Nanoscale Device Modelling: CMOS and beyond

1. Nanoscale Device Modelling:CMOS and beyond G. Iannaccone Università di Pisa and IU.NET [Italian Universities Nanoelectronics Consortium] Via Caruso 16, I-56122, Pisa, Italy. g.iannaccone@iet.unipi.it

2. Acknowledgments • People that did (are doing) the “real” work • A. Campera, P. Coli, G. Curatola, G. Fiori, F. Crupi, G. Mugnaini, A. Nannipieri, F. Nardi, M. Pala, L. Perniola • Partners • IMEC, LETI, STM, Silvaco (EU FinFlash Project) • Univ. Wuerzburg, ETH Zurich, TU Vienna, MPG Stuttgart, NMRC Cork (EU NanoTCAD Project) • EU Sinano NoE (43 partners)  Next: PullNANO IP • IU.NET Italian Universities Nanoelectronics Corsortium • Univ. Bologna, Univ. Udine, Univ. Roma (PRIN Programme) • Philips Research Leuven, Purdue University, Univ. Illinois at Urbana Champaign, Samsung • Funding (past and present) • European Commission, Italian Ministry of University, Italian National Research Council, Foundation of Pisa Savings Bank, Silvaco International

3. The Problem “Yesterday’s technology modeled tomorrow” (M.E.Law, 2004) TCAD and numerical modeling tools – both for process and device simulation – are accurate, or “predictive”, only for a sufficiently stable and “mature” technology, and after a lengthy calibration procedure.

4. Modeling as a Strategic Activity Modeling is a strategic activity because it enables to • perform an early evaluationof technology options • make choicesandcutunpromising initiatives • strategically position and focus R&D efforts Modeling supports the definition and the implementation of a R&D strategy

5. Emerging Research Devices Nanocrystal and discrete trap flash memories Quantum dots and single electron transistors CNT-FETs Resonant Tunneling Devices Fundamentals of Nanoelectronics Decoherence and dephasing Spin-dependent transport Mesoscopic transport ITRS Roadmap Issues Quantum ballistic and quasiballistic modeling of nanoscale MOSFETs (2D-3D) Alternative device structures (DG MOSFETs, FINFETs, SNWTs) Tunneling currents through oxides and high-k gate stacks, also in the presence of defects (SILCs, etc.) Atomistic effects in nanoscale MOSFETs Compact modeling of nanoscale MOSFETs Present activity in Pisa

6. ITRS Roadmap Issues Quantum ballistic and quasiballistic modeling of nanoscale MOSFETs (2D-3D) Alternative device structures (DG MOSFETs, FINFETs, SNWTs) Tunneling currents through oxides and high-k gate stacks, also in the presence of defects (SILCs, etc.) Atomistic effects in nanoscale MOSFETs Compact modeling of nanoscale MOSFETs Emerging Research Devices Nanocrystal and discrete trap flash memories Quantum dots and single electron transistors CNT-FETs Resonant Tunneling Devices Fundamentals of Nanoelectronics Decoherence and dephasing Spin-dependent transport Mesoscopic transport Present activity in Pisa

7. NanoTCAD3D 3D Non linear Poisson 1D Schrödinger per slice 2D Schrödinger per section 3D Schrödinger + + Ballistic Transport Ballistic Transport DD per each 2D subband DD per each 1D subband • The many body Schrödinger equation is solved with DFT-LDA, effective mass approximation • The Kohn-Sham equation for electrons is solved for each pair of minima in the conduction band (three times) • The Kohn-Sham equation for holes is solved for heavy and light holes

8. Depending on device architecture, multiple regions different types of confinement may be considered: Planar MOSFET: 1D vertical confinement Nanowire: 2D confinement in the transversal cross section Dots: 3D Many body Schrödinger equation solved with DFT-LDA, effective mass approximation NanoTCAD3D 2D 1D y x z 3D

9. Quantum ballistic and quasiballistic modeling of nanoscale MOSFETs (3D) Lead: G. Fiori

10. Silicon Nanowire Transistors (SNWT) Candidate device structures for MOSFETs with channel length of order 10 nm – Suppressed SCE

11. Two models for current Ballistic transport in each subband (including tunneling) Drift-Diffusion transport in each 1D subband (Ei). (note: The mobility model must be improved). Transport models in the 1D subbands 1D subband profiles 4th 3rd The 3D electron density is obtained as : 2nd 1st

12. SNWT simulated structures : same transversal cross-section (5x5 nm, 1.5 nm oxide) different channel lengths (L=7,10,15,25 nm) Simulation of SNWT (I)

13. Electrostatic potential in a y-z cross section in the middle of the channel : Vds = 0.5 V ; Vgs = 0.5 V Electron Density Isosurface n=1.4x1019cm-3; L=15 nm; Vgs=0.5 V; Vds=0.5V Simulation of SNWT (II) gate drain source

14. Simulation of SNWT (III) • S degrades for small L but is still acceptable and almost insensitive to the transport mechanism • DIBL is much higher for ballistic than for DD transport.

