# A Two-Stage Adverse Weather Semantic Segmentation Method for WeatherProof
Challenge CVPR 2024 Workshop UG${}^{\textbf{2}}$+

Jianzhao Wang, Yanyan Wei, Dehua Hu, Yilin Zhang, Shengeng Tang, Dan Guo, Zhao
Zhang
Hefei University of Technology
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
eslzzyl@mail.hfut.edu.cn,{tangsg<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

This technical report presents our team’s solution for the WeatherProof
Dataset Challenge: Semantic Segmentation in Adverse Weather at CVPR’24 UG2+.
We propose a two-stage deep learning framework for this task. In the first
stage, we preprocess the provided dataset by concatenating images into video
sequences. Subsequently, we leverage a low-rank video deraining method to
generate high-fidelity pseudo ground truths. These pseudo ground truths offer
superior alignment compared to the original ground truths, facilitating model
convergence during training. In the second stage, we employ the InternImage
network to train for the semantic segmentation task using the generated pseudo
ground truths. Notably, our meticulously designed framework demonstrates
robustness to degraded data captured under adverse weather conditions. In the
challenge, our solution achieved a competitive score of 0.43 on the Mean
Intersection over Union (mIoU) metric, securing a respectable rank of 4th.

##  1 Introduction

Semantic segmentation, the process of assigning a distinct class label to each
pixel within an image, encounters substantial impediments when confronted with
adverse weather conditions such as rain and fog. The WeatherProof Dataset
Challenge: Semantic Segmentation in Adverse Weather (CVPR’24 UG2+) serves as a
platform for assessing the resilience of semantic segmentation techniques
under these conditions.

This challenge mandates the development of an efficient solution for
performing semantic segmentation on a diverse collection of real-world image
sequences captured under rainy and foggy conditions. The provided sequences
exhibit variations in rain intensity, fog density, and scene complexity,
necessitating a robust algorithm capable of accurately segmenting objects
while maintaining structural and contextual information.

To tackle this challenge, we propose a two-stage framework. The initial stage
leverages a low-rank video deraining method[1] to generate high-fidelity
pseudo ground truth images. This method accomplishes this by removing rain
streaks and restoring image structures from the aligned rainy frames.
Subsequently, the second stage employs a pre-trained InternImage network[2], a
Convolutional Neural Network (CNN) based semantic segmentation architecture,
fine-tuned on the aforementioned pseudo ground truth images.

This report furnishes a comprehensive overview of our proposed methodology,
encompassing data analysis, intricate details of the framework, and the
outcomes of our experimentation.

The remaining sections cover our method (Section 2) and Experimental settings
(Section 3).

##  2 Overview of Methods

Inspired by previous works that employed a two-stage approach in image
deraining tasks[3], we have also designed a two-stage framework to address the
semantic segmentation challenge in the WeatherProof dataset[4], aiming to
mitigate the impact of adverse weather conditions on image quality.

In the first stage, we combined the 300 images from the test set published in
the final testing phase of the competition into a video sequence.
Subsequently, we applied the Low-Rank Tensor Recovery (LLRT)[1] algorithm for
video deraining preprocessing of this sequence, utilizing information from
multi-frame aligned images to generate high-quality pseudo ground truth
images.

In the second stage, we utilized the CNN-based InternImage[2] semantic
segmentation network. We trained the InternImage solely with the training and
validation set data provided by the competition, without any additional
preprocessing of the training data. Finally, we input the pseudo ground truth
images generated in the first stage into the well-trained InternImage to
obtain the final semantic segmentation predictions.

Through this two-stage strategy, we were able to fully leverage the advantages
of the video deraining algorithm to eliminate the impact of adverse weather
conditions (such as rain and fog) on image quality during the testing phase,
laying the foundation for subsequent semantic segmentation tasks. At the same
time, the CNN semantic segmentation network can learn effective feature
representations on ample training data, achieving precise pixel-level
classification. This framework integrates the strengths of video deraining and
single image semantic segmentation, making it an efficient solution.

The following Section 2.1 and Section 2.2 will respectively introduce the
specific details of the LLRT video deraining algorithm and the InternImage
semantic segmentation network that we used.

###  2.1 Low-Rank Tensor Recovery

Video deraining is a highly challenging task that requires the simultaneous
use of both temporal and spatial dimensions of information. The Low-Rank
Tensor Recovery (LLRT) algorithm proposed by Chang et al.[1] for multi-
spectral image denoising tasks can effectively capture the inherent structural
correlations within an image sequence and is therefore also applicable to
video deraining preprocessing.

The core of the LLRT algorithm is a unidirectional low-rank tensor recovery
model. It constructs a third-order tensor to jointly model spatial local
sparsity, non-local self-similarity, and spectral correlation. Unlike other
works that simply sum the low-rank properties of each mode, LLRT, through
detailed analysis, finds that the low-rank nature corresponding to non-local
self-similarity is far superior to spatial and spectral modes. Based on this
finding, LLRT imposes low-rank constraints only on the non-local self-
similarity mode, more reasonably describing the intrinsic structure of the
data.

In implementation, the authors designed an efficient optimization algorithm
that can quickly solve the sub-problems of unidirectional low-rank tensor
recovery and spectral gradient sparsification. With all these innovations, the
LLRT algorithm has achieved excellent performance in multi-spectral image
denoising.

In this work, we treat the 300 images of the test set as a video sequence and
apply the LLRT algorithm for deraining preprocessing. By leveraging redundant
information in both temporal and spatial dimensions, LLRT can effectively
remove the effects caused by adverse weather conditions, generating high-
quality pseudo ground truth images for subsequent semantic segmentation tasks.

###  2.2 CNN-based method: InternImage

The InternImage[2] semantic segmentation network is a cutting-edge deep
learning model that has demonstrated remarkable performance in the field of
computer vision, particularly in the context of the COCO dataset where it
achieved an impressive 65.4 mAP, leading the state-of-the-art benchmarks. The
model’s success has been recognized and it has been highlighted as a CVPR 2023
highlight paper, ranking in the top 2.5% of submissions.

InternImage is distinguished by its innovative approach to large-scale vision
foundation models, incorporating deformable convolutions to adapt to various
image distortions and irregularities. This feature is particularly useful in
semantic segmentation tasks where the model must accurately identify and
classify different objects within an image, often under challenging conditions
such as adverse weather.

In our application of InternImage to the WeatherProof dataset[4], we have
fine-tuned the model using the provided training and validation datasets. The
pseudo ground truth images generated from the LLRT video deraining
preprocessing serve as input to the InternImage network, enabling it to
produce highly accurate semantic segmentation predictions. The integration of
InternImage into our two-stage framework has been instrumental in enhancing
the overall performance of our system, capitalizing on the strengths of both
video deraining and CNN-based semantic segmentation.

##  3 Experimental settings

Dataset. In our experiments, we utilized the training and validation sets
provided by the official WeatherProof dataset for training our model.
Additionally, the InternImage model was initialized with weights pre-trained
on the ImageNet dataset, providing a solid foundation for feature extraction
and accelerating convergence on the specific task. After training, the model
was applied to the test set that had been preprocessed by the video deraining
algorithm. This step leveraged temporal information from the video sequence to
mitigate the effects of adverse weather conditions, such as rain and fog,
generating high-quality pseudo ground truth images. These pseudo ground truth
images served as the final reference labels for assessing the model’s semantic
segmentation performance under actual adverse weather conditions.

Training setting. We fine-tuned the InternImage-H semantic segmentation model
on the official WeatherProof training and validation datasets without any
additional preprocessing of the training data. For the fine-tuning, we
utilized pre-trained weights from ImageNet and scaled the original images to
an input resolution of 1024×256 pixels, followed by random cropping to 256×256
pixel patches. Data preprocessing involved random flipping, color distortion,
and other augmentation techniques, along with normalization using the mean
values [103.336, 104.443, 100.035] and standard deviations [39.329, 38.147,
42.803]. The optimizer was AdamW with an initial learning rate of 1e-5, a
polynomial decay strategy, a 1500-iteration warmup, and gradient clipping with
a norm of 0.1. The loss function was a weighted cross-entropy loss that
assigned different weights to various classes to balance their significance.
Training settings included a batch size of 2 per GPU, a maximum of 30,000
iterations, and evaluations using the mIoU metric every 100,000 iterations to
save the best model. The experiments were conducted on a server equipped with
one NVIDIA Tesla L20 GPU 48GB, an Intel(R) Xeon(R) Platinum 8457C CPU, Ubuntu
20.04.4 LTS operating system, and PyTorch version 1.11.0.

