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Sensors and Materials, Vol. 33, No. 11 (2021) 4003–4016
MYU Tokyo
S & M 2741

Terahertz Imaging of ICs Using K-means Clustering for
Scale-Invariant Feature Transform Featureand Fusion Model of Wavelet Transform
Xiao-Xiang Pu,1 Chih-Cheng Chen,2,5* Tie-Jun Li,3 Wei-Lung Mao,4** and Zhen Liu3
1Chongqing Electric Power College, Chongqing 400053, China

2Department of Automatic Control Engineering, Feng Chia University, Taichung 40724, Taiwan

3School of Ocean Information Engineering, Jimei University, Fujian Province, Xiamen 361021, China
4Department of Electrical Engineering, National Yunlin University of Science and Technology,

Yunlin 64002, Taiwan, R.O.C.

5Department of Aeronautical Engineering, Chaoyang University of Technology, Taichung 413, Taiwan(Received July 1, 2021; accepted November 22, 2021)

Keywords: terahertz spectral image, IC chip, SIFT feature, wavelet fusion

Terahertz spectral imaging is widely used in the failure analysis of ICs. However, owing to
the limitations of current imaging hardware, the quality of terahertz images is not high enoughto show the internal structure of chips and analyze chip failure. Thus, to improve the detection
capability of chip failure in different packaging materials, we propose a terahertz imaging model
based on scale-invariant feature transform (SIFT) feature extraction with the K-means clusteringof images from multiple sources and the wavelet fusion method. The model creates a terahertz
image data set from images drawn from multiple sources in the time and frequency domains.
Then, the images drawn from the multiple sources are compared to select a representative image,and the SIFT features of the image are also extracted. The high-quality images obtained frommultiple sources are searched and selected by K-means clustering. The images are reconstructedby wavelet image fusion. Experimental results on terahertz imaging in various packaging
materials show that the model can quickly and effectively create high-quality images in theinternal structure of ICs, which is essential for the nondestructive analysis of chip failures.

1.

Introduction

IC chips are widely used in MEMS to achieve high performance in image-based detection,pressure sensing, acceleration, and so forth. However, the manufacturing of IC chips involves
tens of operations and various devices, and this complex process may generate defects inside oron the surfaces of the chips. Thus, failure analysis is important in the production and use of
semiconductor chips. Electrical function tests and the microscopic examination of fragments arecommonly used methods in chip failure analysis.(1,2) Recently, the development of terahertz
technology has contributed to improving the technique of nondestructive analysis. Many studies
have used terahertz spectral images for the failure analysis of IC chips.(3–5) However, the optical*Corresponding author: e-mail: chenccheng@fcu.edu.tw**Corresponding author: e-mail: wlmao@yuntech.edu.twhttps://doi.org/10.18494/SAM.2021.3521

ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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resolution of terahertz time-domain spectroscopy (THz-TDS) is not high enough to provide theterahertz image quality required for nondestructive tests. Therefore, improved image resolution,a key indicator in tests, is required for the accurate identification of the internal faults of IC
chips.(6)
To develop a new method of terahertz imaging, we obtain terahertz images of IC chips indifferent packaging materials by various imaging methods and analyze them quantitatively to
select the images with high resolution and quality. To acquire high-quality images for nondestructive analysis, a large number of terahertz images must be processed effectively andefficiently. Therefore, we propose a matching method for terahertz spectral images based on the
combination of scale-invariant feature transform (SIFT)(7) feature extraction and K-meansclustering.(8) The model processes terahertz images efficiently and generates high-quality
images, enabling the internal faults of IC chips appearing at multiple angles and in different
channels to be revealed. The clustering of similar images ensures the efficiency and effectivenessof fusion processing from the image source. Experimental results show that the new method
provides terahertz images of high quality that are appropriate for nondestructive analysis andhas better performance than the previous method of processing single terahertz images.(9-11)

2.

