Outline Wednesday January 30Evolution of Computational PowerCost of Computing Power Versus TimeStorage Capacity vs TimeImage & Template Cross-correlationAlignment MarksNano-electronics LBNL/UC BerkeleyPinhole FabricationPinhole PerfomanceSpectral Purity Filter PerformanceBinary Phase HologramEEC 235Advanced Patterning,Electron Beam Lithography,EUV Lithography,for NanofabricationErik H. Anderson Center for X-Ray OpticsMaterials Sciences Division, Lawrence Berkeley National LaboratoryOutline Wednesday January 301. Introduction 2. Patterning Technology Overview3. Fundamentals of E-Beam Systems1. Electron Optics2. System concepts3. Proximity correction4. Alignment and calibration5. ExamplesOutline Monday February 41. Patterning for Nanolithography1. Requirements and trade-offs2. EUV Fundamentals1. Optics2. Sources3. Metrology3. Future OutlookEvolution of Computational Powerhttp://www.transhumanist.com/volume1/moravec.htmHans Moravec, Journal of Evolution and Technology. 1998. Vol. 1Cost of Computing Power Versus Time1880 1900 1920 1940 1960 1980 2000 2020YearMIPS/1997 k$10-1110-1010-910-810-710-610-510-410-310-210-110 010 110 210 3MechanicalTubeDiscreteICElectro-Mechanical2.6GHz P4Inflation adjusted $’s:http://oregonstate.edu/dept/pol_sci/fac/sahr/sahr.htm10 4Complexity of Modern ElectronicsImage Courtesy of AMDImage Courtesy of IBMStorage Capacity vs TimeDavid B. Bogy, UCBLithography TradeoffsResolutionPlacementThroughputCostLitho SystemLithography Tradeoffs Resolution vs RateWavelength vs Feature Size ReductionVolume Production tool cost vs TimeUsing E-Beam Lithography to explore Nano PatterningTypical R&D system• Column, Stage, and Ancillary Hardware based on Leica VB6-HR• Pattern Generator, Data Path Developed at Berkeley Lab• Beam Voltage 20-100KV• Beam Size 5-10nm⇒5-8nm• Deflection Rate 25MHz• Resolution 16 Bit• Interferometer λ/1024• Wafer Size 75-200mm• Electron Detection Backscattered and TransmissionHistorical Evolution: Dedicated E-Beam SystemsBellLabsIBM JEOL Cambridge PhillipsEBES VS seriesEL seriesEBMF EBPGJBX-5DIILeica JenoptikEtecVB series ZBA, LIONVistecMEBESElectron Optics Basics• Sources•Lenses• Deflectors•Blankers• Resolution • Spherical, Chromatic, and Diffraction• VB6 Electron Optics Layout (Typical of State-of-the-art column)Basic Physics for electron Optics –Classical and Modern PhysicsF = dp/dtp = mv/(1-(v/c)2) = γmvKE + mc2= γmc2= (m2c4+ p2c2)1/2dp/dt = q(E + v x B) B = ∇xA, ∇·B = 0 B = µ0H (free space)∇·D = ρ D = ε0E (free space)∇xH = J + dD/dt∇xE= -dB/dtE = hν p = h/λE = ħω p = ħkh = 6.625x10-34Joule-secε0= 8.854 x10 –12Farad/mµ0= 4π10 –6Henry/mc = 2.998 x10 8 meter/secq = 1.602 x10 –19 CoulMelectron= 9.11 x10 –31KgWavelength of an Electron Non-Relativistic CalculationWhat is the wavelength of and electron?Non-relativistic calculationKE = (p2/2m) or p = (2m*KE)1/2and λ = h/pUse 1000eV for example:p = (1000*1.6x10–19 *2*9.11x10-31)^1/2 =1.2x10-23kg*m/secλ = h/p = 6.6250x10–34 kg*m2/sec/ (1.2x10–23 kg*m/sec)= 3.88x10-11m or .0388nmWavelength of an Electron Relativistic CalculationRelativistic CalculationKE + mc2= γmc2= (m2c4+ p2c2)1/2(V*q + mc2)2-m2c4 = p2c2 V = 1000eVP = sqrt((1000*q + mc2)2-m2c4 )/c= 1.7889x10-23kg*m/sec λ= h/p = 6.6250x10–34 kg*m2/sec/ (1.7889-23kg*m/sec)λ = 3.875x10-11m or .038nmElectron Wavelength as a function of EnergyEnergy Relativistic Non-Relativistic100eV 1.2270e-010 1.2270e-0101KeV 3.8783e-011 3.8802e-01110KeV 1.2211e-011 1.2270e-01150KeV 5.3581e-012 5.4874e-012100KeV 3.7035e-012 3.8802e-012200KeV 2.5095e-012 2.7437e-012Unit metersPhoton Wavelength as a function of EnergyEnergy Electron Photon100eV 1.2270e-010 1.2414e-0081KeV 3.8783e-011 1.2414e-00910KeV 1.2211e-011 1.2414e-01050KeV 5.3581e-012 2.4827e-011100KeV 3.7035e-012 1.2414e-011200KeV 2.5095e-012 6.2068e-012E = hν= hc/ λElectron Optics Basics - SourcesSource• Tungsten •LaB6• Thermal Field Emitter (Schottky)• Cold Field EmitterElectron Optics Basics – Sources ThermalVacuum Tube Terms• Cathode•Grid• AnodeIs= AT2e-(B/T)Electron emission, Is (amps/cm2), as a function of the absolute temperature, T, of athermionic emitter is given by Richardson's equation: where A and B are constants that are determined empiricallyElectron Optics Basics – Sources TFEAnodeSource Characteristics: BrightnessSource Type Brightness [amp/cm2/str]SourceSizeEnergy SpreadVacuum Required (Torr)Tungeston10525um 2-3eV 10-6LaB610610um 2-3eV 10-8TFE10825nm 0.9eV 10-9Cold FE1095nm 0.22eV 10-10Electron Optics Basics - Brightness• If the beam energy is constant, brightness is conserved in the column or reduced by apertures• Analogous to brightness in an photon (optical) system• This is a consequence of classical statistical mechanics where the volume of momentum-position “phase space” is conserved (Liouville equation) as the charged particles traverse the column• dxdydzdpxdpydpz)start= dxdydzdpxdpydpz)endBrightness for a single thin lens system in small angel approximation1/Ω1I/d12 =? 1/Ω2I/d22 πθ12I/ d12 =? πθ22I/ d22 v2d12 =? u2d22OKSmall angle approximation:θ1= Lr/u θ2= Lr/v2 π (1 – cos(θ)) = πθ2Electron Optics Basics – Electrostatic LensF = q(E)V0-V1V0Speed up Slow down Net PushElectron Optics Basics – Magnetic Lensdp/dt = q(v x B)f = KV/(NI)2Paraxial Equations for Magnetic LensF = q(E+vxB) (the Lorentz force) where F is the force,q is the charge on the particle, E is the electric field, v the particle's velocity and B is the magnetic field. • F = q(E+vxB) •Fr = -evθBz(z)•Fr = -(e2/(4m))B2r•F = ma•d2r/dt2+ (e2/(4m)) B2r = 0• (1/2) m vz2= eV•d2r/dz2 = -(e/(8m)) B2r/vrElectron Optics Basics – Aberrationsdsa= Csα3/2 Spherical aberrationswhere Cs= spherical aberration coefficient, and α = semi angular aperture of the lens. ddi= 0.61λ/NA = 0.61λ/ α (λ = 0.0037 nm for 100kV) Diffractiondca= Cc α (∆V/V) Chromaticα = half (semi) angleElectron Optics Basics – Estimating Current and Spot size• Lens Aberrations•∆V/V• Brightness • Estimate using a sum in quadratureDt2= (source/M) 2+ (dsa)2+ (ddi)2+ (dca)2I = β*(παd/2)2Electron Optics Basics – Stigmator / DeflectorElectron Optical Layout for the Leica VB6Vector Beam Block Diagram and eye chartTop Level of E-Beam System ArchitectureExposedWafersUnexposedWafersE-BeamSystemHow do we get the pattern we want?•Resist• ProximityHSQ Dots Diameter measured by Low Voltage SEM
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