Strain Analysis in Daily Life Lecture 9 • Strained-Si Technology I: Device Physics – Background – Planar MOSFETs –FinFETs Reading: • Y. Sun, S. Thompson, T. Nishida, “Strain Effects in Semiconductors,” Springer, 2010. • multiple research articles (reference list at the end of this lecture) Mechanical Stress/Strain Analysis Fs Stress: results from the repulsive electromagnetic force between Fn ionic cores when the lattice L ∆L atoms deviate from their equilibrium positions. Stress = lim Strain = lim Stress Types Stress Tensor Extensional Shear Tensile Compressive 10/25/2013 Nuo Xu EE 290D, Fall 2013 2 Strain-Stress Relationship Elasticity Tensor: • assuming strain has linear response to stress (Hooke’s Law) • can be simplified into 3 independent variables, for cubic lattices (e.g. Si) If x, y, z along main crystal axis: OR for a certain direction: Extensional Strain/Stress Shear Strain/Stress 10/25/2013 Nuo Xu EE 290D, Fall 2013 3 Impact of Strain on Semiconductors • Energy Band Splitting • Evs. k curvature change Si Ge w/o s w/ hs w/ us GaAs CB 4 2 VB HH 1GPa <110> LH Unstrained Compressive Y. Sun, JAP (2007) 10/25/2013 Nuo Xu EE 290D, Fall 2013 4 Strain Impact on Si Bandstructure: Planar N-MOSFET Gate Gate Gate [110] Source Drain Source Drain Source Drain Unstrained Longitudinal Vertical Electrons Δ2 Electron applying strain Energy Splitting E-k Curvature Lower DOS available for Sub-band reoccupation Change Scattering Lowered average m* Transport m* Reduced (Inter-valley) Reduction Scattering Rates 10/25/2013 Nuo Xu EE 290D, Fall 2013 K. Uchida, IEDM (2008) 5 Strain Impact on Si Bandstructure: Planar P-MOSFET [110] Gate Gate Gate Source Drain Source Drain Source Drain Unstrained Longitudinal Vertical Holes Heavy Hole Light Hole Split-off Hole applying strain Energy Splitting E-k Curvature Change Lower DOS available for Sub-band reoccupation Transport m* Reduction Scattering Lowered average m* Reduced (Inter-sub-band) Scattering Rates 10/25/2013 Nuo Xu EE 290D, Fall 2013 6 Strain Enhancement on Si MOSFET Carrier Mobility [110] Electron Hole D. Esseni, JCE (2009) F. Conzati, SSE (2009) • For N-MOSFET, electron mobility enhancement saturates at ~1.5 GPa <110>-uniaxial tensile stress . • For P-MOSFET, hole mobility enhancement saturates at very high <110>-uniaxial compressive stress. 10/25/2013 Nuo Xu EE 290D, Fall 2013 7 Impact of Quantum Confinement Electrons under Biaxial Tensile Stress Holes under Uniaxial Comp. Stress O. Weber, IEDM (2007) E. X. Wang, TED (2006) • N-MOSFET: e% degrades at higher Eeff, due to the quantum confinement counters the strain-induced sub-band splitting. * • P-MOSFET: h% maintains vs. Eeff due to the dominant m reduction. 10/25/2013 Nuo Xu EE 290D, Fall 2013 8 Analytical Modeling for Carrier Mobility Enhancement due to Strain • Piezoresistance (PR) Model Too simple Limited predictive ability (by ignoring Eeff, Strain- dependence…) • Sub-band Reoccupation Model Analytically models the energy-band top and m* change vs. strain Trade-off between computing loads and accuracy J.