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## Nanowire

Simulate 3D nanowire transport in the effective mass approximation and 3D Poisson solution

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#### Abstract

Silicon nanowire transistors are promising device structures for future integrated circuits. Short channel effects are becoming more and more important in the nanoscale regime, and therefore effective gate control will be necessary to achieve good device performance.
Devices based on silicon nanowires can be manufactured with multigate and gate-all-around transistors and you can explore them with this tool.
In contrast to planar MOSFETs which have uniform charge and potential profiles in the transverse direction (i.e., normal to both the gate and the source-drain direction), a silicon nanowire transistor has a genuinely 3D distribution of electron density and electrostatic
potential. Therefore self-consistent 3D simulations are mandatory, and you run them with this tool. One of the transport models assumes ballistic transport, which gives the upper performance limit of the devices. The effective-mass mode space approach (either coupled or uncoupled) produces high computational efficiency that makes this
simulator practical for extensive device simulation and
design. Scattering is treated by so-called BÃ¼ttiker probes, which was previously used in metal-oxide-semiconductor field effect transistor simulations. The effects of scattering on both internal device
characteristics and terminal currents can be examined, which enables our simulator to be used for the exploration of realistic performance limits of silicon-nanowire transistors.
The mode space approach treats quantum confinement and transport separately. The simulations you can perform consist of the following steps:

- Solve the 3D Poisson equation for the electrostatic potential.
- Solve the 2D Schrodinger equation with closed boundary conditions for each cross section (or slice) of the nanowire transistor to obtain the electron subbands (along the nanowire) and eigenfunctions.
- Solve the coupled or uncoupled nonequilibrium Green function (NEGF) transport equations for the electron charge density.
- Go to step (1) to calculate the electrostatic potential. If the self-consistent loop has converged, calculate the electron current using the NEGF approach and show the results.

- Uncoupled mode space with averaging of the potential on the slices. This is the fastest option.Default setting would take 15 min per bias point
- Uncoupled mode space with scattering by Buttiker probes and no averaging of the potential. This option takes much more time.Default setting would take about 45 min per bias point
- Coupled mode space without scattering and without averaging of the potential. Due to the coupling of the modes, this option is also much slower than the first one. But no worries; you can start the simulation and login back later to check the results. This option would take about 50 min per bias point

- 2.1 - Enabled quick runs for Uncoupled mode.
- 2.0.2 - Added E Vs T(E) curve
- 2.0.1 - Fixed for error in units 1D electron density
- 2.0 - Improvements in
*Rappture Input*- Added mesh fineness factor, Added different orientation <100>,<110> & <111>, Added material properties, Added different transport orientation, Added pre-run examples- Channel formation, Uncoupled Mode Space with averaging, Coupled Mode Space, Uncoupled Mode Space with scattering. Improvements in*Rappture Output*-3D Eigenfunctions,3D potential,3D electron density,3D Density of states,1D electron density,1D Potential profile in sequence for each bias point.

**Improvements / modifications in subsequent releases:**

#### Credits

This tool is based on the work of Jing Wang, Eric Polizzi, and Clemens Heitzinger.

#### Cite this work

Researchers should cite this work as follows:

- Jing Wang, Eric Polizzi, Mark Lundstrom, "A three-dimensional quantum simulation of silicon nanowire transistors with the effective-mass approximation,"
*Journal of Applied Physics***96**(4), pages 2192-2203, 2004.