View source for Lithography Calibration - Analyzing a Focus-Exposure Matrix

On tools that have motorized autofocus (steppers & direct-write litho tools), you often need to analyze both the Focus Offset & Exposure Dose simultaneously.  (Remember that "Focus Offset" is an offset from the autofocus' "zero" position of the wafer surface.) These tools will have a function for shooting a "Focus Exposure Matrix/Array", or "FEM/FEA", which exposes a grid with Dose varying in one direction, and Focus varying in another, for example:
{| class="wikitable"
!
! colspan="6" |Dose →
|-
! rowspan="6" |'''Focus ↓'''
!
!11mJ
!12mJ
!13mJ
!14mJ
!15mJ
|-
!-0.2µm
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|-
!-0.1µm
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|-
!0
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!+0.1µm
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!+0.2µm
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==== General process: ====

# Run a "Coarse" (wide-range) Focus-Exposure Matrix using the "starting params" from the wiki for your PR/tool.
## "Coarse" Dose typically means ~10% of a "nominal" dose - starter Doses can be found on the Litho Recipes pages for the tool and resist you are using.
# Analyze (microscope or SEM) to find the edges of the [https://en.wikipedia.org/wiki/Process_window '''process window'''] in both Focus & Dose. This can often be done somewhat fast by eye and optical microscope, without detailed measurements, allowing you to locate the center of the process window based on the rows/cols that are obviously "Bad".
## Tip: If possible, mark up your wafer with sharpie, scribes or other marks to make the grid easier to analyze, especially to avoid getting "lost" on the SEM/microscope.
# Run a "Fine" FEM with finer step size.
## On the ASML, you can now keep the Focus constant according to the central Focus value from your Coarse FEM, and do only an Energy serpentine.
# Analyze to measure actual feature size, according to your process tolerance.

==== Process Window ====
You need to find the '''center of the ''Viable [https://en.wikipedia.org/wiki/Process_window Process Window]''''' - meaning you need to see the BAD dose (too high + too low) and BAD focus (too high + too low) then choose a Dose+Focus in the ''middle'' of this range. This allows your process to work even if the focus or some other process varies.

A '''common mistake is to look for "''the best die''"''' - but this die could be (and often is) at the edge of the working process window, so a small process variation (wafer thickness, hotplate temperature) will put your process outside the process window - you'll have chosen a very tight process that easily goes out of spec with random fluctuation in the process.

==== Tolerance ====
You'll need to decide what "good enough" looks like on your feature inspection - this is your process '''''tolerance'''''. In physical manufacturing you simply can never achieve "perfect" features, with 6 decimals points of precision - or you will spend a lot of time and money trying to do so.

For example instead of looking for "''the feature that is exactly 300nm wide''", you may want to look for Dose/Focus where "''the feature is between 250-350nm, or 300nm±50nm''". Thus your process has a viable tolerance to normal fabrication variations. You may want to run simulations or other estimates for what the tolerance may be.

==== Example FEMs ====
An ideal FEM would look like this, for example for a Photoresist process where the "nominal" process from our Litho Recipes pages shows 15mJ dose & +0.1µm focus.

'''√''': process within tolerance, eg. linewidth is 200nm ± 50nm

'''X''': out of tolerance, or entirely failed (no feature)
{| class="wikitable"
!
! colspan="8" |→ Dose →
!
|-
! rowspan="8" |↓
'''Focus'''

'''↓'''
!
!11mJ
!12mJ
!13mJ
!14mJ
!15mJ
!16mJ
!17mJ
!18mJ
|-
!-0.2µm
|X
|X
|X
|X
|X
|X
|X
|X
|-
!-0.1µm
|X
|X
|X
|√
|X
|X
|X
|X
|-
!0
|X
|X
|√
|√
|√
|√
|X
|X
|-
!+0.1µm
|X
|√
|√
|√
|√
|√
|X
|X
|-
!+0.2µm
|X
|√
|√
|√
|√
|√
|X
|X
|-
!+0.3µm
|X
|X
|√
|√
|√
|X
|X
|X
|-
!+0.4µm
|X
|X
|X
|X
|X
|X
|X
|X
|}
(Yes, this takes some time on a microscope and/or SEM to analyze!)

