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Study of Transport Properties in strained MOSFETs: Multi-scale Approach

Study of Transport Properties in strained MOSFETs: Multi-scale Approach. Maxime FERAILLE June, the 17 th 2009 CIFRE Thesis prepared with collaboration of Institut des nanotechnologies de Lyon and STMicroelectronics Supervisor Pr. Alain PONCET (INSA)

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Study of Transport Properties in strained MOSFETs: Multi-scale Approach

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  1. Study of Transport Propertiesin strained MOSFETs: Multi-scale Approach Maxime FERAILLE June, the 17th 2009 CIFRE Thesis prepared with collaboration of Institut des nanotechnologies de Lyon and STMicroelectronics Supervisor Pr. Alain PONCET (INSA) Co-supervisor Dr. Denis RIDEAU (STM)

  2. Study of Transport Properties in Strained MOSFETs: Multi-scale Approach • Introduction • Bandstructure Calculations • Transport in Strained nMOSFETs • Transport in Strained and Confined Systems • Experimental Validation for holes • Conclusions

  3. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Outline • Introduction • Context • Relation between strain and transport • BandstructureCalculations • Transport in Strained nMOSFETs • Transport in Confined Systems • Experimental validation • Conclusions

  4. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Fromwafer to transistor 45° Wafer Transistor MOSFET <110> <-110> <010> 300mm <110> <100> Several ten nm <1-10> <110> ezz eyy <001> exx 65nm technologynode Wafer tilted → <100>-channel <100> Transport direction G S D Influence of stress vs. transport orientation Si crystal

  5. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Lowermobility Lower performance! Technology Motivation Doping vs. Scaling Increasing doping leads to higher effective field Increase doping to limit short channeleffects Mobilitydegradation Needs of technology boosters for mobility improvement

  6. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Performance EnhancementProcess STI CESL SMT S. Ito IEDM’00 C. Le Cam VLSI’06 K. Ota IEDM’02 Parasitic stress… • … stress engineering W Large Uniaxial stress <110> / <100> impact ? Uniaxial Stress

  7. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Transport simulation under stress Empirical model Drift-diffusion m,vsat→ constant stress Industrial Piezoresistance model First investigation Microscopic model Monte Carlo Kubo-Greenwood m → v(k), t(k) stress Bandstructurecalculation Includingstraineffects Advanced

  8. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Mobility variation: piezoresitance model • Empirical Model: Mobility variation stress Piezoresistancetensor withonly 3 coefficients p11, p12 and p44

  9. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Mobility variation: piezoresitance model σ<110> • Coefficients measuredusing wafer Bending setup σ<100> σ<010> G G σ<110> σ<110> S S G D D G S D S D Uniaxial Stress σ<110> σ<010> Setup A Setup B Channel <110> Channel <100> σ<100> Thomson et al., 2006 Thomson et al., 2006 Gallon, et al., 2003 p11+p12+p44 p11+p12-p44 p11 2 2 p12

  10. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Holepiezoresistance coefficients a C. M. Smith, PR 94, 42 (1954) b K. Matsuda et al., JAP 73, 1838 (1993) c S. E. Thompson et al., TED 53, 1010 (2006) d C. Gallon et al., SSE 48 , 561 (2004) ≠ Setup A Deduced +&/2 Setup B 1.45 needsunderstanding

  11. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions transport simulation under stress Empirical model Drift-diffusion m,vsat→ constant stress Industrial Piezoresistance model New measurements Microscopic model Monte Carlo Kubo-Greenwood m → m*, v, t stress Bandstructurecalculation Includingstraineffects Advanced Transport investigation

  12. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions 1 0.5 /a units] 0 kz [2p 0 kx [2p /a units] 0 1 0.5 1 ky [2p /a units] Relaxed Si buffer: bandstructure basics 40 meV Conduction Bands (electrons) hh and lhdegenerancy atG Gap Dx, Dy, Dz equienergy Si ∆-valleys → {100} Valence Bands (holes) 50 meV Kz(108.m-1) Ky(108.m-1) Kx(108.m-1) N Kz(108.m-1) L G Relation dispersion U X W K Ky(108.m-1) Kx(108.m-1) Kz(108.m-1) -0.5 -1 -1 -1 Γ-valleysat [000] -0.5 First Brillouin Zone Ky(108.m-1) Kx(108.m-1)