##  4 Conclusion

We proposed a two-stage framework to tackle the WeatherProof semantic
segmentation challenge at CVPR’24 UG2+. First, we employed a low-rank based
video deraining method to generate high-quality pseudo ground truths, then
fine-tuned the InternImage semantic segmentation network on these pseudo
ground truths. This framework ingeniously combined the strengths of video
deraining and single image semantic segmentation, achieving a mIoU score of
0.43 and ranking 4th in this challenge. Our method not only performed well in
this challenge but also exhibited great generalizability, being applicable to
other vision tasks requiring robustness against adverse environmental
conditions.

## References

  * [1] Y. Chang, L. Yan, and S. Zhong, “Hyper-laplacian regularized unidirectional low-rank tensor recovery for multispectral image denoising,” in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 5901–5909, 2017.
  * [2] W. Wang, J. Dai, Z. Chen, Z. Huang, Z. Li, X. Zhu, X. Hu, T. Lu, L. Lu, H. Li, et al., “Internimage: Exploring large-scale vision foundation models with deformable convolutions,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 14408–14419, 2023.
  * [3] Y. Guo, X. Xiao, X. Wang, Y. Li, Y. Chang, and L. Yan, “A two-stage real image deraining method for gt-rain challenge cvpr 2023 workshop ug${}^{\textbf{2}}$\+ track 3,” arXiv preprint arXiv:2305.07979, 2023.
  * [4] B. Gella, H. Zhang, R. Upadhyay, T. Chang, M. Waliman, Y. Ba, A. Wong, and A. Kadambi, “Weatherproof: A paired-dataset approach to semantic segmentation in adverse weather,” arXiv preprint arXiv:2312.09534, 2023.


11institutetext:  Institute of Image Analysis and Computer Vision, Faculty of
Informatics and Data Science, University of Regensburg, Regensburg, Germany
22institutetext: School of Electrical Engineering, Iran University of Science
and Technology, Iran 33institutetext: Faculty of Electrical Engineering and
Information Technology, RWTH Aachen University, Aachen, Germany
44institutetext: Fraunhofer Institute for Digital Medicine MEVIS, Bremen,
Germany
44email<EMAIL_ADDRESS>
$\textdagger$ Indicates equal contribution

# DermoSegDiff: A Boundary-aware Segmentation Diffusion Model for Skin Lesion
Delineation

Afshin Bozorgpour† 11 Yousef Sadegheih† 11 Amirhossein Kazerouni† 22 Reza Azad
33 Dorit Merhof 1144

###### Abstract

Skin lesion segmentation plays a critical role in the early detection and
accurate diagnosis of dermatological conditions. Denoising Diffusion
Probabilistic Models (DDPMs) have recently gained attention for their
exceptional image-generation capabilities. Building on these advancements, we
propose DermoSegDiff, a novel framework for skin lesion segmentation that
incorporates boundary information during the learning process. Our approach
introduces a novel loss function that prioritizes the boundaries during
training, gradually reducing the significance of other regions. We also
introduce a novel U-Net-based denoising network that proficiently integrates
noise and semantic information inside the network. Experimental results on
multiple skin segmentation datasets demonstrate the superiority of
DermoSegDiff over existing CNN, transformer, and diffusion-based approaches,
showcasing its effectiveness and generalization in various scenarios. The
implementation is publicly accessible on GitHub.

###### Keywords:

Deep learning Diffusion models Skin Segmentation.

##  1 Introduction

In medical image analysis, skin lesion segmentation aims at identifying skin
abnormalities or lesions from dermatological images. Dermatologists
traditionally rely on visual examination and manual delineation to diagnose
skin lesions, including melanoma, basal cell carcinoma, squamous cell
carcinoma, and other benign or malignant growths. However, the accurate and
rapid segmentation of these lesions plays a crucial role in early detection,
treatment planning, and monitoring of disease progression. Automated medical
image segmentation methods have garnered significant attention in recent years
due to their potential to enhance diagnosis result accuracy and reliability.
The success of these models in medical image segmentation tasks can be
attributed to the advancements in deep learning techniques, including
convolutional neural networks (CNNs) [2, 23, 13], implicit neural
representations [21] and vision transformers [29, 4].

Lately, Denoising Diffusion Probabilistic Models (DDPMs) [11] have gained
considerable interest due to their remarkable performance in the field of
image generation. This newfound recognition has led to a surge in interest and
exploration of DDPMs, propelled by their exceptional capabilities in
generating high-quality and diverse samples. Building on this momentum,
researchers have successfully proposed new medical image segmentation methods
that leverage diffusion models to tackle this challenging task [14]. EnsDiff
[30] utilizes ground truth segmentation as training data and input images as
priors to generate segmentation distributions, enabling the creation of
uncertainty maps and an implicit ensemble of segmentations. Kim et al. [16]
propose a novel framework for self-supervised vessel segmentation. MedSegDiff
[31] introduces DPM-based medical image segmentation with dynamic conditional
encoding and FF-Parser to mitigate high-frequency noise effects. MedSegDiff-V2
[32] enhances it with a conditional U-Net for improved noise-semantic feature
interaction.

Boundary information has proven crucial in the segmentation of skin images,
particularly when it comes to accurately localizing and distinguishing skin
lesions from the surrounding healthy tissue [19, 29, 15]. Boundary information
provides spatial relationships between different regions within the skin and
holds greater significance compared to other areas. By emphasizing these
regions during the training phase, we can achieve more accurate results by
encouraging the model to focus on intensifying boundary regions while reducing
the impact of other areas. However, most diffusion-based segmentation methods
overlook this importance and designate equal importance to all regions.
Another critical consideration is the choice of a denoising architecture,
which directly impacts the model’s capacity to learn complex data
relationships. Most methods have followed a baseline approach [11, 22],
neglecting the fact that incorporating semantic and noise interaction within
the network more effectively.

To address these shortcomings, we propose a novel and straightforward
framework called DermoSegDiff. Our approach tackles the abovementioned issues
by considering the importance of boundary information during training and
presenting a novel denoising network that facilitates a more effective
understanding of the relationship between noise and semantic information.
Specifically, we propose a novel loss function to prioritize the
distinguishing boundaries in the segmentation. By incorporating a dynamic
parameter into the loss function, we increase the emphasis on boundary regions
while gradually diminishing the significance of other regions as we move
further away from the boundaries. Moreover, we present a novel U-Net-based
denoising network structure that enhances the integration of guidance
throughout the denoising process by incorporating a carefully designed dual-
path encoder. This encoder effectively combines noise and semantic
information, extracting complementary and discriminative features. Our model
also has a unique bottleneck incorporating linear attention [26] and original
self-attention [10] in parallel. Finally, the decoder receives the output,
combined with the two outputs transferred from the encoder, and utilizes this
information to estimate the amount of noise. Our experimental results
demonstrate the superiority of our proposed method compared to CNN,
transformer, and diffusion-based state-of-the-art (SOTA) approaches on ISIC
2018 [9], PH2 [20], and HAM10000 [27] skin segmentation datasets, showcasing
the effectiveness and generalization of our method in various scenarios.
Contributions of this paper are as follows: ❶ We highlight the importance of
incorporating boundary information in skin lesion segmentation by introducing
a novel loss function that encourages the model to prioritize boundary areas.
❷ We present a novel denoising network that significantly improves noise
reduction and enhances semantic interaction, demonstrating faster convergence
compared to the baseline model on the different skin lesion datasets. ❸ Our
approach surpasses state-of-the-art methods, including CNNs, transformers, and
diffusion-based techniques, across four diverse skin segmentation datasets.

(a) Baseline

(b) DermoSegDiff

Figure 1: (a) illustrates the architecture of the baseline, and (b) presents
our proposed DermoSegDiff framework.

##  2 Method

Figure 1 provides an overview of our baseline DDPM model and presents our
proposed DermoSegDiff framework for skin lesion segmentation. While
traditional diffusion-based medical image segmentation methods focus on
denoising the noisy segmentation mask conditioning by the input image, we
propose that incorporating boundary information during the learning process
can significantly improve performance. By leveraging edge information to
distinguish overlapped objects, we aim to address the challenges posed by
fuzzy boundaries in difficult cases and cases where lesions and backgrounds
have similar colors. We begin by presenting our baseline method. Subsequently,
we delve into how the inclusion of boundary information can enhance skin
lesion segmentation and propose a novel approach to incorporate this
information into the learning process. Finally, we introduce our network
structure, which facilitates the integration of guidance through the denoising
process more effectively.