Methods

2.1

System model

To select high-quality terahertz images, IC chips are scanned by a spectral imaging system.
Then, the spectral data of each scanned pixel of an image in the time domain are obtained andprocessed by the windowed Fourier transform, which transforms the spectrum to the frequency
domain. The data of the images are included in an image data set for nondestructive tests of IC
chips. Next, to select a representative image from the data set that can best reflect the failure
characteristics, the images are evaluated according to the terahertz spectrum and various
evaluation parameters. Then, the SIFT feature–K-means extraction method is used to identify agroup of similar images from the image data set. Finally, wavelet fusion is used to reconstruct animage of high quality. The overall process of the model is shown in Fig. 1.
2.2

Multimodal imaging

Terahertz spectral imaging is different from light intensity information imaging as it obtains
the time-domain waveform and the electric field intensity of each pixel of a sample image in theentire terahertz band. The Fourier transform on the terahertz time-domain spectrum allows thefrequency-domain spectrum of each scanned pixel to be acquired. Through the selection ofdifferent physical parameters in the time and frequency domains, a two-dimensional (2D) imageof different spectral resolution is obtained. Terahertz spectral imaging is mainly divided into
time- and frequency-domain methods.

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Fig. 1. Flowchart of selecting the representative image of an IC chip by terahertz imaging based on SIFT feature–
K-means clustering.

2.2.1 Time-domain information
The time-domain method mainly uses the physical parameters of a time-domain waveform.
Amplitude and phase are two commonly used parameters. The amplitude of an image, whichreflects the absorption strength of the image in the terahertz wave, refers to the peak and averagevalue of the field strength in the time-domain waveform. The phase indicates the timecorresponding to the minimum or maximum peak of the amplitude. Figure 2 shows theamplitude of terahertz imaging, in which a is the maximum peak revealing the characteristics ofimage refraction and scattering, and A is the time when the minimum peak occurs.
2.2.2 Frequency-domain information
Frequency-domain information is obtained from the physical parameters of frequencydomain spectra. These are amplitude, phase, energy, and absorption coefficient at a specificfrequency and reflect the differences in the physical characteristics of images at different
frequencies. Figure 3 shows the change in power spectral density with the frequency, in which B
indicates the power spectral density.
Since the terahertz energy spectrum reflects the absorption of the terahertz wave by theimage, we use the energy parameter of the energy density spectrum. The energy parameter iscalculated by using Parseval’s theorem,

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Fig. 2. (Color online) Information of terahertz
imaging in the time domain.

=E∞s 2 (t )dt∫=−∞

Fig. 3. (Color online) Information of terahertz
imaging in the frequency domain.

∞

∫−∞

2

S ( f ) df ,(1)

where E is the energy and |S( f )|2 is the spectral energy density.
2.2.3 Image selection with multi-evaluation index
The different needs of nondestructive testing require the recognition of various targets interahertz images to evaluate image quality. Four indexes are used in this study to evaluate thequality of a digital image:(12,13) standard deviation (SD), information entropy (H), average
gradient (AG), and spatial frequency (SF). The cutoff frequency of the terahertz transmission
spectrum of packaging materials is also used for evaluation. Since H and AG are essential
information on the internal defects of an image, they are used as crucial indicators with large
weights. The cutoff frequency of the terahertz transmission spectrum of packaging materials is
an indicator of noise. The noise is the most important indicator when reconstructing the internal
image from the frequency information of an IC chip. After the evaluation indicators of all
terahertz images in the image data set are compared and calculated, an image is extracted fromthe image library to obtain a high-quality terahertz image. The weights of the indexes decreasein the order of terahertz spectrum cutoff frequency > AG > H > SF > SD.
2.3

Image matching based on SIFT feature–K-means clustering

The SIFT is an operator based on invariant technology used to describe a local feature of animage. The SIFT algorithm finds extreme points in spaces of different scales and calculates thesize, direction, and scale of the extreme points. The extreme points of information can describe
the characteristics of the image. The SIFT features are extracted and matched in the process ofcomparing the extreme points. A common matching method is to calculate the Euclidean

