Three-dimensional quantum transport simulation of ultra-small FinFETs

1
Three-dimensional quantum transport simulation
of ultra-small FinFETs

• H. Takeda and N. Mori
• Osaka University

2
Introduction

• FinFET Non-planar multiple gate MOSFET

• Quantum Mechanical Effects

• Direct S/D tunneling
• Subband quantization

• Scattering

• Phonon scattering
• Interface roughness

3D quantum transport simulation based on NEGF
method
3
3D NEGF Simulation

• Green痴 function
• Eigen-mode expansion method

3D electron density Electric current

• 3D Poisson equation

Self-consistent calculation
4
Scattering

• Intra-valley phonon scattering

• Constant matrix element
• Self-consistent calculation

Scattering function (Self energy)
Green痴 function (Correlation function)

• Interface roughness

• Random roughness patterns
• Gaussian form

Correlation length
Average displacement
5
Device
Gate length
SiO2 thickness
Length
Source / Drain
Width
Gate
Height
6
Electron Density
Electron density profile
Normalized electron density profile ( cross
section)
7
Electron-Phonon Interaction
Electron density profile
8
Device Characteristics
Ballistic
Phonon scattering
About 20 decrease (ION) Almost the same (IOFF)
characteristics
9
Phonon Assisted Tunneling
Off-state
Phonon scattering reduces current
10
Phonon Assisted Tunneling
Off-state
Phonon scattering reduces current
Phonon absorption enhances current
compensate
11
Phonon Assisted Tunneling
On-state
Very low channel barrier
Phonon scattering reduces current
Tunneling current can be neglected
Drain current is reduced by phonon scattering
12
Interface Roughness
without Roughness
Roughness affects current flow
with Roughness
13
Effect of Interface Roughness

• Roughness 10 patterns
• Threshold voltage

Ballistic
Roughness
characteristics
14
Summery

• We have simulated characteristics of
  the gate-length FinFETs by 3D NEGF
  simulation including the intra-valley phonon
  scattering and the interface roughness.
• The phonon scattering reduces only the
  on-current.
• The interface roughness affects not only the
  on-current but also the off-current.
• Large fluctuation of the threshold voltage is
  caused by the interface roughness in the
  ultra-small FinFETs.