  13. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Physical relation betweenstrain and mobility ezz e┴ eyy Phonons interactions e ║(2) exx e║(1) Lattice Stress Silicon Reciprocal space Mobility Dispersion relation

  14. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Outline • Introduction • Bandstructure Calculations • Methods • Relaxed buffer • Strain introduction • Impact of uniaxial strain • Transport in Strained nMOSFETs • Transport in Confined Systems • Experimental validation • Conclusions

  15. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Bandstructure calculation methods Schrödinger Bloch function Development Centered-Bloch function Plane waves Semi-empirical EPM 30-bands k.p Pseudo-potentialCouplingterms (P,Q,..) • Ab initio (DFT+LDA) • Kohn-Shamequation • GW correction Methods www.abinit.org UTOX (In-house ST code) Solving Matrixdiagonalization Self-consistent Time fast veryfast Very slow

  16. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Relaxed buffers bandstructures • Ab initiocalculations as relevant bandstructures GW Energy [eV] Energy [eV] EPM k.p Ge Si • k.p 30 bands methodparametersfittedaccording to a least square optimization on energies and curvature masses atseveralk-points D. RIDEAU, M. FERAILLE, et al., Phys. Rev. B 74, p. 195208 (2006)

  17. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Strain introduction Si on [111]-Ge e║(1) e ║(2) e┴ Latticenode (continuum mecanics) Ab initio Shearstrain → Internaldisplacement Atoms position EPM New interpolation Non local pseudo-potential Pseudo-potentiall [Ry] Si Ge (Symbol) Relaxed G2 Face-centeredcubic Oh 30-bands k.p Symmetrybroken Perturbativetheoryapproach Supplementarycouplingparameters (l ,m ,n , ..) Methods Parametersimpacted

  18. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Bandstructure of Bulk Si under stress • k.p 30 bands methodparametersfittedaccording to a least square optimizationatseveralk-points Conduction and valence valleys shifts Energy [eV] GW EPM k.p Samecalculationswith L 10 Gpauniaxial stress along <110> Relaxed [0.0277 0.0277 -0.0214 0 0 0] [0.0277 0.0277 -0.0214 0 0 0.0314] ε xx εyyεzzεyzεxzεxy Shear uniaxial Energy [eV] Shear component straininvolves large bandstructure modification D. RIDEAU, M. FERAILLE, et al., Phys. Rev. B 74, p. 195208 (2006)

  19. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Uniaxial stress <110>: Conduction bands 1BZ 2BZ Dx, DyValleys Bands displacement DzValleys ε=[0.55 0.55 -0.47 0 0 0.63] Dz –valleyscoupling Proportional to εxy stress stress Z-point GW EPM Masses Variations Relative mass [r. u.] k.p Str. <110> Stress [MPa]

  20. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Uniaxial stress <110>: Valence bands hh lh Bands displacement so GW Energy [eV] EPM k.p Stress <110> [GPa] HH valence Isoenergy surface (25meV) Masses Variations Stress -500 → 0 MPa

  21. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Key ideas on bandstructurecalculations • Semi-classicalmethodsfitswell Ab initioresults but the computationalcostismuchlower • Dz-valley transverse mass variation due to <110>-uniaxial stress

  22. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Transport in strained nMOS • Introduction • Bandstructure Calculations • Transport in Strained nMOSFETs • Monte-Carlo methods • Bandstructure inclusion in Monte-Carlo Simulations • Strained nMOSFETs simulations • Transport in Confined Systems • Experimental validation • Conclusions

  23. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Monte-Carlo Methods Statisticalsolving of the Master Boltzmann Transport Equation Surface roughness Monte Carlo Transport Poisson equation Principle phonons Ionizedimpurity Drain current estimation F Quantum-based Interactions SPARTA (ISE): Simple Particule methods 1 particle Qpart=Qtot

  24. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Structure SINANO nMOSFET High performance transistor of 65nm technologynode Ngrid Tox Nldd Nldd Lgate 50 nm 50 nm Nch Tox:16Ǻ Nch:3,0 .1018 cm-3 Ngrid:1,0 .1020 cm-3 Nldd:1,0 .1020 cm-3 Lgate: 32 nm

