11institutetext: Division of Cancer Sciences, The University of Manchester
11email<EMAIL_ADDRESS>
# A multi-channel cycleGAN for CBCT to CT synthesis

Chelsea A. H. Sargeant  0000-0002-8737-4835 Edward G. A. Henderson
0000-0003-3752-4054 Dónal M. McSweeney  0000-0002-7099-8270 Aaron G. Rankin
0000-0002-0386-1119 Denis Page Authors listed in order of contribution.
0009-0005-9015-180X

###### Abstract

Image synthesis is used to generate synthetic CTs (sCTs) from on-treatment
cone-beam CTs (CBCTs) with a view to improving image quality and enabling
accurate dose computation to facilitate a CBCT-based adaptive radiotherapy
workflow. As this area of research gains momentum, developments in sCT
generation methods are difficult to compare due to the lack of large public
datasets and sizeable variation in training procedure. To compare and assess
the latest advancements in sCT generation, the SynthRAD2023 challenge provides
a public dataset and evaluation framework for both MR and CBCT to sCT
synthesis. Our contribution focuses on the second task, CBCT-to-sCT synthesis.
By leveraging a multi-channel input to emphasize specific image features, our
approach effectively addresses some of the challenges inherent in CBCT
imaging, whilst restoring contrast necessary for accurate visualisation of
patients anatomy. Additionally, we introduce an auxiliary fusion network to
further enhance the fidelity of generated sCT images.

###### Keywords:

synthetic CT multi-channel cycleGAN CBCT quality

##  1 Introduction

In photon and proton radiotherapy, on-treatment cone-beam computed tomography
(CBCT) imaging plays a crucial role in detecting anatomical changes and
ensuring accurate patient positioning for precise treatment setup [7].
However, CBCT image quality often suffers from artefacts such as scatter,
noise and beam hardening, resulting in inferior image quality compared to
planning CT (pCT) scans. These artefacts lead to inaccuracies in Hounsfield
unit (HU) values, rendering CBCT images unsuitable for accurate dose
calculation.

To address these challenges, deep learning-based image synthesis techniques
have been successfully employed to enhance CBCT image quality to a level
comparable to CT scans. This involves using neural networks to discover a
complex mapping between source (CBCT) and target (CT) image domains, enabling
the generation of synthetic CT (sCT) images directly from CBCT data [9]. The
primary objective is to produce sCT images that retain the anatomical
structure of the CBCT scans while closely approximating the HU of the pCT
images to facilitate accurate dose calculation using on-treatment imaging.

Cycle-consistent generative adversarial networks (cycleGANs) have emerged as
the dominant methodology for the conversion of CBCT to CT images for various
anatomical sites [1, 3, 4]. CycleGANs use two generator-discriminator network
pairs, trained concurrently, to allow the model to learn the translation
function from unpaired images [13]. The generative networks are responsible
for converting between the CBCT and CT image domains. One generator produces
CT-like output (a sCT) from CBCT input, while the other performs the reverse
conversion. The discriminators learn to differentiate between real and
synthetic images. Once trained, a single generator is employed for the desired
translation, in this context, the CBCT-to-CT generator.

Our approach is an extension of the 2D cycleGAN architecture originally
proposed by Zhu et al. [13]. The generator architecture has been modified to
incorporate long-range skip connections and self-attention layers to improve
model performance. Crucially, we separate the input CBCT and CT images into
multiple channels, each emphasizing specific image features, and introduce an
auxiliary fusion network to recombine the multi-channel predictions. The
incorporation of multi-channel information and subsequent fusion of these
channels accounts for the diverse variety of input images and contributes to
the enhanced fidelity of generated sCT images. Our method is robust to the
challenges of CBCT imaging. It effectively mitigates the impact of significant
scatter artefacts often encountered in CBCT scans, whilst successfully
restoring contrast necessary for accurate visualisation of the soft tissues
within the patients. This approach enables the generation of high-quality
synthetic CT images from CBCT scans. With these extensions, we aim to produce
sCT images of high enough quality to facilitate accurate dose calculations on
data acquired from on-treatment CBCT imaging.

##  2 Method

###  2.1 Dataset

Imaging data of patients who underwent brain or pelvis radiotherapy were
collected from three Dutch institutions: Radboud University Medical Center,
University Medical Center Utrecht and University Medical Center Groningen for
the SynthRAD2023 challenge. Here, we focused on the second of two tasks, which
involved generating synthetic CTs from CBCTs. The training, validation and
testing cohorts were determined prior to the challenge by the organisers, more
details can be found in Table 1 in Thummerer et al. [11]. A total of 360 CBCT-
CT pairs were available, split evenly across the brain and pelvis.

All pre and post-processing was applied to 3D images, however, individual
axial slices were extracted from all image volumes (CT and CBCT) for training.
A random 80/20 split was used to create train-time training and validation
sets. In our case, two separate site-specific models were trained: one for
brain scans and another for pelvis scans. Training and validation splits for
each site categorised by center name (A, B, C; as in [11]) are shown in Table
1. For image acquisition parameters, see [11].

