Integrated circuits are becoming more complex and compact. Quality and reliability are increasingly important, yet system components still commonly fail. Failure analysis (FA) can provide valuable insight into the causes of failures and provide inputs to improve products and evaluate reliability [1]. In FA, a confocal laser scanning optical microscope is used for collecting reflection images of the electronic-component pattern of the semiconductor substrate through the device backside. However, continuous downscaling of electronic components necessitates higher-resolution optical microscopic images for FA. A silicon solid immersion lens (Si-SIL) has been used to match the refractive index of Si substrates to increase the resolution of optical microscopic images [2,3]. A Si-SIL can collect the diffracted light from the pattern side with wide angles as a consequence of suppressing the total internal reflection (TIR) at the interface between the Si substrate and air. Thus, the numerical aperture (NA) and resolution increase. However, the curvature of radius designing of a Si-SIL depends on the incident spherical wavefront of the illumination laser generated by the objective lens. Therefore, the magnification and NA are limited to the physical properties of the objective lens. To increase the NA for a thick Si substrate, a combination of a thicker and wider Si-SIL and objective lens with high NA are also required, which may exceed the physical limitations of such optical microscope systems. To achieve high NA with an objective lens, the working distance (the distance between the front edge of the objective lens and sample surface) will generally become small, which might interfere with the Si-SIL surface. Thus, an ultrathin lens that achieves a high NA is required as an alternative optic of a Si-SIL.

Although there are several candidates to achieve an ultrathin lens by using semiconductor technologies, we focused on subwavelength metasurface structure lenses, which can be made ultrathin and flat [4–10]. Such a “metalens” can be fabricated at a flat interface or substrate surface, and an effective wavevector along the interface can bend transmitted light in arbitrary directions inside the substrate with the gradient of an interfacial optical phase jump [6]. This enables the diffracted light from the observing object to be collected beyond the critical angle of the TIR at the interface to heighten the resolution of optical microscopic images. There have been reports of solid immersion metalenses for focusing on semiconductor substrates [11,12]. However, a solid immersion metalens needs to be directly formed onto the observing semiconductor substrate. This means that the observing point will be fixed by the position of manufactured metalenses, which is not suitable in practical FA that requires an arbitrary observation point or scanned image of a whole area of interest.

We introduce an individual contact metalens that works as a lens only while contacting the semiconductor substrate. It is suitable for FA because it can cope with observation-spot switching. For a proof of concept, we evaluated the contact metalens and demonstrated that it improves the resolution of optical microscopic images in FA.

Optical microscopic images for FA are acquired to collect diffracted light from the focusing-pattern side of a Si substrate, as shown in Fig. 1(a). Illumination light is focused onto the device pattern on the device backside with an objective lens via a dielectric interface. The incident light from the backside of the Si substrate is required to avoid the reflection of the electrode patterns on the surface of the substrate when observing the inside of the substrate. The focusing light will be shined onto the observing object with the maximal half-angle of the cone of light in object space $ \theta $. The optical resolution limit is determined by Abbe’s diffraction limit, described as $d = \lambda /({2{\rm NA}})$, where $ d $ is the resolvable minimum distance, $\lambda$ is the free space wavelength, and ${\rm NA} = n\;{ \sin }\theta$ if $ n $ is the refractive index in object space. To obtain a high-resolution optical microscopic image, diffracted light from the focusing-pattern side of the Si substrate must be collected as widely as possible. However, diffracted light from the pattern side of the Si substrate with a wide angle is not collected due to the TIR at the interface and NA of the objective lens.

 

Fig. 1. Ideal integration of metalens and objective lens applied in FA. (a) Schematic of usual method to observe pattern side of Si substrate with objective lens. (b) Schematic of method for observing pattern side of Si substrate with objective lens and metalens as combination lens to collect diffracted light from pattern side beyond critical angle of TIR.