###  2.1 Baseline

The core architecture employed in this paper is based on DDPMs [11, 30] (see
Figure 1(a)). Diffusion models primarily utilize $T$ timesteps to learn the
underlying distribution of the training data, denoted as $q(x_{0})$, by
performing variational inference on a Markovian process. The framework
consists of two processes: forward and reverse. During the forward process,
the model starts with the ground truth segmentation mask
($x_{0}\in\mathbb{R}^{H\times W\times 1}$) and adds a Gaussian noise in
successive steps, gradually transforming it into a noisy mask:

$q\left(x_{t}\mid
x_{t-1}\right)=\mathcal{N}\left(x_{t};\sqrt{1-\beta_{t}}\cdot
x_{t-1},\beta_{t}\cdot\mathbf{I}\right),\forall t\in\\{1,\ldots,T\\},$ (1)

in which ${\beta}_{1},\dots,{\beta}_{t-1},{\beta}_{T}$ represent the variance
schedule across diffusion steps. We can then simply sample an arbitrary step
of the noisy mask conditioned on the ground truth segmentation as follows:

$q\left(\mathbf{x}_{t}\mid\mathbf{x}_{0}\right)=N\left(\mathbf{x}_{t};\sqrt{\bar{\alpha}_{t}}\mathbf{x}_{0},\left(1-\bar{\alpha}_{t}\right)\mathbf{I}\right)$
(2)
${{x}_{t}}=\sqrt{{{{\bar{\alpha}}}_{t}}}{{x}_{0}}+\sqrt{1-{{{\bar{\alpha}}}_{t}}}\epsilon,$
(3)

where ${{{\alpha}}_{t}}:=1-{{\beta}_{t}}$,
${{\bar{\alpha}}_{t}}:=\prod\nolimits_{j=1}^{t}{{{\alpha}_{j}}}$ and
$\epsilon\sim\mathcal{N}(0,\textbf{I})$. In the reverse process, the objective
is to reconstruct the original structure of the mask perturbed during the
diffusion process given the input image as guidance ($g\in\mathbb{R}^{H\times
W\times 3}$), by leveraging a neural network to learn the underlying process.
To achieve this, we concatenate the $x_{t}$ and $g$, and denote the
concatenated output as $I_{t}:=x_{t}\mathbin{\|}g$, where
$I_{t}\in\mathbb{R}^{H\times W\times(3+1)}$. Hence, the reverse process is
defined as

$p_{\theta}\left(\mathbf{x}_{t-1}\mid\mathbf{x}_{t}\right)=\mathcal{N}\left(\mathbf{x}_{t-1};\mu_{\theta}\left(I_{t},t\right),\Sigma_{\theta}\left(I_{t},t\right)\right),$
(4)

where Ho et al. [11] conclude that instead of directly predicting
$\mu_{\theta}$ using the neural network, we can train a model to predict the
added noise, $\epsilon_{\theta}$, leading to a simplified objective as
$\mathcal{L}_{b}=\left\|\epsilon-\epsilon_{\theta}\left(I_{t},t\right)\right\|^{2}$.

###  2.2 Boundary-Aware Importance

While diffusion models have shown promising results in medical image
segmentation, there is a notable limitation in how we treat all pixels of a
segmentation mask equally during training. This approach can lead to saturated
results, undermining the model’s performance. In the case of segmentation
tasks like skin lesion segmentation, it becomes evident that boundary regions
carry significantly more importance than other areas. This is because the
boundaries delineate the edges and contours of objects, providing crucial
spatial information that aids in distinguishing between the two classes. To
address this issue, we present DermoSegDiff, which effectively incorporates
boundary information into the learning process and encourages the model to
prioritize capturing and preserving boundary details, leading to a faster
convergence rate compared to the baseline method. Our approach follows a
straightforward yet highly effective strategy for controlling the learning
denoising process. It focuses on intensifying the significance of boundaries
while gradually reducing this emphasis as we move away from the boundary
region utilizing a novel loss function. As depicted in Figure 1, our forward
process aligns with our baseline, and both denoising networks produce output
$\epsilon_{\theta}$. However, the divergence between the two becomes apparent
when computing the loss function. We define our loss function as follows:

$\mathcal{L}_{w}=(1+\alpha
W_{\Theta})\left\|\epsilon-\epsilon_{\theta}\left(x_{t},g,t\right)\right\|^{2}$
(5)

where $W_{\Theta}\in\mathbb{R}^{H\times W\times 1}$ is a dynamic parameter
intended to increase the weight of noise prediction in boundary areas while
decreasing its weight as we move away from the boundaries (see Figure 5).
$W_{\Theta}$ is obtained through a two-step process involving the calculation
of a distance map and subsequent computation of boundary attention.
Additionally, $W_{\Theta}$ is dynamically parameterized, depending on the
point of time (t) at which the distance map is calculated. It means it
functions as a variable that dynamically adjusts according to the specific
characteristics of each image at time step $t$.

Our distance map function operates by taking the ground truth segmentation
mask as input. Initially, it identifies the border pixels by assigning a value
of one to them while setting all other pixels to zero. To enhance the
resolution of the resulting distance map, we extend the border points
horizontally from both the left and right sides by $\left\lceil
H\%\right\rceil$ (e.g., for a $256\times 256$ image, each row would have seven
boundary pixels). To obtain the distance map, we employ the distance transform
function [17], which is a commonly used image processing technique for binary
images. This function calculates the Euclidean distance between each non-zero
(foreground) pixel in the image and the nearest zero (background) pixel. The
result is a gray-level image where the intensities of points within foreground
regions are modified to represent the distances to the closest boundaries from
each individual point. To normalize the intensity levels of the distance map
and improve its suitability as a dynamic weighting matrix $W_{\Theta}$, we
employ the technique of gamma correction from image processing to calculate
the boundary attention. By adjusting the gamma value, we gain control over the
overall intensity of the distance map, resulting in a smoother representation
that enhances its effectiveness in the loss function.

Figure 2: The overview of the proposed denoising network architecture. The
notation L-Att, RB, EM, DM, LS-Att, and S-Att correspond to the Linear
Attention, ResNet Block, Encoder Modules, Decoder Modules, Linear Self-
Attention, and Self-Attention modules, respectively.

###  2.3 Network Architecture

Encoder: The overall architecture of our proposed denoising network is
depicted in Figure 2. We propose a modification to the U-Net network
architecture for predicting added noise $\epsilon_{\theta}$ to a noisy
segmentation mask $x_{i-1}^{enc}$, guided by the guidance image $g_{i-1}$ and
time embedding $t$, where $i$ refers to the $i-th$ encoder. The encoder
consists of a series of stacked Encoder Modules (EM), which are subsequently
followed by a convolution layer to achieve a four-by-four tensor at the output
of the encoder. Instead of simply concatenating $x_{i-1}^{enc}$ and $g_{i-1}$
and feeding into the network [30], our approach enhances the conditioning
process by employing a two-path feature extraction strategy in each Encoder
Module (EM), focusing on the mutual effect that the noisy segmentation mask
and the guidance image can have on each other. Each path includes two ResNet
blocks (RB) and is followed by a Linear Attention (L-Att) [26], which is
computationally efficient and generates non-redundant feature representation.
To incorporate temporal information, time embedding is introduced into each
RB. The time embedding is obtained by passing $t$ through a sinusoidal
positional embedding, followed by a linear layer, a GeLU activation function,
and another linear layer. We use two time embeddings, one for $g_{i-1}$
($t_{g}$) and another for $x_{i-1}^{enc}$ ($t_{x}$), to capture the temporal
aspects specific to each input. Furthermore, we leverage the knowledge
captured by $RB_{1}^{x}$ by transferring and concatenating it with the
guidance branch, resulting in $h_{i}$. By incorporating two paths, we capture
specific representations that provide a comprehensive view of the data. The
left path extracts noise-related features, while the right path focuses on
semantic information. This combination enables the model to incorporate
complementary and discriminative features. After applying $RB_{2}^{g}$, we
introduce a feedback mechanism that takes a convolution of the $RB_{2}^{g}$
output and connects to the $RB_{2}^{x}$ input. This feedback allows the
resultant features, which contain overall information about both the guidance
and noise, to be shared with the noise path. By doing so and multiplying the
feature maps, we emphasize important features while attenuating less
significant ones. This multiplication operation acts as a form of attention
mechanism, where the shared features guide the noise path to focus on relevant
and informative regions. After the linear attention of the left path and
before the right path, we provide another feature concatenation of these two
paths, referred to as $b_{i}$. At the end of each EM block, we obtain four
outputs: $h_{i}$ and $b_{i}$, which are used for skip connections from the
encoder to the decoder, and resultant enriched $x_{i}^{enc}$ and $g_{i}$ are
fed into the next EM block to continue the feature extraction process.