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distance between SIFT features in two images.(14,15) Since each image generates thousands of
SIFT feature points, the matching requires a large amount of calculation, especially when theamount of image data is large.
To improve the efficiency of extraction and matching of the images, the traditional matching
method using SIFT feature points is improved in this study. First, the SIFT feature points of all
images are extracted, and the K-means clustering algorithm is used to cluster these points togenerate a new vector with a K-dimensional feature for each image. Then, the vectors of different
images are matched to each other by a similarity measurement calculation of the two images.
Here, the K-means clustering algorithm is utilized to perform statistical analysis on SIFT featurepoints. In this method, only two K-dimensional feature vectors of two images are measured,
which greatly reduces the computation. This process can also decrease the complexity andimprove the performance of the algorithm. The procedure of the K-means clustering algorithm
for SIFT feature points is as follows.
(1) The SIFT feature points of all images are extracted from the image data set, and a subset X =(X1d, X2d, …, Xnd) of the SIFT feature points is selected, where X1d (i = 1, 2, …, n) represents
the ith feature point. Its dimension d is 128, that is, each feature point contains a
128-dimensional vector.
(2) K appropriate clusters and K SIFT points are randomly selected from the subset as initialcluster centers (centroids).
(3) The distance from each SIFT point to the cluster center is calculated as the Euclidean
distance. Using the Euclidean distance, each SIFT point in the subset is assigned to thenearest centroid in turn to form K clusters.
(4) The cluster centers are iteratively updated by considering the Euclidean distances and using
the sum of the squared error (SSE) as the objective function of clustering,k

SSE = ∑ ∑ dist (ci , x) 2 ,(2)=i 1 x∈ci

where k is the number of cluster centers, ci is the number of centers, and dist is the Euclidean
distance.
The Kth centroid Ck is calculated to minimize the SSE as follows.
∂
∂ k
SSE
=
∑ ∑ (ci − x)2∂ck∂ck =i 1 x∈cik∂(ci − x) 2 ⇒c∂k=i 1 x∈c=∑ ∑i= ∑ 2(ck − xk ) =
0
x∈ck

mk c=
k

1

∑ xk ⇒ c=k m ∑ xkx∈ck

k x∈ck(3)

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Here, mk is the number of feature points in the Kth centroid.
The average of all the feature points in each cluster is calculated using Eq. (2). The average
is used to generate the corresponding average vector as the cluster center for calculating theobjective function, and the K-means test is run twice to produce two different clusters. Then,the average vector with the smallest objective function is regarded as the new centroid.
(5) The convergence of the algorithm is determined to establish whether the clustering centerand the objective function have changed. If they are unchanged, the clustering results of K
clusters are output. If they have changed, the procedure returns to the third step. The common
convergence condition of the algorithm is as follows: when the cluster does not change, thatis, no new feature points are redistributed, the maximum number of iterations is reached.
Here, the cluster no longer changes according to the algorithm convergence condition.
(6) The cosine similarity is used to distinguish various images. First, the cosine value of theangle between the feature vectors of two images is calculated. All image feature vectors in
the image data set are sorted according to the cosine values, and eight images with the largest
cosine values are selected as the best matched images.
2.4

Image fusion based on wavelet transform

The wavelet transform is typically used in frequency-domain image fusion.(16) The wavelet
transform can deal with the low-frequency information of the image and high-frequency
information in horizontal, vertical, and diagonal directions at the same time. By choosing asuitable wavelet basis and a suitable number of decomposition layers, the noise is reduced andedges are sharpened. Image fusion based on the wavelet transform transforms the fusion
coefficients of multiple images inversely to obtain the final fused image. To enhance image
fusion efficiency, the data of multiple images to be fused in different frequency bands areprocessed by a wavelet-transform-based fusion method. A flowchart of the image fusion
algorithm based on the wavelet transform is shown in Fig. 4.

3.