  25. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Bandstructure inclusion in Monte-Carlo methods Full-band Monte-Carlo simulators Bandstructure Dispersion relation Scattering rates 30-bands k.pmethods Sparta Unstrained (1/48) General strain (1/2) Meshing in k-space

  26. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Strained nMOSFET: current variation Str <100> Vg-Vth=1V Str <110> 200 MPa Vs=0V Vd Vb=0V Drain current Tensile Ilin Ilon Current variation (%) Ilin Ilon Compressive • Variation reduction • high-field transport regim <100>-channel Ilin → Vd=0.1V SPARTA Ion → Vd= 1V 32 nm gatelength

  27. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Strained nMOSFET: Variation summarize • Variation trends withhigh-field transport regim Drain current G S • Variation trends withshorternMOSFETs D Non-equilibriumeffects <110> <100> • <110>-Orientedchannel: variation between Stress <-110> <110> <100> • <100>-orientedchannel: Larger variation for Stress <100> <-110> → Transport re-orientedalong <100>

  28. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Electron: Monte Carlo 3Dk vs. p-model nMOSFET 32 nm channellength Monte Carlo simulation IlinVd=0.1V IlinVd=0.1V Ch. <100> Ch. <110> Electron p44 coefficients isassociated to the Dz curvature mass modification along <110>

  29. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Electrons inversion layer π-coefficients New electronp-coefficients determination

  30. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Extractedelectron coefficients vs. literature Measured Deduced a C. M. Smith, PR 94, 42 (1954) f Measuredfrom Wafer Bending b K. Matsuda et al., JAP 73, 1838 (1993) c S. E. Thompson et al., TED 53, 1010 (2006) g Deducedfrom <110> and <-110> stress measurements d S. E. Thompson et al., IEDM , 415 (2006) e C. Gallon et al., SSE 48 , 561 (2004) Our measurements are consistent vs. Literature

  31. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Key ideas on transport in strainednMOS • Experimentalmobility variation iswellreproducedwith Monte carlo simulation • p44 coefficient isrelated to the curvature modification of Dz valley

  32. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Outline • Introduction • Bandstructure Calculations • Transport in Strained nMOSFETs • Transport in Confined Systems • Confinement introduction • Bandstructure in a relaxed Quantum Well • Bandstructure in a strained Quantum Well • Holes transport in confined systems • Experimental validation • Conclusions

  33. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Confinement introduction • Confinement appear for Lsystem< Lbroglie • Translation symmetrybroken in the confinement direction • → First Brillouin zone reduction to 2D 3D crystal Z L U Y K X W 2D system Z’ Y’ X’ K’ E3’ E3 • → Sub-bands structure E2’ E2 E1’ E1 D4 E0’ E0 D2 Strained MOSFET Inversion layer Strained bulk Unstrained

  34. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Methods for confined states Channel Substrat oxide Si-ox Confined System (e.g SOI MOSFET) Conduction band Vb: 0.4 V(z) Vc LQW Vc: 0.3 z Vb Valence band LA Hamiltonian k.p 30-bands k.p 6-bands Effective Mass Approximation Plane waves Envelopfunction Methods : quantization mass curvature mass along the confinement direction

  35. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Conduction sub-bands in relaxed QW LQW 5 nm EMA 30-bands k.p First sub-bands energymap Energy shifts Good adequationbetweenk.p 30 bands and EMA methods: isolatedD-valleys <001> confinement orientation

  36. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Valence sub-bands in relaxed Quantum-Well <001> confinement orientation 5 nm E0 [eV] E1 E2 <100> <110> 30-bandsk.p E0’ 6-bands k.p E1’ E2’ First sub-bands energymap Dispersion relation DiscrepanciesIncreasebetween 6 and 30 bands k.pmethodsresults with layer widthreduction Couplingbetweenhh and conduction Bands doesn’texistk.p 6 bands

  37. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Stress impact on subbands 5 nm Conduction Subbands Dz Isocontours 10 meV-spaced k.pmethods Stress <110> Relaxed mass modification Valence Subbands First sub-band Isocontour 40 meV-spaced Str <110> <001> confinement orientation

  38. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Dz sub-band masses vs. stress <110> LQW Str <110> Dz is the lowestsub-bands Bulk-like Strain Strain+ Confinement Enhanced variation 30-bands k.p Curvature mass <110> 2Dk vs. 3Dk Simulation expected to be in good agreements for weaklyconfined system <001> confinement orientation D. RIDEAU, M. FERAILLE, et al., Solid- State Electronics 53, p.452 (2008).

