Optimizing critical dimension uniformity utilizing a resist bake plate simulator
View Patent ↗A system for optimizing critical dimension uniformity in semiconductor manufacturing processes is provided. The system comprises a bake plate simulator to model a physical bake plate. A finite element analysis engine uses information from the bake plate simulator to calculate missing information. A lithography simulator predicts outcomes of a lithography process using information from the bake plate simulator and the finite element analysis engine. The system can be used in a predictive capacity or as part of a process control system.
1. A system for optimizing critical dimension uniformity in semiconductor manufacturing processes, comprising:
a bake plate simulator that includes a thermal model of a bake plate;
a finite element analysis engine that accesses data from the thermal model and calculates a heat diffusion equation wherein the heat diffusion equation differentiates temperature with respect to at least two spatial coordinates of a zone; and
a lithography simulator that uses calculation results from the finite element analysis engine to derive predicted results of a lithographic process.
2. The system of claim 1 , wherein the thermal model is a model of a multi-zone bake plate.
3. The system of claim 2 , wherein the heat diffusion equation is a two-dimensional steady state heat diffusion equation.
4. The system of claim 3 , wherein the heat diffusion equation is:
∂
∂
x
(
k
∂
T
∂
x
)
+
∂
∂
y
(
k
∂
T
∂
y
)
+
S
i
-
h
i
(
T
-
T
a
)
=
0
where k is thermal conductivity, T is temperature, S i is heating power of an i th zone of a plurality of zones, h i is an effective convection coefficient of the i th zone, and T a is the ambient temperature.
5. The system of claim 1 , further comprising a controller that adjusts a lithography process based at least in part upon predicted results from the lithography simulator.
6. The system of claim 5 , further comprising a graphical user interface that accepts user input for system components.
7. The system of claim 6 , wherein the graphical user interface includes graphical representations of critical dimension information.
8. The system of claim 7 , wherein the graphical user interface includes contour map representations and altitude map representations of temperature information in graphical depictions.
9. The system of claim 6 , wherein the graphical user interface includes contour map representations and altitude map representations of temperature information in graphical depictions.
10. A system for optimizing critical dimension uniformity in semiconductor manufacturing processes, comprising:
a module configured to accept user input in the form of bake plate settings;
a memory containing critical dimension metrology data and post-exposure bake temperature data therein; and
a simulation engine that uses a bake plate simulator, a finite element analysis that calculates a heat diffusion equation wherein the heat diffusion equation differentiates temperature with respect to at least two spatial coordinates of a zone, and a lithography simulator to calculate a post-exposure temperature distribution and a critical dimension distribution.
11. The system of claim 10 , wherein the lithography simulator is a data library.
12. The system of claim 11 , wherein the data library is a data storeselected from the group consisting of a relational database, an object-oriented database, a data definition file, an extensible markup language file, and a text file.
13. The system of claim 10 , wherein the finite element analysis engine calculates a solution for a two-dimensional heat diffusion equation.
14. The system of claim 13 , wherein the two-dimensional heat diffusion equation is:
∂
∂
x
(
k
∂
T
∂
x
)
+
∂
∂
y
(
k
∂
T
∂
y
)
+
S
i
-
h
i
(
T
-
T
a
)
=
0
where k is thermal conductivity, T is temperature, S i is heating power of an i th zone of a plurality of zones, h i is an effective convection coefficient of the i th zone, and T a is the ambient temperature.
15. The system of claim 10 , further comprising a tuning module for adjusting parameters of the bake plate simulator.
16. A method for predicting post-exposure bake results in a semiconductor manufacturing process, comprising:
simulating parameters of a bake plate;
using the simulated parameters to calculate missing parameters in a heat diffusion equation wherein the heat diffusion equation differentiates temperature with respect to at least two spatial coordinates of a zone; and
using the simulated parameters and calculated parameters to predict a resulting critical dimension distribution.
17. The method of claim 16 , further comprising:
calibrating simulated parameters based upon bake plate measurements.
18. The method of claim 17 , further comprising:
using the critical dimension distribution to calculate a post-exposure bake temperature distribution.
19. The method of claim 18 , further comprising:
using the post-exposure bake temperature distribution to adjust bake plate settings.
20. The method of claim 16 , further comprising:
creating a graphical representation of the critical dimension distribution.
21. A system for predicting post-exposure bake results in a semiconductor manufacturing process, comprising:
means for simulating parameters of a bake plate;
means for using the simulated parameters to calculate missing parameters in a heat diffusion equation wherein the heat diffusion equation differentiates temperature with respect to at least two spatial coordinates of a zone; and
means for using the simulated parameters and calculated parameters, to predict a resulting critical dimension distribution.
22. The system of claim 21 , further comprising:
means for calibrating simulated parameters based upon bake plate measurements.
23. The system of claim 22 , further comprising:
means for using the critical dimension distribution to calculate a post-exposure bake temperature distribution.
24. The system of claim 23 , further comprising:
means for using the post-exposure bake temperature distribution to adjust bake plate settings.
25. The system of claim 21 , further comprising:
means for creating a graphical representation of the critical dimension distribution.