-S. Lim, EDL (2004) 10/25/2013 Nuo Xu EE 290D, Fall 2013 9 Numerical Approach: Self-Consistent Poisson-Schrödinger Simulation scPS Approach 6x6 Luttinger-Kohn Hamiltonian for Holes Schrödinger equation L 2 PQ L M02 M 222 22 2 Pkkk () d 2m 1 x yz 3 0 ez() () z E () z LPQ 02 M Q L *2 nnn 2 2 2mdzz Qkkk (2)22 2 3 2 x yz M 02PQ L L Q 2m0 2 2 gn nz() dkfE ( ) (,) kz L nn2 k 02MLPQM 2 2 2 k Lkikk3( 3 x yz ) m L 3 0 22QLMP 0 2 2 2 22 nz() n () z M 3[23 (kkxy ) ikk 2 xy ) n 3 L 2m 220MLQ P 0 n 2 2 ddz() ()z eNDA N pz () nz () Impacts of strain on energy-band dz dz top as well as curvature change Poisson equation will be completely included into the Hamiltonian. Computationally intensive. 10/25/2013 Nuo Xu EE 290D, Fall 2013 10 Impact of Si Body Thickness Scaling [110] scPS simulations, N. Xu, VLSI-T (2011) N-Channel (Electron) P-Channel (Hole) 400 0.35 1.4 160 Electron Mobility Change 380 0.30 1.2 Hole Mobility Change ) 140 1GPa Longi. Comp. ) 1.0 /V.s 0.25 2 360 1GPa Longitudinal Tensile 1GPa Verti. Tens. 1GPa Trans. Tens. /V.s cm 1GPa Vertical Compressive 2 0.8 ( 120 Unstrained 0.20 Unstrained 340 cm ( 0.6 0.15 100 320 0.4 (100)/<110> 0.10 80 ( N =1.0e13cm-2 300 inv 0.2 h ( 0.05 Hole Mobility Mobility Hole h Electron Mobility 60 ) e 0.0 280 -2 e (100)/<110> P =1.0e13cm 0.00 ) inv 40 4 6 8 10 12 14 4 6 8 10 12 14 Silicon Film Thickness (nm) Silicon Film Thickness (nm) • Stress enhancement diminishes for electrons as tSOI scaled below 5nm, but not for holes. 10/25/2013 Nuo Xu EE 290D, Fall 2013 11 Impact of tSi Scaling on Piezoresistive Coefficients [110] Open symbols Simulated Closed Symbols Measured N-Channel (Electron) P-Channel (Hole) 80 20 zz 60 ) ) -1 Vertical zz 10 -1 Pa Transverse xx yy Pa 40 Longitudinal -11 xx Longitudinal -11 10 0 xx Transverse ( 10 yy Uchida, IEDM 04,08 ( 20 yy Vertical -10 Xu, VLSI 11 zz Uchida, IEDM 08 0 Xu, VLSI 11 -20 -20 -30 xx Piezo-Coefficient yy -40 Piezo-Coefficient -40 zz -50 -60 246810122 4 6 8 10 12 Silicon Body Thickness (nm) Silicon Body Thickness (nm) • As tSi decreases, Πxx decreases due to diminished sub-band reoccupation and inter-valley scattering reduction. N. Xu, SOI Conf. (2012) 10/25/2013 Nuo Xu EE 290D, Fall 2013 12 Strain Enhancement on FinFET [110] Carrier Mobility: Electrons (110)-sidewall N-FinFET Unstrained Strained nd ∆4, 2 st ∆2,1 st ∆4, 1 (100)-sidewall N-FinFET (110)-sidewall N-FinFET N. Serra, TED (2010) 10/25/2013 Nuo Xu EE 290D, Fall 2013 13 Strain Enhancement on FinFET Carrier Mobility: Holes Equi-energy contours from the 1st HH Planar MOSFET (100)/<110> (100) Surface [110] FinFET (110)/<110> [110] (110) Surface unstrained σx = -1 GPa Courtesy of L. Smith (Synopsys) 10/25/2013 Nuo Xu EE 290D, Fall 2013 14 Impact of Fin Width Scaling on [110] Piezoresistive Coefficients Open symbols Simulated Closed Symbols Measured N-Channel (Electron) P-Channel (Hole) 80 80 60 