Table 1: Train-time training and validation splits. Values represent number of axial slices from each center. | Brain |  | Pelvis
---|---|---|---
| A | B | C | Total |  | A | B | C | Total
Training | 10,955 | 8,262 | 10,434 | 29,651 |  | 4,772 | 4,111 | 2,369 | 11,252
Validation | 2,711 | 2,012 | 2,690 | 7,413 |  | 1,194 | 1,056 | 563 | 2,813
Total | 13,666 | 10,274 | 13,124 | 37,064 |  | 5,916 | 5,167 | 2932 | 14,065

###  2.2 Pre-Processing

Preprocessing was performed by the challenge organisers resulting in 3D CT and
CBCT images with corresponding binary masks of the patient. All images of an
anatomical region were resampled to the same voxel spacing: $1\times 1\times
1\text{mm}^{3}$ and $1\times 1\times 2.5\text{mm}^{3}$ for the brain and
pelvis, respectively. A full description of the preprocessing can be found in
[11].

Following the initial preprocessing, images were processed as follows:

  * –

Correction of masks and CBCT image range;

  * –

Overflow correction for pelvis patients;

  * –

Mask application;

  * –

Multi-channel range selection and normalisation;

  * –

Padding/Cropping.

These preprocessing steps were also applied on inference (with the exception
of the mask correction). The challenge dataset was curated to represent the
variation in a realistic multi-centre setting; this included variation in
image protocol, CBCT quality, field-of-view (FOV) and severity of artefacts.
To capture as much information as possible, we opted to include all available
patients in the training set and handle the variability of the dataset with a
multi-channel approach. Below, we present a more detailed description of this
pipeline.

####  2.2.1 Mask and image range correction

All provided images and masks were visually inspected to ensure consistency
across the training cohort. For a large number of pelvis cases, the masks
included large abnormalities resulting in missing regions within patient body
and were deemed unsuitable for training. As a result, the masks were
regenerated using thresholding and binary dilation and morphological closing
functions from SimpleITK. The CBCTs from centre A had to be shifted by $-1024$
HU to ensure the CBCTs from all centres were contained within a consistent
range of $[-1024,3000]$ HU.

####  2.2.2 Overflow correction

Upon visual inspection it was also noticed that CBCTs from $55/60$ pelvis
patients from Centre C suffered from high intensity artefacts on the surface
of the patient that were not seen in the corresponding CT. We believed this to
be due to a numerical overflow error occurring during the CBCT image
reconstruction. This was corrected prior to training by overwriting the
artefact voxels with air (-1024 HU). In detail, a distance transform was used
to create a $\sim 40\text{mm}$ thick hull around the external contour of the
patient to capture high-intensity values (>1000 HU) resulting from the
overflow error. This correction was applied to all pelvis patients since
centre identity was unavailable on testing.

####  2.2.3 Multi-channel input

The CT and CBCT scans were normalised in three separate channels using
windowing to enhance the contrast of structures within the patient. In the
first channel, we use the full width of the image range $[-1024,3000]$ HU. In
channel two, we use a contrast setting used to view soft tissue structures
within the region of interest; for the CT this was $[-150,150]$ HU and
$[-100,100]$ HU for the pelvis and brain, respectively, chosen to be centred
on the water peak. Due to a lack of calibration of the CBCT images, both
within and among centres, an automated peak finder was implemented. For this
we used the $find\\_peaks$ function from the SciPy package. The window width
remained the same; either $\pm 150$ HU and $\pm 100$ HU depending on the image
site, however, the level varied on a patient basis depending on the peak found
within the image intensity histogram as shown in Figure 1. In the final
channel, both the CT and CBCT images were clipped to $[600,3000]$ HU to
capture information about the high-density structures within the patient:
high-density bone and any metal present due to artificial hips, pins, and
dental work, for example. Each channel was then independently scaled to the
range $[0,1]$ using min-max normalisation to improve training stability.
Figure 2 depicts the three-channel input for both the CBCT and CT images
following range selection and min-max normalisation.

Figure 1: CBCT and CT image histogram for a pelvis scan. Below the histogram
shows the ranges of each of the three input channels. Channel one accounts for
the entire image. Channel two captures soft tissue information by centering
the channel on either the water peak in the case of the CT image or on a peak
found on a per-patient basis on the CBCT. In either case a window of $\pm 150$
was used. High-density structures, such as certain bones or artificial metal
implants, were accounted for in the third channel. Figure 2: Three channel
input for the brain and pelvis model. Channel one captures the full image
window, channel two is the soft tissue window and channel three captures high-
density structures such as high-density bone in the brain patient and metal
implants in the pelvis patient displayed. The range is reported in HU, and
each channel is independently normalised to [0, 1].

####  2.2.4 Cropping

The three-channel images were padded or cropped to height and width of
$448\times 448$ voxels for the pelvis and $304\times 304$ voxels for the
brain.

####  2.2.5 Model input

The model input consisted of three-channel CT/CBCT axial slices, paired only
by rigid registration.

###  2.3 Proposed Method

Our method is based on a traditional cycleGAN architecture [13] with some
specific modifications for this challenge. CycleGANs consist of two sets of
competing generator and discriminator networks trained simultaneously to
enable unpaired training. The generators learn to produce CT-like output from
CBCT input (a sCT) and vice versa (synthetic CBCT (sCBCT) output from CT
input). The discriminators learn to classify CT/sCT and CBCT/sCBCT input as
real and fake. Additionally, cycle consistency was enforced by inputting the
synthetic image into the reverse generator to reverse the translation back to
the original image modality.