Results and Discussion

3.1

Terahertz spectral scan in time domain

Three failed IC chips, in which faults were generated by applying a high voltage, wereselected in the experiment: a ceramic SDIP40 packaged chip (Sample 1), an epoxy resin SDIP40
packaged chip (Sample 2), and an epoxy resin LCC21 packaged chip (Sample 3). During theexperiment, a terahertz wave transmitter and a terahertz receiver were fixed on a horizontal
optical rail. The samples were placed on a 2D scanning platform that moved in the x-and y-axis
directions from the focus position of the terahertz pulse. The terahertz spectra of the samples
were acquired by 2D scanning as shown in Fig. 5.
Figure 5(b) shows that the terahertz pulse effectively penetrates the three different samples.
The time-domain spectra of the samples appear behind the reference spectrum on the timeline,
and the amplitude of the electric field intensity after transmission is attenuated to some extent.

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Fig. 4.

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Flowchart of image fusion algorithm based on wavelet transform.

(a)

(b)

Fig. 5. (Color online) (a) Transmission spectra of samples in the time domain; (b) transmission spectra of samples
in the frequency domain.

Although Sample 3 (green line) shows a larger attenuation than Samples 1 (red line) and 2 (blueline), their peak values are almost the same. The transmission spectrum in the frequency domain[Fig. 5(b)] reveals that the effective frequency bandwidth for terahertz imaging is about 0.2‒2.0
THz (gray area in the figure). The cutoff frequencies of Samples 1–3 are about 0.7, 1.0, and 1.0
THz, respectively. The difference in the frequency originates from the different packaging
materials.

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Multimodal imaging and image quality evaluation

A multimodal imaging process is used to generate a spectral image data set of samples. Six
images are drawn from the time domain to obtain information on the electric field intensity.
Each image contains the maximum peak amplitude, minimum peak amplitude, peak-to-peakamplitude, average amplitude, maximum peak phase of the amplitude, and minimum peak phaseof the amplitude. The number of images used in energy information imaging with a frequency
interval of 3.125 GHz is 1120 in the frequency domain. The total number of terahertz images ofeach sample is 1126. Multiple evaluation indicators are used to evaluate the quality of images inthe data set. Figures 6–8 show the quantitative experimental results of different imaging modes.
The experimental results show that the terahertz image quality is poor for the indirect
imaging of the peak electric field intensity and phase information in the time domain. The effectof the energy-based imaging at different frequencies in the frequency domain is better than thatof imaging using time-domain information (Figs. 6–8).
A comparison of the imaging effects of terahertz transmission energy at different frequencies
reveals that (1) the terahertz image resolution of the three samples at a low frequency is low
owing to the low wavelength of the terahertz wave and is affected by the diffraction limit, (2) theinternal defects of the sample are clearly revealed in the mid-frequency range, and (3) the energy

Fig. 6.

Fig. 7.

(Color online) Comparison of imaging results of ceramic SDIP40 packaged chip (Sample 1).

(Color online) Comparison of imaging results of epoxy resin SDIP40 packaged chip (Sample 2).

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Fig. 8.

4011(Color online) Comparison of imaging results of epoxy resin LCC21 packaged chip (Sample 3).

