Modulation Transfer Function

1. Modulation Transfer Function

2. Fraunhofer Diffraction • The measure of the quality of the aerial image is given by • The MTF is really a measure of the contrast in the aerial image • The optical system needs to produce MTFs of 0.5 or more for a resist to properly resolve the features • The MTF depends on the feature size in the image; for large features MTF=1 • As the feature size decreases, diffractions effects casue MTF to degrade

3. Change in MTF versus Wavelength

4. Contact and Proximity Systems • These systems operate in the near field or Fresnel regime • Assume the mask and the resist are separated by some small distance “g” • Assume a plane wave is incident on the mask. • Because of diffraction, light is bent away for the aperture edges • The effect is shown in the next slide • Note the small maximum at the edge; this results from constructive interference • Also note the ringing • To reduce these effect, we often use light sources with multiple wavelengths

5. Fresnel Diffraction

6. Fresnel Diffraction • As g increases, the quality of the image decreases because diffraction effects become more important • The aerial image can generally be computed accurately whenwhere W is the feature size • Within this regime, the minimum resolvable feature size is

7. Resolution • A more exact solution for the theoretical resolution for proximity or contact aligners is given by: • Where l is the wavelength of light used to exposure the pattern, g is the distance between the bottom of the mask and the top of the photoresist, z is the thickness of the photoresist (typically 0.8-1.2mm).

8. Fresnel Number • Fresnel diffraction when F ≥ 1 • Fraunhofer diffraction when F << 1

9. Summary of the Three Systems

10. Comparison of Depth of Focus http://www.research.ibm.com/journal/rd/411/holm1.gif

11. Photoresists • Photoresists change their chemical properties when exposed to light • Almost all photoresists are based on hydrocarbons • There are some inorganic resists (e.g., As2S3) • The light breaks chemical bonds in these materials • The photoresist then chemically rearranges itself into a more stable compound • Some positive photoresists may form smaller polymer chains, which are more soluble in developer after exposure • Negative photoresist forms larger polymer chains, which are less soluble in developer after exposure

12. Photoresists • Most resists in use today are positive resists because they have better resolution • Negative resists swell when exposed to light • Generally, resists are liquid at room temperature and are applied by placing a drop on the wafer and then spinning at high angular velocity (3-6k rpm) • The viscosity and spin speed determine the resist thickness. • Controlled by the type and volume of solvent • Once spun on, the wafer undergoes a pre-bake to drive off the solvent

13. http://www.lithoguru.com/scientist/lithobasics.html

14. Photoresists • Following pre-bake, the resist is exposed and developed • Developing is performed either by immersion or by spraying a developer (base) • After developing, the resist is baked again (postbake) to harden it and improve its resistance to etches • Long UV exposure can also be used to cross-link the polymer chains in the remaining photoresist • After the etch step, the resist is removed in an oxygen plasma or by a wet removal • Acetone if minimal hardbake • Variation on RCA etch or nitric acid

15. Photoresists • Parameters that determine the usefulness of the resist include • Sensitivity • - a measure of how much light is required to expose the resist • - typically 100mJ/cm2 • Resolution • - exposure, baking, developing must not degrade the quality of the image • Polymer used in Resist • - it must withstand the etching or ion implantation after the mask pattern is transferred to the resist

16. Photoresists • Photoresists usually contain three components • An inactive resin (usually a hydrocarbon which forms the base material) • Photoactive compound (PAC) • Solvent that is used to adjust the viscosity • The most common g- and i-line resists use • Diazonaphthoquinones (DNQ) as the PAC • Novolac as the resin • Propylene Glycol Monomethyl Ether Acetate (PGMEA) as the solvent • - this has replaced Cellosolve Acetate, which is a toxic hazard

17. Basic Structure of Novolac • Novolac is a polymer containing hydrocarbon rings with 2 methyl groups and 1 OH group • The basic ring structure is repeated to form a long chain polymer • Novolac readily dissolves in developer at a rate of ~15 nm/s

18. Diazoquinone • The photoactive part of the molecule is the part above the SO2 • The remainder of the molecule is represented by “R”

19. Diazoquinone • The function of the PAC is to inhibit the dissolution of the resin in the developer • DNQ is essentially insoluble in developer prior to exposure to light • When dissolved in the resin, they reduce the resist dissolution rate to 1—2 nm/s • When the resist is exposed to light, the diazoquinone molecule changes chemically

