Quantum Capacitance Effects In Carbon Nanotube Field-Effect Devices

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Reference Bernhard Stojetz et al. Phys.Rev.Lett. 94, (2005)

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Presentation transcript:

Quantum Capacitance Effects In Carbon Nanotube Field-Effect Devices L. Latessa, A. Pecchia, A. Di Carlo University of Rome ‘Tor Vergata’ P. Lugli Lehrstuhl fur Nanoelectronic, Munchen

Devices based on field effect (CNTFET) Planar geometry top/bottom gate (IBM) ULSI Devices Quasi-1D coherent transport over long distances Si integrable technology Vertical Geometry coaxial gate (Infineon)

gDFTB Green’s functions Density Functional Tight-Binding (A.Pecchia, L.Latessa, A.Di Carlo) Atomistic simulations: Quantum treatment Approximated DFT:

A. Pecchia, A. Di Carlo, Rep Prog Phys 67, 1-65 (2004) NEGF Extention L R Density Matrix Mullikan Charges SCC loop A. Pecchia, A. Di Carlo, Rep Prog Phys 67, 1-65 (2004)

3D Poisson Multigrid The cylindrical gate is added as an appropiate Dirichlet boundary condition Metal Gate Insulating dielectric and CNT

Coaxially gated CNTFET Working mechanisms: Schottky barrier modulation at the contacts local modulation of channel conductance Model: semiconducting CNT(10,0) neglect Schottky barrier Charge injection from p-doped CNT contacts

CNTFET control capacities Cox CQ Vg VCNT CS CG CG CD (S.Luryi, Appl.Phys.Lett. 52, 501 (1988), sistemi 2DES)

Gate capacitance Gate is a Macroscopic metal Oxide CNT In a classic MOS CQ >> Cox => modulation depends on Cox In a well-tempered MOS CG >> CS,CD In 1D systems CQ is small Vds can influence the channel charge and barrier

Caratteristiche di uscita IDS/VDS Source Drain Source Drain

Calculation of CQ Bare Potential Partial Screening

Over-screening in CNT Negative CQ Ctot > Cins The can CNT better than a metal!

Negative compressibility Experimental measurements in GaAs quantum wells J.P.Eisenstein et al., Phys.Rev.Lett. 68, 647 (1992)  Analytic results for quasi-1D electron systems L.Calmels, A.Gold, Phys. Rev.B. 53, 10846 (1996) K0 : free electrons compressibility KHFA: Hartree-Fock exchange compress.

Many-body exchange effect Calcolo DFT Charge carrier density nC: TOTAL SCREENING CNT ~ macroscopico CQ= e2(EF) High density: PARTIAL SCREENING Dominated by DOS Low density: OVER-SCREENING Exchange interaction preveal

XC in gDFTB In DFTB the XC term is treated with a Hubbard on-site energy Substituting UH with Uee accounts only for Hartree rs=5.03 rs=6.71 rs=10.06 rs=20.12 The capacity becomes positive again

Quantum Capacitance vs DOS

Over-screening and modulation VGS Unconventional Trans-characteristics Possible applications ? VGS

Conclusions Comprehensive calculation of Quantum Capacity in a CNT(10,0) using NEGF XC effects can give deviations from “classical” CQ Negative CQ below a crytical carrier density which compares well with analytic results in quasi 1D systems More complicated behaviour when more subbands are occupied