Introduction to compact 3D resist models used in Optical Proximity Correction for IC Manufacturing

1. Christian Zuniga, PhD
From SPIE Papers in 2014 and 2015
Christian Zuniga, et al “Resist Profile Modeling with
Compact Resist Model” Proc SPIE 9426 2015

2. Overview
 Introduction: OPC models
 Optical Parameters
 Center focus
 Sampling Plane
 Need for 3D Models
 Resist Modeling
 Challenges
 Summary

3. Introduction: IC Manufacturing
https://www.semiwiki.com/forum/showwiki.php?title=Semi%20Wiki:Semiconductor%20Fab%20Wiki
Optical Proximity Correction (OPC) needed

4. Optical Proximity Correction in
IC Manufacturing
 Optical diffraction causes proximity
effects
 Iso-dense bias
 Corner rounding
 Mask must be corrected to print desired
image
http://scale.engin.brown.edu/classes/EN0291S40F06/lecture11.pdf

5. OPC Model
5
Compact mask, optical and resist model that predict
resist contours and used to correct mask
Optical Model Compact
Semi-Empirical
Resist Model
mask
i(x,y) ir(x,y)
Resist contours
Model parameters must be calibrated
CM

6. OPC Model Calibration
 Test patterns
exposed and
measured
 Model parameters
obtained by
minimizing CD
RMS Error
https://commons.wikimedia.org/wiki/File:Simple_model_of_Scanner_(Semiconducter_lithography).P
NGhttp://
OPC
Model
CDm,k CDs,k(p)
Scanner

7. Optical Model
 Calibrated Parameters
 Center Focus: Image focus
without resist film
 Sampling Plane: location in
film where intensity is
sampled
 Calibration Process
 Originally calibrated with
nominal CD data (best
focus, best dose)
 Ok for large k1 but lose
information about
○ Focus
○ Height

8. Center Focus and Sampling
Plane z
 Generally dependent
 Approximate relation
fc »
ni
nr
z
Places best CD focus at 0

9. Center Focus and Sampling
Plane
 Center focus
correlates with
defocus in scanner
 Improve process
window performance
by properly calibrating
center focus
 Sampling plane
remains a fitting
parameter

10. Need for 3D Models?
PTD Resists
Features with resist loss
can become etching hotspots
Low k1 imaging can increase
Resist loss
Sidewall angle degradation
𝐷𝑜𝑠𝑒 ∙ 𝑖 𝑇𝑜𝑝 > 𝐷𝑜𝑠𝑒_𝑐𝑙𝑒𝑎𝑟
10

11. 3D OPC Model: Practical
Usage 3D Model indicates contour at a chosen height
 OPC can use 3D model as an additional process
condition
 Etching hotspots needed to form a good ORC recipe
11
Contours:
Red: height 1nm or regular
OPC model
Pink: height 45 nm
Orange: height 63 nm
3D model indicates
weak spot.

12. 3D Model for SRAF Print
Modeling
12
Dimpling on resist top Scumming on resist bottom
Model gives extent of printing through height

13. 3D OPC Model
13
Compact mask, optical and resist model that predict
resist profiles after development
Optical Model Compact
Semi-Empirical
Resist Model
mask
i(x,z) ir(x,z)
Resist Profiles
Resist contours
at z for full chip
simulation
z
x
y
CM

14. Sampling Plane Calibration
 Typically only 2D
SEM CD data
available for OPC
model calibration
 Resist model
calibrated at
Incorrect sampling
plane leads to poor
resist profiles

15. Sampling Plane Location?
Your Initials, Presentation Title,
Month Year 15
 For calibration, sampling plane should be where CD is
measured
 CDSEM adds uncertainty to the z location where CD was
measured
Sample Rigorous Resist Model with isolated
lines
In the 4 cases, the calibrated plane agrees
with the actual plane where CDs were
measured
70
50
30
?
70
50
?
10
70
?
30
10
?
50
30
10

16. 3D OPC Model: Resist
Model
 Compact model includes acid neutralization and
diffusion effects*
 Sample compact resist model
 CD obtained by thresholding ’resist’ intensity
 Parameters calibrated to measured CD data
 For improved accuracy, z-dependent resist effects need
to be included
 Example: 3D acid diffusion separated into lateral and vertical
diffusion
𝐶1 𝑖 𝐶𝐷, 𝑧 + 𝐶2 𝑖+𝑏1 ∗ 𝐺σ1 + 𝐶2 𝑖−𝑏2 ∗ 𝐺σ2=T
*Y Granik “Toward Standard OPC Model for OPC” Proc. SPIE 6520
(2007)

17. 3D OPC Model: Resist Model
PEB
 PEB: 3D acid diffusion separated into lateral
and vertical diffusion
ℎ 𝑥, 𝑧, 𝑡 = 𝑓 𝑥, 𝑡 𝑔(𝑧, 𝑡).
𝑑𝑓(𝑥, 𝑡)
𝑑𝑡
= 𝐷ℎ
𝜕2 𝑓(𝑥, 𝑡)
𝜕𝑥2 − 𝑘𝑓 𝑥, 𝑡 𝑞
𝑑𝑔(𝑧, 𝑡)
𝑑𝑡
= 𝐷ℎ
𝜕2
𝑔(𝑧, 𝑡)
𝜕𝑧2
Vertical diffusion incorporated into optical model
𝜕ℎ(𝑥, 𝑧, 𝑡)
𝜕𝑡
= 𝐷ℎ 𝛻2ℎ 𝑥, 𝑧, 𝑡 − 𝑘ℎ 𝑥, 𝑧, 𝑡 𝑞
Lateral diffusion + neutralization
4
ℎ(𝑥, 𝑧, 𝑡 = 0) ≈ 𝑘1 𝑖(𝑥, 𝑧)
Initial acid concentration
linearly related to intensity
𝑖 𝑉𝐷 𝑥, 𝑧, 𝑡 =
𝑘=1
𝑁
λ 𝑘 ϕ 𝑘,𝑉𝐷(𝑥, 𝑧, 𝑡) ⊗ 𝑡3𝐷(𝑥)
2

18. Sample Comparison: SRAF
Printing
18
 Used Rigorous pre-calibrated resist model for PTD resist
 Good overall match to SRAF printing profile

19. 3D OPC Model Challenges
 Improve model accuracy
 NTD resists
 Decrease accuracy of a 3D model vs.
specialized model
 Test patterns and metrology
 CD-SEM doesn’t provide height information
 AFM measurements not typically done for
OPC

20. Summary
 Traditional OPC models are 2D
 Proper calibration of optical parameters
can turn OPC model into 3D
 More accurate for PTD resists
 Additional z-dependent resist effects need to
be included
 Metrology requirements remain
challenging
 Profile data needed to calibrate model
 AFM measurements are expensive