1. Analysis of Strain Effect in Ballistic Carbon Nanotube FETs
Nov. 30, 2006
Youngki Yoon
Dept. of Electrical & Computer Engineering
University of Florida

2. Outline Carbon nanotube field-effect transistor
Uniaxial strain on CNTs
Material properties of strained CNTs
Strain effect on Eg
Strain effect on band-structure-limited velocity
Simulated device structure & approach
Simulation results
I-V characteristics
Strain effect on Imin
Strain effect on Ion
Strain effect on intrinsic delay
Concluding remarks

3. What is CNTFET? G S D CNTFET Conventional MOSFET
CNTFET with doped source drain extentions
CNTFET with metal source drain contacts

4. Why strained CNTs?
J. Cao et al., PRL (2003)
(a) Tensile uniaxial strain and (b) compressive uniaxial strain on the channel of a CNTFET.
Conductance is change by several orders of magnitude
Sentitivity change is available.
T. Tombler et al., Nature (2000)

5. Let’s apply uniaxial strain!
(16,0) CNT
Band gap is increased (Egh=0.33eV to 0.44eV).
Slope (band-structrue-limited velocity) is decreased.

6. Strain effect on CNTs (Variation of Eg and band-structure-limited velocity)
Tensile strain
Eg of (16,0) CNT ↑ (n=3q+1 group)
Eg of (17,0) CNT ↓ (n=3q+2 group)
Compressive strain
Eg of (16,0) CNT ↓ (n=3q+1 group)
Eg of (17,0) CNT ↑ (n=3q+2 group)
Eg vs. uniaxial strain strength
Band-structure-limited velocity:
Tensile strain
B.S.L. vel. of (16,0) CNT ↓ (n=3q+1 group)
B.S.L. vel. of of (17,0) CNT ↑ (n=3q+2 group)
Compressive strain
B.S.L. vel. of of (16,0) CNT ↑ (n=3q+1 group)
B.S.L. vel. of of (17,0) CNT ↓ (n=3q+2 group)
The lowest subbands of (16,0) CNTs.
Solid lines: unstrained (16,0) CNT.
Dashed lines: 2% strained CNT.

7. Device structure & approach
Coaxially gated Schottky Barrier CNTFET ( )
3nm HfO2 gate oxide with a dielectric constant of 16
40nm strained (16,0) and (17,0) CNT channel
0.4V power supply
Approach
Self-consistent NEGF formalism with Poisson equation
Mode space approach M
Gate
Strained CNT
Device structure

8. Mode space approach Real space approach Mode space approach
A part of (n,0) zigzag nanotube lattice in real space
Mode space approach
(n,0) ZNT is decoupled into n one-dimensional mode space lattice.
Mode space lattice

9. ID-VG characteristics
(16,0) CNTFET w/ uniaxial strain
(17,0) CNTFET w/ uniaxial strain
Device characteristics strongly depend on the band gap of the channel material.
ID-VG characteristics change significantly with even a small strain.

10. Strain effect on Imin Imin ≡ minimum current delivered (VG=0.2V)
Main figure
Solid line: (16,0) CNTFET
Dashed line: (17,0) CNTFET
Subset: band profile vs. channl position at VG=0.2V
Solid line: unstrained (16,0) CNTFET
Dashed line: 2% strained (16,0) CNTFET
Imin ≡ minimum current delivered (VG=0.2V)
A simple estimation for Imin

11. Strain effect on Ion Ion ≡ current at VG=Von=Voff+VDD ,
Ioff
VDD=0.4V
Solid line: (16,0) CNTFET
Dashed line: (17,0) CNTFET
(16,0) CNTFET w/ uniaxial strain
Ion ≡ current at VG=Von=Voff+VDD ,
where Voff is the voltage at Ioff=10-7A.
unstrained 2%
unstrained
2% uniaxial
(16,0) CNTFET at on-state

12. Strain effect on intrinsic delay
(16,0) CNTFET w/ uniaxial strain
(17,0) CNTFET w/ uniaxial strain ON
OFF
Quantum reflection 0% 2% 0% 2%
Lowest conduction band of (16,0) CNT
Ec vs. X for the same Ion/Ioff

13. Summary
Two important material property changes after applying uniaxial strains: Eg
Band-structure-limited velocity
Nominal device & approach
Coaxially gated CNT SBFET with half band gap SB height
Self-consistent NEGF with Poisson’s eq.
Mode space approach
Results
I-V characteristics are changed a lot with even a small strain strength.
Imin , Ion , and intrinsic delay are affected by Eg and B.S.L velocity changes.
Strain engineering can be effectively used to tune up the device performance, but trade-off should be carefully considered.
Thank you