1. NCN www.nanoHUB.org 1 Neophytos Neophytou Advisory Committee Chairs: Mark Lundstrom, Gerhard Klimeck Members: Ashraful Alam, Ahmed Sameh Network for Computational Nanotechnology Purdue University West Lafayette, Indiana USA Quantum and atomistic effects in nano-electronic devices Ph.D. Thesis Defense, May 22 nd, 2008

2. www.nanoHUB.org NCN 2 Introduction – Device trend Device Challenges: 1)Atoms are countable 2)Strain 3) Material /potential variations on nanoscale 4) Crystal orientation 5) III-V, Ge, InGaAs Electronic structure features: 1) Strong quantization 2) Band coupling 3) Non-parabolicities 4) Quantum mechanics Design Challenges 1)Low dimensionality 2)Parameter fluctuations 3)Scalable – last for 2 generations

3. www.nanoHUB.org NCN 3 Si MOSFET alternatives? CNTs Issues:  Chirality  Metallic vs. Semiconducting  Alignment CNT (Delft group-1998) Top gate+High-k (Javey et. al.) BTBT(IBM) Oscillator (IBM)

4. www.nanoHUB.org NCN 4 Si MOSFET alternatives? NWs Singapore group (IEDM 2006) Samuelson group EDL 2006  Still based on Si, so might have easier integration  Gate all around for better electrostatics  Scattering in 1D – surface roughness?  Bandstructure effects? Samsung (APL 2008) D=8nm L=22nm

5. www.nanoHUB.org NCN 5 Si MOSFET alternatives? III-Vs Kim et. al. 2006 60nm InGaAs Kim et. al. 2007 40nm InAs Freescale IEDM 2007 Intel EDL 2008  High mobility, high speed, close to the ballistic limit, but low DOS (DOS Bottleneck)  Lower V D, low dissipation - tunneling/leakage?  Large series resistance

6. www.nanoHUB.org NCN 6 Open questions  How will these devices perform at the scaling limit?  What parameters control their performance?  Low dimensionality: Sensitivity to defects and fluctuations?  Are they advantageous to the Si MOSFET? Modeling tools used here:  Quantum transport – NEGF (CNT, III-V HEMT)  3D (CNTs)  Atomistic bandstructure (NWs)

7. www.nanoHUB.org NCN 7 Why atomistic is needed –motivation Valley splitting Band coupling Valence band anisotropy Warped bands m* valid m* NOT valid

8. www.nanoHUB.org NCN 8 Motivation for TB NN sp 3 d 5 s*-SO The bulk bandstructure (from Anisur Rahman’s thesis) [100] [110] [111] Based on Localized Atomic Orbitals Suitable for:  Structure deformations, strain  Material variations, heterostructures  Surface truncation  Potential variations: treated easily  Needs a large set of fitting parameters  Computationally expensive

9. www.nanoHUB.org NCN 9 Outline 1)1D channel sensitivity to atomistic defects 2)Bandstructure effects in nanowires:  Self consistent model for NWs  Electron transport  Hole transport 3)III-V HEMT devices 4)Conclusions – Future work

10. www.nanoHUB.org NCN 10 Defects in 1D channels vacancy Neophytou APL 2006, APL 2007, JCE 2007 1) NEGF 2) 3D electrostatics 3) Atomistic TB CNTFET on nanoHUB.org I D : ~27% reduction Dangling bonds in NWs I D: ~30% reduction charged impurity

11. www.nanoHUB.org NCN 11 Outline 1)1D channel sensitivity to atomistic defects 2)Bandstructure effects in nanowires:  Self consistent model for NWs  Electron transport  Hole transport 3)III-V HEMT devices 4)Conclusions – Future work

12. www.nanoHUB.org NCN 12 The self-consistent model for NWs Bandstructure (states) Transport (state filling - charge) Poisson Charge Potential Simple model but provides physical insight

13. www.nanoHUB.org NCN 13 Why need a SC model? ~0.5nm Neophytou SISPAD 2007 Charge Variations C S Ec changes Ev changes