####  2.3.1 Disciminator network

The discriminator used in our modified cycleGAN was standard and directly
adapted from the PatchGAN [2]. The total loss for the discriminators is

$\mathcal{L}_{D}=\mathcal{L}_{D_{CT}}+\mathcal{L}_{D_{CBCT}}$ (1)

where ${D_{CT}}$ is the discriminator aiming to classify sCT from pCT and
${D_{CBCT}}$ is the discriminator aiming to classify sCBCT from CBCT. The loss
function used was binary cross-entropy.

####  2.3.2 Generator network

The generator architecture used for our cycleGAN was based on the
convolutional neural network detailed by Zhu et al. [13]. This has three
convolutional layers with pooling, followed by nine residual convolutional
blocks and then three resize convolutional layers, described by Odena et al.,
to re-establish the original spatial dimensions [6]. We added UNet-like long-
range skip connections between corresponding down- and up-sampling
convolutional levels to preserve contextual information [8]. Finally, we added
attention gates to the skip connections to emphasize salient features
propagated forward from earlier in the network [10].

The generator receives three-channel input and produces three-channel output.
This is performed for ease of implementation of the cycle consistency aspect,
where the output of each generator is also sent through the reverse generator.

####  2.3.3 Fusion network

An auxiliary fusion network was added onto the cycleGAN to fuse the output
three channels from the CBCT-sCT generator into a single-channel greyscale
image. This final network had identical architecture to the generators but
contained only a single residual block, and short-range residual connections
across all convolutional layers as in Milletari et al. to speed up convergence
[5].

A mean square error loss term was added to train the fusion network to
maximise the similarity between the output single-channel image and the CT.

The total loss for the generators is

$\displaystyle\mathcal{L}_{G}$ $\displaystyle=$
$\displaystyle\mathcal{L}_{G_{\text{GAN-sCT}}}+\mathcal{L}_{G_{\text{GAN-
sCBCT}}}$ $\displaystyle+\alpha(\mathcal{L}_{G_{\text{cycle-
CT}}}+\mathcal{L}_{G_{\text{cycle-CBCT}}})$
$\displaystyle+\beta(\mathcal{L}_{G_{\text{identity-
CT}}}+\mathcal{L}_{G_{\text{identity-CBCT}}})$
$\displaystyle+\mathcal{L}_{G_{\text{fusion-sCT}}}$

where $\alpha=10$ and $\beta=5$. Each generator loss was calculated using the
mean squared error. The $\mathcal{L}_{G_{\text{GAN}}}$ loss terms reward the
generator for deceiving the discriminator. The
$\mathcal{L}_{G_{\text{cycle}}}$ loss terms, or consistency loss, are
performed between CT and sCT (or CBCT and sCBCT) pairs where the synthetic
image has been passed through both generators in a cycle.
$\mathcal{L}_{G_{\text{identity}}}$ are the identity losses which is
calculated between the real images (CT or CBCT) and the same real image after
it has been passed through the opposite generator (CBCT-to-sCT or CT-to-sCBCT
respectively) to enforce an identity constraint.

Figure 3: The cycleGAN architecture is used to convert between CBCT and CT
image domains, with an additional fusion network following CBCT-to-CT
synthesis. Three-channel CBCT and CT images are input into the cycleGAN
generators to produce three-channel synthetic CT (sCT) and CBCT output
(sCBCT). The fusion network is only applied to the sCT images to recombine
channels into a single greyscale sCT.

##  3 Implementation Details

The model was implemented in PyTorch Lightning version 1.5.10 and two networks
were trained independently for each anatomical site. Each model was trained
using a single NVidia GeForce RTX 3090 GPU with 24GB VRAM. The training
protocols used are shown in Table 2.

Table 2: Training protocols.

Data augmentation |  none
---|---
Batch size |  1
Maximum epochs |  200
Optimizer |  Adam
Initial learning rates |  Generator: 0.0001 Discriminator: 0.0002
Learning rate decay schedule |  After 5 epochs, decay to $80\%$ of learning rate every 2 epochs for both generator and discriminator.
Stopping criteria, and optimal model selection criteria |  Early stopping when the total generator validation loss does not improve for 20 epochs. Optimal model is chosen based on best image similarity metrics calculated on train-time validation data
Loss functions |  Mean-squared error on the generators and binary cross-entropy on the discriminators.
Training time |  Brain: $\sim 9$ hours per epoch Pelvis: $\sim 3$ hours per epoch

###  3.1 Post-Processing / Channel Fusion

Upon inference, the trained three-channel CBCT-to-sCT generator network was
applied to preprocessed CBCTs (as described in 2.2) to generate a three-
channel sCT. After a forward pass of the CBCT-to-sCT generator, the three-
channel sCT was input into the fusion network to generate a single-channel
fused sCT.

