in logarithmic scale) for a suitably chosen value of the effective electron mass. Notice the ability of the model in reproducing the negative differential resistance that is typical in these applications.

 
Authors: S.Micheletti, R.Sacco, P.Simioni

 
Authors: S.Micheletti, R.Sacco, P.Simioni

Relevant publications:
[DegThe01] , [SCEE02b]

5. Numerical solution of the 3D HD transport model using stabilized finite elements.

Participants :
Riccardo Sacco - Dipartimento di Matematica, Politecnico di Milano
Degree students:
Carlo de Falco, Giovanni Scrofani

The activity aims at devising efficient and stable discretizations of the fully 3D Navier-Stokes/Euler system for semiconductor device modeling. This step of the research is absolutely necessary for a state-of-the-art simulation of real-life devices. The huge computational effort demands for proper algorithms to manage complex geometries and requires a multi-processor environment. These issues are currently being investigated in collaboration with the degree students Carlo de Falco and Giovanni Scrofani. The discretization employs the 3D parallel tetrahedral-based software for the solution of the Navier-Stokes/Euler system developed by Prof. Carlo L. Bottasso, Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano. The code uses the time-discontinuous stabilized finite element formulation proposed by T.J.R. Hughes and co-workers. This collaboration is part of the IPACS project under the Large Scale Computing (LSC) initiative developed in the last two years at Politecnico di Milano.

The next figures, concerning with the study of a n+-n-n+ndiode structure, show the doping density, expressed in um^-3, the electron density, expressed in um^-3, the electron velocity, expressed in 10^7 um/s and the electron temperature, expressed in units of T_0=77 K (the data of the last three figures are sampled along the red line of the 3D figure).

     
Authors: C. de Falco, R. Sacco, G. Scrofani

The next figures, concerning with the study of a 3D diode structure, show the space charge density and the computed electric potential distribution in the device along with the electron velocity field.

Authors: C. de Falco, R. Sacco, G. Scrofani

The following movies show the electric potential, the electric field and the electric field strength in different sections of the device (click on the thumbnails to see animations).

Authors: C. de Falco, R. Sacco, G. Scrofani

The last simulated device is a simplified model of an EEPROM memory cell. The following pictures show the geometry and doping profile of the device, and the electric potential distribution.

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