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

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 14 2008 Slava V Rotkin

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 14 2008 Slava V Rotkin

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 14 2008 Slava V Rotkin

? ITRS Grand Challenges: The Heat S. Borkar, “Design challenges of technology scaling,” IEEE Micro, vol. 19 (4), 23–29, Jul.–Aug. 1999. 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 14 2008 Slava V Rotkin

COT Open House Oct 14 2008 Slava V Rotkin NT-Array Thin Film Transistors _____________ COT Open House Oct 14 2008 Slava V Rotkin

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 COT Open House Oct 14 2008 Slava V Rotkin

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 14 2008 Slava V Rotkin

COT Open House Oct 14 2008 Slava V Rotkin 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 14 2008 Slava V Rotkin

Saturation Regime and Heat Dissipation Problem _____________

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 14 2008 Slava V Rotkin

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 14 2008 Slava V Rotkin

COT Open House Oct 14 2008 Slava V Rotkin 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 14 2008 Slava V Rotkin

Surface Phonon Polariton _____________

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

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

Details of SPP: NT on SiO2 Interaction with the polar substrate is mediated by emission of virtual photons, namely Surface Phonon-Polariton modes COT Open House Oct 14 2008 Slava V Rotkin

Remote Polariton Scattering _____________

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

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 COT Open House Oct 14 2008 Slava V Rotkin

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 14 2008 Slava V Rotkin

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 14 2008 Slava V Rotkin

COT Open House Oct 14 2008 Slava V Rotkin 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 COT Open House Oct 14 2008 Slava V Rotkin

COT Open House Oct 14 2008 Slava V Rotkin 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 COT Open House Oct 14 2008 Slava V Rotkin

COT Open House Oct 14 2008 Slava V Rotkin

COT Open House Oct 14 2008 Slava V Rotkin