zz ) ) -1 -1 60 Pa Pa 40 xx -11 -11 40 Saitoh, VLSI 08 20 Xu, EDL 12 Shin, EDL 06 20 Xu, EDL 12 Saitoh, VLSI 08 Serra, TED 10 Suthram, EDL 08 Krishinamohan, IEDM 08 Suthram, EDL 08 0 0 yy -20 zz -20 -40 Piezo-Coefficient (10 Piezo-Coefficient Piezo-Coefficient (10 xx -40 yy -60 6 9 12 15 18 21 24 6 9 12 15 18 21 24 Silicon Fin Width (nm) Silicon Fin Width (nm) • No substantial degradation in piezo-resistance is seen with decreasing fin width. N. Xu, SOI Conf. (2012) 10/25/2013 Nuo Xu EE 290D, Fall 2013 15 Impact of Fin Aspect-Ratio scPS simulations, N. Xu, IEDM (2010) N-Channel (Electron) P-Channel (Hole) 12 -2 Open: H = 58nm, W = 20nm 400 N = 9x10 cm 500 Si Si inv Filled: H = 20nm, W = 58nm Si Si CESL(Uniaxial) /Vs) 2 Biaxial Compressive /Vs) 400 2 Biaxial Tensile 300 <110> Fin <100> CESL (Uniaxial) 300 <100> Biaxial Tensile 200 <110> CESL (Uniaxial) <110> Biaxial Tensile 200 Hole Mobility (cm Mobility Hole Open: H = 58nm, W = 20nm Electron Mobility (cm Electron Si Si P =1x1013cm-2 Filled: H = 20nm, W = 58nm inv Si Si 100 100 0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 1200 1400 Stress (MPa) Stress (MPa) • μn is highest for <100> uniaxial-strained Tri-Gate, μp is highest for <110> uniaxial-strained Tri-Gate at high level stress. 10/25/2013 Nuo Xu EE 290D, Fall 2013 16 Strain Enhancement on Short-Channel MOSFET Performance Expt. results, N. Xu, VLSI-T (2011,2012) Mobility vs. Gate Length ΔION/ION vs. Δidlin/I dlin under strain 12 14 p-channel FDSOI S = 0.59 Long Channel +12% 10 Lg = 30nm ~ 80nm 12 -2 P =7.0e12cm inv 8 |=1V (%) 10 ds Forward Back Bias 6 V = -0.5 ~ -1.0V S = 0.54 8 back 300K 4 P =9.5e12cm-2 6 inv Increase @ |V on short channel % I 2 Wafer Bending S = -70 ~ -170MPa 4 I % xx d,lin Stress-induced Enhancement (%) 0 30 40 50 60 70 80 90 100 0 2 4 6 8 101214161820 I Increase @ |V |=10mV (%) Gate Length (nm) d,lin ds • Enhancement in apparent mobility is maintained vs. Lg scaling. • ~50% of Δµ/µ can be transferred to ΔION/ION. 10/25/2013 Nuo Xu EE 290D, Fall 2013 17 References 1. Y. Sun et al., “Physics of Strain Effects in Semiconductors and metal-oxide-semiconductor field- effect transistors,” Journal of Applied Physics, 101, 104503, 2007. 2. F. Conzati et al., ”Drain Current Improvements in Uniaxially Strained P-MOSFETs: A Multi-Subband Monte Carlo Study,” Solid-State Electronics, vol.53, pp.706-711, 2009. 3. D. Esseni et al.,”Semi-Classical Transport Modeling of CMOS Transistors with Arbitrary Crystal Orientations and Strain Engineering,” Journal of Computational Electronics, vol.8, pp.209-224, 2009. 4. N. Xu et al., “Stress-induced Performance Enhancement in Ultra-Thin-Body Fully Depleted SOI MOSFETs: Impacts of Scaling,” Symposium on VLSI Technology Dig., p.162-163, 2011. 5. K. Uchida et al., “Physical Mechanisms of Electron Mobility Enhancement in Uniaxial Stressed MOSFETs and Impacts of Uniaxial Stress Engineering in Ballistic Regime,” IEEE International Electron Device Meeting, Tech.