Working with sidewall angles¶

Introduction¶

This notebook uses PreFab to predict and correct the fabrication result of a 400 nm-wide ring nanostructure on a silicon nitride (SiN) e-beam lithography process that has angled sidewalls. This tutorial is structured as follows:

1. Preparing a test device for prediction
2. Executing a prediction
3. Analyzing the prediction and uncertainty
4. Correcting the device and discussion of sidewall angles

To begin, we need to import the necessary libraries:

In [1]:

import matplotlib.pyplot as plt
import prefab as pf

import matplotlib.pyplot as plt import prefab as pf

Loading a device¶

In this tutorial, we'll use a small ring structure, but feel free to explore other structures available in the shapes.py module, or load your own from a GDS file.

In [34]:

device = pf.shapes.ring(width=400, border_width=100)
device.plot(show_buffer=False)

device = pf.shapes.ring(width=400, border_width=100) device.plot(show_buffer=False)

Out[34]:

<Axes: xlabel='x (nm)', ylabel='y (nm)'>

Predicting a device¶

The prediction process is similar to previous notebook examples, but we'll use a model trained on SiN structures with angled sidewalls. This model outputs three segments: core (yellow), sidewall of the core (green), and cladding (purple), unlike the previous examples' models which had only core and cladding (indicating a vertical sidewall).

Note: Initial prediction/correction may take longer due to server startup and model loading. Subsequent predictions should be quicker.

In [35]:

MODEL_NAME = "ANT_SiN_ANF1_d1"
prediction = device.predict(model=pf.models[MODEL_NAME])
prediction_bin = prediction.binarize()

prediction.plot(show_buffer=False)
prediction_bin.plot(show_buffer=False)

MODEL_NAME = "ANT_SiN_ANF1_d1" prediction = device.predict(model=pf.models[MODEL_NAME]) prediction_bin = prediction.binarize() prediction.plot(show_buffer=False) prediction_bin.plot(show_buffer=False)

Prediction: 100%|██████████████████████████████| 100/100 [00:06<00:00, 16.13%/s]

Out[35]:

<Axes: xlabel='x (nm)', ylabel='y (nm)'>

The model outputs an NxMx2 array, where the third dimension represents the top and bottom edges of the structure. We can visualize these edges separately using the level parameter.

In [13]:

prediction.plot(level=0, show_buffer=False)
prediction.plot(level=1, show_buffer=False)

prediction.plot(level=0, show_buffer=False) prediction.plot(level=1, show_buffer=False)

Out[13]:

<Axes: xlabel='x (nm)', ylabel='y (nm)'>

Analyzing a prediction¶

We can overlay the contour of the nominal device on the prediction to visualize the differences between the nominal and predicted geometries. This comparison reveals significant erosion at the top level or edge, and shows that the outer sidewall is wider than the inner sidewall, indicating a non-uniform, feature-dependent sidewall angle.

In [36]:

fig, ax = plt.subplots(1, 1, figsize=(10, 5))
prediction_bin.plot(show_buffer=False, ax=ax)
device.plot_contour(show_buffer=False, ax=ax)
plt.show()

fig, ax = plt.subplots(1, 1, figsize=(10, 5)) prediction_bin.plot(show_buffer=False, ax=ax) device.plot_contour(show_buffer=False, ax=ax) plt.show()

Likewise, each edge carries its own level of uncertainty. We are still investigating the relationship between edge uncertainty and sidewall angle, and how they vary from device to device and fabrication run to run. The less these uncertainties overlap with the optical signal, the more robust the device will be to fabrication variations.

In [37]:

prediction.plot_uncertainty(show_buffer=False)

prediction.plot_uncertainty(show_buffer=False)

Out[37]:

<Axes: xlabel='x (nm)', ylabel='y (nm)'>