  39. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Valence subbands vs. strain <110> Str <110> 5 nm F=1MV/cm Relaxed Str <110>: 500 Mpa <001> confinement orientation

  40. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Holes Transport in inversion layer • Self-consistent bandstructurecalculations Staticproperties k.p-Poisson (1D)-Schrödinger solving Bandstructure Density • Inversion layer linear transport Transport properties Kubo-Greenwood Transport formula

  41. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions k.p-Poisson-Schrödinger self-consistent calculations Poisson 6-bands k.p-Schrödinger Eigenvalues , Eigenvectors -k-points mesh V(z) -predictor-corrector iterationscheme Confinement potential -Matrixeigenvalues: Lanczos + spectral transformation Bandstructurecalculation

  42. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Kubo-Greenwood solvers • transport formula comingfrom Boltzmann equationlinearization Density Bandstructure 3Dk 2Dk Phonon relaxation time • Elasticacoustic • Inelasticnonpolar Optical Wang et al., TED 53, 1840 (2006) hh bands isoenergy Stress <110> -500 Mpa → 0 MPa Threetopmost sub-bands energies

  43. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions 3Dk vs. 2Dk Kubo-Greenwood solvers Self-consistent k.p-poisson Inversion layer 2Dk bandstructure Crystal 3Dk bandstructure Low-field Monte Carlo simulations equivalent Kubo-Greenwood mobility

  44. Introduction Electrons <110>-curvature mass modification similar in 2Dk and 3Dk systems Confinement involvesstrong impact on holebandstructure variation vs. Stress k.p-poison-schrödingerused in transport propertiesstudied in hole inversion layer Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Key ideas on transport in confined system

  45. Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions • Introduction • Bandstructure Calculations • Transport in Strained nMOSFETs • Transport in Confined Systems • Experimental validation for holes • Wafer Bending experiments • Holes mobility extraction • Hole piezoresistance coefficients determination • Advanced transport simulations validation • Conclusions Outline

  46. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Strain: setup 1 130nm technologynode σ<110> σ<100> σ<110> σ<110> G G G S D S D S D σ<100> Unusual σ<110> <110> <110> <110>-orientedchannel <001> p11+p12+p44 p11+p12 p11+p12-p44 . . . σ σ σ = = = 2 2 2 Dμ Dμ Dμ μ μ μ

  47. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Strain: setup 2 130nm technologynode σ<100> G G S S D D σ<100> <110> σ<100> <110> <100> and <010>-orientedchannel <001> . . p12 p11 σ σ = = Dμ Dμ Our wafer bendingexperiments allows a completedetermination of p-coefficients σ<100> μ μ

  48. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions mobility variation extraction Linear transportproperties Vd=0.1V <110> Vd=0.1V <100> <-110> Device B Mobility variation extractedfrom drain current ratio betweenrelaxed and straineddevices Vd=0.1V Channel <110> K. HUET, M. FERAILLE et al., Proc. IEEE. ESSDERC, p. 234 (2008)

  49. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Holes inversion layer π-coefficients • Bulk values are not satifactory to adjustmobility variation p-coefficients must befitted • Experimentaldeterminationdone. Device B K. HUET, M. FERAILLE et al., Proc. IEEE. ESSDERC, p. 234 (2008)

  50. Introduction BandstructureCalculations Transport in Strained nMOS Transport in confined Systems Experimental Validation Conclusions Extractedhole coefficients vs. Literature Coherent Setup 1 a C. M. Smith, PR 94, 42 (1954) b K. Matsuda et al., JAP 73, 1838 (1993) c S. E. Thompson et al., TED 53, 1010 (2006) d S. E. Thompson et al., IEDM , 415 (2006) e C. Gallon et al., SSE 48 , 561 (2004) f New measurements Setup 2 g Cefficientsdeducedfrom <110> and <-110> stress measurements Difference

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