Bottleneck: Next, we concatenate the outputs, $x_{L}^{enc}$ and $g_{L}$, from
the last EM block and pass them alongside the time embedding $t_{x}$ through a
Bottleneck Module (BM), which contains a ResNet block, a Linear Self-Attention
(LS-Att), and another ResNet block. LS-Att is a dual attention module that
combines original Self-Attention (S-Att) for spatial relationships and L-Att
for capturing semantic context in parallel, enhancing the overall feature
representation. The output of BM is then fed into the decoder.

Decoder: The decoder consists of stacked Decoder Modules (DM) followed by a
convolutional block that outputs $\epsilon_{\theta}$. The number of stacked
DMs is the same as the number of EMs in the encoder. Unlike the EM blocks,
which are dual-path modules, each DM block is a single-path module. It
includes two consecutive RB blocks and one L-Att module. $b_{i}$ and $h_{i}$
from the encoder are concatenated with the feature map before and after
applying $RB_{1}^{d}$, respectively. By incorporating these features, the
decoder gains access to refined information from the encoder, thereby aiding
in better estimating the amount of noise added during the forward process and
recovering missing information during the learning process. In addition, to
preserve the impact of noise during the decoding process, we implement an
additional skip connection from $x$ to the final layer of the decoder. This
involves concatenating the resulting feature map of the $DM_{1}$ with $x$ and
passing them together through the last convolutional block to output the
estimated noise $\epsilon_{\theta}$.

##  3 Results

The proposed method has been implemented using the PyTorch library (version
1.14.0) and has undergone training on a single NVIDIA A100 graphics processing
unit (80 GB VRAM). The training procedure employs a batch size of $32$ and
utilizes the Adam optimizer with a base learning rate of $0.0001$. The
learning rate is decreased by a factor of $0.5$ in the event that there is no
improvement in the loss function after ten epochs. In all experiments, we
established $T$ as 250 and maintained the forward process variances as
constants that progressively increased from $\beta_{start}=0.0004$ to
$\beta_{end}=0.08$ linearly. Furthermore, in the training process, data
augmentation techniques have been employed using Albumentations [5], including
spatial augmentation methods such as Affine and Flip transforms and
CoarseDropout, as well as pixel augmentation methods such as GaussNoise and
RGBShift transforms. For each dataset, the network was trained for 40000
iterations. Moreover, we set $\alpha$ empirically as 0.2. The duration of the
training process was approximately 1.35 seconds per sample. Notably, in our
evaluation process, we employ a sampling strategy to generate nine different
segmentation masks for each image in the test set. To obtain a final
segmentation result, we average these generated masks and apply a threshold of
0. The reported results in terms of performance metrics are based on this
ensemble strategy.

###  3.1 Datasets

To evaluate the proposed methodology, three publicly available skin lesion
segmentation datasets, ISIC 2018 [9], PH2 [20], and HAM10000 [27] are
utilized. The same pre-processing criteria described in [3] are used to train
and evaluate the first three datasets mentioned. The HAM10000 dataset is also
a subset of the ISIC archive containing 10015 dermoscopy images along with
their corresponding segmentation masks. 7200 images are used as training, 1800
as validation, and 1015 as test data. Each sample of all datasets is downsized
to $128\times 128$ pixels using the same pre-processing as [1].

Table 1: Performance comparison of the proposed method against the SOTA
approaches on skin lesion segmentation benchmarks. Blue indicates the best
result, and red displays the second-best.

Methods | ISIC 2018 | $\mathbf{PH^{2}}$ | HAM10000
---|---|---|---
DSC | SE | SP | ACC | DSC | SE | SP | ACC | DSC | SE | SP | ACC
U-Net [23] | 0.8545 | 0.8800 | 0.9697 | 0.9404 | 0.8936 | 0.9125 | 0.9588 | 0.9233 | 0.9167 | 0.9085 | 0.9738 | 0.9567
DAGAN [18] | 0.8807 | 0.9072 | 0.9588 | 0.9324 | 0.9201 | 0.8320 | 0.9640 | 0.9425 | - | - | - | -
TransUNet [7] | 0.8499 | 0.8578 | 0.9653 | 0.9452 | 0.8840 | 0.9063 | 0.9427 | 0.9200 | 0.9353 | 0.9225 | 0.9851 | 0.9649
Swin-Unet [6] | 0.8946 | 0.9056 | 0.9798 | 0.9645 | 0.9449 | 0.9410 | 0.9564 | 0.9678 | 0.9263 | 0.9316 | 0.9723 | 0.9616
DeepLabv3+ [8] | 0.8820 | 0.8560 | 0.9770 | 0.9510 | 0.9202 | 0.8818 | 0.9832 | 0.9503 | 0.9251 | 0.9015 | 0.9794 | 0.9607
Att-UNet [24] | 0.8566 | 0.8674 | 0.9863 | 0.9376 | 0.9003 | 0.9205 | 0.9640 | 0.9276 | 0.9268 | 0.9403 | 0.9684 | 0.9610
UCTransNet [28] | 0.8838 | 0.9825 | 0.8429 | 0.9527 | 0.9093 | 0.9698 | 0.8835 | 0.9408 | 0.9346 | 0.9205 | 0.9825 | 0.9684
MissFormer [12] | 0.8631 | 0.9690 | 0.8458 | 0.9427 | 0.8550 | 0.9738 | 0.7817 | 0.9050 | 0.9211 | 0.9287 | 0.9725 | 0.9621
Baseline (EnsDiff) [30] | 0.8775 | 0.8358 | 0.9812 | 0.9502 | 0.9117 | 0.8752 | 0.9774 | 0.9431 | 0.9277 | 0.9213 | 0.9771 | 0.9625
DermoSegDiff-A | 0.9005 | 0.8761 | 0.9811 | 0.9587 | 0.9450 | 0.9296 | 0.9810 | 0.9637 | 0.9386 | 0.9308 | 0.9814 | 0.9681
DermoSegDiff-B | 0.8966 | 0.8642 | 0.9828 | 0.9575 | 0.9467 | 0.9308 | 0.9814 | 0.9650 | 0.9430 | 0.9326 | 0.9839 | 0.9704

|  |  |  |  |  |
---|---|---|---|---|---|---
|  |  |  |  |  |
Image | Ground Truth | DermoSegDiff-B | DermoSegDiff-A | TransUNet | Baseline | U-Net

Figure 3: Visual comparisons of different methods on the ISIC 2018 skin lesion
dataset. Ground truth boundaries are shown in green, and predicted boundaries
are shown in blue.

###  3.2 Quantitative and qualitative results

Table 1 presents the performance analysis of our proposed DermoSegDiff on all
four skin lesion segmentation datasets. The evaluation incorporates several
metrics, including Dice Score (DSC), Sensitivity (SE), Specificity (SP), and
Accuracy (ACC), to establish comprehensive evaluation criteria. In our
notation, the model with the baseline loss function is referred to as
DermoSegDiff-A, while the model with the proposed loss function is denoted as
DermoSegDiff-B. The results demonstrate that DermoSegDiff-B surpasses both CNN
and Transformer-based approaches, showcasing its superior performance and
generalization capabilities across diverse datasets. Specifically, our main
approach demonstrates superior performance compared to pure transformer-based
methods such as Swin-Unet [6], CNN-based methods like DeepLabv3+ [8], and
hybrid methods like UCTransNet [28]. Moreover, DermoSegDiff-B exhibits
enhanced performance compared to the baseline model (EnsDiff) [30], achieving
an increase of +2.18%, +3.83%, and +1.65% in DSC score on ISIC 2018, PH2, and
HAM10000 datasets, respectively. Furthermore, in Figure 3, we visually compare
the outcomes generated by various skin lesion segmentation models. The results
clearly illustrate that our proposed approach excels in capturing intricate
structures and producing more accurate boundaries compared to its
counterparts. This visual evidence underscores the superior performance
achieved by carefully integrating boundary information into the learning
process.

