Analysis of Strain Effect in Ballistic Carbon Nanotube FETs

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 D S CNTFET Conventional MOSFET CNTFET with metal source drain contacts CNTFET with doped source drain extentions

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. Gate M M Strained CNT Gate Device structure & approach • Device Structure • 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 Device structure

8. Mode space approach Real 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 • Main figure • Solid line: (16,0) CNTFET • Dashed line: (17,0) CNTFET • Imin ≡ minimum current delivered (VG=0.2V) • A simple estimation for Imin • Subset: band profile vs. channl position at VG=0.2V • Solid line: unstrained (16,0) CNTFET • Dashed line: 2% strained (16,0) CNTFET

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

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

13. Thank you 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.