CSPLAT for Photolithography Simulation

Transcription

1 CSPLAT for Photolithography Simulation Guoxiong Wang Institute of VLSI Design, Zhejiang University

2 Outline Photolithographic system Resolution enhancement technologies Photomask techniques Optical proximity correction Phase-shifting mask Traditional simulation method Simulation Tool SPLAT and CSPLAT Some examples

3 Optical part of photolithographic system Figure 1 Schematic of a typical stepper

4 Schematic of the optical part Figure 2 Approximation of a projection exposure system

5 Feature size limit in photolithography processes CD = k 1 λ NA 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.

6 Roadmap of illumination source wavelength reduction

7 Photolithography technologies The physical limit of NA is 1.0, maximum for feasible NA is about 0.75 to k1 represents lithography aggressiveness (0.75 to 0.35, 0.25 as the theoretical lower limit) Modified illumination Annular illumination Quadrupole illumination Photomask techniques Optical proximity correction Phase-shifting masks Pupil filtering Multiple exposures Antireflective layer Top surface imaging

8 Optical proximity correction Intentionally 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.

9 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

10 Phase-shifting Masks Note: E denotes electric field and I denotes intensity (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.

11 Types of phase-shifting masks

12 Traditional simulation method Aerial image simulation Hopkins partial coherence model Photoresist exposure/bleaching simulation Dill s exposure model Photoresist bake/development Simulation Plasma etching and diffusion simulation for different layers.

13 Simulation Tool SPLAT A 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.

14 SPLAT Simulation Flow Optical parameters Hopkins equation TCC Mask profile Fourier transform The Fourier transform of intensity Fourier inverse transform Output image intensity

15 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 kernels Intensity lookup table for geometrical primitives. Post-imaging model. Variable intensity threshold (line width) Gaussian filters set (line end and corner rounding)

16 New Simulation Tool -----CSPLAT Model training from wafer measurement Test patterns Isolated line line-width Isolated line-end space Pitch structure Regression method Definitive searching Neural network training The 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.

17 Convolution kernels Model based correction is calculated based on predefined kernel functions and the mask patterns A 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

18 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

19 CSPLAT Simulation Flow Optical parameters Hopkins equation TCC decomposition Set of kernels Table calculation Mask profile tables Post-imaging model Simulated contours

20 Post-imaging model training Test pattern Optical simulator Print on wafer Aerial image measurement extraction Model parameters Variable Threshold model

21 Comparison a c (a) (b) (c) b The error between SPLAT and CSPLAT The calculation result through SPLAT The calculation result through CSPLAT

22 Layout of a real chip

23 A partial layout geometries

24 The simulation result of using CSPLAT

25 Comparison of layout geometries and simulation result

26 Thank You