of the terahertz wave in a high-frequency band gradually decreases, which results in its reduced
penetration.
Therefore, although the terahertz images have a higher resolution in the high-frequency band
than in the low-frequency band, the image noise increases. As the frequency increases, theuseful information of the image is gradually masked, making it impossible to effectively reveal
the inside of the samples. Therefore, the image quality evaluation indicators are necessary toevaluate the images acquired from the library and improve the images. The evaluation results
are shown in Table 1.
According to the objective evaluation indexes in Table 1, Sample 1 has the best comprehensive
evaluation indicators for energy imaging at 0.6375 THz. The outline and internal edges of theimage are clear in Fig. 6(g). The internal die area has sharp edges, which implies that theterahertz image is a representative image of Sample 1. The packaging materials of Samples 2
and 3 are the same, so the terahertz transmission spectra are similar [Fig. 5(b)] and the evaluation
indicators are similar. Samples 2 and 3 have the best evaluation results of energy imaging at
0.83125 and 0.66562 THz, respectively. Compared with other images, the values of AG, H, andSF at the selected representative image are higher. For instance, for Sample 2, the values of AG
and SF of the images at 0.83125 THz are higher than those of the images at 0.36875 and 0.61875
THz, but the value of H is slightly smaller. Although the values of AG and SF are higher for theimages at 1.0781 THz, these images are noisy, as shown in Fig. 7(h). Figures 7(g) and 8(f) show
the positioning hole of the packaging and an internal die defect, respectively. In particular, Fig.
7(g) reveals pin lead information in the die area, which is not shown in the images of Sample 1.
Thus, the best imaging effect for Sample 2 is at 0.66562 THz. For Sample 3, the values of AG,
SF, and H for the image at 0.66562 THz are all higher than those for the images at 0.5 and
0.76875 THz. Similarly, although the values of AG and SF are higher for the images at 0.9875
THz, these images are noisy, as shown in Fig. 8(h). Therefore, these two images (imaging at
0.83125 THz for Sample 2 and 0.66562 THz for Sample 3) are regarded as representative
terahertz images of the samples.

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Table 1Comparison of objective evaluation indexes for image quality.
Sample 1
SD
Peak-to-peak amplitude imaging
96.4144
Maximum peak phase of amplitude imaging
104.7158
Energy imaging at 0.25937 THz
68.6096
Energy imaging at 0.575 THz
81.2686
Energy imaging at 0.6375 THz
77.8948
Energy imaging at 0.90937 THz
57.4804
Sample 2SD
Peak-to-peak amplitude imaging
94.2230
Maximum peak phase of amplitude imaging
84.3356
Energy imaging at 0.36875 THz
63.8748
Energy imaging at 0.61875 THz
55.9518
Energy imaging at 0.83125 THz
49.9157
Energy imaging at 1.0781 THz
53.4474
Sample 3SD
Peak-to-peak amplitude imaging
88.0291
Maximum peak phase of amplitude imaging
44.4462
Energy imaging at 0.5 THz
40.1138
Energy imaging at 0.66562 THz
54.5763
Energy imaging at 0.76875 THz
44.0045
Energy imaging at 0.9875 THz
35.9417H
7.19583.16897.3271
6.76506.6411
6.3358H
7.46264.62137.07906.49636.31596.4112H
7.14964.2407
6.29966.44736.08885.76663.3

AG
1.52082.55432.18013.62184.64258.1409AG
3.5304
6.39932.45952.80944.17258.7161AG
1.20311.40562.9991
4.19643.68765.7284SF
8.443025.2883
3.80166.98009.453420.1919SF
8.711426.81214.9203
6.276010.2933
20.8962SF
8.073115.9233
7.933410.1841
8.941712.6513

Representative image matching extraction based on SIFT feature clustering

The SIFT feature–K-means model extracts 1126 terahertz images of each sample asrepresentative images selected by the comprehensive evaluation. The eight images with thehighest similarity are selected as the source images for Samples 1–3 as shown in Figs. 9‒11,
respectively. In the experiment, the Gaussian scale of SIFT feature point extraction is set as 1.6
and the number of K-means clusters is K = 500. Specific model parameter settings are shown in
Table 2. The image clustering and matching in this study effectively retrieve the representative
images of high quality from a large amount of image data. Clear images are obtained by energy
imaging in the frequency domain. Although there is a slight difference in contrast between theimages, the details of the images are well revealed, such as the sample outlines and internal
defects.
3.4

Image reconstruction by wavelet fusion

The quantitative analysis of the SIFT feature–K-means model allows eight representative
images of high quality of each sample to be used to identify the faults of the samples. To verify
the effect of image processing after wavelet fusion, we perform wavelet fusion processing on the
representative images of the samples. The image quality evaluation indicators are adopted tocompare the effects of each processing. The result of the fusion is shown in Fig. 12, and theobjective evaluation results are presented in Table 3. The results indicate that the fusion results
and objective evaluation indicators are improved by wavelet fusion. After wavelet fusion, theSensors and Materials, Vol. 33, No. 11 (2021)

Fig. 9.