The padding or cropping performed during preprocessing was reversed to restore
the sCTs to the original CBCT image size. Next, the HU intensity range of each
channel was restored using a linear re-scaling: the fused sCT and channel one
of the three-channel sCT were rescaled to [-1024, 3000] HU; channel two was
re-scaled to [-100, 100] or [-150, 150] HU for the brain and pelvis,
respectively, and channel three was re-scaled to [600, 3000] HU.

Given the three-channel output from our adapted cycleGAN and the single
channel from the fusion bolt-on network, two methods of combining the multi-
channel information were explored in preliminary testing. Initially, the
fusion network output alone was evaluated. Secondly, a post-processing
approach was explored to manually combine the three-channel output into a
single-channel image.

This is performed by inserting the second and third (soft tissue and high-
density) channels into a full window range output. We tested using both the
fused sCT and the first channel sCT from the adapted cycleGAN as the reference
full-width intensity range for this approach.

###  3.2 Checkpoint Selection

To select the best model, the top five epochs were saved during training
according to the total generator validation loss (Eq. 2.3.3).

Independently, the validation data is loaded and image similarity metrics
(listed in section 4) are calculated between all slices of the sCT and
corresponding CT for each checkpoint. The metrics are averaged across the
validation set and ranked according to performance. We select the top-
performing model across image similarity metrics.

##  4 Evaluation

Full details of the evaluation can be found in [12]. Briefly, for the
validation phase, the generated sCTs were assessed according to image
similarity metrics:

  * –

Mean absolute error (MAE)

  * –

Structural similarity index (SSIM)

  * –

Peak signal-to-noise ratio (PSNR)

The image similarity evaluation was complemented with dosimetric analysis for
the test phase. Relative dose difference, dose-volume histogram, and gamma
index were used. The dosimetric evaluation was performed for both photon and
proton treatment plans.

##  5 Results

###  5.1 sCT fusion

In preliminary testing, we evaluated the direct sCT output from the fusion
network. While the direct fused output produced sCTs in a reasonable HU
intensity range, the image quality was fairly poor; the soft tissue contrast
was subpar and the network failed to reproduce regions of air as shown in
Figure 4. As a result, the three channels output by the CBCT-to-CT generator
were recombined manually. However, as the cycleGAN generator and fusion
network were trained end-to-end, we still anticipate that the fusion network
may have been a useful meta-learning task which could have aided the model to
leverage all three channels by learning their true grey-level relations.

For the pelvis patients, we used channel one of the three-channel output of
our model (channel one sCT) as the full range image and reinserted the second
and third channels. For the brain, we used the output from the fusion network
(fused sCT) as our base image.

Figure 4: All available synthetic images; the proposed sCT, fused sCT, and
individual channel sCTs, with input CBCT and ground truth CT. These images
were generated during train-time validation. The first five images are
displayed in HU range [-1024, 3000], while channel three range is [600, 3000]
and the channel two ranges are [-150, 150] and [-100, 100] for the pelvis and
brain, respectively.

###  5.2 Results for challenge validation set

Table 3 and Figure 5 summarise the quantitative results obtained by image
similarity metrics; MAE, PSNR and SSIM. For both anatomical sites, our
proposed methods achieve the highest performance on patients from center C,
with reduced MAE and increased PSNR and SSIM. Whilst all centers suffer from
outliers, our model performs least consistently for patients from center A.

Table 3: Quantitative comparison between the sCTs and ground truth, the pCT. Anatomical Site | MAE (HU) | PSNR (dB) | SSIM
---|---|---|---
Brain (Validation) | $69.70\pm 15.54$ | $29.20\pm 1.77$ | $0.89\pm 0.03$
Pelvis (Validation) | $73.91\pm 15.13$ | $27.69\pm 1.57$ | $0.83\pm 0.03$
Full data set (Validation) | $71.83\pm 15.00$ | $28.44\pm 1.85$ | $0.86\pm 0.05$
Figure 5: Image similarity metrics; mean absolute error (MAE), structural
similarity index measure (SSIM) and peak signal-noise ratio (PSNR) calculated
between ground truth CT and sCTs generated from CBCTs in the validation
dataset.

The sCTs generated by our method are displayed in Figure 6 for a subset of
patients for each anatomical site from the validation dataset alongside the
original CBCT. Visually, the methods preserve the anatomical structure of the
CBCT images and the contrast in soft tissue is enhanced for both pelvis and
brain patients. For the brain, high-quality sCTs are generated despite the
significant decrease in the quality of CBCTs from center B.

Figure 6: CBCT and sCT generated by our methods. Pelvis and brain results are
shown with HU scale of [-400,1200] and [250, 2500], respectively.

Observed on the CBCT for pelvis patient 2PB069 in Figure 6 are significant
artefacts on the axial CBCT slice that have been considerably suppressed by
our method. Whilst we see a large reduction in streaking artefacts, improving
visualisation of internal anatomy, the artefacts appear to have influenced the
sCT body contour. This is also noticed for patient 2PA033.

Our method is also robust to scatter artefacts caused by high-density features
such as metal hip implants. The CBCT and sCT for a pelvis patient with an
artificial hip are shown in Figure 7, demonstrating accurate preservation of
the metal and reduction in streaking in the nearby tissue.

