1. Thermal Interface between Carbon Nanotubes and Polar Materials
Slava V. Rotkin
Physics Department & CAMN
Lehigh University

2. COT Open House Oct 14 2008 Slava V Rotkin
Acknowledgements
Dr. A.G. Petrov (Ioffe)
Prof. J.A. Rogers (UIUC)
Dr. V. Perebeinos and Dr. Ph. Avouris (IBM)
Prof. K. Hess (UIUC) and Prof. P. Vogl (UVienna)
COT Open House Oct Slava V Rotkin

3. COT Open House Oct 14 2008 Slava V Rotkin
OUTLINE
Motivation: NT array Thin Film Transistors (TFT)
The old "new" Surface Scattering
- Surface Phonon-Polariton (SPP)
- Remote Polariton Scattering
Physics of SPP thermal conductivity
SPP and heat dissipation in NT devices
Conclusions
COT Open House Oct Slava V Rotkin

4. ITRS Grand Challenges: The Heat
Main performance metrics to be compared with the existing Si-CMOS technology:
Cost
Speed
Integration
and...
Power
Among main evaluation parameters for novel semiconductor electronics technologies the power consumption, and in particular the power dissipation become more and more important
COT Open House Oct Slava V Rotkin

5. ? ITRS Grand Challenges: The Heat
S. Borkar, “Design challenges of technology scaling,” IEEE Micro, vol. 19 (4), 23–29, Jul.–Aug
Among main evaluation parameters for novel semiconductor electronics technologies the power consumption, and in particular the power dissipation become more and more important
COT Open House Oct Slava V Rotkin

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NT-Array Thin Film Transistors
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7. NT aligned array : Novel type TFT
Novel fabrication technique (Left) allows fabrication of Thin-Film Transistors of parallel NT arrays.
Courtesy Prof. John Rogers (UIUC)
Courtesy Prof. John Rogers (UIUC)
SEM of NT growth on different quartz facets
Y-cut [01-10]
Z-cut [0001]
X-cut [2-1-10]
SEM reconstruction ("fake" 3D view) of NT-TFT and gold electrodes.
NTs can be transferred on plastic
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8. Quantum physics of TFT capacitance
Fabrication of NT-Array TFTs revealed new "old" physics.
very large gate coupling – too strong if not taking into account intertube coupling
non-uniformity of the channel – self-screening and "defect healing"
multi-layer dielectrics and surface E/M modes
interface scattering
Most of the tubes are parallel, but the distance between neighbor tubes may vary.
For TFT applications only semiconductor tubes are needed. Thus one needs to destroy (burn out) metallic tubes. Which randomizes the channel.
self-consistent modeling (Poisson+Schroedinger eqs) including e/m response
COT Open House Oct Slava V Rotkin

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Random Array Coupling: Self-healing
Current nonuniformity is a deficiency for device production.
Consider Dr due to non-uniform screening.
-0.35
-0.25
-0.15
DC/C
d=40 nm
d=600 nm
Three sample distributions of the tubes in the random-tube array (d=160 nm, 80% variance).
One may expect a severe variance in device characteristics because of non-uniform Cg
COT Open House Oct Slava V Rotkin

10. Saturation Regime and Heat Dissipation Problem
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11. Saturation Regime: Heat Generation
Scattering in 1D systems is weak due to restricted phase space available for the electron: k -> -k.
However, the strong scattering at high drift electric field is inevitable: saturation regime. The scattering mechanism is an optical phonon emission which results in fast relaxation rates for the hot electrons and holes.
Inelastic scattering rates have been calculated for SWNTs earlier:
However, recent optics experiments indicated that the relaxation rates for hot electrons are even faster, which suggests a possibility for a new unknown scattering mechanism.
COT Open House Oct Slava V Rotkin

12. Saturation Regime: Heat Generation
What was known so far?
Inelastic optical phonon relaxation scattering is likely a factor determining the saturation current in SWNTs :
The hot electron energy is transferred to the SWNT phonon subsystem.
The energy dissipation depends on the environment (thermal coupling).
COT Open House Oct Slava V Rotkin

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Heat Generation (2) j q q j Vd
q~area~nm2
channel heating due to Joule losses and low thermal coupling to leads
It exists, however, a relaxation mechanism which transfers the energy directly to the substrate without intermediate exchange with the SWNT lattice (phonons) which is an inelastic remote optical phonon scattering
Pioneering work by K. Hess and P. Vogl – back to 1972 – RIP-S in Si.
The mechanism appeared to be ineffective for Si MOS-FETs and was almost forgotten for decades...
COT Open House Oct Slava V Rotkin

14. Surface Phonon Polariton
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15. Surface Polariton in SiO2
Specifics of surface polaritons:
electric field is not normal to the surface (at 45o)
electric field decays exponentially from the surface (not a uniform solution of Maxwell equations)
existence of a surface mode essentially depends on existence of the anomalous dispersion region e<0
Surface phonons in polar dielectrics:
due to the dielectric function difference between the substrate and the air, a surface e.m.w. could exist
dielectric function of the polar insulator has a singularity at the LO phonon frequency
surface wave with a strong decay of the electric field in the air appears and interacts with the NT charges

16. COT Open House Oct 14 2008 Slava V Rotkin
Digression:
A tutorial on SPP
COT Open House Oct Slava V Rotkin

17. Details of SPP: NT on SiO2
Interaction with the polar substrate is mediated by emission of virtual photons, namely Surface Phonon-Polariton modes
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18. Remote Polariton Scattering
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19. Physics of SPP scattering in SiO2
Estimates for SiO2-quartz:
electric field in the air is proportional to decay constant, determined from MEq+BC, and F-factor
relevant l is proportional to the wavelength of hot electron
electric field ~107 V/m
finally the scattering time
for vF~108 cm/s
and wSO~150meV :
e ~ 105 V/cm

20. Surface Polariton Scattering Rate
for the SiO2 (quartz) substrate the SPP scattering is likely prevailing over inelastic scattering by NT (own) optical phonons for the small distance to the polar substrate < l ~ 4 nm;
the effect is even stronger for high-k dielectrics due to increase of the Froehlich constant : x20 and more;
the effect is independent of the radius of the NT, thus for narrow NTs it will dominate over the other 1/R mechanisms
JETP Letters, 2006
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21. SPP and Saturation Regime
Inverse drain current vs. inverse applied
electric field
Linear slope clearly shows a saturation regime
low-F and high-F
Is are essentially different, being determined by
different scattering mechanisms
[17,0] NT at the doping level 0.1 e/nm
COT Open House Oct Slava V Rotkin

22. SPP and Saturation Regime
Inverse drain current vs. inverse applied
electric field
Linear slope clearly shows a saturation regime
low-F and high-F
Is are essentially different, being determined by
different scattering mechanisms
low-F scattering is due to NT intrinsic phonon modes and high-F scattering is due to SPP mechanism
COT Open House Oct Slava V Rotkin

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SPP and Overheating
overheating of the channel : neglecting the thermal sink in the leads (~nm2) j qC
where
qph
QSPP
two scattering mechanisms :
NT phonons warm the NT lattice but are inefficient
SPP phonons take the heat directly into bulk substrate;
Joule losses - IsF are for the total energy loss; while NT phonons take only a small fraction of that
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Conclusions
Physics of interactions in NTs at the hetero-interface with Si/SiO2 is rich
Hot electron scattering due to SPP modes provides a new and very effective thermo-conductivity mechanism
New thermal conductivity mechanism is not NT/SiO2 specific – more examples in molecular electronics are expected to exist
Graphenes – another example of nano-hetero-interface where quantum effects may nicely develop into effects useful for applications
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