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Representative images of Sample 1 at different frequencies.

Fig. 10. Representative images of Sample 2 at different frequencies.

Fig. 11. Representative images of Sample 3 at different frequencies.
Table 2Model parameters of the samples.
Parameterσ
S
SIFT descriptor
Value
1.6
3
128

K
500

Image size
560 × 368

Number of images
1126

Output images
8

image brightness, definition, and contrast are enhanced, while the image information is retained.
This demonstrates the effectiveness of wavelet fusion.

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Fig. 12. Results of fusion imaging of samples.

Table 3
Objective evaluation indexes after image fusion.
SampleSD
H
AG
Sample 128.4969
6.33104.1178Sample 217.10105.69004.6641
Sample 328.56426.33244.15444.

SF
11.7488
8.218912.0321

Conclusions

Terahertz spectral imaging has attracted increasing attention in the field of chip
nondestructive testing and analysis. However, in practice, the quality of terahertz spectral
images of chips often fails to meet the requirements. To solve this problem, we propose aterahertz image processing method, where a multimode imaging method and image quantitative
analysis are used to generate a large number of source images. Moreover, SIFT feature extraction
and K-means clustering are combined to select high-quality terahertz images. The wavelet
fusion image processing method is also used to improve the quality of the terahertz images.
Through experimental analysis, it is found that the proposed method can quickly and effectively
select high-quality terahertz images from a large number of multiple-source terahertz image
data. Moreover, the image clarity, information entropy, and other key indicators are greatly
improved compared with those for methods involving processing single terahertz images,
enabling the proposed method to meet the requirements of chip failure analysis.

Acknowledgments
This work was supported by the Natural Science Foundation of Fujian Province, China(Grant Nos. 2020J01714 and 2020J01713).

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About the Authors
Xiao-Xiang Pu has been an associate professor at Chongqing Electric Power
College, China, since 2010. She received her M.S. degree from Chongqing
University, China, in 2004. She has published 12 academic articles and three
textbooks. Her research interests are in control engineering, electric circuit
theory, and electronic technology. (puxiaoxiang_cq@sina.com)

Chih-Cheng Chen has been a professor at Jimei University, China, since2017. He became a member of IEEE in 2011 and a senior member in 2016. He
earned his M.S. degree in 2005 and has recently earned his Ph.D. degree fromthe Department of Mechatronics Engineering, National Changhua Universityof Education. He has published 43 academic articles and owns three patents.
He has also implemented several projects funded by the National Natural
Science Foundation of China, Fujian Province. His research interests include
AIoT technology, machine learning, information security, and RFID
applications. (chenccheng@fcu.edu.tw).

		Tie-Jun Li has been an associate professor at Jimei University, China, since2015. He received his B.S., M.S., and Ph.D. degrees from Chongqing
University, China, in 2000, 2005, and 2018, respectively. He has published 21
academic articles and owns 11 patents. He also implemented several projects
by the Natural Science Foundation of China, Fujian Province. His researchinterests are in machine learning, terahertz technology, and sensors.
(litiejun@jmu.edu.cn)

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Wei-Lung Mao was born in Taiwan, R.O.C., in 1972. He received his B.S.
degree in electrical engineering from National Taiwan University of Scienceand Technology in 1994 and his M.S. and Ph.D. degrees in electricalengineering from National Taiwan University in 1996 and 2004, respectively.
He is now a professor in the Department of Electrical Engineering and
Graduate School of Engineering Science and Technology, National Yunlin
University of Science and Technology. His research interests are in satellite
navigation systems, intelligent and adaptive control systems, adaptive signal
processing, neural networks, and precision control. (wlmao@yuntech.edu.tw)
Zhen Liu is currently studying for a master’s degree at Jimei University,
China. His research interests include deep learning, signal processing, image
recognition, and bearing fault diagnosis.