CSPLAT for Photolithography Simulationcadlab.cs.ucla.edu/.../CSPLAT_Guongxi.pdfSimulation Tool-----...
Transcript of CSPLAT for Photolithography Simulationcadlab.cs.ucla.edu/.../CSPLAT_Guongxi.pdfSimulation Tool-----...
CSPLAT for Photolithography Simulation
Guoxiong [email protected]
Institute of VLSI Design, Zhejiang University2001.8.31
Outline
Photolithographic systemResolution enhancement technologiesPhotomask techniques
Optical proximity correctionPhase-shifting mask
Traditional simulation methodSimulation Tool –SPLAT and CSPLATSome examples
Optical part of photolithographic system
Figure 1 Schematic of a typical stepper
Schematic of the optical part
Figure 2 Approximation of a projection exposure system
NAkCD λ
1=
Feature size limit in photolithography processes
Where CD is Critical Dimension,(also refers to the resolution, i.e.,the minimal printable feature size). lambda is wavelength, NA is Numerical Aperture, k1 is a characteristic constant of the specific lithography process. this formula states the CD limit of a certain litho-process.
Roadmap of illumination source wavelength reduction
The physical limit of NA is 1.0,maximum for feasible NA is about 0.75 to 0.85.k1 represents lithography aggressiveness (0.75 to 0.35, 0.25 as the theoretical lower limit)
Modified illuminationAnnular illuminationQuadrupole illumination
Photomask techniquesOptical proximity correctionPhase-shifting masks
Pupil filteringMultiple exposuresAntireflective layerTop surface imaging
Photolithography technologies
Optical proximity correctionIntentionally and systematically distort the mask in such a way as to compensate for optical diffraction limit and process non-idealities.
Enables smaller features with closer proximities to be printed on the same area.Increases the process latitude, decreases the variations of linewidth across a chip and could potentially enhance yield;
�Applicability of combination of OPC and PSM leads to better resolution when the minimum feature dimensions and spacing decrease below the wavelength of the light source.
Types of Optical Proximity Correction
�Model-based OPC
– use process simulation to determine corrections on-line
– longer design time,increased mask complexity
– suitable for aggressive designs
�Rule-based OPC– apply corrections based on a
set of predetermined rules
– fast design time,lower mask complexity
– suitable for less aggressive designs
Phase-shifting Masks
(a)Light diffracted by two adjacent apertures constructively interferes, increasing the light intensity in the dark area of the wafer between the apertures.
(b)with the (alternating)phase-shifting mask,the phase shifter reverses the sign of the electric field, and destructive interference minimizes light intensity at the wafer in the dark area between apertures.
Note: E denotes electric field and I denotes intensity
Types of phase-shifting masks
Traditional simulation method
Aerial image simulationHopkins partial coherence model
Photoresist exposure/bleaching simulationDill’s exposure model
Photoresist bake/development SimulationPlasma etching and diffusion simulation for different layers.
Simulation Tool------ SPLATA lithography simulation tool developed in UC Berkeley.Based on the Hopkins Equation for partially coherent imaging.Use the method of two dimension Fourier transform.Calculates sampling intensities on a line or a rectangular area.Unsuitable to deal with sparse aerial point simulation.
SPLAT Simulation Flow
Opticalparameters TCC
Maskprofile
Outputimage
intensity
Hopkins equation
The Fourier transform of
intensityFouriertransform
Fourier inverse transform
New Simulation Tool -----CSPLAT
Written in C, using similar syntax as in SPLAT.Fast sparse aerial points intensity simulation.
Hopkins Equation (Bi-linear )Decomposition of convolution kernelsIntensity lookup table for geometrical primitives.
Post-imaging model.Variable intensity threshold (line width)Gaussian filters set (line end and corner rounding)
New Simulation Tool -----CSPLATModel training from wafer measurement
Test patternsIsolated line line-widthIsolated line-end spacePitch structure
Regression methodDefinitive searchingNeural network trainingThe goal of model calibration is to capture the CD variations caused by the the process distortions. The more information we have about these sub-processes and the more complex models we use for the simulations,the more accurate the simulation results we should obtain.
Convolution kernels
Model –based correction is calculated based on predefined kernel functions and the mask patternsA convolution value at any specific point (x,y) is found by:
Centering a “convolution kernel” function over the point (x,y)Multiplying the pattern and the “convolution kernel”Summing the total volume
The shape of a convolution kernel ultimately determines the behavior of a model
Convolution kernels
1) a partially coherent imaging system with a superposition of coherent imaging system.
2)Reduce to “principal waves”
3)The first few principal wave could meet the accuracy
CSPLAT Simulation Flow
Opticalparameters
TCC
tables
Set of kernels
Mask profile
Simulatedcontours
Hopkins equation
decomposition
Table calculation
Post-imagingmodel
Post-imaging model training
Test pattern
Optical simulator
Print onwafer
Aerial image
measurement
VariableThreshold
model
Model param
eters
extraction
Comparison
a b
c
(a) The error between SPLAT and CSPLAT
(b) The calculation result through SPLAT
(c) The calculation result through CSPLAT
Layout of a real chip
A partial layout geometries
The simulation result of using CSPLAT
Comparison of layout geometries and simulation result
Thank You