Figure 7: CBCT and sCT generated by our methods for example pelvis patient
with metal implant in the hip. Images are shown with HU scale of [-400,1200]
and [250, 2500], respectively.

###  5.3 Results for challenge test set

Tables 4 and 5 provide a summary of the quantitative results derived from both
image similarity and dose evaluation metrics, calculated on the test set
provided by the challenge organisers. Our methods demonstrate consistent and
commendable performance on this test dataset, showing marginal improvements
across the average image similarity metrics.

Table 4: Quantitative image comparison between the sCTs and ground truth, the pCT, calculated by challenge organisers for test data set. Anatomical Site | MAE (HU) | PSNR (dB) | SSIM
---|---|---|---
Full data set (Test) | $71.58\pm 13.79$ | $28.34\pm 1.50$ | $0.86\pm 0.04$

Our methods demonstrate good accuracy in dose evaluation for photon intensity-
modulated treatment plans, with a gamma index of $98.42\%$ when using a $2\%$
dose-difference criteria with $2mm$ distance-to-agreement criteria. However,
this accuracy is diminished when applied to proton plans. This is expected due
to the heightened sensitivity of proton doses to small anatomical variations.

Table 5: Quantitative dose comparison between the sCTs and ground truth, the pCT, calculated by challenge organisers for the test data set. Plan | DVH | Gamma Index (%) | Dose MAE
---|---|---|---
Photon | $0.07\pm 0.02$ | $98.42\pm 4.95$ | $0.01\pm 0.01$
Proton | $0.27\pm 0.27$ | $92.32\pm 5.87$ | $0.07\pm 0.04$

##  6 Discussion and Conclusion

Our approach demonstrates the successful generation of high-quality synthetic
CT images from CBCT scans. The incorporation of image data at varying
windows/levels within a concatenated multi-channel input has allowed us to
effectively address several challenges inherent in CBCT imaging. We observe
notable improvements in the preservation of fine soft tissue details,
suppression of artefacts such as streaking, and accurate representation of
high-density features within the patient anatomy. Our reported image
similarity metrics on the validation dataset show an average MAE of $71.83\pm
15.00$ HU, PSNR of $28.44\pm 1.85$ dB, and SSIM of $0.86\pm 0.05$. Similarly,
on the test dataset, the average MAE is $71.58\pm 13.79$ HU, PSNR is $28.34\pm
1.50$ dB, and SSIM is $0.86\pm 0.04$. These results indicate a high degree of
similarity to the ground truth images, which are CT scans registered via non-
rigid image registration to the input CBCTs.

Based on current validation metrics, we have observed that sCTs generated from
center C outperform those from both center A and B for both brain and pelvis
patients, despite center C having a reduced number of slices (approximately
half) in the pelvis training set. Specifically, the MAE is $64.51\pm 9.11$ HU
for center C, compared to $82.21\pm 18.71$ HU and $75.19\pm 9.62$ HU for
centers A and B, respectively. This outcome suggests that our model
generalises effectively between centers, and we attribute the discrepancy
partially to the fact that images from center C appear cropped, particularly
in regions where higher errors are observed for other centers - the end
slices. Since these slices lack clinical significance, the performance of
center C is more indicative of our model effectiveness.

We chose to exploit a multi-channel input to capture specific information
about both the CBCT and CT images. The first channel spans the full image
range for simplicity upon training, while the second channel focuses on narrow
window widths to enhance soft tissue contrast. For high-intensity features and
dense bone, the third channel is employed. Our investigations into training
with different channel widths indicate a sensitivity of learned features to
window width, necessitating further research into the optimal window/level for
each channel as well as channel quantity.

Our fusion methods differ between brain and pelvis sites. In the case of brain
images, the fused sCT can be used in the recombination of the three channels.
However, it negatively affects the quality of the sCT images for pelvis
patients. The fusion network architecture is modelled after the generator
network in the cycleGAN. In this setup, the output is compared to a CT image
registered only through rigid image registration. Since pelvis patients’
anatomy can change unpredictably over even short time intervals, the semi-
paired nature of our training could be inappropriate. On the other hand, brain
patients experience fewer such changes, allowing the fusion network to perform
well despite the absence of deformable image registration between the CBCT and
CT images. While cycleGANs are designed to operate in an unsupervised manner
with unpaired data, there is an expectation that incorporating non-rigid image
registration into the training process could lead to an overall performance
improvement. Our future efforts will concentrate on refining the fusion
process, including optimizing the design of the fusion network architecture

CBCT to sCT image synthesis holds the potential to enhance visualization and
improve dose calculations for adaptive radiotherapy [9]. Our method succeeds
in generating high-quality synthetic CT images from on-treatment CBCTs. We
demonstrate that by incorporating multiple window/level inputs and effectively
fusing them, we can enhance the quality of the resulting sCT images and
achieve good dose accuracy.

####  6.0.1 Acknowledgements

The authors of this paper declare that the method implemented for
participation in the SynthRAD2023 challenge has not used any pre-trained
models nor additional datasets other than those provided by the organisers.
This work would not have been possible without the support of the
radiotherapy-related research group in Manchester. The authors would like to
give special thanks to Marcel van Herk, Alan McWilliam, Eliana Vasquez Osorio,
Andrew Green, Robert Chuter and Jane Shortall for their support and guidance.
CS is funded by Elekta AB.