15. Silicon Nanowire Transistors (IV) Source-drain tunneling above threshold gives a contribution only slightly dependent on L , and significant already for L=25 nm.

16. High-k dielectrics Lead: Andrea Campera

17. Structures investigated Poly-Si Poly-Si Poly-Si HfO2 HfSiON HfSiON 4 nm 2 nm 1 nm 1 nm 1 nm 1 nm SiO2 SiON SiON bulk bulk bulk • Experimental data: I-V, C-V and I(T)-V • In all three cases the substrate is p-doped with NA=5∙1017 cm-3 • C-V characteristics have been measured for capacitors of area 70 µm x 70 µm • J-V curves have been measured for n-MOSFET with W=10 µm and L=1, 5 and 10 µm ( we show results only for L=5 µm) • Temperature from 298 to 473 K

18. 1D Poisson-Schrödinger solver • Poly depletion and finite density of states in the bulk • Self-consistent solution of the P-S equation, taking into account • quantum confinement at the emitter, • quantum confinement in the poly • mass anisotropy in CB, • light and heavy holes • Extraction of the band profile with the quasi-equilibrium approx., eigenvalues and eigenvectors for electrons and holes

19. Results: I-V and C-V

20. Experiment: Temperature-dependent I-V • HfO2 and HfSiON shows a different temperature dependence • A pure tunneling current can explain only transport in HfSiON but not in HfO2 • In HfO2 we can observe a strong temperature dependence

21. Temperature-dependent transport model g1= g1c+ g1v g2= g2c+ g2v r1= r1c+ r1v r2= r2c+ r2v • We assume that transport in HfO2 is due to Trap Assisted Tunneling • giand ridepend on the properties of traps responsible for transport • They depend on the capture cross section, that we have assumed to be “Arrhenius like” • The TAT current reads

22. Energy position of traps • Traps in hafnium oxide from ab-initio calculations • From simulations we observe that traps must be within the energy range 1÷2 eV below the HfO2 conduction band in order to allow us to reproduce the shape of J-V characteristics Gavartin, Shluger, Foster, Bersuker Jour. Appl. Phys 2005 • We consider that relevant traps are located 1.6 eV below the hafnium oxide CB

23. Simulations of I(V) with varying T • From ETRAP=1.6 eV we can extract Г from the slope of the J-V @ 475 K and σ(475) from the amplitude of the same J-V • At T=475 K TAT is the entire current density • We assume that σ hasan Arrhenius temperature dependence and that Г is constant: • Then we can extractσas a function of temperature

24. Main results HfSiON HfO2 • Transport in HfSiON can be described by pure tunneling processes • Transport in HfO2 can be described by temperature dependent TAT • Arrhenius like capture cross section • Traps involved in transport processes are 1.6 eV below thehafnium oxide CB (this traps states have been recently found by ab-initio calculations, Gavartin et al. Jour. Appl. Phys 2005)

25. Decoherence and dephasing Lead: Marco Pala* M. Pala, G. Iannaccone, PRB vol. 69, 235304 (2004) M. Pala, G. Iannaccone, PRL vol. 93, 256803 (2004) * now with IMEP-CNRS, Grenoble

26. Transport in mesoscopic structures • Landauer-Büttiker theory of transport • Eigenvalues of the tt† matrix as enables us to compute conductance and shot noise • Transmission and reflection matrices can be obtained computing the scattering matrix (S-matrix) of the system • The domain is subdivided in several tiny slices in the propagation direction • The S-matrix of the system is obtained by combining the S-matrices of all adjacent slices

27. Monte Carlo approach (M. Pala, G. Iannaccone, PRB 2004) • Random fluctuation of the phase of all modes • The propagation in each slice is described by a diagonal term in the transmission matrix • We modify the transmission matrix by adding a random phase to each diagonal term • The random phase has a Gaussian distribution with zero average and variance inversely proportional to the dephasing lenght • Each S-matrix is a particular occurrence and the average transport properties are obtained by averaging over a sufficient number of runs

28. Aharonov-Bohm rings • Simulation recover experimental results due to the suppression of quantum coherence • Non integer conductance steps are recovered • Corrections are of the order of G0 B=0 Tesla Experiments by A.H.Hansen et al., PRB 2004