Download Full Size | PDF

Figure 1(b) shows an ideal integrated design of a metalens and objective lens for FA. For the metalens, we can create the lens function at the interface without the refraction at the interface because the metalens has subwavelength thickness [13]. Thus, diffracted light from the focusing-pattern side of the Si substrate can be collected beyond the critical angle of TIR. Therefore, we expect optical microscopic images for FA to have high resolution.

The contact metalens was fabricated on a 500-µm-thick glass substrate. Incident light from the opposite side of a glass substrate goes through the metalens, which will be focused inside the Si substrate at the designed focal length $ f $. The phase distribution $\varphi$ of the contact metalens follows Eq. (1):

Phase modulation of the metalens can be controlled by the diameter of the Si nano pillars with a subwavelength structure. The period of Si nano pillars needs to be set less than the structure cutoff scale defined by the wavelength and refractive index, $\lambda /{n_{{\rm Si}}}$. For our case, the period of the Si nano pillars should be less than 371 nm. We chose 350 nm for manufacturing accuracy. We designed the diameter of the Si nano pillars to vary from 130 to 320 nm within a period of 350 nm to create a ${2}\pi$ phase modulation amount in eight discrete phase steps. We set the fixed height of the Si nano pillars to 750 nm to maintain the low aspect ratio. The Si nano pillars were arranged on the basis of the calculated phase distribution from Eq. (1).

Si nano pillars were fabricated on a glass substrate (${10} \times 10\;{\rm mm}$) by using electron beam lithography and a dry etching process. Figure 2(a) shows a photograph of the fabricated contact metalens on a glass substrate. The device whose one side of the square was 400 µm with an eight-discrete-phase-steps lens pattern. Figure 2(b) shows a scanning electron microscope (SEM) image of parts of the fabricated Si nano pillars. The Si nano pillars were in the desired period and size with an accurate cylindrical pillar shape.

 

Fig. 2. Fabricated contact metalens images. (a) Photograph of fabricated metalens on glass substrate (${10} \times 10\;{\rm mm}$). Corresponding area is indicated with red box. Scale bar is 10 mm. (b) SEM image of parts of nano pillars of fabricated metalens. The period of the fabricated metalens is 350 nm. The scale bar is 300 nm.

Download Full Size | PDF

To evaluate the optical properties of the fabricated contact metalens, we integrated it into a high-resolution scanning confocal microscope for use in an FA system (Hamamatsu Photonics, PHEMOS-1000, C11222-16). This FA system detects the accurate failure locations in semiconductor devices by detecting the weak light emissions and heat emissions caused by semiconductor device defects. In this experiment, we observed a device sample with a typical “epi-illumination scanning microscope mode” to confirm the effectiveness of the metalens.

The optical setup of the FA system is shown in Fig. 3(a). A collimated laser with $\lambda = 1300\;{\rm nm}$ is raster-scanned with Galvano mirrors and focused into the sample with an objective lens (Mitsutoyo, MPlanApoNIR 20x, ${\rm NA} = 0.4$). The Galvano mirrors deflect the light for two-dimensional (2D) scanning, and the detector detects reflection from each scan point of the pattern side of the Si substrate to acquire a reflection intensity image of the pattern side of the Si substrate. Diffracted light from the sample will be collected again with the objective lens and detected with an InGaAs photo detector. An image is reconstructed with a personal computer (PC) within one second. Figure 3(b) shows a photograph of the sample set in the FA system. The fabricated contact metalens was directly set onto the backside of several Si substrate samples with a device pattern with a known structure. The thickness of the experimental sample was varied from 70 to 80 µm. The objective lens was placed above the fabricated metalens.

 

Fig. 3. (a) Schematic of setup design of fabricated contact metalens integrated into scanning confocal microscope for FA. (b) Photograph of fabricated contact metalens placed on backside of Si substrate.