Now if we highlight the "good" region, we can identify the Process Window:
{| class="wikitable"
!
! colspan="8" |→ Dose →
!
|-
! rowspan="8" |↓
'''Focus'''

'''↓'''
!
!11mJ
!12mJ
!13mJ
!14mJ
!15mJ
!16mJ
!17mJ
!18mJ
|-
!-0.2µm
|
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|-
!-0.1µm
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|√
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|-
!0
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|√
|√
|√
|√
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|-
!+0.1µm
|
|√
|√
|√
|√
|√
|
|
|-
!+0.2µm
|
|√
|√
|√
|√
|√
|
|
|-
!+0.3µm
|
|
|√
|√
|√
|
|
|
|-
!+0.4µm
|
|
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|
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|}
This shows that the middle of the Process Window should be at approx.:

* Dose = 14mJ
* Focus Offset = +0.15µm

And the process tolerance is:

* Dose ±2mJ
* Focus Offset ± 0.15µm

Hopefully the litho tool you are using can control better than ±2mJ and ±0.15µm focus!  Different litho tools may have different random variation in these parameters.  Your photoresist thickness, spin repeatability, and substrate flatness (causing focus variations) will all contribute to litho fluctuations.

The wider the process tolerance, the less we have to rework or calibrate the process, so the faster we can finish our lithography!
[[File:FEM example analysis GMoody Group 2024-11-04 v2.png|alt=screenshot of tabulated good/bad die|none|thumb|415x415px|Example analysis of a focus-exposure matrix for 200nm wide isolated lines (waveguides), on the ASML Stepper. The middle of the process window is '''Dose=15mJ, Defocus=–0.05µm''', indicated with an X.

Image Credit: Xuefeng Li, Joshua Castro, Lillian Thiel, Max Meunier, [https://qpl.ece.ucsb.edu/members/galan-moody Prof. Galan Moody]]]

==== FEM Problems ====
A common problem with a coarse FEM is to miss the process window - if you don't see the "BAD" die on all sides, then you never know whether you are in the center.  This might be acceptable if you know the litho tool/process is tolerant enough (eg. very large feature sizes), but if you have a finite process window (eg. small feature sizes), then this could be an issue.
{| class="wikitable"
!
! colspan="8" |→ Dose →
!
|-
! rowspan="8" |↓
'''Focus'''

'''↓'''
!
!11mJ
!12mJ
!13mJ
!14mJ
!15mJ
!16mJ
!17mJ
!18mJ
|-
!-0.2µm
|
|
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|-
!-0.1µm
|
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|-
!0
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|-
!+0.1µm
|
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|-
!+0.2µm
|
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|√
|√
|√
|
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|-
!+0.3µm
|
|√
|√
|√
|√
|√
|
|
|-
!+0.4µm
|
|
|√
|√
|√
|√
|
|
|}
If your process window is small compared to the variation, then you need to go back and shoot another coarse FEM, for example higher Focus = +0.4µm → +0.8µm and same Dose range as before.

Another issue is to see an non-contiguous FEM, like so:
{| class="wikitable"
!
! colspan="8" |→ Dose →
!
|-
! rowspan="8" |↓
'''Focus'''

'''↓'''
!
!11mJ
!12mJ
!13mJ
!14mJ
!15mJ
!16mJ
!17mJ
!18mJ
|-
!-0.2µm
|
|
|
|
|
|
|
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|-
!-0.1µm
|
|
|
|
|
|
|
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|-
!0
|
|
|√
|
|
|√
|√
|
|-
!+0.1µm
|
|
|√
|
|
|√
|√
|
|-
!+0.2µm
|
|
|√
|√
|
|√
|√
|
|-
!+0.3µm
|
|√
|√
|√
|
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|-
!+0.4µm
|
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|√
|√
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|}
This may be due to a location-dependent variation.  For example, the wafer surface has large-area bumps (eg. delaminating thin-films), or particles on the back of the wafer during exposure, either of which cause the topside focus-level to change depending on wafer location, or major defects in the photoresist spin (streaks etc).

The above FEM might actually have a very wide process window, but the center of the wafer had a defect causing bad resolution.
 ''Written by [[Demis D. John]], 2024-10-22''