##  4 Ablation studies

|  |  |  |  |  |  |  |
---|---|---|---|---|---|---|---|---
Mask at $0.05T$ | Guidance Image | Ground Truth | DSD-B: $x_{3}$ | DSD-A: $x_{3}$ | DSD-B: $g_{3}$ | DSD-A: $g_{3}$ | DSD-B: feedback | DSD-A: feedback
|  |  |  |  |  |  |  |
Mask at $0.25T$ | Guidance Image | Ground Truth | DSD-B: $x_{3}$ | DSD-A: $x_{3}$ | DSD-B: $g_{3}$ | DSD-A: $g_{3}$ | DSD-B: feedback | DSD-A: feedback

Figure 4: An illustration of how our proposed loss function concentrates on
the segmentation boundary in contrast to the conventional $\mathcal{L}_{b}$
loss in DermoSegDiff-A. The heatmaps are obtained from the $EM_{3}$ using
GradCAM [25]. Notably, DSD is an abbreviation of DermoSegDiff.

Figure 4 illustrates the effects of our innovative loss function. The heatmaps
are produced utilizing the GradCAM [25], which visually represents the
gradients of the output originating from the $EM_{3}$. Incorporating a novel
loss function results in a shift of emphasis towards the boundary region,
leading to a 0.51% enhancement compared to DermoSegDiff-A in the overall DSC
score on the ISIC 2018 dataset. The analysis reveals a distinct behavior
within our model. In the noise path, the model primarily emphasizes local
boundary information, while in the guidance branch, it aims to capture more
global information. This knowledge is then transferred through feedback to the
noise branch, providing complementary information. This combination of local
and global information allows our model to effectively leverage both aspects
and achieve improved results. Figure 5 depicts the evolution of $W_{\Theta}$
with respect to $T$. In the initial stages of the denoising process, when the
effect of noise is significant, the changes in the boundary area are
relatively smooth. During this phase, the model focuses on capturing more
global information about the image. As the denoising process progresses and it
becomes easier to distinguish between the foreground and background in the
resulting image, the weight shifts, placing increased emphasis on the boundary
region while disregarding the regions that are further away from it.
Additionally, as we approach $x_{0}$, the emphasis on the boundary information
becomes more pronounced. These observations highlight the adaptive nature of
$W_{\Theta}$ and its role in effectively preserving boundary details during
the denoising process.

|  |  |  |  |
---|---|---|---|---|---
Guidance Image | Ground Truth | Distance Map |  $W_{\Theta}$ at 0.25T |  $W_{\Theta}$ at 0.50T |  $W_{\Theta}$ at 0.75T

Figure 5: An illustration of how the $W_{\Theta}$ variable varies dependent on
the network’s current time step of diffusion.

|  |
---|---|---

(a) Annotation limitation

|  |
---|---|---

(b) Model limitation

Figure 6: (a) Illustrates the limitation imposed by annotation of the dataset,
and (b) presents some of the limitations of our proposed model. Ground truth
boundaries are shown in green, and predicted boundaries are shown in blue.

##  5 Limitations

Despite these promising results, there are also some limitations. For example,
some annotations within the datasets may not be entirely precise. Figure 6(a)
portrays certain inconsistencies in the annotations of data. However, despite
these annotation challenges, our proposed method demonstrates superior
precision in the segmentation of skin lesions in comparison to the annotators.
The results indicate that with more meticulous annotation of the masks, our
proposed approach could have achieved even higher scores across all evaluation
metrics. It is worth noting that there were instances where our model deviated
from the accurate annotation and erroneously partitioned the area. Figure 6(b)
depicts instances where our proposed methodology fails to segment the skin
lesion accurately. The difficulty in accurately demarcating the boundary
between the foreground and background in skin images arises from the high
similarity between these regions and requires more work that we aim to address
in future work.

##  6 Conclusion

This paper introduced the DermoSegDiff diffusion network for skin lesion
segmentation. Our approach introduced a novel loss function that emphasizes
the importance of the segmentation’s boundary region and assigns it higher
weight during training. Further, we proposed a denoising network that
effectively models the noise-semantic information and results in performance
improvement.

## References

  * [1] Alom, M.Z., Hasan, M., Yakopcic, C., Taha, T.M., Asari, V.K.: Recurrent residual convolutional neural network based on u-net (r2u-net) for medical image segmentation. arXiv preprint arXiv:1802.06955 (2018)
  * [2] Azad, R., Aghdam, E.K., Rauland, A., Jia, Y., Avval, A.H., Bozorgpour, A., Karimijafarbigloo, S., Cohen, J.P., Adeli, E., Merhof, D.: Medical image segmentation review: The success of u-net. arXiv preprint arXiv:2211.14830 (2022)
  * [3] Azad, R., Al-Antary, M.T., Heidari, M., Merhof, D.: Transnorm: Transformer provides a strong spatial normalization mechanism for a deep segmentation model. IEEE Access 10, 108205–108215 (2022)
  * [4] Azad, R., Kazerouni, A., Heidari, M., Aghdam, E.K., Molaei, A., Jia, Y., Jose, A., Roy, R., Merhof, D.: Advances in medical image analysis with vision transformers: A comprehensive review. arXiv preprint arXiv:2301.03505 (2023)
  * [5] Buslaev, A., Iglovikov, V.I., Khvedchenya, E., Parinov, A., Druzhinin, M., Kalinin, A.A.: Albumentations: Fast and flexible image augmentations. Information 11(2) (2020). https://doi.org/10.3390/info11020125
  * [6] Cao, H., Wang, Y., Chen, J., Jiang, D., Zhang, X., Tian, Q., Wang, M.: Swin-unet: Unet-like pure transformer for medical image segmentation. arXiv preprint arXiv:2105.05537 (2021)
  * [7] Chen, J., Lu, Y., Yu, Q., Luo, X., Adeli, E., Wang, Y., Lu, L., Yuille, A.L., Zhou, Y.: Transunet: Transformers make strong encoders for medical image segmentation. arXiv preprint arXiv:2102.04306 (2021)
  * [8] Chen, L.C., Zhu, Y., Papandreou, G., Schroff, F., Adam, H.: Encoder-decoder with atrous separable convolution for semantic image segmentation. In: Proceedings of the European conference on computer vision (ECCV). pp. 801–818 (2018)
  * [9] Codella, N., Rotemberg, V., Tschandl, P., Celebi, M.E., Dusza, S., Gutman, D., Helba, B., Kalloo, A., Liopyris, K., Marchetti, M., et al.: Skin lesion analysis toward melanoma detection 2018: A challenge hosted by the international skin imaging collaboration (isic). arXiv preprint arXiv:1902.03368 (2019)
  * [10] Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., et al.: An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929 (2020)
  * [11] Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems 33, 6840–6851 (2020)
  * [12] Huang, X., Deng, Z., Li, D., Yuan, X.: Missformer: An effective medical image segmentation transformer. arXiv preprint arXiv:2109.07162 (2021)
  * [13] Isensee, F., Jaeger, P.F., Kohl, S.A., Petersen, J., Maier-Hein, K.H.: nnu-net: a self-configuring method for deep learning-based biomedical image segmentation. Nature methods 18(2), 203–211 (2021)
  * [14] Kazerouni, A., Aghdam, E.K., Heidari, M., Azad, R., Fayyaz, M., Hacihaliloglu, I., Merhof, D.: Diffusion models in medical imaging: A comprehensive survey. Medical Image Analysis p. 102846 (2023)
  * [15] Kervadec, H., Bouchtiba, J., Desrosiers, C., Granger, E., Dolz, J., Ayed, I.B.: Boundary loss for highly unbalanced segmentation. In: International conference on medical imaging with deep learning. pp. 285–296. PMLR (2019)
  * [16] Kim, B., Oh, Y., Ye, J.C.: Diffusion adversarial representation learning for self-supervised vessel segmentation. In: The Eleventh International Conference on Learning Representations (2023)
  * [17] Kimmel, R., Kiryati, N., Bruckstein, A.M.: Sub-pixel distance maps and weighted distance transforms. Journal of Mathematical Imaging and Vision 6, 223–233 (1996)
  * [18] Lei, B., Xia, Z., Jiang, F., Jiang, X., Ge, Z., Xu, Y., Qin, J., Chen, S., Wang, T., Wang, S.: Skin lesion segmentation via generative adversarial networks with dual discriminators. Medical Image Analysis 64, 101716 (2020)
  * [19] Liu, X., Yang, L., Chen, J., Yu, S., Li, K.: Region-to-boundary deep learning model with multi-scale feature fusion for medical image segmentation. Biomedical Signal Processing and Control 71, 103165 (2022)
  * [20] Mendonça, T., Ferreira, P.M., Marques, J.S., Marcal, A.R., Rozeira, J.: Ph 2-a dermoscopic image database for research and benchmarking. In: 2013 35th annual international conference of the IEEE engineering in medicine and biology society (EMBC). pp. 5437–5440. IEEE (2013)
  * [21] Molaei, A., Aminimehr, A., Tavakoli, A., Kazerouni, A., Azad, B., Azad, R., Merhof, D.: Implicit neural representation in medical imaging: A comparative survey. arXiv preprint arXiv:2307.16142 (2023)
  * [22] Nichol, A.Q., Dhariwal, P.: Improved denoising diffusion probabilistic models. In: International Conference on Machine Learning. pp. 8162–8171. PMLR (2021)
  * [23] Ronneberger, O., Fischer, P., Brox, T.: U-net: Convolutional networks for biomedical image segmentation. In: International Conference on Medical image computing and computer-assisted intervention. pp. 234–241. Springer (2015)
  * [24] Schlemper, J., Oktay, O., Schaap, M., Heinrich, M., Kainz, B., Glocker, B., Rueckert, D.: Attention gated networks: Learning to leverage salient regions in medical images. Medical image analysis 53, 197–207 (2019)
  * [25] Selvaraju, R.R., Cogswell, M., Das, A., Vedantam, R., Parikh, D., Batra, D.: Grad-cam: Visual explanations from deep networks via gradient-based localization. In: Proceedings of the IEEE international conference on computer vision. pp. 618–626 (2017)
  * [26] Shen, Z., Zhang, M., Zhao, H., Yi, S., Li, H.: Efficient attention: Attention with linear complexities. In: Proceedings of the IEEE/CVF winter conference on applications of computer vision. pp. 3531–3539 (2021)
  * [27] Tschandl, P., Rosendahl, C., Kittler, H.: The ham10000 dataset, a large collection of multi-source dermatoscopic images of common pigmented skin lesions. Scientific data 5(1), 1–9 (2018)
  * [28] Wang, H., Cao, P., Wang, J., Zaiane, O.R.: Uctransnet: rethinking the skip connections in u-net from a channel-wise perspective with transformer. In: Proceedings of the AAAI conference on artificial intelligence. vol. 36, pp. 2441–2449 (2022)
  * [29] Wang, J., Wei, L., Wang, L., Zhou, Q., Zhu, L., Qin, J.: Boundary-aware transformers for skin lesion segmentation. In: Medical Image Computing and Computer Assisted Intervention–MICCAI 2021: 24th International Conference, Strasbourg, France, September 27–October 1, 2021, Proceedings, Part I 24. pp. 206–216. Springer (2021)
  * [30] Wolleb, J., Sandkühler, R., Bieder, F., Valmaggia, P., Cattin, P.C.: Diffusion models for implicit image segmentation ensembles. In: International Conference on Medical Imaging with Deep Learning. pp. 1336–1348. PMLR (2022)
  * [31] Wu, J., Fang, H., Zhang, Y., Yang, Y., Xu, Y.: Medsegdiff: Medical image segmentation with diffusion probabilistic model. arXiv preprint arXiv:2211.00611 (2022)
  * [32] Wu, J., Fu, R., Fang, H., Zhang, Y., Xu, Y.: Medsegdiff-v2: Diffusion based medical image segmentation with transformer. arXiv preprint arXiv:2301.11798 (2023)