Download Full Size | PDF

We compared the optical microscopic images with and without the contact metalens. Figures 4(a) and 4(b) show optical microscopic images of device patterns in the same position without and with the contact metalens, respectively. Figure 4(c) illustrates the observed microstructure of the substrate surrounded with the dotted white rectangle in Figs. 4(a) and 4(b). The observation pattern had a 1.22 µm period (P), 500 nm width (W1), and 250 nm width (W2). This sample was 70-µm-thick and consists of many kinds of electrode patterns on the surface of the Si substrate including the square-shaped patches. In this experiment without the metalens, we used a higher NA objective lens (Hamamatsu, High NA objective lens 50x for IR-OBIRCH, A8018, ${\rm NA} = 0.76$) to achieve the best resolved images for comparison. We successfully resolved the microstructure with the metalens shown in Fig. 4(b), in contrast to the unresolved image without the metalens in Fig. 4(a), even with the higher NA objective lens. We found that the contact metalens improves the resolution of the optical microscopic image. Note that the resolution was worse than Abbe’s diffraction limit due to the effect of spherical aberration from refractive index mismatching between the Si substrate and air.

 

Fig. 4. Optical microscopic images of conventional objective lens setup (a) without metalens and (b) with metalens. Scale bar: 5 µm. (c) Design of observation pattern surrounded with dotted white rectangle in (b).

Download Full Size | PDF

To investigate the characteristics of the effective NA of the fabricated contact metalens, we simulated the propagation of focusing incident light with $\lambda = 1300\;{\rm nm}$ through the fabricated ${1600}\;\unicode{x00B5}{\rm m}^2$ contact metalens. A finite-difference time-domain (FDTD) calculation was conducted using a 2D FDTD Maxwell’s solver (Lumerical, Lumerical Solutions Inc.). Considering the experimental setup, ${\rm NA} = 0.4$ of the objective lens was set as the light source. The spherical wave from the light source was refracted at the glass substrate interface, phase modulated at the metalens, and focused on the device sample at 70 µm depth inside the Si substrate. The $ z $ position of the objective lens (i.e., the curvature radius of the spherical wave) was optimized to fix the focusing position near the designed focal length.

Figure 5 shows the simulation results. The intensity (normalized ${| E |^2}$) of the transmitted beam was distributed on the ${x} {\text -} {z}$ plane at $y = 0$. The metalens was centered at $x = 0$, and the lens range was from ${-}{200}$ to 200 µm consisting of 1142 Si nano pillars. The calculated intensity distribution in Fig. 5 shows that the transmitted beam was strongly focused at 70 µm. From the qualitative analysis shown in Fig. 5, the area surrounded with the dashed red triangle can be assumed to be the light contributing to the focusing on the sample. We found that the effective radius ${R_{{\rm ms}}}$ for focusing the designed metalens is 29.9 µm, so the maximal half-angle ${\theta _{{\rm Si}}}$ of the cone of light in the Si substrate is considered to be 23.1 deg. We assumed that the effective NA of the fabricated contact metalens is 1.37 in this case, which is much larger than the largest NA of the objective lens used in conventional FA systems (0.76), as shown in Fig. 4(a). This suggests that the spatial resolution was significantly enhanced by the metalens.

 

Fig. 5. FDTD simulation of contact metalens focusing. Dashed white line indicates focal length $f = 70\;\unicode{x00B5}{\rm m}$. Color scale is from ${{10}^{- 3}}$ intensity (blue) to maximum ${{10}^0}$ intensity (red).

Download Full Size | PDF

In summary, we proposed a contact metalens suitable for practical FA to acquire high-resolution optical microscopic images. For a proof of concept, we evaluated the contact metalens by using a laser confocal microscope to compare semiconductor-device-structure resolution with and without the metalens. We found that the contact metalens successfully improved the resolution of optical microscopic images. We also investigated the effective NA of the contact metalens to conduct FDTD simulations and estimated the NA of the contact metalens to be 1.37, which is much larger than that of a conventional objective lens. We also found that the proposed contact metalens is ultrathin and flat enough to produce high-resolution optical microscopic images in FA. For future work, we plan to further improve the resolution of the optical microscopic images to correct the phase design, which reflects the scanning optical system (oblique incidence), and combine our metalens with an objective lens. We also plan to optimize the design of the metalens element for collecting light with a large diffraction angle [14].