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# Coherent Fourier Scatterometry for detection of killer defects on silicon
carbide samples

Jila Rafighdoost  Optics Research Group, Imaging Physics Department, Faculty
of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628 CJ
Delft, The Netherlands  Dmytro Kolenov  Optics Research Group, Imaging Physics
Department, Faculty of Applied Sciences, Delft University of Technology,
Lorentzweg 1, 2628 CJ Delft, The Netherlands  and Silvania F. Pereira  Optics
Research Group, Imaging Physics Department, Faculty of Applied Sciences, Delft
University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

###### Abstract

It has been a widely growing interest in using silicon carbide (SiC) in high-
power electronic devices. Yet, SiC wafers may contain killer defects that
could reduce fabrication yield and make the device fall into unexpected
failures. To prevent these failures from happening, it is very important to
develop inspection tools that can detect, characterize and locate these
defects in a non-invasive way. Current inspection techniques such as Dark
Field or Bright field microscopy are effectively able to visualize most such
defects; however, there are some scenarios where the inspection becomes
problematic or almost impossible, such as when the defects are too small or
have low contrast or if the defects lie deep into the substrate. Thus, an
alternative method is needed to face these challenges. In this paper, we
demonstrate the application of coherent Fourier scatterometry (CFS) as a
complementary tool in addition to the conventional techniques to overcome
different and problematic scenarios of killer defects inspection on SiC
samples. Scanning electron microscopy (SEM) has been used to assess the same
defects to validate the findings of CFS. Great consistency has been
demonstrated in the comparison between the results obtained with CFS and SEM.

##  1 Introduction

Silicon carbide (SiC) has earned its place in the semiconductor industry and
its applications especially in power electronic devices [1, 2, 3]. SiC-based
devices are mainly known for their high thermal conductivity, a large bandgap,
and also their high break-down electric fields [4]. SiC is transparent, but
its transparency varies with wavelength. This is due to the material’s
electronic structure, with the material being more transparent at longer
wavelengths. At visible wavelengths, the real part of n $\sim$ 2.6 and the
imaginary part is low, indicating low absorption. However, at shorter
wavelengths, the imaginary part increases. As a result, its use has been
rapidly growing in power electronic devices such as aerospace materials,
automotive driving, and high power converters [5, 6, 7]. They can be
considered as the third generation of semiconductor which also happens to show
a better performance compared to silicon (Si) and gallium arsenide (GaAs) as
the first and second generations of semiconductors, respectively [8].Yet, due
to fabrication issues, SiC wafers might still contain a variety of defects
that can put the device’s performance at risk [9, 10, 11, 12, 13, 14, 15].
Defects in such semiconductor wafers can be classified into two categories -
crystallographic defects found within the wafer, and morphological defects
present on or near the wafer surface. The so-called killer defects that can
cause device deterioration are mostly morphological and have been identified
and classified [16, 17, 18, 19, 20].

In order to avoid failures in the fabrication of devices on SiC wafers, defect
inspection plays an important role. In the literature, one finds several high
resolution imaging techniques that are used for inspection such as electron
microscopy (TEM and SEM), atomic force microscopy (AFM), near field microscopy
(SNOM). Although these techniques provide a high resolution mapping of the
location and shape of the defects, there are drawbacks such as low throughput,
invasiveness and they are not easily applicable for in-line inspection [21,
22, 23, 24, 25, 26, 27].

These drawbacks can be avoided if one considers far field optical-based
techniques such as optical coherence tomography (OCT), dark field (DF), bright
Field (BF) or confocal differential interference contrast microscopy
(CDIC)[28, 29, 30, 31, 32]. Among these methods, both BF and DF microscopy
have proven to be the most optimal options, primarily due to their remarkable
speed and cost-effectiveness .Yet there are difficulties in applying them when
it comes to resolve the shape of very small and/or low contrast defects
located on the surface or deeper within the sample. In these scenarios a
complementary approach is needed to deal with the challenging defects.

In this paper, we present a new approach for defect characterization, namely
Coherent Fourier Scatterometry (CFS) [33, 34, 35, 36]. We show that by using
CFS a complete characterization of killer defects such as stacking faults and
polytype inclusions on 4H-SiC wafer can be obtained with high visibility. To
validate and compare CFS with other techniques, the same sample has been
inspected with BF and DF microscopy. Also, SEM was used as a calibration tool
(ground truth). Given that this method is a far field scattering technique
that uses low light power and it is not limited by diffraction, we believe
that it can be considered as a complementary tool to BF and DF microscopy in
scenarios like partially buried defects or isolated defects that are very
small in at least one dimension such as thin lines. In addition, since the
light is focused on the sample, the scattered signal is less affected by
neighboring structures as it is the case of DF microscopy. For defects that
lie deeper into the sample, re-focusing could be used. At last, since most of
the killer defects are of the extended type, inspection is required for each
step of the production. Therefore, the inspection needs to be conducted
throughout the process flow, meaning that an in-line and non-destructive
method is crucial. CFS also fits these needs since it can be made very compact
and easy to be mounted in in-line tools.