# Characterization of the response of IHEP-IME LGAD with shallow carbon to
Gamma Irradiation

Weiyi Sun  Yunyun Fan11footnotetext: Corresponding author. Han Cui  Chengjun
Yu  Shuqi Li  Yuan Feng  Xinhui Huang  Zhijun Liang  Xuewei Jia  Wei Wang
Tianya Wu  Mengzhao Li  João Guimarães da Costa  and Gaobo Xu

###### Abstract

Low Gain Avalanche Detectors (LGAD), as part of High-Granularity Timing
Detector (HGTD), is crucial to reducing pileup in the upgrading to HL-LHC.
Many studies have been done on the bulk damages of the LGAD. However, there’s
no study about the surface radiation hardness of the LGAD sensors with carbon
implanted. The IHEP-IME LGAD version 3 with the shallow carbon and different
interpad separations were irradiated up to 2 MGy by gamma irradiation. The
performance of the IHEP-IME LGAD version 3 before and after irradiation had
been tested, such as the leakage current, break-down voltage, capacitance,
Vgl, and inter-pad resistance. The results showed that apart from minor
fluctuations in some samples, no significant changes concerning inter-pad
separation were observed before and after irradiation. Leakage current and
break-down voltage increase after irradiation, which is considered due to
surface passivation; the overall inter-pad resistance are larger than $10^{9}\
\Omega$ before and after irradiation; capacitance is found to be less than 4.5
pF with a slight drop in Vgl after irradiation. All parameters meet the
requirements of HGTD, and the results indicated that IHEP-IME LGAD v3 has
excellent anti-irradiation performance.

##  1 Introduction

The Phase-II upgrade of the Large Hadron Collider (LHC), or the High
Luminosity LHC (HL-LHC), is designed to achieve a luminosity of $5\times
10^{34}$ cm-2s-1, an increase of an order of magnitude compared to the LHC[1,
2, 3]. Higher luminosity brings severe pile-up, averaging about 200, and
therefore a High-Granularity Timing Detector (HGTD) containing a new type
silicon sensor, which the Low Gain Avalanche Detector (LGAD), is planned for
the forward region of the ATLAS detector to perform timing measurements of
charged tracks and help in the suppression of pileup. [4].

LGAD is a type of silicon sensor that offers moderate internal gain, which
enhances the signal amplitude and enables high time and spatial resolutions of
several picoseconds and micrometers, respectively[5, 6, 7]. Due to the nature
of semiconductor detectors, high beams and irradiation intensity environments
in HL-LHC can cause serious damage to LGAD’s lifetime and performance through
several effects [8, 5, 9]. Hence, the ATLAS committee has set stringent
requirements for the detector’s resistance to irradiation.

BNL, FBK, NDL, and several other institutes have conducted various types of
bulk damages irradiation studies on LGADs and have observed numerous adverse
effects of irradiation on LGADs [10, 11, 12]. Surface damage of HPK LGAD
without carbon implantion was studied [13]. However, the surface damage
studies on the LGADs with carbon implantion has not been sutdied carefully.
This study will focous on the surface damage of LGADs with shallow carbon
implanted by gamma ray.

In order to achieve excellent irradiation hardness, the institute of High
Energy Physics (IHEP) has has designed a new carbon-doped LGAD, fabricated by
the Institute of Microelectronics (IME), which is IHEP-IME LGAD . Performance
and radiation hardness of the first version of IHEP-IME LGAD under neutron
fluence was reported [14, 15]. Afterwards, the second version was designed and
manufactured according to the best design parameters of the first version
[16], and the third version (IHEP-IME LGAD v3) was optimized based on the
second version.

In this paper, we investigate the performance of IHEP-IME LGAD v3 under 60Co
gamma irradiation with maximum dose of 2M Gy. Such irradiation causes surface
damage at the SiO2 and the Si-SiO2 interface by inducing oxide charges and
interface traps, and point defects in silicon sensors by Compton electrons and
photoelectrons [17, 18]. This investigation aims to optimize the surface
parameters of LGAD design.

We present the IHEP-IME v3 LGAD and describe the irradiation and test setups
in Sections 2 and 3, present and analyze the experimental results in Section
4, and provide a conclusion in Section 5.

##  2 Samples

All LGAD samples used in this study were taken from wafer 12 of v3. The device
structure from top to bottom is passivation layer, pad, SiO2, n++ layer, p+
layer (gain layer), p-layer (multiplication layer), p+ layer and aluminum
chunk as illustrated in Figure 1.

Figure 1: Structure schematic of IHEP-IME LGAD.

Upper of multiplication layer is fabricated by Floating Zone (FZ) technique
with a thickness of 50 $\mu$m and higher resistivity, and the lower layer is
fabricated by Czochralski (CZ) technique with a thickness of 725 $\mu$m and
lower resistivity. A p-stop and JTEs between n++ and p+ layers are designed to
reduce the lateral current, and all tested LGADs are quad square pad ($2\times
2$ pads, 2 mm $\times$ 2 mm for each pad) structures with different inter-pad
separation (IPs) from 50 $\mu$m to 100 $\mu$m, surrounded by guard-ring, as
shown in Figure 2. The scratch are on the windows of the pads, and the rest is
covered by the passivation layer. Since damage to the LGAD caused by 60Co
irradiation is mainly concentrated at the SiO2 surface, different IP designs
have different SiO2 areas, and studying the variation pattern among IPs can
help optimize the IP design.