14. www.nanoHUB.org NCN 14 Numerical issues of the SC model Hamiltonian size – (dep. on wire size and orientation) 3nm x 3nm with SO: 4k x 4k - 9k x 9k 12m x 12nm with SO: 55k x 55k eigenvalue problem 150 k-points, 60 eigenvalues Parallelized per bias point: Vd is constant Vg is varied Timing (per bias point): 3nm device: a few hours 12nm devices: 1 – 2 days

15. www.nanoHUB.org NCN 15 Outline 1)1D channel sensitivity to atomistic defects 2)Bandstructure effects in nanowires:  Self consistent model for NWs  Electron transport  Hole transport 3)III-V HEMT devices 4)Conclusions – Future work

16. www.nanoHUB.org NCN 16 NMOS [100], [110], [111] wire comparison C ox CSCS VGVG ψsψs GND  Same capacitance/ charge in all wires  [110], [100], then [111] on performance Neophytou TED 2008 C S : - C Q (30%) -potential/charge variations

17. www.nanoHUB.org NCN 17 Masses change with quantization z x y NW mass is controlled by quantization of the 6 ellipsoids  [100], [111] wire masses increase  [110] mass decreases Neophytou TED 2008

18. www.nanoHUB.org NCN 18 Non-parabolicity and anisotropy in the dispersion kx Neophytou TED 2008 [010] [110]

19. www.nanoHUB.org NCN 19 Outline 1)1D channel sensitivity to atomistic defects 2)Bandstructure effects in nanowires:  Self consistent model for NWs  Electron transport  Hole transport 3)III-V HEMT devices 4)Conclusions – Future work

20. www.nanoHUB.org NCN 20 Ek for holes in 6nm wires  Corner effects – electrostatics  Directionality in the charge - bandstructure High gate bias Neophytou TED 2008 (100) (1-10) (010) (11-2) (1-10) (001) Energy surfaces [100] [110] [111]

21. www.nanoHUB.org NCN 21 Anisotropy implications on the device performance Kobayashi et. al. JAP 103, 2008  [110] side variations, do not affect the device – V T, Ion  [100] side variations, affect the device

22. www.nanoHUB.org NCN 22 Outline 1)1D channel sensitivity to atomistic defects 2)Bandstructure effects in nanowires:  Self consistent model for NWs  Electron transport  Hole transport 3)III-V HEMT devices 4)Conclusions – Future work

23. www.nanoHUB.org NCN 23 Motivation: del Alamo group HEMTs Typical I DS vs. V DS Reference: Dae-Hyun Kim et al. IEDM 2006 how close to ballistic limit? role of mobility degradation of g m at high V G Typical Gm vs. V GS

24. www.nanoHUB.org NCN 24 Approach Simulation: 2D Poisson in the cross section NEGF in the channel and upper buffer layer (ballistic) Include Rs to fit low V DS conductance to experiment Bulk material masses (In 0.7 Ga 0.3 As) Adjust Φ B to achieve the experimental V T Parallelization: One V G set per CPU (constant V D ) 2 hours per bias point – 20 hours per I-V

25. www.nanoHUB.org NCN 25 Series resistance and “Ballistic” mobility (Depending on the Tins) ballistic simulation measured (T ins = 3 nm, L = 60 nm) ballistic + R s = 400  -  m “ballistic mobility:”

26. www.nanoHUB.org NCN 26 L G = 60 nm vs. Tins Tins=3nmTins=11nmTins=7nm 1)Except for high V G, all results can be explained as a ballistic FET with series R 2)Series resistance increases as Tins decreases

27. www.nanoHUB.org NCN 27 Source limits 2) Barrier collapses Gm rolls off in the ballistic model too. 1) OFF state 3) Gate loses control

28. www.nanoHUB.org NCN 28 Charge C S degrades C ins by 2.5 x Q=C ins (V G -V T )

29. www.nanoHUB.org NCN 29 Velocity 1)Non-parabolicity degrades the velocity by ~10% Velocity is low: Due to quantum mechanical reflections and tunneling v ~ 2.7 v~ 4 v~ 3.6

30. www.nanoHUB.org NCN 30 Outline 1)1D channel sensitivity to atomistic defects 2)Bandstructure effects in nanowires:  Self consistent model  Electron transport  Hole transport 3)III-V HEMT devices 4)Conclusions – Future work

