Simulation of Enhanced Hole Ballistic Velocity in Asymmetrically Strained Germanium Nanowire Trigate p-MOSFETs James Teherani , Winston Chern Profs. Dimitri Antoniadis, Judy Hoyt 2013 International Electron Devices Meeting, Washington DC December 11 th , 2013 1
High Hole Mobility in Strained Ge • Strain-induced high hole mobility and ballistic velocity can be used to increase current drive and decrease power consumption of p-FETs. Experimental Data 2000 NW (w=49 nm) Chern, IEDM 2012 1500 2 /Vs) NW (w=40 nm) eff (cm 1000 Ikeda, VLSI 2013 Chern, IEDM 2012 500 G Planar (biaxial strain) QWFET (biaxial strain) Chern, IEDM 2012 Pillarisetty, IEDM 2010 S D 0 2 4 6 8 10 HfO 2 12 cm -2 ) N inv (10 James T. Teherani, MIT 2
High Hole Mobility in Strained Ge • Strain-induced high hole mobility and ballistic velocity can be used to increase current drive and decrease power consumption of p-FETs. Experimental Data 2000 NW (w=49 nm) Chern, IEDM 2012 1500 2 /Vs) NW (w=40 nm) eff (cm 1000 Ikeda, VLSI 2013 Chern, IEDM 2012 500 G Planar (biaxial strain) QWFET (biaxial strain) Chern, IEDM 2012 Pillarisetty, IEDM 2010 S D 0 2 4 6 8 10 HfO 2 12 cm -2 ) Silicon Hole N inv (10 Universal James T. Teherani, MIT 3
High Hole Mobility in Strained Ge • Strain-induced high hole mobility and ballistic velocity can be used to increase current drive and decrease power consumption of p-FETs. • This work explains mobility results through QM simulations and extends analysis to ballistic velocity. Experimental Data 2000 NW (w=49 nm) Chern, IEDM 2012 1500 2 /Vs) NW (w=40 nm) eff (cm 1000 Ikeda, VLSI 2013 Chern, IEDM 2012 500 G Planar (biaxial strain) QWFET (biaxial strain) Chern, IEDM 2012 Pillarisetty, IEDM 2010 S D 0 2 4 6 8 10 HfO 2 12 cm -2 ) Silicon Hole N inv (10 Universal James T. Teherani, MIT 4
Mobility, Current, and Ballistic Velocity Long-channel device (drift-diffusion): 𝐷 𝑝𝑦 𝑋 𝑟𝜐 𝑢ℎ 2 𝐽 𝐸,𝑡𝑏𝑢 = 2𝑀 𝜈 𝑊 𝐻𝑇 − 𝑊 𝜈 = 𝑛 ∗ Short-channel devices (ballistic transport): 𝑢ℎ ∙ 1 − 𝑠 𝑑 𝐽 𝐸,𝑡𝑏𝑢 = 𝐷 𝑝𝑦 𝑋 𝑊 𝐻𝑇 − 𝑊 𝑤 𝜄 1 + 𝑠 𝑑 2𝑙𝑈 𝑤 𝜄 = 𝜌𝑛 ∗ Lundstrom, EDL 1997 James T. Teherani, MIT 5
Mobility, Current, and Ballistic Velocity Long-channel device (drift-diffusion): 𝐷 𝑝𝑦 𝑋 𝑟𝜐 𝑢ℎ 2 𝐽 𝐸,𝑡𝑏𝑢 = 2𝑀 𝜈 𝑊 𝐻𝑇 − 𝑊 𝜈 = 𝑛 ∗ Short-channel device (ballistic transport): 𝑢ℎ ∙ 1 − 𝑠 𝑑 𝐽 𝐸,𝑡𝑏𝑢 = 𝐷 𝑝𝑦 𝑋 𝑊 𝐻𝑇 − 𝑊 𝑤 𝜄 1 + 𝑠 𝑑 2𝑙𝑈 𝑤 𝜄 = 𝜌𝑛 ∗ Lundstrom, EDL 1997 James T. Teherani, MIT 6
Experimental Device Fabrication 1) s-GOI Substrate 2) Electron Beam Patterning 3) Dielectric Deposition Si Biaxial Lateral Compression Relaxation Ge Ge HfO 2 Ge 10 nm Ge SiO 2 𝒙 𝑶𝑿 • Begin with biaxially strained Ge on insulator 4) Final Device Structure • Nanowire patterning creates free surfaces G lateral strain relaxation S D • Final strain is asymmetric HfO 2 • Neither biaxial nor uniaxial W. Chern et al. , IEDM 2012 James T. Teherani, MIT 7