20. Decomposition of DNQ

21. Diazoquinone • When exposed to light, the bonds to the weakly bound nitrogen are broken leaving a highly active carbon site • The molecule stabilizes itself by moving a carbon outside the ring and covalently bonding to an oxygen becoming a ketene molecule • This is known as the Wolf rearrangement • The ketene transform into carbolic acid in the presence of water • The carbolic acid is readily soluble in a basic developer • - TMAH – tetramethyl ammonium hydroxide, KOH or NaOH dissolved in water • The exposed resist now dissolves at about 100 – 200 nm/s • 10-100 times faster than the unexposed resist

22. Properties and Characteristics of Resists • Two parameters are used to define the properties of photoresists • Contrast • - Contrast is the ability of the photoresist to distinguish between dark and light • It is experimentally determined by exposing the resist to differing amounts of light, developed for a fixed time, and measuring the thickness of resist remaining after developing • Critical modulation transfer function (CMTF)

23. Photoresist Contrast

24. Photoresist Contrast • For positive resists, material exposed to low light will not be attacked by the developer; material exposed to large doses will be completely removed • Intermediate doses will result in partial removal • The contrast is the slope of this curve and is given by • Typical g- and i-line resists will achieve a contrast of 2—3 and Qf values of 100 mJ/cm2

25. Photoresist Contrast • The contrast is not a constant, but depends on process variables such as • development chemistry, • bake times, • temperatures before and after exposure, • wavelength of light, • age of resist, and • underlying structure • It is desirable to have as high a contrast as possible in order to produce the sharpest edges in the developed pattern

26. http://www.research.ibm.com/journal/rd/411/holm4.gif

27. Photoresist Contrast This ‘poor’ quality image has been used to create periodic sine wave patterns in resist for optical gratings.

28. Modulation Transfer Function • We defined the MTF before in terms of a measure of the dark versus light intensities in the aerial image produced by the projection system • We define a similar quantity for the resist—the critical modulation transfer function (CMTF) • The CMTF is the minimum optical transfer function necessary to resolve a pattern in the resist • For g- and i-line resists, CMTF  0.4 • The CMTF must be less than the aerial image MTF if the resist is to resolve the aerial image

29. Effect of Resist Thickness • Resists usually do not have uniform thickness on the wafer • Edge bead: The build-up of resist along the circumference of the wafer • - There are edge bead removal systems • Step coverage Centrifugal Force

30. Effect of Resist Thickness • The resist can be underexposed where it is thicker and overexposed where it is thinner • This can lead to linewidth variations • Light intensity varies with depth below the surface due to absorptionwhere  is the optical absorption coefficient • Thus, the resist near the surface is exposed first • We have good fortune. There is a process called bleaching in which the exposed material becomes almost transparent • i.e.,  decreases after exposure to light • - Therefore, more light goes to deeper layers

31. Photoresist Absorption • If the photoresist becomes transparent, and if the underlying surface is reflective, reflected light from the wafer will expose the photoresist in areas we do not want it to. • However, this leads to the possibility of standing waves (due to interference), with resultant waviness of the developed resist • We can solve this by putting an antireflective coating on the surface before spinning the photoresist  increases process complexity

32. Standing Waves due to Reflections

33. Standing Waves Due to Reflections http://www.lithoguru.com/scientist/lithobasics.html

34. Removal of Standing Wave Pattern (a)                                     (b)                                (c) Diffusion during a post-exposure bake (PEB) is often used to reduce standing waves. Photoresist profile simulations as a function of the PEB diffusion length: (a) 20nm, (b) 40nm, and (c) 60nm. http://www.lithoguru.com/scientist/lithobasics.html

35. Mask Engineering • There are two ways to improve the quality of the image transferred to the photoresist • Optical Proximity Correction (OPC) • Phase Shift Masks (PSM) • We note that the lenses in projections systems are both finite and circular • Most features on the mask are square • We lose the high frequency components of the pattern • We thus lose information about the “squareness” of the corners

36. Mask Engineering • The effects are quite predictable • We can correct them by adjusting feature dimensions and shapes in the masks

37. Mask Engineering

38. Phase Shift Masks • In a projection system, the amplitudes of the diffracted light at the wafer add • Closely spaced lines interact; the intensity at the wafer is smeared • If we put a material of proper index of refraction on part of the mask, we can retard some of the light and change its phase by 180 degrees • Properly done, the amplitudes interfere • The thickness of the PS layer is n is the index of refraction of the phase shift material

39. Phase Shift Masks (PSM) Intensity pattern is barely sufficient to resolve the two patterns.