The post-flow test results show that the breakdown voltage of the whole wafer
is more than 95% consistent, and the yield is better than 0.95. Therefore, we
assume that the randomly selected samples are representative of the overall
situation.

Figure 2: Layout of IHEP-IME LGAD prototypes 2-5(a) and 2-9(b). Three pads and
the guard ring of 2-9 are bounded by gold wires.

The wafer was uniformly doped with carbon in order to improve the irradiation
resistance, and the doping concentration distribution is shown in Figure 3.
After flow and testing, the carbon doping was considered to be homogeneous as
expected.

Figure 3: Doping concentration distribution of Carbon.

##  3 Irradiation and Experiment Setups

###  3.1 Irradiation

Irradiation test was carried out at China Institute of Atomic Energy (CIAE).
Samples are fixed using Kapton capes, and placed in the aluminium boxes,
around the cylindrical 60Co irradiation source, which causes damage in silicon
sensors by Compton electrons and photoelectrons, as shown in Figure 4.

|
---|---

Figure 4: Fixed samples on Kapton tapes (a) are placed in aluminium boxes
around the cylindrical irradiation source (b).

Irradiation dose rate is 10000$\pm$15% Gy/h ( 2.77$\pm$15% Gy/s), and total
doses are 10k Gy, 100k Gy, and, 2M Gy. Due to the small sample size compared
to the diameter of the radiation source, we assume that the irradiation is
uniform.

###  3.2 Experiment Steups

All tests, including IV, CV, and Inter-pad resistance, were conducted in the
clean room of IHEP at a temperature of 20-22 ∘C and a humidity of 10-12%. The
errors of the measuring apparatus are summarized in Table 1.

Table 1: Errors of experiment apparatus. Apparatus | Accuracy | Used in measurement
---|---|---
Keithley 2400 | 0.012% | IV CV Resistance
Keithley 2410 | 0.02% | IV Resistance
Keysight E4980A | 0.05% | CV

The leakage currents are measured from $10^{-13}$ A to $10^{-4}$ A, and break-
down current is defined as 1 $\mu$A. Negative bias potential is applied to
chunk in 2V increment for IV and inter-pad resistances, and in 0.5V increment
for CV.

For IV and CV tests, one pad and guard ring are grounded, with the rest pads
floating. For inter-pad resistance, three pads and the guard ring are
connected by gold wires and grounded, as illustrated in Figure 2 (b). The
floating pad (pad 4) is biased with a voltage range of -1 V to 1 V in 0.5 V
increments, and leakage current is measured here.

Since different experiments require different wiring methods, the effects of
different wiring methods with respect to guard ring plus 0, 1, 2, and 3 pads
floating are analyzed. No significant change in leakage current and break-down
voltage are observed by changing wiring method, and therefore the following
experimental results can be excluded as a result of the test method.

##  4 Description and Analysis of Result

Results of Leakage Current versus Bias Voltage(I-V) and break-down voltage(BV)
are shown in 4.1; capacitance versus Bias Voltage(C-V), Vgl, and acceptor
removal constant are investigated in 4.2; inter-pad resistance is analyzed in
4.3.

###  4.1 Leakage Current versus Bias Voltage(I-V)

In general, we observe an increase in both leakage current and break-down
voltage after irradiation. This conclusion holds for all IPs. The following is
the detailed analysis process.

Leakage Current versus Bias Voltage (I-V) characteristics of IHEP-IME LGAD v1
and v3 before and after irradiation are measured as shown in Figure 5. We take
IHEP-IME LGAD version 1 (v1) and v3 2-5 as examples.

Figure 5: IV characteristic of IHEP-IME LGAD v1 and v3 2-5.

The figure shows the leakage current of v1 is greater than v3, and BV is lower
than v3 before irradiation. The BV of v1 decreases dramatically after
irradiation, indicating that v1 is damaged. V3 added passivation process
compared to v1, which may be responsible for the increased irradiation
hardness, but remains to be further investigated. Version 1 will not be
studied in the following due to poor performance.

For v3 sample 2-5, the leakage currents increase with the increase of
irradiation dose, and rise to 3 times the pre-irradiation value after 2M Gy
irradiation. The difference of BV among irradiation doses are about 5 V. IV
curves all show four stages before and after irradiation: slow rise(I), rapid
rise(II), plateau(III), and break-down (IV), due to depletion of different
layers and break-down .

All samples are investigated in a similar way, and results are shown in Figure
6. Break-down voltage increases with increasing irradiation dose, rising by 5
V-30 V for different samples after 2M Gy irradiation. This trend is
particularly significant in samples 2-7, 2-8, 2-9, and 2-10, where the rise is
greater than 20 V. Considering the BV of the whole wafer before irradiation
has about 10% spread, a change of 19V or more in BV after irradiation can be
considered caused by irradiation. Therefore, the rise in BV of samples 2-7,
2-8, 2-9, and 2-10 can be confirmed to be caused by irradiation, whereas the
cause of the rise in BV of other samples remains to be investigated.

Figure 6: Break-down voltage of all IPs under different irradiation doses.

###  4.2 Capacitance (C-V) and related quantities

Capacitance versus bias voltage (CV), Vgl, acceptor removal constant are
studied in this section.

The CVs of sample 2-5 with IP 50 $\mu$m are shown in Figure 7. The figure
shows the capacitance values are all less than 4.5 pF and no significant
change in shape is observed before and after 2M Gy irradiation, and all other
samples show the same properties.

Figure 7: Capacitance versus bias voltage characteristic after irradiation of
IHEP-IME LGAD 2-5 with IP 50 $\mu$m.

$\frac{1}{C^{2}}$-V characteristics for sample 2-5 are shown in Figure 8, with
linear fitting using 3-4 points after the inflection point. Vgls are
calculated by finding the intersection of the fitting line and line y=0 and
Vfd is the intersection of the fitting line and saturation vertical line. For
this example, Vgls are calculated to be 24.537 V $\pm 0.0489$ V before and
23.989 V$\pm 0.1689$ V after 2M Gy irradiation, from where one can find a
voltage drop of about 0.5 V due to irradiation, and the fluctuation of
$\frac{1}{C^{2}}$ after full depletion gets more intense with increasing
irradiation dose. Vfd is 42.215 V $\pm 0.1416$ V before but is considered
invalid due to sharp fluctuations after irradiation.

Figure 8: $\frac{1}{C^{2}}$ versus full bias voltage characteristic before and
after irradiation for IHEP-IME LGAD 2-5 with IP 50 $\mu$m. Data are drawn in
dashed lines and fittings are drawn in solid.

Vgls are calculated similarly for other samples and are fitted to (4.1), where
Vgl and V0,gl are the gain layer depletion voltages before and after
irradiation; $\phi$ is the total ionizing dose with the unit of Gy; c is the
acceptor removal constant with the team of 1/Gy. Fitting results are shown in
Figure 9, and constant c are extracted in Table 2. One can conclude that Vgls
are all greater than 24 V before irradiation and drop of about 0.5V to equal
or slightly less than 24 V after 2M Gy of irradiation, and those trends are
not related to IP. The decrease rate of Vgl in 2-6 and 2-7 is slightly smaller
than the other samples. For the acceptor removal constant c, no significant
trend is observed with IP and can be considered independent of IP.

${\rm V}_{gl}={\rm V}_{0,gl}e^{-c\phi}$ (4.1)

Table 2: Acceptor removal constant c of all samples Sample |  IP ($\mu$m) |  V0,gl (V) |  Vgl under 2MGy (V) |  c ($\times\frac{10^{-9}}{Gy}$)
---|---|---|---|---
2-5 |  50 |  24.537$\pm$0.0489 |  23.989$\pm$0.1689 |  11.67$\pm$4.810
2-6 |  60 |  24.204$\pm$0.0412 |  23.878$\pm$0.1860 |  6.50$\pm$1.490
2-7 |  70 |  24.237$\pm$0.0309 |  24.034$\pm$0.0797 |  4.09$\pm$0.984
2-8 |  80 |  24.514$\pm$0.0319 |  24.036$\pm$0.1206 |  10.00$\pm$2.032
2-9 |  90 |  24.484$\pm$0.0391 |  24.035$\pm$0.0902 |  9.272$\pm$2.146
2-10 |  100 |  24.576$\pm$0.0387 |  24.011$\pm$0.0217 |  11.935$\pm$3.390

Figure 9:  Fitting of gain layer depletion voltage Vgl as a function of dose
to the function ${\rm V}_{gl}={\rm V}_{0,gl}e^{-c\phi}$ for all samples.

