Processable Electronics Lecture 10 (2024) PDF

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Imperial College London

2024

Dr F. Torrisi

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two-dimensional materials graphene electronic properties

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This document contains lecture notes on Processable Electronics for Autumn 2024. It discusses two-dimensional materials, with a focus on graphene and its properties, along with various electronic applications. The notes provide a summary of different aspects of graphene and its use.

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Processable Electronics: from materials chemistry to device applications Lecture 10: Two-dimensional materials for processable electronics Dr F. Torrisi [email protected] Autumn ter...

Processable Electronics: from materials chemistry to device applications Lecture 10: Two-dimensional materials for processable electronics Dr F. Torrisi [email protected] Autumn term 2024 - Introduction to Family of Layered materials - Electronic, optical and mechanical Properties, - Synthesis of 2D materials for printed and flexible electronics - Flexible devices with graphene and 2D materials Graphene-based, flexible proof of concept devices OLED Solar cell Transparent Flexible Heater Nature Photon.6:105 Nanotechnology 23:344013 Nano Lett. 11:5154 Flexible touch screen Flexible Transistors Flexible smart window Nature Nanotech. 5:574 Nano Lett. 10:3464 Nature Photon. 4:661 The graphene example Graphene Superlatives Linear Spectrum One Atom Thin (broad-band from UV to IR) (~0.33 nm thin) High Mobility Strength (up to 2 x 106 cm2 V-1 s-1) (Young’s modulus ~1TPa) Highly Stretchable Unique Optical (fracture strain up to 23%) Properties (tunable ultrafast dynamics) 4 Electronic properties of graphene - In first approximation the electronic and optical properties of single layer graphene can be derived from the two π-bands. - σ-bands are well separated in energy and can be neglected. - π-bands are linear near K,K’ point. ± Linear energy dispersion 𝐸 (𝒌) = ±ħ𝑣𝐹|𝑘| Charge carriers are mass-less Dirac EF particles! Castro Neto et al. Rev. Mod. Phys. (2009) High mobility graphene Suspended graphene Graphene in h-BN Up to µ=2x106 cm2 V-1 s-1 Up to µ=5x105 cm2 V-1 s-1 (>105 cm2 V-1 s-1 ) A. S. Mayorov et al. Nano Lett., 11, 2012 A. S. Mayorov et al. Nano Lett., 11, 2011 Graphene on graphite Up to µ=107 cm2 V-1 s-1 P. Neugebauer, Phys Rev Lett 103, 136403, 2009 Electrostatic doping in graphene VS-D graphene SiO2 VG p++ Si E Electron-doping k 𝑆 𝐶 = 𝜀0𝜀𝑟 EF 𝑑 𝐶 Hole-doping 𝑛 = × (𝑉𝐺 − 𝑉𝐷) 𝑆 For 300 nm SiO2 C/S≈ 10nF/cm2 Kelvin method 1 2 3 4 S1 S2 S3 The Right Honorable Lord William T. Kelvin Assuming t < S/2 and W,L >> S then OM, GCVO, PC, PRS, PRSE 𝜋 𝑉 𝑉 1 Graphene’s case (n≈0) 𝑅𝑠 = = 4.532 = ln(2) 𝐼 𝐼 𝜎𝑡 𝜎2𝐷 , 𝑚𝑖𝑛~4𝑒2/ℎ For N=1 number of layers 𝑅𝑠 = 1/(𝑁𝜎2𝐷 , 𝑚𝑖𝑛)~6𝑘Ω/□ e.g. for 10nm thin copper film 𝑅𝑠~1 − 5Ω/□ Contact resistance Contact resistance 𝑡 𝑉 𝜌 𝑅 = = 2𝑅𝑚𝑒𝑡𝑎𝑙 + 2𝑅𝑐𝑜𝑛𝑡𝑎𝑐𝑡 + 𝑅𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑅𝑠 = 𝐼 𝑡 Optical properties of graphene: transmittance The optical transmittance for a graphene film at normal light incidence can be defined as: 𝜋𝛼 −2 𝑇= 1 + ≈ 1 − 𝜋𝛼 2 hence 𝐴 ≈ 𝜋𝛼 ≈ 2.3% 𝜎0𝑍0 is the fine where 𝛼= structure constant 𝜋 the universal optical conductance is 𝑒2 𝜎0 ≈ = 𝜋𝜀0𝛼𝑐 4ħ the impedance of free space is 𝑍0 = 377Ω How about going 2D? Top-down approach Bottom-up approach - Strong in-plane bonds - Metal substrate - Weak Van der Waals inter- - Carbon precursor planar forces it is possible to grow it is possible to split layered materials into individual atomic individual atomic planes. planes. Cost/performance: Graphene for low-cost flexible electronics Cost Chemical synthesis Molecular beam epitaxy Inks/composites Mechanical cleavage Functionalized Lab-scale samples material Lab-scale samples Large-area Transparent Chemical Vapour conductors Depositions Wafer scale transistor Hight T (1000oC) Large-area Transparent Liquid Phase conductors Exfoliation Inks/Composites Room T Performance Exfoliation energy Exfoliation energy 𝐸𝑒𝑥 ≈ 50𝑚𝑒𝑉 Graphene has delocalized electrons on each side. Mechanical exfoliation of graphite Yi et al. J. Mater. Chem. A, 2015, 3, 11700–11715 Cost/performance: Graphene for low-cost flexible electronics Cost Chemical synthesis Molecular beam epitaxy Inks/composites Mechanical cleavage Functionalized Lab-scale samples material Lab-scale samples Large-area Transparent Chemical Vapour conductors Depositions Wafer scale transistor Hight T (1000oC) Large-area Transparent Liquid Phase conductors Exfoliation Inks/Composites Room T Performance Liquid Phase Exfoliation Solvent Natural Graphite Graphene dispersion Power Shear forces enable exfoliation N. Paton et al. Nature mater. (2014) T. Hasan, F. Torrisi et al. Phys.Stat. Sol. B (2010) Y. Hernandez et al., Nature nano. (2008) Liquid Phase Exfoliation Dispersion in Dispersion in water- organic solvent surfactant solution Solvent with high surface tension prevents re-aggregations! Surfactant compensates repulsion between water and graphene. Y. Hernandez et al. Nat. Nano. (2008) M. Lotya et al. JACS (2009) Liquid Phase Exfoliation in organic solvents N-Methyl-2-Pyrrolidone Dichlorobenzene Chloroform Absorbance (a.u.) Ethil Acetate Dimethylformamide δg ~70 mJm-2 600 800 1000 1200 1400 Y. Hernandez et al. Nat. Nano. (2008) Wavelength (nm) T. Hasan, F. Torrisi et al. Phys. Stat. Sol. B (2010) 49.4 60.4 51.1 61.7 70.6 19 Liquid Phase Exfoliation in organic solvents Stable dispersion ΔGmix = ΔHmix -TΔSmix

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