29. Magnetoconductance Experiment (Hansen et al., PRB 2004) Theory (Pala et al., 2004)

30. Density of states • Computation of the partial density of states • Application: Aharonov-Bohm oscillations of a ring [M.G. Pala and G. Iannaccone, PRB 69, 235304 (2004)] • The wave-like behavior of the propagating mode is destroyed when a strong decoherence is present

31. Influence on shot noise (M. Pala et al. PRL 2004) • Aharonov Bohm ring • First order cumulant of the current proportional to conductance • Second order cumulant of the current = Fano factor (prop to noise)

32. Perspectives of Carbon Nanotube Field Effect Transistors Lead: G. Fiori Collaboration with Purdue University, G. Fiori et al., IEDM 2005 – to be published on IEEE-TED, new results at ESSDERC 2006

33. Self-consistent 3D Poisson/NEGF solver • The 3D Poisson equation reads • while p(f), ND+(f), NA-(f) e n(f)are computed semiclassically elsewhere. Transport is ballistic. • In particular, the Schrödinger equation has been solved using a tight-binding hamiltonian with an atomistic (pz-orbital) real space basis n(f)in the nanotube by means of NEGF • Discretization : box-integration. • Newton-Raphson method with predictor corrector scheme.

34. Non-Equilibrium Green’s Function • The Green’s Function can be expressed as • A point charge approximation is assumed, i.e. all the free charge around each carbon atoms is condensed in the elementary cell including the atom. • Current is computed through the Landauer’s formula

35. By defining different geometries, we can study how short channel effects can be controlled through different device architectures. Considered CNT-FET (11,0) zig-zag nanotube doping molar fraction f = 10-3. gatelength 15 nm SiO2 as gate dielectric. single, double and triple gate layout. Short Channel Effect in CNT-FETs (I)

36. Short Channel Effect in CNT-FETs (II) • Quasi-ideal S are obtained for the double gate structure, also for thick oxide thickness. • Good S and DIBL for the single gate device are obtained for tox=2nm. As expected, triple gate layout show better S and DIBL

37. Ion per unit width • Ion is one order of magnitude higher than that typically obtained in silicon • warning: ballistic transport and very dense CNTs considered

38. High frequency perspectives • Optimistic estimate (zero stray capacitances) • Perspective for THz applications • High frequency behaviour is only limited by stray gate capacitance

39. Transconductance

40. Ioff per unit width • the Ion/Ioff requirement is met for a tube density smaller than 0.1

41. Effects of bound states in HOMO (I) Efs holes Efd electrons • For large drain-to-source voltages, electrons in bound states in the channel can tunnel to states in the drain, leaving holes in the channel. Such effect lowers the barrier seen by propagating electrons in the channel. Charge density computed for Vgs=0 and Vds=0.6 V LDOS for Vgs=0, Vds=0.6 V

42. Effects of bound states in HOMO (II) • As the drain-to-source voltage is increased, holes are accumulated in the channel and the gate loses control of the potential over the channel, with a degradation of the current in the off-state. • Transfer characteristic for a double gate (14,0) nanotube, with L=10 nm and tox=2 nm

43. Work in Progress

44. in Progress: Mobility in Si Nanowires • Phonon scattering (acousting and optical) • Surface Roughness and Cross Section Fluctuations • Impurity Scattering 5 nm

45. Partially ballistic transport • Boltzmann Transport Equation solved in each 2D subband • Direct solution (no Montecarlo) Ballistic peak S D t = 10 ps

46. Partially ballistic transport • Boltzmann Transport Equation solved in each 2D subband • Direct solution (no Montecarlo) Ballistic peak S D t = 1 ps

47. Partially ballistic transport • Boltzmann Transport Equation solved in each 2D subband • Direct solution (no Montecarlo) Ballistic peak S D t = 0.1 ps

48. Partially ballistic transport • Boltzmann Transport Equation solved in each 2D subband • Direct solution (no Montecarlo) S D t = 0.01 ps

49. Personal Conclusion • Critical objectives of nanoscale device modeling: • Provide useful insights of device behavior, • helping us to understand • what are the relevant physical aspects for the issues at hand • what are the main trends • what we should focus on and what we should stop. • Such mission does not requires huge do-it-all tools, but simulation tools with different degrees of sophistication, tailored to the particular problem at hand.

50. Modeling of ballistic and quasi-ballistic MOSFETs Lead: G. Curatola* In collaboration with Philips Research Leuven, G. Curatola et al. IEEE-TED vol. 52, p. 1851-1858, 2005 * now with Philips Research Leuven