To summarize, except for the decrease in Vgl after irradiation, no significant
effects of irradiation on other parameters are observed.

###  4.3 Inter-pad Resistance versus Bias Voltage

Inter-pad resistances (IpRs) are measured for samples 2-5 to 2-10. IpR is the
resistance among electrodes, which is the resistance between the grounded and
floating pads. LGADs in operation may generate lateral currents between
electrodes, increasing noise and reducing signal-to-noise ratio; larger IpR
helps reduce lateral currents.

Bias voltage on pad four $vs.$ current on grounded pads is drawn, and a linear
fit to the slope of this V-I characteristic yields the resistance. In Figure
10, we show the VI characteristic and its linear fit for sample 2-5 at a chunk
bias of 85 V before irradiation. The plot exhibits excellent linearity with
$R^{2}>0.99999$.

Figure 10: VI characteristic (solid black line) and linear fit (red broken-out
line) of sample 2-5 before irradiation at chunk bias 85 V.

As the LGADs will operate alongside other detectors with higher operating
voltage, we have chosen 100V as the reference operating voltage for our study,
and IpRs of all samples are shown in Figure 11. IpRs of all samples are all
greater than $10^{9}\ \Omega$ including samples irradiated by 2M Gy, two
orders greater than non-carbon-doped HPK LGAD irradiated by 2.5M Gy, of which
IpR decreases by 4 orders after irradiation [13]. We observed no significant
trend, including shift, increase, or decrease in IpR, which indicates that
irradiation did not significantly affect IpR. Given that all samples have IpRs
greater than $10^{9}\ \Omega$, we conclude that the design of IHEP-IME LGAD v3
is capable of meeting design requirements greater than 1G $\Omega$.

Figure 11: Inter-pad resistance at chunk bias 85 V of all samples before and
after irradiation.

##  5 Conclusion

The internal and surface component of LGADs are found to be affected after
60Co irradiation, whereby the characteristic parameters we studied have
changed. The effects of irradiation on LGADs are summarized as follows:

  * •

Increase in leakage current of about half an order and small increase in
breakdown voltage after irradiation are observed.

  * •

Capacitance remains the same whereas Vgl droped after irradiation.

  * •

No significant change in IpR before and after irradiation is observed in IHEP-
IME LGAD v3, but IpRs of non-carbon-doped HPK samples decrease by two orders
after irradiation.

  * •

No correlation of results with IP was observed in all tests.

We conclude that IHEP-IME LGAD v3 has good irradiation hardness indicators in
terms of capacitance, inter-pad resistance, and break-down voltage resistance
to Gamma irradiation. The results of this experiment, along with the design
parameters of IHEP-IME v3, will help to optimize the future design of the LGAD
surface, such as the inter-pad distance and the gap between the active edge
and the edge, and the maximum fill factor.

Based on the differences between this experiment and the non carbon-doped LGAD
after gamma irradiation, the mechanisms of the effects of carbon doping and
surface passivation on irradiation hardness needs to be further investigated.

## Acknowledgments

This work was supported in part by the National Natural Science Foundation of
China under Grant 12105298, Grant 12275290 and Grant 12175252; in part by the
State Key Laboratory of Particle Detection and Electronics under Grant
No.SKLPDE-ZZ-202214.

## References

  * [1] O Aberle et al.  “submitter: High-Luminosity Large Hadron Collider (HL-LHC): Technical design report”, 2020  DOI: https://doi.org/10.23731/CYRM-2020-0010
  * [2] “High-Luminosity Large Hadron Collider (HL-LHC) : Preliminary Design Report”, 2015  DOI: 10.5170/CERN-2015-005
  * [3] Charlotte Cooke  “Upgrade of the CMS Barrel Electromagnetic Calorimeter for the High Luminosity LHC”  In _Instruments_ 6.3, 2022  DOI: 10.3390/instruments6030029
  * [4] “Technical Proposal: A High-Granularity Timing Detector for the ATLAS Phase-II Upgrade”  DOI: 10.17181/CERN.CIUJ.KS4H
  * [5] Michael Moll  “Displacement Damage in Silicon Detectors for High Energy Physics”  In _IEEE Trans. Nucl. Sci._ 65.8, 2018, pp. 1561–1582  DOI: 10.1109/tns.2018.2819506
  * [6] N. Moffat et al.  “Low Gain Avalanche Detectors (LGAD) for particle physics and synchrotron applications”  In _J. Instrum._ 13.03, 2018, pp. C03014  DOI: 10.1088/1748-0221/13/03/C03014
  * [7] C.H. Li et al.  “Performance of LGAD sensors with carbon enriched gain layer produced by USTC”  In _Nucl. Instrum. Methods Phys. Res. A: Accel. Spectrom. Detect. Assoc. Equip._ 1039, 2022, pp. 167008  DOI: https://doi.org/10.1016/j.nima.2022.167008
  * [8] Shudhashil Bharthuar et al.  “Effect of Thermal Donors Induced in Bulk and Variation in P-stop Dose on the No-gain Region Width Measurements of LGADs”  In _Proceedings of the 29th International Workshop on Vertex Detectors (VERTEX2020)_ Journal of the Physical Society of Japan, 2021, pp. 010020  DOI: 10.7566/jpscp.34.010020
  * [9] Tao Yang et al.  “Leakage current simulations of Low Gain Avalanche Diode with improved Radiation Damage Modeling”  In _Nucl. Instrum. Methods Phys. Res. A: Accel. Spectrom. Detect. Assoc. Equip._ 1040, 2022, pp. 167111  DOI: https://doi.org/10.1016/j.nima.2022.167111
  * [10] R. Heller et al.  “Characterization of BNL and HPK AC-LGAD sensors with a 120 GeV proton beam”  In _J. Instrum._ 17.05 IOP Publishing, 2022, pp. P05001  DOI: 10.1088/1748-0221/17/05/P05001
  * [11] M. Ferrero et al.  “Radiation resistant LGAD design”  In _Nucl. Instrum. Methods Phys. Res. A: Accel. Spectrom. Detect. Assoc. Equip._ 919, 2019, pp. 16–26  DOI: https://doi.org/10.1016/j.nima.2018.11.121
  * [12] Yuhang Tan et al.  “Radiation effects on NDL prototype LGAD sensors after proton irradiation”  In _Nucl. Instrum. Methods Phys. Res. A: Accel. Spectrom. Detect. Assoc. Equip._ 1010, 2021, pp. 165559  DOI: https://doi.org/10.1016/j.nima.2021.165559
  * [13] Martin Hoeferkamp et al.  “Characterization of Low Gain Avalanche Detector Prototypes’ Response to Gamma Radiation”  In _Front. Phys._ Frontiers, 2022, pp. 105  DOI: 10.3389/fphy.2022.838463
  * [14] Mengzhao Li et al.  “Effects of Shallow Carbon and Deep N++ Layer on the Radiation Hardness of IHEP-IME LGAD Sensors”  In _IEEE Trans. Nucl. Sci._ 69.5, 2022, pp. 1098–1103  DOI: 10.1109/TNS.2022.3161048
  * [15] Mei Zhao et al.  “Low Gain Avalanche Detectors with good time resolution developed by IHEP and IME for ATLAS HGTD project”  In _Nucl. Instrum. Methods Phys. Res. A: Accel. Spectrom. Detect. Assoc. Equip._ 1033, 2022, pp. 166604  DOI: https://doi.org/10.1016/j.nima.2022.166604
  * [16] Kewei Wu et al.  “Design and testing of LGAD sensor with shallow carbon implantation”  In _Nucl. Instrum. Methods Phys. Res. A: Accel. Spectrom. Detect. Assoc. Equip._ 1046, 2023, pp. 167697  DOI: https://doi.org/10.1016/j.nima.2022.167697
  * [17] J Zhang et al.  “Investigation of X-ray induced radiation damage at the Si-SiO2 interface of silicon sensors for the European XFEL”  In _J. Instrum._ 7.12, 2012, pp. C12012  DOI: 10.1088/1748-0221/7/12/C12012
  * [18] P. Lecoq  “Scintillation Detectors for Charged Particles and Photons”  In _Particle Physics Reference Library: Volume 2: Detectors for Particles and Radiation_ Cham: Springer International Publishing, 2020, pp. 45–89  DOI: 10.1007/978-3-030-35318-6_3