31. www.nanoHUB.org NCN 31 Conclusions (1) 1)1D channel are sensitivity to single atomistic defects:  Vacancy, charged impurities, dangling bonds 2)Transport in nanowires:  Non-parabolicity, anisotropy causes mass variations, charge distribution variations  EMA cannot be used in general  NMOS: [110], [100] perform better, [111] worse  PMOS: [111], [110] perform better, [100] worse

32. www.nanoHUB.org NCN 32 Conclusions (2) 3)III-V HEMT devices:  Ballistic channel + R SD  Low charge and velocity, low “apparent” mobility  Importance of the source design

33. www.nanoHUB.org NCN 33 General concluding comments Low dimensional devices:  Importance of C S, C Q, that degrade C OX  But variations in parameters that influence C do not affect the device  Velocity is important  But, low mass tunnels more so the velocity can be reduced  Device is mostly controlled by external parameters rather than the channel (R SD, parasitics)

34. www.nanoHUB.org NCN 34 Future work Identifying the ultimate MOSFET:  Perform appropriate comparisons between Si MOSFETs and UTB, NW devices at the scaling limit.  Power, speed, Ion, Ion/Ioff, leakage, parasitics  Device to circuit level  Optimal strain and wafer/transport orientation, material, Is it different at each technology node?  Which device for which application – identify appropriate use Modeling for nanoscale devices:  Contacts in low dimensional devices: DD + Ballistic NEGF, dephasing mechanisms (equilibrium or not?) Schottky barriers  Inexpensive treatment and use of complex bandstructures, and distortions. (zone unfolding).  NEGF + TB – real or mode space for PMOS in NWs and UTB

35. www.nanoHUB.org NCN 35 Acknowledgements Prof. Mark Lundstrom Prof. Gerhard Klimeck Prof. Ashraful Alam Prof. Ahmed Sameh Jin Guo, Siyu Koswatta, M.P. Anantram (CNT) Diego Kienle, Eric Polizzi, Shaikh Ahmed (CNTFET) Anisur Rahman, Jing Wang, Mathieu Luisier (Bandstructure) Abhijeet Paul (generalized poisson for SC model) Titash Rakshit (HEMT) Yang Liu (UTB work) Gengchiau Liang, Dmitri Nikonov (Graphene) All others in EE350 NCN for the computational resources Cheryl Haines

36. www.nanoHUB.org NCN 36 BACKUP Neophytou APL 2006

37. www.nanoHUB.org NCN 37 Explanations for the Ek - transport [100] subbands[110] subbands Quantization surfaces -Structural -Electrostatic Neophytou TED 2008

38. www.nanoHUB.org NCN 38 Anisotropy implications on the device performance Neophytou, in preparation [100] [1-10] (i) (ii) (iii) (vii) (vi) (v) (iv) (110) (100) B A

39. www.nanoHUB.org NCN 39 Figure 1 – The different quantizations of the different surfaces (110) surface(100) surface

40. www.nanoHUB.org NCN 40 Figure 2 – Current surface for variation of the dimensions [100] [1-10] (i) (ii) (iii) (vii) (vi) (v) (iv) (110) (100) B A

41. www.nanoHUB.org NCN 41 Tins / gate length dependence - Low DOS degrades charge - At high V G the measured current deviates from the ballistic limit. - As L G decreases, I D approaches the ballistic limit

42. www.nanoHUB.org NCN 42 3nm wire dispersions in different orientations 3nm-[100] 3nm-[110] 3nm-[111]  Mass at Γ: 0.27 (0.19)  Degeneracy : 4  Excited states shift down  Mass at Γ: 0.16 (0.19)  Degeneracy : 2  Valley Splitting  Mass: 0.46 (0.43)  Degeneracy: 6 OFF-Γ

43. www.nanoHUB.org NCN 43 Approach - Bandstructure In 0.7 Ga 0.3 As – undistorted m*=0.048m 0 (matches DOS up to 0.2eV) (account for non-parabolicity) L valleys are too high

44. www.nanoHUB.org NCN 44 Transconductance degradation 1)Cannot be explained by series resistance 2)Possibly scattering at high V G (not loss of confinement or upper valleys 3)Is there a ballistic mechanism that can explain this?