##  2 CFS technique and experimental setup

Scatterometry-based techniques utilize the properties of scattered light to
extract information about the object being illuminated. In our implementation,
we use coherent light from a laser source to illuminate the object and observe
the scattered light in the far field. The details of the setup are shown in
Figure 1. A collimated He-Ne laser with a wavelength of $\lambda$ = 632nm
passes through a non-polarising 50-50% beam splitter (BS1). The input light is
linearly polarized in arbitrary direction before it passes through the beam
splitter BS1(hereby we note that the polarization direction has negligible
effect on the detection of the defects). The light then is focused on the
sample plane by a high numerical aperture objective (NA=0.9). In this
approach, the high numerical aperture objective allows us to illuminate the
sample and collect the diffracted field in a large number of angles in one
shot.

The sample is mounted on a 2D piezo-electric stage (Physik Instrumente
P-629.2CD) that is programmed to be moved in the lateral direction in raster
scan mode. The focus position can also be adapted with a 1D piezo-electric
stage (Physik Instrumente P-620.ZCD). Given that the focus depth is very short
($\sim 1\mu$m), one can focus the light onto different depths within the
sample. The reflected and scattered field is captured by the same objective
lens and directed back to BS1. However, due to the small depth of focus,
finding the correct focal plane is challenging. We solved this issue by
allowing the reflected beam from the sample to interfere with a reference beam
by placing temporarily a mirror at the open port of beam splitter BS1(not
shown in Figure 1). In this case, when flat interference fringes are observed
between the two beams, we can ensure that the light is focused on the sample
plane. The reference beam is then removed during the data acquisition. The
back focal plane of the objective is imaged simultaneously into the camera and
the split detector (ODD3W2 Bi-Cell Silicon Photodiode) using the telescope
arrangements formed by lenses L1, L2 and L3. The camera is only used for
general localization of features on the sample. The split detector is a bi-
cell detector, i.e., a detector whose area is divided in two halves, with the
latter being aligned perpendicular to the scan direction of one line of the
raster scan. During the scan, the photocurrents of the two halves of the
detector are subtracted from each other, resulting in a differential photo-
current $I_{-}$ that is recorded for every scan position. After the raster
scan, a 2D mapping with the values of $I_{-}$ for each scan position are
plotted in a 2D graph. In order to interpret the scan maps, one can see that
if there are no defects on the sample, the photo-current $I_{-}$ $\sim$ 0
(given that the scattered signal will correspond to the spurious reflection of
the sample). However, when a defect passes through the focused light beam
while the stage is being scanned, the far field will show asymmetries and will
generate a non-zero $I_{-}$.

Figure 1: The schematic of the CFS setup. The sample is placed on the stage
with a piezo-electric translator, BS1 and BS2: 50-50 non-polarizing
beamsplitters, L1, L2, and L3: positive lenses; Camera: CCD camera used for
localizing features on the sample; SD: split detector (bi-cell silicon
photodiode). A collimated and uniform He-Ne laser is used as the coherent
source. The split detector is aligned perpendicular to the scan direction of
one line of the raster scan.

##  3 Results and Discussion

Most defects are formed through the production process in which they not only
occur on the substrate but are also generated or even modified by other layers
during the wafer planarization process. As a result, the majority of defects
can be classified as extended defects.

Here, we measured defects on a 4H-SiC wafer with four degrees off-cut angle
and 12$\pm$2 $\mu$m thickness that includes four killer defects, three
stacking faults, and one polytype inclusion. As BF and DF microscopy are the
primary methodologies for general surface inspection, we have first obtained
DF and BF images from a Keyence digital microscope (model VHX-6000).
Furthermore, to verify the capabilities of CFS to detect such defects, we
compared the defect shape with SEM images (Novanano, captured at 10 KV with
1000X and some with 800X magnification). In the coming subsections, we show
the results.

It should be noted that besides the observation of the aimed killer defects,
some images show extra particles around the defects. This is due to the fact
that the data has been captured in different labs and over different days.
Unfortunately, the samples tend to accumulate dirt and contaminants from the
environment. To avoid causing any damage to the samples, cleaning procedures
have not been pursued.

###  3.1 Stacking Faults

Extended defects with a planar shape are generally classified into three
different groups named, stacking fault, stacking fault propagated, and
stacking fault complex. Stacking faults usually appear triangular with a
distant outline on the surface of SiC wafers. Propagated stacking faults have
a trapezoidal structure. Our sample did not contain any stacking fault
propagated and therefore we only have results for the stacking fault. Here,
Figure 2(a)-(d) show the BF and DF images, the CFS scattering map and SEM
image, respectively. One can clearly see that although all methods are able to
detect the defect, CFS shows a better visibility with respect to the
background as compared to the other techniques. In addition, when comparing BF
and DF images with CFS, the latter recovers the object even if it is not in
one plane on the substrate but could extend deep into the substrate.

