Refractive Power of a Surface. Exposure Sources. Thin Lenses. Thick Lenses. High Pressure Hg Arc Lamp Spectrum

Size: px

Start display at page:

Download "Refractive Power of a Surface. Exposure Sources. Thin Lenses. Thick Lenses. High Pressure Hg Arc Lamp Spectrum"

Grant Hardy
5 years ago
Views:

1 eractive Power o a Surace The reractive power P is measured in diopters when the radius is expressed in meters. n and n are the reractive indices o the two media. EE-57: icrofabrication n n P n n Exposure and maging Thin Lenses Exposure Sources OBJECT h ocal ray d d parallel ray F e d object distance d image distance, ocal lengths e,e extraocal distances h, h object/image heights chie ray F AGE e h Photons white light Hg arc lamp iltered Hg arc lamp excimer laser x-rays rom synchrotron Electrons ocused electron beam direct write ons ocused ion beam direct write Thick Lenses High Pressure Hg Arc Lamp Spectrum OBJECT d t d AGE deep UV mid UV near UV -line H-line G-line E-line h F e N N F e h 89 wavelength, nm d object distance d image distance, ocal lengths e,e extraocal distances h, h object/image heights H H Cardinal Points o a Lens: Focal Points: F, F Nodal Points: N, N Principal Points: H, H spectral reerence; also used or sterilization The -line at 365 nm is the strongest.

2 Projection Lithography equirements b minimum eature size (spot or line) b minimum period o line-space pattern λ exposure wavelength Using b θ min, obtain that b λ/na. The depth o ocus can be shown to be d ± λ/(na) A voxel is a volume pixel. For highest resolution lithograpy, desire the tallest aspect ratio voxel. Thus, wish to maximize the ratio d /b /NA. SO: it all depends upon the NA o the lens! b Want the tallest aspect ratio o the exposed voxel. n n, then d d Lens-aker s Formula n n d d This can also be expressed as: or: n n n n ( n ) P ( d )( d ) e e ±d Sample Calculation Primary reduction camera in WTC-FL uses a projection lens with /6.8 and 9.5 in. 4.3 mm. Lens diameter is 4.3 mm/ mm.40 in. The numerical aperture is NA /* For exposure in the middle green, λ 550 nm. Thus, the minimum eature size is b 550 nm/* µm or a line, or.0 * 3.7 µm 4.56 µm or a spot. The tightest grating pitch that could be printed using this lens is thereore b 7.44 µm. Lens Apertures The -number o a lens (/#) is the ocal length divided by the diameter. t is a measure o the light gathering ability. The numerical aperture (NA) o a lens is n*sin α, where α is the hal-angle o the largest cone o light entering the lens. α α NA 4 /# NA nsinα /# Lens Aberrations Chromatic aberration ispersion: change o reractive index with wavelength onochromatic aberrations transverse ocal shit longitudinal ocal shit spherical aberration coma astigmatism ield curvature distortion esolving Power o a Lens ayleigh criterion: inimum angular ray separation to resolve two spots rom one is: sin θ min.0 λ/. Since θ min is small, θ min.0 λ/. is the diameter o a circular aperture..0 is the irst zero o the Bessel unction J m (x). An Airy unction results rom Fraunhoer diraction rom a circular aperture. Straight line pattern: inimum angular ray separation to resolve two lines rom one is: sin θ min λ/, or approximately θ min λ/.

3 Standing Waves - Standing waves are enhanced by relective waer suraces. the waer or substrate is transparent, relections rom the aligner chuck can create standing wave patterns, also. This can be eliminated by using: a lat black chuck (anodized aluminum) an optical absorber under the waer (lint ree black paper) a transparent glass chuck (used on Karl Suss JB3) Exposures can be greatly miscalculated by the presence o standing waves and relective waers or chucks. Projection Optics t is exceeding diicult to make large NA reractive optics due to aberration limits. The best lenses used in projection lithography have NA A lens with NA 0.50 is a /.00 lens: its ocal length and eective diameter are the same! The largest NA lenses ever made were a NA 0.54 and a NA 0.60 by Nikon. elective optics are better suited or large NA applications. But they are physically larger, and usually require close temperature stability to keep their proper contours and alignment. Combinations (catadioptric) systems are also used. This is very common in SW (stepper) lithography equipment. Photographic Exposure Equation Contact and Proximity Lithography esolution T SB American Standards Association (ASA) ilm speed is the dose required to produce an optical density o 0. in a ilm media. T exposure time in seconds -number o projection lens S ASA or SO ilm speed B scene brightness in candles/t German N ilm speed is: N 0 log 0 (ASA) 00 ASA N λ exposure wavelength d resist thickness b minimum pitch o line-space pattern s spacing between the mask and the resist Contact Printing: b 3 0.5λd At λ 400 nm, d µm, obtain b 0.7 µm linewidth. Proximity Printing: b 3 λ( s 0.5d) At λ 400 nm, s 0 µm, d µm, obtain b 3.0 µm linewidth. Optical Absorbance and ensity Standing Waves - optical absorber Typical optical densities: xerox transparency: O photographic emulsion plate: O -3 chrome photomask: O 5-6 T A T transmittance absorbance O log0 ( A) optical density Short exposure wavelengths can create standing waves in a layer o photoresist. egions o constructive intererence create increased exposure. These can impair the structure o the resist, but can be eliminated by: use o multiple wavelength sources postbaking Eects are most noticeable at the edge o the resist. wave pattern appears on the edge o the resist

4 Optical odulation optical intensity, W/cm optical modulation within a scene or image T modulation transer actor or an optical element imensional Latitude: (typically want less than 0.05) Line Width, L Exposure Latitude L' L δ L' negative P positive P max max min when min 0. min L LNES SPACES drawn mask eature size T out in SPACES LNES Exposure odulation Transer Function Proximity Exposure Eect - The modulation transer unction (TF) is the modulus o the Fourier transorm o the linespread unction: TF( ) πjx L( x) e dx is the spatial requency light ield 50:50 grating dark ield Optics obeys linear system theory: TF(system) TF(element ) TF(element ) TF(element 3 )... Optimum exposure depends upon the pattern!!! Adjacent clear (bright) regions add additional exposure to a given region because o overlap rom Gaussian tail o the linespread unction. odulation Transer Function in Photolithography TF(system) TF(mask) TF(optics) TF(resist) TF() photoresist Spread Functions uniorm illumination uniorm illumination mask plate mask plate overall system mask and optics Gaussian distribution ntensity L(x) ntensity J(x) 0 increase in spatial requency due to nonlinearity o resist spatial requency, x x Line Spread Function L(x) Edge Spread Function J(x) dj ( x) L( x) J ( x) dx x L( x') dx'

5 Proximity Exposure Eect - photomask Phase Shiting asks photomask chrome λ/ phase shiting layer

EE-527: MicroFabrication

EE-527: MicroFabrication EE-57: MicroFabrication Exposure and Imaging Photons white light Hg arc lamp filtered Hg arc lamp excimer laser x-rays from synchrotron Electrons Ions Exposure Sources focused electron beam direct write