Electron Beam Lithography Contrast Calculator

Enter dose, thickness, beam current, and threshold values. Review gamma, latitude, slope, and exposure time. Export clear results with charts, tables, and formulas quickly.

Contrast Calculator Inputs

nm
µC/cm²
µC/cm²
%
%
µC/cm²
nA
mm²
%
% of midpoint

Dose Response Plot

This graph shows the modeled resist thickness transition between the lower and upper threshold doses.

Formula Used

Main contrast formula

γ = 1 / log10(Dhigh / Dlow)

Dhigh is the upper clearing or transition dose. Dlow is the lower transition dose. A smaller dose ratio gives a larger gamma value.

Process latitude

Latitude % = ((Dhigh - Dlow) / Dmid) × 100

Dmid is the average of the upper and lower doses. This value estimates the practical dose window width.

Thickness response slope

Slope = |T_high - T_low| / log10(Dhigh / Dlow)

The calculator reports normalized slope and thickness slope in nanometers per dose decade.

Exposure time

Time = Dose × Area / Current

The area is converted from mm² to cm². Current is converted from nA to microcoulombs per second.

How to Use This Calculator

  1. Enter the lower transition dose from your dose matrix.
  2. Enter the upper clearing or full transition dose.
  3. Add the initial resist thickness and measured remaining thickness values.
  4. Enter the target dose, beam current, and written field area.
  5. Set a minimum acceptable contrast for process screening.
  6. Press the calculate button to show results above the form.
  7. Use the graph to review the modeled transition curve.
  8. Download the CSV or PDF file for lab records.

Example Data Table

Resist Thickness Dlow Dhigh Dose ratio Approx gamma Use case
PMMA sample 100 nm 180 µC/cm² 320 µC/cm² 1.78 4.00 Positive tone calibration
ZEP sample 150 nm 90 µC/cm² 145 µC/cm² 1.61 4.82 Fast process screen
HSQ sample 80 nm 650 µC/cm² 1050 µC/cm² 1.62 4.80 Negative tone patterning
CAR sample 60 nm 35 µC/cm² 70 µC/cm² 2.00 3.32 Chemically amplified resist

Understanding Contrast in Electron Beam Lithography

Why Contrast Matters

Electron beam lithography needs careful dose control. A small change in dose can change the final line width. Contrast describes how sharply a resist changes from insoluble to soluble, or from soluble to insoluble. A higher value means a steeper transition. That usually gives cleaner edges and a wider process choice.

How This Tool Works

This calculator uses two threshold doses. The lower dose marks the start of the transition. The upper dose marks the clearing or full crosslink point. Their ratio gives the main contrast value. The tool also checks process latitude, thickness slope, exposure time, and dose margin. These extra numbers help compare recipes before a wafer run.

Positive and Negative Resists

For positive resist, remaining thickness falls as dose rises. For negative resist, remaining thickness rises as dose rises. The same logarithmic dose method still works. The chart displays the expected transition across the dose range. It is a model, not a replacement for measured contrast curves.

Input Quality

Good input data matters. Use doses measured from a real dose matrix. Keep development time, developer strength, bake settings, beam energy, and substrate conditions fixed. Then compare only one variable at a time. This improves repeatability. It also makes the calculated gamma more useful.

Reading the Result

A low contrast result suggests a shallow process response. You may need a better bake, a fresher developer, a different resist thickness, or a smaller dose step. A very high result can look attractive, but it may also demand tight dose control. Check the exposure tool stability before using it.

Planning Exposure Time

The exposure time estimate uses dose, area, and beam current. It helps plan writing time for test fields. The result ignores stage moves, blanker delays, and proximity correction overhead. Use it as a quick planning value. Confirm final throughput with the tool software.

Record Keeping

Use the CSV export for lab notes. Use the PDF export for recipe reviews. Save the graph with your dose matrix results. Over time, these records reveal trends in resist age, developer strength, and beam setup.

Repeatable Process Notes

Always label every sample. Record beam energy and aperture size. Note the measurement method for thickness. These details explain changes that a single contrast number cannot show. They also help another operator repeat the process.

FAQs

What is contrast in electron beam lithography?

Contrast is the sharpness of the resist response against exposure dose. A higher value means the resist changes more quickly over a smaller dose range.

Which doses should I enter?

Enter the lower transition dose and the upper clearing or full transition dose from a measured dose matrix. Keep process conditions fixed.

Can I use this for positive resist?

Yes. Use a high remaining thickness at the lower dose and a low remaining thickness at the upper dose for positive resist behavior.

Can I use this for negative resist?

Yes. For negative resist, remaining thickness usually increases with dose. Enter thickness percentages that match your measured curve.

Why is logarithmic dose used?

Resist contrast is commonly compared over dose decades. The logarithmic ratio makes recipes with different absolute dose levels easier to compare.

What does process latitude mean?

Process latitude estimates the usable dose window between the lower and upper thresholds. Larger latitude can make exposure control easier.

Is the exposure time exact?

No. It estimates writing time from dose, area, and beam current. It does not include stage movement, overhead, or correction delays.

Why should I export the results?

Exports help preserve calibration records. They make it easier to compare resist lots, development conditions, and beam settings later.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.