Asymmetric Strain (1/2) James T. Teherani, MIT 8
Asymmetric Strain (2/2) 1.7% -2.4% James T. Teherani, MIT 9
Measured & Simulated Strain 3.0 Biaxially strained substrate Average Compressive Lateral Strain, 𝜗 𝑦𝑦 (%) 2.5 x Experiment 2.0 Simulation 1.5 ∆𝜕 = −404 (𝜗 𝑦𝑦 + 𝜗 𝑨𝑨 ) 2 𝜗 𝑨z =2.56% W. Chern et al. , IEDM 2012 1.0 Xia, Univ. British Columbia 20 40 60 80 100 W NW (nm) • Measured strain from Ge-Ge Raman peak shift • Simulated strain from elastic energy minimization ( nextnano3 ) James T. Teherani, MIT 10
Impact of Strain on Valence Band Si • Strain shifts the valence band through deformation potentials • 150 meV energy shift due to lateral strain relaxation near sidewalls James T. Teherani, MIT 11
Hole Density Across Device Hole Density ( N inv =3×10 12 cm -2 ) Valence Band Offset s-Si s-Ge WN HfO 2 Si Δ𝐹 𝑤 ~ 770 meV J. Teherani et al. , PRB 2012 • Holes cluster near side gate due to • Strain relaxation near sidewall valence band shift • Favorable gate electrostatics • Few carriers near top gate, Si acts as dielectric due to large valence band offset with Ge James T. Teherani, MIT 12
Quantum Mechanical Simulation Details First Hole Eigenstate WN HfO 2 Si infinite 2D simulation structure E-k z Dispersion for 1 st Eigenstate 0.2 Energy (eV) • Performed 2D numerical simulations using nextnano3 assuming infinite 0 E F nanowire length • Solved Schrödinger-Poisson equation -0.2 using 6x6 k∙p quantization method -0.15 0 0.15 𝑙 𝑨 ( 1/Å ) James T. Teherani, MIT 13
Inverse Effective Mass Calculation E-k z Dispersion for 80 Eigenstates 𝜖𝐹 𝑤 = 𝑊 𝐺𝐶 − 0.5 V ⇒ 𝜖ℏ𝑙 𝑂 𝑗𝑜𝑤 = 3 × 10 12 cm −2 𝑛(𝑙) = 𝑤 1 ℏ𝑙 • Solved Schrödinger-Poisson for 80 eigenstates • Strain mixes heavy -hole and light -hole valence bands • Small 𝑛 ∗ for small 𝑙 𝑨 ( light -hole characteristics) • Large 𝑛 ∗ for large 𝑙 𝑨 ( heavy -hole characteristics) James T. Teherani, MIT 14
Inverse Effective Mass (1/2) 𝜈 = 𝑟𝜐 𝑛 ∗ James T. Teherani, MIT 15
Inverse Effective Mass (2/2) 𝜈 = 𝑟𝜐 𝑛 ∗ Inverse Effective Mass As Function of Position WN HfO 2 Si Inverse effective mass • Peaks near the sidewalls • Same location as hole density peak • Dips in center of device where higher 𝑙 𝑨 states are occupied N inv =3×10 12 cm -2 James T. Teherani, MIT 16
Inverse Effective Mass (2/2) 𝜈 = 𝑟𝜐 𝑛 ∗ Inverse Effective Mass As Function of Position WN HfO 2 Si Inverse effective mass • Peaks near the sidewalls • Same location as hole density peak • Dips in center of device where higher 𝑙 𝑨 states are occupied N inv =3×10 12 cm -2 James T. Teherani, MIT 17