The next detected defect was the Stacking fault complex, which is usually
called carrot. This is also a major morphological defect that has a shape of a
long and thin needle that gradually becomes even thinner at one end of the
line. In Figure 3 we show images of two different carrots obtained with
BF(Figure 3(a) and (c)) and DF images (Figure 3(b) and (d)). In Figure 4 we
compare the detection of the same carrot defects using CFS (Figure 4(a) and
(c)) and SEM (Figure 4(b) and (d)). Similar argument with the previous defect
is also valid here. The thick head and thin tail of the defect is clearly
visible with CFS and not so clear using the other techniques.

To compare the detected signal from the defect and the surrounding background
for both CFS and BF, the visibility was determined in various regions of the
second Stacking Fault shown in Fig. 3(c) (BF) and Fig. 4(c) (CFS) by averaging
the background ($I_{background}$) and taking the intensity of the defect
($I_{signal}$) at various points within the defect. The visibility is obtained
from the expression $V$
=$(I_{defect}-I_{background})/(I_{defect}+I_{background})$. The values around
the thinner tail region of the defect were $V$ = 0.06 for BF and $V$ = 0.8 for
CFS. If one would take the brightest value within the defect (around the the
middle of the defect), the visibility $V$ = 0.35 for BF, while the
corresponding value for CFS was $V\sim$ 1\. The visibilities of the other
defects shown in Fig. 2, 3, and 4 are also in the same order.

Figure 2: (a) and (b) BF and DF images of the stacking fault defect,
respectively. (c) CFS scan map of the stacking fault defect, and (d) SEM image
of the same defect. Figure 3: (a) and (c) BF images of different defects, and
(b) and (d) DF images corresponding to (a) and (c), respectively. Figure 4:
(a)(c) and (b)(d) represent the CFS scan map (left colunm) and the SEM images
(right colunm) of these defects. Figure 5: (a) is a BF image of the defect
while (b) and (c) are also DF images of the same defects. (c) is saturated in
order to see the entire defect.

###  3.2 Polytype inclusion

Polytype inclusion defects are another type of morphological defect that
appear as triangular with long and thin arms with a big spherical particle
called downfall located at the apex of the triangle. Polytype inclusion could
be formed by dropping a foreign material during the process of epitaxial
growth on the SiC epilayer.

Figure 5(a) shows the BF image of a polytype inclusion, while Figure (b) and
(c) are both DF images with different powers. Figure 5(c) is saturated in
order to reveal parts of the defect that are buried. Figure 6(a) shows the
scattering CFS map and Figure 6(b) and (c) the SEM image of the same defect.
The two SEM images are obtained at 10 and 30 KV, respectively to also
highlight different parts of the defect. By comparing these images, one can
see that with CFS, the triangle next to the big spherical defect is clearly
revealed (see also the inset of Figure 6(a)) while all other techniques (BF,
DF and SEM) fail to image it properly. We believe that this is due to two
reasons: first, the contrast was too low, and second, the triangle is in a
different depth than the downfall. This is one scenario where both optical
microscopy and SEM would fail to have a comprehensive inspection due to the
low penetration depth and/or low contrast. Therefore, when it comes to very
narrow and features that lie partially outside the sample plane, CFS can
outperform the conventional methods and become a complementary tool to them.
The comparison between the results of all techniques indeed shows good
consistency and demonstrates CFS’s capability in visualizing and locating
killer defects.

Figure 6: (a) CFS scan map, (b) and (c) are SEM images of the same defect with
10 and 30 KV, respectively. In the inset in 6(a) we highlight the parts of the
defect that is not clearly observed with other techniques.

##  4 Conclusion

In this paper, we demonstrate CFS as an inspection technique for defect
detection on SiC wafers that could be considered as a complementary tool to
optical microscopy. It offers some advantages including its superior
visibility with respect to the background and its ability to detect defects
within the substrate.

We present a proof-of-principle experiment of the technique at one wavelength
(635 nm) and one numerical aperture (NA=0.9) but other wavelengths or NAs
could be used as well. Shorter wavelengths/high NA are ideal for studying
smaller defects, while longer wavelengths could be used to look deeper in to
the sample due to longer penetration depth. Even though CFS is not an imaging
technique, we have shown that it is perfectly able to determine the shape and
other details of killer defects on SiC wafers. The results shown here were
verified by SEM and even though the defects are visible using all techniques,
CFS scattering maps provide very high visibility thanks to the differential
detection scheme that highlights asymmetries of the scattered field due to the
presence of the defect interacting the light beam. Furthermore, since CFS
collects the scattering from different depths within the focal depth at once,
it allows us to detect parts of the defect that are extended and formed in
different layers in a much better way than the SEM. The major drawback so far
of CFS is that it is scanning technique and it is relatively slow compared to
DF or BF. In the work we show here, the scanning was performed with piezo-
electric translator and it takes a couple of minutes to obtain an entire scan
map. Thus in order to make this technique applicable for large area
inspection, further developments are needed towards fast scan combined with
parallel probes techniques such as parallel optical data storage or real time
confocal microscopy.

## Funding

This work is financed by the Project 20IND09 “PowerElec” within the program
EMPIR. The project is jointly supported by the European Commission and the
participating countries within the European Association of National Metrology
Institutes (EURAMET).

## Acknowledgements

We acknowledge AIXTRON for providing high quality state-of-the-art samples
that have been used for these measurements and for fruitful discussions on
different types of defects on SiC wafers.

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