Planar Simulations To understand nanowire results, we performed a simulation experiment in which we changed strain in planar structures. James T. Teherani, MIT 18
Impact of Strain on E-k Dispersion (1/3) 110 𝜗 𝑨𝑨 (transport direction) Biaxial Compression 110 Strained Ge 𝜗 𝑦𝑦 James T. Teherani, MIT 19
Impact of Strain on E-k Dispersion (2/3) 110 𝜗 𝑨𝑨 (transport direction) Biaxial Compression 110 Strained Ge 𝜗 𝑦𝑦 -2.4% Lateral strain relaxation ( 𝜗 𝑦𝑦 ) • Significantly reduces 𝑛 ∗ in the transport direction James T. Teherani, MIT 20
Impact of Strain on E-k Dispersion (3/3) 110 𝜗 𝑨𝑨 (transport direction) Biaxial Compression 110 Strained Ge 𝜗 𝑦𝑦 -2.4% Lateral strain relaxation ( 𝜗 𝑦𝑦 ) • Significantly reduces 𝑛 ∗ in the transport direction 1.7% Vertical strain relaxation ( 𝜗 𝑧𝑧 ) (out-of-plane strain) • No effect James T. Teherani, MIT 21
Mass Decrease with 𝜗 𝑦𝑦 (1/3) (transport direction) 𝜗 𝑨𝑨 𝜗 𝑦𝑦 𝜈 = 𝑟𝜐 𝑛 ∗ 𝑂 𝑗𝑜𝑤 = 2.5 × 10 12 cm −2 1/𝑛 𝑨 and 𝑤 𝜄 significantly increase as 𝜗 𝑦𝑦 is reduced James T. Teherani, MIT 22
Mass Decrease with 𝜗 𝑦𝑦 (2/3) (transport direction) 𝜗 𝑨𝑨 𝜗 𝑦𝑦 𝜈 = 𝑟𝜐 𝑛 ∗ 𝑤 𝜄 = 2𝑙𝑈 1/𝑛 𝑨 /𝜌 𝑂 𝑗𝑜𝑤 = 2.5 × 10 12 cm −2 1/𝑛 𝑨 and 𝑤 𝜄 significantly increase as 𝜗 𝑦𝑦 is reduced James T. Teherani, MIT 23
Mass Decrease with 𝜗 𝑦𝑦 (3/3) (transport direction) 𝜗 𝑨𝑨 𝜗 𝑦𝑦 𝜈 = 𝑟𝜐 𝑛 ∗ 𝑤 𝜄 = 2𝑙𝑈 1/𝑛 𝑨 /𝜌 𝑂 𝑗𝑜𝑤 = 2.5 × 10 12 cm −2 1/𝑛 𝑨 and 𝑤 𝜄 significantly increase as 𝜗 𝑦𝑦 is reduced James T. Teherani, MIT 24
↓ 𝜗 𝑦𝑦 in Experimental NWs 𝑥 𝑂𝑋 Lateral strain 𝜗 𝑦𝑦 decreases with decreasing NW width James T. Teherani, MIT 25
Increased Mobility for Narrow NWs (1/3) 𝑥 𝑂𝑋 1/𝑛 𝑨 and 𝑤 𝜄 increase as 𝑥 𝑂𝑋 ↓ James T. Teherani, MIT 26
Increased Mobility for Narrow NWs (2/3) NW (w=49 nm) W. Chern et al. , IEDM 2012 1500 2 /Vs) 1.8 × 1000 eff (cm Biaxial Ge 500 Si Hole Universal 0 2 4 6 8 12 cm -2 ) N inv (10 𝑥 𝑂𝑋 1/𝑛 𝑨 and 𝑤 𝜄 increase as 𝑥 𝑂𝑋 ↓ James T. Teherani, MIT 27
Increased Velocity for Narrow NWs (3/3) 𝑥 𝑂𝑋 1/𝑛 𝑨 and 𝑤 𝜄 increase as 𝑥 𝑂𝑋 ↓ James T. Teherani, MIT 28
Drive Current Improvement 𝑢ℎ ∙ 1 − 𝑠 𝑑 𝐽 𝐸,𝑡𝑏𝑢 = 𝐷 𝑝𝑦 𝑋 𝑊 𝐻𝑇 − 𝑊 𝑤 𝜄 1 + 𝑠 𝑑 𝐽 𝐸,𝑡𝑏𝑢 = 𝑅 ∙ 𝐶𝑤 𝜄 ballisticity ballistic velocity inversion charge • 𝑤 𝜄 improvement of 2.8× with respect to unstrained Si • 𝑤 𝜄 improvement of 1.6× with respect to 1% uniaxial Si • 𝐶 also improves as strain splits bands and reduces scattering • Reduced backscattering inferred from highly enhanced experimental s-Ge hole mobility ⇒ 𝑱 𝑬 improvement of at least 2× with respect to 1% uniaxial Si James T. Teherani, MIT 29
Summary • Asymmetric lateral strain in NW device structure • Significant lateral relaxation for small nanowire widths James T. Teherani, MIT 30
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